## The Mathematical Biosciences Institute Online Colloquium

Thousands of scientists working at the interface of the mathematical and biological sciences have participated in programs at the Mathematical Biosciences Institute (MBI), where they have found out about the latest advances in their fields. MBI has expanded its program with the MBI Online Colloquium. Now in its second year, this series is available as an online interactive event and as on-demand streaming. The colloquia will cover the many fields of mathematical biology. The goal of this program is twofold: to enable large numbers of researchers to hear about recent advances in the field, and to connect the mathematical biology community worldwide.

The MBI Online Colloquium gives individuals and groups the opportunity to hear from outstanding mathematical biologists and to be an active part of colloquium discussions. You can interact with leading researchers and key opinion leaders from your classroom to the comfort of your own office. If you are unable to make a talk, you can view it on-demand at a later date.

Click here for detailed instructions on how to participate.

### 2018-2019

This CTW is a collaborative workshop for researchers and students with research interests in collective behavior and emergent phenomena in biology and its applications. The participants will be organized into interdisciplinary teams according to their interests and complementary skills. Each team will be tasked with exploring, analyzing and modeling original data sets provided by biologist attendees. The event will be similar in spirit to a hackathon in computer science, with the goal of finding new ways to understand the provided biological data. We emphasize that the workshop is meant to involve active participation with attendees working together across disciplines to solve problems in current research. In addition, regular debriefing sessions will be organized throughout the days of the workshop in order for each team to provide updates to and receive feedback from the rest of the participants on their progress.

### List of Projects

# | Leaders | Co-leaders | Titles |
---|---|---|---|

1 | Helen McCreery | Justin Werfel | Exploring group strategy and cohesion during obstacle navigation |

2 | Ted Pavlic | Tomer Czaczkes | Collectives and tradeoffs: Self-organized decision-making with multiple competing objectives |

3 | Albert Kao | James Crall | Choosing between rigid and flexible behavioral strategies: thermoregulation in the bumblebee Bombus impatiens as a case study |

4 | James Curley | Lisa O'Bryan | Modeling conflict strategies in social hierarchies |

5 | Erol Akcay | Elizabeth Hobson | Dynamic feedbacks between social structure and behaviors |

6 | Simon Garnier | Jason M Graham | Models of multi-constraint optimization in self-organized systems |

Detailed descriptions of each of the projects are available here.

This minisymposium, co-hosted by the Chronic Brain Injury Discovery Theme (CBI), will showcase a variety of quantitative approaches to brain and spinal cord injury, neurodegeneration, cognitive neuroscience, and related research topics. Talks will highlight opportunities at the intersection of neuroscience and computation, and participants will have the opportunity to share perspectives on current work and the future of these disciplines.

The goal of the event is to foster interactions and to create new collaborations between neuroscientists and faculty in mathematics, statistics, and engineering.

**Apply here: ****http://go.osu.edu/QuantNeuro**

**The event will be held in the MBI Auditorium, 355 Jennings Hall.**

### Featured Speakers:

**Anthony Brown, PhD. - Department of Neuroscience, The Ohio State University**

Dr. Brown is a Professor in the Department of Neuroscience, Director of the Ohio State University Neuroscience Center Core and Co-Director of the Interdisciplinary Graduate Program in Molecular, Cellular and Developmental Biology. He is a neuronal cell biologist with more than 30 years of experience studying intracellular transport and the cytoskeleton in nerve cells (www.neurofilament.osu.edu). He has a long-standing NSF-funded collaboration with Dr. Peter Jung, Distinguished Professor at Ohio University, to use computational modeling to explore the relationship between axonal transport and axonal morphology. Drs. Brown and Jung are co-mentoring Dr. Veronica Ciocanel, MBI post-doc, in a computational modeling project on neurofilament transport across nodes of Ranvier.

**Veronica Ciocanel, Ph.D. - Mathematical Biosciences Institute, The Ohio State University**

Veronica Ciocanel received her PhD in Applied Mathematics from Brown University in 2017, where her work focused on modeling spatial differentiation in early developing organisms such as frog oocytes. She joined the Mathematical Biosciences Institute at Ohio State as a Postdoctoral Fellow, and in 2018 she was selected in the inaugural class of President’s Postdoctoral Scholars at The Ohio State University. At OSU, she collaborates with Dr. Anthony Brown and Dr. Peter Jung (Ohio University) to model axonal transport kinetics through nodes of Ranvier, and with Adriana Dawes to understand motor-filament interactions leading to contractile rings in the worm reproductive system.

**Kiryung Lee, Ph.D. - Department of Electrical & Computer Engineering, The Ohio State University**

Kiryung Lee is joining the Ohio State Univeristy as an Assistant Professor in the Department of Electrical and Computer Engineering (ECE), starting August 2018. His research focuses on developing mathematical theory and optimization algorithms for inverse problems in signal processing, imaging, machine learning, statistics, and data science. Dr. Lee received the B.S. and the M.S. degrees in Electrical Engineering from Seoul National University and the Ph.D. degree in ECE from the University of Illinois at Urbana-Champaign (UIUC). He was a Research Scientist II at Georgia Tech and a Postdoctoral Research Associate, a Visiting Lecturer, and a Visiting Assistant Professor in Statistics at UIUC. He has also worked in industry as a Member of Research Staff at the Electronic Telecommunications Research Institute and a Senior Research Engineer at the Mobile Multimedia Laboratory of the LG Electronics.

**Alexander Petrov, Ph.D. - Department of Psychology, The Ohio State University**

Dr. Alexander Petrov is a cognitive scientist with broad interdisciplinary interests. Holding a degree in computer science, he currently is an Associate Professor at the Department of Psychology. His research involves a combination of behavioral and psychophysical experimentation, mathematical and computational modeling, eyetracking and pupillometry. His recent work includes neural-network models of the visual system and a simulated autonomous agent that illustrates certain foundational claims in philosophy of mind.

### Lightning Talks:

**James Jontes - Department of Neuroscience:**The Development of Zebrafish Brain Networks Determined by Multiplane Calcium Imaging**Elly Kaizar - Department of Statistics:**Multiply Imputed Data Banks for Hard-To-Study Populations: An Example in Pediatric Traumatic Brain Injury**Olga Kokiko-Cochran - Department of Neuroscience:**Considering the Effects Post-Traumatic Brain Injury Sleep Disruption**Yune Lee - Department of Speech and Hearing:**Shared Neural Network Between Music and Language**Facundo Memoli - Department of Mathematics:**The Importance of Forgetting: Limiting Memory Improves Recovery of Topological Characteristics from Neural Data**David Osher - Department of Psychology:**Computational Models of Brain Connectivity that Predict Neural Responses and Behavior**Mario Peruggia - Department of Statistics:**Bayesian Models for Response Times in Cognitive Experiments**Francesco Sammartino - Department of Neurosurgery:**Analysis of Longitudinal Micro-Structural Changes After Focused Ultrasound Thalamotomy**Zeynep Saygin - Department of Psychology:**Machine Learning to Study the Developing Human Mind and Brain**Kristina Witcher - Department of Neuroscience:**Transcriptomics of Immune Signaling in Brain Injury and Aging**Chuan Xue - Department of Mathematics:**A Mathematical Model for the Formation of Axonal Varicosities Induced by Mechanical Stress that Mimicks Brain Concussion**Min Zhou - Department of Neuroscience:**Astrocyte Networks**Dhabaleswar Panda - Department of Computer Science and Engineering:**Updates from the Advanced Computational Neuroscience Network

The field of Genetic Epidemiology has historically focused on the inheritance of genetic factors and phenotypes within families. However, the increase in ever improving technologies brought a shift from familial study designs to genome wide association studies (GWAS) utilizing samples of unrelated individuals. While GWAS has yielded greater knowledge of genomic structure and disease associated variants, the estimated effect sizes are small and often to not explain a large proportion of disease heritability. One of the explanations for the missing heritability is that the variants identified in GWAS are common (> 5%) and thus we are missing an entire class of variation (rare) that substantially contributes to disease risk. The innovation of next-generation sequencing technology made the comprehensive discovery of rare variants feasible, however the sample size of unrelated individuals needed to identify associations between these rare variants and diseases is in the thousands (> 10,000 samples are necessary to detect a variant showing evidence of modest association with minor allele frequency 0.1%). While sequencing costs have decreased, the financial burden is still nontrivial and sample heterogeneity can easily confound results. Thus, efficient study designs and improved statistical approaches are necessary to untangle the contribution of rare variation to complex disease. Family studies have always been robust to confounding and a powerful approach for identifying genetic variation. In the age of sequencing, family studies are again an appealing approach for studying the relationship between complex disease and genetic variation.

This workshop will focus on the use of family studies in the hunt for disease associated genes, include the development of novel methodologies and statistics for assessing variant disease relationships as well as the important role of the family study design in a clinical sequencing setting.

**All participants are encouraged to bring posters to display. Posters should not necessarily be limited to work on family-based data and can cover any topics in statistical genetics, genomics, and bioinformatics.**

**This MBI workshop is being co-sponsored by the National Institute of Statistical Sciences.**

### Poster Presenters

**Chenggong Han:**Differential Methylation Analysis Adjusted for Covariates by Bayesian Curve Credible Bands Approach**Alyssa Clay-Gilmour:**Rare Germline Variants Segregating in Chronic Lymphocytic Leukemia (CLL) Families**Shuyuan Lou:**ChIA-Sim - A Simulator of 3D Interactions Data and Evaluation of Methods**Catherine Stein:**Association Between Immunity Genes, Severity of TB and Interaction with M. Tuberculosis Lineage**Lara Sucheston-Campbell:**Exomechip Analyses Identify Genes affecting Mortality after HLA-Matched Unrelated Donor Blood and Marrow Transplantation**Rosalie Waller:**Novel Strategy to Map GWAS Functional Variants Using Sequencing in High-Risk Cases Identifies Putative Risk-Variants in Myeloma

Goals of this workshop include:

- Identify the questions, challenges, tools, and needs for microbiome studies at Ohio State University (OSU) and in the greater Columbus area.
- Stimulate interdisciplinary collaborations at OSU and in the greater Columbus area (e.g. Nationwide Children’s Hospital, Battelle).

The intended workshop participants are faculty / PIs who are laboratory scientists, mathematicians, statisticians, or metabolic modelers working on or interested in questions that involve the microbiome.

As such, preference will be given to OSU or local faculty applicants for this workshop.

From the bacteria in our guts, to microbes involved in biodegradation and crop growth, to viruses in the ocean, some of Earth’s tiniest organisms play some of the most important roles in global health, food production, and climate change. Advances in metagenomic sequencing technology including 16S, viromics, and mycobiomics - along with metabolomics, transcriptomics, and proteomics allow us to characterize these complex microbial communities and begin to understand their functions. This Big Data creates opportunities for data driven discovery and new data analytics, but Big Data also comes with challenges: Meaningful integration of multi-omic data has become increasingly critical to microbiome studies as recent work highlights the importance of community dynamics, interactions, and microbial ecology over the roles of individual microbes. For example, microbial metabolisms are now recognized to often be ‘distributed’ across consortia; viruses manipulate microbial metabolisms and population dynamics, and co-occurring fungi in most ecosystems are virtually unstudied but likely play key roles as well. Data integration techniques range from correlations to network analyses to genome-scale microbial community metabolic models that assess metabolite flux to ecosystem models that provide predictive power of which organisms drive key features of the system. Some of these techniques, like correlations, accommodate many types of –omic data but cannot account for the complex biology or ecology of a system. Other techniques, like metabolic modeling, better account for this complexity, but do not yet integrate phenotypic –omic data (i.e. metabolomics, proteomics) well. Each of these techniques has advantages and limitations and new computational tools for data integration and modeling have rapidly developed over the last 2 years. Besides data integration, Whether studying environmental, gut, or industrial microbes, the ability to accurately identify and predict the structure and function of microbial communities has far-reaching potential and paves the way for microbial engineering in bioremediation, probiotic development, and sustainable agriculture.

In this 3 day workshop, we will take a genome to phonome approach with broad perspectives provided by mathematicians, biologists, and statisticians. We will also develop interdisciplinary working subgroups to consider the questions, challenges, tools, and needs of data integration and modeling in microbiome studies. Each participant will present a short talk (5 minutes, 3 slides) highlighting his or her research, perspectives, and challenges. The goal is to help develop a broadly collaborative community of math-enabled microbiome scientists with common research goals.

**This workshop is co-sponsored by the Mathematical Biosciences Institute, the National Institute of Statistical Sciences, and the Infectious Diseases Institute at Ohio State University.**

### Avner Friedman

Distinguished University Professor, Department of Mathematics, The Ohio State University Using Mathematical Models to Conduct Cancer Clinical TrialsMost cancer clinical trials with combination therapy in phase II have failed in phase III. One of the reasons for this failure is that no sufficient forethought was given to the interactions between the two (or more) agents. Before embarking on a clinical trial with (say) two agents, one should address the following questions:

1) If the two drugs are positively correlated at any dose amounts, how to achieve the same tumor volume reduction with minimal negative side-effects?

2) If the two drugs are antagonistic at certain ranges of the doses, how to avoid these zones of antagonism?

What schedule is most effective in reducing tumor burden? e.g. in which order to give the drugs?

3) How to reduce drug resistance by the tumor cells?

We use mathematical models to address these questions, and give several examples with different drugs.

Florence Nightingale Day is for middle and high school students and their teachers. Throughout the day you will meet successful women in statistics and data science, take on data challenges and have fun!

**For more information, please visit: https://sites.google.com/view/fnday2018/home**

Registration begins at 8AM on Thursday, November 1st.

**This event will be hosted in the MBI Auditorium, Jennings Hall 355**

In recent years, the focus of social network theory in behavioral ecology and the social sciences has shifted to understanding the dynamics of social networks. Data analytical methods such as relational state models and others have been used to address patterns of network change over time as agents gain or lose ties and how network structure coevolves with the attributes of agents in real-world networks. Network models are beginning to incorporate data at multiple scales and multiple types of interactions. New technologies have facilitated collection of large quantities of data in many systems allowing increasingly sophisticated analyses of changes in social structure over time.

Mathematical and empirical challenges arise because social networks are complex systems that emerge from, as well as influence, the interacting decisions of multiple, autonomous, objective-maximizing or goal-oriented agents. Agents often have multiple types of relations, resulting in multilayer (multiplex) networks. Current techniques for data analysis of dynamic networks are best suited to address enduring relationships, rather than momentary interactions, but many social interactions are better described by the latter. Consequences of agent decisions to pursue interactions can depend on attributes at multiple levels, and decisions that maximize agent objectives may be in conflict with those of others or with beneficial outcomes for the network as a whole. In humans and non-human animals, opportunities for interaction are constrained by factors such as location and mobility. Social networks frequently involve a small number of agents, and stochastic processes are likely to be important influences on network dynamics. Key emerging problems include how to incorporate multilayer and momentary data into network models, the roles of feedbacks between space use and network processes, how individual decisions interact with the evolution of network attributes, and the fitness or other consequences of such behaviors.

This workshop will consider these emerging problems with an interdisciplinary approach incorporating modeling and empirical work from the social sciences, behavioral biology, mathematics, and statistics. In addition, because many of the challenges inherent to the study of social network dynamics are not unique to such networks, this workshop aims to include perspectives from other areas of network research.

**This MBI workshop is being co-sponsored by the National Institute of Statistical Sciences.**

### Gunnar Carlsson

Department of Mathematics, Stanford University The Shape of Biological DataIn recent years it has become clear that the methods of topology, the mathematical study of shape, can be used to advantage in obtaining understanding of large and complex data sets. Biological data of various kinds are particularly interesting from this point of view. I will discuss the methods from topology, with numerous examples.

### Mark Lewis

Canada Research Chair in Mathematical Biology, University of Alberta Using Mathematics to Understand Animal Movement PatternsAnimal movement patterns have long been the subject of mathematical and ecological interest. How do individual behavioral decision rules translate into macroscale patterns of space use such as foraging, patrolling or territories? I will show how mechanistic models, using random walks, stochastic processes, first passage time analysis and partial differential equations can be used to connect underlying processes to the observed patterns. Here interactions are complex and may involve memory of past events, as well as a cognitive map. I will make applications to a spectrum of different emerging patterns, ranging from territories in Amazonian birds to patrolling in wolves.

### Michael Jordan

Pehong Chen Distinguished Professor, Department of Statistics, University of California, Berkeley Machine Learning: Dynamical, Economic and Stochastic PerspectivesAnimal movement patterns have long been the subject of mathematical and ecological interest. How do individual behavioral decision rules translate into macroscale patterns of space use such as foraging, patrolling or territories? I will show how mechanistic models, using random walks, stochastic processes, first passage time analysis and partial differential equations can be used to connect underlying processes to the observed patterns. Here interactions are complex and may involve memory of past events, as well as a cognitive map. I will make applications to a spectrum of different emerging patterns, ranging from territories in Amazonian birds to patrolling in wolves.

### Michael Mackey

Applied Mathematics in Bioscience and Medicine, Physiology, McGill UniversityTitle TBD

Abstract TBD

### Franziska Michor

Professor of Computational Biology, Department of Biostatistics, Harvard UniversityTitle TBD

Abstract TBD

Mass extinctions are important intervals of biodiversity loss, ecosystem upheaval and change in the evolution of life. Modern biodiversity loss and the possibility of it representing a 6th mass extinction caused by human pressures, makes it pertinent to understand the dynamics of past mass extinctions. Recognized in the fossil record through pronounced changes in fossil assemblages, mass extinctions are attributed to large-scale environmental disasters. However, their dynamics are often poorly understood. In particular, how populations decline to the point of the extinction of a species, how ecosystems interact with climate and if these interactions can modify the earth into a new climate state (a tipping point), are all poorly constrained. Many ecosystem-related feedbacks in the complex climate system, including those that have serious societal implications, are not and may never be precisely and definitively modeled on a deterministic basis. Compounding uncertainties and emergent interactions often reduce the power of top-down and bottom-up simulations to predict ecosystem processes. **We need to develop a new approach to simulate ecosystem disturbance and extinction by using stochastic, nonlinear multi-scale models validated with data of ecosystem diversity and activity.**

The main questions to be discussed:

- How to quantify biomass and biodiversity for different (long and short) time intervals using new methods of deep learning from data science. How to reconstruct biogeographical and evolutionary histories for climate sensitive taxa.
- How to simulate the nonlinear/stochastic changes in the dynamics of (paleo) ecosystems under climate change applying the approaches of dynamical system theory and statistical mechanics. How to mathematically/biologically determine a mass extinction.
- How to compute the mass extinction/harmful biodiversity impact on climate feedbacks. How to connect bifurcation points in ecosystem dynamics to climate tipping points.

**Plenary Speakers:**

Ben Abbott, Department of Plant and Wildlife Sciences, Brigham Young University, UT

Sergei Petrovskii, Department of Mathematics, University of Leicester, UK

Matthew Pound, Department of Geography and Environmental Sciences, Northumbria University, UK

Daniel Rothman, Department of Earth, Atmospheric and Planetary Sciences, Massachusetts Institute of Technology, MA

Uno Wennergren, Department of Physics, Chemistry and Biology, Linkoping University, Sweden

TBA

This meeting is co-sponsored by the Mathematical Biosciences Institute, the Department of Physics at the University of Dayton, and Swedish Foundation for International Cooperation in Research and Higher Education.

### Denise Kirschner

Professor, Microbiology, University of Michigan Building, Analyzing and Calibrating Multi-Scale Models in 2D and 3D: Tuberculosis as a Case StudyAbstract TBD

Workshop description TBD

Workshop description TBD

## 2019 Undergraduate Research Program

The Mathematical Biosciences Institute (MBI) is hosting a multi-institution REU program in the mathematical biosciences, facilitated by the Mathematical Biosciences Institute (MBI) located on the campus of The Ohio State University. The objectives of the program are: (1) to introduce a diverse cohort of undergraduate students to the mathematical biosciences, broadly interpreted to include areas such as biostatistics, bioinformatics, and computational biology, in addition to biologically-inspired mathematical modeling; (2) to encourage students to pursue graduate study in the mathematical biosciences; and (3) to increase the number of students who enter the workforce with training in this field.

REU participants work on projects in areas such as molecular evolution, neuronal oscillatory patterning, cancer genetics, epidemics and vaccination strategies, and animal movement. Participants work individually or in pairs under the guidance of expert mentors to make specific research contributions in these areas, often leading to a peer-reviewed publication and conference presentations. The REU program incorporates various professional and research-skills development activities throughout the summer to help ensure the participants’ success in completing their summer project and to prepare them for graduate study or entering the workforce.

The program consists of three parts:

**Mathematical Biosciences Bootcamp**(June 10th-14th, 2019) at the MBI

At the MBI, participants are introduced to various areas of the mathematical biosciences via lectures and computer labs and visit various biological labs on campus.**Mentored Research Experience**(June 17th-August 2nd, 2019) at the REU host sites

During the second component of the program, participants complete a mentored research project individually or in pairs at one of MBI's partner institutions. Participants also attend a weekly online seminar series and virtual all-program meeting.**Capstone Conference**(August 5th-8th, 2019) at the MBI

For the final week of the program, the students return to the MBI to participate in the Capstone Conference. A student-centered conference featuring talks and posters by students doing research in mathematical biology, keynote talks by prominent mathematical biologists, a graduate studies recruitment fair, and other special features including a conference dinner and social event.**Note that the Capstone Conference is open to all undergraduate students doing research in the mathematical biosciences, not only to students participating in the MBI REU.**

## Application Process

Applications for the 2019 REU program will be available early in 2019.

The goal of this MBI NSF-funded program is to introduce students to exciting new areas of mathematical biology, to involve them in collaborative research with their peers and faculty mentors, and to increase their interest in mathematical biology. The program consists of three parts - each including a mix of educational and social experiences. See this website for more info. http://mbi.osu.edu/education/summer-undergraduate-program/

Biological systems are extremely diverse and complex, possessing enormous variation. Understanding the mechanisms by which biological systems work is one of the fundamental scientific challenges of our time. Rules of Life offer principles - which are broadly applicable across bacteria, plants, and animals - that can be the basis for organized research programs that address the challenge of understanding nature. Unlike a traditional workshop or conference, the format of the Summit is designed to build interdisciplinary connections through provocative talks, panel discussions, and focused break-out sessions. Additionally, talks on emerging technologies and methods will broaden the perspectives of participants who may not have prior exposure to these tools. The two follow-up workshops will encourage participants to plan how connections made at the Summit can be long lasting and lead to concrete outcomes.

The Mathematical Biosciences Institute (MBI) will organize a Summit on the Rules of Life in June 2019. This project will support the development of a networked community of researchers seeking to better understand the fundamental mechanisms that govern biological systems. This community will be convened at a Summit on the Rules of Life held at the Mathematical Biosciences Institute in Columbus, OH. Prominent biological scientists from across the world, together with newer researchers and individuals with expertise in emerging technologies and mathematical/statistical methodologies, will jointly explore the common principles that govern biological systems. Video of the plenary lectures, panel discussions, and emerging technologies/methods talks delivered at the Summit will be live streamed and archived on the MBI website for later viewing. The Summit will lead to two shorter follow-up workshops on emerging themes.

The Curriculum Design Workshop is the first phase of MBI's TRIPODS+X:EDU: TGDA+Neuro program, a partnership with Ohio State's TGDA@OSU. Faculty participants in the workshop will follow a modified course design experience facilitated by The Ohio State University Center for the Advancement of Teaching. The curriculum will be designed around the following program objectives:

- To understand the purpose and use of different imaging modalities, in neuroscience research.
- To understand the data processing steps from raw images to working data files for analysis. These usually include co-registration of structural and functional imaging modalities, motion correction and spatial smoothing, among others.
- To understand the potential of geometric and topological methods for neuroscience data analysis to extract relevant features, and provide insight into the underlying structure in the data.
- To be proficient in the use of standard computational packages based on TGDA methods.
- To be able to communicate results from TGDA methods applied to neuroscience data to diverse audiences.

Participation in the workshop is limited to members of the TGDA+Neuro Program organizing committee.

The MBI Capstone Conference is a student-centered conference featuring talks and posters by students doing research in the mathematical biosciences, keynote talks by prominent mathematical biologists, a graduate studies recruitment event, panels on mathematical biosciences fields of research and career opportunities, and a conference social event.

**The Capstone Conference is open to all undergraduate students doing research in the mathematical biosciences, not only to students participating in the MBI REU.**

### 2017-2018

This workshop is open to all postdoctoral individuals and junior faculty at The Ohio State University who wish to train and gain expertise in genomic data analyses.

Biological dynamical systems are typically multidimensional, nonlinear, hierarchical, and noisy. Problems of control are ubiquitous; examples include fixed-point control (maintenance of posture, homeostatic control), control of rhythmic movements (locomotion, respiratory control), control of rhythmic processes (circadian activation, oscillatory neural activity). Nearly all areas of control theory have potential application to biological neural and motor systems, including feedback control; estimation and control of nonlinear systems; geometric control; optimization-based control; stability analysis; model identification and parameter estimation; model predictive control; observability and controllability in coupled networks; and stochastic control. At the same time, biological control problems can stretch control theory in new directions. For example, control theory has focused on negative feedback control (i.e. homeostasis) while neuromodulation may involve the interaction of multiple positive and negative feedback components. Moreover, neural and motor systems may prioritize robustness over optimality. Nonlinear control theory for limit cycle or other rhythmic dynamics is also much less developed than for linear systems and other forms of dynamics. The workshop will bring together experimental biologists, control theorists, mathematical biologists, and clinicians to forge new interdisciplinary connections to understand control of biological neuronal and motor systems.

One area of focus will be the rhythmic activity patterns that some brain areas produce through intrinsic dynamics, perhaps activated by tonic (sustained or transient) input signals. In some cases, these activity patterns drive repetitive behaviors such as various forms of locomotion, respiration, and mastication; similar dynamics may arise in circadian and sleep rhythms. An organism interacts with some aspect of its environment through these behaviors, and these interactions result in feedback signals that can alter the ongoing intrinsic dynamics to maintain homeostasis, meet metabolic demands, or optimize reward. Problems in this area include modeling the closed loop circuits involved, determining the control principles that modulate neural activity and behavior, and applying external (i.e., man-made) controls to remedy related disorders or otherwise improve performance.

A second major theme will be non-oscillatory motor behaviors that include stationary control problems (maintenance of posture, balancing a vertical rod) as well as nonstationary problems (maintaining one's gaze on a moving target) and single movement control problems (reaching and grasping; hitting a golf ball). Some aspects of these problems are classical, such as the mathematics of stabilizing an inverted pendulum. There is a rich body of relevant theory: state estimation and feedforward control, stabilization and negative feedback control, and internal and inverse models. But the relationship between such idealized systems and the noisy, overcomplete space of near-optimal solutions used by biological motor systems for such tasks is still poorly understood.

The workshop topics will also include the use of control to modulate pathological brain states, such as synchronization arising in epilepsy and oscillations arising in parkinsonism. Closed loop control of a distributed neuronal circuit based on sparse data represents an important frontier that arises in these clinical applications.

### Tutorial Videos

**Introduction to Linear Systems Theory Tutorial**

Kenneth Loparo

This talk will provide an introduction to linear systems theory including (1) dynamical systems terminology and basic concepts (e.g. equilibrium, linearization, stability and control); (2) input/output maps, state space realizations, control...

**Feedback, Sensitivity, and Excitability Tutorial**

Rodolphe Sepulchre

Feedback and sensitivity are core concepts of control theory, but the theory is grounded in the frequency-domain analysis of open dynamical systems and mature only for linear time-invariant (LTI) systems. Excitability is a core concept of...

**Modeling Practices for Control - a Model Predictive Control (MPC) Tutorial**

Robert Parker

The concept of automated closed-loop feedback control has been used in the chemical industries since the 1950s. While these feedback control methods work well in industrial practice, the challenges of biological systems -- including...

**Nonlinear Filters for the Linearly-inclined Tutorial**

Terence Sanger

Abstract not submitted.

### James Collins

Professor, Department of Biological Engineering, Massachusetts Institute of Technology Synthetic Biology: Life RedesignedSynthetic biology is bringing together engineers, mathematicians and biologists to model, design and construct biological circuits out of proteins, genes and other bits of DNA, and to use these circuits to rewire and reprogram organisms. These re-engineered organisms are going to change our lives in the coming years, leading to cheaper drugs, rapid diagnostic tests, and synthetic probiotics to treat infections and a range of complex diseases. In this talk, we highlight recent efforts to model and create synthetic gene networks and programmable cells, and discuss a variety of synthetic biology applications in biotechnology and biomedicine.

The rapid development of novel experimental methods in molecular and cell biology has fed an expansion in the sophistication of models for regulatory systems in living cells. The molecular networks involved in regulation of gene expression, cell signaling, and myriad homeostatic mechanisms naturally lend themselves to analysis within the framework of control theory. Moreover, the use of nonlinear system identification methods to reverse engineer these networks is an important step along the way, as is the development of theoretical ideas such as modularity, retroactivity, and feedback design. At the same time, synthetic biology – the design of de novo cellular regulatory systems – provides an exciting testbed for systems and control ideas, and fertile ground for new interactions between the fields of mathematical biology, control engineering and genetic, regulatory and cellular biology.

Many of the open problems in systems and control analysis of biochemical networks lead to new mathematical challenges. For example, how do structural properties of networks lead to desirable features or dynamic behaviors, including stability, robustness, multistationarity and the presence of oscillations? How are networks organized to maintain homeostasis while retaining the ability to respond effectively to environmental challenges? How can one simultaneously optimize different objectives in signaling cascades such as signal amplification, noise reduction, specificity and ultrasensitivity? How is the performance of biochemical networks affected by stochastic effects due to low protein copy numbers? And how can control systems be reliably built inside a cell using biological molecules?

This workshop will consider how new mathematical ideas from control theory, stochastic processes, graph theory, information theory, optimization, and dynamical systems will help to answer these and other related questions concerning the interplay between cellular biology and control theory.

### John Tyson

Computational Cell Biology, Virginia Polytechnic Institute and State University Network Dynamics and Cell PhysiologyThe physiological properties of living cells are determined by underlying networks of interacting genes, mRNAs, proteins and metabolites. These biochemical networks are staggeringly complex, highly nonlinear, dynamical systems that process information in time and space, in order to determine the optimal responses of a cell to challenging environmental conditions and its own internal damage-reporting mechanisms. To ferret out these interactions is a problem for molecular cell biologists, but to understand how biochemical networks coordinate cellular responses is a problem in applied mathematics. Using some simple examples of cellular decision-making (bistable switches) and time-keeping (limit cycle oscillations), I will show how dynamical systems theory and numerical simulations can shed considerable light on the molecular basis of cell physiology.

One of the main tasks of medicine is to develop and implement means to restore functionality of damaged physiological subsystems and their interactions with other subsystems to an adequate level that is as close as possible to the functionality of the healthy organism. Difficulties in these endeavors are caused by the complexity of the systems which have to be considered, and the fact that many physiological mechanisms are not yet well understood or even known. The real challenge, however, is to account for the individual variability across the patient population of those physiological subsystems that must be considered for a given problem. Therefore it is necessary to adapt medical treatments to individual patients, which is extremely important in case of chronic diseases such as hypertension, diabetes, or end-stage chronic kidney disease.

In a large number of cases the medical treatment is a drug treatment, which involves the problem caused by the individually different responses of patients to various drugs and the problem of dosing and administration strategies adapted to individual patients. The first problem requires characterizing the response of a patient to a drug as determined by the patient’s genetic profile, which requires intensive research in the area of pharmacokinetics, and particularly also in the area of genetic sequencing. The second problem leads to model-based administration strategies which pose a number of severe challenges for mathematical methods. Not every treatment strategy will involve drug administration, but can also be based on nonpharmacological intervention as, for example, provided by an implantable cardioverter defibrillator in order to treat arrhythmias of the heart. Of course, devices can also be employed in drug administration, such as a closed-loop artificial pancreas for type 1 diabetes.

The challenges for mathematical and medical research are caused by the complexity of the physiological systems that must be considered, which leads to complex mathematical models with a large number of parameters where at least the key parameters must be determined for each patient. An additional challenge is caused by the limited amount of routinely available data in a clinical environment, and the fact that physiological subsystems in patients will change over time. Intensive research is required in areas like parameter estimation, parameter subset selection, optimization and optimal control theory, optimal experimental design, filtering methods, etc. Successful research in these areas requires interdisciplinary cooperation between mathematicians, statisticians and clinicians under the premises that the medical problem has absolute priority, which necessitates that the mathematicians and statisticians involved are able to participate in productive discussions on the medical problem at hand.

### Kristin Swanson

Doctor, Neurosurgery, Mayo Clinic Every Patient Deserves Their Own Equation: Patient-Specific Mathematical NeuroOncologyGlioblastoma are notoriously aggressive, malignant brain tumors that have variable response to treatment. Mathematical neuro-oncology (MNO) is a young and burgeoning field that leverages mathematical models to predict and quantify response to therapies. These mathematical models can form the basis of modern "precision medicine" approaches to tailor therapy in a patient-specific manner. Patient-specific models (PSMs) can be used to overcome imaging limitations, improve prognostic predictions, stratify patients, and assess treatment response in silico. The information gleaned from such models can aid in the construction and efficacy of clinical trials and treatment protocols, accelerating the pace of clinical research in the war on cancer. This talk will focus on the growing translation of PSM to clinical neuro-oncology. It will also provide a forward-looking view on a new era of patient-specific MNO.

Despite much progress in animal locomotion and robotics, humans and other animals still typically outperform robots in many movement tasks, for instance, in versatility, stability, robustness, and energy consumption. What will it take to produce robots and software that are as good as humans and other animals? By trying to build robots that mimic animal performance, we understand better the problems that animals need to solve. And by understanding animal sensorimotor control, we might inform the development of better robots.

This workshop on sensorimotor control of animal and robot movement would be attended by researchers studying humans and non-human animals and those that try to build robots, performing movements of different types. The participants will include a wide variety of perspectives, with a good mixture of applied mathematicians, engineers (specifically dynamicists and control theorists), biologists, biomechanics researchers, roboticists including computer scientists, and cognitive scientists.

Of specific interest will be the performance of ecological movement tasks far from either an equilibrium or periodic steady state and movement in the presence of considerable uncertainly about the system, the environment and the forces on the animal or the robot. We have reasonably effective mathematical techniques and control theoretic tools for the study and design of equilibria (such as standing still or other posture) and periodic motion (such as steady legged locomotion or steady hovering by flapping). However, we have a vastly poorer understanding of how tasks such as playing soccer or swing dancing is accomplished by humans or could be accomplished by robots. It is unclear what the most appropriate mathematical language is for even describing these complex always-transient movements. One of the goals of this workshop will be to develop a set of benchmark movement tasks and metrics of performance in these tasks towards developing a rigorous formalism for thinking about these tasks. Discussions during this workshop will aim to categorize movement tasks into those that are ‘too easy or well-understood’, tasks that are at the ‘boundary of what we understand or can accomplish’, and tasks that are ‘far beyond what we currently understand or can accomplish’. We will aim for precise descriptions of these tasks, so that they are amenable to mathematical analysis. Our long-term goal is to promote a unified treatment or understanding of a broad class of tasks, rather than a narrow task-specific approach. We will focus on the sensing, estimation, actuation, control, and whole body dynamical aspects of the (bio- or robot-) mechanics.

### Lisa Fauci

Department of Mathematics, Tulane University Biological Fluid Dynamics at the Microscale: Nonlinearities in a Linear WorldPhytoplankton moving in the ocean, spermatozoa making their way through the female reproductive tract and harmful bacteria that form biofilms on implanted medical devices interact with a surrounding fluid. Their length scales are small enough so that viscous effects dominate inertial effects allowing the resulting fluid dynamics to be described by the linear Stokes equations. However, nonlinear behavior can occur because these structures are flexible and their form evolves with the flow.

In addition, the fluid environment may also be complex because of embedded microstructures that further complicate the dynamics.

We will discuss recent successes and challenges in describing these elastohydrodynamic systems.

### Alan Perelson

Senior Fellow, Theoretical Biology and Biophysics Group, Los Alamos National Laboratory Modeling Antibodies and HIV CureThe French VISCONTI study identified 14 HIV+ patients, who received antiretroviral treatment during primary infection for a median duration of 36.5 months and maintained post-treatment control of their virus below the limit of detection for a median of 89 months after stopping therapy. Byrareddy et al., Science 2016, showed that SIV-infected rhesus macaques on ART given a rhesus monoclonal antibody against the integrin 47 could maintain undetectable plasma viremia for over 9 months after all treatment was stopped. These examples provide proof-of-concept that a “functional cure” of HIV-1 infection, i.e. long-term control of HIV without continued treatment, is achievable.

In dynamical terms, functional cure of HIV corresponds to the infection having two (or more) stable steady states, one that corresponds to a high viral load and a second that is low, possibly below the limit of detection, as in the two examples above. I will discuss a model that has this property of bistability and provide examples of how it can be applied to explain experimental data.

In addition, there is great interest in using antibodies as therapeutics and possibly as a means of attaining functional cure. I will present a modeling analysis of both clinical and experimental data in which anti-HIV broadly neutralizing antibodies were given to infected subjects and lead to substantial decreases in plasma viral load. Antibodies can not only neutralize virus but can also enhance their clearance and cause the loss of HIV-infected cells through antibody-dependent cellular cytotoxicity, antibody-dependent cellular phagocytosis or through complement fixation. Understanding the in vivo effects of particular antibodies is a current challenge and mathematical modeling may provide mechanistic understanding of their modes of action.

### Alan Hastings

Professor, Department of Environmental Science and Policy, University of California, Davis Dynamics and control of spatial ecological populationsInfection and immune response modeling, particularly within tissues, has gained increasing prominence in the research agenda. Modeling, combined with experimentation, is answering important questions about health and disease biology, biomarkers, and therapeutic and vaccine intervention. Experimental advances in interrogating the adaptation of infectious agents within the host as well as the host immune response are generating large and complex datasets. These data create mathematical challenges in understanding the newly observed phenomena and making predictions regarding the underlying mechanisms and networks. The purpose of this workshop is to bring together researchers from several disciplines and perspectives on these issues to foster cross-disciplinary discussion and collaboration. We expect such interaction will advance the field by providing new strategies for modeling approaches that will accelerate understanding of infectious disease pathogenesis as well as the development of novel diagnostics, therapies and vaccines. In addition to the benefits to infection and immunological research, modeling efforts in this area will lead to new developments in applied mathematics techniques (for example, previous models in these areas have led to interesting developments in applied stochastics and applied dynamical systems research).

Simon Levin, in his address as the 2004 recipient of the Heineken award, recognized the relationship between social practices and behavior and the spread of infectious diseases:

A great challenge before us is thus to understand the dynamics of social norms, how they arise, how they spread, how they are sustained and how they change. Models of these dynamics have many of the same features as models of epidemic spread, no great surprise, since many aspects of culture have the characteristics of being social diseases. 1998 Heineken award winner Paul Ehrlich and I have been directing our collective energies to this problem, convinced that it is as important to understand the dynamics of the social systems in which we live as it is to understand the ecological systems themselves. Understanding the links between individual behavior and societal consequences, and characterizing the networks of interaction and influence, create the potential to change the reward structures so that the social costs of individual actions are brought down to the level of individual payoffs. It is a daunting task, both because of the amount we still must learn, and because of the ethical dilemmas that are implicit in any form of social engineering. But it is a task from which we cannot shrink, lest we squander the last of our diminishing resources.

The integration of social and biological theory is particularly poignant in the context of epidemics, where the dynamics, control, and evolution of communicable and vector-borne diseases are intimately connected to the joint dynamics of epidemiological, behavioral, and mobility processes that operate across multiple spatial, temporal, and organizational scales. It is therefore important to identify and quantify the individual-level processes responsible for observed epidemiological patterns: the result of individual interactions in changing social and ecological landscapes, which includes the construction of an encompassing theoretical explanatory framework that can identify the limitations of existing theory. This workshop will seek to disentangle the role of epidemiologic and socioeconomic forces on human disease dynamics.

Three key areas that are ripe for development include:

**Adaptive human behavior.**The science and management of infectious disease increasingly focuses on motivating people, for instance through social distancing policies that alter their behavior to reduce contacts and subsequent public disease risk since person-to-person contacts drive human disease dynamics. What an economic view brings into play is the perspective that since individuals value such contacts, they are also willing to accept some disease risk to gain contact-related benefits. The cost–benefit trade-offs that shape contact behavior, and hence the course of epidemics, are often only implicitly incorporated in epidemiological models. Phenomenological approaches make it difficult to identify the effects of adaptive behavior. Epidemiological–economic models of disease dynamics can be used to model the tradeoffs that drive person-to-person contact decisions explicitly. Preliminary research has shown that adaptive human behavior significantly changes the predicted course of epidemics, and such perspective brings up a myriad of challenges and opportunities. The inclusion of adaptive human behavior has implications for parameter estimation and interpretation and for the development of social distancing policies. The incorporation of adaptive behavior demands a shift in thinking about epidemiological processes and parameters as well as an analysis of its consequences at higher levels of organization, including the population, community, regional and global levels.**Feedbacks between disease, labor, and poverty.**Individual behaviors influence the transmission of infectious agents, which give rise to disease, which induce sickness behaviors. Thus, there is a feedback loop between behavior and disease dynamics. One key area where sickness behaviors are manifest is the performance of productive labor (i.e., work missed, effect of chronic disease on job retention, and attendant effects on individual wealth). Such feedbacks in which the “sick get sicker” can result in bistable social-epidemiological systems with dramatic effects for entire societies, particularly in developing societies where individual income levels may significantly affect nutrition and access to health care, leading to systemic health disparities reinforced by the intrinsic dynamics of transmission. The importance of addressing health disparities led NIH to the establishment an institute focused on finding strategies that reduce their deleterious effects across highly heterogeneous populations. Studying the impact of large scale intervention measures and the effectiveness that may emerge from targeting specific populations are but two of the important questions that are being considered.**Role of behavior in containment.**Individual choices about patterns of activity, personal protection, and risk-taking underlie many opportunities for infection. Although these processes are understood at a sociological level, they have rarely been incorporated in models for infectious disease dynamics and control, which often focus instead on public policies such as mass vaccination. A better understanding of individual behaviors and their plasticity would enable a more holistic theory of transmission dynamics and suggest opportunities for less top down interventions. But, little is known about directional shifts in behavior (willingness to be hospitalized, vaccinated, isolated, or quarantined), the conditions under which individuals perceive their personal choices to be efficacious and how these are related to the changing state of an epidemic, relaxation of temporarily adopted behavior patterns, and the role of variation in infection control practices by health care providers.

Other areas of interest include: effects of daily activity patterns on exposure and opportunities for transmission (e.g. models that consider spatial-temporal overlap); effects of age, risk-taking behavior, immunological status, gender, location, or other individual level traits on contact patterns; as well as local and non-local mobility patterns (travel, use of mass transportation and more), violence and social unrest.

### Philip Maini

Professor, Centre for Mathematical Biology, University of Oxford Modelling Collective Cell Motion in BiologyCollective motion is ubiquitous in biology, occurring in normal development, wound healing, and pathological cases, such as cancer. Here, I will review work that we have done on three problems: neural crest cell invasion, angiogenesis, and epithelial sheet movement. Each of these requires a different modelling paradigm, ranging from agent-based models, to partial differential equations. I will show how these problems lead to new mathematical challenges and how, with close collaboration with experimentalists, in some cases we have unearthed new biology.

The 2014 West Africa Ebola outbreak and the arrival of Zika underscore the spatio-temporal ecological factors that influence disease dynamics. Disease ecology has been a very fruitful area for collaboration between theoreticians and experimentalists, and the relevance for public health is apparent with concerns of zoonotic and vector borne diseases, interconnectedness between different communities at several scales, pathogen resistance, and the impacts of climate change, habitat fragmentation, and biodiversity loss on disease dynamics. These challenges call for novel data collection and usage, as well as new mathematical models and theoretical results. The aims of this workshop are to bring together researchers working in these different areas, in order to stimulate collaboration and discussion, with the goal of informing possible effective public health interventions. Specific themes for the workshop are given below.

**A. Habitat quality and connectivity.**

A central issue in disease ecology is heterogeneity in myriad forms, including of the host, pathogen, and environment. Habitat quality, broadly defined, varies widely in both space and time. This includes environmental conditions for arthropod disease vectors such as Zika or pathogens able to persist outside of human hosts such as cholera, as well as socioeconomic drivers of disease such as health care and sanitation infrastructure, vaccine availability, and access to clean water. New datasets from these topics are increasingly available, including through the Demographic and Health Surveys, Landsat, satellite imagery, detailed hydrologic models, and more. A related consideration is how different communities are connected with one another at scales ranging from the individual (e.g. sexual contact networks) to global (e.g. airline transportation networks). There is a wealth of data on different kinds of networks relevant for disease dynamics, including data on dispersal patterns, habitat fragmentation, and land use that is increasingly being used to build mathematical and computational models. Many modeling approaches have been fruitful, including metapopulations, differential equations, stochastic models, dynamics on networks, and agent-based models. Challenges include incorporating data into models effectively, developing theoretical results that improve understanding of disease dynamics in applied settings, and integrating data, simulation, and theory to inform public health decisions.

**B. Spillover and spillback dynamics with wildlife reservoirs**

Many diseases are driven by spillover and spillback between wildlife, human and domesticated hosts. Spillover infection occurs when a reservoir population with high pathogen prevalence comes in contact with a new host population. Spillback occurs if the host population re-infects the reservoir. These dynamics operate in many ways. For example, spillover of Ebola virus, and hantavirus from animal reservoirs to human hosts have resulted in major health concerns. Fish ectoparasites have spilled over from wildlife reservoirs to domesticated hosts, resulting in economic losses. The fish ectoparasites have then spilled back to wild populations, affecting population viability. Canine parvovirus has spilled over from domesticated host reservoirs to wolves and wild dogs, impacting wildlife population viability. A particularly troubling example is the spillover of pathogens from commercial reservoirs to wild bee hosts, resulting in severe population declines. In all of these cases, the ecology of the temporal and spatial interactions between reservoir and host groups is crucial for understanding and controlling the disease spread. Indeed, it is only through the lens of ecology that these spillover and spillback disease dynamics can be understood. Thus, a quantitative modelling structure that embraces both disease dynamics and ecology is required for predicting dynamics and suggesting effective control measures. Although there are some cases where this eco-epidemiological modelling structure exists, there is great deal of opportunity to develop this field further.

**C. Life history, community structure, and disease dynamics.**

Disease dynamics are profoundly shaped by the ecological context in which they occur. This includes pathogen interactions in microbial communities (e.g. within the gut), in association with species across taxa (e.g. Vibrio cholerae and plankton; malaria and multiple non-human primate species; pathogens such as schistosomiasis with life histories requiring multiple host species), competitive interactions (e.g. antibody-dependent enhancement and strain competition in dengue), and more. Habitat fragmentation, biodiversity loss, and climate change are pressing ecological issues, and understanding their impact on disease is important. These issues are particularly relevant for zoonotic diseases, and for understanding the interplay between wildlife, domesticated animals, and human disease. Ecology has a rich modeling tradition, and extensive theory has been developed. Developing new theoretical results to include the coupling of ecological and epidemiological dynamics, both through simplified models to gain qualitative insight as well as more detailed models for quantitative estimates for control in specific settings of interest, are important. A very relevant theme in this context is the incorporation of ecosystem structure into epidemiological models. The challenge is to not only look at ecological dynamics of host species for an infectious agent, but to also include interaction with species in the same ecosystem that are not hosts for that particular agent. Ecological interaction mediates transmission and epidemiological dynamics also indirectly via non-host species. Understanding the dynamics of infections in their natural-ecosystem context calls for integration of ecological and epidemiological theory and new models formulated and explored in that framework.

**D. Practical implementation of disease prevention and control efforts.**

Translating modeling results to public health decisions requires communication across disciplines and agencies. Model outputs in different disease scenarios are evaluated within an economic context, as interventions such as travel restrictions and school closures can have large economic consequences. Similarly, interventions such as vector habitat control, vaccine prioritization for populations driving transmission or at high risk of severe outcome, or decisions about antiviral usage in the context of resistance are all sensitive issues requiring cooperation between communities with potentially conflicting interests. This workshop will include researchers from public health agencies, industry, and the social sciences, in an effort to facilitate open discussion on these issues. Topics will include comparison of how practical modeling approaches compare over different time scales, the types of theoretical advances that are needed to practically inform policy, and ways in which young researchers can develop careers using mathematical models in applied settings for disease control.

### Marc Suchard

Biomathematics and Human Genetics, University of California, Los Angeles High-dimensional Phenotypes on Evolutionary Trees: Efficient Algorithms and New ModelsModern methods of genomic data collection reveal a great heterogeneity and diversity among strains of pathogens with different genotypes infecting hosts with significant differences in virulence, immunogenicity, and antigenic variation on a micro-scale (Workshop 1). The presence/persistence of specific different sub-groups of such pathogens depends heavily on macro-scale interactions of various human and animal hosts, travel patterns, environment, and intervention strategies (Workshop 2-3). In order to properly understand the main drivers of transmission of infectious disease, these ecological, molecular, and immunological factors need to be analyzed together, and their joint correct characterization requires a comprehensive interdisciplinary and multi-scale modeling approach. We expect that different infection outcomes are the result of the interplay of events at organ tissue cellular and molecular as well as ecosystem scales over the time course of minutes to years. A recent example is the Zika virus epidemic where a 3-5 days infection of a pregnant woman can result in birth defects lasting for the newborn’s lifetime. In order to study such problems, the unifying modeling framework for simultaneously analyzing multiple scales of empirical information from the level of single cells to organs, organisms, population and ecosystems appears necessary.

However, integrating the information from the micro- and macro-scales presents a great scientific challenge as the data on different scales is generated by different mechanisms and comes with different characteristics and uncertainties. In fact, integration across scales can be seen as the fundamental challenge for biology in the 21st century. The mathematical challenges raised are truly substantial, as the integration requires dealing with multiple temporal and spatial scales, as well as organizational scales. If scales in time and space are well separated, there exist, at least for deterministic systems, methods based on perturbation approaches that can be used. However, even these approaches are difficult to apply to systems with the kinds of underlying heterogeneities that will be found in systems with diseases. There are methods for averaging over heterogeneities but these methods as well have limitations. And, the different time scales of observations and the different framework that models at different scales use present substantial challenges.

This workshop will bring together scientists from multiple disciplines, to exchange ideas about new perspectives for the quantification of within-host dynamics and between-host transmission of infectious disease as well as integration over multiple temporal and spatial scales. Approaches that consider how to integrate approaches at different scales that range from deterministic to stochastic to computational will be a central theme, including how to incorporate data and how to deal with situations with limited data. It is assumed that a representative subset of participants in Workshops 1-3 will also participate. In the context of some of the problems Participants will discuss novel molecular and ecological data that has become available ('omic, clinical, entomological, and epidemiological data), and will discuss modeling perspectives that will allow their integration beyond traditional epidemiological models of transmission with the goals of improving public health practice and policies.

### Daily Themes

Monday |
Molecular Scale |

Tuesday |
Geographic Scale |

Wednesday |
Physiologic Scale |

Thursday |
Aggregations Across Scales and Multi Scale |

Friday |
Roundtable Discussion |

Preceding the TGDA@OSU Tripods Center Workshop, there will be a 5-day "Summer School: Theory and Foundations of TGDA" at OSU from May 14-18. The summer school aims to cover some basics as well as recent developments on several important topics in Topology, Geometry and Data Analysis. In particular, the topics will include: recent developments in persistent homology, topological algorithms, and statistics on manifolds and shape spaces. The summer school, organized by the TGDA group at OSU, will be primarily aimed at early-career researchers. Most of our funding will support participation of graduate students, but we may also fund postdoctoral researchers or undergraduate students with strong backgrounds. More details will be announced soon.

#### Advisory Committee

Larry A. Wasserman, Statistics, CMU

Peter Bubenik, Mathematics, U. Florida

#### Travel and Lodging Info

**Lodging**- There are several great hotel and lodging options available near the Ohio State University Campus. For a full list of options and more information go here. The MBI is located in Jennings Hall at 1735 Neil Avenue on the 3rd floor and most OSU hotels should offer shuttle transportation to get you to and from the MBI on campus for the workshop each day.**Airport**- When you arrive at John Glenn Columbus International airport-CMH you can take a taxi to your hotel (or find your hotel shuttle if offered) by going to the ground transportation area of the terminal where they offer 24-hour Airport taxi service.**Driving to MBI & Campus Parking**- If you are driving to the workshop, the closest public parking garage near the MBI is the 12th Avenue Garage. The MBI is just a short walk east from here on 12th Ave. to the Intersection of Neil Ave. where we are located in Jennings Hall on the 3rd floor. Here is a Google walking map.

We very gratefully acknowledge funding and support from our NSF TRIPODS grant, our NSF RTG grant, The Ohio State Math Research Institute MRI and the Ohio State Mathematical Biosciences Institute MBI.

Preceding the TGDA@OSU Tripods Center Workshop, there will be a 5-day "Summer School: Theory and Foundations of TGDA" at OSU from May 14-18. The summer school aims to cover some basics as well as recent developments on several important topics in Topology, Geometry and Data Analysis. In particular, the topics will include: recent developments in persistent homology, topological algorithms, and statistics on manifolds and shape spaces. The summer school will be primarily aimed at early-career researchers. Most of our funding will support participation of graduate students, but we may also fund postdoctoral researchers or undergraduate students with strong backgrounds. More details will be announced soon.

#### Travel and Lodging Info

**Lodging**- There are several great hotel and lodging options available near the Ohio State University Campus. For a full list of options and more information go here. The MBI is located in Jennings Hall at 1735 Neil Avenue on the 3rd floor and most OSU hotels should offer shuttle transportation to get you to and from the MBI on campus for the workshop each day.**Airport**- When you arrive at John Glenn Columbus International airport-CMH you can take a taxi to your hotel (or find your hotel shuttle if offered) by going to the ground transportation area of the terminal where they offer 24-hour Airport taxi service.**Driving to MBI & Campus Parking**- If you are driving to the workshop, the closest public parking garage near the MBI is the 12th Avenue Garage. The MBI is just a short walk east from here on 12th Ave. to the Intersection of Neil Ave. where we are located in Jennings Hall on the 3rd floor. Here is a Google walking map.

We very gratefully acknowledge funding and support from our NSF TRIPODS grant, our NSF RTG grant, The Ohio State Math Research Institute MRI and the Ohio State Mathematical Biosciences Institute MBI.

Topological and geometric ideas have already shown promises in producing novel perspectives and powerful algorithms for analyzing complex and diverse data. As the theory and foundations of topological data analysis continue to mature, we are presented with great opportunities to consolidate existing synergy as well as to establish new connections and collaborations among computational scientists, mathematicians, and statisticians, so as to form new perspectives and develop novel methodologies / algorithms for modern data analysis. This workshop, organized by the TGDA group at OSU, presents a timely platform to help achieve these goals.

Current PhD students and young researchers within 5 years of the PhD degree are qualified to apply for partial travel / accommodation support to attend the TGDA workshop.

There is also a one week summer school program that preceeds the workshop.

#### Advisory Committee

Larry A. Wasserman, Statistics, CMU

Peter Bubenik, Mathematics, U. Florida

#### Travel and Lodging Info

**Lodging**- There are several great hotel and lodging options available near the Ohio State University Campus. For a full list of options and more information go here. The MBI is located in Jennings Hall at 1735 Neil Avenue on the 3rd floor and most OSU hotels should offer shuttle transportation to get you to and from the MBI on campus for the workshop each day.**Airport**- When you arrive at John Glenn Columbus International airport-CMH you can take a taxi to your hotel (or find your hotel shuttle if offered) by going to the ground transportation area of the terminal where they offer 24-hour Airport taxi service.**Driving to MBI & Campus Parking**- If you are driving to the workshop, the closest public parking garage near the MBI is the 12th Avenue Garage. The MBI is just a short walk east from here on 12th Ave. to the Intersection of Neil Ave. where we are located in Jennings Hall on the 3rd floor. Here is a Google walking map.

We very gratefully acknowledge funding and support from our NSF TRIPODS grant, our NSF RTG grant, The Ohio State Math Research Institute MRI and the Ohio State Mathematical Biosciences Institute MBI.

REU participants will work on projects in areas such as molecular evolution, neuronal oscillatory patterning, cancer genetics, epidemics and vaccination strategies, and animal movement. Participants will work individually or in pairs under the guidance of expert mentors to make specific research contributions in these areas, often leading to a peer-reviewed publication and conference presentations. The REU program will incorporate various professional and research-skills development activities throughout the summer to help ensure the participants’ success in completing their summer project and to prepare them for graduate study or entering the workforce.

The program consists of three parts:

**Introduction to Mathematical Biosciences**(June 11th-15th, 2018) at the MBI

At the MBI, participants are introduced to various areas of mathematical biology via lectures and computer labs and visit various biological labs on campus.**Mentored Research Experience**(June 18th-August 3rd, 2018) at IUPUI, NJIT, or PSU

During the second component of the program, participants complete a mentored research project individually or in pairs at one of MBI’s IP. Participants also attend a weekly online seminar series and virtual all-program meeting.**Capstone Conference**(August 6th-9th, 2018) at the MBI

For the final week of the program, the students return to the MBI to participate in the Capstone Conference. A student-centered conference featuring talks and posters by students doing research in mathematical biology, keynote talks by prominent mathematical biologists, a graduate studies recruitment fair, and other special features including a conference dinner and social event.**Note that the Capstone Conference is open to all undergraduate students doing research in the mathematical biosciences, not only to students participating in the MBI REU.**

## Project Descriptions

### Indiana University – Purdue University Indianapolis (IUPUI)

Site Leader: Julia Arciero

**Project 1**: Using a Mathematical Model to Understand How Pairs of Red Blood Cells Interact in Linear Shear Flow

Mentor: Dr. Jared Barber

Description: Blood is composed of mainly red blood cells (45%) and plasma. As blood flows through vessels, cells near walls are pushed towards the vessel center by wall interactions but pushed away from the vessel center by interactions with other cells. These competing effects have a primary role in how cells are distributed across the vessel which, in turn, affect distribution of other important quantities like oxygen. We have developed a two-dimensional computational model of red blood cell motion to investigate how two isolated cells interact near vessel walls. The project will be use a previously-developed model to consider different types of interactions that pairs of cells undergo in this environment, how these interactions affect diffusion and mixing of cells, and the effects of various parameters like cell flexibility and size on these results.**Project 2**: Implementation of Advanced Topology Optimization Methods

Mentor: Dr. Andres Tovar

Description: In applied mathematics and engineering, topology optimization is known as the most effective material distribution numerical approach for synthesizing structures without any preconceived shape. Currently, a number of topology optimization algorithms is freely available in Matlab and other programming languages. Most of these algorithms use so-called density-based method, which can be used in 2D and 3D structures. The objective of this work is to implement more advanced topology optimization methods such as the level set-based and/or the phase field-based method. The student participating in this project will gain a complete understanding of the mathematics behind topology optimization and exposed to all related Matlab tools. The result of this research experience is the numerical implementation, analysis, and application of advanced topology optimization methods in structural optimization.**Project 3**: Using a Mathematical Model of Sepsis to Predict Survivability Conditions

Mentor: Dr. Julia Arciero

Description: Sepsis is a very serious and life-threatening illness caused by the body’s response to an infection. Experiments conducted in rats have shown that once a bacteria load exceeds a certain level, the rats do not survive. The presence of bacteria in the blood leads to a significant inflammatory response which in turn causes rapid damage to the body’s tissues that triggers a self-sustaining loop of damage and inflammation, eventually leading to either septic (bacteria-driven) or aseptic (inflammation-driven) death. The objective of this study is to use a mathematical model to predict the survivability range for an infection given varying doses or degrees of virulence of a bacterial infection. A model of ordinary differential equations will be used to simulate interacting populations of the bacteria and immune system. Experimental data from rat sepsis studies will be used to estimate several model parameters. The model will be used to predict conditions that lead to disease or health outcomes.

### New Jersey Institute of Technology (NJIT)

Site Leader: Simon Garnier

**Project 1**: Modeling Slime Mold Decision-Making as Systems of Coupled Oscillators

Mentors: Simon Garnier and Jason Graham

Description: In a complex and dynamic world, how do you choose the best of multiple options when you do not possess a brain, or even the beginnings of a nervous system? From bacteria and immune cells to fungi and plants, the large majority of living beings face this problem every day. Nevertheless our knowledge of decision-making mechanisms is mostly limited to those of neuronal animals, and in particular vertebrates. The goal of this project is for students to explore with University of Scranton Assistant Professor Jason Graham and NJIT Assistant Professor Simon Garnier the choice-making abilities of a non-neuronal model organism: the slime mold Physarum polycephalum. Using models of coupled oscillators, the students will study the integration of noisy and contradictory information and the role of memory during decision-making by P. polycephalum. They will also compare their results to experimental data collected by Garnier’s lab as part of an IOS NSF-funded research effort. The results of this work will help understand information pro- cessing in organisms without a brain, thereby advancing our comprehension of the emergence of cognitive processes in biological systems.**Project 2**: Emergent oscillations in electrically coupled neuronal networks

Mentors: Jorge Golowasch and Farzan Nadim

Description: Electrical coupling of neurons via gap junctions can produce network oscillatory activity in the absence of any oscillatory components. Such oscillations depend on network activity spreading through closed loops (re-entry) through which action potentials can spread, thus producing periodic potential firing patterns of the component neurons (Gansert et al, 2007, J. Neurophysiol). The properties of these re-entrant loops and the types of activity they can generate are mostly unknown. This project will combine computational modeling and mathematical analysis to characterize the types of activities that such networks can produce. Specific questions that will be addressed are: 1) What role does the size of the network play in the activity generated; 2) What is the role of electrical coupling strength; 3) What is the network output capacity; 4) How do intrinsic properties of neurons, specifically membrane potential resonance, influence network output.

### Penn State University (PSU)

Site Leader: Dennis Pearl

**Project 1**: Assessing the Value of ChIP Data

Mentor: Qunhua Li

Description: ChIP-exo is a high-throughput technology for identifying protein binding sites on DNA. It has near single-bp resolution, providing detailed structural information on the organization of protein-DNA complexes at a fine scale. However, robust measures for assessing its quality and reproducibility are still lacking. While there are quality measures for similar but lower-resolution technologies, such as ChIP-seq data, these measures do not work well for ChIP-exo due to its high resolution. This project aims to use machine learning techniques to build a predictive model for automatically classify quality and reproducibility of ChIP-exo experiments and extract predictive features.**Project 2**: Space-Time Models for Infectious Diseases

Mentor: Murali Haran

Description: Space-time models for infectious diseases: Infectious diseases like rotavirus, pertussis, measles, and meningitis have a major impact on populations all over the world, particularly on children in sub-Saharan Africa. These disease present a number of important challenges including estimating the current burden and anticipating the future burden of these diseases, as well as studying the impact of different vaccination strategies on controlling their spread. These research problems involve developing models for the diseases and combining disparate sources of information such as surveillance data and hospital records. In these projects students will be introduced to infectious disease modeling via susceptible-infected-recovered (SIR) models. They will learn simulation techniques, as well as estimation and computational methods for fitting these models to data, both via maximum likelihood and Bayesian methods. They will learn these methods through simulated examples and by applying them to real data sets obtained from collaborators at the Center for Infectious Disease Dynamics (CIDD) at Penn State.**Project 3**: Nonparametric Models for Animal Movement

Mentor: Ephraim Hanks

Description: Movement is a fundamental process underlying the spread of infectious disease, the spread of invasive species, and the flow of information and resources in social species. Understanding and predicting realistic movement of humans and animals can lead to improved surveillance of disease and more accurate predictions of the effects of changing landscapes. Animal movement is highly complex, exhibiting dependence in time, correlation in movements between conspecifics, changing behavior across seasons, hard constraints such as rivers and cliffs, and response to local environmental cues. Current statistical models for animal movement fail to capture this complexity fully. Based on Taken's theorem (Taken 1981), complex dynamical systems such as animal movement can often be well-represented by a lower-dimensional dynamical system, and the dynamics are often captured well by considering lagged time observations of the system. This suggests a nonparametric approach for modeling movement based on (1) the current local environment, (2) the animal's current movement state, and (3) the animal's state at multiple previous time steps. In this project, students will use modern machine learning approaches to build models that capture and replicate the complexity of animal movement, and will apply these models to various animal systems, including social movements of ants in a nest, sea lion foraging trips, and elk migrations.**Project 4**: Estimating the Distribution of Amino Acids in the Pre-biotic Period

Mentor: Dennis Pearl

Description: Estimating the Distribution of Amino Acids in the Pre-biotic period. When reconstructing phylogenetic histories from highly conserved sequences in all domains of life, recent evidence in several ancient enzymes shows that the distribution of amino acids is different at the root of the "tree of life" than in more rapidly changing newer enzymes. This provides a signal for the distribution of amino acids associated with a pre-biotic era (Pollack et al., 2013). In this project students will develop estimates of the pre-biotic distribution of amino acids from a variety of perspectives and combine evidence from phylogenetic and laboratory assessments. They will also develop and apply a new model of molecular evolution that allows for the amino acid distribution to vary with the level of site conservation. Students will advance their knowledge of stochastic evolutionary processes, and become skilled in aspects of probability and statistic inference associated with their use.

#### UPDATE!

Additional conference materials can be found at: https://www.asc.ohio-state.edu/kurtek.1/cbms.html

#### Topic Area

This Conference Board of the Mathematical Sciences (CBMS) conference will feature an intensive lecture series on elastic methods for statistical analysis of functional and shape data, using tools from Riemannian geometry, Hilbert space methods, and computational science. The main focus of this conference is on geometric approaches, especially on using elastic Riemannian metrics with desired invariance properties, and square-root representations that simplify computations. These approaches allow joint registration and statistical analysis of functional data, and are termed elastic for that reason. The statistical goals include comparisons, summarization, clustering, modeling, and testing of functional and shape data objects.

There is no travel/accomodation funding remaining, however we are still accepting applications to participate.

#### Travel and Lodging Info

**Lodging**- There are several great hotel and lodging options available near the Ohio State University Campus. For a full list of options and more information go here. The MBI is located in Jennings Hall at 1735 Neil Avenue on the 3rd floor and most OSU hotels should offer shuttle transportation to get you to and from the MBI on campus for the workshop each day.**Airport**- When you arrive at John Glenn Columbus International airport-CMH you can take a taxi to your hotel (or find your hotel shuttle if offered) by going to the ground transportation area of the terminal where they offer 24-hour Airport taxi service.**Driving to MBI & Campus Parking**- If you are driving to the workshop, the closest public parking garage near the MBI is the 12th Avenue Garage. The MBI is just a short walk east from here on 12th Ave. to the Intersection of Neil Ave. where we are located in Jennings Hall on the 3rd floor. Here is a Google walking map.

#### Primary Lecturer

Prof. Anuj Srivastava is a Professor of Statistics and a Distinguished Research Professor at Florida State University (FSU) in Tallahassee, FL. His main expertise lies in the use of techniques from algebra and differential geometry in deriving statistical inferences on nonlinear manifolds. Specifically, along with his colleagues, he has developed comprehensive Riemannian frameworks for shape analysis of objects, including scalar functions, Euclidean curves, 2D surfaces, and neuronal trees. He is an author, along with Prof. Eric Klassen of FSU, of a recently published Springer textbook on Functional and Shape Data Analysis. He has also published more than 200 papers in refereed journals and proceedings of refereed international conferences. He is a fellow of the IEEE, IAPR, and ASA.

#### Additional Lecturers

Prof. Eric Klassen, Department of Mathematics, Florida State University

Prof. Veera Baladandayuthapani, Department of Biostatistics, University of Texas MD Anderson Cancer Center

Prof. Laurent Younes, Department of Applied Mathematics and Statistics, Johns Hopkins University

Prof. Zhengwu Zhang, Department of Biostatistics and Computational Biology, University of Rochester

We gratefully acknowledge funding and support from the National Science Foundation CBMS grant, the Mathematics Research Institute, the Mathematical Biosciences Institute, the Department of Statistics at Ohio State, and the NSF TRIPODS grant.

The MBI Capstone Conference is a student-centered conference featuring talks and posters by students doing research in the mathematical biosciences, keynote talks by prominent mathematical biologists, a graduate studies recruitment event, panels on mathematical biosciences fields of research and career opportunities, and a social event at the Columbus Zoo and Aquarium.

The Capstone Conference is open to all undergraduate students doing research in the mathematical biosciences, not only to students participating in the MBI REU.** All accepted applicants will be given full-to-partial funding for hotel and travel!**

Featured Keynote Talks:

**Jonathan Rubin, Ph.D. – Professor and Chair, Department of Mathematics, University of Pittsburgh**

Dr. Rubin majored in Mathematics as an undergraduate at The College of William and Mary and received his Ph.D. in Applied Mathematics from Brown University in 1996. He was a Zassenhaus Assistant Professor and then a National Science Foundation Postdoctoral Fellow in the Department of Mathematics at The Ohio State University before joining the University of Pittsburgh Mathematics faculty in 2000. In addition to his Mathematics position, he is a Graduate Faculty member, a Center for Neuroscience at University of Pittsburgh Graduate Training Faculty member, a member of the Center for the Basis of Neural Cognition, an affiliate of the McGowan Institute for Regenerative Medicine, and a Visiting Professor in Computational Biology. Six students have completed their Ph.Ds at Pitt under Dr. Rubin's supervision.

The general topic of Dr. Rubin’s research is spatiotemporal pattern formation in coupled cell networks. The overall goal of this research is to understand how the intrinsic dynamics of network elements interacts with the architecture and properties of coupling to drive network activity. Most of his work is motivated by neuroscience applications, such as understanding transitions between activity patterns in respiratory pacemaker networks or figuring out the mechanism underlying the therapeutic efficacy of deep brain stimulation for Parkinson's disease.

**Carolyn Cho, Ph.D. – Immunology Pharmacometrics Therapeutic Area Lead, Merck Research Laboratories (MRL)**

Carolyn has worked in the pharmaceutical industry for 20 years, applying modeling and systems biology approaches to the discovery and development of therapeutic treatments for diabetes, osteoporosis, and immunology-related disease. She serves on the Board of Trustees of the Mathematical Biosciences Institute, and the boards of Propel Careers (past), and Mass. AWIS (past). She currently oversees modeling across the immunology pipeline at MRL, and has previously led the Systems Biology Targets group at Pfizer, was Global Head of Computational Systems Biology at Novartis Institutes for Biomedical Research (NIBR), and has held positions at Physiome Sciences (Princeton, NJ), SmithKline Beecham Pharmaceuticals (King of Prussia, PA), and Princeton University. Carolyn received her Ph.D. in biological physics from the University of Toronto.

**Nancy McMillan, Ph.D., PMP – Resource Group Manager, Advanced Analytics, Battelle**

After earning a BS in Mathematics and Computer Science from Muskingum University and an MS and PhD in Statistics from The Ohio State University, Dr. McMillan completed a two-year postdoc with the National Institute of Statistical Sciences then started a 23-year career at Battelle. Over that time period she has worked and published on environmental exposure and risk assessment, transportation safety benefits, quantitative risk assessment related to CBRN terrorism, and bioinformatics (analysis of genomic data). Dr. McMillan’s environmental, transportation, risk assessment, and bioinformatics work have all focused on providing quantitative analysis that captures uncertainty to support science-based decision-making. Dr. McMillan is currently working primarily in digital surveillance, including analysis of unstructured text data from scientific literature and social media. Dr. McMillan has been a group manager for 12 years. Her first 11 years of management experience involved leading a group of first 8-10 statisticians and then a larger team focused on knowledge management and cognitive computing that included computer scientists, statisticians, applied mathematicians, and knowledge management experts. Currently Dr. McMillan is the manager of Battelle’s Advanced Analytics capability; her group supports data science activities across Battelle’s Health, Environment & Infrastructure, National Security Division, and Chemical, Biological, Radiological, Nuclear, and Explosive (CBRNE) Defense business units.

**Graduate Programs Represented in the Recruitment Event:**

Arizona State School of Mathematical and Statistical Sciences

Case Western Reserve University Department of Mathematics

Cornell University Center for Applied Math

Indiana University - Purdue University, Indianapolis Department of Mathematical Sciences

North Carolina State University Department of Biomathematics

Purdue University Department of Statistics

Ohio State University Department of Biostatistics

Ohio State University Interdisciplinary Biophysics Program

Ohio State University Department of Statistics

University of California, Irvine Department of Mathematics

University of Iowa Department of Biostatistics

University of Maryland, Baltimore County Department of Statistics

University of Michigan Department of Biostatistics

University of Michigan Department of Mathematics

University of Minnesota Department of Biostatistics

University of Pittsburgh Department of Mathematics

Virginia Commonwealth University Department of Statistics

Virginia Tech Department of Statistics

### 2016-2017

This workshop is open to all postdoctoral individuals and junior faculty at The Ohio State University who wish to train and gain expertise in genomic data analyses.

This workshop will leverage the expertise of faculty and staff at OSU, including Guy Brock, PhD (BMI); Kevin Coombes, PhD (BMI); Soledad Fernndez, PhD (BMI); Shili Lin, PhD (StaDsDcs); Joseph McElroy, PhD (BMI); Gulcin Ozer, PhD (BMI); Maciej Pietrzak, PhD (MBI); Grzegorz Rempala, PhD, DSc (CPH/MBI); Amy Webb, PhD (BMI); Lianbo Yu, PhD (BMI)

Fee to Partcipate (includes lunch): $140 early registration, $180 after August 15th

Register at go.osu.edu/genomics2016

Algebraic topology is the standard mathematical tool for studying and classify global nonlinear structures and functions. The construction of scientific computational tools make it possible to apply techniques from algebraic topology directly to experimental or numerical data; the development of persistent homology provides methods to quantify and measure the size and relevance of features in data. These advances are in turn driving the development of statistical tools based on topological invariants and thus opening the door to novel techniques in data analysis. Biology is inherently multiscale (both in time and space), often nonlinear (reflecting the fact that most biological processes are themselves nonlinear), and noisy (both in how it is measured and intrinsically). Hence, biology provides an enormous variety of natural applications and challenges for these new topological techniques. The intertwining of biology and topology is not new. Knot theory and low dimensional topology play an important role in understanding the complicated three-dimensional structures of DNA and RNA. However, as the following examples show there has been a recent explosion in the breath of topics being addressed from a topological perspective. Persistent homology is being used to relate geometric features of proteins with their biochemical properties and functions. Topological analysis is being applied to genomic data to characterize cancer. Topological models are being built to understand explain neuronal codes, structures, and functions. Because topological tools can also be used to capture the dynamics of nonlinear systems, they are being used in the analysis and modeling of gene regulatory/signal transduction networks. Characterizing the motility of cancer cells provides problems where the robustness of topological tools may prove to be uniquely suited. New developments in algebraic topology show tremendous potential to provide novel tools for use in a wide variety of biological applications. However, substantial progress will require close collaboration between mathematicians and life scientists, both to convey the power of the topological tools and to further refine and develop these tools to meet specific challenges. The purpose of this workshop is to greatly broaden this dialogue.

### Michael Shuler

Professor, Biomedical Engineering, Cornell University Modeling LifeWe seek to construct physical and mathematical models of life. Such models allow us to test our understanding of how living systems function and how they respond to human imposed stimuli. One system is a genomically and chemically complete model of a minimal cell. This cell is a hypothetical bacterium with the fewest number of genes possible. Such a minimal cell provides a platform to ask about the essential features of a living cell and forms a platform to investigate "synthetic biology." A second system is "Body-on-a-Chip" (or microphysiological system) which is a microfabricated, microfluidic system with cells or tissue constructs representing various organs in the body. That physical model is based on a physiologically based pharmacokinetic-pharmacodynamics (PBPK-PD) model. The ratio of organ sizes and the flow to each component is physiological. It can be constructed from human or animal cells and used in drug discovery development, or to predict response to exposure to environmental chemicals. Both the computer and the physical models provide insight into the underlying biology and provide new tools to make use of the understanding to provide benefits to society.

### Simon Levin

Professor, Department of Ecology & Evolutionary Biology, Princeton University Mathematical Ecology: A Century of Progress, and Challenges for the Next CenturyMathematical ecology is one of the oldest and most successful branches of mathematical biology, and one that has profited both ecology and mathematics. The great mathematician Volterra was a pioneer a century ago, and the subject has built on the dynamical systems approaches he introduced. As attention has turned to the ecological challenges of the present- climate change, biodiversity loss, critical transitions and the management of the global commons, new methods have entered from stochastic processes to game theory, from statistical physics to topological data analysis, and with a heavy emphasis on high-speed computation. In this talk, I will trace out some of the historic successes, and introduce modern challenges.

High throughput sequencing provides an unprecedented opportunity to interrogate somatic alterations in single cells, individual patients and large cohorts, across multiple spatial and time points and in response to treatment. However, the sheer amount and complexity of these very heterogeneous sequencing data pose significant challenges in integration, modeling and interpretation. For example, single cell measurements allow a very fine-grained view of cancer biology, but are based on limited amount of biological material and are intrinsically noisy and biased, with high missingness of data, which calls for development of new methods for inference based on partial observations. Time series of measurements, across multiple data types, will provide insights into the processes behind tumor evolution and understanding the forces that shape tumor progression, but methods for modeling multimodal biological time series data are in the very early stages. Questions about how tumor subpopulations evolve, interact with each other and the immune system, and how they respond to individual and combinations of drugs all remain open. Integrating all this diverse sequencing information and building better models of tumor progression promises to provide guidelines for individually optimized, time-adaptive treatment for cancer patients.

Powerful technologies exist - and continue to emerge - for large-scale recording and manipulation of neuronal activity. However, even as neuronal data become increasingly rich and imaging procedures become increasingly sophisticated, only a small fraction of neuronal activity (e.g., a neuron's voltage, or calcium flux) remains observed. A fundamental challenge in neuroscience is to link these observed activities to the unobserved biophysical mechanisms that produce it. In some cases, experimental manipulations permit detailed assessment of these mechanisms. However, as emerging technologies facilitate high-throughput experiments and accelerate the number of neurons observed simultaneously, targeted experimental manipulations become infeasible or intractable. Therefore, the challenge of rigorously connecting observed neuronal activity to underlying biophysical mechanisms is becoming increasingly critical to address fundamental questions in neuroscience. One powerful strategy to address the challenge of linking data to mechanisms is through the development of computational models in which unobserved biological mechanisms can be expressed and controlled. These computational models typically possess many variables and parameters, and rigorous 'matching' of the model dynamics to the observed neuronal data remains difficult. In this workshop, we will assemble an interdisciplinary group of researchers that combine expertise in complex neuronal data, computational modeling, and statistical methods with a focus on methodologies that constrain the diverse biophysical mechanisms that support neuronal activity. In doing so, a primary goal will be to develop and share resources that facilitate a coherent synthesis of information collected from observational data and expressed in computational models, and provide rigorous approaches for uncertainty management and model validation. Critical to the development of this framework are interactions among statistical neuroscientists, mathematical neuroscientists, and experimental / clinical neuroscientists. However, these interactions are typically rather limited, and therefore the methodologies applied to a given data set may be quite distinct. Among the various reasons for the segregation among communities is the lack of a forum for reconciling differences in the language and approaches typical to each discipline in a pedagogical manner. For example, the notion of a 'model' for a statistical neuroscientist (e.g., a Poisson process), mathematical neuroscientist (e.g., the Hodgkin-Huxley equations), and clinical neuroscientist (e.g., an in vitro preparation) may be quite different. This workshop will bring together a diverse group of researchers interested in principled statistical techniques that link complex neuronal data with mathematical models of neuronal activity. Researchers will present a variety of data assimilation techniques, which will include estimation of model parameters, as well as estimation of latent dynamical variables, model identification, goodness-of-fit assessment, and a broader characterization of the space of dynamical models that are consistent with complex neuronal data. Additionally, we recognize that other fields have made progress assimilating complex data into dynamical models, notably climate modeling and weather prediction. Representative researchers from these fields will be invited to share their insights and experiences, and to explore the utility of their techniques on physiological data. The workshop will include research talks and informal tutorials, and be appropriate both for researchers in the field and those interested in methods to connect statistical, mathematical, and experimental neuroscience through principled data assimilation techniques. Specifically, the duration of the workshop will be five days. A two-day tutorial will be followed by three days of research talks, with ample time for interactions among the participants. Students and postdocs will be encouraged to participate in the poster session. The tutorials will include not only introductory talks but also hands-on work with realistic data, which will be provided to participants in advance of the workshop.

### Charles Peskin

Professor, Courant Institute of Mathematical Sciences, New York University Fiber Architecture (Differential Geometry) of the Heart and its ValvesCardiac tissue is highly anisotropic. The fibers that are responsible for this anisotropy are primarily the muscle fibers in the heart walls, and collagen fibers in the heart valve leaflets. The fiber architecture of the heart is remarkable. In the left ventricle, there are nested toroidal surfaces along which the muscle fibers run, following approximately geodesic spiral paths. In the aortic and pulmonic valves, the collagen fibers form a branching braided hammock-like structure that looks as if it might have a fractal character. The goal of the work described in this talk is to derive the fiber architecture of the heart from first principles. Our approach is to formulate partial differential equations for a system of fibers under tension supporting a pressure load, and then to see to what extent these equations predict the observed fiber architecture of the heart and its valves.

### Elizabeth Thompson

Professor, Department of Statistics, University of Washington Finding genes via Relatedness and the Co-ancestry of GenomeA major goal of genetic analysis is to find the genes that underlie traits of medical or economic importance. The associations between trait data and marker DNA arise from the descent of genome to related individuals. Thus, we consider these associations through analyses of relatedness as measured by shared ancestry of genome, or identity by descent (IBD). To achieve this, we present models for IBD both among individuals and across the genome, and thence a framework for realizations of IBD given genome-wide marker data. In general, model-based probabilities of trait data jointly on individuals depend only on the joint IBD among them at the relevant loci. We consider the particular case of a variance component model for a quantitative trait, where only location-specific pairwise relatedness between individuals is required.

Models of populations have played a central role in diverse biological contexts, including in studies of cellular, molecular, organismal, and ecological systems. The study of such models also has a long history in the mathematics community. However, recent advances in the sensing of biological systems have generated extremely large data sets, and these data have only started to be integrated effectively with population models in ways that provide meaningful insight and accurate prediction. Examples of these big data include the genetics of microbial communities over time and space in environments as small as the human gut and as large as river estuaries, cell phone signals that can provide information on human movement patterns with high temporal and spatial resolution, and real-time disease surveillance data during epidemic outbreaks. While the incorporation of these types of data into population models has the potential for improving our understanding of how biological systems function, new intellectual challenges arise from these data, many of which are mathematical and statistical in nature. For example, are there principled approaches for simplifying the data being analyzed to minimize loss of information? How can dependencies between data sets be best handled? Can population models guide the collection of these data sets or should they simply respond to the available data? Will the future see some types of data be replaced by other types of data, or will different types of data act synergistically in guiding our understanding of what biological processes are important in the population dynamics we observe? These questions arise across biological scales of organization. Whether at the scale of cells or the scale of ecosystems, the availability of these new types of data, and the extensiveness of these data, should also enable the design of mathematical models with greater predictive accuracy. However, the design of such predictive models poses difficult new challenges. In tumor biology, how does one integrate probabilistic models for cell evolution with PDE models for the growth of tumors with many competing subpopulations? In epidemiology, how does one bridge the gap between models of intrahost pathogen evolution and epidemic models of the spread of disease within populations? How should we model external pressures, for example antibiotic treatment, on the microbial populations residing in humans? Progress on these challenges is important for the development of excellent policy alternatives for human health and the ecology of the planet. A major goal of this workshop is to bring together the large and active group of mathematicians working in population biology with biological practitioners using large data techniques.

### Arthur Lander

Professor, Center for Complex Biological Systems, University of California, Irvine Understanding Growth ControlAll multicellular animals develop through a process of controlled proliferation that, in many cases, exhibits impressive speed and extraordinary precision. Organs and tissues often stop growing at sizes that are independent of body size, independent of cellular growth rate, independent of elapsed time, independent of cell size, and nearly independent of initial conditions. Such control involves feedback regulation of cell proliferation, and although some of the molecular signals have been elucidated, the strategies by which feedback achieves the objectives of growing organs and tissues are only beginning to become clear. Drawing on both modeling and experiments, I will discuss how the coupling of feedback regulation to cell lineage progression provides the degrees of freedom that allow proliferating systems to achieve stability, set-point control, and a remarkable ability to generate controlled final sizes that are larger than the spatial ranges over which feedback signals themselves act.

### Leah Edelstein-Keshet

Professor, Mathematics, University of British Columbia Navigating Biochemical Pathways for Cell Polarization and Motility (A Personal Journey)Many cell types, including cells of the immune system, are able to polarize and crawl in response to chemical or mechanical stimuli. In this way, they can perform vital functions such as immune surveillance, wound healing, and tissue development. I will describe our efforts to understand the underlying biochemistry governing the initial direction sensing, polarization, cell shape change, and motility. While much of the biology is undergoing rapid discovery, we have found that mathematical ideas supply additional tools. Such tools help to decipher underlying mechanism, to weed between competing hypotheses, and to suggest new experimental tests. On the same journey, we also encountered some new and interesting mathematics.

### Joel Cohen

Professor of Populations & Head of Laboratory, Laboratory of Populations, Rockefeller & Columbia Universities The variation is the theme: Taylor's law from Chagas disease vector control to tornado outbreaksThis workshop will be devoted to exploring the diversity of morphogenetic processes and to presenting the challenges biologists have faced in understanding and explaining these processes. Special emphasis will be placed on problems that are likely to be tractable to mathematical modeling and where such modeling can help shed light on the biological process.

Morphogenesis constitutes an exceptionally diverse set of processes that gradually transform simple tissues, initially mostly clumps and sheets of cells, into complex organs ranging from the leaves of trees to the brains of vertebrates. Morphogenesis not only gives shape to tissues, organs and appendages, but often involves the coordinate transformation of tissues with different origins into an integrated structure that performs a particular function (for instance the eye or the hand). The mechanisms of morphogenesis have proven very difficult to elucidate and are only partially understood. Mathematical modeling has played a critical role in assessing the feasibility of specific mechanisms and in exploring possible mechanism that have eluded experimental approaches.

In recognition that the timing of this workshop will coincide with the hundredth anniversary of D’Arcy Thompson’s On Growth and Form, we plan to begin the workshop with a celebratory D’Arcy Thompson Day. For this session we will have speakers who will outline the history of studies in morphogenesis (including the role D’Arcy Thompson’s work has played), with emphasis on how old problems have been solved and how new problems have arisen with the advent of new insights and new technologies.

The remainder of the workshop will be devoted to the exploration of the diversity of morphogenetic mechanisms. We plan to invite developmental biologists who have approached their problems quantitatively, rather than just descriptively. Topics that will be discussed are how physical forces guide morphogenesis, how branching patterns in vascular systems arise, the role of cell sorting and rearrangement in tissue morphogenesis, the role of patterned cell death, segmentation and somite formation, mechanisms of gastrulation and dorsal closure, tooth morphogenesis, planar cell polarity and tissue polarity, and the evolution of morphogenetic mechanisms.

Morphological evolution is due to the evolution of morphogenetic processes. This means that morphogenetic processes diverge as lineages diverge. How much of this is due to quantitative variation of a mechanism or to qualitative changes in the mechanism is often not understood, and this is a place where mathematical modeling can shed light on what is feasible within a given mechanism and what morphological changes cannot be achieved by simple quantitative tuning. The last portion of this workshop will highlight evolutionary and comparative problems in morphogenesis and the contributions mathematics can play (and has played) in developing an understanding of these complex problems.

This workshop is specifically devoted to study problems in morphogenesis and development in which growth and mechanics play a key role.

By its very nature, biology raises many challenges that mathematical modellers have not had to address in other areas of application. For example, in early development there is an enormous amount of growth of tissue and large-scale tissue rearrangements. During these processes there are significant mechanical changes and, in many cases, the phenomena are intrinsically three-dimensional. Thus, even the crudest models pose computational challenges. Once proposed, models must be validated and here is another challenge. How does one image complex evolving surfaces and extract summary metrics for model validation?

There are a number of ways to model growth and rearrangement. The purely continuum approach describes tissue as a visco-elastic-plastic deformable material satisfying the laws of continuum mechanics. This approach has the advantages of generating a small system of (albeit highly nonlinear) coupled partial differential equations with a limited number of parameters and a history of mathematical theory underpinning them. The disadvantages are that they are too coarse to account for changes in cell shape or for cell-level properties. To account for the latter, discrete cell-based models have been developed (for example, cell-centred, vertex, Potts). These allow for extraction of detailed metrics on cell size, number of sides (in the case of epithelial tissues, which are well approximated by polygonal cell shapes) etc., which, in principle, can be compared with data. Disadvantages are that there are many more free parameters in such models, and there is no rigorous mathematical theory underlying these models. Whichever modelling framework is adopted, there is the challenge of model parameterization, identifiability and validation.

This workshop is timely because of the advances in computational techniques that now allow us to begin to compute the outcome of the above modelling approaches, and because of the rapidly developing field of imaging which is beginning to provide data for model validation. Therefore the lack of reliable and detailed spatiotemporal data, the major stumbling block for the acceptance of such models, may now become somewhat less of issue, putting us on the threshold of a new era of model validation and application.

The workshop will have two underlying themes:

- Specific applications. These will include, but are not limited to, tissue (for example, brain) mechanics, growth and shaping of sea shells, epithelial sheet dynamics (for example, growth control in Drosophila wing disc), neural crest cell invasion, etc;
- Mathematical challenges. These include, developing a theory to underpin many of the different modelling approaches so that they can be compared with each other; addressing the problems that arise in gathering summary metrics and subsequent model validation, new computational techniques for partial differential equations on evolving surfaces.

### Uri Alon

Professor, Department of Molecular Cell Biology, Weizmann Institute of Science Evolutionary tradeoffs and the geometry of phenotype spaceEvolutionary tradeoffs lead to phenotypes that lie in polytopes in trait space, allowing evolutionary tasks to be inferred from data on animal morphology, single cell gene expression and other systems.

The aim of this workshop is to review the state of the art in hybrid multi-scale modelling in cancer and development with an emphasis in the crucial issue of how tissue structure and individual cell behaviour come together to robustly generate a functional tissue.

Recent results regarding tumorigenesis in epithelial tissues have shown that the geometrical arrangement of cells within epithelial sheets, analysed in terms of a Voronoi tessellation, is a key factor in determining whether malignantly infected cells are likely to invade the tissue. This scenario implies that, beyond the emergence of cells with malignant phenotypes generated by gene mutations or other mechanisms, other factors such as tissue geometrical organization must be taken into consideration. Furthermore, this situation requires the formulation and analysis of models that account for both individual cell behaviour and tissue organisation at a larger scale, i.e. we must resort to hybrid multi-scale mathematical frameworks. By studying the mechanisms that must be de-regulated in order to allow for tumours to emerge, we expect that we can reverse-engineer the underlying mechanisms that have been evolved to guarantee robust, normal tissue function and geometrical structure.

A key element in this approach is the interface between mathematical models and image acquisition and analysis. This is a critical issue, as this interface is essential for crucial steps in the modelling process such as model parametrisation and model validation. In fact, this workshop is timely because, due to huge recent advances in the general area of biomedical imaging, the major obstacle for the acceptance of these models, namely, lack of appropriate data to carry out parametrisation and validation, may become easier to overcome in the near future.

The workshop will be organised around three main areas:

- Individual cell behaviour. This area will explore the mechanisms for cell fate decision and their connection to cancer and development. Two subject of particular interest are (cancer) stem cells and the effect of random noise on cell-decision making.
- Image analysis. The emphasis in this theme will be on the interface between mathematical models and image analysis techniques by exploring, for example, how vertex models of epithelial tissues can be calibrated from images obtained by confocal microscopy.
- Hybrid multi-scale modelling. This theme will explore the state-of-the-art on the subject trying to emphasise how models of individual cell behaviour can be coupled to larger-scale models accounting for tissue organisation and, particularly, the interface between hybrid models and image analysis.

### James Keener

Professor, Dept of Math, University of Utah Cell Physiology: Making Diffusion Your FriendDiffusion is the enemy of life. This is because diffusion causes small particles to spread out, and for aggregates of particles to dissipate. Thus, in order to be alive and maintain its structure, an organism must have ways to counteract the constant tendency of things to spread out. And indeed they do. Plants, for example, are able to harness the energy of the sun to convert carbon dioxide and water into high energy compounds such as carbohydrates. These high energy compounds are then carefully deconstructed by living organisms to do work moving things around and building and repairing their structures. In this way, living things are able to combat the tendency of structures to dissipate and fall apart.

However, living organisms do much more than simply counteract diffusion; they actually exploit it for specific purposes. That is, they expend energy to concentrate molecules and then use the fact that molecules move by diffusion down their concentration gradient to do useful things. How do they do this? The short answer is that they couple diffusion with appropriate chemical reactions and are thereby able to exploit the inherent diffusive motion of molecules. Indeed, many of the processes that take place in living cells can be described as the interaction of reacting and diffusing chemical species. This realization has led to the mathematical description of many interesting biological processes and this in turn has led to an increased understanding of how biological systems work.

In this talk, I give several examples of the ways that cells use diffusion to their advantage, and describe the equations that model these processes. In particular, I will describe how molecular diffusion and reaction are used to make signals, to create functional aggregates, to take a census, and to make length measurements.

In this way, I hope to convince you that living organisms have made diffusion their friend, not their enemy, and in the process, demonstrate the importance of understanding the solutions of the equations governing diffusion-reaction processes.

This workshop will tackle a variety of biological and medical questions using mathematical models to understand complex system dynamics. Working in collaborative teams of 4-5, each with a senior research mentor, participants will spend a week making significant progress with a research project and foster innovation in the application of mathematical, statistical, and computational methods in the resolution of significant problems in the biosciences. By matching senior research mentors with junior mathematicians, the workshop will expand and support the community of scholars in mathematical biosciences. In addition to the modeling goals, an aim of this workshop is to foster research collaboration among women in mathematical biology. Results from the workshop will be published in a peer-reviewed volume, highlighting the contributions of the newly-formed collaborative groups. Previous workshops in this series have occurred at IMA and NIMBioS.

This workshop will have a special format designed to facilitate effective collaborations.

- Six senior women working in mathematical biology will present a problem and lead a research group.
- Each group leader will choose a more junior co-leader, someone with whom they do not have a long-standing collaboration, but who has enough experience to take on a leadership role.
- Additional team members will be chosen from applicants and invitees. We anticipate a total of five or six people per group.
- It is expected that each group will continue to work on their project together after the workshop, and that they will submit results to the Proceedings volume for the workshop.

The benefit of such a structured program with leaders, projects and working groups planned in advance is based on the successful WIN, Women In Numbers, conferences and is intended to provide vertically integrated mentoring: senior women will meet, mentor, and collaborate with the brightest young women in their field on a part of their research agenda of their choosing, and junior women and graduate students will develop their network of colleagues and supporters and encounter important new research areas to work in, thereby fostering a successful research career. This workshop is sponsored in part by Microsoft Research.

This workshop is partially supported by NSF-HRD 1500481 - AWM ADVANCE grant.

### List of Projects

Leaders | Co-leaders | Topic |
---|---|---|

Linda Allen | Angela Peace | Stochastic modeling of infectious diseases |

Jen-Mei Chang | Kellie Archer and Karamatou Djima | Explaining Autism Spectrum Disorder with Placenta |

Nina Fefferman | Shelby Wilson | Ectoparasites and Allogrooming: Evolutionary Trade-offs in Animal Community Health |

Holly Gaff | Gaby Hamerlinck | Modeling Argasid Ticks |

Laura Miller | Wanda Strychalski | Mechanics of super-fast nematocyst firing |

Helen Moore | Nessy Tania | Disease and Combination Therapy Dynamics |

Detailed descriptions of each of the projects are available here.

**The deadline to apply for this event is Saturday, December 10th, 2016.**

The goal of this MBI NSF-funded program is to introduce students to exciting new areas of mathematical biology, to involve them in collaborative research with their peers and faculty mentors, and to increase their interest in mathematical biology.

The goal of this MBI NSF-funded program is to introduce students to exciting new areas of mathematical biology, to involve them in collaborative research with their peers and faculty mentors, and to increase their interest in mathematical biology. The program consists of three parts - each including a mix of educational and social experiences. See this website for more info. http://mbi.osu.edu/education/summer-undergraduate-program/

The MBI Capstone Conference offers undergraduate student researchers in the mathematical biosciences an opportunity to present their work on the national stage.

This student centered conference features:

- A recruitment fair for graduate studies
- Panels on jobs and graduate opportunities
- A social event at the Columbus Zoo and Aquarium
- Talks and posters by student researchers
- Keynote presentations will include:
- Zachary Kilpatrick, University of Colorado – "Evidence accumulation in changing environments: Neurons, organisms, and groups"
- Molly Maleckar, Allen Institute – "Open science: how the Allen Institute for Cell Science wants to revolutionize cell biology"
- Catherine Stein, Case Western Reserve University – "Novel human genetic approaches to studying tuberculosis resistance"

Applications submitted by July 20, 2017 will receive full consideration. There is no application fee.

### 2015-2016

This workshop is open to all postdoctoral individuals and junior faculty at The Ohio State University who wish to train and gain expertise in genomic data analyses.

This workshop will leverage the expertise of faculty and staff at OSU, including: Kevin Coombes, PhD (BMI), Soledad Fernndez, PhD (BMI), Shili Lin, PhD (Statistics), Joseph McElroy, PhD (BMI), Lianbo Yu, PhD (BMI), Glin zer, PhD (BMI), Grzegorz Rempala, PhD, DSc (CPH/MBI)

### Haim Bar

Assistant Professor, Department of Statistics, University of Connecticut An Empirical Bayes Approach to Variable Selection and QTL AnalysisWe develop a model-based empirical Bayes approach to variable selection problems where the number of predictors is very large, possibly much larger than the number of responses (the so-called “large p, small n” problem). Motivated by QTL (quantitative trait loci) studies, we consider the multiple linear regression setting, where the response is assumed to be a continuous variable, and it is a linear function of the predictors. The explanatory variables in the linear model can have a positive effect on the response, a negative effect, or no effect. Thus, we model the effects of the linear predictors as a three-component mixture, where each component follows a normal distribution with mean μ, −μ, or 0. A key assumption in our approach is that only a small fraction of the candidate predictors have a non-zero effect on the response variable. By treating the putative variables as random effects we get shrinkage estimation, which results in increased power. This approach is computationally efficient because the number of parameters that have to be estimated is small, and remains constant regardless of the number of explanatory variables in the linear regression model. The model parameters are estimated using the EM algorithm which leads to significantly faster convergence, compared with simulation-based methods. Furthermore, we employ computational tricks which allow us to increase the speed of our algorithm, to handle a very large number of putative variables, and to avoid multicollinearity in the regression model.

Modern biological sciences build their foundations on molecular descriptions of DNA, RNA and proteins as essential components. The molecular mechanisms of and the interactions between these components are pivotal to the fundamental secrets of life. Biomolecular structural information can be obtained via a number of experimental techniques, including X-ray crystallography, NMR, EPR, cryo-electron microscopy tomography, multiangle light scattering, confocal laser-scanning microscopy, small angle scattering, and ultra fast laser spectroscopy, to name only a few. However, it is the geometric and topological modeling that interprets and translates such data into three-dimensional structures. In addition to straightforward geometric visualization, geometric modeling bridges the gap between imaging and the mathematical modeling of the structure-function relation, allowing the structural information to be integrated into physical models that shed new light on the molecular mechanisms of life due to the structure-function relation. However, a major challenge in geometric and topological modeling is the handling of the rapidly increasing massive experimental data, often with low signal to noise ratio (SNR) and low fidelity, as in the case of those collected from the structure determination of subcellular structures, organelles and large multiprotein complexes such as viruses. Currently, mean curvature flow, Willmore flow, level set, generalized Laplace-Beltrami operator and partial differential equation transforms are commonly used mathematical techniques for biomolecular geometric and topological modeling, but also applications of group and graph theory have been pioneered in the context of virology. Additionally, wavelets, frames, harmonic analysis and compressive sensing are popular tools for biomolecular visualization and data processing. Moreover, differential geometry, topology and geometric measure theory are powerful approaches for the multiscale modeling of biomolecular structure, dynamics and transport. Finally, persistently stable manifold, topological invariant, Euler characteristic, Frenet frame, and machine learning are vital to the dimensionality reduction of extremely massive biomolecular data. These ideas have been successfully paired with current investigation and discovery of molecular biosciences, and approaches developed in tandem with experiment have demonstrated the power of an interdisciplinary approach. The objective of this workshop is to encourage biologists to outline problems and challenges in experimental data collection and analysis, and mathematicians to come up with new creative and efficient solutions. This program will enable this process to be iterative, with mathematical techniques developed with repeated input and feedback from experimentalists to ensure the real life impact of the work. We plan to enable this by bringing together experts in biomolecular imaging technology and in applied mathematics who share a passion for understanding the molecular mechanism of life on Earth. We expect the workshop to provide a platform for interdisciplinary research collaborations.

### Matthew Sullivan

Principal Investigator, Department of Microbiology, The Ohio State University Math in the Virosphere: Needs and opportunitiesMicrobes are recently recognized as driving the energy and nutrient transformations that fuel Earth’s ecosystems in soils, oceans and humans. Where studied, viruses appear to modulate these microbial impacts in ways ranging from mortality and nutrient recycling to complete metabolic reprogramming during infection. As environmental virology strives to get a handle on the global virosphere (the diversity of viruses in nature) clear challenges are emerging where collaboration with mathematicians will be powerfully enabling. I will present a few ripe research avenues where we (environmental virologists) could use some help from mathematicians to better understand the nanoscale (viruses) and microscale (microbes) entities that drive Earth’s ecosystems.

Electrostatic interactions are fundamental in nature and ubiquitous in all biomolecules, including proteins, nucleic acids, lipid bilayers, sugars, etc. Electrostatic interactions are inherently of long range, which leads to computational challenges. Since 65-90 percent of cellular mass is water under physiological condition, biomolecules live in a heterogeneous environment, where they interact with a wide range of aqueous ions, counterions, and other molecules. As a result, electrostatic interactions often manifest themselves in a vast variety of different forms, due to polarization, hyperpolarization, vibrational and rotational averages, screening effect, etc, to mention just a few. The importance of electrostatics in biomolecular systems cannot be overemphasized because they underpin the molecular mechanism for almost all important biological processes, including signal transduction, DNA recognition, transcription, post-translational modification, translation, protein folding and protein ligand binding. In general, electrostatics is often the fundamental mechanism for macromolecular structure, function, dynamics and transport. Modeling and understanding the role of electrostatics in biomolecular systems are challenging tasks, since these systems are very complicated, made of macromolecules composed of hundreds of thousands or millions of atoms, and at the same time, surrounded by millions of water molecules, which in turn constantly change their positions and orientations. The number of degrees of freedom in explicit modeling of biomolecular systems is so large that it is frequently computationally prohibited for large systems or cases involving extremely large dimensions. Implicit models and multiscale approaches offer an alternative approach that dramatically reduces the computational cost, while being accurate enough to predict experimentally measurable quantities. Despite enormous efforts in the past two decades, important challenges remain in electrostatic modeling and computation. These include the definition of solvent-solute interfaces, nonlocal dielectric effects, finite size effects, nonlinear solvent response to solute perturbation, the representation of solvent microstructures, the solution of the corresponding nonlinear partial differential equations (PDEs) for irregularly shaped molecular boundaries, the treatment of solvent polarization and multi-valent ions, the formulation and solution of nonlinear integral equations (IEs), liquid density functional theory, and variational multiscale modeling of the dynamics and transport of biomolecular systems. The advantages and limitations of various methodologies are to be explored. Successful approaches to these challenges require combined efforts of physicists, mathematicians, computer scientists and biologists. This workshop will enable interactions between scientists from a diverse set of relevant disciplines. In particular, it will be of interest to mathematicians working in the areas of multiscale modeling, differential geometry of surfaces, PDE analysis, numerical PDE, and fast algorithm, to name a few. It will significantly strengthen the leading role that the US researchers can play in mathematical molecular biosciences by pursuing cutting-edge research and collaboratively training a new generation of mathematicians in this emerging interdisciplinary field.

### Seth Sullivant

Mathematics, North Carolina State University Statistically Consistent K-Mer Methods for Phylogenetic Tree ReconstructionPhylogenetic construction algorithms based on k-mers of DNA or protein sequences are nonparametric distance methods for reconstructing phylogenetic trees from sequence data that do not depend on first constructing alignments. The methods are often used to construct the guide tree used in multiple sequence alignment. We show that when applied to data generated from a statistical model of sequence evolution, the standard k-mer methods are inconsistent, that is, even with arbitrary amounts of data, they will reconstruct the wrong tree. We also show how to derive model-based corrections that make the methods statistically consistent, and report on simulation studies comparing methods. This is joint work with Elizabeth Allman and John Rhodes.

Uncertainty underlines almost every problem in mathematical ecology, and understanding its implications leads to substantial new mathematical challenges. Issues of uncertainty arise particularly in the structure of models, as reflected by the choice of state variables and model functions, uncertainty in parameters, initial conditions, etc. Uncertainty can greatly affect the determination of the current ecosystem state (e.g., stochastic versus deterministic description) and hence prediction of its dynamics. In ecological models uncertainty can be a real nuisance due to the phenomenon known as model sensitivity: models can be sensitive to the mathematical formulations of the constituent functions. This structural sensitivity can substantially reduce predictability of models. Whereas parameter-based sensitivity methods are now relatively well-developed, the mathematical framework to investigate structural sensitivity, when the entire function is unknown, is in its early stage and this represents a major challenge both in mathematics and ecology. In particular, there is a strong need for reliable mathematical tools to investigate structural sensitivity of biological models directly from data.

In addition, ecosystems are known to sometimes exhibit a sudden (catastrophic) regime shift, which is referred to as the tipping points, and this can be linked to a bifurcation in the model as a response to parameter changes (e.g., due to global climate changes). Development of robust techniques to identify reliable early warning signals of approaching catastrophic transition is a major challenge since the current methods are not always reliable and could result in false alarms, which can be very costly.

One of the goals of the ecosystem management is to estimate the risk of undesirable events. Coping with uncertainty (e.g., by providing the minimal required amount of information about the system) is therefore crucial to enable ecosystem managers to make the right decision in order to guarantee that the risk of undesirable event will not exceed the critical level. Lack of information about underlining processes calls into question the assumption that classical optimal control theory will always be successful. More research is needed to develop the mathematical framework for ecosystem management, in particular looking for an optimal balance between models complexity and their predictive power under a given level of uncertainty.

The main goal of the workshop is to bring together applied mathematicians, theoretical ecologists, empiricists and statisticians in order to address the above raised issues related to ecosystem understanding, modelling, and management to cope with uncertainty

### Marsha Rosner

Professor, The Ben May Department for Cancer Research, The University of Chicago Heterogeneity and Robustness in CancerIn the United States, the lifetime probability of developing cancer in one's lifetime is ~40%, and the lifetime probability of dying from cancer is ~20%. The second leading cause of death behind heart disease, cancer is a particularly challenging disease. Unlike heart disease, cancer includes multiple disorders dependent upon the specific tissue type and tumor cell. Cancer is largely driven by genes that push cancer progression, and is enabled by loss of tumor suppressors that normally confer feedback regulation and robustness to cells. For solid tumors, the metastatic process involving colonization of different tissues by cells from the primary tumor is actually the cause of death.

One of the major challenges to treatment of cancer is the evolutionary nature of the process that leads to tumor cell heterogeneity. This process enables cancer cells to adapt to stressful environments and eventual drug resistance. The mechanisms leading to such heterogeneity have largely been attributed to "genetic" processes that mutate DNA and "epigenetic" processes that modify transcription, e.g., the translation of DNA to RNA. However, we have recently published studies that demonstrate a role for very different stochastic, nongenetic processes (that can be either heritable or nonheritable) in establishing phenotypic heterogeneity.

In addition, since single drug treatments have been largely unsuccessful, we have been exploring conceptual frameworks for predicting optimal drug combinations to treat cancer. Cancer drugs ideally kill cancer cells while limiting harm to healthy cells. However, the inherent variance among cells in both cancer and healthy cell populations increases the difficulty of selective drug action. The lack of success with current cancer treatments suggests that we need alternative methodologies that would benefit from interdisciplinary approaches. The goal of my talk is to highlight these aspects of cancer that can potentially be addressed by mathematical analysis.

Frank, S.A., and Rosner, M.R., Nonheritable Cellular Variability Accelerates the Evolutionary Processes of Cancer. PLoS Biology, 10(4):e1001296. Epub. (2012) PMCID: PMC3317895

Lee, J., Yun, J., Yeung, K., Bevilacqua, Balzsi, G., and Rosner, M.R., BACH1 and RKIP participate in a Bistable Network that affects Progression to Metastasis in Breast Cancer, PNAS, 111(3):E364-73 (2014). PMCID: PMC4096871

Lee U1, Skinner JJ2, Reinitz J3, Rosner MR4, Kim EJ.PLoS One. Noise-Driven Phenotypic Heterogeneity with Finite Correlation Time in Clonal Populations. 2015 Jul 23;10(7):e0132397. doi: 10.1371/journal.pone.0132397. eCollection 2015.

Lawlor PN1, Kalisky T2, Rosner R3, Rosner MR4, Kording KP. Conceptualizing cancer drugs as classifiers. PLoS One. 2014 Sep 23;9(9):e106444. doi: 10.1371/journal.pone.0106444. eCollection 2014.

### Paul Stoodley

Professor, Department of Microbial Infection and Immunity, The Ohio State University Bacterial biofilms as complex liquids: from Kelvin-Helmholtz instabilities to chronic medical and dental infectionsBacterial biofilms are communities of single-celled organisms attached to solid surfaces that embed themselves in an extracellular polymeric slime matrix. Previous studies by our group and others have shown that mechanically biofilms behave as complex viscoelastic liquids. It has been hypothesized that this property is an adapted trait that allows bacteria to remain attached to surfaces when subjected to steady or transient overlying shear forces. Biofilms are ubiquitous in nature and the manmade world, causing serious problems including chronic implant infections, oral diseases, microbial contamination of industrial systems, and increased pressure drop and drag burdens in pipelines and ship hulls. In addition, the fossil record suggests that biofilm formation is an ancient adaptation of early life that allowed bacterial proliferation and survival on surfaces. Recent studies of ripple-like structures found in sedimentary fossils have raised the hypothesis that such structures may be the result of Kelvin-Helmholtz (KH) instabilities. We have recently discovered such instabilities can form in living biofilms with the use of a high-speed camera recording high-velocity water drop impacts to determine mechanical mechanisms of biofilm disruption. We found that the impact patterns rapidly dissipate (within milliseconds) and thus would fail to be detected by conventional microscopic methods. We have mathematically modeled the experimental data using a classical linear stability analysis, which supports the hypotheses that these instabilities are indeed of the KH type. These experiments provide strong support that living biofilms behave as liquids, and further go on to suggest they can develop internal turbulence.

All fundamental self-sustaining processes of living organisms are based on their ability to receive, process, create and transmit signals. Human sensory systems receive a vast variety of signals, including photonic, acoustic, thermal, mechanical, and chemical ones. All of these signals must be converted into electric signals for the brain to process. Ion channels are the devices that transform all kind of mechanical, physical, and chemical signals into electric signals, which are transferred to the brain via neurons. Ion channels control a wide variety of important physiological processes, ranging from nerve and muscle excitation, muscle contraction, action potential generation and resting, sensory transduction, cell volume and blood pressure regulation, cell proliferation, hormone secretion, fertilization, maintenance of salt and water balance, metabolism of certain viruses, neurotoxicology, learning and memory, to programmed cell death. Some genetic diseases (channelopathies) are directly linked to malfunctioning of ion channel components. The impact of trauma or chronic traumatic encephalopathy on cell membranes, ion channels of axons and neurons and astrocytes is an active research front. Ion channel aggregation and collective motion play a significant role in synaptic plasticity and memory. Due to their paramount importance, there is a huge ion-channel community in contemporary biology. About 40% of all drugs target ion channels. Similarly, gap junctions are intercellular channels that allow various molecules and ions to pass between cells. Transmembrane brushes and transmembrane transporters are important for maintaining a proper material balance in cells. Ion channels, gap junctions and transmembrane transporters can vary two orders in their spatial and time scales. Currently, the study of ion channels, gap junctions and transmembrane transporters is an underrepresented field in the mathematical biology community. Apparently, a major barrier for mathematical scientists to work in this exciting field is the lack of knowledge concerning recent experiments on ion channels and gap junctions, while a major barrier for biologists in formulating sophisticated computational models is their lack of knowledge concerning the development in the last couple decades of modern mathematical tools and techniques. This workshop is designed to help bridge gaps between biologists and mathematicians. This workshop will cover a wide range of topics in mathematical modeling of ion channels and gap junctions, and their applications to specific research problems. The specific range will of course depend on the ultimate list of participants and speakers, but example topics are ion channels structures; ion channel-membrane interaction; ion channel gating mechanism; ion channel-neuron interfaces; Brownian dynamics; Langevin dynamics; stochastic models; rare event analysis; Markov process and master equation; molecular dynamics; mean field models; generalized Poisson-Nernst-Planck equations; electro-elastic models; fluid-electro-elastic models; complex fluid; inverse design; micro-macro models; continuum-discrete models; electrohydrodynamics of ion channel systems; and differential geometry based multiscale models. Emphasis will be placed on the application of the aforementioned models, theories, methods and algorithms to the better understanding of the structure, dynamics and transport of ion channels and gap junctions. This workshop will take the advantage of recently mathematical advances in stochastic and stochastic-hybrid systems for ion channel analysis. This workshop will significantly strengthen the existing collaborations between mathematicians and biologists, broaden their horizons to higher synergies, and further stimulate information flow "from biology to mathematics", i.e., to introduce new bio-inspired mathematical models, such as partial differential equations (PDEs), molecular manifolds, molecular Euler characteristics, etc, to graduate students and recent doctoral recipients.

Rational drug design and protein design have a profound impact to human health care. A fundamental goal is to predict whether a given molecule will bind to a biomolecule, such as a protein, so as to activate or inhibit its function, which in turn results in a therapeutic benefit to the patient. Typical drugs are small organic molecules, but biopolymer-based and protein-based drugs are becoming increasingly common. Computer-aided drug design and the design of protein containers for drug delivery have established a proven record of success, not only because of improved understanding of the basic science --- the molecular mechanism of drug and protein interactions, but also because of advances in mathematical models, geometric representations, computational algorithms, optimization procedure, and the availability of massive parallel and GPU computers. Indeed, mathematics plays an essential role in rational drug design and the development of new drug delivery systems, from consensus scoring, geometric analysis, cluster analysis, to global optimization. Moreover, mathematical approaches, such geometric analysis for high throughput drug screening, persistent homology for protein-drug binding detection, reduced manifold representation for discriminating false protein-protein and protein-drug interfaces, and machine learning techniques for protein-drug binding site analysis, have great potentials for drug design and drug discovery. Despite significant accomplishments, drug discovery rates seem to have reached a plateau, due to metabolism instability, side effects, and limitations in the understanding of fundamental drug-target interactions. An ideal drug should be acceptable to the human metabolic system, not to affect any other important ``off-target" molecules or antitargets that may be similar to the target molecule, and bind to a target sufficiently strongly. In fact, the molecular mechanism of drug design has its roots in another closely related field, the protein design, which tests the fundamental principles of protein-protein and protein-ligand interactions. Both protein-protein and protein-drug binding are subject to a large number of effects, from stereospecificity, polarization, hydrogen bond, electrostatic effect and solvation to allosteric modulation, to mention only a few. The application of molecular mechanism towards entire proteomes, enzyme pathways/families (e.g. catecholamine biosynthesis, botulinum neurotoxins), and high value drug targets, including G-protein coupled receptors (GPCRs) are now starting to emerge. Nano-bio technologies for drug transport and drug delivery have been a hot area of research. To design efficient drugs and functional protein, it takes collaborative efforts from biologists, biophysicists, biochemists, computer scientists and mathematicians to come up with better homology modeling, geometric models, molecular docking algorithms, molecular dynamics, quantum calculation, de novo design and statistical models. This workshop will bring together experts from both academia and industry that have an open mind to cross their line of defense to share their problems. We will create a forum for researchers to jointly find solutions and explore applications to the design of new drugs and delivery systems. This workshop will be of particular benefit to junior mathematicians who are looking for ways of applying their mathematical skills and tools also outside of academia and want to use their skills to make an impact in society via innovations benefiting the health sector. The interaction between mathematicians and pharmaceutical industry will be encouraged in this workshop.

Network structures underlie models for the dynamical descriptions and bifurcations in a wide range of biological phenomena. These include models for subcellular genomic and signaling processes, neural models at single-cell or multiple-cell level, high-level cognitive models, and many forms of chemically reacting systems. Naturally arising networks often have properties that make them especially pliant mathematically:

- Networks with special overall architectures (having, for example, special symmetries or special node-coupling rules) enable one to pose and answer questions about network dynamics by techniques that exploit those architectures.
- Networks often have natural and precise restrictions on the behavior of nodes or edges (for example, mass action kinetics, piecewise linear dynamics, or Boolean dynamics) that can lead to fairly deep and general theorems about network behavior.
- Small networks, quotient networks, factor networks, or network motifs can be used as building blocks to understand the dynamics of larger networks, allowing one to think of network structures in a constructive and synthetic way.

This workshop will explore the current state of affairs and ways of unifying emerging mathematical techniques by focusing on a variety of special biologically motivated structures. A few examples of applications with such structures include:

a. **Chemical reaction network theory**: In recent years separate theories have been developed for the dynamics of chemical reaction networks and for general networks with symmetry. Both theories have yielded interesting and nontrivial results. What has not been explored, however, are networks of identical and interconnected chemical cells. Although the dynamics within the cells themselves might exhibit a high degree of stability, there remain questions about the dynamics of the full multi-cell assembly that can exhibit important behavior through symmetry-breaking pattern formation.

b. **Neuroscience**: Classic central pattern generators and recent Wilson networks describing generalized rivalry have symmetries that dictate preferred kinds of patterned oscillation.

c. **Gene expression networks**: New technologies are providing massive data concerning the connectivity and functional control of these networks. Theoretical models based on these data typically incorporate combinatorial logical control of gene expression in dynamical models.

d. **Epidemiology**: Heterosexual contact networks are best explored by (quasi-) bipartite graphs, usually with fairly strong restrictions on degree distributions within each partition. Exploring sexually transmitted infection dynamics relies strongly on both this architecture (especially as the global description is preserved over time while local descriptions shift), but also on the time ordering of edge presence.

Development and analysis of models like these provide a rich source of new mathematical problems involving classification of dynamic states, bifurcations, and reverse engineering of complex networks based on observed dynamics.

### Marty Golubitsky

Director, Mathematical Biosciences Institute, The Ohio State University Properties of Solutions of Coupled SystemsNetworks of differential equations can be defined by directed graphs. The graphs (or network architecture) indicate who is talking to whom and when they are saying the same thing. We ask: Which properties of solutions of coupled equations follow from network architecture. Answers include "patterns of synchrony" for equilibria and "patterns of phase-shift synchrony" for time-periodic solutions. We show how these properties can be used to explain surprising results in binocular rivalry experiments and we discuss how homeostasis can be thought of as a network phenomenon.

Recent advances in in vitro and in vivo experimental techniques now generate data on living systems from single molecule length scales to whole cell populations and time scales not previously achievable. Concurrently, there have been significant advances in the mathematical modeling of living systems. Despite these advances, models rarely capture the complex and nuanced mechanisms that detailed biological data are poised to provide.

Here we are focused on three critical challenges:

1) How to use data collected at small length scales to draw quantitative inferences about emergent biological phenomena at larger scales. In other words, integrating models valid at smaller scales to explain behavior at larger scales such as an entire cell or even a tissue.

2) How to build first-principles models motivated from the data and, subsequently, infer model features and parameters that will provide a principled mechanistic understanding of the system.

3) How to use in vitro data (collected under presumably vastly different conditions than its poorly controlled in vivo counter-part) to help motivate and build in vivo models.

### Luis Carvalho

Mathematics and Statistics, Boston University A Gene-Proximity Model and Computational Methods for Genome-Wide Association StudiesGenome-wide association studies (GWAS) attempt to determine which genomic markers are predictors of genetic traits, most commonly human diseases. In practice, despite the extreme imbalance of having millions of markers recorded for only a few thousand individuals, it is of great interest to glean as much information as possible from this type of data. To this end, we propose a novel statistical model that exploits a hierarchical structure between markers and genes to leverage information between levels and alleviate the "large-p small-n" regimen while still attaining a reasonably complex and realistic model. Fitting the model is challenging due to the high number of variables to select, so we discuss efficient computational approaches that we explored to estimate the parameters. Finally, we illustrate the proposed model and estimation procedures on simulated data and on a real-world data set from the Wellcome Trust Consortium. If time permits, we also discuss a latent genotype procedure that aims to correct genotypical correlations. This is joint work with Ian Johnston.

Many advances in modern biosciences will depend on our ability to harness the vast amounts of data coming from increasingly more complicated experimental techniques by using sophisticated methods of mathematical analysis. The modeling challenges include the ability to abstract common concepts across various mathematical sub-fields and to develop methods that are robust in the presence of noise, variations in model assumptions, uncertainty about models dynamics and parameter values.

This workshop will focus on dynamic models of biological networks that involve both deterministic and stochastic aspects. An important aim of the workshop is to bring together mathematical researchers in dynamical systems, probability, and statistics, together with biologists, to share their expertise towards analyzing dynamic biological network problems. Network structure can constrain and thereby impact the behavior of dynamic systems in various ways. Examples of such constraints are topological constraints, limitations on the size of quantities, limitations on resources, and delays in propagation of signals. Particular emphasis will be placed on how network structure can be exploited and how it impacts dynamic behavior.

The interplay of deterministic and stochastic dynamics can occur in a variety of different forms in biological dynamical models. In some biological systems such as gene regulatory networks, some species need to be modeled stochastically while other species can be modeled using deterministic dynamical systems. Analyzing the interactions between these different types of species on behavior presents challenging mathematical problems. Neuronal dynamics is another arena where dynamical behavior, stochastic influences, and network structure affect behavior and require innovative analysis. Some biological systems, from subcellullar to whole organisms switch stochastically from one dynamics to another. For, example, insect trachea are large collections of tubes that connect the cells of insects to the outside atmosphere. Insects open and close the networks stochastically in order to gain oxygen and lose carbon dioxide. The analysis of such biological systems requires understanding how system behavior changes when important properties of the network (like the existence of edges or the existence of inputs) change stochastically. Analyzing the relationship between stochastic changes, network structure, and network dynamics poses difficult, new, analytical questions.

There are many statistical issues associated with modeling such networks. Over the last two decades many sophisticated experimental methods have been developed that allow for the partial observation of a time trajectory of a biological network (for instance a gene regulatory network). The natural question of interest is how such longitudinal data may be used for the inference about various network characteristics, both quantitative and qualitative, as well as for predicting network behavior. In particular, the issue of proper quantification of the inference uncertainty must be addressed.

### Andrew Noymer

Associate Professor, Public Health, University of California, Irvine What levels of vaccination are necessary for measles control and eradiction? A mathematical model of measles transmission in developing countriesWe present a mathematical model of measles virus transmission that is tailored to a dataset on a large outbreak from rural Burundi in the 1980s, in which a major outbreak occurred despite reasonably high vaccination levels. So-called post-honeymoon outbreaks occur after the introduction of vaccination, and punctuate a vaccine-induced quiet period. These are demographic-epidemiologic phenomena, since they involve accumulation of cohorts of susceptible individuals when vaccination rates are below about 95%. We estimate an age-explicit "SEIR" PDE model with realistic demography, and discuss the insights for vaccination policy gleaned from the math model. Some of the insights are also applicable to the 2015 "Disneyland" measles outbreak.

The majority of current research efforts that explore network-based biological questions make a series of simplifying assumptions about the nature of the networks themselves. The primary purpose of such assumptions has been to enable the application of existing techniques from subjects such as graph theory and linear algebra rather than to enable either biological accuracy or rigorous examination of the mathematical impact of the simplifications. Within this class of assumptions, four assumptions have the greatest potential to compromise the generation of valid, novel biological understanding:

- The network has only a single type of interaction among entities
- The interactions among entities can be completely described as pairwise
- The network is static over time
- The impact of noise can be ignored

To describe and study many networks in almost all areas of biology --- from protein interaction networks to functional brain networks and animal behavior networks --- it is necessary to relax these assumptions. It is important to capture time-dependence among interaction strengths and the presence of interactions themselves, explicitly consider interactions among arbitrary numbers of entities in a mathematically natural way, and make explicit the impact of noise in both descriptive and predictive methods. Generalizing existing diagnostics and analytical techniques to make them suitable for these more general situations is also necessary.

For example, as with human social networks, animals communicate over multiple channels and in ways that are not aptly described as pairwise. Indeed, each of the assumptions (1)-(4) is violated. Social insects communicate with each other using a mixture of chemical signaling, direct physical contact, visual cues, and auditory cues. These modes of communication occur simultaneously, reach different numbers of insects over different ranges, and are time-dependent. Often, individual behaviors are a function of many different types of received communications (and how they change) over time. Traditional dyadic representations fail to provide natural mathematical tools by which to characterize and predict how information flows, individuals make decisions, and consensus building is achieved.

Recent efforts, often employing differential-equation models and/or methods from statistical mechanics, have begun to study network dynamics both in time-dependent network structures and in the biological processes that operate on static network structures. There have also been many recent attempts at generalizing "ordinary" network theory and diagnostics --- both independent of, and in application to, a diverse array of biological systems. For example, hypergraphs, which provide a means to go beyond pairwise interactions, have been used to study local and global alignment across multiple species in protein-protein interaction networks. Simplicial complexes have provided novel insights into electrophysiological networks. Tensors, which provide a means to consider multiple types of interactions simultaneously, have been used to examine the learning of simple motor skills in functional brain networks. Moreover, all of these mathematical structures should incorporate noise, because noise in real biological networks has fundamental effects. The development of these new mathematical structures with built-in stochasticity will enable the translation of mathematical theory to empirically falsifiable biological hypotheses.

Existing and anticipated efforts to relax the standard four limiting assumptions represent valuable attempts at bringing a deeper and more accurate mathematical framework for the investigation of networked biological systems. The richest insights from the interface between biological and mathematical questions often arise when mathematical tools are used to make comparisons across different biological systems. Thus, by developing more general mathematical descriptions, one can enable cross-comparison of networks and thereby use theoretical and computational tools to facilitate technology transfer among different areas of biology. This makes it possible to simultaneously capture fundamental properties of biological networks (and the systems that they represent) and opens myriad possibilities for generating new, deep problems in mathematics.

### Michael Summers

Chemistry and Biochemistry, Chemistry and Biochemistry, University of Maryland Structure of the HIV-1 RNA Packaging SignalThe 5-leader of the HIV-1 genome directs the selection and packaging of two copies of the unspliced viral RNA into assembling virions. Using a suite of ^2 H-edited NMR methods, including a novel fragmentation-based ^2 H-edited approach, we have determined the structure of a 156-nucleotide 5-leader RNA element that binds the cognate nucleocapsid (NC) protein with high affinity and is independently capable of directing RNA packaging into virus-like particles (Core Encapsidation Signal, Ψ^CES ). The RNA adopts an unexpected secondary structure that differs considerably from models (more than 20) proposed on the basis of chemical and enzymatic probing. Residues important for splicing and translation are sequestered by base pairing within the core of the RNA, and clusters of unpaired “junction guanosines” are maintained in partially exposed conformations, apparently to promote high affinity NC binding. Long-range Adenosine Interaction Detection (lr-AID) NMR experiments indicate that the structure observed for the isolated Ψ^CES RNA also exists in the context of the full-length, 712 nucleotide dimeric 5-leader. The structure reveals how splicing is attenuated, and dimerization and Gag binding are promoted, by the RNA conformer that directs genome packaging. Progress toward the 3D structure determination of the intact, 712 nucleotide dimeric 5-leader will be presented.

Control and dynamical systems go hand in hand in biology. Dynamic networks and processes that occur on them can be used to describe many biological processes. Understanding the emergent properties of these systems, how they are influenced, and how one might influence them lends itself to ideas of mathematical control theory. Throughout biology, it is important to use control to achieve desired dynamics and prevent undesired behaviors. Thus, the study of network control is significant both to reveal naturally evolved control mechanisms that underlie the functioning of biological systems and to develop human-designed control interventions to recover lost function, mitigate failures, or repurpose biological networks. Application areas include cell biology, neuroscience, and ecology as well as bioinspired engineering applications (e.g., swarming behavior and other forms of collective formation in moving sensors).

In ecological networks, for example, 'compensatory perturbations' and other network-based countermeasures to correct imbalances can provide useful ecosystem-management tools to help prevent species extinctions. In neuroscience, it is of interest to understand and influence the collective dynamics of neurons, as well as investigate their relation to the sensory system and outputs such as motor control. In intracellular networks, understanding the workings of the regulatory system has much to contribute to the identification of therapeutic interventions and the development of synthetic biology. On the methodological side, decentralized control of multi-agent systems is an application area of network control that is relevant for numerous natural as well as engineered systems.

Progress in these and many other areas can benefit from the development of quantitative methods to characterize stability, control, observability, and robustness of biological networks. Major challenges in such development are often mathematical in nature, because biological networks of scientific interest often have:

(i) Limited ability to measure the dynamical state of a system.

(ii) Presence of noise and/or parameter uncertainty.

(iii) High dimensionality of the associated state space and/or combinatorial explosion.

(iv) Nonlinearity of the underlying dynamics.

(v) (Possibly unknown) constraints on physically realizable controls.

(vi) Decentralized evolution and operation of a system.

Such properties make it difficult to recognize control mechanisms that are both effective and efficient.

Despite these challenges, there has been significant progress on the modeling of network control mechanisms, as well as on the development of mathematical and computational control approaches in fields such as dynamical systems, network science, and life sciences. This workshop will stimulate progress by promoting interactions between experts working in these disparate fields, thereby facilitating the combination of approaches from different domains and the integration of system-specific knowledge about biological or bio-inspired networks.

### Domitilla Del Vecchio

Professor, Department of Mechanical Engineering, Massachusetts Institute of Technology Hidden interactions in gene networks and their mitigation through distributed feedback controlThe behavior of gene circuits is context-dependent, that is, the input/output functionality of a circuit depends on its context. Context includes other systems to which the circuit directly connects, which apply a load (retroactivity), and systems that are simply present in the cellular environment. The latter ones, in particular, also affect the functionality of the circuit due to sharing a common pool of limited resources. Because of these context-effects, a set of new “hidden” interactions appear in gene networks, which dramatically change the expected network’s behavior. These hidden interactions confound both the design of de novo systems in synthetic biology and the analysis of existing natural systems. In this talk, I will present a systematic modeling framework that captures hidden interactions in a network’s description and provides simple graphical rules to draw them. I will then present recent experimental results performed in our lab that validate these predictions. Finally, I will illustrate that a distributed control scheme, in which the local negative feedback at each node is realized through mRNA interference, can mitigate the effects of those hidden interactions due to scarcity of resources needed for gene expression.

### Arni S.R. Srinivasa Rao

Associate Professor, Biostatistics and Epidemiology, Augusta University Stationary PopulationsUnderstanding the properties of stationary populations is treated in this talk from the perspective of mathematical history of population dynamics as well as modern experiments conducted on insects longevity. The subject of population dynamics is hundreds of years old and is been studied by famous mathematicians such as Fibinocci, d’Alambert Daniel Bernoulli, Euler, etc, Concepts such as stability and stationarity of population are essential pillars of population dynamics. In the last century the works by Alfred Lotka laid the foundation for the population stability theory, which was developed further by William Feller through renewal equations. Ansley Coale and Norman Ryder (during 1960s and 1970s) brought several properties of stationary populations from the Life Table perspective. table perspective. During the last decade (early 2000s) new identities of stationary populations have emerged regarding life-lived and left, first with work by James Carey and his UC Davis colleagues Hans Mller and Jane-Ling Wang, followed by contributions by James Vaupel (who coined the identity Carey’s Equality) and Josh Goldstein. Rao & Carey (2013) have proved a fundamental theorem in stationary population using insights from Carey’s equality by blending with algebraic and combinatory principles. These newer results bring similar patterns that are comparable to renewal type of theory due to Lotka, Feller and others. This talk concludes with implications of Carey’s equality in other areas of population dynamics, including in non-stationary populations and direction of research in stationary populations.

### Giovanni Parmigiani

Harvard University Cross-study Performance of Predictions, with Application to GenomicsNumerous gene signatures of patient prognosis for late-stage, high-grade ovarian cancer have been published, but diverse data and methods have made these difficult to compare objectively. However, the corresponding large volume of publicly available expression data creates an opportunity to validate previous findings and to develop more robust signatures. We thus built a database of uniformly processed and curated public ovarian cancer microarray data and clinical annotations, and re-implemented and validated 14 prognostic signatures published between 2007 and 2012. In this lecture I will describe the methodology and tools we developed for evaluating published signatures in this context. I will also use this application as the springboard for a more general discussion on how to evaluate statistical learning methods based on a collection of related studies.

### Herschel Rabitz

Princeton University Control in the Sciences over Vast Length and Time ScalesThe control of physical, chemical, and biological phenomena are pervasive in the sciences. The dynamics involved span vast length and time scales with the associated controls ranging from shaped laser pulses out to the application of special chemical reagents and processing conditions. Despite all of these differences, there is clear common behavior found upon seeking optimal control in these various domains. Evidence of this common behavior will be presented from the control of quantum, chemical, and biological processes. The most evident finding is that control efforts can easily beat the so-called "curse of dimensionality" upon satisfaction of assumptions that are expected to widely hold. Quantum phenomena provide a setting to quantitatively test the control principles. The potential consequences of the observations will be discussed.

The goal of this MBI NSF-funded program is to introduce students to exciting new areas of mathematical biology, to involve them in collaborative research with their peers and faculty mentors, and to increase their interest in mathematical biology.

The goal of this MBI NSF-funded program is to introduce students to exciting new areas of mathematical biology, to involve them in collaborative research with their peers and faculty mentors, and to increase their interest in mathematical biology. The program consists of three parts - each including a mix of educational and social experiences. See this website for more info. http://mbi.osu.edu/education/summer-undergraduate-program/

Download the 2016 Summer School: Mathematical Modeling of Infection Disease Spread Flyer

Graduate students from the mathematical and life sciences, public health, and related fields are encouraged to apply to the 2016 Graduate Summer School on Mathematical Modeling of Infectious Disease Spread, to be held at the Mathematical Biosciences Institute in Columbus, Ohio. The program for this 10-day summer school will feature researchers from the mathematical and biological sciences, who will deliver lectures, case study presentations, and mentor the school participants in special project groups. The case study lectures will focus on public health issues, and will be open to the university community. During the summer program each student will work on a research project in a team of approximately five participants. Topics to be covered include: deterministic and stochastic frameworks for modeling disease dynamics; disease dynamics on social networks; metapopulations; host behavior and disease evolution; vector-borne diseases; zoonotic diseases; pathogen dynamics and co-infection.

The summer school will provide students with broad high-level training in Mathematical Biology that is unattainable at most institutions. The school will focus on the mathematical modeling of infectious diseases, a field that is growing in importance because of the many issues in disease spread and control arising from new or newly emerging diseases (e.g., SARS, Ebola, West Nile virus), and because new data sources are now available to study disease transmission, pathogen evolution, and the impact of the social behavior of hosts (e.g., genotyping databases, cell phone networks and air travel tickets, social networks). Capitalizing on new data sources to understand and control these impacts on disease spread requires detailed modeling of interactions amongst pathogens and hosts, the training of sophisticated modelers, and the development of new mathematics. This summer school will seek to prepare students to study such models in their future research.

Applications for acceptance to the school received before January 31, 2016 will receive full consideration. There is no tuition charged to summer school participants. Financial support for local expenses may be available, depending upon availability of funds.

The summer school is co-sponsored by the Mathematical Biosciences Institute (MBI, Ohio State), the National Institute for Mathematical and Biological Synthesis (NIMBioS, Tennesee –Knoxville), the Fields Institute (Toronto), the Centre for Disease Modelling (CDM, York University), the Centre for Applied Mathematics in Bioscience and Medicine (CAMBAM), and the Atlantic Association for Research in the Mathematical Sciences (AARMS). The Army Research Office (ARO), the National Science Foundation (DMS/NSF) and the Society for Mathematical Biology (SMB) have also provided generous support.

A student centered conference featuring talks and posters by students doing research in mathematical biology, keynotes by prominent mathematical biologists, a graduate studies recruitment fair, and other special features including a conference dinner and social event.

### 2014-2015

Beginning with PC Nowell's work in the 1970s, we know that starting from a single clone, cancers show a striking amount of intratumor heterogeneity. This heterogeneity results from the accumulation of genetic mutations and epigenetic changes as cells divide and means that tumor cells inside the same tumor can be different. Not all genetic mutations have the same impact on the fitness of a tumor cell: We know evolution selects for phenotypes (and the genotypes responsible for those phenotypes) that can better exploit the dynamic environment in which they live. Thus those cells that can better take advantage of their environment in terms of other tumor and non-tumor cells as well as the physical microenvironment (space, oxygen, nutrients...) will be more successful and eventually constitute the majority of the tumor population. Understanding the interactions between the cellular and physical agents in the tumor microenvironment will require an evolutionary and ecological perspective that can only be fulfilled with the help of mathematical models that can integrate the wealth of biological and clinical data being produced. This workshop will bring together cancer researchers and mathematical oncologists as well as ecologists with the aim of understanding how ecological principles can be used to understand cancer, how the mathematical tools used by theoretical ecologists could be used to gain new insights in cancer research and what principles of ecological management could be used to produce new therapies to treat cancer in the clinic.

### Stephen Ruberg

Senior Research Fellow, Distinguished Senior Research Fellow, Eli Lilly and Company Strength of Evidence* for Clinical Trials and Biomarkers** in Tailored Therapeutics***This talk will cover the convergence of two high profile themes in the scientific/medical literature (and even the lay press): personalized medicine and lack of reproducibility of scientific results. There have been many high profile examples of scientific findings related to genetic (or more generally) biomarker predictors of disease or drug effect that have not been confirmed with subsequent experimentation or investigation. Some recent literature suggests that inappropriate use of statistical analysis or inadequate use of statistical design principles play a major role in false positive findings. This talk will address the use of Bayesian statistical principles for how to assess the strength of evidence for a finding and how that can be applied generally to clinical trials and laboratory research.

* Likelihood of truth

** Any biological measurement to describe a patient

*** AKA personalized medicine, precision medicine, targeted medicine

Mathematical models typically start out in simple form. One writes down a few differential equations, estimates the parameters, explores the output, and checks to see if it can predict behavior reasonably well. After that, the process begins to take on a life of its own. Since the model is greatly abstracted and simplified, it captures some aspects of the system, but fails in others, so new variables and more inputs are added. Alternative mechanisms are investigated. At some point, the question arises: How can one tell if this is a good model? The aim of this bootcamp is to provide tools to answer that question. We will frame the question in a way that respects both the biology and the underlying mathematics.Two organizers of the bootcamp, Pedro Mendes and Stefan Hoops, have spent the last twenty years creating a bridge between these paradigms, in the form of a software package called COPASI (COmplex PAthway SImulator).. COPASI is a simulation software that allows one to translate the biochemical interactions between species into dynamical systems represented by sets of either stochastic or deterministic equations. The boot camp will consist of short lectures introducing concepts followed by simulation and analysis of various cancer models using the software. These models focus on a wide array of cancers (colon, lung) and different levels of representation (signaling pathways, cell cycle, cell populations). The first day is dedicated to basic simulation and model analysis, mainly steady state and dynamic simulation. The second day will focus on methods, like optimization, to interrogate models about specific properties of interest, such as which drug targets are the more effective. The third day will be focused on calibrating models against experimental data.

**Preparation**

Participants are encouraged to familiarize themselves with the COPASI software before arriving to the Boot Camp by:

• Viewing the short online videos on COPASI: www.copasi.org/VideoTutorials

• Reading a tutorial paper: “Computational Modeling of Biochemical Networks Using COPASI.” in Methods in Molecular Biology , Humana Press. 500:17-59.

• Downloading and installing the software on their computers (help will be available at the Boot Camp for those who have not done so): www.copasi.org

During the Boot Camp participants will use the software to analyze models that have been previously published. Getting familiar with these publications beforehand will be very helpful. If some of these papers are too technical/mathematical for you, read the introduction and discussion so that you have an overview of the work and the biological aspects, rather than trying to understand it completely – leave the technical aspects to the Boot Camp. The following papers will be discussed:

• Huang CY, Ferrell JE Jr (1996) Ultrasensitivity in the mitogen-activated protein kinase cascade. *Proc. Natl. Acad. Sci. USA* 93(19):10078-10083. doi:10.1073/pnas.93.19.10078 PMID:8816754

• Kholodenko BN (2000) Negative feedback and ultrasensitivity can bring about oscillations in the mitogen-activated protein kinase cascades. *Eur. J. Biochem*. 267(6):1583-8 doi:10.1046/j.1432-1327.2000.01197.x PMID:10712587

• Bianconi F, Baldelli E, Ludovini V, Crin L, Flacco A, Valigi P (2012) Computational model of EGFR and IGF1R pathways in lung cancer: a systems biology approach for translational oncology. *Biotechnol Adv.* 30(1):142-53. doi:10.1016/j.biotechadv.2011.05.010 PMID:21620944

• Kim D, Rath O, Kolch W, Cho KH (2007) A hidden oncogenic positive feedback loop caused by crosstalk between Wnt and ERK pathways. *Oncogene* 26(31):4571-9. doi:10.1038/sj.onc.1210230 PMID:17237813

• Schoeberl B, Eichler-Jonsson C, Gilles ED, Mller G. (2002) Computational modeling of the dynamics of the MAP kinase cascade activated by surface and internalized EGF receptors. *Nature Biotechnol*. 20(4):370-5. doi:10.1038/nbt0402-370 PMID:11923843

• Conradie R, Bruggeman FJ, Ciliberto A, Csiksz-Nagy A, Novk B, Westerhoff HV, Snoep JL (2009) Restriction point control of the mammalian cell cycle via the cyclin E/Cdk2:p27 complex. *FEBS J*. 277(2):357-67. doi:10.1111/j.1742-4658.2009.07473.x PMID:20015233

• Smallbone K, Corfe BM (2014) A mathematical model of the colon crypt capturing compositional dynamic interactions between cell types. *Int. J. Exp. Pathol*. 95(1):1-7. doi:10.1111/iep.12062 PMID:24354351

### Nick Grishin

Southwestern Medical Center, University of Texas Similarity and homology in proteins.Evolutionary relationships (i.e., homology) detected between proteins helps predict their properties such as spatial structures and functions. Homology is frequently obscured by sequence divergence, spatial structure changes and resemblance between unrelated 3D structures. Computational approaches to the analysis of distant homologs and their discrimination from proteins with fortuitous similarities will be discussed and examples of how this theoretical and bioinformatics work facilitates experimental discoveries will be given.

Initially solid tumors are avascular, i.e., they do not have their own blood supply, and rely on diffusion from the surrounding vasculature to supply oxygen and nutrients. When the tumor becomes too large diffusion is too slow, growth in the core stops, and can resume only if the tumor becomes vascularized i.e. if it becomes permeated with a network of capillaries. Avascular tumors release growth factors into their environment to induce nearby blood vessels to grow new capillaries to vascularize the tumor through a process called angiogenesis. This results in the creation of a new capillary network that extends from a primary vessel into the growth-factor-secreting tumor, thereby bringing essential nutrients to the tumor and providing a shorter route for the spread of cancer cells to other parts of the body. Metastasis is the process by which tumor cells detach from a primary tumor and migrate to nearby blood vessels or the lymph system, and are thereby able to spread to other organs in the host. Cancer cells invade the surrounding tissue either as individuals or as small groups of cells, and may secrete enzymes that degrade the ECM to facilitate passage of cells. This workshop will address the mathematical and computational issues that arise from models of angiogenesis and metastasis. Such models are frequently hybrid models, that describe cells (either those building the vessel or those involved in metastasis) at a detailed level that treats their biochemical and mechanical responses to their environment, and couple this cell-based description with partial differential equations that describe the mechanics of the surrounding tissue and the reaction and transport of growth factors and chemotactic signals. Major topics to be treated are how to model the movement of single cells through the extracellular matrix, how to describe in sufficient detail the process by which new vessels grow toward a tumor, how to cope with the computational problems raised by such hybrid models, and what the implications are for our understanding of the underlying basic science and how that understanding can be translated into improved therapeutic regimens.

### Jinchao Xu

Director, Center for Computational Mathematics and Applications, Department of Mathematics, Pennsylvania State University Stable Discretizations and Robust Preconditioners for Multi-physical SystemsIn this talk, I will report some recent results on the qualitative and numerical analysis of structure-preserving discretizations and robust preconditioners for several mathematical models that couple with the Navier-Stokes equations. I will study the Navier-Stokes equations coupled with elasticity equations, the Maxwell's equations, and the Poisson-Nernst-Planck system. These systems model fluid-structure interaction, magnetohydrodynamics, and electrokinetic phenomena, respectively, and are widely used in physics, biology, and engineering. I will also give some numerical examples to validate our analyses and models.

### Elliot Meyerowitz

Biology and Biological Engineering, California Institute of Technology Mechanical and Chemical Signaling Between Plant Stem Cells: Computational Models and ExperimentsExperiments indicate that physical stress in the shoot apical meristem of *Arabidopsis* controls at least two aspects of cell biology – the cortical cytoskeleton, and the subcellular location of the PIN1 auxin transporter. Cortical microtubules align in shoot apical meristem epidermal cells such that they are parallel to the principal direction of maximal stress when the stress is highly anisotropic. PIN1 is asymmetrically distributed in the plasma membranes of the same cells, with the highest amount in the membrane adjacent to the most stressed side wall.

Cellulose synthase complexes ride the cortical microtubules, thereby reinforcing cells in the direction of maximal stress, which is a negative feedback on stress, and tends to cause cells to expand orthogonally to the maximal stress direction. Auxin, however, weakens walls, allowing cells to expand proportionally to their auxin concentration. As expanding cells (whose direction of expansion depends upon wall anisotropy) stress their neighbors, the neighbors transport auxin preferentially to expanding cells, further increasing their auxin concentration. This is a positive feedback – high auxin in a cell attracts more auxin, and creates more stress.

These sets of feedbacks create a supracellular, tissue-wide feedback system that creates plant shape, controls phyllotaxis, and regulates hormone flow. This system has been amenable to computational modeling. The present set of models successfully predicts phyllotactic pattern (as auxin induces new leaves and flowers, and models of auxin transport reproduce the pattern of the new organs), rates of cell expansion, and developing models also treat direction of expansion and planes of cell division (which are dictated by the microtubule array).

Therefore, including cellular responses to physical stress is as important as including cell-cell signaling in models of shoot meristem morphogenesis, and considering the effects of mechanical stress (and therefore of tissue shape and cell wall properties) leads to highly predictive models.

A fundamental question in neurobiology is how do axons, the thin cellular cables that transmit information in the nervous system, grow? Since ~95% of total protein found in the axon is made in the cell body, it is widely recognized that axonal transport is essential for this process. In parallel, there is a deep interest in developing a better understanding of how growth cone mechanics, at the tip of the axon, modulate the rate and control the direction of axonal elongation. While these topics lend themselves well to mathematical modeling there has been limited direct interaction between experimentalists and theoreticians. Answering these questions is important for understanding the development of the nervous system, the pathological progression of neurodegenerative diseases such as Alzheimer's, and for designing novel approaches to promote neuronal regeneration following disease, stroke, or trauma. Recent progress in the field, facilitated by the development of novel experimental and theoretical approaches, has led to new insights and interest in interdisciplinary studies of axonal transport and neuromechanics. The goal of this workshop is to bring together leading cell biologists, engineers, physicists, and mathematicians to openly discuss exciting new findings, long-standing questions, and the future of our field. The timeliness of this meeting and its relevance to the mission of the MBI is most evident from three recent reviews by the organizers (Bressloff and Newby, 2013; Franze et al., 2013; Suter and Miller, 2011). In brief these reviews discuss the emerging role of forces in axonal elongation, mathematical models that have been developed to study the contribution of axonal transport to elongation, and the importance of developing mathematical models to study neuromechanics.

### Alexandra Jilkine

Assistant Professor, ACMS, University of Notre Dame Stochastic Models of Stem Cell Renewal and Dedifferentiation in CancerRecent evidence suggests that, like many normal tissues, many cancers are maintained by a small population of cancer stem cells that divide indefinitely to produce more differentiated cancerous cells. Tissues, however, contain many more differentiated cells than stem cells, and mutations may cause such cells to "dedifferentiate" into a stem-like state. We study the effects of dedifferentiation on the time to cancer onset and found that the effect of dedifferentiation depends critically on how stem cell numbers are controlled by the body. If homeostasis is very tight (due to all divisions being asymmetric), then dedifferentiation has little effect, but if homeostatic control is looser (allowing both symmetric and asymmetric divisions), then dedifferentiation can dramatically hasten cancer onset and lead to exponential growth of the cancer stem cell population. We consider both space-free and spatial versions of this process to look at effect that tissue architecture can play in this process. Our results suggest that dedifferentiation may be a very important factor in cancer and that more study of dedifferentiation and stem cell control is necessary to understand and prevent cancer onset.

Cancer immunology is the study of the interactions between the immune system and cancer cells. The aim is to discover innovative therapies using the immune system to retard the progression of the disease. The immune system aims to identify and destroy pathogenic microorganisms that invade our body. Cancer cells, however, are cells of our body, so the immune system may not recognize them as "enemy." In fact, cancer cells often even exploit the immune cells to help them proliferate. Tumor associated macrophages, for instance, are known to influence cancer cells by modulating immune functions, and accelerating angiogenesis, but not much is known on the cytokine signaling network that regulate this process. Recent years have seen the development of cancer immunotherapy, that is, the use of the immune system to attack malignant tumor cells. This can be achieved either by immunization of the patient by a vaccine, or by administering a therapeutic antibody as a drug which will recruit the immune system to recognize and destroy tumor cells. Recent years have also seen the development of mathematical models that aim to represent, at least at the conceptual level, the cancer-immune interactions, as well as models that represent immunotherapy processes. These models are formulated by systems of ODEs or PDEs. The present workshop will bring together cancer biologists and mathematical modelers to review the state of present knowledge and explore future directions. It will also provide an environment that will encourage communication and new contacts among the biologists and mathematicians. Formal lecture and informal discussions will articulate future directions where mathematical models can significantly enhance understanding of the complex relations between tumor cells and the immune cells, and suggest novel approaches to therapy.

### Hans Othmer

School of Mathematics, University of Minnesota The Role of Mathematical Models in Understanding Pattern Formation in Developmental BiologyIn a Wall Street Journal article published in 2013, E. O. Wilson attempted to make the case that biologists don't really need to learn any mathematics -- whenever they run into difficulty with numerical issues they can find a technician (aka mathematician) to help them out of their difficulty. He formalizes this in Wilson's Principle No. 1: "It is far easier for scientists to acquire needed collaboration from mathematicians and statisticians than it is for mathematicians and statisticians to find scientists able to make use of their equations." This reflects a complete misunderstanding of the role of mathematics in all sciences throughout history. To Wilson mathematics is mere number crunching, but as Galileo said long ago, The laws of Nature are written in the language of mathematics... the symbols are triangles, circles and other geometrical figures, without whose help it is impossible to comprehend a single word. Mathematics has moved beyond the geometry-based model of Galileo's time, and in a rebuttal to Wilson, E. Frenkel has pointed out the role of mathematics in synthesizing the general principles in science. In this talk we will take this a step further and show how mathematics has been used to make new and experimentally-verified discoveries and how mathematics is essential for understanding a problem that has puzzled experimentalists for decades -- that of how organisms can scale in size. Mathematical analysis alone cannot "solve" these problems since the validation lies at the molecular level, but conversely, a growing number of questions in biology cannot be solved without mathematical analysis and modeling. We will highlight a few instances where modeling has been used to push experiments forward and highlight problems in biology that cannot be adequately addressed without mathematical modeling.

### Kevin Passino

EEOB, The Ohio State University Swarm Cognition in Honey BeesWe synthesize findings from neuroscience, psychology, and behavioral biology to show that some key features of cognition in the neuron-based brains of vertebrates are also present in the insect-based swarm of honey bees. We present our ideas in the context of the cognitive task of nest-site selection by honey bee swarms. After reviewing the mechanisms of distributed evidence gathering and processing that are the basis of decision-making in bee swarms, we point out numerous similarities in the functional organization of vertebrate brains and honey bee swarms. These include the existence of interconnected subunits, parallel processing of information, a spatially distributed memory, layered processing of information, lateral inhibition, and mechanisms of focusing attention on critical stimuli. We also review the performance of simulated swarms in standard psychological tests of decision making: tests of discrimination ability and assessments of distractor effects.

### Jeremy Taylor

Biostatistics - School of Public Health, University of Michigan A multistate model for time to cancer recurrence and death incorporating a cured fractionMotivated by data from multiple randomized trials of colon cancer, we model time-to-cancer-recurrence and time-to-death using a multi-state model. We incorporate a latent cured state into the model to allow for subjects who will never recur. Parametric models that assume Weibull hazards and include baseline covariates are used. Information from the multiple trials are included using a hierarchical model. Bayesian estimation methods are used. The model is used to assess whether there is improved efficiency in the analysis of the effect of treatment on time-to-death in each trial by using the information provided by earlier cancer recurrence. For subjects who are censored for death, multiple imputation is used to impute death times, where the imputation distribution is derived from the estimated model. Gains in efficiency are possible, although sometimes modest, using the extra information provided by the recurrence time.

Heterogeneity in cancer is an observed fact, both genetically and phenotypically. Cell-cell variation is seen in almost all aspects of cancer from early development through to invasion and subsequent metastasis. Our current understanding of this heterogeneity has mainly focused at the genetic scale with little information on how this variation translates to actual changes in cell phenotypic behavior. Given that many genotypes can lead to the same cellular phenotype, we must also understand the range and scope of this heterogeneity at the phenotypic scale as ultimately this variability will dictate the aggressiveness of the tumor and its treatability. Central to our understanding of this heterogeneity is how the tumor cells interact with each other and with their microenvironment.

The tumor microenvironment is not simply the extra cellular matrix, but a complex milieu consisting of growth promoting and inhibiting factors, nutrients (including oxygen and glucose), chemokines, and importantly other cell types including (but not limited to) fibroblasts, immune cells, endothelial cells and normal epithelial cells. These microenvironmental factors and different cell types interact with one another and the tumor as it grows. The role of endothelial cells and the immune system in cancer development are fairly well established, but less is known about the function of host fibroblasts in this process. Most solid tumors present as dense fibrotic masses, which suggests that fibroblasts contribute to tumor growth by infiltrating and depositing extracellular matrix proteins. In addition, the phenotype of fibroblasts found within and around tumors (activated fibroblasts or cancer associated fibroblasts: CAFs) is different to normal fibroblasts, and closely resembles myofibroblasts. Fibroblasts act in wound healing, angiogenesis and tissue remodeling by releasing growth factors and proteases such as matrix metalloproteinases. They also deposit matrix proteins such as laminin, tenascin and fibronectin. Therefore, if the growing tumor can co-opt such fibroblasts it has an unlimited source of many of the fundamental elements required for growth and invasion.

The two central themes of this workshop are:

- Heterogeneity (be it phenotypic, signaling or genotypic), and
- Microenvironment (ECM, nutrients, fibroblasts and immune cells).

Since a highly heterogeneous tumor has the potential to adapt to any microenvironment, understanding how interactions between the growing tumor and its microenvironment modulate tumor heterogeneity is critical to unraveling the mechanisms of cancer initiation.

### Michael Summers

Chemistry and Biochemistry, Chemistry and Biochemistry, University of Maryland TBDAbstract coming soon.

**Co-sponsor: Physical Sciences-Oncology Program of the Division of Cancer Biology, National Cancer Institute, National Institutes of Health, U.S. Department of Health and Human Services.**

While the primary forms of tumor treatment remain chemotherapy and radiation, generic cytotoxic therapies, the increasing understanding of the nature of the disease as being both heterogeneous and genetically unstable has induced a trend to design and create therapies tailored to the specific tumor (patient-specific) and to combat the many different subpopulations of cells with combination therapies. Despite these efforts, tumor resistance and recurrence remain an unfortunate challenge of clinical trials. However, the clinical focus has been primarily on the genetic heterogeneity in tumor cell populations, with minimal focus on the impacts of treatment on the subpopulations phenotypic interactions, either competitive or cooperative, the induced microenvironment, or the evolutionary pressures created. One likely reason is the inability of traditional clinical trials to quantify or meaningfully analyze these phenomena. Examining the impact of particular drug therapies and their scheduling on the local microenvironment and individual cellular behavior in both the long and short term is almost impossible in a clinical setting and extremely difficult in laboratory experiments. Limiting factors include inadequate observation tools, e.g. most imaging methodologies are too coarse to properly resolve the dynamics, changing the system by observing it, such as when resecting grown tumors in animals for closer observation, time for disease development and money. Mathematical models offer an approach to investigate many different types of therapies along with their impact on the microenvironment, and to explore optimal dosing combinations and schedules while bypassing the many limitations encountered in the clinic and laboratory. There are many different varieties of models, though they can generally be categorized into discrete, continuum, or statistical, each offering its own advantage for considering various scales or effects. They can be designed utilizing a basic understanding of the primary phenotypes and genotypes present in a tumor to investigate the likely induced microenvironment from various therapies and evolutionary selection pressures leading to resistance. It is even possible to use them to perform virtual clinical trials and compare different treatments on theoretical populations. This workshop will focus on two broad topics: Mathematical modeling of cancer treatment strategies and how to model resistance of cancers to drug treatments. Use of mathematical models to compare clinical trial arms and virtually simulate clinical trials outcomes. The workshop will highlight modeling applications that are as close as possible to direct clinical impact including design of multi-institutional clinical trials for patient-specific radiation dose strategies, quantification of patient-specific response to treatment that can be useful in predicting outcomes and treatment design, as well as include discussions of sequencing of drug treatments, optimal scheduling, and modeling of combination therapies which are useful in rapidly mutating diseases, such as cancer and HIV. The workshop will also discuss ways to implement the use of mathematical models in a clinical setting.

### Bjorn Sandstede

Professor of Applied Mathematics, Mathematics, Brown University Modelling Stripe Formation in ZebrafishZebrafish is a small fish with distinctive black and yellow stripes that form during early development due to cell differentiation and movement. I will discuss an agent-based model for stripe formation in zebrafish that incorporates biological data. This model can reproduce ablation experiment and make predictions for the development of stripes from a larval pre-pattern and the effect of mutations. Among the conclusions are that fish growth shortens the necessary scale for long-range interactions and that iridophores, a third type of pigment cell, help maintain stripe boundary integrity.

### Sergey Gavrilets

Mathematics, University of Tennessee Collective action and the collaborative brainHumans are unique both in their cognitive abilities and in the extent of cooperation in large groups of unrelated individuals. How our species evolved high intelligence in spite of various costs of having a large brain is perplexing. Equally puzzling is how our ancestors managed to overcome the collective action problem and evolve strong innate preferences for cooperative behaviour. Here, I theoretically study the evolution of social-cognitive competencies as driven by selection emerging from the need to produce public goods in games against nature or in direct competition with other groups. I use collaborative ability in collective actions as a proxy for social-cognitive competencies. My results suggest that collaborative ability is more likely to evolve first by between-group conflicts and then later be utilized and improved in games against nature. Evolution of collaborative ability creates conditions for the subsequent evolution of collaborative communication and cultural learning.

### Bard Ermentrout

Professor, Department of Mathematics, University of Pittsburgh All the way with Gaston Floquet: A theory for flicker hallucinationsWhen the human visual system is subjected to diffuse flickering light in the range of 5-25 Hz, many subjects report beautiful swirling colorful geometric patterns. In the years since Jan Purkinje first described them, there have been many qualitative and quantitative analyses of the conditions in which they occur. Here, we use a simple excitatory-inhibitory neural network to explain the dynamics of these fascinating patterns. We employ a combination of computational and mathematical methods to show why these patterns arise. We demonstrate that the geometric forms of the patterns are intimately tied to the frequency of the flickering stimuli. We also show that the patters that arise are completely expected based on symmetric bifurcation arguments.

A fundamental property of cancer is uncontrolled cell proliferation. Much knowledge has accumulated on altered genetic and signaling networks that drive uncontrolled proliferation. Recently, there has been a resurgence of interest in the intimate link between proliferation and metabolism, absolutely required to fulfill energy and biomass demands for cell division. In cancer, metabolic networks are highly adaptable, and often metabolism of cancer cells relies largely on aerobic glycolysis, a property referred to as the Warburg effect and akin to fermentation: even in the presence of oxygen, energy metabolism bypasses mitochondrial respiration. The dysregulated interface between metabolic networks and oncogene-modified proliferation networks is emerging as a fertile area to identify critical target nodes, or strategies to defy the drive to ever-adaptable uncontrolled proliferation. This workshop will encompass a mix of experimentalists and mathematicians. Ideally, the former will be engaged on the production of large datasets on cancer cell proliferation, both at the cell population and single-cell level, and in response to microenvironment perturbations including anti-proliferative drugs. The latter will focus on mathematical models of proliferation and metabolism at several scales, including genetic, signaling and cellular, including a focus on the ability of cancer cell populations to regenerate and reprogram in response to hostile microenvironment and to targeted treatment, ultimately persisting in their proliferative state. Multi-scale models connecting the growth of cultured cancer cells and/or individual tumors to epidemiological data will also be considered. Although tumor growth and cancer cell proliferation have been modeled mathematically for decades, adequate datasets have been scarce and fragmentary due to experimental limitations. Recently, several game-changing high-throughput technologies, including genomics, proteomics, and automated microscopy, have created remarkable opportunities for renewed modeling efforts. Furthermore, small-molecule drugs with exquisite specificity for signaling network nodes are in an intensive phase of development and deployment into clinical trials. As these targeted agents increasingly enter standard clinical practice, a major challenge is to improve outcomes by rational drugging strategies. Sheer combinatorics makes drug strategy testing in the field prohibitively expensive, both financially and temporally, opening avenues for mathematical and statistical approaches that, combined with experimentation, have the power to streamline testing.

### Mark Segal

Department of Biostatistics, University of California, San Francisco 3D Genome Reconstruction: How and WhyThe three-dimensional (3D) configuration of chromosomes within the eukaryote nucleus is consequential for several cellular functions, including gene expression regulation, and is also associated with cancer-causing translocation events. While visualization of such architecture remains limited to low resolutions, the ability to infer structures at high resolution has been enabled by recently-devised chromosome conformation capture assays. In particular, when coupled with next generation sequencing, such methods yield a genome-wide inventory of chromatin interactions. Various algorithms have been advanced to operate on such data to produce reconstructed 3D configurations. Several studies have shown that such reconstructions provide added value over raw interaction data with respect to downstream biological analysis.

However, such added value has yet to be fully realized for higher eukaryotes since no high resolution genome-wide reconstructions have been inferred for these organisms because of computational bottlenecks and organismal complexity. After overviewing existing reconstruction approaches we propose a two-stage algorithm, deploying multi-dimensional scaling and Procrustes transformation, that overcomes these barriers. 3D architectures for mouse and human are presented and methods for evaluating these solutions discussed. Finally, reverting to yeast, we demonstrate the advantages bestowed by 3D structures with respect to identifying co-regulatory elements.

Most tissues are hierarchically organized into lineages. A lineage is a set of progenitor-progeny relationships within which progressive changes in cell character occur. Typically, lineages are traced back to a self-perpetuating stem cell (SC), and end with a postmitotic terminal cell. One of the most exciting recent developments in the field of cancer biology is the recognition that lineage progression continues to occur in tumors. In particular there is an increasing body of evidence that like normal tissues, tumor cells that have the potential for unlimited self-renewal give rise in large numbers to cells that lack this potential - the so-called cancer stem cell hypothesis. By focusing for so many years on the majority cell populations in tumors, and not on the rarer cancer stem cells (cancer initiating cells), scientists and clinicians may have missed out on opportunities to understand, diagnose and treat the processes in cancer that matter most. Further, there is increasing evidence that cell stemness may be a function of the local environment rather than being a predetermined property of a cell. What are the consequences of this plasticity in cell behavior? Other important open questions in the field include: What cell types within the normal tissues are capable of being the cells of origin for tumors? What is the relationship between normal tissue stem cells and tumor-initiating cells (e.g., cancer stem cells)? Which signaling and other regulatory networks are altered in tumors relative to the normal tissues, and how do they function within the tumor? Finally, there is growing evidence that therapies aimed at the major cell types in tumors may sometimes make things worse, by leading to an expansion in the fraction of cancer stem cells. How can this be avoided? This workshop will address these and other questions through discussions among mathematical and computational modelers and experimentalists. In particular, the strong connections between normal development, tumor growth and the use of novel treatment strategies will be discussed.

### Andrzej Kloczkowski

New methods to improve modeling and prediction of protein structure, dynamics and function

We have developed and combined several novel methods to improve protein structure prediction from the amino acid sequence, and modeling of protein dynamics. One of the most promising developments in protein structure prediction are many-body potentials that take into account dense packing, and cooperativity of interactions in protein cores. We developed a method that uses whole protein information filtered through machine learners to score protein models based on their likeness to native structures. These results were published by us [1], and tested successfully in CASP 9, where our prediction group 4_BODY_POTENTIALS was among top three predictors in the category of template-free modeling for the most difficult targets. Recently we have significantly improved our potentials by considering electrostatic interactions and residue depth and used them for the prediction of protein structure and blind tested them in CASP 10. Our prediction group Kloczkowski_Lab was ranked as the third one in prediction of structure (based on the single model) for all targets, and ranked also as the second one for template free-modeling (see: http://www.predictioncenter.org/casp10/groups_analysis.cgi ) [2]. By combing statistical contact potentials with entropies from the elastic network models of proteins we can compute free energy and improve coarse-grained modeling of protein structure and dynamics [3]. The consideration of protein flexibility and its fluctuational dynamics improves protein structure prediction, leads to a better refinement of computational models of proteins, and significantly improves protein docking [4,5]. We studied also the self-assembly of FVFLM peptide and its influence on the kinetics of Aβ16-20 oligomerization.

1. P. Gniewek, A. Kolinski, R.L. Jernigan, and A. Kloczkowski, Proteins 79, 1923 (2011)

2. E. Faraggi and A. Kloczkowski, Proteins 82, 3170-6, (2014)

3. M.T. Zimmermann, S.P. Leelananda, A. Kloczkowski, and R.L. Jernigan, JPC B116, 6725 (2012)

4. P. Gniewek, A. Kolinski, R.L. Jernigan, and A. Kloczkowski, JCP 136, 195101 (2012)

5. P. Gniewek, A. Kolinski, R.L. Jernigan, and A. Kloczkowski, Proteins 80, 335 (2012)

Evolutionary game theory, along with replicator equations, has been applied successfully to modeling evolution of various biological or social systems, ranging from virus infection to bacteria development, from plant succession to animal breeding, and from trace of evolutionary history to study of biodiversity and ecology. Applications in areas such as population genetics, animal behaviors, and evolution of social cooperation have especially seen great developments and impacts. In evolutionary game theory, species are considered as if they are players in a game, competing for resources, for survival, and for reproduction. A mathematical (game) model can then be established for study of any given population of competing species, and for analysis of population changes and prediction of equilibrium states and their stabilities. The theory involves such mathematical branches as game theory, optimization theory, and ordinary differential equations, and further extends to graph theory, stochastic processes, and partial differential equations as appropriate. Although emerged as a powerful mathematical tool for evolutionary and ecological modeling, the evolutionary game theory is still in the stage of early development. Theoretical issues remain to be addressed and computational methods need to be developed, for equilibrium computation, dynamic simulation, and stability analysis. Application problems are arising and yet to be investigated in many critical fields of biology such as development of energy-efficient or nutrition-rich plants and animals, analysis of human microbiome genomic data, control of infectious diseases, modeling immune-defense systems of biological species, etc. This workshop is to bring an interdisciplinary group of experts as well as biologists and mathematicians who are interested in evolutionary game modeling, to have an extensive discussion on current and future development of evolutionary game theory and applications. Topics include reviews or reports on recent theoretical or computational developments, or critical applications. The goal of the workshop is to increase communications among researchers and especially between biologists and mathematicians, in order to have a better understanding of the theory, to identify challenges and applications of the field, to promote interdisciplinary collaborations, and to accelerate future developments of the field.

The purpose of this four day workshop is to reflect on the current state of equivariant dynamical systems and coupled cell systems theory, focusing on a selection of interconnected research directions. The workshop will feature some of the main contributors to the theory and its numerous applications, highlight promising future directions, and mark the contribution of Professor Martin Golubitsky as one of the leaders of the field on the occasion of his 70th birthday.

Themes:

- Equivariant dynamics and applications
- Coupled cell systems and applications
- Pattern formation in natural sciences
- Network Dynamics Mathematical Neuroscience

This workshop is being co-sponsored by the OSU Department of Mathematics and The Institute for Mathematics and its Applications (IMA).

Quantitative bioscience is the application of mathematics, physics and numerical computations to all spheres of biology. It provides a common currency to the understanding of life at the microscopic and macroscopic level, from single molecules to complex ecosystems. It underlies the development of personalized biomedical devices, optimized drug delivery to patients and the prediction of ecosystem health in changing environments. While these challenges are typically addressed within each research area, the required quantitative (mathematical, physical and computational) tools are shared across all areas. The rich stream of experimental data has made it possible for bioscientists to build testable and predictive models that are based on sound data. It is these models, accompanied by statistical and computational approaches, that have provided a patform for experimentalists to undertand the dynamics of their respective biological systems and to guide new experiments. As a result, the field of mathematical and computational modeling has been felt strongly across the biological sciences, including neuroscience, cancer biology, immunology, epidemiology, ecology, and evolutionary biology.

In this summer school, we aim to provide a new generation of trainees with the opportunity to learn more about the basics of this field and give them an overview of the latest advancements made in quantitative biosciences.

For more information please visit The Joint 2015 CAMBAM-MBI-NIMBioS Summer School.

The goal of this MBI NSF-funded program is to introduce students to exciting new areas of mathematical biology, to involve them in collaborative research with their peers and faculty mentors, and to increase their interest in mathematical biology.

In biology, ecology, and public health there has been a growth in the use of stochastic differential equations (SDEs) to model scientific phenomena over time. SDEs have the ability to simultaneously capture he known deterministic dynamics of the variable of interest (e.g., chemical levels within a cell, the chemical or physical characteristics of a river, the presence, absence and spread of a disease), while enabling a modeler to capture the unknown dynamics or measurement processes in a stochastic setting.

In this four-day workshop, participants will learn about the use of SDEs to model physical phenomena in the biological sciences. Students will learn how to define and manipulate SDEs, and will understand the difficulties in performing statistical inference on the parameters of SDEs using data. They will relate the modeling of SDEs to the theory of spatial and temporal data analysis, and will carry out a small group project to discover and investigate how to model data from various disciplines within the biological sciences.

The lectures will be taught by a selection of external and internal speakers, each of which have a different experience in different aspects of modeling using SDEs, as well as in spatial and temporal data analysis. Students will learn the material through practical exercises.

Students should come to the workshop with two years of graduate experience in Statistics or equivalent. They should be comfortable with statistical models and theory, likelihood inference, and have some exposure to Monte Carlo techniques. Students should have taken a course in linear models, and have knowledge of the statistical software package called R (http://www.r-project.org). Some exposure to time series analysis and spatial statistics is helpful, but not essential. Students should bring a laptop to the workshop, preloaded with R.

Supplementary materials related to the workshop will be hosted here for the workshop's duration.

Partial support is available for students to attend this workshop.

Additional workshop support is being provided by STATMOS, a NSF-funded Research Network for Statistical Methods for Atmospheric and Oceanic Sciences.

A student centered conference featuring talks and posters by students doing research in mathematical biology, keynotes by prominent mathematical biologists, a graduate studies recruitment fair, and other special features including a conference dinner and social event.

### Tim Elston

Professor, Applied Mathematics, University of North Carolina, Chapel Hill Gradient sensing in yeastYeast cells are able to direct growth toward gradients of mating pheromone (chemotropism). During chemotropism, the site of new cell growth is determined by a patch of polarity factors that wanders around the cell cortex. Interestingly, yeast also polarize their receptors in response to pheromone, but the benefit of such polarization was unknown. Mathematical modeling suggests a novel mechanism for gradient sensing in which active receptors and associated G proteins lag behind the polarity patch and act as an effective drag on patch movement. Because the strength of this effective drag is proportional to the local pheromone concentration, the location of the polarity patch, and hence cell growth, tend to align with the pheromone gradient. Consistent with model predictions, the polarity patch is trailed by a G protein-rich domain, and this polarized distribution of G proteins is required to constrain patch wandering. Our findings explain why receptor polarization is beneficial, and illuminate a novel mechanism for gradient tracking.

### 2013-2014

### Jack Cowan

Professor, Mathematics, University of Chicago Stochastic Wilson-Cowan equations for networks of excitatory and inhibitory neuronsNot long ago we found a way to describe the large-scale statistical dynamics of neocortical neural activity in terms of (a) the equilibria of the mean-field Wilson-Cowan equations, and (b) the fluctuations about such equilibria due to intrinsic noise, as modeled by a stochastic version of such equations. Major results of this formulation include a role for critical branching, and the demonstration that there exists a nonequilibrium phase transition in the statistical dynamics which is in the same universality class as directed percolation (DP). Here we show how the mean-field dynamics of interacting excitatory and inhibitory neural populations is organized around a Bogdanov-Takens bifurcation, and how this property is related to the DP phase transition in the statistical dynamics. The resulting theory can be used to explain the origins and properties of random bursts of synchronous activity (avalanches), population oscillations(quasi-cycles), synchronous oscillations (limit-cycles)and fluctuation-driven spatial patterns (quasi-patterns). We will also show how such a system of interacting neural populations can be made to self-organize to a state near the Bogdanov-Takens bifurcation, if the coupling constants(synaptic weights) are activity-dependent, and follow approximately, a generalization of the Vogels et al. version of spike-time dependent synaptic plasticity (STDP).

Creating usable models for the sustainability of ecosystems has many mathematical challenges. Ecosystems are complex because they involve multiple interactions among organisms and between organisms and the physical environment, at multiple spatial and temporal scales, and with multiple feedback loops making connections between and across scales. The issue of scaling and deriving models at one scale from another is well known to lead to substantial mathematical issues, as in going from descriptions of stochastic spatial movement at the population scale from the individual scale and as in getting diffusion limits. Here, for example, recent work has focussed on alternatives to the diffusion limit. The mathematical challenges in the analysis of full ecosystems are truly great. Many modeling approaches have been used in studying ecosystems, ranging from simple dynamical systems to highly detailed computational models. Relatively simple models are essential to gain insight into fundamental features of complex systems and the mechanisms behind them, whereas highly detailed models are essential for making predictions about the specific effects that changes may have on ecosystem functioning. The complex ones include agent-based models and models that place biological models into realistic and detailed models for physical processes such as ocean dynamics. There is a need to develop new mathematical tools for making connections among different processes at different scales and thus provide a robust framework for assessing the sustainability of ecosystem processes. Understanding models at multiple scales also requires case studies of particular systems. Plankton dynamics provide a good case study. At one extreme, low dimensional Nutrient-Phytoplankton-Zooplankton (NPZ) models give insight into the balance between light penetration and nutrient upwelling that underlie patterns of plankton blooms. At the other extreme, computational models of a myriad competing plankton species, rapidly evolving in the face of changing ocean temperature and salinity, are numerically incorporated into global climate models. As a second example, forests and savanna are complex systems where organisms interact with physical processes, specifically fire and hydrology, and they have been studied from the viewpoint of individual-based modeling but also with simple models. This workshop aims to engage computational and mathematical modelers, empiricists, and mathematicians in a dialogue about how to best address the problems raised by the pressing need to understand complex ecological interactions at many scales. Its ultimate goal is to initiate transformative research that will provide new approaches and techniques, and perhaps new paradigms, for modeling complex systems and for connecting different types of models operating at different levels of detail. An important feature of the workshop will be afternoon sessions devoted to case studies rather than lectures with the goal of starting new collaborations and new research directions.

### Paul Sajda

Professor, Biomedical Engineering and Radiology, Columbia University Neurally and ocularly informed graph-based models for searching 3D environmentsAs we move through an environment, we are constantly making assessments, judgments, and decisions about the things we encounter. Some are acted upon immediately, but many more become mental notes or fleeting impressions -- our implicit "labeling" of the world. In this talk I will describe our work using physiological correlates of this labeling to construct a hybrid brain-computer interface (hBCI) system for efficient navigation of a 3D environment. Specifically, we record electroencephalographic (EEG), saccadic, and pupillary data from subjects as they move through a small part of a 3D virtual city under free-viewing conditions. Using machine learning, we integrate the neural and ocular signals evoked by the objects they encounter to infer which ones are of subjective interest. These inferred labels are propagated through a large computer vision graph of objects in the city, using semi-supervised learning to identify other, unseen objects that are visually similar to those that are labelled. Finally, the system plots an efficient route so that subjects visit similar objects of interest. We show that by exploiting the subjects' implicit labeling, the median search precision is increased from 25% to 97%, and the median subject need only travel 40% of the distance to see 84% of the objects of interest. We also find that the neural and ocular signals contribute in a complementary fashion to the classifiers' inference of subjects' implicit labeling. In summary, we show that neural and ocular signals reflecting subjective assessment of objects in a 3D environment can be used to inform a graph-based learning model of that environment, resulting in an hBCI system that improves navigation and information delivery specific to the user's interests.

Although evolution is often thought of as a slow process that proceeds on the time scale of millennia, in fact there are many very rapid evolutionary processes, often called contemporary evolution, that have profound effects on human health and welfare. For example: (1) In agriculture, plants and pests can rapidly evolve resistance to herbicides and pesticides, respectively; (2) The influenza virus, and other viruses and bacteria, often evolve within an individual host making treatment strategies difficult and/or temporary; (3) The evolution of bacteria to become resistant to most antibiotics poses a serious threat to mankind; (4) Some parasites, for example African trypanosomes, can change the proteins that they express on their surfaces and thus can become invisible to the immune system; and (5) Harvested populations may show rapid evolution in size or age at maturity, which affects both yield and recovery from depleted states. Understanding the dynamic behavior of such problems is difficult because one is typically studying the co-evolution of two or more interacting complex systems. The mathematical challenges are daunting. On the local level (for example, the evolution of influenza within a host) mutations are driven by stochastic processes. However, one is not interested in the number of mutations per se, but in the number of successful mutations that can establish themselves in the host. This depends on the immune status of the host, including resources available to the mutant and the history of previous infections. Even when this is understood one must face the problem of transmission and spatial spread of the mutant strain in the whole population. Thus, not only is the biology very difficult, but these questions naturally involve stochastic processes and ordinary and partial differential equations on several different time scales. Giving or not giving drugs, choosing to use or not use pesticides, or choosing when to use them, are choices that have political, ethical and economic consequences. The consequences themselves depend in many cases on changing human cultural behavior, changing technology, and climate change. Mathematical modeling, including the invention of new mathematical structures, can help us understand these rapidly co-evolving systems and thus make clear the likely consequences of various policy choices.

### Bernie Krause

Wild Sanctuary Unraveling the mysteries of SoundscapesSoundscape Ecology and the concept of biophonies and geophonies in particular, form the basis of an emerging field that is only about dozen years old. While it is being defined to some extent in cultural, acoustic, and biological terms, translating these phenomena to numbers has been elusive and challenging. While my field of expertise is neither mathematics nor statistics — it is limited primarily to field recording, archiving and preliminary analysis of natural soundscapes — this discussion will provide some historical background and then focus on the ways in which biophonies and geophonies, in particular, might be framed through the lens of various statistical models and lay the groundwork for new ones.

This Special Topics Workshop will address the development of mathematical and computational modeling techniques that can be used to facilitate the development and optimal design of cardiac valve prostheses and other cardiovascular devices. Workshop topics will include the design of tissue scaffolds and cardiovascular stents used in bioartificial heart valve design and replacement, and also fluid-structure interaction between blood and cardiovascular tissue. The speakers will include mathematicians, biomedical engineers, and medical specialists. Poster presentations by students and post-doctoral researchers will also be included.

Natural resources, such as forests, fish, land, and biodiversity, while renewable, are being pushed to the brink and beyond by sectorial mismanagement and the resulting cumulative impacts on the macroscopic environmental and ecosystem conditions. For many, the solution is to take a more holistic or ecosystem-based approach to management (EBM). While this approach seems intuitive, there are many unanswered questions as to the information and modeling requirements for implementing EBM and the potential impacts both at a micro and macroscopic level that it would have on the sustainability of natural resources and the communities that rely on them. It is clear that EBM requires a synthesis of our understanding of ecology and economics, which are both complex systems in their own right. Each has its own highly developed mathematical models and modeling approaches. Methods from optimal control have been applied in the context of fisheries and forestry, as exemplified by the classic text by Colin Clark, Mathematical Bioeconomics. These approaches have proved extremely useful, but for the most part have focused on single species questions. Extending these ideas to questions that are larger in scope in terms of more species and including spatial heterogeneity is a real mathematical challenge. Optimal control theory provides one potential framework for evaluating EBM, but the complexities of spatially distributed, age structured, and/or stochastic population models will push the frontier of analytical and numerical analysis. Answering the many questions surrounding the implementation and effects of EBM also requires developing mathematical tools and methods for understanding complex coupled natural-human systems, that is, the interaction between ecosystem dynamics and human community dynamics. Mathematical models for EBM need to take into account both the dynamics of coupled ecological and economic systems and the game theoretic issues arising from the differing interests and values of different stakeholders. Some mathematical approaches to those issues have been developed in both ecology and economics. On the ecological side there are ideas such as the theory of adaptive dynamics. On the economic side there is the theory of differential games, where the single control parameter that can be used for optimization in traditional control theory is replaced by a collection of controls, and where different controls are in the hands of different stakeholders who may want to optimize different things. What is needed for scientific progress is a high level synthesis of these and other ideas, which can occur only if experts on modeling in both ecology and economics collaborate with each other and with experts in mathematical sub-disciplines that are likely to be relevant, including game theory, control theory, dynamical systems, and stochastic processes. An important goal of the mathematical modeling is to analyze the likely consequences of policy choices proposed by Congress, government agencies, or eco-system managers. These choices will have important consequences not only for ecological systems, but also for the health and economic well being of human communities. Therefore, this workshop will have a public policy component, and representatives of policy makers and fellows of public policy institutes will be invited. At least two afternoons will be devoted to case studies which will develop new research directions, rather than lectures.

### Steven Gross

Professor, Developmental and Cell Biology, University of California, Irvine Molecular-motor based transport: how does it function, and what can theoretical modeling contribute to understanding it?Cells are highly ordered, and much of this organization is controlled by active molecular-motor based transport. At the single-molecule level, biophysical studies have been very effective at determining how motors work. However, in cells, motors do not function by themselves, but rather, act in groups. How these groups function is less well understood. In this talk I will discuss our experimental evidence underlying the statement that motors function in groups, and will then discuss how modeling can be used as a key tool to understand both how groups of motors function, and also which aspects of their single-molecule properties are particularly important for controlling this ensemble function.

### Thomas Magliery

Chemistry, The Ohio State University The Interplay of Conservation and Correlation in Enzyme StabilityDespite remarkable advances in protein structure prediction and design, an accurate predictive model of the thermodynamic effects of even point mutations remains elusive. The post-genomic era is a remarkable time to consider the problem of protein stability from a statistical perspective. How is information distributed in protein sequences? What protein properties are encoded by conserved and co-varying amino acids? And how can we use this information to engineer more stable proteins? We have been analyzing the effects of sequence conservation and correlation on enzyme function and physical properties, by engineering consensus and correlated mutations, or fully consensus variants, of the ubiquitous and well-studied metabolic enzymes triosephosphate isomerse (TIM) and adenylate kinase (ADK). We have established useful methods for calculating and visualizing conservation and correlation. From two consensus variants of TIM, we showed that correlated networks in weakly conserved positions can contribute strongly to protein biophysical properties. We also showed that consensus mutations are more likely to stabilize at more conserved positions, unless those positions strongly co-vary with other positions. I will review these results and discuss further efforts to refine our sequence-based algorithm for protein stabilization, and establish its generality. I will also briefly discuss experiments to explore the effects of correlated mutations directly, including through the use of a TIM-knockout based selection we pioneered in our lab.

The frontier of biology and medicine is defined by our ability to decipher the mechanisms that underlie basic phenomena. These phenomena may include cell motility and migration, cell division, cell reprogramming, and cell communication that may be manifested in a wide range of questions in development and disease. Thus, examples from stem cell, developmental, neural, and cancer biology have the potential to allow examination of basic biological processes within the context of real, in vivo phenomena. However, a major challenge has been the lack of a means to identify biologically tractable problems and link these problems to applications-oriented experts from imaging and mathematics.

The rate at which this frontier advances depends, at least in part, on how fast technology evolves and on how data is interpreted and translated into a better understanding of basic mechanisms. In the past 10 years, dramatic advances in imaging technology and mathematics have provided new tools and models for discovery that have enabled new observations and hypotheses to be tested. These tools, which are often designed for general applications, find their way into the hands of biologists who then see ways to use them. In some cases, specific mathematical models and applications drive innovations. The mathematical methods involved include PDEs, moving boundary value problems, dynamic geometric changes, optimal transport, stochastic modeling, and the analysis of large data sets. Advances in imaging technology that will be discussed include serial block-face scanning electron microscopy, superresolution microscopy, fluorescence resonance energy transfer (FRET)-based activity biosensors, detection of forces in cells and tissue, multispectral and multiphoton deep tissue imaging, and fluorescence light-sheet microscopy.

The goal of this workshop is to encourage biologiststo describe tough questions and to jointly think about approaches that inspire new developments and interdisciplinary research collaborations. We plan to do this by combining input and discussion from experts in imaging technology and mathematics with cell, developmental and cancer biologists that share a passion for solving the riddles that underlie complex phenomena in dynamic living systems. We suggest that both groups of participants blend what is technically possible with what exists only in dream space, with the hope that together we will learn something new and be stimulated to explore new ways to visualize, model and better understand complex processes.

### Santiago Schnell

Department of Molecular & Integrative Biology, Department of Computational Medicine & Bioinformatics, Brehm Center for Diabetes Research, University of Michigan Modeling dominant protein interactions that influence the pathogenesis of protein folding diseasesProtein folding diseases occur when a specific protein fails to fold into its correct functional state as a consequence of mutation in the protein amino acid sequence. In this talk, I present a model of the folded and misfolded protein expression, processing and their interactions, which we have used to investigate how protein folding disease phenotypes develop from mutated genotypes. Modeling protein processing as a continuous flow reactor, we found that the pathogenesis of protein folding diseases can be modulated by a combination of the transition time of folded and misfolded proteins in the reactor, the ratio of folded and misfolded protein inflow rates in the reactor and a chemical interaction parameter between folded and misfolded proteins. Our analysis reveals therapeutic strategies targeting the modulation of protein folding diseases, which have been recently explored in cellular and animal models of Mutant INS-gene Induced Diabetes of Youth and Congenital Hypothyroidism with deficient thyroglobulin.

### Troy Day

Professor, Mathematics and Statistics, Queen's University Computability, Gödel’s Incompleteness Theorem, and an Inherent limit on the Predictability of EvolutionI will briefly review a main way in which mathematical modeling has been used to understand and predict evolutionary change. I will then highlight an important shortcoming of such approaches and consider an alternative that attempts to overcome the problem. This alternative encompasses what I refer to as "open-ended" evolution. I will then present a proof, using this approach, that certain evolutionary questions are inherently unanswerable unless the process of evolution has specific properties. The cause of this limitation on evolutionary theory is shown to be fundamentally the same as that underlying the Halting Problem from computability theory and Gdel’s Incompleteness Theorem.

This workshop addresses the broad class of imaging problems in the life sciences that rely on shape or geometry to characterize biological processes and parameters. Of course, the strategy of observing shape and its relationships to biology is a classical undertaking, but in recent years, the availability of 3D imaging and better computational tools has opened up new possibilities for systematic, quantitative analyses of biological shape. This, in turn, has resulted in new demands for more fundamental approaches, based in mathematics, for quantifying and analyzing geometric objects. The problem of quantifying shapes arises in clinical science, where the shapes of neurological or musculoskeletal structures are thought to be related to growth, function, pathology, and degeneration. More recently, computational strategies for shape analysis have become widespread throughout the life sciences, with compelling applications in anthropology, cell and tissue biology, botany, etc. The mathematical contributions to shape analysis have resulted in new tools for modeling or characterizing shapes and for analyzing both shape dynamics and the statistics of populations of shapes. However, the applications of these methods are typically limited by somewhat strong assumptions about the classes of shapes, such as smoothness, correspondence, and homogeneity or underlying simplifications in morphogenetic processes. This workshop focuses on the frontiers of this technology with an eye toward new applications, such as cell biology and biological morphogenesis, which have yet to benefit from robust, comprehensive approaches. Of particular interest are more general tools for handling nonmanifold shapes, such as networks or trees, as well as tools that can handle relatively heterogeneous collections of objects, such as those seen in cell or tissue biology. Also important is the analysis of dynamic shapes as in morphogenesis and regeneration, and the links to other data such as lineage, genomics, and proteomics. Participants will consist of life scientists with compelling scientific and clinical examples, engineers with computational tools for shape analysis, and mathematicians with insights into fundamental approaches for representing and quantifying shape.

### Naomi Leonard

Professor, Mechanical and Aerospace Engineering, Princeton University Models, Mechanisms, and Bifurcations of Collective Animal BehaviorFrom bird flocks to fish schools, animal groups exhibit a remarkable ability to manage a variety of challenging tasks that individuals could not manage on their own. Despite limitations on individual-level sensing, computation, and actuation, and with no centralized instruction, animal groups make decisions quickly, accurately, robustly and adaptively in an uncertain and changing environment. I will describe recent development of analytically tractable models and methods for studying the mechanisms of collective movement and decision-making dynamics in animal groups. I will focus on the application of bifurcation analysis to systematically elucidate the dependence of the collective dynamics on parameters that model the networked multi-agent system and the environment.

*Naomi Ehrich Leonard is the Edwin S. Wilsey Professor of Mechanical and Aerospace Engineering and an associated faculty member of the Program in Applied and Computational Mathematics at Princeton. She is currently Director of Princeton's Council on Science and Technology and an affiliated faculty member of the Princeton Neuroscience Institute and Program on Quantitative and Computational Biology. Her research and teaching are in control and dynamical systems with current interests in coordinated control for multi-agent systems, mobile sensor networks and ocean sampling, collective animal behavior, and human and animal decision dynamics. In 2013 she was elected to the American Academy of Arts and Sciences. She received a John D. and Catherine T. MacArthur Foundation Fellowship in 2004, the Mohammed Dahleh Award in 2005, and an Inaugural Distinguished ECE Alumni Award from the University of Maryland in 2012. She is a Fellow of the IEEE, ASME, SIAM, and IFAC. She received the B.S.E. degree in Mechanical Engineering from Princeton University in 1985 and the M.S. and Ph.D. degrees in Electrical Engineering from the University of Maryland in 1991 and 1994. From 1985 to 1989, she worked as an engineer in the electric power industry.*

### Arthur Sherman

National Institutes of Health Understanding the Causes and Cures of Type 2 Diabetes with a Mathematical ModelWe present a mathematical model for regulation of beta-cell mass and function based on the pioneering work of Topp et al, J. Theor. Biol. 206:605 2000. Their model added a layer of slow negative feedback to the classic insulin-glucose loop in the form of a glucose-dependent growth-death law for beta-cell mass. We add to that model regulation of beta-cell function on intermediate time scales. The model quantifies the relative contributions of insulin action and insulin secretion defects to type 2 diabetes (T2D) and explains why prevention is easier than cure. The latter is a consequence of bistability, which also underlies the success of bariatric surgery and acute caloric restriction in reversing T2D. With a further enhancement to include the dynamics of exocytosis, the model describes the mechanistic bases of the canonical pathways to T2D, elevated fasting glucose vs. elevated post-prandial glucose, and clarifies their relationship to the early transient and late sustained phases of insulin secretion. The model gives new insight into the significance of the fact that insulin secretion is higher for pre-diabetics and early diabetics than for normal individuals ("Starling's law of the pancreas"), which has led some to question whether impaired insulin secretion is necessary for diabetes or even to propose that excessive insulin secretion triggers the disease. The presentation will serve as an example of how theorists can use relatively elementary mathematics to engage constructively in important debates in the experimental community.

Merging imaging modalities is increasingly important for biomedical questions related to time and space scales including function and anatomy. Integrating modalities from multiple scales can assist with understanding development and function, disease, diagnosis and treatment. This workshop will bring together researchers who are attempting to combine and integrate different imaging modalities to better understand anatomy, function and disease from the cellular to organ level. Methodologies and challenges in combining imaging data from multiple sources, such as MRI, fMRI, DTI, PET, EEG, MEG, CT, ultrasound, NMR, x-ray diffraction, electron microscopy, proteomic and genomic data will be explored. Merging data from different modality time scales (functional time scales from nanoseconds to minutes; developmental time scales from embryonic to adult) and space scales (from microns to millimeters) present many mathematical questions. Interpretation, analysis and modeling of multi-modality data as it applies to development, disease models and therapies will also be explored. The heterogeneity of the data presents many difficult challenges that are suited for mathematical exploration. The focus will include brain and cardiac imaging related to multiscale and bioscale data collection, merging data, modeling and analysis. This workshop will be of interest to mathematicians working in areas of statistical analysis, PDE modeling, inverse problems, differential geometry, computational visualization and multiscale problems. Biomedical researchers interested in merging imaging modalities to investigate questions related to genomics, gene expression and biomarkers and the role they play in macroscopic function would benefit from this workshop.

### Daniel Turnbull

Professor, Radiology and Skirball Institute, New York University School of Medicine In Vivo Imaging of the Developing Mouse Brain: From Morphology to MoleculesExtensive genetic information and the expanding number of techniques available to manipulate the genome of the mouse have led to its widespread use in studies of brain development and to model human neurodevelopmental diseases. We are developing a combination of ultrasound and magnetic resonance micro-imaging approaches with sufficient resolution and sensitivity to provide noninvasive structural, functional and molecular data on developmental and disease processes in normal and genetically-engineered mice. Our efforts over the past decade have focused on in utero and early postnatal imaging and analysis of the developing brain and cerebral vasculature. The advantages and limitations of both ultrasound and MRI for imaging mouse development will be discussed, and examples provided to illustrate the utility of these approaches for 4D mutant phenotype analysis. Recent advances have also made in the area of molecular imaging, including the generation of novel reporter mice that enable cell-specific imaging with ultrasound and MRI contrast agents. Future directions for molecular imaging of mouse brain development will be discussed.

### Stephen Pacala

Professor, Ecology and Ecolutionary Biology, Princeton University The Fate of the Global Carbon SinkModels of the global terrestrial biosphere in current Earth system models (climate models with coupled atmosphere, ocean and biosphere) uniformly predict a large current carbon sink caused by CO2 fertilization of terrestrial vegetation that sequesters 1-2 GtC/y. Models with a nitrogen cycle generally predict that a large fraction of the sink will disappear by midcentury because of nitrogen limitation. The models all include some form of Liebig’s Law of the Minimum for nitrogen. All models currently predict that water limited systems will see large and sustained sinks because water use efficiency is increased by elevated CO2. However, FACE experiments and other recent evidence implies that the opposite is true: CO2 fertilization sinks are observed to persist despite N-limitation and the benefits of enhanced water use efficiency have not been observed. We developed a mechanistic version of forest simulation models with competition for light, water and nutrients that can be analyzed mathematically. We used it to compute the most competitive strategies of allocation to foliage, stem wood and fine roots as a function of soils and climate. When fertilized by CO2, these most competitive strategies predict the results of FACE experiments and the opposite of previous global models: sustained CO2 sinks in the face of N-limitation and the absence of sinks in water –limited systems. I explain the cause of these results, the mechanism behind them and how one would test them in the field.

With the advent of genomics, we have learned that microdiversity among strains of the vast majority of pathogens is extensive; each genotype infecting a host can present significant differences in virulence, immunogenicity, and antigenic variation. Thus, pathogens in circulation are not uniform; instead, they are comprised of sub-groups that can be defined by the expression of different genetic, pathogenic and population dynamic traits. The circulation of these parasites depends heavily on human movement dynamics, and, in some situations, vector availability and competence. Together, these anthropological, ecological, molecular, and immunological factors are fundamental drivers in the transmission of infectious disease, and their correct characterization requires a comprehensive interdisciplinary multi-scale modeling approach. This workshop will bring together scientists from multiple disciplines to exchange ideas about new perspectives for the quantification of within-host dynamics and between-host transmission of infectious disease. Attendants will discuss novel molecular and ecological data that has become available at an unprecedented level of detail ('omic, clinical, entomological, and epidemiological data), and will discuss the application of mathematical perspectives that go beyond traditional epidemiological models of transmission.

### Alexander Anderson

Integrated Mathematical Oncology, H. Lee Moffitt Cancer Center & Research Institute Phase I trials in melanoma: Optimizing order and timing of combination therapyMetastatic melanoma is known to be resistant to standard chemotherapy. During the last few years, targeted therapeutic approaches have emerged as the dominant treatment choice, primarily because they target tumor cells that harbor specific genetic mutations. However, even these targeted drugs have limited long term success in treating metastatic melanoma patients, since eventually resistance emerges. Surprisingly, when these treatments are given in combination much better treatment responses are observed. However, little is known about why the combinations are more successful. Our recent experimental results suggest a possible mechanism, in that these treatments differentially induce autophagy (the process of self-digestion by a cell to temporarily extend its life under stressful conditions) in tumor cells. To better understand how autophagy induction might facilitate better treatment response, we developed a mathematical model comprising of a system of ordinary differential equations that explain the dynamics of melanoma cells under different treatments. Specifically, we incorporated an autophagy cell population and examined how this population affects treatment success. Model parameters, such as the growth and death rates with and without treatments, were estimated by comparing model predictions with in vitro experimental data. Model results show that the combination therapy is effective in controlling tumor population over an extended period of time. The resistance, however, eventually emerges driven in part by the autophagy population. To overcome this resistance, we applied a drug that targets the autophagy population and were able to show that additional administration of this drug inhibited growth of the resistant population. In order to place these results in a more clinically relevant setting (e.g. clinical tumor volume doubling times), we generated a small cohort of virtual patients by varying model parameters to capture the diversity of disease response observed in the clinic. Parameters varied include initial proportion of different cell types, net growth rate, autophagy rate, and cell death rates. We then applied 10 different treatment schedules that were composed of different combinations (order and duration) of AKT inhibitor, Chemotherapy and autophagy inhibitor to this virtual patient cohort. This effectively allowed us to implement a “virtual clinical trial” or phase i trial with our model and select the optimal therapeutic approach across a range of patients.

This workshop focuses on the challenges presented by the analysis and visualization of large data sets that are collected in biomedical imaging, genomics and proteomics. The sheer size of data (easily in the range of terabytes, and growing) requires computationally efficient techniques for the sampling, representation, organization, and filtering of data; ideas and techniques from signal processing, geometric and topological analysis, stochastic dynamical systems, machine learning and statistical modeling are needed to extract patterns and characterize features of interest. Visualization enables interaction with data, algorithms, and outputs. Data sets from biomedical imaging, genomics and proteomics often have unique characteristics that differentiate them from other data sets, such as extremely high-dimensionality, high heterogeneity due to different data modalities (across different spatial and temporal scales, but also across different biological layers) that need to be fused, large stochastic components and noise, low sample size and possibly low reproducibility of per-patient data. These unique aspects, as well as the large size, pose challenges to many existing techniques aimed at solving the problems above. The workshop will bring together biologists, computer scientists, engineers, mathematicians and statisticians working in a wide of areas of expertise, with the goal of pushing existing techniques, and developing novel ones, for tackling the unique challenges offered by large data sets in biomedical imaging.

More than a decade after the completion of the Human Genome Project, our ability to predict important high-level phenotypes from molecular information at the cellular level remains woefully inadequate. Statistical mapping between variants identified by genome -wide association studies and complex traits such as hypertension do not effectively explain the range of phenotypes in the population, nor do they provide useful predictions of disease risk. In short, the standard machinery of statistical genetics has fallen short as a tool to understand complex disease. This provides the opportunity and motivation for a more comprehensive approach to the grand challenge of understanding the mechanistic relationships between high-level phenotypes and molecular information.

Multi-scale simulation of physiological systems represents a powerful vehicle for linking multiple levels of causality. Mathematical modeling in combination with high-performance computing and high-resolution data has led to tremendously sophisticated and reliable multi-scale multi-physics based simulations of certain physiological systems. In particular, system dynamics from the cellular to the system levels have long been studied using mathematical modeling, for example, computer models of the heart. Yet such dynamics models rarely make any use of data gathered at the molecular level, and therefore cannot capitalize on the emerging availability of patient data collected at multiple scales (e.g. genome information). This workshop will discuss the state-of-the-art mathematical techniques (and outstanding needs) for effectively synthesizing data ranging from genomic through molecular and organ up to the system level with multi-scale computational techniques. Efforts will be focused on addressing how models can be adapted to couple data measured at different scales and from different species, yet belong to the same physiological system. This question will be studied within the respiratory, cardiovascular, and renal systems. We expect that it is possible to extract common features from these systems, and that techniques applied will have applicability outside the systems studied.

This workshop will bring together domain experts from physiology, mathematics, and statistics. Physiologists and statisticians will help identify key data sets of interest and address questions related to uncertainty in data sampling, including discussion of known variation within species, and between in-vivo and in-vitro sampling. Mathematicians will bring expertise in modeling, model reduction, and solving inverse problems. The aim will be to discuss ways to combine data from multiple sources and scales with relevant models to predict patient specific responses. New techniques that have shown promise for solving these types of problems include reformulation of models using techniques from algebra, uncertainty quantification, parameter estimation, and networks. This diverse group of researchers will have potential to generate new projects and ideas for linking statistical and physics-based techniques for building multi-scale mathematical models that incorporate physiological data from multiple sources and scales, which may eventually elucidate relationships between phenotypes and the underlying physiology.

In this talk we will give an overview of a series of methods for 3D blood flow modeling, ranging from Kalman filtering techniques for automatic outflow and material parameter estimation to baroreflex model for automatic control of blood pressure. We will also discuss recent progress made on the validation of CFD predictions of pressure gradients in coarctation patients at rest and stress using clinical pressure data.

The occasion of the annual Board meeting of the International Council for Industrial and Applied Mathematics (ICIAM) provides a confluence of distinguished applied mathematicians from around the world. This workshop provides a forum to exchange ideas, to review recent developments in applied mathematics, and to allow the local community of mathematical scientists to share this international perspective.

The theme of the meeting will be broad, reflecting the range of expertise of these scientists.

The workshop is hosted by the Mathematical Biosciences Institute at OSU, with additional funding provided by the Mathematics Research Institute of OSU and by the Institute for Mathematics and its Applications (University of Minnesota).

The grant from the IMA allows us to support speakers and participants from neighboring institutions in Ohio and throughout the Midwest. In particular, we would like to invite graduate students to attend.

Partial support is available for students and junior participants. We solicit contributions for a poster session.

The goal of this MBI NSF-funded program is to introduce students to exciting new areas of mathematical biology, to involve them in collaborative research with their peers and faculty mentors, and to increase their interest in mathematical biology. The program consists of three parts - each including a mix of educational and social experiences:

Two-week Introduction (June 2-13, 2014): Tutorials, computer labs, and short-term team efforts designed to introduce students to a variety of topics in mathematical biology.

REU Program (June 16 - August 8, 2014): An 8 week individualized research experience as part of a research team at one of the participating host institutions.

Capstone Conference (August 11-15, 2014): A student centered conference featuring talks and posters by students doing research in mathematical biology, keynotes by prominent mathematical biologists, a graduate studies recruitment fair, and other special features including a conference dinner and social event.

The application will require:

Two letters of reference

A ranked list of three projects that you want to participate in

A statement indicating your reasons for wanting to participate in this program

Students accepted into the full summer-long research program will receive room and board and they will be paid $4500 (this includes a stipend of $3000 plus $1500 for travel and related expenses). This will be paid in three increments:

$1000 paid following the Two-Week Introduction (June 2-13, 2014)

$2500 paid during the REU Program (June 16-August 8, 2014)

$1000 paid following the Capstone Conference (August 11-15, 2014)

Tutorials, computer labs, and short-term team efforts designed to introduce students to a variety of topics in mathematical biology.

Review papers used for Study Groups & Team Investigations:

1) "A Review of Image Denoising Algorithms, With a New One" by Buades, Coll, and Morel, SIAM Review 2005 [Group led by Leopold Matamba Messi]

2) "Exploring Complex Networks" by Steven Strogatz, Nature 2001 [Group led by Deena Schmidt]

3) “How Does the Crayfish Swimmeret System Work? Insights from Nearest-Neighbor Coupled Oscillator Models” by Skinner, Kopell, and Mulloney, JCNS 1997 [Group led by Lucy Spardy]

4) "The Mathematics of Infectious Diseases" by Herbert Hethcote, SIAM Review 2000 [Group led by Joy Zhou]

This summer school will focus on the theory, mathematical modeling and experimental study of biological rhythms. The workshop will begin with a bootcamp introducing the basic mathematical tools and techniques used in studying biological rhythms. In depth explorations of specific problems will then be presented. Students will also work in small groups on projects, which will be presented at the end of the two week workshop.

All applicants selected for the MBI Summer Graduate Program will receive lodging (single dorm room) and a campus meal card loaded with daily breakfast, lunch and dinner through their entire stay. Also, selected applicants will receive partial reimbursement for travel expenses. There is no tuition charged to summer school participants.

**Apply by March 3rd, 2014 for full consideration.**

A student centered conference featuring talks and posters by students doing research in mathematical biology, keynotes by prominent mathematical biologists, a graduate studies recruitment fair, and other special features including a conference dinner and social event.

**Graduate studies in the Mathematical Biosciences Panel: **This panel will focus on opportunities for graduate studies in the Mathematical Biosciences. Presenters from Arizona State University (**Fabio Milner**) and Ohio State University (**Elizabeth Stasny**) will discuss the different types of graduate programs offered in the Mathematical Biosciences and how to position yourself to present your best case for admission and to be successful in your graduate training. **Jennifer Slimowitz-Pearl** from the National Science Foundation will describe the fellowship and research opportunities for graduate students available from NSF.

Deadline for applications: July 12, 2014

The workshop is intended to broaden the scientific perspective of young researchers (primarily junior faculty, postdocs, and senior graduate students) in mathematical biology and to encourage interactions with other scientists. Workshop activities include plenary talks and poster sessions, as well as group discussions on issues relevant to mathematical biologists. Several abstracts will be chosen for short talks as well as to be presented as a poster. We cordially invite young mathematical biologists to participate. **For full consideration, please apply by May 31, 2014.**

### 2012-2013

### Leslie Loew

University of Connecticut Health Center, University of Connecticut The Virtual Cell ProjectThe shape of a cell, the sizes of subcellular compartments and the spatial distribution of molecules within the cytoplasm can all control how molecules interact to produce a cellular behavior. This talk describes how these spatial features can be included in mechanistic mathematical models of cell biology. The Virtual Cell (VCell) computational modeling and simulation software is designed for spatial modeling of cellular reaction-diffusion systems. VCell facilitates choices between physical formulations that implicitly or explicitly account for cell geometry and between deterministic vs, stochastic formulations for biochemical reactions. VCell allows modelers to separately define the model physiology, which includes the molecules, their reactions and membrane transport processes. As a first step toward constructing a spatial model, the geometry needs to be specified and associated with the molecules, reactions and membrane flux processes of the reaction network. Initial conditions, diffusion coefficients, velocities and boundary conditions complete the specifications required to define the mathematics of the model. The numerical methods used to solve reaction-diffusion problems both deterministically and stochastically include a variety of ODE, PDE, and probabilistic solvers. A study of actin dynamics provides an example of the insights that can be gained in interpreting experimental results through the application of spatial modeling.

MBI's 10th Anniversary Meeting The meeting will feature talks about areas in which exciting progress has been made in recent years and in which future advances can be expected. Speakers: Reka Albert (Penn State) Bill Bialek (Princeton) Emery Brown (MIT/ Mass General) Jim Collins (BU) Nicholas Jewell (Berkeley) Nancy Kopell (BU) Simon Levin (Princeton) Philip Maini (Oxford) Martin Nowak (Harvard - Keynote Speaker) Lior Pachter (Berkeley)

We will focus on dynamics and information processing in large, nonlinear networks. The aim is to highlight a set of mathematical questions that recur across neuroscience, and to discuss both recent progress and outstanding problems. The final day will feature a series of retrospective talks on the interplay of mathematics and neuroscience, leading into moderated discussions of future prospects. These sessions will align with the major themes of the workshop, which are proposed to be as follows: Linking large-scale network structure and dynamics: The heterogeneous components and vast scale and connectivity of neural systems make for an overwhelming range of possible networks. However, network architectures are constrained by key principles - for example, each cell produces connections of only one sign, leading to non-normal connectivity matrices (Murphy and Miller). What are the consequences of such features for general properties of network dynamics? We will focus on this and other systematic departures from random connectivity, including small-world structures, localized connection "neighborhoods," feedforward inhibition circuits, and the impact of highly recurrent, and hence bistable, network components. In addition, we will cover the latest results on how basic assumptions about single-neuron properties do and do not impact network-wide dynamics. Bridging scales -- mean field models: What mathematical tools can bridge scales from networks of spiking cells to averaged statistical variables that usefully summarize the activity of large networks? Mean-field techniques have yielded major advances in mathematical neuroscience for decades, but many developments remain to be realized, especially for networks with nonsparse connections and hence partial synchrony among spikes. Information and coding in large spiking networks: Information-theoretic studies have shown that certain patterns of correlated, or partially synchronized, spiking across large networks enhances the fidelity with which they can transmit information. But what network dynamics lead to such patterns? We will highlight general mathematical results that connect architecture and information processing. Plasticity and learning in network connections: Perhaps the most fascinating aspect of neural dynamics is how network activity drives network architecture to evolve over time. We will focus on mathematical tools for understanding the consequences of such rules, both in terms of the general connectivity structures that they produce and in terms of network function - e.g., encoding and releasing "memories" of past inputs. A related theme is robustness and variability in neural circuits - for example, how widely can connection strengths and intrinsic properties vary while preserving basic features of a network's dynamics? (Please note that this last might instead be covered in a separate short workshop on control theory in neuroscience.)

Cilia and flagella are ubiquitous in cell biology, acting either in a coordinated fashion to move surrounding fluid such as in lung airways, or as a propeller for cell locomotion such as on sperm or eukaryotic microorganisms, or as a sensory immotile but flexible antenna such as the primary cilia in essentially every cell in vertebrates and many vertebrate and invertebrate sense organs. The fluid dynamics induced by cilia and flagella, the mechanisms of coordination of motile cilia and flagella, and the fluid dynamic feedback to intra-ciliary and intra-flagellar transport and signaling, are essential to biology. The purpose of this workshop is to convene experts in biology, physics, mathematical modeling, and scientific computation to collectively assess progress and identify challenges to be undertaken in cilia- and flagella-induced fluid dynamics. A list of outstanding challenges and computational strategies will be highlighted through lectures and subsequent discussions and open forums: (i) methods to compute and resolve the fluid-structure interaction of a cilium or flagellum, in either a viscous or viscoelastic fluid; (ii) stochastic (based on molecular motors) versus deterministic coarse-grained models of cilia and flagella beat cycles; (iii) the coordination mechanisms of cilia and flagella through the intervening fluid and/or the cells they emanate from; (iv) fluid mechanical sensing by the cilium or flagellum and the feedback response; (v) fundamental questions of optimization and efficiency (tuning of ciliary or flagellar motion or tuning of fluid properties to optimize motility or fluid transport; (vi) experimental and engineering approaches to support and challenge new modeling approaches. These challenges require assessment of current formulations and analysis of the governing equations for existing models, attention to accuracy, stiffness, time-stepping, adaptive mesh refinement, parallel implementation, and computing architectures.

### Michael Mackey

Applied Mathematics in Bioscience and Medicine, Physiology, McGill University Using mathematics to understand, treat, and avoid hematological diseaseIn this talk I describe work directed at understanding the origin of periodic hematological diseases, and how the mathematical modeling has led to better treatment strategies. I will also describe how our mathematical modeling may be useful in helping to avoid the hematological side effects of chemotherapy

### Lisa Fauci

Mathematics, Tulane University Spiny Disks, Flexible Fibers and Waving Rings: Explorations in Phytoplankton Fluid DynamicsPhytoplankton motion in the ocean, at the scale of individual cells, involves the interaction of passive and actuated elastic structures with a surrounding fluid - a common theme in biological fluid dynamics. We present recent modeling results that shed light on the active swimming of dinoflagellates, as well as the passive motion of diatoms in shear flows. These diatoms may form chains or bear spines. In addition to examining how the flexibility and geometry of the diatoms affect their rotational dynamics, we will discuss how laboratory experiments and computational simulations are being calibrated in an effort to characterize the elastic properties of different species of chain-forming diatoms.

Background: We often see in functional measurements of data over time, space and other continua that salient features in the resulting curves and surfaces vary in position from one recording to another. Children vary in the timing of puberty, human movement in activities like handwriting and golf swings speed and up and slow down from one instance to another , seasonal events like hurricanes arrive early some years and late in others, and traffic jams vary in location over city streets from one day to another. At the same time, each of the events can also vary in intensity. We refer to positional variation as phase variation, and intensity variation as amplitude variation; and it is now evident that many processes unfold over a system time that not only does not unroll at the same rate as physical clock time, but also tends to vary in a random way from one realization of a functional event to another. Amplitude and phase variation are illustrated in the Figure. Unfortunately most statistical technology, such as even the calculation of means, variances and correlations, cease to work properly if carried out over phase-varying data; that is, most of the classical statistical methodology was developed to assess only amplitude variation. For example, variation summary methods such as principal components analysis tend to spread the signal power of quite simple phase variation over a large number of components, and tend to blend amplitude and phase variation in confusing ways. As a consequence, methods for eliminating phase variation by nonlinearly transforming or warping time, space and so forth have been the subject of much recent research, and are referred to as registration methods. Registration leads to three interesting types of further analysis. First investigation of amplitude variation is straightforward, using conventional methods on the registered curves or surfaces. Second, various approaches to phase variation comes from study and analysis of the domain transformations, which are usually required to be diffeomorphic. Third, the joint variation, between the warpings and the amplitude variation can be understood and analyzed. This bi-partite or bi-stochastic nature of functional variation now appears to have very widespread implications for statistical science, and links directly to older problems such as shape analysis, as well as newer statistical topics such as dynamic systems. Fisher-Rao and Historical connection: One natural approach to such functional analysis is a Riemannian one, under the Fisher-Rao metric. While the parametric form of this metric has famously been used for analyzing (parametric) families, for example by Kass, Barndorff- Nielson, Le Cam, Amari, and others, its nonparametric version has proven important in curve and functional analysis (Srivastava, Younes, Mumford, etc). Historically, its use has been restricted to the submanifolds of parametric densities, deriving inference bounds and density comparisons. More recent work allows analysis of all densities, including nonparametric forms, and indeed to functions in general. Its invariance to parameterizations provides a natural framework for alignments of functions and curves, and for separating phase and amplitude variability in functional data. The workshop and subsequent meetings at SAMSI resulted in fruitful interactions between functional data analysts and shape analysts, and has led to this promising framework that it will be interesting to test in a variety of real applications. Workshop Ideas: Instead of the usual passive speaker-audience format, workshop activities will be centered around applying a wide variety of statistical methods to a common collection of data sets. The focus will be the various analytic approaches of several different Analysis Groups, to some common data sets, featuring careful discussion of the strengths and weaknesses of the various analyses. Main presentations will be made by the Analysis Groups, who will agree to analyze (before the workshop) each of the agreed upon data sets, and will present their results at the workshop. For context, each data set will have an Owner, who will be responsible for answering questions about the data while the analysis is under way, and who will at the beginning of the workshop give a brief description of the data, plus the main statistical questions. Following the analytic presentations, there will be group discussion with the goal of evaluation of the different methods used. It is anticipated that this will result in a list of the pros and cons of each approach, and in particular a clear view of the varying circumstances under which each method has advantages over the others. Dissemination of the results is intended to be through an article, co-authored by the major participants, aimed at a journal such as Statistical Science, or a top level computational statistics journal.

### Peter Mohler

Davis Heart and Lung Institute, The Ohio State University New Paradigms for Human Excitable Cell DiseaseOur research focuses on the molecular mechanisms underlying ion channel and transporter targeting in cardiac and other excitable cells. In particular, we are interested in the role of membrane-associated ankyrin family of polypeptides in the targeting and function of ion channels and transporters. Our work establishes that loss-of-function mutation in ankyrin-B is the basis for a human cardiac arrhythmia syndrome associated with sinus node dysfunction, repolarization defects, and polymorphic tachyarrhythmia in response to stress and/or exercise ("ankyrin-B syndrome"). Additionally, our work revealed that reduction of ankyrin-B in mice results in reduced levels and abnormal localization of Na/Ca exchanger, Na/K ATPase, and InsP3 receptor at T-tubule/SR sites in cardiomyocytes and leads to altered Ca2+ signaling and extrasystoles that provide a rationale for the arrhythmia. A second line of work in the lab is focused on the role of ankyrin-G for targeting voltage-g ated Na channels in heart. These studies establish a physiological requirement for ankyrins in localization of a variety of ion channels in excitable membranes in the heart and demonstrate a new class of functional 'channelopathies' due to abnormal cellular localization of functionally-related ion channels and transporters.

### Prahlad Ram

Department of Systems Biology, University of Texas M. D. Anderson Cancer Center Mathematical and experimental analysis of biological networks to identify targets for therapyIntracellular biological networks are highly complex and contain numerous regulatory loops. One of the challenges in cancer biology is to be able to understand and target sub-network that are aberrantly functioning in cancer cells. In this talk I will describe our integrated mathematical and experimental approach to understanding network function and identify targets for cancer therapy. The talk will focus on using network motif structures to reduce complexity and use of time course experimental proteomic data to train mathematical and computational models to identify targets.

Cognitive neuroscience presents superb opportunities for mathematical contributions, especially in connecting different theoretical and experimental frameworks. On the experimental side, methods ranging from single-neuron recording to human behavioral tests are flourishing, and mathematical models are beginning to suggest how one leads to the other. Rigorous theoretical treatments from microeconomics are often applied, including Bayesian estimation and optimization, but details of how they might be implemented in stochastic, dynamic neural circuits have only recently been proposed. By bringing together experimentalists and theorists working on different levels, a workshop will move the field closer to a long-held goal of understanding and predicting behavior in increasingly rich cognitive tasks. Each day will feature a different theme, as described in more detail below, and will emphasize both work at the level of algorithms and phenomena, and at the level of implementation by circuits of spiking cells. The organizing committee suggests that this workshop include a select group of students and post-docs as participants. Time could be made available each day for brief student/post-doc presentations (short talks and/or poster sessions), and the day capped by evening sessions that encourage interactions among the students and post-docs. In addition, a student or postdoc will be chosen to be a "reporter" for each day to summarize the day's events and highlights. These will then be assembled into an overall workshop report that could be published by pre-arrangement with an appropriate journal. Attention: Where are attentional effects "generated," how are they coordinated across multiple brain areas, how is attention fed back to earlier levels of sensory processing, and what are the underlying mechanisms at the level of circuits of spiking cells? Decision making: How are diverse sensory and task cues integrated over time and combined into a "single" decision signal, how are decision rules applied to this signal, and what is the role of dopamine and other modulators in this process? Coordination of neural circuits: Under different behavioral constraints, different brain areas form cooperative units. What is the role of thalamocortical and basal ganglia circuitry here? Nascent physiological work is in need of a theoretical counterpart, both to reveal how signals are gated and amplified, and to compare the performance and efficiency of different possible mechanisms and network architectures. Reinforcement learning: Complex tasks require learning and updating of rules that relate reward to action in changing environments. What algorithms can perform this updating optimally, in the face of uncertainty about rewards and sensory cues? What neural circuitry can implement these algorithms?

### John Reinitz

Professor, Departments of Statistics, Institute of Genomics & Systems Biology, University of Chicago Transcriptional control in the Drosophila blastodermThe syncytial organization of the blastoderm stage of Drosophila development affords unique advantages for the study of transcriptional control. With respect to the control of transcription, it is possible to use the entire embryo as a spatially resolved microarray in which the response of reporters to quantitatively assayed transcription factors can be monitored at cellular resolution. This affords the opportunity to construct quantitative and predictive models of transcriptional control that are not limited to single enhancers. I will discuss progress in constructing such models, including applications to evolution and synthetic biology.

### David Van Essen

Professor, Anatomy & Neurobiology, Washington University The Human Connectome Project: Computational Challenges and OpportunitiesRecent advances in noninvasive neuroimaging have set the stage for the systematic exploration of human brain circuits in health and disease. One such effort is the Human Connectome Project (HCP), which will characterize brain circuitry and its variability in healthy adults. A consortium of investigators at Washington University, University of Minnesota, University of Oxford, and 7 other institutions is engaged in a 5-year project to characterize the human connectome in 1,200 individuals (twins and their non-twin siblings). Information about structural and functional connectivity will be acquired using diffusion MRI and resting-state fMRI, respectively. Additional modalities will include task-evoked fMRI and MEG/EEG, plus extensive behavioral testing and genotyping. Advanced visualization and analysis methods will enable characterization of brain circuits in individuals and group averages at high spatial resolution and at the level of functionally distinct brain parcels (cortical areas and subcortical nuclei). Comparisons across subjects will reveal aspects of brain circuitry which are related to particular behavioral capacities and which are heritable or related to specific genetic variants. Data from the HCP will be made freely available to the neuroscience community. A user-friendly informatics platform will enable investigators around the world to carry out many types of data mining on these freely accessible, information-rich datasets. The emergence of massive amounts of high quality and consistently acquired neuroimaging and behavioral data from the HCP and other large-scale projects raises exciting opportunities and challenges on the computational and informatics fronts. Just as bioinformatics emerged as an exciting new discipline once vast amounts of genomic and proteomic data became available, it is likely that neuroinformatics will rapidly evolve as new methods and approaches are developed to capitalize on the ongoing explosion of human neuroimaging data.

Mathematical neuroscience is required to understand the normal functions of the computational brain. As a corollary, we can translate our fundamental understanding of the nervous system to better understand and treat disorders of the brain. There are a variety of brain diseases that are considered dynamical - where the symptoms are consequences of pathological parameters of the underlying neuronal elements and network. Several dynamical diseases have steadily improving mechanistic understanding, embodied into computational models that increasingly reflect the dynamics of the disease symptoms. These include Parkinson's disease and epilepsy. We suspect that other more complex brain diseases are revealing a dynamical component, such as depression and schizophrenia. Along with the advent of improving with computational models, the technical ability to perform open or closed loop deep brain stimulation is now becoming increasingly applied to treat these dynamical diseases. Thus as we better understand dynamical disease, the ability to dynamically probe and control them is now at hand. Another area of medical application of mathematical theory is in the area of brain interfaces. Here, measurement arrays (electrodes or optical) can be used to extract dynamics from ensembles of neurons, and functions are created to decode such information. Such decodings enable us to understand the neural code, and to drive robotic devices or encode information to stimulate the brain. In addition to devices that can adapt to the brain's activity, it is now clear that the brain co-adapts to such devices - learning to use them to accomplish tasks. The cutting edge of interfacing with decoding from and encoding information for the brain is an important cutting edge of mathematical biosciences. Lastly, genomic variability is an inherent aspect of the robustness of species --- it is the plausibility of life itself. Yet the dynamical expression of genomic variability may remain within, or branch across species boundaries --- speciation requires a phenotypic dynamical expression. In neuronal circuits, there is substantial variation in the levels of active channel proteins, and computationally, there are wide varieties of building equivalent dynamics from available genetic protein products. In epilepsy, there is increasing evidence that the combinatorics of multiple channel protein variations may contribute to producing similar expression of the dynamics of epilepsy. In depression, the autoreceptors and reuptake transporters on dopaminergic and serotonergic neurons change their expression levels in response to long-term changes in extracellular concentrations of neurotransmitters. Thus understanding the mechanisms by which SSRIs work necessarily involves understanding gene regulation, biochemistry, and electrophysiology, and how they influence each other dynamically in neurons. We will explore the intersection of evolution, genetic variability, and dynamical disease.

### Robert Miura

Distinguished Professor, Department of Mathematical Sciences, New Jersey Institute of Technology Cortical Spreading Depression and Neurovascular CouplingAbstract. Cortical spreading depression (CSD) is a slowly propagating wave of ionic and metabolic disturbances in cortical brain tissue. In addition to massive cellular depolarization, CSD involves significant changes in tissue perfusion and metabolism. CSD has been linked to migraine with aura, which affects about 20% of the people who suffer from migraine. The triggers for this disease are mainly undiagnosed. To devise rational treatments of migraine with aura, we need to learn much more about the brain and about CSD. CSD was discovered almost 70 years ago by A.A.P. Leao, a Brazilian physiologist during his PhD research on epilepsy at the Harvard Medical School. CSD is characterized by nonlinear chemical waves that propagate at very slow speeds, on the order of mm/min, in the cortex of different brain structures in various experimental animals, and occurs in humans. CSD waves generate massive changes in extracellular ion concentrations. In this talk, I will review some of the characteristics of CSD wave propagation and describe some of the mechanisms that are believed to be important for CSD. We develop a new mathematical model for CSD where the sodium-potassium ATPase, responsible for cellular polarization and recovery from CSD, operates at a rate that is dependent on local oxygen concentration. The supply of oxygen is determined by modeling blood flow through a lumped vascular tree. Our model replicates the qualitative and quantitative behavior of CSD found in experimental studies and elucidates the effect of oxygen deprivation on CSD recovery. Our key findings are that during CSD, the metabolic activity of the cortex exceeds the physiological limits placed on oxygen delivery and changes in perfusion alter the intensity and duration of the event. The combination of experimentation and modeling should accelerate our understanding of how these mechanisms conspire to form CSD.

The emergence of complexity in self-organizing biological systems poses exciting challenges to their quantitative description and prediction. The imaging and visualization of complex biomolecules, such as proteins, DNAs, RNAs, molecular motors and viruses, are crucial in understanding and conceptualization of biomolecular systems, which in turn can have significant impact in biomedicine, rational drug design, drug discovery and gene therapy. On the other hand, biomedical imaging and visualization are indispensable tools for examining, revealing and diagnosing diseases, and for monitoring the effectiveness of medical treatments. Mathematics provides foundations for visualization and principles for the design of biomolecular/biomedical imaging modalities, such as single-molecule fluorophores, confocal imaging, X-ray crystallography and tomography, cryoelectron microscopy, and magnetic resonance force microscopy, nuclear magnetic resonance (NMR), magnetic resonance imaging (MRI), ultrasonography, positron emission tomography (PET), etc. Currently, mean curvature flow, Willmore flow, level set, generalized Laplace-Beltrami operator and partial differential equation transform are commonly used mathematical techniques for biomolecular surface generations and visualization. Additionally, wavelets, frames, harmonic analysis and compressive sensing are popular tools for biomolecular visualization and image processing. Moreover, topology, differential geometry, and geometric measure theory are powerful approaches for the multiscale modeling of biomolecular structure, dynamics and transport. Finally, persistently stable manifold, topological invariant, Euler characteristic, Frenet frame and machine learning are vital to the dimensionality reduction of extremely massive biomolecular data. These ideas have been successfully paired with current investigations and discovery of molecular biosciences. Mathematical challenges include the well-posedness of mathematical models under physical and biological constraints, lack of maximum-minimum principle, numerical analysis of multiply coupled partial differential equations, effectiveness of approximation theory and the modeling of complex biomolecular phenomena. This weeklong MBI workshop, in conjugation with the Mathematics Planet Earth (MPE) 2013 initiative, will seek greater understanding of imaging and visualization. It provides a forum to bring together mathematicians, biological and biomedical scientists to exchange ideas and results related to research in biomolecular/biomedical imaging and visualization, and to foster interdisciplinary research collaborations. It will also stimulate information flow of "biology to mathematics" and facilitate advances in biological science as a result of "mathematics to biology."

### Dirk Gillespie

Associate Professor, Molecular Biophysics and Physiology, Rush University Medical Center Calcium movement in cardiac muscleHeart muscle starts to contract when Ca^{2+} released from the sarcoplasmic reticulum (SR) binds to contractile proteins. The Ca^{2+} is released from the SR (a Ca^{2+} storage organelle) through calcium-selective ion channels called ryanodine receptors (RyRs). RyRs are activated (opened) by changes in cytosolic Ca^{2+} concentrations. Therefore, when some RyRs open to release Ca^{2+}, neighboring RyRs are activated to release even more Ca^{2+} in a process called calcium-induced calcium release (CICR). Experiments suggest that this positive-feedback process does, however, terminate long before the SR is depleted of Ca^{2+}, but how is not currently understood.

Several aspects of this Ca^{2+} movement will be discussed from the point of view of physics and mathematics. These include how RyRs select and efficiently conduct Ca^{2+} for sustained release, how probability theory can help us understand CICR, and how the physics of phase transitions might explain CICR initiation and, more importantly, its termination before the SR is deleted of Ca^{2+}.

### Louis Gross

Ecology and Evolutionary Biology & Math , University of Tennessee Savannas, Invasions and Lessons from Some Mathematical ModelsOne of the long-standing questions in plant community ecology concerns the maintenance of savannas and other communities which exclude plant species which would typically out-compete the species present in the system. Savannas are communities that exist in many locations around the world, consisting of a mixture of grass-dominated ground cover and an over-story of trees with a distinct canopy layer. Savannas are open to invasion by species such as hardwood trees which out-compete the species present. I will present a collection of models that elaborate one of the proposed mechanisms to maintain savanna communities: disturbance arising from processes such as fire and hurricanes. A focus in these models is the nature of the feedbacks and the potential for climate change to impact the disturbance regime and modify the global pattern of savanna systems. As a cautionary tale, I will end with a discussion of limits to prediction in complex ecological systems, and discuss the potential computational irreducibility of invasion and global change projections.

This workshop will focus on how mathematics can help us determine the functional roles that oscillations play in the nervous system. This workshop is timely in view of recent evidence that oscillations are critical for cognitive states and sensory processing. A broad range of oscillatory activity will be covered, including hippocampal and cortical oscillations, motor patterns, sensory processing and circadian rhythms. Competing theories will be presented on controversial issues, such as the role of gamma oscillations in binding of sensory information and the role of theta oscillations in hippocampal circuitry, with a view to how mathematics might help to resolve these controversies. We will try to draw parallels across different systems to see if central organizing principles emerge. Recent theoretical advances in the understanding of several central pattern generators (CPGs) will be compared and contrasted, including the CPG for coordinating crawfish swimmerets, the CPG for respiratory pattern generation, the pyloric circuit, and spinal CPGs involved in human gaits. Circadian rhythms will be addressed at the level of the molecular clocks underlying the diurnal rhythm and at the level of the interaction of these clocks with the electrical activity of the suprachiasmatic nucleus. Sensory systems will be represented by theoretical and experimental studies on the role of oscillations in distinguishing odors. Theoretical results on the nonlinear dynamics of coupled oscillators in the presence of noise will be presented and integrated into the context of the specific examples presented for different systems.

### Samuel Kou

Professor, Department of Statistics, Harvard University Statistical sampling in protein foldingPredicting the native structure of a protein from its amino acid sequence is a long standing problem. A significant bottleneck of computational prediction is the lack of efficient sampling algorithms to explore the configuration space of a protein. In this talk we will introduce a sequential Monte Carlo method to address this challenge: fragment regrowth via energy-guided sequential sampling (FRESS). The FRESS algorithm combines statistical learning (namely, learning from the protein data bank) with sequential sampling to guide the computation, resulting in a fast and effective exploration of the configurations. We will illustrate the FRESS algorithm through examples.

It is natural think about the brain and brain function on four different levels: genomics, biochemistry, electrophysiology, and behavior. Enormous amounts of new information are becoming available on associations between genotypes and behavior. The causal mechanisms, which are mostly unknown, necessarily involve the effects of genotype on development, cellular biochemistry, and electrophysiology. The cellular biochemistry and morphology of neurons is fundamental for understanding the electrophysiological properties of neurons and networks. And the network properties then give rise to the brain functions that we label with terms such as memory, mood, decision-making, motor control, and so forth. This simple characterization is misleading because the use of the word "level" suggests that there is bottom up control, the genes control the chemistry that controls the electrophysiology that controls behavior. The scientific issues are so difficult and interesting precisely because this is not true. Behavior affects gene expression levels, electrophysiology induces short and long term changes in cell biochemistry and morphology, which in turn influence the electrophysiology. On each of these levels, mathematicians and computational neuroscientists have created models to give conceptual understanding, to organize data, and to explore causal mechanisms. This workshop will focus on three particular areas. Morphology of neurons and electrophysiological processing. The great variety of dendritic morphologies suggest functional roles for different geometries and it is now understood that dendrites are often not passive conductors. Mathematical models have shown how the distribution of channels and receptor trafficking influence electrophysiological signaling. However, it is also known that electrophysiological signaling affects dendritic processing by affecting synapses and spines and other changes in morphology. For example, gonadotropin-releasing hormone cells of the hypothalamus drive the transition through puberty via changes in cellular- and population-level firing patterns. This change in electrical activity is accompanied by dendritic pruning that alters the electrical/conductance properties of the neuron. Medial superior olive (MSO) neurons in the auditory brainstem decrease their dendritic arborization during postnatal development, eventually achieving bipolar morphology. Mathematical models of the MSO and other neural populations suggest that not only the morphology but also the distribution of different ion channels contributes to dendritic computation. Mathematical models that relate cellular properties to the electrophysiology of neurons often raise new questions in deterministic and stochastic dynamical systems. These include the origins of mixed mode oscillations and bursting behavior, as well as the interplay of stochasticity and synchony. From signaling molecules to behavior. The brain can be in different states with different corresponding behaviors. Signaling molecules play an important role in modulating state, and behavior interacts with the signaling molecules. For instance, the extracellular concentration of the neuromodulator adenosine, which increases during wakefulness and decreases during sleep, appears to increase propensity to transition from waking to sleep by inhibiting wake-active cholinergic cells. In turn, cholinergic cells play a role in inducing REM sleep as well as mediating cognitive functions via signaling on multiple time scales, and acetylcholine has long been recognized as a slow-acting neuromodulator of arousal states. While awake, behavioral activity can provide positive feedback helping to sustain wakefulness in the face of accumulating adenosine. Molecular and electrical signals interact to develop the neuronal network underlying the interactions described above. Moreover, cells have intrinsic mechanisms to tune properties of the electrical signal. For instance, cortical networks have mechanisms that facilitate context-dependent synchronization of different subnetworks within a fixed architecture. In other networks, such as the basal ganglia and spinal interneurons, ion channel mechanisms actively maintain a lack of correlation between nearby cells and this decorrelation may be important for executing smooth movements. Deterministic and stochastic dynamical systems models have been used to investigate the connections between molecular signaling and behavior. Robustness and plasticity. An important property of brain function is that it must continue to operate at each of the four levels outlined in the introductory paragraph despite variation and change in the properties at individual levels. This is true within individuals where properties change as a function of time due to development, meals, emotional and environmental factors, and synapse and cell death. It is also important to understand why system properties are so similar between individuals despite great differences in local detail. And finally, assumptions about the stability of function across species form the basis for conducting experiments on animals and drawing conclusions about human brain function. These kinds of "homeostasis" questions occur in all biological systems, but they are particularly interesting and important in studying brain function for two reasons. First, since neurons are inherently sloppy and stochastic devices, there must be active processes at both the cellular and network level to reliably detect and sharpen electrophysiological signals in the stochastic and noisy environment. Second, one of the most important properties of brain function at all four levels is that it is flexible and changeable on both short and long time-scales. How can brain systems be controlled and homeostatic, yet flexible and changeable at the same time? The answers will be fundamental for understanding brain function and will likely require new advances in stochastic dynamical systems.

### Katie Pollard

Gladstone Institutes, UCSF Human accelerated regions drive unique expression patterns during embryonic developmentThe dramatic diversity of form and function found between closely related species is likely driven by changes to non-coding DNA that modify the complex patterns of gene expression observed throughout development. To pinpoint regions of the human genome that evolved rapidly since divergence from the chimp-human ancestor, we developed a statistical phylogenetic method for detecting lineage-specific changes in the rate or pattern of nucleotide substitutions. We analyzed vertebrate whole-genome multiple sequence alignments and found 721 Human Accelerated Regions (HARs). The vast majority of HARs are located in unannotated non-coding regions of the human genome. However, they are enriched nearby transcription factors and developmental genes, and many have epigenetic marks and transcription factor binding sites suggestive of enhancer function. To test this hypothesis we trained a multi-kernel support vector machine using experimentally validated developmental enhancers and diverse feature data (e.g., k-mers, transcription factor (TF) binding sites, cell type specific histone modifications, chromatin state). We predicted that ~2% of the human genome and over 200 HARs function as enhancers in different embryonic tissues. To explore whether human mutations in HARs alter their function, we developed a novel measure of regulatory sequence divergence based on cumulative loss and gain of predicted TF binding sites and showed that it identifies enhancers whose mutations affect activity in vivo. We used regulatory divergence in combination with expression patterns and functions of nearby genes to predict which candidate HAR enhancers are most likely to affect human-specific developmental gene regulation. We tested 15 of these predictions with transient transgenic mouse enhancer assays that compare activity of ancestral and derived HAR sequences. We found many novel developmental enhancers, several of which have human-specific activity.

### Veronica Vieland

Professor, Pediatrics and Statistics, Nationwide Childrens Hospital Is the universe made of information?Previous work has suggested deep connections between statistical mechanics and certain aspects of both information theory and statistical inference, based primarily on the shared concept of entropy. In this talk I go beyond familiar information theoretic treatments of entropy to develop purely information-based interpretations of both the 1st and 2nd laws of thermodynamics. This allows us to ask and answer a question that has gone begging until now: What is the analogue of temperature (T) on the information/inferential side? I argue that the physical quantity T has a familiar, but surprising, interpretation as statistical evidence. Moreover, this formulation provides a template for measuring evidence on an absolute (Kelvin) scale for the first time. This has far reaching implications for bioinformatics, since the measurement and interpretation of statistical evidence is a critical element of how we make scientific use of bioinformatic results. In a more speculative vein, this work also raises the question of whether our physical theories require us to posit the existence of matter. If fundamental physical laws can be interpreted in purely informational terms, perhaps it is mathematically cogent to say that the universe is in fact made of information.

Mathematical analysis and modeling have played influential roles in the current and classical descriptions of sensory processing, object identification and representation. The bases for these descriptions have involved the properties of feedforward interactions, receptive-fields, and firing rates or spike counts and stimuli have typically been static in time and stereotypical (oriented bars, pure tones, ...). Successes include Hubel and Weisel (1981 Nobel Prize shared with Roger Sperry) and Barlow (Swartz Prize for Computational Neuroscience, 2009). There is a growing awareness that processing is not passive but active (e.g., Kleinfeld, Bower) that involves dynamic feedback loops and recurrent processing and that feedback may extend down to the sensory receptor level. This workshop will address the evolving research area of active sensory processing, such as the top-down responsive control of whiskers in the rat somatosensory system, and the mathematical modeling of these feedback systems and the principles and optimizations that might pertain. The notion of static receptive fields as described in over-idealized and restricted stimulus sets in laboratory settings is also under challenge when one considers that in real-world settings the scenes are much more complex and they are dynamic, constantly changing. A statistical framework for natural scene analysis seems much more appropriate. The workshop will consider the approaches of statistical representation of scenes and their possible realization in the brain. Futhermore, sensory systems are capable of rapid adaptation to scene dynamics, including the statistics of changing scenes, and models for such are under development (Fairhall, Riecke). So, what does the brain do with the processed sensory input? What scene aspects/cues are used in object identification and segregation; what commonalities group different individuals together; how do we categorize objects? Modeling challenges are presented by these questions and some will be addressed during the workshop. An interesting paradigm arises in the context of ambiguous scenes, such as the Necker cube or the face-vase image, in which multiple interpretations are perceived alternately. The dynamics of such alternations are stochastic and the differential equation models typically involve competition through mutual inhibition amongst the model neural subpopulations that are hypothesized to represent the two or more percepts. In the auditory context there are dynamic ambiguous stimuli that introduce another temporal layer and raise issues of what cues are used to define and track an auditory object through time. Issues that arise in the neural representations of scenes lead naturally to neural coding. What language/means do neuronal systems use internally to encode the features of an image? These questions are usually addressed from an information theory point of view. In which context is the temporal patterning of spike trains significant or is the mean firing adequate to carry the information? How do cell ensembles mutually represent features, i.e., what is the population code? Perceptions must be developed on the fly. Given some sensory tuning properties how might the parameters be chosen amongst cells to give the most efficient and rapid population code? Throughout the workshop we will ask about plausible mechanistic models that can implement the notions of active processing, coding strategies, adaptation features, and so on.

Two-week program May 20-31, 2013 is designed to introduce students to a variety of areas in Mathematical Biology through morning tutorials, afternoon computer labs, study groups on related topics, and tours of experimental laboratories doing quantitative work.

Nathan Keyfitz (1913--2010) made fundamental and highly influential contributions to demography over a long and productive career. His work was characterized by an elegance of approach and a depth of insight that came from a deep recognition of the interplay among models, data, and interpretation. This symposium, marking the 100th anniversary of his birth, will bring together a diverse set of scientists studying, to use Keyfitz's term, the mathematics of population. The main goal of the Symposium is to serve as a forum for presentation of ongoing research on the mathematics of population. The program will encompass research on human and non-human populations, and both theoretical and applied research. In bringing together both mathematical demographers and population biologists, the symposium will adhere to Keyfitz's view, from his first book to his last, that population itself as an object worthy of study, not limited to particular species: ``[This book] tries to gather together, and as far as possible to systematize, the most relevant parts of that large body of mathematical theory concerned with the growth processes of human and animal populations. '' Introduction to the Mathematics of Population (1968) ``... the general drift of their replies was that ... there was nothing that could be usefully added. We were monumentally wrong. We hadn't noticed the world of whales and birds and land animals, i.e., the world of biology.'' Applied Mathematical Demography, 3rd Edition (2005) The symposium program will be a mix of theoretical and applied work -- mathematical exercises as well as empirical work that make use of models and techniques that draw on mathematical demography. The symposium program will be structured so as to encourage maximum exchange among scholars in attendance. Sharing of work in progress will be encouraged (and therefore there will be no requirement to prepare manuscripts of presentations). The goal is to stimulate discussion, cooperation, and collaboration.

In the last decade, methods from modern discrete mathematics have been used with great success for solving a wide range of biological problems. Graph theory, Boolean networks, polynomial dynamical systems (including many agent-based models), Petri nets, Groebner bases and other elements from algebraic geometry and modern algebra have rapidly gained popularity and have become essential tools for mathematical biology research. Relatively little progress has been made, however, in introducing those techniques to the mainstream undergraduate mathematical biology curriculum even though for many of them the level of mathematical sophistication and the nature of the material are often entirely appropriate. Thus, while the more traditional mathematical biology topics including ODEs, PDEs, difference equations, and continuous dynamical systems have already successfully worked their way into classes and have become standard curriculum, discrete and algebraic mathematical techniques have remained relatively invisible. There is a growing gap between research and education with regard to utilizing algebraic methods and there is pressing need in the colleges and universities across the country for: 1) identifying and developing curricular materials focusing on discrete and algebraic methods for biology, and 2) preparing faculty with research interests in mathematical biology to teach undergraduate courses that stress the importance of these methods.

The workshop has two major goals: 1) Introduce current problems from biology that utilize discrete and algebraic methods at a level appropriate for undergraduates and outline the methods, models, and software as well as existing materials with examples, exercises, and projects. 2) Produce outlines of new curricular materials based on some of the workshop talks on topics for which no materials for undergraduate courses are available. Speakers will provide introductory examples and exercises/projects and participants will work through those, provide additional ones, and compile a list of notes and solution guidelines and outlines that, together with outlines of the main biological questions and mathematical methods, will form the core of new instructional modules on those topics. Links to the existing and newly developed material, together with approved video recordings of the lectures and the presentation slides, will be posted on the MBI's site to make the materials available to anyone who wishes to introduce the respective topics in their classes.

The workshop is intended to broaden the scientific perspective of young researchers (primarily junior faculty, postdocs, and senior graduate students) in mathematical biology and to encourage interactions with other scientists. Workshop activities include plenary talks and poster sessions, as well as group discussions on issues relevant to mathematical biologists. Several abstracts will be chosen for short talks as well as to be presented as a poster. We cordially invite young mathematical biologists to participate. For full consideration, please apply by May 1, 2013.

### 2011-2012

This workshop will be divided into two parts, a tutorial and a conference. The first two days are intended to introduce probabilists to important biological problems that can engage probability theorists.

These lectures will be delivered by well-known biologists. The last three days will focus on new mathematical questions in probability and statistics that have been stimulated by recent biological research.

An important goal of MBI is to communicate these questions to the mathematics community. Therefore it is intended that the talks will be accessible to probabilists who have not previously worked on questions arising in biology. The lectures will begin by giving the necessary biological background. Topics will include stochastic spatial models and other aspects of ecology and epidemiology; adaptive dynamics; population genetics and evolution including coalescent theory; cancer modeling; stochastic models in neuroscience; and systems/synthetic biology.

### Tony Ives

Zoology, University of Wisconsin Alternative states in long-term ecological time series### Guido Marcucci

Hem/Onc, The Ohio State University Gene-microRNA networks in Acute Myeloid Leukemia: biology, prognostic and therapeutic implicationsSpread of infectious diseases remains a major threat. It has been a central and current challenge in mathematical biology to show how mathematical modeling and analysis can facilitate understanding of mechanisms of disease transmissions and thereby, provide guidance for designing disease control strategies under rapid social and environmental changes. Among the various factors that affect the disease spread are spatial dispersal and time lags, with the former due to the increasing inter-connections of the world/environmental changes and the latter as a result of the disease latency (e.g., in Influenza, HIV and and Malaria), postponed relapses of diseases (e.g., Herpes and TB), the stage-development of hosts, as well as the delay in implementing intervention strategies. The worldwide spread of SARS in 2003-04 and the 2009 H1N1 influenza pandemic clearly demonstrate the importance of incorporating time delay and spatial dispersal into human infectious disease models, and the rapid spread and establishment of West Nile virus and Lyme disease in North American is another example showing how spatial movement of migratory animals facilitates the spatial propagation. In order to reflect the aspects of spatial dispersal and time lag, ordinary and partial differential equation models need to be replaced by models with infection age and spatial structure, leading to systems of delay differential equation with spatial diffusion/dispersal which are infinite dimensional by nature. Disease evolution and ecology also have significant impact on the spread dynamics and need to be incorporated into models.

This workshop aims to bring together applied mathematicians, biologists and researchers from health institutes/departments to (i) examine and refine exiting models; (ii) present new results on disease models with time lags, spatial dispersal and evolutionary factors incorporated; (iii) exchange ideas among researchers in the related areas; (iii) discuss future directions in research of disease dynamics; and (iv) initiate collaborations in focused areas related to global air traffic network; seasonally migratory birds; impact of environmental changes on animal dispersal networks and disease spread.

### Dalin Tang

Professor, Department of Mathematical Sciences, Worcester Polytechnic Institute Computational Human Ventricle Models for Surgical Optimization Based on Patient-Specific Magnetic Resonance ImagingAcknowledgement: This research was in collaboration with Pedro Del Nido, MD, William E. Ladd Professor of Surgery, Chairman of Cardiac Surgery, and Tal Geva, MD, Director of Cardiac MRI Department, Children's Hospital Boston, Harvard Medical School, USA. It was supported in part by NIH R01 HL089269 (del Nido, Tang, Geva), NIH-R01 HL63095 (PJdN), and NIH- 5P50 HL074734 (Clinical Trial, PI-Geva).

Many stochastic features of intracellular processes have close counterparts in population biology. Intrinsic and extrinsic noise in gene expression are similar to demographic and environmental noise in the sizes of metapopulations, with expression bursts corresponding to litter sizes. The near-critical dynamics when two subunits form hetero-dimers are in turn similar to gender-balance fluctuations for organisms that form couples, while intracellular incompatibility is similar to the mutual exclusion principle in ecology. The effects of the cell cycle on chemical abundances resemble seasonality effects on populations, while partitioning errors at cell division are similar to the combination of migration and death before returning to breeding grounds. Both fields also study density-dependent negative and positive feedback loops formed through mutual interactions between agents.

Though the selective pressures are different, there are very strong synergies between these two fields, both in terms of the effects studied and the mathematical methods used. This workshop will exploit those synergies by bringing together researchers who study stochastic aspects of cell and population biology.

### Steven Cox

Department of Computational & Applied Mathematics, Rice University Toward a minimal model of a large spiking cell### Charles (Russ) Hille

Professor, Department of Biochemistry, University of California, Riverside Mathematical Models for Enzyme Reactivity: A Case Study in Xanthine OxidaseFree boundary problems (FBPs) are concerned with the solution of a system of PDEs in a domain whose boundary is unknown in advance. As a part of the solution one needs to determine the (free) boundary of the domain. Classical FBPs include melting or solidification of materials, contact problem in elasticity, and fluid flows. The study of these problems led to the development of general theories, including the theory of variational inequalities and the regularity theory of the free boundary for variety of problems.

More recently new FBPs have emerged in mathematical biology, such as models arising from tumor growth, wound healing, and movement of cellular organisms.

The proposed workshop is, in a sense, a follow-up to the program on FBPs held at MSRI during the first half of 2011. The workshop will bring together researchers, including some who participated in that program, together with mathematical biologists who are working on FBPs arising in biology.

The aim of the workshop is to introduce a broad FBPs community to new free boundary problems that arise from significant biological processes, with the hope that the study of such problems will stimulate the development of new mathematical theories, as well as advance theoretical biology.

### Leonid Berlyand

Professor, Department of Mathematics, Pennsylvania State University Kinetic models of swimming bacteria in semi-dilute limit* Numerical modeling. Bacteria are modeled as self-propelled point force dipoles subject to two types of forces: hydrodynamic interactions with the surrounding fluid and excluded volume interactions with other bacteria modeled by a Lennard-Jones-type potential. This model, allowing for numerical simulations of a large number of particles, is implemented on the Graphical Processing Units (GPU), and is in agreement with experiments.

* Analytical study of dilute suspensions. We introduced a model for swimming bacteria and obtained explicit asymptotic formula for the effective viscosity in terms of known physical parameters. This formula is compared with that derived in our PDE model for a dilute suspension of prolate spheroids driven by a stochastic torque, which models random reorientation of bacteria ("tumbling"). It is shown that the steady-state probability distributions of single particle configurations are identical for the dilute and semi-dilute models in the limiting case of particles becoming spheres. Thus, a deterministic system incorporating pairwise hydrodynamic interactions and excluded volume constraints behaves as a system with a random stochastic torque. This phenomenon of stochasticity arising from a deterministic system is referred to as self-induced noise.

* Kinetic collisional model-work in progress. Most of the previous work on bacterial suspensions ignores collisions. These inelastic interactions lead to an alignment of the nearby-swimming bacteria, which has been indeed observed experimentally. To understand the onset of collective motion in the above model, we investigate the correlation of bacterial velocities and orientations as a function of the interparticle distance. We seek to capture a phase transition in the bacterial suspension - an appearance of correlations and local preferential alignment with an increase of concentration. A probabilistic model for the distribution function for bacterial positions and orientations will be derived in the presence of self-induced noise.

Collaborators: PSU students S. Ryan and B. Haines, and DOE scientists I. Aronson and D. Karpeev (both Argonne Nat. Lab)

### Brent Lindquist

Applied Mathematics & Statistics, Stony Brook University Data-Based Analysis of Winner-Loser Models of Hierarchy Formation among AnimalsWe review winner-loser models, the currently popular explanation for the occurrence of linear dominance hierarchies, via a three-part approach. 1) We isolate the two most significant components of the mathematical formulation of three of the most widely-cited models and rigorously evaluate the components' predictions against data collected on hierarchy formation in groups of hens. 2) We evaluate the experimental support in the literature for the basic assumptions contained in winner-loser models. 3) We apply new techniques to the hen data to uncover several behavioral dynamics of hierarchy formation not previously described. The mathematical formulations of these models do not show satisfactory agreement with the hen data, and key model assumptions have either little, or no conclusive, support from experimental findings in the literature. In agreement with the latest experimental results concerning social cognition, the new behavioral dynamics of hierarchy formation discovered in the hen data suggest that members of groups are intensely aware both of their own interactions as well as interactions occurring among other members of their group. We suggest that more adequate models of hierarchy formation should be based upon behavioral dynamics that reflect more sophisticated levels of social cognition.

### Mark Berliner

Statistics, The Ohio State University Statistical Approaches to Combining Models and ObservationsNumerical models and observational data are critical in modern science and engineering. Since both of these information sources involve uncertainty, the use of statistical, probabilistic methods play a fundamental role. I discuss a general Bayesian framework for combining uncertain information and indicate how various approaches (ensemble forecasting, UQ, etc.) fit in this framework. A paleoclimate analysis illustrates the use of simple physics and statistical modeling to produce inferences. A second example involves glacial dynamics and illustrates how updating models and data can lead to estimates of model error. A third example involves the extraction of information from multi-model ensembles in climate projection studies.

Most biological systems from the subcellular to the population population level must solve the following difficult problem. They must continue to function reliably despite continually changing environmental inputs and despite individual differences in internal parameters due to genetic polymorphisms. That is, their functions should be robust to natural biological variability. On the other hand, these systems must also respond robustly and change their functions in response to biologically important external or internal signals. The biological systems that we see have evolved elaborate regulatory mechanisms in order that they can accomplish both tasks. Examples include metabolic and neural networks, development, adaptation, and population diversity. Most of these systems are not resting at equilibria, but rather exist in a dynamic stochastic equilibrium. Thus the mathematical issues involve understanding when this stochastic equilibrium is relatively stable and when it makes large shifts in response to appropriate biological signals.

The era of quantitative biology, and abundant data, calls for theoreticians and and experimentalists to address a fundamental scientific question: how can we learn as much as possible about the biological system we are studying - and make justified inferential statements about it - on the basis of combining theoretical models and experimental data? Related questions include: how to identify model parameters or test hypotheses given experimental data; how to evaluate model adequacy and inform model refinement; how to choose amongst a set of candidate models; and how to determine optimal experimental design to maximise information in the data.

Exciting progress is being made on these challenging issues. This workshop will bring together foremost researchers from the fields of biology, applied mathematics, statistics, and computer science to discuss recent advances in statistical inference for mathematical biology.

### Sarah Wheelan

Assistant Professor, Oncology Biostatistics and Bioinformatics, Johns Hopkins University The "top ten" are just the tail: A correlation method to uncover the rest of the elephant in high throughput biology data### Xihong Lin

Professor, Department of Biostatistics, Harvard University Design and Analysis of Whole Exome (Genome) Sequencing Association StudiesThe study of epidemiology, evolutionary biology and immunology are well-developed fields in their own right. However, current problems in disease dynamics have arisen that cross these disciplinary boundaries and where stochastic modeling and methods are essential to progress in these fields. Stochasticity plays an important role in the study of emergence of new diseases, pathogen evolution in response to control strategies or therapies, chance interactions of multiple species or multiple pathogens, variability in the host immune response, and disease propagation locally and globally. Tools from branching processes, percolation theory and network theory have demonstrated the importance of connectivity and cluster size in disease spread. The study of stochastic epidemic models has provided information about the duration and final size distributions, the probability of pathogen extinction or persistence and the quasistationary distribution. The availability of increasing amounts of data on within-host pathogens and on recent epidemics and the increase in computational power allow more accurate predictions of future trends and enable model predictions to be statistically tested and the uncertainty quantified. New mathematical, statistical and computational approaches for discrete- and continuous-time processes are needed to realistically model, analyze, compute and test the within-host and the between-host variability in response to a pathogen invasion and to connect the large-scale stochastic spatial epidemic or pandemic models to the small-scale within-host pathogen dynamics. Through collaboration among mathematicians, statisticians and applied scientists, important interdisciplinary problems in epidemiology, immunology and evolutionary biology can be addressed which will involve challenges in model development, statistical analysis, and computational methodology.

### Paul Bressloff

Mathematics Department, University of Utah Traveling waves in a neural field model of binocular rivalryA number of phenomena in visual perception involve wave-like propagation dynamics. Examples include perceptual filling-in, migraine aura, and the expansion of illusory contours. Another important example is the wave-like propagation of perceptual dominance during binocular rivalry. Binocular rivalry is the phenomenon where perception switches back and forth between different images presented to the two eyes. The resulting fluctuations in perceptual dominance and suppression provide a basis for non-invasive studies of the human visual system and the identification of possible neural mechanisms underlying conscious visual awareness. In this talk we present a neural field model of binocular rivalry waves in visual cortex. For each eye we consider a one-dimensional network of neurons that respond maximally to a particular feature of the corresponding image such as the orientation of a grating stimulus. Recurrent connections within each one-dimensional network are assumed to be excitatory, whereas connections between the two networks are taken to be inhibitory (cross-inhibition). Slow adaptationis incorporated into the model by taking the network connections to exhibit synaptic depression. We derive an analytical expression for the speed of a binocular rivalry wave as a function of various neurophysiological parameters, and show how properties of the wave are consistent with the wave-like propagation of perceptual dominance observed in recent psychophysical experiments. In addition to providing an analytical framework for studying binocular rivalry waves, we show how neural field methods provide insights into the mechanisms underlying the generation of the waves. In particular, we highlight the important role of slow adaptation in providing a "symmetry breaking mechanism" that allows waves to propagate. We end by discussing recent work on the effects of noise.

### Brian Smith

Professor, Department of Entomology, Arizona State University Plasticity in early sensory coding: It's role in solving the generalization problem for complex, variable natural odorsOdors are important cues for identification of many types of objects that animals need for survival. Natural odors are typically mixtures of up to a few dozen chemical components. Important information about odor 'objects' is often encoded in the ratio of components in the mixture. However, this odor mixture problem is complicated by two factors. First, many times the information channel is composed of a submixture of the overall mixture composition. Second, the ratios of components in the submixture can vary from one object to the next, which means that animals must learn to 'generalize' across a range of variation among objects that mean the same thing. Floral odors, for example, are important for honey bees to locate nectar and pollen sources that their colony needs for survival. Honey bees need to learn about the range of variation in odor composition so that they can optimally include flowers that have resources and exclude flowers with similar odors but which do not have nectar or pollen. I argue that nonassociative and associative plasticity in neural networks involved in early sensory coding is critical for extracting the relevant features of an odor mixture and setting up categories of odor objects. This plasticity can enhance decisions about pattern matching and multimodal associations in later processing in the brain.

In many situations it is adequate to assume that systems are homogeneously mixing and to take the limit of large populations, but in a number of cases the spatial distribution of individuals changes the behavior of the system. This workshop will focus on the impact of these effects on a wide variety of systems ranging from the scale of microbes to populations of plants and animals on a local and global scale. The workshop will bring together people who prove theoretical results about models, those use numerical and simulation results in their analysis, and involve a number of participants who work closely with biologists to analyze data. In this way we seek to stimulate the development, analysis, and application of new models.

### Greg Wray

Duke University Evolutionary origins of human transcriptomesThe genetic differences that separate humans from other great apes seem modest, yet we are a prominent phenotypic outlier in several regards. Although little is known about the genetic and molecular bases underlying uniquely human traits, changes in gene regulation are likely an important component. My group is currently investigating changes in the transcriptomes of multiple tissues that accompanied human origins. We use genome-wide functional assays to identify the molecular mechanisms that mediate evolutionary changes in transcription, including the role of chromatin configuration and the function of noncoding RNAs. These assays highlight genomic regions of particular interest, where we have carried out focused functional analyses that provide insights into the evolution of human diet and brain size.

Over the past 40 years, tissue engineering / regenerative medicine (TERM) has grown from concepts to established medical treatments used in over one million patients. As of 2007, there were approximately 50 firms offering TERM products with annual sales in excess of $1.3 billion, which represent more than a ten-fold increase from 5 years before. Despite the impressive economic growth of the field and its growing impact on human health, often TERM is understood largely at a phenomenological level. If one considers a historical perspective, developing fields often begin at such a phenomenological stage. For example, chemical engineering initially considered each type of chemical plant as unique. Later in the field's development, it was recognized that regardless of what chemical is being made, a number of 'unit operations' were involved (e.g., distillation, mixing, pumping). A major development in the practice of chemical engineering was made when it was recognized that these different unit operations could be understood in the terms of just a few fundamental processes such as transport phenomena, reaction kinetics, and thermodynamics. Importantly these fundamental processes can be rigorously understood with mathematics, thereby enabling one to understand and rationally design complex systems from a bottom-up approach. TERM has already advanced from considering each application (e.g., tissue engineering of a blood vessel) as unique to considering the underlying and unifying fundamental processes such as cell proliferation, differentiation, and migration. A critical challenge in the TERM field is to develop a rigorous mathematical understanding of these fundamental processes and to develop appropriate mathematical or computational approaches to enable one to use this rigorous understanding to rationally design complex biological systems relevant to TERM. The workshop will contribute to this critical challenge by bringing together a mix of participants with clinical, basic biology, engineering and mathematical backgrounds.

Molecular networks drive many of the cellular and organismal processes that influence the phenotype of an organism, and have become a central focus of systems biology. To understand the complex dynamics underlying these processes, dynamic mathematical and computational models are needed. Several different approaches have been used successfully for this purpose. Beyond differential equations models, a range of discrete models has been used for this purpose, both deterministic and stochastic, for instance Boolean networks and their generalizations, and dynamic Bayesian networks. This workshop will focus on modeling of molecular networks, in particular gene regulatory networks, with an emphasis on discrete modeling approaches, including stochastic aspects of networks. In addition to models of specific molecular networks, it will explore questions such as the relationship between network structure and their dynamics, design principles of molecular networks, and the evolution of networks. Both mathematical and biological aspects of molecular network modeling will be discussed, and the workshop will open with tutorial talks on both.

Modern statistics problems, from areas such as evolutionary biology, medical imaging, and shape analysis, increasingly deal with data sampled from spaces that are singular but naturally stratified; that is, the spaces behave nicely at most points, but at certain points the smooth structure becomes degenerate, such as when the space is composed of two or more intersecting smooth pieces. Key examples of stratified spaces are shape spaces (representing equivalence classes of point configurations under operations such as rotation, translation, scaling, projective transformations, or other non-linear transformations) and tree spaces (representing metric phylogenetic trees on fixed sets of taxa). Generalizing these two examples leads to algebraic varieties and polyhedral complexes, respectively. Applications require knowledge of the asymptotics of distributions on such spaces. Developments in this "stratified statistics" take their cue from more classical geometric statistics, where data points are sampled from smooth manifolds, or from neighborhoods of embedded manifolds. Now, however, interesting algebraic geometry and combinatorics join the mix as methods for controlling behavior near strata of lower dimension, where the sample space can be singular nearby. Asymptotics on such spaces are governed not only by their local structure, but also by global topology (of the space and the data). Thus there has been increasing interest in the recently emerged method of statistical persistent homology. First results from the systematic study of nonparametric statistics on data sampled from stratified spaces include central limit theorems (CLTs) that illustrate nonclassical behavior, particularly when the mean lies on a lower stratum. The related asymptotics in this surprisingly common circumstance can depend in a crucial way on global geometry. Other first results include concrete combinatorial constructions of sample spaces. Interpretations for these results, particularly nonclassical CLTs, are immediately useful in specific applied problems from phylogenetics, brain imaging, and human binocular vision, but they raise fundamental pure mathematical questions relating curvature to asymptotics of probability distributions in non-smooth settings. Many of these investigations were initiated by a Working Group at the Statistical and Applied Mathematical Sciences Institute (SAMSI) program on analysis of object data. This MBI workshop aims to stimulate progress and cross-fertilization in the rapidly moving areas of theoretical and applied stratified statistics by gathering a mix of researchers with interests in biology, geometry, combinatorics, topology, probability, and statistics. The hope is to develop stratified methods to solve problems arising from investigations on existing biological and medical data sets, particularly those involving trees and more general shapes.

Two-week program May 29 to June 8 designed to introduce students to a variety of areas in Mathematical Biology through morning tutorials, afternoon computer labs, study groups on related topics, and tours of experimental laboratories doing quantitative work.

The Workshop will be held at the Mathematical Biosciences Institute and will have instructors from across North America whose research expertise is stochastic modeling in biological systems. Some of the topics to be covered include Markov chains, birth and death processes, branching processes, Brownian motion and diffusion processes, stochastic differential equations, and agent-based models. Applications of stochastic processes will come from epidemiology, ecology, phylogenetics, microbiology, evolutionary biology, and genetics. The workshop will consist of lectures on mathematical and statistical methods for stochastic processes in biological systems and daily computer and analysis activities. In addition, each student will work on a research project over the duration of the program with a team of four or five participants. Applications received by January 13, 2012 will receive full consideration. Members of the organizing committee are: Linda Allen (Texas Tech), Laura Kubatko (Ohio State University), Suzanne Lenhart (University of Tennessee, Knoxville); Libby Marschall (Ohio State University), and Lea Popovic (Concordia University).

PSW@MBI is a week-long workshop where participating mathematical modelers tackle questions proposed by life science researchers. Similar workshops have provided fresh perspectives and new ideas to proposed questions and established new interdisciplinary collaborations between theoreticians and life scientists. The workshop gives the opportunity to practitioners and researchers in medicine and the biosciences who present problems to exploit the expertise of applied mathematical faculty, postdoctoral fellows, and graduate students in working toward solutions to their problems. Workshop Format Participants will include between 50-60 applied mathematicians, statisticians and domain experts. Problems will be presented on the first day and participants will divide into teams of 6-10 self-selected people each. The teams will collaborate and brain-storm on their problems, and present their solution on the final day of the workshop. Problem presenters have domain knowledge, which is needed throughout the workshop and will be available during the workshop to provide background information. Deliverables The teams will prepare reports for the problem sponsors shortly after the end of the workshop. Cost Accepted participants will receive partial travel support, hotel, and a small per diem.

The workshop is intended to broaden the scientific perspective of young researchers (primarily junior faculty, postdocs, and senior graduate students) in mathematical biology and to encourage interactions with other scientists. Workshop activities include plenary talks and poster sessions, as well as group discussions on issues relevant to mathematical biologists. Several abstracts will be chosen for short talks as well as to be presented as a poster. We cordially invite young mathematical biologists to participate. For full consideration, please apply by May 1, 2012.

### 2010-2011

The MBI Bootcamp on Cancer Modeling is aimed at young researchers in the biological and biomedical sciences, although young researchers in the mathematical sciences will both benefit from and be accepted into the bootcamp. The bootcamp will focus on three themes surrounding cancer modeling: signaling pathways, tumor growth, and radiotherapy.

Three speakers will address each theme: the first will provide the general biological background to the theme, the second will review the relevant modeling, while the third will deliver a state-of-the-art talk and suggest directions/challenges for future research. Each theme will also include a lab session where participants can experiment with pre-programmed models.

Plant development can be considered far beyond the original context of timing and elementary topology of organ development. We may explore its process origins in biochemistry; its mutual coupling to the environment as in energy balance and organ microclimate; the geometry of resources (rectilinear radiation, patchy and diffusive nutrients) that in turn conditions the necessary geometry of plant organs; the selection pressures that drive the evolution of diverse patterns of geometry and timing, and the population-genetic and phylogenetic constraints on such evolution; the ecological interactions with conspecifics as both competitors and mates, other resource competitors, herbivores, pollinators, diseases, and other biota that condition timing and geometry and the responsiveness of both. Exploration of these topics offers opportunities for biologists and mathematicians to meet in modes of modelling from first principles, inverse modelling, empirical modelling and data analysis, and to inform not only each other's major disciplines but also to link subfields within each discipline. Forward models may originate as functional models from basic levels of biochemistry and biophysics. One may also formulate models that begin with selection pressures to estimate how plants "should" function - simple optimization models, which must be generalized to address constraints that are variously functional, population-genetic, or phylogenetic.

The workshop has a goal of addressing these topics as items of intrinsic interest. Furthermore, it has a goal of involving young researchers to continue the development of mathematical biology and to take it in new directions. Finally, the workshop should engage us in defining the major challenges that remain. As an example of this last item, we may consider the problem of non-extinction: What is the geometry of the high-dimensional niche space that allows individual species to persist despite great numbers of extreme events in abiotic and biotic conditions, and how does this particularly relate to their biology, both physiological and developmental?

### Kc Huang

Professor, Biochemistry and Electrical Engineering, Stanford University Physical mechanisms for bacterial cell shape determination### H.T. Banks

Professor, Center for Research in Scientific Computation, Center for Quantitative Sciences in Biomedicine, North Carolina State University Relaxed Controls, Preisach Hysteresis, And Mixing Distributions In Statistical Inverse ProblemsCircadian (~24-hour) rhythms control the timing of many biological processes including leaf movements in plants and sporulation in fungi. Advances in understanding the biological mechanism of plant and fungal clocks have also helped inspire clock research in higher organisms. This workshop brings together theorists and experimentalists to better understanding timekeeping in plants and fungi and how they relate to clocks in higher organisms.

We plan to organize this workshop around the following themes:

- How do multiple feedback loops within the Neurospora and aribidopsis clocks interact? How do individual feedback loops regulate circadian behavior?
- How do circadian clocks keep a near constant period despite a widely changing environmental conditions?
- How can mathematical models be matched to time series data?
- How do circadian rhythms synchronize to the external world and the circadian clocks of other cells?

The goals of this workshop are to bring together theorists and experimentalists, some of whom are new to mathematical modelling or circadian rhythms, to foster interdisciplinary collaborations. The workshop will begin with a 2 day tutorial focusing on theory for experimentalists one day and the basics of circadian timekeeping for theorists on the second.

This is the sixth in a series of biannual conferences honoring David Blackwell and Richard Tapia, two seminal figures who inspired a generation of African-American, Native American and Latino/Latina students to pursue careers in mathematics.

Carrying forward their work, this one and a half day conference will:

- Recognize and showcase mathematical excellence by minority researchers
- Recognize and disseminate successful efforts to address under-representation
- Inform students and mathematicians about career opportunities in mathematics, especially outside academia
- Provide networking opportunities for mathematical researchers at all points in the higher education/career trajectory

The conference will include a mix of activities including scientific talks; poster presentations; a panel discussion of career opportunities in mathematics, and another panel on recruitment and retention of a diverse mathematics workforce; and ample opportunities for discussion and interaction.

**2010 Blackwell-Tapia Prize:** The National Blackwell-Tapia Committee is pleased to announce that the 2010 Blackwell-Tapia Prize will be awarded to Dr. Trachette Jackson (Department of Mathematics, University of Michigan). This prize is awarded every second year in honor of the legacy of David H. Blackwell and Richard A. Tapia.

**Special Event:** Dr. Richard Tapia will give a public lecture at the Columbus Science Museum (COSI) on Thursday evening November 4 at 7:00pm. Admission is free and the public is welcome.

### Daniel Schoenberg

Molecular & Cellular Biochemistry, The Ohio State University Re-capping messenger RNAs in the cytoplasm: A new aspect of gene expression that redefines the scope of the transcriptomeIn the dogma of molecular biology cap addition only occurs in the nucleus and its loss in the cytoplasm is irreversible. There are numerous reasons why this made sense, the most compelling of which is the concentration of the responsible protein (capping enzyme( in the nucleus and the biochemistry of cap addition, which requires a substrate with 2 phosphate groups, not the single phosphate that is left after the cap is removed. I will present work from my lab describing a new mechanism by which the cap can be restored onto cytoplasmic mRNAs after it has been removed by decapping or endonuclease cleavage. This work began with re-examination of results published in 1992 and never followed up describing a cap or cap-like structure on decay products of Ÿ-globin mRNA in patients with Ÿ-thalassemia (Cooley's anemia), a fatal disorder of hemoglobin production that is caused by inheriting two copies of this gene with a premature termination codon. I will describe how we validated those results, some of the basic biochemistry behind the re-capping process, and the identification and properties of a cytoplasmic complex that contains the enzymes that are responsible for mRNA re-capping. The loss of the cap is one of the key steps by which microRNAs repress translation and silence gene expression, and my talk will cover the cycle by which cytoplasmic re-capping may function in re-activating these silenced mRNAs. I will also touch on the possible links between cytoplasmic capping and the activation of neuronal or maternal mRNAs that must be kept in a silenced state until their translation is required. Although at this point it is highly speculative, cytoplasmic capping may also expand the proteome by enabling the translation of different forms of a protein from mRNAs that have lost the cap and sequences from their 5' ends, and the challenges the complexity of this process presents for bioinformatics, molecular and cell biology.

### Stephen Ellner

Department of Ecology and Evolutionary Biology, Cornell University Rapid evolution: coupling ecological and evolutionary dynamics### Thierry Emonet

Professor, Molecular, Cellular and Developmental Biology, Yale University Chemotaxis of the individual bacterium### David Cowburn

Professor, Albert Einstein College of Medicine, Yeshiva University Nmr/structural biology - future promise needs new applied mathThe experimental process is very slow because of

Intrinsic low sensitivity of method

Buggy whip approaches to data analysis and use of prior known information -over-focus on graphical interfaces and link to spectroscopy

There is no 'master equation'

Need improved, faster methods which incorporate chemical information appropriately, use probability methods in an integrated way, and make reasonable assumptions about averaging and motions.

Incorporate known information into experiment design for assignment and data collection

Break separation of assignment and structure calculation

Identify region of conformational spaces available from NMR data

Complete the loop of analysis and place complete analysis in a proper statistical framework

Use predictive power of integrated approach for

Speed up for structural genomics

Synthetic reconstruction and analysis of muilti-domain/ complexes for therapeutic target evaluation

Predictive structure/ function relationships for newly engineered systems (including de novo biology)

### Daniel Janies

Department of Biomedical Informatics, The Ohio State University Assembling the tree of life### Michael Reed

Professor, Mathematics, Duke University Mathematical models of serotonin metabolism: What is the mechanism of action of SSRIs?Despite more than 50 years of research, the etiology of depressive illness remains unknown. A hypothesis that has been central to much work in pharmacology and electrophysiology is that depression is caused by dysfunction in the serotonergic signaling system. In recent work, with Janet Best (OSU) and H. Frederik Nijhout (Duke), a mathematical model of a serotonergic synapse was created to study regulatory mechanisms in the serotonin system. After an introduction to the serotonin system, the model will be described as well as comparisons to experimental results. We will discuss why it is so difficult to understand the mechanism of efficacy of selective serotonin reuptake inhibitors (SSRIs). We will present predictions of the model as well as a new hypothesis for the mechanism of action of the SSRIs.

The spread of invasive species is a key applied problem in ecology. In North America, invasive exotic species are widespread, ranging from gypsy moth to Asian longhorn beetle to weedy plants. The associated costs are immense, by some estimates exceeding $100 billion US per year. While many invasive species are introduced from Asia or Europe, others, like mountain pine beetle, are simply spreading into new areas of North America, due to processes such as climatic change.

Early models for invasive species were nonlinear reaction diffusion equations such as Fisher's equation, which describes quadratic growth coupled to Brownian motion. Here the analysis of traveling waves and of the convergence of initial data to wave solutions has been a fruitful area of classical mathematical research. The traveling wave speed, interpreted biologically as the rate of spread of the introduced population, has successfully predicted spread rates of many introduced species, but has failed dramatically with others. Modifications of these equations to include long-distance dispersal, stage structure, spatial heterogeneity, stochasticity, Allee effects, and nonlinear interactions with resident species (eg, competition or predation) have driven new advances in the theory of nonlinear dynamical systems, while, at the same time, providing a more realistic framework for the study of invasions.

The nonlinear dynamical systems models are not simply mathematical abstractions of key processes. They are the quantitative formulation of underlying hypotheses, and they provide the means for testing the hypotheses against data.

In parallel with the development of new mathematical models, has been increasing availability of detailed spatio-temporal datasets that can be used to track actual invasion processes. These datasets can be accessed via Geographic Information Systems (GIS), and, in some cases, they show yearly changes in the extent of invaders. Classic data sets include those for mountain pine beetle in western Canada and US, gypsy moth in the eastern US, and Spartina in coastal California.

New powerful statistical methods based on intensive computational algorithms such as the Markov Chain Monte Carlo methods, data cloning, profile likelihood based on cascading parameters, composite likelihood and estimating functions make it possible to interface these detailed data sets with the new realistic dynamical system models. This interface allows the models to be assessed, tested and validated against the real data for the invasions. Hypotheses regarding key factors governing invasions can be evaluated, and the means for controlling the invasions/adapting to the invasions can be investigated. This interface between nonlinear dynamical systems, large datasets and statistical and computer methods has only become possible recently, with the growth of large data sets via remote sensing, with the advent of new powerful computers, and with the development of new statistical methods. This interface provides fertile ground for new mathematical, statistical and scientific advances.

The purpose of the MBI workshop on invasive species is to bring together researchers from different groups: mathematicians, biologists and statisticians to develop the new interdisciplinary approaches to biological invasions described above. Possible participants are given below.

### Katia Koelle

Professor, Department of Biology, Duke University A dimensionless number for understanding the evolutionary dynamics of antigenically variable RNA viruses### Hugh Wilson

Spatial and Computational Vision, York University Nonlinear Dynamics of Binocular Rivalry & Migraine AurasInsect groups generate a wide range of interesting collective patterns and behaviours, for example the formation of ant trails, the building of elaborate nests, collective movement of honey bee swarms and marching locust bands, to name just a few. The complex non-linear nature of the mechanisms underlying such collective behaviour has generated a great deal of theoretical interest from mathematicians and physicists. Collective insect behaviour is one area where mathematical modelling and experiment have lived well side by side.

Collective insect behaviour is interesting from the point of view of evolution because understanding the non-linear dynamics provides insights into self-organization in natural systems which in turn serves as an inspiration for computer algorithms and robots. Many of the emergent collective phenomena involve synchronization where large numbers of individuals move in the same direction or co-ordinate their activities. Lastly, mass movement of insects such as grasshoppers and crickets involve large-scale interactions with the environment, whereby feedback between individuals within a group and their environment determine collective patterns.

The biosciences provide rich grounds for mathematical problems, and many questions require the development of new mathematical theory and algorithms. With this workshop we give particular attention to new ideas and developments in dynamical systems. We have chosen four themes to showcase how the biosciences inspired recent progress: systems with delays, systems with multiple scales, dynamics of networks, and stochastic bifurcation theory. The meeting will highlight and discuss new directions of fundamental research in each of the themes, how they are connected, and how they contribute to the understanding of specific questions in bioscience applications.

### A.J. Hudspeth

Professor, Laboratory of Sensory Neuroscience, Rockefeller University Making an effort to listen: mechanical amplification by myosin molecules and ion channels in hair cells of the inner earPlant-insect interactions have played a pivotal role in the development of modern coevolutionary theory, beginning with Darwin's initial insights into reciprocal adaptation between plants and pollinators. When Ehrlich and Raven published their now classic study of coevolution between butterflies and plants in 1964, the link between the development of coevolutionary theory and plant-insect interactions was cemented. Since this time, numerous studies of plant-insect interactions have revealed an important role for coevolution, even as the perceived importance of coevolution for the overall structure of plant-insect communities has waxed and waned. Currently, much of the research on the ecology and evolution of plant-insect interactions, both mutualistic and antagonistic, is expanding from simpler two-species frameworks to consider coevoluton in the context of multispecies communities.

*The Geographic Mosaic Theory:* The geographic mosaic theory focuses on how spatial variability in the abiotic and biotic environment shapes ecological and evolutionary dynamics of interspecific interactions. The geographic mosaic theory explicitly identifies coevolution as the driving force underlying the ecological dynamics and structure of biological communities. Much of the empirical work motivated by the geographic mosaic theory has focused on quantifying patterns of trait matching or local adaptation in interacting species, with plant-insect interactions representing several of the best studied cases. A general result that has emerged from this work is that species interactions exhibit a complex mix of local adaptation, local maladaptation, trait matching, and trait mismatching as predicted by the verbal theory. A substantial body of mathematical theory has been developed to elucidate whether these patterns are consistent with a geographic mosaic process, and if so, whether such a process is more likely than other simpler processes. The development of a robust mathematical framework for the geographic mosaic is essential for interpreting existing data and designing future empirical studies.

*Community Genetics:* Community genetics focuses on the role the genetic structure of component species plays in shaping the ecological structure and dynamics of biological communities. Thus, community genetics represents a marriage of the traditional disciplines of quantitative genetics, population genetics, and community ecology. As it is usually articulated, community genetics does not explicitly integrate the process of coevolution, although its potential importance is generally acknowledged. Empirical studies of community genetics have relied heavily on interactions between insects and plants. For instance, the long running studies of interactions between cottonwoods and insects conducted by Thomas Whitham and colleagues have clearly demonstrated that host genetics strongly influence the community of associated insect species. A wide variety of other studies, conducted in a diverse array of taxa, support the basic argument of community genetics - that integrating the genetic structure of the interacting species is important for any cohesive theory of community ecology. From a theoretical perspective, work in community genetics has been somewhat piecemeal, although excellent models have been developed and analyzed to address particular topics (e.g., see Neuhauser et al. for a particularly nice collection of examples). The development of a general theoretical framework for community genetics is an important goal, and essential for interpreting rapidly accumulating empirical data.

*The importance of evolutionary history:* A third area receiving increased attention recently has been the exploration of the role of evolutionary history in the assembly of communities and in the evolution of plant defense against insects, and insect adaptations. To date, there have been a few studies examining co-diversification of plants and insects. (Futuyma, Becerra, Funk), and ants and fungi (Mueller). Another set of studies explores the role of host plants in sympatric speciation and host shifts (Nosil, Feder); yet a third group examines multivariate trait space to understand constraints and tradeoffs in the evolution of defense under different biotic and abiotic conditions. The degree to which phylogenetic history predicts host use by insects varies among systems, and may benefit from broader theoretical approaches to this question.

*Synthesis:* Neutral theory suggests that how communities are assembled is largely agnostic to evolutionary processes. In contrast, strong evidence for coevolution between interacting species flies in the face of such approaches. We seek to understand how complex biological communities are assembled, what factors contribute to their stability or instability, and why the structure of such communities is often spatially variable. Discussing profitable avenues for the development of a mathematical framework which unifies multiple approaches to understanding the interplay between coevolution and community assembly will be an important focus of this workshop. An additional focus will be the development of statistical tools that can be used to evaluate the importance of reciprocal selection and ongoing coevolution for the composition, structure, and stability of plant-insect communities.

*Goals of the Workshop:*

- To discuss metrics (e.g., network structure, local adaptation, community heritability) with robust theoretical/statistical underpinnings that can be used elucidate the importance of coevolutionary processes in structuring plant-insect communities at local and regional scales.
- To discuss statistical techniques (e.g., path analysis; selective source analysis, etc.) for evaluating the importance of ongoing coevolutionary selection in multispecies communities of plants and insects.
- To discuss profitable avenues for the development of a cohesive theoretical framework that incorporates coevolution, multiple interacting species, spatial structure, evolutionary history and variable abiotic environments. This framework will thus formally link several of these different empirical approaches to communities.

### David Botstein

Professor, Department of Molecular Biology, Princeton University Extracting Biological Insight from Complex Genome-Scale Data: Connecting Growth Control and Stress Response in YeastThe results of these studies, which have involved collaborations with many other laboratories in the Lewis-Sigler Institute, include the following:

1) Expression of a substantial fraction (ca. 1/4) of the yeast genes is strongly correlated with the growth rate regardless of the limiting nutrient. Some genes are expressed more as growth rate increases (positive slope) and others are expressed more as the growth rate decreases (negative slope). These slopes are related to the periodic expression of the same genes in the metabolic cycle, which we have shown, by counting individual mRNAs by fluorescence in situ hybridization (FISH), is an intrinsic feature of yeast cell metabolism.

2) The levels of intracellular metabolites, in contrast, depend strongly on the limiting nutrient and relatively little on the growth rate. Only two (glutathione and trehalose) show strong negative slopes and a handful (e.g. ribose phosphate and fructose bis-phosphate) show strong positive slopes.

3) Starvation for phosphorus, sulfur or nitrogen ("natural nutrients") results in cell-cycle arrest, long-term (weeks) survival and sparing of residual glucose. Starvation, in auxotrophs, for leucine, uracil or histidine, in contrast, fail to arrest the cell cycle promptly, die much more rapidly and waste residual glucose. The glucose wasting is reminiscent of the Warburg effect seen in tumor cells.

4) Mutants that suppress starvation lethality and glucose wasting appear in genes already implicated in nutrient sensing. Genome-scale assessment of fitness during starvation provides a quantitative assessment of the contribution of each of the non-essential yeast genes to nutrient sensing and/or starvation survival.

It seems to us that much of what has been described as "stress response" would better be described as the consequence of slowing growth. The metabolic cycle, which separates oxidative and fermentative metabolism, appears to play a central role in growth-rate regulation. We are testing models in which metabolite levels, position in the metabolic cycle, external nutrient sensing as well as cell size are used to gate entry into the S-phase of the cell division cycle.

### Qing Nie

Biomedical Engineering & Mathematics, University of California, Irvine Noise Attenuation in Biological SystemsIn this talk, we will first introduce a new quantity called Signed Activation Time (SAT), which is found to be critical in determining noise attenuation capability of a feedback system. We will next study how noise amplification rates of several biological examples may depend on SAT and investigate strategies for noise attenuation in systems involving both extra-cellular and intra-cellular components. In particular, we will study boundary sharpening during Zebrafish embryonic development.

A major feature of biological science in the 21st century will be its transition from phenomenological and descriptive science to quantitative science. Revolutionary opportunities have emerged for mathematically driven advances in biological research. Currently, most experimental research in the life sciences is based on molecular biology or molecular level understanding. However, a much smaller amount of mathematical biology activity is based on molecular level understanding. Therefore, it is imperative to strengthen molecular based mathematical biology, particularly, the modeling and computation of molecular structure and dynamics. It can be envisioned that a dramatic transition in mathematical biology research will occur in the near future. Many of the next generation of leaders in mathematical biology will be working on molecular based research. Multiscale modeling and computation, a subject that has its root in mathematics, will be an important topic in mathematical biology.

This weeklong workshop will cover a wide range of topics in multiscale mathematical modeling of biological/biomolecular systems and their application to specific research problems. Topics include atomistic models; molecular dynamics; Brownian dynamics; continuum-discrete models; micro-macro models; implicit solvation models; electro-elastic models; fluid-electro-elastic models; Poisson-Boltzmann equation; Poisson-Nernst-Planck equations; microfluidics; nano-bio systems; man-made nanopores; biomolecular transport; synthetic (biomedical) and biological membranes; electrohydrodynamics of biomolecular systems; and differential geometry based multiscale models. Emphasis will be placed on the application of these models, theories and methods to protein structure and function, protein folding, DNA specification, protein-protein interaction, membrane proteins, ion channels, stimulus and ionic transport in membrane proteins, man-made nanopores, rational drug design, and drug discovery and delivery and protein sieving in an artificial kidney.

### Qiang Du

Pennsylvania State University Diffuse interface modeling of biomimetic membranesWe discuss diffuse interface (phase field) models of both single-component and multi-component vesicle membranes. We also consider models for the interactions of vesicles with an adhesive substrate and those with a background fluid. We present the mathematical derivations and compare results of numerical simulations with experimental findings.

### George Karniadakis

Department of Applied Mathematics, Brown University Multiscale Modeling of Hematological DisordersI will first present recent developments on the Dissipative particle Dynamics (DPD) -- a Lagrangian method that bridges the gap between continuum and atomistic scales. In particular, I will first discuss theoretical foundations of DPD, its relation to molecular dynamics (MD), and its use in modeling seamlessly blood flow interacting with blood cells (platelets, white cells and red blood cells (RBCs). Specific examples will be given for cerebral malaria and sickle cell anemia.

This work is supported by NIH and by the DOE/INCITE program and NSF/NICS for computations.

The goal of the workshop is to bring together biologists studying ocean and polar ecologies; oceanographers, biogeochemists, and climate scientists studying the changing physical habitats; and mathematicians with ecological and physical expertise. The two-way feedback interactions between ocean ecological systems and their physical environments have the potential to dramatically impact both marine biodiversity, and the planetary response to the changing atmosphere. The types of mathematics used to model ecological and physical processes are typically quite different. One of the exciting aspects of this workshop, and a reason to run it at MBI, is that we anticipate interesting new mathematical challenges arising from combining these different approaches to focus on modeling the feedback interactions between the ecological and physical systems.

The workshop will focus on two main themes:

1. Polar and sea ice ecologies

2. Phytoplankton and the carbon cycle.

These themes are particularly timely in that the impact of climate change on these systems has been quite pronounced. Moreover, these areas are further tied together through the interplay of a wide range of the length scales involved, from microscopic to many kilometers over oceanic regions. As with all aspects of mathematics and climate change, this is an emerging area, and part of the reason for running the workshop is to help identify the mathematical challenges and opportunities the emerging topics present.

Joint 2011 MBI-NIMBioS-CAMBAM Summer Graduate Program Mathematical Ecology and Evolution The 2011 Summer Graduate Program will be held at the Mathematical Biosciences Institute from July 25 to August 5, 2011. Summer school topics will include infectious disease, resource management, invasive species and evolution biology. Members of the organizing committee are: Fred Guichard (McGill University); Suzanne Lenhart (University of Tennessee at Knoxville); Yuan Lou (Ohio State University); and Libby Marschall (Ohio State University).

The Program will feature a number of researchers from the mathematical and biological sciences, each of them will work with the students for one day. The speakers will lecture in the mornings, followed by afternoon computer and analysis activity including work on projects. During the summer program each student is expected to work on one research project in a team of four or five participants. The following is a partial list of speakers:

* Linda Allen and Ed Allen, Texas Tech

* Chris Cosner, University of Miami

* Fred Guichard, McGill University

* Ian Hamilton, Ohio State University

* Alan Hastings, University of California at Davis

* Suzanne Lenhart, University of Tennessee at Knoxville

* Lea Popovic, Concordia University

* Joe Tien, Ohio State University

Graduate students from the mathematical, physical and life sciences are encouraged to apply. Application link will be posted soon. You will be asked to submit the following three items:

1. CV

2. Statement of your research interests (up to one page).

3. At least one letter of recommendation, addressing your academic background and suitability for the program.

Applications received by March 15, 2011 will receive full consideration. The Joint 2011 MBI-NIMBioS-CAMBAM Summer Graduate Program is a satellite summer school of ICIAM 2011, Vancouver BC, July 18-22, 2011 (http://www.iciam2011.com/).

The workshop is intended to broaden the scientific perspective of young researchers in mathematical biology and to encourage interactions with other scientists.

Workshop activities include plenary talks and poster sessions, as well as group discussions on issues relevant to mathematical biologists. Several abstracts will be chosen for short talks as well as to be presented as a poster.

We cordially invite young mathematical biologists to participate.

### 2009-2010

As network approaches have become an important tool to study a wide range of complex systems for which traditional reductionist approaches have enjoyed limited success, maybe the biggest enthusiasm and triumphs have been noted in biology. In particular within the cell, the variety of interactions between genes, proteins and metabolites are well captured by network representations. The dramatic availability of quantitative data from large-scale genomic experiments has begged for systemic approaches with the ability to simultaneously integrate information from multiple sources. In response, the advent of "systems biology" methods has been heavily influenced by network methods. Although recent network analyses have shed light on organizational principles of the proteome as well as the metabolome, there is, however, an increasing need for developing even more sophisticated, integrative approaches as higher quality data is becoming available. These challenges include developing systematic methods for integrating proteomic and metabolic information, thus coupling their mostly separated analyses; incorporating spatial localization of cellular constituents, and developing new tools to include stochastic and time varying measurements. Noteworthy, most network oriented workshops and conferences have an interdisciplinary and broad focus, as network approaches flourish in many fields. However, there is a need to bring biologists together with network scientists to discuss sharply defined topics within network biology. The goal of this workshop is to facilitate information exchange between biologists (experimental as theoretical) and network scientists, making them aware of each others capabilities and methodologies, as well as fostering collaborative interactions. Analysis and modeling of metabolic and protein interaction networks typically involves graph theory, optimization, and statistics.

Many mathematical models of biological systems have addressed only an isolated aspect of the system -- such as its biochemistry or mechanics -- and these simplified (yet not simple) models have shed much light on fundamental processes. Recently, biological modeling has now advanced to the point where integrative models that couple multiple processes are often developed. Typically, such models involve different spatial and temporal scales. Examples include models of tumor growth that couple solid mechanics with cell signaling and biochemistry and models of blood flow in the heart that couple solid mechanics, fluid mechanics, and bioelectricity. Common to these integrative models is the inclusion of experimental data that has high resolution both in time and space. The effective use of such models calls for new mathematical and numerical techniques; for instance, in the solution of inverse problems, in the derivation of more robust methods for parameter estimation, and in the determination of better numerical methods for the handling of multiscale coupling. This workshop seeks to address some of these challenges through a series of lectures and discussions.

### Avner Friedman

Distinguished University Professor, Department of Mathematics, The Ohio State University Mathematical Models May Lead to Better Treatment of Chronic WoundsChronic wound healing is a staggering public health problem worldwide. It affects 6.5 million individuals in the U.S., including 1.3 million to 3 million having pressure ulcers (bedsores). As many as 10-15% of the 20 million indiviuals with diabetes in the U.S. are at risk of developing chronic ulcers. Ischemia, caused primarily by peripheral artery diseases, represents a major complicating factor in cutaneous wound healing. In this talk I will explain the wound healing process, which involves interactions among different types of cells and the extracellular matrix. I will describe pre-clinical experiments with ischemic wounds carried out in the Comprehensive Wound Center at OSU, and will present recent mathematical modeling results in a joint work with Chuan Xue and Chandan Sen

### Clay Marsh

Department of Internal Medicine, The Ohio State University Exploring Systems Approaches to Understand Molecular Networks in Health and DiseaseA number of human diseases do not have a known cause and lack effective treatment. One of such diseases is idiopathic pulmonary fibrosis (IPF), a progressive scarring disease of the lung without known cause or pharmacological treatment. To date, the only effective treatment is lung transplantation and the mean time of survival from diagnosis is 5 years. We have taken a systems- and discovery-based approach to identify key regulatory networks and targets in the lungs of people with this disorder and have correlated these network changes with progression of lung function testing abnormalities. We have taken advantage of the observation that in gene networks, microRNA are identified as potential regulators of hubs. We will explore the regulation of microRNAs in IPF and discuss how changes in these microRNA may serve as a key regulatory role in the human disease. In this presentation, we will also discuss scale free networks and provide new insights into the mechanisms and potential treatment of this disorder. Our goal is to create platform approaches that can be applied to human health and disease.

### Noel Cressie

Department of Statistics, The Ohio State University Biometry, R.A. Fisher, and Statistical Sciencenformation about the environment, which organisms collect by membrane receptors, is processed by a complex network of signaling reactions to generate appropriate responses in terms of gene expression, development and differentiation, motility, cell growth and division, and programmed cell death. To survive and exist in harmony with its environment, the cell has to arrive at responses that are robust, specific and consistent with its role in a cell ensemble. The information processing system is replete with nonlinear interactions, which create bistable switches, signal relaying, adaptation, limit cycle oscillations, and other exotic responses. The purpose of this workshop is to survey recent advances in our understanding of the signal-response characteristics of living cells, and to foster deeper and more fruitful collaborations between theorists and experimentalists.

The application of sophisticated methods of biochemistry and molecular genetics in a variety of experimentally convenient organisms - budding yeast (Saccharomyces), fruit flies (Drosophila), green plants (Arabidopsis), nematodes (Caenorhabditis), and mammals (mice and men) - have provided many clues about the molecular mechanisms underlying signal processing and response regulation. Experimental studies of in vitro chemical and biochemical reaction networks have shown surprisingly similar dynamic behaviors, such as excitability, oscillations, multiple steady states, and signal propagation. During recent years mathematical models, based on realistic biochemistry and biophysics, have delivered useful insights into the dynamical principles underlying information processing by switches and clocks in living organisms. In addition, theoretical models have drawn attention to unexpected properties, such as hysteresis and critical slowing-down, which can be tested in the laboratory.

Mathematical analysis of large-scale transcriptome and interactome maps use graph theory, discrete mathematics, dynamical systems and signal processing theory, and elements of statistical mechanics. Modeling the dynamics of gene-protein regulatory networks involves all the tools from nonlinear dynamical systems theory: bifurcations of vector fields, numerical simulation, parameter estimation, hybrid systems (continuous-discrete, and deterministic-stochastic), sensitivity analysis, robust design, and multi-scale modeling. In most situations, new approaches are needed to adapt tools developed for engineering applications (such as control theory) to life science problems. Of crucial importance are algorithms and software to enable modelers to build larger, more complex and realistic models of information processing in cells.

This workshop will focus on significant theorems, theories and algorithms in mathematics that have been or are being inspired by problems in biology. Topics will be chosen from dynamical systems, combinatorics, partial differential equations, probability, statistics, topology, algebraic geometry, and others. The primary goal is to bring new, deep, and interesting mathematical questions to the attention of the entire mathematical sciences community. We plan strong efforts to attract mathematical scientists who have had little previous contact with the biosciences. We believe that through workshops such as this, the MBI can contribute to the enrichment of fundamental research in the mathematical sciences. We plan more extensive MBI programs like this in the future.

### Tina Henkin

Microbiology, The Ohio State University Riboswitch RNAs: Sensing metabolic signals with RNA transcriptsDirect sensing of a physiological signal by a nascent RNA transcript has emerged recently as a common mechanism for regulation of gene expression in bacteria. RNAs of this type, termed "riboswitches," interact with the cognate regulatory signal. This interaction can modulate the structure of the nascent transcript, which in turn can determine whether the RNA folds into the helix of an intrinsic terminator, resulting in premature termination of transcription. Similar RNA rearrangements mediate translational regulation by sequestration of the ribosome binding site; in this case, regulation can occur by interaction of the effector with either the nascent RNA or the full-length transcript. We have identified several systems of this type, including the T box system, which monitors the charging ratio of a specific tRNA, the S box and SMK box systems, which respond to S-adenosylmethionine (SAM), and the L box system, which responds to lysine. Each class of riboswitch RNA recognizes its signal with high specificity and an affinity appropriate to the in vivo pools of the effector. Characterization of the RNA-effector interaction in these systems has provided new information about how different classes of effectors are recognized, and about the impact of these regulatory mechanisms on the cell.

### Peter Abrams

Professor, Ecology and Evolutionary Biology, University of Toronto Density dependence and the structure of ecological theoryThe talk will begin with some general comments on the role of ecological theory and its history. I will argue that a key element of a successful theory in any discipline - understanding of how and why simple models differ from more complex models - is largely lacking in theoretical ecology. This has meant that many specific simplifications have often become fixtures of almost all models without any knowledge of the either the adequacy or consequences of these simplifications. Models of density dependence and competition are, in most cases, simplified representations of the interactions of consumers exploiting resources that limit population growth. However, the most commonly used models of both density dependence and competition have features that are inconsistent with the majority of plausible consumer-resource models. Some other issues dealing with the choice of variables in ecological models will be discussed.

### Larry Schlesinger

President/CEO, The Ohio State University Unraveling the molecular events in the lung innate immune response to tuberculosisTuberculosis continues to cause the suffering and death of millions of people in the world each year. Growing numbers of multi drug- and extensively drug-resistant bacterial strains are contributing to the problem as well as coincident HIV infection and a vaccine with variable efficacy. New therapies and vaccines require a more complete and integrated knowledge of the host immune response to infection. During infection, M. tuberculosis bacilli traverse the lung airways and settle in the alveolar spaces where they encounter alveolar macrophages (AMF). The alveolus is a highly immune-regulated microenvironment and AMF contribute to this by displaying an anti-inflammatory phenotype also known as an "alternative activation state". This biological state allows AMF to effectively clear microbes and particles within the alveolus while minimizing collateral inflammatory damage, but on the other hand may be exploited by the host-adapted M. tuberculosis. Our ongoing studies are characterizing the unique interactions that occur between M. tuberculosis, macrophages and components of the innate immune system during lung infection, including aspects related to host susceptibility. Examples of the scientific platforms being used will be highlighted during this seminar.

### Jian-Qiu Wu

Molecular Genetics and MCB, The Ohio State University Molecular Mechanism of Contractile-Ring Assembly in CytokinesisDuring cytokinesis an actomyosin contractile ring assembles and constricts in coordination with mitosis to properly segregate genetic materials into two daughter cells. The molecular mechanism of contractile-ring assembly remains poorly understood and controversial. We test several assumptions of the two prevailing models for contractile-ring assembly during cytokinesis in the fission yeast *Schizosaccharomyces pombe*: the spot/leading cable model and the search, capture, pull, and release (SCPR) model. The two models differ in their predictions for the number of initiation sites of actin assembly and in the role of myosin-II. Monte Carlo simulations of the SCPR model require that the formin Cdc12p is present in >30 nodes from which actin filaments are nucleated and captured by myosin-II in neighboring nodes. The force produced by myosin motors pulls the nodes together to form a compact contractile ring. Live microscopy of cells expressing formin Cdc12p fluorescent fusion proteins shows that Cdc12p localizes to a broad band of 30 to 50 dynamic nodes, where actin filaments are nucleated in random directions. Perturbations of myosin-II motor activity demonstrated that it is required to condense the nodes into a contractile ring. Taken together, these data provide strong support for the stochastic SCPR model of contractile-ring formation in cytokinesis.

### Cynthia Kenyon

Department of Biophysics and Biochemistry, University of California, San Francisco Genes and Cells that Influence the Rate of Aging in C. elegansAging has long been assumed to be a passive consequence of molecular wear and tear. But it's not so simple. Genetic studies have shown that the aging process, like everything else in biology, is under exquisite regulation, in this case, by a complex, multifaceted hormonal and transcriptional system that affects aging in many species, including humans. In 1993, we showed that changing a single gene in the small roundworm C. elegans can double its lifespan. This gene encodes an insulin/IGF-1 like receptor, which indicates that aging is regulated hormonally. By manipulating genes and cells, we have now been able to extend the lifespan and period of youthfulness of healthy, active C. elegans by six times. We have found that signals from the reproductive system and sensory neurons influence the lifespan of C. elegans, and these processes, too, may be evolutionarily conserved. These signals act, at least in part, to control the expression of a wide variety of subordinate genes, including metabolic, stress response, antimicrobial, and novel genes, whose activities act in a cumulative fashion to determine the lifespan of the animal. Some of these subordinate genes can also influence the progression of age-related disease, including cancer. In this way, this hormone system couples the natural aging process to age-related disease susceptibility.

Synthetic biology is concerned with the design of genetic networks that perform desired functions in single cell and in multi-cellular environments. Such synthetic circuits can be used to gain insight into the molecular components of gene regulation, thus reducing the complexity of gene regulatory networks of cells. This emerging field holds promise for improved understanding of biological processes, and applications in varied areas such as programmed tissue engineering, biomaterial fabrication, and biosensing.

The construction of de-novo genetic circuits begins with assembly of genetic components that regulate transcription, translation, phosphorilation, and synthesis of the response to signaling molecules in bacteria and in Eukaryotes. These components are then assembled in various network topologies in a programmed fashion, which combines tools from nonlinear dynamics and statistical physics with extensive array of techniques in traditional molecular biology.

The workshop will begin with foundational technologies such as library parts, modules construction and prediction. Transcriptional networks with feedback and feedforward will then be presented. Applications will include engineering metabolic networks, cancer detection and therapy by engineered bacteria, biosensing, and energy production.

The workshop will bring together biologists, electrical engineers, and mathematical modelers. The mathematical tools will include network design, nonlinear dynamics, signal detection, and control theory.

### De Witt Sumners

Department of Mathematics, Florida State University DNA TopologyCellular DNA is a long, thread-like molecule with remarkably complex topology. Enzymes that manipulate the geometry and topology of cellular DNA perform many vital cellular processes (including segregation of daughter chromosomes, gene regulation, DNA repair, and generation of antibody diversity). Some enzymes pass DNA through itself via enzyme-bridged transient breaks in the DNA; other enzymes break the DNA apart and reconnect it to different ends. In the topological approach to enzymology, circular DNA is incubated with an enzyme, producing an enzyme signature in the form of DNA knots and links. By observing the changes in DNA geometry (supercoiling) and topology (knotting and linking) due to enzyme action, the enzyme binding and mechanism can often be characterized. This talk will discuss topological models for DNA strand passage and exchange, including the analysis of site-specific recombination experiments on circular DNA and the analysis of packing geometry of DNA in viral capsids.

### Joyce McLaughlin

Director, IPRPI, Inverse Problems Center, Rensselaer Polytechnic Institute Biomechanical Imaging: Viscoelastic Models, Algorithms, Reconstructions; Application to Breast, Prostate and BrainWe will briefly show some of our recent work in cancer identification created from data with the characteristics (1) or (2) above. The remaining talk will concentrate on the mathematical model, algorithms and reconstructions from movie data acquired when the tissue is undergoing response to a single or multifrequency harmonic oscillation. We discuss viscoelastic and elastic models, our current choice for viscoelastic model and its properties. We discuss approximations to the mathematical model, estimates of the error made by the approximation, the algorithms inspired by the full model and the approximate model and their stability and accuracy properties, why some biomechanical parameters cannot be reliably recovered, and current questions about biomechanical parameters that inspire our work. We present images created by our algorithms both from synthetic, in vivo and in vitro data.

### Zena Werb

Department of Anatomy, University of California, San Francisco Of mice and women: How studying development gives us insights into cancerWe have focused on the cell behaviors underlying mammary development and during breast cancer tumor progression. We have taken a combined imaging, cell biological, genetic and pharmacological approach to determine the tissue transformations underlying branching morphogenesis and neoplastic progression, then to dissect the molecular regulation of these cell behaviors and interactions.

- Egeblad, M., A. J. Ewald, et al. (2008). Visualizing stromal cell dynamics in different tumor microenvironments by spinning disk confocal microscopy. Dis. Model. Mech. 1:155-167. PMID: 1904807
- Ewald, A.J., A. Brenot, M. Duong, B.S. Chan & Z. Werb (2008). Collective epithelial migration and cell rearrangements drive mammary branching morphogenesis. Dev. Cell. 14:570-581. PMID: 18410732.
- Kouros-Mehr, H., S. K. Bechis, et al. (2008). GATA-3 links tumor differentiation and dissemination in a luminal breast cancer model. Cancer Cell. 13:141-52. PMID: 18242514.
- Lu, P. & Z. Werb (2008). Patterning mechanisms of branched organs. Science. 322:1506-1509. PMID: 19056977.
- Welm, B.E, G. J. P. Dijkgraaf, A. S. Bledau, A. L. Welm & Z. Werb (2008). Lentiviral transduction of stem cells for genetic analysis of mammary development and breast cancer. Cell Stem Cell. 2:90-102. PMID: 18371425.

The past decade has witnessed the transition of computational biology, population genetics, and evolutionary biology, from relatively data-sparse and theory-driven subjects, into highly empirical and data-driven disciplines. The continuing data-explosion has meant that descriptive studies have tended to outpace more in-depth theory development and statistical modeling. Nevertheless, in the past decade our understanding of genome and population biology and evolution has increased dramatically, and combined with the availability of data, it seems that the time is ripe to reap the benefits of these developments, by giving a new impetus to statistical modeling and theory development in computational biology, broadly defined.

In this workshop, we aim to bring together leading experts on genome biology and evolution, with an interest in quantitative modeling. We hope to create an interesting mix of, on the one hand, researchers whose main focus is on biology or evolution, with researchers who are primarily interested in the modeling aspects of these biological problems, from a mathematical, statistical, or algorithmic perspective.

The program is organized around the following five interest areas:

- Viruses and pathogens
- Paleogenetics and reconstruction
- Genome and pathway evolution
- Human diversity and populations
- Comparative genomics

The workshop will feature about 20 short talks spread over 5 days, with plenty of time in between. In these slots it will be possible (and strongly encouraged) to organize informal breakout sessions in smaller groups, to discuss topical problems in more depth.

### Rafael Irizarry

Professor, Department of Biostatistics, Johns Hopkins University Stochastic epigenetic variation in evolutionary adaptation and common diseaseThe elucidation of the structure of DNA was a watershed event in the history of biology. In one fell sloop it provided the molecular basis of the gene and explained how genes are propagated from mother to daughter cell. Its crowning achievement is the central dogma of molecular biology which describes information flow from DNA to protein via messenger RNA. Over fifty years of DNA research since then has lead to a detailed understanding of practically all the molecular players of the central dogma, and their mutual interactions. More recently, a new view of the information encoded by DNA has emerged, one that goes beyond DNA as the physical embodiment of the gene. Unlike genomic information which is encoded in the base sequence, this information is carried by interactions of DNA with DNA-binding proteins.

This workshop will bring together researchers from the mathematical, physical and biological sciences interested in protein-DNA interactions and how they steer cellular processes such as transcription, replication and DNA packing. The workshop will attempt to bridge scales starting from single molecules and macromolecular complexes, all the way to whole cells, and to highlight the fundamental mathematical problems posed by each one.

This workshop will attempt to take a snapshot of the field of DNA-protein interactions and examine it from a number of viewpoints provided by different length and time scales. These will include single-molecule studies of DNA-protein interactions, such as those by DNA motors and DNA packaging proteins (histones in eukaryotes and histone-like proteins in prokaryotes) as well as whole-genome studies that seek to uncover regulatory motifs that bind transcription factors.

One of the main thrusts of the workshop will be to highlight opportunities for mathematicians and physicists interested in applying ideas from statistics, stochastic equations, statistical and continuum mechanics to the burgeoning field of protein-DNA interactions.

### Michael Waterman

Professor, Biological Sciences and Mathematics, University of Southern California Reading DNA Sequences Along Eulerian Paths### David Terman

Department of Mathematics, The Ohio State University Does Neuroscience Need Mathematics? And vice-versa?In this talk, I will give examples in which issues raised in the study of specific neuronal systems, computational modeling and mathematical analysis have all benefited from each other. In particular, I will describe work on Parkinsonian rhythms generated in the basal ganglia, sensory processing in the insect's antennal lobe and models for working memory.

### Bin Yu

Department of Statistics, University of California, Berkeley Sparse modeling: unifying theory and human visual pathwayInformation technology has enabled collection of massive amounts of data in science, engineering, social science, finance and beyond. Extracting useful information from massive and high-dimensional data is the focus of today's statistical research and practice. After broad success of statistical machine learning on prediction through regularization, interpretability is gaining attention and sparsity is being used as its proxy. With the virtues of both regularization and sparsity, sparse modeling methods (e.g. Lasso) has attracted much attention for theoretial research and for data modeling.

In this talk, I would like to discuss both theory and pratcice of sparse modeling. First, I will present some recent theoretical results on bounding L2-estimation error (when p>>n) for a class of M-estimation methods with decomposable penalities. As special cases, our results cover Lasso, L1-penalized GLMs, grouped Lasso, and low-rank sparse matrix estimation. Second, I will present on-going research with the Gallant Lab at Berkeley on understanding visual pathway. In particular, sparse models (linear, non-linear, and graphical) have been built to relate natural images to fMRI responses in human primary visual cortex area V1. Issues of model validation will be discussed.

### Wolfgang Sadee

Department of Pharmacology, The Ohio State University Genetics of Human Phenotypic Variability - Searching for Disease Risk Factors along Evolutionary PathsGenome-wide surveys have suggested that genetic variation affecting the regulation of mRNA expression, processing, and translation predominates over those that directly alter the amino acid sequence of encoded proteins. While the latter are easy to spot with use of extensive sequencing, regulatory variants often remain hidden. We have developed a comprehensive approach to detecting such regulatory variants, unexpectedly finding that many key genes involved in disease and drug therapy carry frequent regulatory variants. In parallel, others have pursued genome-wide association studies (GWAS), finding indications of numerous disease risk genes, but the overwhelming majority of the genetic risk remains unknown. Our research program therefore is beginning to address the question as to why the underlying genetic factors remain uncertain. One hypothesis is that regulatory variants could play a key role, but to account for disease risk we must search for frequent alleles that can fill the gap. For such variants to reach high frequency, positive selection during evolution is likely to play a role. In this seminar I will discuss why GWAS may have missed such genes/alleles, and what our approach should be to discover the main disease risk alleles, with an eye on the nexus between evolution, wellness, fitness, and disease.

### Chris Johnson

Scientific Computing and Imaging Institute, University of Utah Image-Based Biomedical Modeling, Simulation and VisualizationIncreasingly, biomedical researchers need to build functional models from images (MRI, CT, EM, etc.). The "pipeline" for building such models includes image analysis (segmentation, registration, filtering), geometric modeling (surface and volume mesh generation), simulation (FE, FD, BE, linear and non-linear solves, etc.), visualization (scalars, vectors, tensors, etc) and evaluation (uncertainty, error, etc.).

I will present research challenges and software tools for image-based biomedical modeling, simulation and visualization and discuss their application for solving important research and clinical problems in neuroscience, cardiology, and genetics.

### Lazlo Szekely

Department of Mathematics, University of South Carolina The amount of information needed for phylogeny reconstructionI will review the phylogeny reconstruction problem, mostly for mutation data, discuss what is expected from phylogeny reconstruction methods and how do they live up to the expectation. I will discuss the amount of information needed for every reconstruction method, and also the amount of information needed for particular methods.

This program consists of two parts: (a) two weeks of introductory lectures plus short projects and a computer lab, and (b) a summer long research experience (6 weeks to be followed immediately after the 2 weeks) devoted to projects in the interface of mathematics, statistics, and biological sciences.

The summer long research experience for undergrads (REU) will begin July 5, and the presentations will be August 13, 2010.

Program Leaders:

- Dennis Pearl: Statistical Phylogenetics (Monday, June 21)
- Victor Jin : Bioinformatics (Tuesday, June 22)
- Joe Verducci: Chemogenomics (Wednesday, June 23)
- Kate Calder: Environmental Statistics (Thursday, June 24)
- Joe Tien: Mathematical Epidemiology (Friday, June 25)

Neuroendocrinology is at the intersection of neuroscience and endocrinology. Of the many endocrine glands in the body, the one that is under the most direct neural control is the pituitary gland, which is located adjacent to the brain region called the hypothalamus. The anterior portion of the pituitary consists of several cell types, each of which is electrically excitable (like neurons) and which secretes a hormone when activated. Neurons within the hypothalamus act on pituitary cells to evoke hormone secretion at the proper times and under the proper physical stimuli. The pituitary hormones then act on other endocrine glands (like pineal, adrenal, ovaries, and testes) to influence secretion of hormones. All of the hormones influence neuron activity within the hypothalamus, closing the loop. Mathematical neuroendocrinology is a new field that uses mathematical modeling and analysis to help interpret neuroendocrine data and design new experiments. Models have been developed at the cellular and systems level.

This workshop is the second in a series (the first was held at AIM) and will continue dialogues and collaborations between mathematicians and experimentalists begun at AIM. One goal is to discuss problems in neuroendocrinology that can be addressed using mathematics. These discussions took place during the first meeting, but we now have a better feel for the types of problems of interest. Another goal is to bring young mathematicians and experimentalists who have never worked with mathematical biologists into the mathematical biology community to spur its growth.

The workshop is intended to broaden the scientific perspective of young researchers in mathematical biology and to encourage interactions with other scientists.

Workshop activities include plenary talks and poster sessions, as well as group discussions on issues relevant to mathematical biologists. Several abstracts will be chosen for short talks as well as to be presented as a poster.

We cordially invite young mathematical biologists to participate.

### 2008-2009

The workshop is intended to broaden the scientific perspective of young researchers in mathematical biology and to encourage interactions with other scientists.

Workshop activities include plenary talks and poster sessions, as well as group discussions on issues relevant to mathematical biologists.

We cordially invite young mathematical biologists to participate.

Cell movement is fundamental to embryogenesis and developmental biology, and is hence an excellent core topic for this special emphasis year. Not only is cell motion important in morphogenesis and formation of the organism but also, it plays a central role in wound healing, immune surveillance, and invasive malignant growth in cancer. In this workshop, we plan to bridge the scales between the subcellular molecular mechanisms implicated in cell motility, the motion and behaviour of single eukaryotic cells, the repertoires of cell aggregates and clusters, and the level of multicellular tissue dynamics, morphogenesis, and mechanics. This workshop will form a bridge between some of the more specific aspects of workshops featured during this year, and, while avoiding overlaps or repetition, will revisit and amplify on aspects of these sister workshops in which cell motion is key.

The workshop will showcase the experimental biology alongside recent advances in mathematical modeling and computational biology. We plan to start at the lowest, microscopic scale, and proceed in a hierarchical way through to the macroscopic tissue level. One of our goals will be to summarize the advances that have already been made, in both experimental and computational methods. We will, where possible, illustrate the diversity of techniques that have been used to approach the underlying biological issues, including classical mathematics (partial and ordinary differential equations) as well as a variety of computational methods. Another, equally important goal will be to identify and highlight new fundamental questions in biology where mathematical, statistical, and computational techniques could prove helpful.

E. coli and Dictyostelium are two of the most widely studied organisms in this area, so this workshop will focus in the main on these, but it is important that it is not restricted to these two examples. Research in this area falls naturally into the two broad categories of (1) single cell, and (2) population level dynamics. We consider each in more detail below:

- At the single cell level, there are a number of phenomena that have been studied to various degrees of depth but for which explanations remain elusive. For example, a full understanding of signal transduction, namely, how do bacteria convert external stimuli into internal dynamics in a robust, yet incredibly sensitive manner (responding to a change in a few molecules over a background range of several orders of magnitude of molecules)? Within this, the goal is to understand gain and amplification. One possible explanation is receptor clustering but recent research suggests that this is not sufficient in itself. There are several alternative models for many of these processes but none are consistent with all the key known experimental behaviours.

Once the signal is internalised, the next question is to elucidate the cascade of reactions that determines response. For example, in E Coli, this triggers the flagellar motor to respond. One then has to understand the mechanism of motor operation and behaviour. - At the cell population level it is known that within the laboratory bacteria can produce complex spatiotemporal patterns. Although this may be viewed as an interesting curiosity, it is felt that it will give important insights into the formation of biofilms which do have significant implications.

Other population level activity includes quorum sensing, differentiation etc. Complex patterns arise in myxobacteria, while in Dictyostelium discoideum (Dd) a range of morphogenetic behaviour is observed that is most likely conserved across species yielding important information for higher organisms. Dd is a powerful modelling paradigm for signal transduction, cell-cell signalling, cell differentiation, cell movement.

The implications of the above behaviours are widespread. For example, bacterial oral infections can lead to vascular disease, while biofilm formation is a major concern for the welfare of patients with surgical implants.

The mathematical disciplines used in the analysis of the models to be discussed in the workshop includes ordinary and partial differential equations, and stochastic equations.

Charles Darwin's book On the Origin of Species, first published in 1859, put forth the theory that organisms evolve over many generations through the process of natural selection. One hundred and fifty years hence, we have determined the chemical basis of inheritance in the structure of DNA, we have sequenced the genomes of thousands of organisms, including our own, and have made good progress in unraveling the molecular mechanisms of many of life's basic processes; and we are finding that Darwinian concepts apply to the evolution of cellular and biomolecular systems. This symposium brings together some of the leading researchers in evolutionary dynamics and mathematical modeling to talk about the evolution itself of Darwin's theory, and its applications to diverse systems such as cancer and infectious diseases.

This workshop will focus on animal morphogensis. Morphogensis involves the development from a single cell to a complex organism. This process involves many interrelated mechanisms including cell-signaling, differentiaion, cell migration, growth, the formation and movement of tissues. The workshop will focus on several well characterized developmental systems including the frog Xenopus, the worm C. elgans, sea squirt Ciona, vertebrate limb development and vertebrate somitogenesis. Each session will include talks from experimentalists and mathematical modelers.

These models of biological systems have attracted the attention of many experimentalists in the past. However, new experimental methods have been developed that provide a much more comprehensive picture of development, and new opportunities to develop novel mathematical methods and models for understanding these complex systems. How should we model the biomechanics of the growing tissues? What about the rheology of the growing limb bud? We have an emerging picture of the gene/protein networks that are involved with cell-signaling and differentiation. How will this be integrated with the mechanical aspects of morphogenic processes?

Cancer and tumor-induced angiogenesis has a natural place in the Special Year on Developmental Biology as cancer is often thought of as a result of a faulty development process. Experimental and clinical oncology forms a massive literature aimed at understanding and treating cancer. Despite the enormity of the data available, clinical oncologists and tumor biologists proceed without a comprehensive theoretical model to help guide the organization and understanding of such data. To quote a recent Nature article on the topic:

Heeding lessons from the physical sciences, one might expect to find oncology aggressively, almost desperately, pursuing quantitative methods to consolidate its vast body of data and integrate the rapidly accumulating new information. In fact, quite the contrary situation exists. Mathematical models are typically denounced as "too simplistic" for complex tumour-related phenomena (ignoring, of course, the fact that similar simplifying assumptions are required in most experimental designs). Articles in cancer journals rarely feature equations. Clinical oncologists and those who are interested in the mathematical modelling of cancer seldom share the same conference platforms. -- Nature 421, 321 (2003).

Naturally, successful modeling approaches to cancer requires scientists willing to communicate and interact extensively across disciplinary boundaries. This workshop aims to do exactly this by having truly interdisciplinary scientists as well as giving a shared platform for both experienced modellers and state-of-the art experimentalists and clinician-scientists discussing their work covering every level of tumor growth.

Each day of the workshop, will consist of 3 primary speakers (1-hour lectures each) that will include an experimentalist laying out the biological problem, a mathematical modeler describing modeling approaches and a imaging specialist describing the type of data (typically imaging) available for model validation and development. Additionally, other attendees will be invited to present posters at the poster session. An expert panel will comprise of leading modelers and experimentalists to discuss current problems in the efficient translation of mathematical modeling techniques to the laboratory and the clinic.

Significant time will be available during the meeting for discussions of current and future problems in the cancer and tumor-induced angiogenesis area.

Abnormal healing of wounds in, for example, diabetics, or aged patients, as well as formation of scar tissue, has resulted in the need to understand the fundamental processes involved in wound healing. This workshop aims to bring together experimentalists, clinicians and theoreticians working at the different scales apparent in this problem and to determine approaches for combining these in a multiscale modeling framework. From a clinical standpoint, we would like to be able to predict from an initial time course what is the longer term prognosis for a wound. At one level, this could be done statistically, as perhaps from data already available trends could be discovered. However, this would not provide a mechanistic understanding which would inform a clinician of what therapeutical intervention to make if the model predicts that a wound would not heal properly.

The first three days will focus on particular spatial scales. Day 1 will begin with an overview talk that will introduce participants to the stages involved in wound healing, together with imaging of actual wound healing processes to illustrate the state of the art in experimental measurement and visualization techniques. It will then investigate aspects of signaling networks within cells which determine cell responses to wounding. Day 2 will focus on angiogenesis, the process by which new vasculature evolves. A specific aim here is to understand the origin of the biphasic response of healing to oxygen tension and its implications, for example, in wound infections where oxygen is used up thus impairing the healing process. Day 3 will address problems arising at the level of cell movement and laying down of matrix with important implications for scar tissue formation.

To arrive at a comprehensive model (or suite of models) one needs to integrate processes occurring on many different time and length scales. It is clearly impossible to simply include everything, so a major challenge for modelers is to extract from detailed models the essence of the processes occurring at each scale and interface them appropriately in a multiscale framework. Day 4 will consist of talks on this subject.

Day 5 will present a number of clinical case studies which will lay down future challenges in developing the generic modeling frameworks presented in the first four days to specific problems. Examples here will include healing in diabetic patients, elderly patients.

The purpose of this two-day workshop is to bring biologists and statisticians/mathematicians together on various aspects of systems biology studies of biological processes and diseases, including both novel biological experiments for systems biology studies of diseases and novel mathematical and statistical methods for integrative analysis of new generation of sequence data, SNP data, gene expression, proteomic, metabolomic and phenotypic data. We propose to have 12 invited talks, about six are on new experimental approaches and new data generation methods for systems biology (mainly given by biologists) and another six talks are on new statistical/computational methods for integrative analysis of these data (mainly given by statisticians or mathematicians). Potential topics to be covered include integrative analysis of sequences and gene expression data for studying complex diseases, methods for analysis of genetic networks and pathways, data generation and analysis methods for epigenetics, methods for analysis of new generations of sequence data and their applications in studying diseases and biological processes.

In the mammalian nervous system, a classic example of pattern formation is the formation of "maps." These include the continuous mapping of the sensory periphery (e.g. the retina, or a fingertip) onto a central structure, preserving topographic relationships, and the continuous mapping of derived stimulus features such as the dominant eye or the preferred stimulus orientation for driving a central visual neuron. Theories of map formation generally involve an interplay between a number of elements: topographic matching of molecular gradients across axons and across the target structure; activity-dependent rules for synaptic growth or stabilization that typically lead to the outcome "neurons that fire together, wire together"; the patterns of activation of the input axons, in some cases driven by the patterns of sensory stimulation; and the interplay of input drive and intrinsic circuitry, both of which are simultaneously developing, in determining patterns of activation in the target structure.

In recent years, there has been great progress in elucidating the molecules involved in topographic map formation and the often non-intuitive effects on the maps of perturbing them, and models are playing a key role in making sense of these observations. There has also been great progress in understanding the dynamical mechanisms underlying feature map formation, and this theoretical work is leading to a new class of experiments involving perturbation of feature maps even in adulthood. Some aspects of feature map formation show "critical periods" -- specific developmental time windows during which abnormal sensory experience greatly alters feature maps, and outside of which the maps are relatively impervious to alterations of sensory experience. Recent years have seen enormous progress in understanding the mechanisms underlying critical periods, in particular with the demonstration that maturation of inhibition in the target structure can be necessary and sufficient to initiate the critical period. This presents enormous challenges for theorists to understand how these changes in target circuitry can radically alter the sensitivity of the development process to changes in input statistics. The workshop will articulate these challenges.

In addition, theory also addresses how particular neuronal response features are learned, a separate question from the organization of preferred features into continuous maps. Recent years have seen progress in understanding mechanisms for development of spatiotemporal, rather than merely spatial, response features such as selectivity for the direction of motion of a stimulus, and in understanding how certain nonlinear response features ("complex cells") can arise. Many open questions exist, including the computational function of observed learning rules, and how different nearby neurons can learn to detect quite diverse features from the same overall set of inputs; these questions too will be discussed in the workshop.

The workshop will cover four broad topics that are particularly well-suited for quantitative analysis: genome analysis, pattern formation of the early embryo and wing imaginal disk, computational modeling of signal transduction pathways, and the elucidation and analysis of gene regulation networks.

As of this writing, the genomes of 12 different Drosophilids have been completely sequenced and assembled. These assemblies provide a rich foundation for the identification of conserved noncoding sequences including microRNA genes and regulatory DNAs.

Whole-genome methods provide the comprehensive identification of just about every gene and associated regulatory DNA responsible for complex developmental processes, including segmentation, gastrulation, neurogenesis, and wing morphogenesis. Current progress in each of these areas of research will be discussed with an eye towards future modeling efforts. Several critical processes such as EGF and TGF signaling have already been successfully modeled, and the insights gleaned from these efforts will be discussed.

The last sessions will be devoted to gene regulatory networks. A combination of gene disruption assays, DNA binding assays, and cis-regulatory analysis permits the construction of networks, or circuit diagrams, that display the functional inter-connections among all of the regulatory genes and cell signaling components responsible for complex developmental processes. These networks can be used to create predictive changes in patterning processes, and to determine the mechanistic basis for the genesis of embryonic diversity and novelty during insect evolution. We will discuss the logic and topology of these networks, and also consider future goals such as the development of better visualization methods.

This program consists of two parts: (a) two weeks of introductory lectures plus short projects and a computer lab, and (b) a summer long research experience (6 weeks to be followed immediately after the 2 weeks) devoted to projects in the interface of mathematics, statistics, and biological sciences.

Program Leaders:

- Dennis Pearl: Statistical Phylogenetics (Monday, June 22)
- Michael Rempe: Mathematical Neuroscience (Tuesday, June 23)
- Joe Verducci: Chemogenomics (Wednesday, June 24)
- Kate Calder: Environmental Statistics (Thursday, June 25)
- Kun Huang: Bioinformatics (Friday, June 26)

This year the program will focus on Mathematical Ecology and Evolution. The program leaders are Ian Hamilton (Department of Ecology, Evolution and Organismal Biology, Ohio State University) and Yuan Lou (Department of Mathematics, Ohio State University).

The first week is spent in a tutorial, which combines morning lectures with active learning laboratories in the afternoon. Dr. Hamilton will give five lectures on the evolutionary ecology of interacting phenotypes, including such topics as the use of game theory in evolutionary ecology, levels of selection, the evolution of cooperation, competition and predator-prey games. Dr. Lou will give five lectures on the theory of Adaptive Dynamics with applications to the evolution of dispersal, consumer-resource models and the evolution of virulence.

The following two weeks are spent working on guided team projects and participating in a mini-conference to share project results. The program is meant primarily for graduate students; college instructors and qualified undergraduates will also be considered. Team projects include the following topics:

- Maintenance of variation in mate choice and mate quality
- Sanctions and cooperative behavior
- Evolution of dispersal in heterogeneous landscapes
- Evolution of virulence

Workshop activities include plenary talks and poster sessions, as well as group discussions on issues relevant to mathematical biologists. Several abstracts will be chosen for short talks as well as to be presented as a poster.

We cordially invite young mathematical biologists to participate.

### 2007-2008

Workshop activities include plenary talks and poster sessions, as well as group discussions on issues relevant to mathematical biologists.

We cordially invite young mathematical biologists to participate.

Broadly defined, metabolic engineering seeks to change the metabolism and physiology of an organism to suit the needs or desires of the farmer, the breeder, the genetic engineer, and the scientist. Targeted selection for more flavorful wines , for higher milk production in cattle, for larger chicken breasts, for sweeter corn, and for larger and more flavorful apples are all examples of metabolic engineering products that have been largely successful. In all of these instances, the metabolism of the organism was altered in such a way as to allow that organism to display the desired traits. However, such breeding-program driven projects are very slow to produce results and often end in failure. The exact changes in the organism that result in the altered phenotype are often unknown, making reproduction of the same changes in these or similar organisms almost impossible.

Although metabolic engineering of plants and microbes is a major scientific activity today, there are numerous biological and, increasingly, mathematical challenges. One can organize the challenges of metabolic engineering roughly into four areas: *measurement technologies* (sensing and quantification) for generating data and monitoring system performance; *mathematical modeling* (formulation, verification, and analysis) for systematic representation and characterization of the system; *molecular tools* (actuators and regulators) for altering the system in a controlled fashion; and *system integration* (system [re]design, prediction, and control) for discovery of system design principles and rational optimization. Advances in one area are obviously dependent on those in the others. New developments in each of these areas will form the interrelated themes of this workshop. Examples from microbes and plants will be emphasized.

The workshop will be organized along the following outline:

- Overview of Organisms, Biological Tools, and Strategies: Microbes, plants and animals, mutagenesis, knockout and transfer of genes, rational design and directed evolution.
- Measurement Technologies and Data Analysis Tools: Metabolites and fluxes, mRNA, protein, miRNA.
- Mathematical Modeling: Metabolic pathways, protein interactions, gene circuitry.
- Molecular Tools: Enzyme design, rewired circuitry, de novo circuitry, biological computing.
- Systems Organization and Integration: Enzymatic networks, gene circuits, miRNA speculations, robust design and control.

The challenges of tissue engineering include the need to overcome mass transport limitations, to exploit biophysical stimuli in enhancing engineered tissue function, to address anisotropic structural requirements in "manufacturing" of the tissue, immunological considerations, as well as the challenge of designing "off the shelf technology" that will be applicable for the needs of specific patients. Engineered tissues of the future will serve as multifunctional molecular delivery devices that provide a microenvironment conducive to cell infiltration and cultivation. To address and optimize these multiple functions, tissue engineers have begun to exploit principles of transport and biophysical stimuli as well as to hone knowledge of cell recruitment, adhesion, migration, proliferation, and differentiation to improve success of cell cultivation in tissue scaffolds. Interestingly, the focus of many tissue engineering symposia appears to be specific to tissue type or a clinical problem; yet, by organizing symposia that bridge across length and time scales, diverse organisms and tissue types, experimental models (in vivo, in vitro, in silico), as well as bioscience and engineering disciplines, it may be possible for the sub-specialists to recognize common themes and solutions that have wide applicability across a variety of tissues. Hence, the goal of this workshop is to bring developmental biologists, cell and tissue engineers, as well as computational modelers together at a joint forum, bridging across specific cell and tissue types as well as model platforms, to recognize common challenges and relevant strategies for addressing these challenges in tissues from diverse organisms, including plants, drosophila, zebrafish and humans. The promise of predictive modeling in accelerating advances in the field of tissue engineering will be highlighted.

Biological movement is governed by a complex interplay between the central nervous system and the musculoskeletal system. The nervous system has conventionally been thought to reside atop a hierarchical control system. The periphery was thought to receive motor commands, with the role of integrating, filtering, and acting upon those commands. However, neuroscientists have gathered increasing evidence that supports a more collaborative control structure. Most evident is the importance of feedback loops that provide sensory information not only locally but also from throughout the periphery. Feedforward components to motor control have gradually given way to feedback, where there is no hierarchy. Instead, each system contributes to the overall behavior of a feedback loop. The nervous system receives sensory information, with the role of integrating, filtering, and acting upon that feedback. Recent evidence indicates that an internal representation of body and environment dynamics contributes to sensorimotor integration for state estimation and motor planning.

The collaboration between sensors, actuators, limbs, and neurons is a systems problem. The physiology of these components is increasingly understood in quantitative terms. The dynamics of these components, however, are not well understood, especially when they interact. A systems approach is ideal for studying the organization of the nervous system and its interplay with the musculoskeletal system. It is critical for experts in areas such as muscle physiology, body and limb mechanics, and neurophysiology, to share knowledge, not only in descriptive terms, but also in a mathematical language amenable to a systems approach.

The goal of this workshop is to foster interaction between experts on muscle, limb, and brain. The proposed speakers include pioneers in the use of mathematical tools in biomechanics, as well as state-of-the-art experimentalists whose approaches may not be quantitative but are nonetheless amenable to a systems approach.

Workshop 4 focuses on the question of how animals are deceptively simple. They push against the world, with legs, fins, tails, wings, or their whole bodies, and the rest is Newton's third and second laws. But of course locomotion emerges from complex interactions among animals' neural, sensory and motor systems, their muscle-body dynamics, and their environments. Three broad approaches reflect this:

- Neurobiology has successfully studied the role of central pattern generators (CPGs) in the control of locomotion. CPGs are networks of neurons that can generate muscular activity in the absense of sensory feedback. By its action, the nervous system can generate a basic neural output that can signal the muscles when to contract. In this mode, the nervous system tells the muscles what to do and muscles pass the message on to limbs, which move the body.
- A closely related approach concentrates on proprioceptive feedback in intralimb and interlimb coordination for shaping locomotory patterns. Thus, what the limbs are doing now, tells them what to do next.
- Biomechanical studies focus on body-limb-environment dynamics and often ignore neural detail. Thus, Newtonian mechanics, with (mostly) passively-generated forces, tell the body what it must do.

All three approaches have generated rich mathematical models of individual neurons and circuits, sensory pathways and state estimators, and body-limb mechanics. Further mathematical modeling, at various spatial and temporal scales, can play a central role in synthesizing these approaches into neuromechanical descriptions of locomotion. Thus, Hodgkin-Huxley meets Newton with A.V. Hill as matchmaker.

This workshop, and the closely-related ones on muscle biomechanics (Workshop 2) and neuroengineering (Workshop 5) will emphasize the development of integrative models. The major mathematical tools will include dynamical systems, stochastic ODE, control theory, and (non-)classical mechanics with intermittent contacts and impacts in running and walking, and unsteady fluid mechanics in swimming and flight.

The field of neural engineering has been transformed by the growth in computer processing power in the last several years. It is now possible to read in multiple neural signals, process those signals, and respond to that processed data in real time. The capability to interact with the nervous system in real time has great potential for the development of new treatments for neurological disorders as well as enabling new experimental studies to further our understanding of the nervous system. For example, areas where real-time interaction can result in improved therapies or treatments include:

- Direct brain control of assistive devices for the paralyzed
- Closed-loop control of deep brain stimulation (DBS) (e.g., for Parkinson's disease)
- Prediction and intervention of epileptic seizures
- Closed-loop stimulation of paralyzed nerves to restore function

This real-time interaction posses special challenges because device design requirements often include minimizing power consumption and device size for implantation. This necessitates implementing efficient algorithms and quantifying the tradeoffs between making algorithms more efficient verses more effective. Another issue common to most chronic neural engineering applications is non-stationarity of the neural interface and of the biological system itself.

The themes of the workshop will include: spike sorting and tracking; cortical decoding of command signals for control of assistive devices; deep brain stimulation; and epilepsy detection and intervention.

This is an annual award meeting for Undergraduates in Biological and Mathematical Sciences (UBM).

Medical imaging has been undergoing a revolution in the past decade with the advent of faster, more accurate, and cheaper imaging modalities. This powerful new hardware has driven the need for corresponding software development, which in turn has provided a major impetus for new algorithms in signal and image processing. Many of these algorithms are based on partial differential equations, curvature driven flows, geometry, and novel statistical techniques. The purpose of this workshop is to bring together researchers from all aspects of medical imaging with the emphasis on brain imaging for a multi-disciplinary workshop in which various views may be shared, and hopefully new research directions may be opened.

A key research area is to formulate biomedical engineering principles based on a rigorous mathematical foundation in order to develop general-purpose software methods that can be integrated into complete therapy delivery systems. Such systems support the more effective delivery of many image-guided procedures--biopsy, minimally invasive surgery, and radiation therapy, among others.

Mathematical models form the basis of biomedical computing in general and medical imaging in particular. Basing those models on data extracted from images continues to be a fundamental technique for achieving scientific progress in experimental, clinical biomedical, and behavioral research. Images, acquired by a range of techniques across all biological scales, are central to understanding biological problems and their impacts on human health purely because images now encompass so many techniques beyond the visible light photographs and microscope images of biology's early years. Today, imaging is better thought of as geometrically arranged arrays of data samples measuring such diverse physical quantities as time-varying hemoglobin deoxygenation during neuronal metabolism or vector-valued measurments of water diffusion through and within tissue. The broadening scope of imaging as a way to organize our observations of the biophysical world has led to a dramatic increase in our ability to apply novel processing techniques and to combine multiple channels of data into sophisticated and complex mathematical models of physiological function and dysfunction.

The workshop will bring together a diverse group of researchers from the medical imaging community with various backgrounds including radiology, psychiatry, signal and image processing, surgery, physics, mathematics, and neurophysiology.

The workshop will focus on the following topics:

- Medical Imaging Modalities for Brain Imagery: MRI, fMRI, DTI, PET, SPECT, CT;
- Medical Imaging Processing and Computation: Registration, segmentation, visualization, computer graphics, shape theory;
- Mathematical Algorithms: Statistical, geometric, partial differential equations;
- Applications: Image guided surgery (e.g., interventional magnetics), imaging for understanding pathology (Alzheimer's disease, Parkinson's, OCD, clinical depression), image processing and deep brain stimulation.

Experimental biology is uncovering the mechanisms supporting decision-making in individual animals (e.g., in monkeys) and social animal groups (e.g., bees and ants). Multiscale mathematical models are being developed and validated for several species, including those for the (i) neuron-to-behavioral levels in cognitive neuroscience (e.g., diffusion or decision field theory models), (ii) organism-to-group levels for social insects (e.g., differential equations and individual-oriented models), and (iii) individual/group-to-ecological levels in behavioral ecology (e.g., optimization or evolutionary game-theoretic models). Several of these models and species share common features; hence there exists significant opportunities for cross-fertilization and progress toward an understanding mechanisms and whole-system emergent properties. Mathematical, statistical, and computational analyses are being to used to study (i) properties of the dynamics of decision making (e.g., feedback mechanisms, coupling, stability, and speed-accuracy trade-offs), (ii) cross-scale effects (e.g., impact of massively parallel mechanisms at one level on emergence of choice discrimination or distractor elimination abilities at a higher level), (iii) effects of context (e.g., similarity and attractivity effects), and (iv) Darwinian evolution of robustness or reliability in the presence of uncertainty (e.g., isolated failures at one level and environmental variations). The goal of this workshop is to facilitate the development of an integrated "systems biology" of decision-making processes that spans multiple spatio-temporal scales and levels of biological organization, and accounts for the perspectives of biologists, psychologists, economists, mathematicians, and engineers.

This program consists of two parts: (a) two weeks of introductory lectures plus short projects and a computer lab, and (b) a summer long research experience (6 weeks to be followed immediately after the 2 weeks) devoted to projects in the interface of mathematics, statistics, and biological sciences.

The 2008 Summer Program dates are June 23 - July 3

Program Leaders:

- David Terman (Department of Mathematics): Mathematical Neuroscience
- Dennis Pearl (Department of Statistics): Statistical Phylogenetics
- Joseph Verducci (Department of Statistics) and Paul Blower (Department of Pharmacology): Chemogenomics
- Mark Berliner (Department of Statistics): Climate Change
- Greg Singer (Center of Integrative Cancer Biology): Bioinformatics

This year the program will focus on Mathematical Bioengineering. The first week is spent in a tutorial, which combines morning lectures with active learning laboratories in the afternoon. The following two weeks are spent working on guided team projects and participating in a mini-conference to share project results. The program is meant primarily for graduate students; college instructors and qualified undergraduates will also be considered.

The 2008 Summer Program dates are July 7 - 25.

#### July 7-11, 2008

Lecturer: Richard Bertram, Department of Mathematics, Florida State University

Title: Mathematical Modeling in Neuroscience and Physiology

In these lectures Bertram will discuss examples of how mathematical modeling is used in the areas of neuroscience and physiology. Topics include the dynamics of electrically excitable cells, calcium dynamics and waves, fast and slow time scales, bursting oscillations, phase oscillators, circadian gene oscillations, and synchronization of oscillators. A basic familiarity with ordinary and partial differential equations is assumed. Techniques for the analysis of nonlinear ordinary differential equations using phase plane and bifurcation diagrams will be discussed throughout the series of lectures.

Monday: We will begin with a description of neuron models and mean field models for neural populations. Analysis of these models through phase plane and bifurcation analysis will also be discussed.

Tuesday: We will discuss the biophysical mechanisms for and mathematical analysis of bursting oscillations. Oscillations of this type are frequently observed in nerve and endocrine cells.

Wednesday: The next discussion will be on mathematical descriptions of stochastic systems. We will look at stochastic ion channel fluctuations in nerve cells, and hybrid deterministic models that include noise. We will also discuss ways that noise itself can amplify a signal, such as stochastic resonance.

Thursday: Memory is stored in synaptic couplings between neurons. A synapse is a tiny structure that is the center of many reactions that are key to short term and long term memory. We will discuss mathematical models for the mechanisms of both types of memory.

Friday: Synchronization is a widespread phenomenon in neural populations. We will discuss some of the ways that synchronization has been analyzed mathematically, using the phase oscillator as a mathematical tool for the analysis.

### 2006-2007

The workshop will concentrate on atrial and ventricular electrophysiology from models of the biophysics of single ion channels to predicting the electrocardiogram recorded at the body's surface. An overarching theme will be how mathematical models can elucidate mechanisms, improve diagnoses, and identify therapeutic targets for cardiac arrhythmias.

Topics will include:

- Molecular Biology of Cardiac Ion Channels and Transporters
- Formulation and Application of Integrative Models of the Cardiac Myoycte
- Tissue and Organ Models
- Arrhythmia Mechanisms
- Excitation-Contraction Coupling

The workshop will address the mechanical function of the heart from models of the biophysics and biochemistry of molecular motors to predicting the three-dimensional mechanical performance of the whole heart. The theme threading through this workshop will be how mathematical models can improve the diagnosis and treatment of cardiac mechanical dysfunction during disease, especially congestive heart failure, and elucidate the mechanisms by which mechanical factors can regulate cardiac remodeling in vivo.

Topics will include:

- Metabolic and Neurohumoral Regulation of Excitation and Contraction
- Cardiac Muscle Contraction
- Cardiac Constitutive Models
- Modeling Cardiac Mechanics
- The Intact Heart

This workshop will address several important aspects of sleep/wake modeling, including interactions between the homeostatic and circadian processes; the link between sleep/wake dynamics, cognitive capabilities and performance; and how individual differences should be incorporated into the models. Although these questions have received previous study, earlier models have been largely phenomenological and thus far have not accounted for many important aspects such as the cumulative effects of chronic sleep restriction. Recent progress in understanding the neuronal and neurochemical substrates underlying the sleep/wake cycle, as well as the development of theoretical tools for analyzing complex biologically inspired models, makes this an auspicious time to forge new modeling approaches. The workshop will bring together a diverse and highly accomplished group of researchers across the spectrum from experimentation to mathematics. The workshop will focus on the link between sleep/wake regulation and human cognitive performance. It will provide a unique opportunity to exchange points of view, forge new collaborations and develop new approaches to modeling these important issues.

The workshop will address three primary themes:

*Modeling the homeostatic system and how it interacts with the circadian system:*Most current models for sleep/wake regulation and for interactions between the circadian and homeostatic processes are directly or indirectly based on the seminal two-process model of sleep regulation. The two-process model has been successful in accounting for the effects of acute sleep deprivation on sleep and performance; however, the model has been less successful in accounting for experiments involving chronic sleep restriction and subsequent recovery sleep periods. This may be because the two-process model assumes that recovery during sleep occurs in an exponential manner; moreover the model assumes that the homeostatic and circadian processes are additive. More detailed models are needed to better describe the homeostatic process and account for the chronic sleep restriction experiments.*Modeling the link between sleep/wake dynamics and cognitive/psychomotor capabilities:*Most current models estimate the general trend of performance decline under conditions of sleep loss and/or circadian misalignment. There is evidence that sleep/wake alterations have differential effects depending on the nature of the performance task-which is not accounted for in contemporary models. Furthermore, time on task effects have thus far not been included. There is a need to develop models in which parameters have specific physiological and/or neuropsychological correlates, so that the behavior of the model may be interpreted biologically and interventions may be incorporated appropriately.*Modeling individual differences:*Sleep/wake and performance modeling thus far has focused on describing and predicting group-average responses. However, there is accumulating evidence for trait-like individual differences in responses to sleep and circadian challenges. Such systematic individual differences tend to represent a considerable portion of the variance and therefore need to be accounted for. It remains to be determined whether capturing individual differences would require variations in model structure or could be handled with subject-specific parameter settings. New modeling strategies are needed to address these important issues.

Computational modeling promises a new era in the fundamental understandings of how lung morphometry and biomechanical/biomaterial properties impact lung function. With continuous improvement in imaging modalities, it is becoming increasingly possible to establish precise physical locations and degrees of structural or functional defects in the lung during disease. Such data will beg the question of how explicit defects of biological components, processes, and structure at specific anatomic locations alter function. Computational power now permits one to develop models that are closer anatomic replicas of a real lung, while incorporating the fundamental biophysical properties and relations for each exquisite component of each airway. Rational and efficient disease management can be enhanced by understanding or predicting how alterations in the individual components of lung structure and properties impact the emergent lung function.

The workshop aims to:

- indentify critical current questions in asthma, emphysema, and respiratory distress syndrome that can be addressed via mathematical modeling integrated across multiple scales;
- identify modeling challenges associated with understanding fundamental biology and physiology of the constituent parts of the lung ranging from parencymal, alveolar and airway smooth muscle cells, to airways and alveoli and microvessels in the lung, to lung tissue;
- identify role imaging can play to advance models of micro and macro structure and to link structure to function via computational models;
- understand how emergent function and dysfunction in the lung for these diseases relates back to its constituent parts.

The function of the systemic circulatory system is to distribute and remove materials and heat as needed throughout the body. Transport is achieved by convection in the blood and diffusive exchange with surrounding tissue. Because diffusion is effective only over short distances, blood must be brought close to every point in the tissue. To make this possible, the peripheral circulation consists of a highly branched system of blood vessels, containing more than 109 segments, ranging in diameter from about 1 cm down to a few m. The vessels of diameter about 100 m or less are referred to as the microcirculation.

This workshop will focus on three areas:

- blood flow and mass transport in the microcirculation;
- short-term regulation of blood flow, including vascular smooth muscle behavior;
- structural adaptation of blood vessels, including angiogenesis.

Mathematical and computational approaches can make important contributions in all these areas. Continuum and multiphase models can be applied to study blood flow. Simulations of mass and heat transport also typically require solution of partial differential equations. Consideration of network properties is critical to understanding short and long-term control of blood flow. The network can be regarded as a dynamic system in which the properties of each segment (diameter, etc.) evolve with time. Simulations of angiogenesis can use a variety of approaches, including deterministic and stochastic models and cellular automata.

The kidney controls the volume and composition of extracellular fluid and participates in the regulation of blood pressure. Its regulatory function can be understood in terms of the action of resident vascular and epithelial cells. The functional unit of the kidney is the nephron, a long epithelial tubule with attendant vasculature. The kidney processes blood in two basic steps: (1) an ultrafiltrate of blood plasma is formed in specialized vascular capillaries and this fluid enters the renal tubule; (2) the renal tubules transform the ultrafiltrate into urine by means of differential transport of solutes and water through the tubule epithelial cells. These two processes influence each other: the ultrafiltration rate impacts tubule function, and tubule transport can modulate ultrafiltration. Both processes are influenced by body fluid composition, and by neural and hormonal signals that impact on the kidney.

The workshop will focus on the application of mathematical models to elucidate renal function in the context of new experimental methods and data. Physiologists, biophysicists, modelers, and mathematicians will present recent work and discuss current controversies and emerging issues. Topics may include: the regulation of ion channels in renal tubular cells, the regulation of renal hemodynamics, tubular-vascular interactions, new insights into the urine concentrating mechanism, new analytical methods, international computational initiatives, and web-based modeling resources.

Workshop activities include plenary talks and poster sessions, as well as group discussions on issues relevant to mathematical biologists.

We cordially invite young mathematical biologists to participate.

The microRNAs (miRNAs) are small non-coding RNAs that regulate the expression of protein-coding genes. Alterations of miRNA genes have been detected in many human tumors. MicroRNAs expression profiling has been exploited to identify miRNAs that are potentially involved in the pathogenesis of human cancers. Profiling has been allowed the definitions of signatures associated with diagnosis, staging, and progression and response to treatment of human tumors. In addition, profiling has been exploited to identify microRNAs genes that are downstream targets of activated oncogenic pathways or that are targeting protein coding genes involved in cancer.

Identification of miRNA targets is an overarching theme in the research of microRNAs. Normal random variation in sequence complementarity requires assessment of the strengths of putative targets. Experimentally validated and excluded targets are valuable for building machine learning tools for systematic target prediction and filtering. Such issues, among many others, are challenging yet provide great opportunities for statistical and bioinformatical research. Thus, one of the goals of this workshop is to bring interested statisticians to interact with biologists, the majority of the invited speakers, to tackle such, and many other problems in microRNA research.

The traditional feedforward model of the visual system invokes a sequence of processing stages, beginning with the relay of retinal input to neurons in the primary visual cortex (V1), via the lateral geniculate nucleus (LGN), and subsequent higher-order processing through a hierarchy of cortical areas. According to this model, neurons at each successive stage process inputs from increasingly larger regions of space, and code for increasingly more complex aspects of visual stimuli. The selectivity of a neuron to a given stimulus parameter (e.g., orientation, color, depth) is assumed to result from the ordered convergence of afferents from the lower stages.

In this workshop, three different aspects of visual information processing will be considered.

- Thalamus: There is growing evidence that thalamocortical and corticothalamic interactions play an important role in controlling the flow of visual information, both at the initial entry stage where it can be modulated by attentional states, and at higher-order stages involving sensory and motor processing.
- Early visual processing: There is considerable physiological and psychophysical evidence that long-distance integration of visual signals can occur at very early stages of processing including V1. In particular, the response of a V1 cell to stimulation of its classical receptive field (RF) can be selectively modulated by contextual stimuli lying far outside its RF.
- Top-down processing: An important source of top-down influences on bottom-up sensory processing arises from selective attention, in which the saliency of an object can be altered in light of behavioral relevance.

Advances in high throughput chemogenomic profiling such as yeast deletion libraries and whole genome shRNA-based loss-of-function arrays for human and mouse genes promise to accelerate the discovery of potential drug targets and increase understanding of complex interactions between components of a biological system. Chemogenomics can be defined as the use of genomics to measure the system-wide effect of a compound on an intact biological system, either single cells or whole organisms. It combines high-throughput genomics or proteomic profiling with chemoinformatic and statistical analysis to study the response of a biological system to chemical compounds. Cellular response is measured by phenotypic readouts in a high-throughput assay. Chemogenomics also investigates the consequences of differential gene/protein expression on cellular response to compound treatment. For example, expression levels of membrane transporters can have a dramatic effect on compound potency.

Chemogenomics as a discipline has been molded by access to the suite of datasets related to a panel of 60 cancer cell lines from the National Cancer Institute (NCI-60). This is an unparalleled public resource for elucidating molecular targets and mechanisms of chemosensitivity/resistance, with cytotoxic potencies for >50,000 compounds, as well as mRNA profiles and proteomes. In addition, the NCI-60 repertory will soon include expression patterns of microRNAs which can resolve discordant relationships between mRNA and protein expression profiles. The response of cancers to drug treatment is a biological process that cannot be understood by studying individual genes or proteins in isolation. The NCI-60 datasets provide significant opportunities for large-scale datamining and applications of statistical modeling of drug potencies based on mRNA/protein/miRNA expression, alone or in combination with aspects of molecular structure of the drug candidates.

In this workshop, we will survey advances in experimental techniques for high throughput profiling, statistical design and assessment for association, and chemoinformatic techniques for large-scale datamining of compound-gene associations. Chemogenomics draws on many scientific disciplines, and this workshop is intended to foster cross-discipline understanding and lead to long-term collaborations among participants. Conference presenters and discussion leaders will include experimental molecular biologists as well as scientists specializing in statistics, chemoinformatics and drug discovery applications.

The human auditory system from the inner ear to the auditory cortex is a complex multilevel pathway of sound information processing. One of the early stages of sound processing occurs in the cochlea, where the vibration pattern of the basilar membrane encodes the frequency and amplitude of incoming sound signals. Though well-known partial differential equations (PDEs) in classical mechanics provide a solid foundation for describing these mechanical activities, additional nonlinearities must be modeled to capture responses such as tonal suppressions and the observed frequency selectivity.

The workshop aims to explore the mathematical models of the ear at a number of different levels, ranging from PDE models of the mechanics of the basilar membrane, to biophysical models of the outer hair cells, to signal processing applications in industry and health sciences.

Specific workshop topics would be:

- Cochlea: models and mechanics.
- Hair cells: biophysics and active feedback.
- Applications of signal processing methods to hearing aids, ear implants and speech recognition.

The program consists of two parts: (a) two weeks of introductory lectures plus short projects and a computer lab, and (b) a summer long research experience (six weeks to be followed immediately after the two weeks) devoted to projects in the interface of mathematics, statistics, and biological sciences.

The 2007 Summer Program dates are July 9 - 20.

Program leaders:

- Dennis Pearl (Department of Statistics): Statistical Phylogenetics
- Dave Terman (Department of Mathematics): Mathematical Neuroscience
- Greg Singer (Center of Integrative Cancer Biology): Bioinformatics
- Kate Calder (Department of Statistics): Environmental statistics
- Joe Verducci (Department of Statistics): Chemogenomics

This year the program will focus on Systems Physiology. The program leaders are Jim Keener and Chiu-Yen Kao. The first week is spent in a tutorial, which combines morning lectures with active learning laboratories in the afternoon. The following two weeks are spent working on guided team projects and participating in a mini-conference to share project results. The program is meant primarily for graduate students; college instructors and qualified undergraduates will also be considered.

The 2007 Summer Program dates are July 23 - August 10.

#### Lecturer: Jim Keener

Title: Mathematical Physiology

In these lectures Keener will give an introduction to mathematical models of cellular physiological processes, based on material found in Keener and Sneyd, Mathematical Physiology. Included will be discussion of enzyme kinetics and biochemical reaction networks, cellular transport processes (channels, transporters, ATPases), membrane excitability, calcium signaling, cell regulatory processes, bursting and secretion, cellular communication and coupling, and waves in continuous and discrete media. The lectures will assume familiarity with ordinary and partial differential equations, and some understanding of stochastic processes (Markov processes).

### 2005-2006

The purpose of this workshop is to examine the dynamics of adapting systems in terms of their self-organizing property, that is, their ability to spontaneously take on particular ordered, rather than disordered states. This property plays a role at many different levels: the molecular, viral, bacterial, network, and ecological. We propose to organize the workshop according to the levels of description, from molecular to trophic food webs. Topics will include self-organization in the transition from nonliving to living, evolution on neutral networks, evolution of biological complexity, adaptive radiation in bacterial evolution, and stability of trophic networks.

The workshop in phylogeography and phylogenetics will focus on the maturation of quantitative techniques that need to occur in these fields. Analytical development is a challenge for researchers seeking clear and unambiguous inferences because both fields use complicated multiparameterized models. A given pattern of genetic diversity between and among species or populations can usually be explained and produced by different scenarios. Maturation of phylogenetic methodologies will be critical if we hope to study such things as the tree of life, linking phenotypic and historical evolution, ancestral character state reconstruction, viral evolution, and the evolution of regulation in protein expression. Likewise, solving the analytical and computational challenges necessary for phylogeographic inferences will be critical for studying dispersal distances, mating systems, sex-biased dispersal, pathogen history, speciation, selection, local adaptation, hybridization, community history, food web stability, the origin of human pathogens, and the evolutionary history of humans.

In this workshop, we will focus on recent advances in phylogenetic analysis of large datasets considering two major aspects. The first is the problem of analysis of datasets with a large number of taxa (exceeding several hundreds). This includes recent improvements in tree search algorithms and synergistic application of parallelization strategies using Beowulf clusters and distributed computing. The workshop participants will also compare and discuss the use of improved search tools for competing methods (e.g., parsimony, maximum likelihood, Bayesian). This discussion will illustrate advantages and problems associated specific to various methods with the analysis of datasets with large number of taxa.

The second point of discussion will be the problems associated with analysis of large comparative genomic datasets with various types of information (homology, rearrangement, origin, loss, and multiplication among loci between ancestor and descendant genomes). This problem includes the generalization of edit cost models to account for of multiple kinds of genomic change rather than only DNA substitution.

In summary, this workshop aims to gather leading researchers in this field to discuss common and specific problems, applications, and new models for large-scale phylogenetic and genomic analysis.

Most biological organisms face biotic and abiotic environments that are spatially heterogeneous across their species ranges. Traditionally, the theoretical studies of the evolutionary consequences of this heterogeneity have concentrated mostly on the conditions for establishment of locally adapted genotypes and on the maintenance of genetic variation across the whole species.

Recently, the interest and emphasis have begun to shift towards biological questions concerning larger scale effects. For example, one important question is about the effects of the immigration of locally deleterious genes on the degree of local adaptation and the ability of species to expand their ranges. Answering this question has implications for the origin and maintenance of biodiversity. Also, the co-evolutionary roles played by organisms can vary substantially across their species ranges, which can result in complex geographic mosaic of co-evolutionary interactions and rapid changes in local populations. The interactions of spatially heterogeneous selection, the limitation of mating possibilities caused by isolation-by-distance, and the evolution of genetically-based mating preferences can result in splitting the initial population into reproductively isolated populations, i.e., in parapatric speciation. The development of adequate population genetic models of parapatric speciation is necessary to guide the development of statistical methods and hypotheses using emerging genomics data to infer the history of speciation in specific groups of biological organisms.

The complexity of the evolutionary dynamics driven by ecological and co-evolutionary interactions in a spatially explicit context requires the development of modeling approaches that are both sophisticated and realistic. This will hardly be possible without genuinely cross-disciplinary interactions. This workshop will bring together physicists, mathematicians, and theoretical and empirical biologists in an attempt to initiate and simplify such interactions.

Phylogenetic trees are commonly used to describe the evolutionary history of a group of species, and may also be used to study rapidly evolving individual organisms such as certain viruses, bacteria or parasites. These trees are high-dimensional, non-real-valued data objects, with a specific pattern of built-in dependencies that violate the assumptions of many traditional methodologies and thus provide a rich source of statistical and mathematical challenges. This tutorial will provide an introduction to the area illustrated with some interesting and important biological problems that can be addressed using phylogenetic techniques.

Reference: Felsenstein, J (2003) Inferring Phylogenies. Sinauer Associates

Central questions in ecology that directly impinge on applications involve an understanding of spatial aspects of natural systems. While much of classical population and community ecology made assumptions about spatial homogeneity of systems, a large body of theory has developed over the past several decades that provide both key results and general framework for taking account of spatial factors as they affect population structure, community composition, and landscape-level structure. Some of the most critical questions that affect our ability to project the future trends of natural systems, and particularly how human actions impact these systems, must take account of spatial factors. This workshop will provide an entree to a variety of questions of ecological interest that rely upon interesting mathematics, and lead to problems that have had, as yet, relatively little mathematical analysis. The intent of the workshop is to provide an overview of some of the areas of spatial ecology that lead to interesting mathematics.

The themes of the workshop are framed at different levels of organization:

Population Level:

- How do underlying spatial heterogeneities affect population dynamics?
- How much of the observed spatial structure in populations is due to biotic versus abiotic factors?

Community Level:

- How do underlying spatial heterogeneities affect community dynamics?
- How much of spatial structure in communities is due to biotic versus abiotic factors?
- The above questions are to be addressed both within and between trophic levels.
- How do spatial aspects of systems affect disease dynamics?

Landscape Level:

- How do the spatial aspects of ecological systems affect natural resource management issues?
- How do social choice criteria interface with ecological spatial dynamics for systems in which there is the potential of human control?
- Can we manage natural systems, e.g, under what circumstances can we expect to be successful in determining the impact of human actions given uncertainties about our models and the stochasticity inherent in natural systems driven by abiotic factors?

To provide a forum for young mathematical biologists to interact with their peers, the Mathematical Biosciences Institute hosted the Second Young Researchers Workshop in Mathematical Biology. The workshop brang together approximately 45 young researchers in mathematical biology to broaden their scientific perspective and to develop connections that will be important for their future careers.

We cordially invited postdoctoral researchers and junior faculty to apply for participation in this workshop. A limited number of advanced graduate students were also accepted.

Each participant presented a poster of current research and gave a five-minute advertisement of the poster. The workshop also featured working group discussions on broad issues relevant to researchers in mathematical biology.

Plenary talks were given by leading researchers in mathematical biology:

- Catherine Carr, University of Maryland
- Leah Edelstein-Keshet, University of British Columbia
- Bard Ermentrout, University of Pittsburgh
- Philip Maini, Oxford University
- Hans Othmer, University of Minnesota
- Timothy Secomb, University of Arizona
- Arthur Sherman, National Institutes of Health
- Kristin Swanson, University of Washington

The field of ecology is becoming increasingly aware of the importance of accurately accounting for multiple sources of uncertainty when modeling ecological phenomena and making forecasts. This development is motivated in part by the desire to provide an accurate picture of the state of knowledge of ecosystems and to be able to better assess the quality of predictions of local and global change. However, accounting for various sources of uncertainty is by no means a simple task. Ecological data are almost always observed incompletely with large and unknown amounts of measurement error or data uncertainty, and often the expense of data collection prohibits collecting as much data as might be desirable. In addition, most ecological phenomena of interest can only be studied by combining various sources of data; aligning these data properly presents interesting statistical challenges. While data plays a large role in most ecological analyses, incorporating scientific knowledge into the analyses through substantive modeling of ecological processes is essential. Often such theoretical contributions are based on competing scientific theories and simplifications of reality. This results in an additional source of uncertainty termed model or process uncertainty. Finally, substantive models must acknowledge parameter uncertainty. For example, more realistic descriptions of ecosystems might allow parameters to vary over space and time.

The aim of this workshop is to present a thorough investigation and discussion of these various sources of uncertainty that typically play a role in ecological analyses and of the statistical techniques that enable proper inferences and predictions to be made in light of these uncertainties. These concepts will be illustrated using new data sources and sophisticated modeling tools developed for studying a diverse collection of ecological phenomena. In addition, there will be a discussion of strategies for reducing some of the sources of uncertainty including improved design of monitoring networks. This discussion will promote increased communication between the theoretical and empirical communities as to prioritizing data collection efforts. One of the largest communities to use these methods for important decision-making is state and federal governments, and they will be involved in the workshop as well. In summary, this workshop will provide an opportunity for the ecological science community to interact with the statistical and abstract-modeling communities and will promote novel, interdisciplinary research developments on complex models, inference, and design in the face of various sources of uncertainty.

Microbial ecology is the study of how micro-organisms interact with each other and with their environment. The whole field is thus a study of a dynamic system where properties of the system emerge from the constraints imposed by the chemistry of the environment, physical laws, and the biological strategies that have evolved in the interacting micro-organisms. The struggle to understand these interactions implies the analysis of phenomena occurring on spatial scales from that of viruses (10-8m) to that of ocean chlorophyll distributions (10^{6}m) and on time scales from milliseconds to a few billion years; for example, from the biophysical processes of photosynthesis to those of biological evolution. Such analysis creates an interface that demands insight into both biology and mathematics.

Microbial ecology is also a field that evolves rapidly. Molecular techniques have allowed experimentalists to address questions concerning, for example, microbial diversity, unanswerable with traditional methods. Micro-organisms unknown a few decades ago have been shown to be among the most abundant organisms on earth such as, for example, the tiny cyanobacteria dominating primary production in large parts of the ocean, and SAR11, a bacterium which is probably the most abundant organism on earth, but whose function in the ecosystem is still obscure.

The objective of this workshop is to describe areas in microbial ecology where the tools of mathematics have been used to provide insight into the phenomena.

The globe is warming because humans are altering the global cycling and distribution of carbon. Fossil fuel burning, land management transfer carbon, and other nutrients formerly in relative stable pools into the atmosphere as CO2 and other gasses. These gasses in turn trap heat and alter the heat/energy budget of the earth, which in turn feeds back and alters element cycles further.

Global element cycles and energy flows present several problems to both ecologists and mathematicians. The most salient feature of the globe as a system is that it is closed to element cycles but open to energy fluxes. What happens when we close a dynamical system by coupling component open systems and still maintain the constraint of conservation of matter?

Element cycles are also not independent of one another but are coupled through relatively constant stoichiometries of elements for specific fluxes or specific compartments. How do changes in these constants alter the stabilities and trajectories of the closed global ecosystem as opposed to the more open sub-ecosystems that comprise it?

Feedbacks between ecosystem components can result in alternative stable states of material cycles. Changes in global control parameters (e.g., temperature, precipitation, and their spatial distributions) could cause rapid shifts between these stable states. What kind of bifurcations might underlie a closed system like the globe?

These are a few of many representative problems of global ecology with interesting biological and mathematical aspects. This workshop will bring together ecologists and mathematicians to explore these or other problems.

Beginning in 2006, the MBI hosted a summer education program for undergraduates. The program consists of two parts: (a) two weeks of introductory lectures plus short projects and a computer lab, and (b) a summer long research experience (six weeks to be followed immediately after the two weeks) devoted to projects in the interface of mathematics, statistics, and biological sciences.

The 2006 Summer Program dates are July 5 - 17.

Program leaders:

- Dennis Pearl
- David Terman
- Kate Calder
- Ramana Davuluri

This year the program will focus on Ecology and Evolution. The program leaders are Kate Calder and Yuan Lou. The first week is spent in a tutorial, which combines morning lectures with active learning laboratories in the afternoon. The following two weeks are spent working on guided team projects and participating in a mini-conference to share project results. The program is meant primarily for graduate students; college instructors and qualified undergraduates will also be considered.

The 2006 Summer Program dates are July 17 - August 4.

#### Topics:

- Effects of spatial heterogeneity on invasions of rare species
- Patterns of multiallelic polymorphism maintained by migration and selection
- Evolution of ranges of species
- Spatial modeling of trends in species abundance
- Modeling wild bird population dynamics from citizen surveys
- Constructing the progression pathway from normal tissue to carcinoma

### 2004-2005

A (protein coding) gene is determined to be expressed in a cell or group of cells when its transcribed messenger RNA (mRNA), or the resulting protein product, is detected. There are a wide variety of techniques for determining and quantifying gene expression, and most of these have substantial analytical components to them.

We measure gene expression in order to compare the expression levels of one or more genes in cells from different sources. Comparisons of interest include tumor versus normal cells, cells from a specific organ in a mutant, or genetically modified organism versus cells from the same organ in a normal organism of the same strain, and cells before and after an intervention such as a drug treatment.

There are many techniques for measuring gene expression, but perhaps most common at the moment are ones which rely on DNA-RNA or DNA-DNA hybridization. This is the process through which single-stranded DNA and RNA molecules find and base-pair with their complementary sequences amidst a complex mixture of many molecules of the same kind.

The older cellular-wide method for measuring gene expression at the protein level was two-dimensional gel (2D-Gel) analysis, where complex mixtures were separated by pH and size using isoelectric focusing and polyacrylamide gel electrophoresis (PAGE). The technique was combined with mass spectrometry (MS) in the 1990s, and now there are a number of electrophoresis-free MS based approaches to measuring protein levels. More recently, protein arrays have been developed, and some of these will be discussed later in the year in Workshop 4.

On what scale do we measure gene expression? Much of the recent interest by statisticians in this area stems from the availability of data sets giving expression measurements on tens of thousands of genes; so-called microarray gene expression data. However, nylon membrane filters with thousands of genes spotted on them have been around for over a decade, and smaller-scale quantitative expression data for much longer. Similarly 2D-Gel data are quite extensive, and MS-techniques, especially when done in conjunction with other separation techniques can produce up to 10^8 data points per sample. There are many differences between these different technologies, but from the analytical viewpoint, many similarities as well.

In this workshop, we will survey some of the computational, mathematical, and statistical models and methods used in analyzing gene expression data. Much of our focus will be on approaches quantifying mRNA, as that is the most well developed. We shall also present a small sample of the extensive biological and technological background to gene expression anaylsis.

It has been over 40 years since Monod and Jacob boldly predicted that such fundamental cellular processes as differentiation and protein regulation are accomplished through signaling pathways resident at the level of the gene. This prediction laid the foundation for the ensuing progress in describing the essential regulatory mechanisms in many specific genetic systems. With the development of the field of nonlinear dynamics and the concurrent advent of available computing, mathematical models describing gene regulation began to appear regularly in the 1970s. Implicit in these studies was the realization that the "wiring" of naturally-occurring gene regulatory networks would be too complex for qualitative descriptions devoid of mathematics. Though this realization proved to be ahead of its time, mainly due to the lack of experimentally deduced regulatory pathways in the "pre-genomic" era, recent experimental advances in both sequencing and genetic engineering have made the analysis and design of gene networks amenable to quantitative analysis. These advances have reignited interest in gene regulatory models that can be used to explain and predict behavior that emerges from gene regulatory networks.

In this workshop, we will focus on recent advances in utilizing mathematical models to describe gene regulatory networks. The workshop will begin by introducing mathematical modeling techniques, including boolean representations, classical kinetic theory, stochastic simulation methods and constraints-based models. This will be followed by descriptions of specific gene regulatory networks, such as those related to the lambda and T7 life cycles, drosophilia segmentation, and xenopus oocytes differentiation. The remainder of the workshop will be devoted to the construction and analysis of synthetic gene regulatory networks, including switches, oscillators, autoregulation, and noise analysis. The workshop will highlight the utility, which an accurate mathematical description of synthetic networks provides, in describing complex naturally-occurring networks.

Proteomics is defined as the study of the total protein complement of a cell. This broad definition covers a lot of ground, including, but not limited to protein identification and quantification in specific cellular environments, structural genomics and fold recognition, identification and characterization of functional domains, and finally, the networks defining the interactions of proteins with bio-molecules (proteins, DNA, etc.). With the sequencing of the genome, and subsequent identification of the parts list (the gene and their protein products), there is a renewed emphasis on studying the proteome.

In this workshop, we will focus on emerging technologies for probing the proteome, with two focal points. The first is the computational analysis of mass spectrometry data. Simply speaking, a mass spectrum is a collection of masses and (relative) intensities of charged molecules. The spectrum of mass fragments of a protein (or peptide) sequence form a fingerprint that can be used for identification and relative quantification. Post translational modifcations can be measured using characteristic shifts in the spectrum. Various computational issues arise in the analysis mass spectrometry data for protein identification and quantification.

The second focus is the analysis of protein function, with an emphasis on combining evidence from emerging high-throughput technologies. Many techniques have been developed to profile protein function directly and indirectly. For example, multiple alignments of evolutionary-conserved protein domains provide direct annotation of functions of a protein; gene expression profiles can be used to cluster proteins with similar functions; protein interactions show how proteins interact with one another to carry the necessary functions. In particular, a large amount of protein interactions have been generated recently by several large-scale techniques such as mass spectrometry, gene-knockout, and yeast two hybrid assays. These data together provide us with a global view of the protein netwrok inside the cell. Analysis of such networks is critical to understand the biological system at the molecular level.

The workshop will aim to bring together the leading researchers in these areas to describe the state of the art, and also to present problems that will challenge the next generation of Bioinformatics researchers.

It is arguable that the genomics revolution is largely technology-driven. Whatever one's view on this question, it is hard to imagine genomics without the polymerase chain reaction (PCR), invented as recently as the mid-1980s, or without high-throughput DNA sequencing, which emerged a little later. More recently, we have had the advent of the microarray (DNA chip) and high-throughput mass spectrometry (MS), which have greatly enriched functional genomics and proteomics, respectively. An inevitable consequence of the wider perspective of genomics and proteomics is the desire to extend assays, once carried out with one gene or one protein, to be as effective with hundreds of thousands of genes at a time, aiming at genome-wide or proteome-wide coverage. Thus, we now have a wide variety of high-throughput assays for measuring gene expression, at both the mRNA and protein levels, emerging ones for measuring DNA-protein and protein-protein interactions, and a constant drive to narrow the focus of the assay (e.g., to a single cell) and reduce the quantity of reagents needed.

Each advance of this kind brings with it many computational, mathematical, and statistical questions, both in the generation and initial processing, and in the analysis and interpretation of the data. While the details of the different technologies necessarily differ, many common themes emerge. These include issues, such as signal processing, signal manipulation, and quantification algorithms, as well as a host of common analysis tasks, such as classification, clustering, and the analysis of time course data. The purpose of this workshop is to introduce participants to some of these emerging technologies, and to have talks, which outline their quantitative needs so that we can highlight common analytical themes.

The Mathematical Biosciences Institute will held the First Young Researchers Workshop in Mathematical Biology, March 29 - April 1, 2005, organized by the MBI Postdoctoral Fellows.

The principal aim of the workshop was to bring together approximately 40 young researchers in Mathematical Biology, to broaden their scientific perspective, and to develop connections that will be important for their future careers.

The workshop included several plenary talks by leading researchers in Mathematical Biosciences. The plenary speakers were: Charles Peskin, James Keener, Tamar Schlick, Claudia Neuhauser, Alex Mogilner, and Louis Gross. There was also a panel discussion led by Kirk Jordan (IBM) and Frank Tobin (GlaxoSmithKline) on "How to develop a career in mathematical biology in industry."

The workshop included poster presentations and short talks by the young researchers, and working group discussions on broad scientific issues that bridge the gap between data, modeling, and applications.

This workshop addresses the issue of the medical application of new scientific technologies, such as microarray and PCR. The medical applications will include use of measurements based on these technologies as biomarkers for diagnosis, disease progression, and effects of treatment. The disease areas in which applications will be considered include HIV and other viral infections, and cancer.

HIV: The new technologies have directly impacted clinical management of HIV infection. HIV gene sequencing is used to evaluate drug susceptibility and thereby select treatment regimens for drug-experienced patients. PCR technology makes it possible to count HIV RNA particles in body compartments. Such measures allow evaluation of drug efficacy in suppressing virus both in plasma and in genital secretions. They also allow modeling of HIV dynamics, providing insight into the mechanisms of drug action. In addition to viral genomics, human genomics is also a developing area of research. In particular, there is interest in determining whether polymorphisms in specific host genes explain patient variability in treatment response, toxicity, and pharmacokinetics of antiretroviral drugs.

The sessions will include methods for relating HIV genotype to resistance phenotype; methods for modeling the accumulation of HIV resistance mutations; and relationship of host genomics to treatment response, toxicity, and pharmacokinetics of ARV therapy.

CANCER: Biomarkers are an important component of oncology practice at present, particularly in monitoring for cancer recurrence and in early detection of some cancers. However, with the recent explosion of genomic and proteomic technologies, biomarkers have the potential to contribute far more broadly to cancer research and oncology practice, including the following areas: early detection of cancer in asymptomatic subjects; differential diagnosis for patients presented with symptoms; monitoring for recurrence; risk stratification for clinical trial eligibility or selection of subjects for prevention/early detection strategies; prognosis; aid in therapeutic decision-making; monitoring the course of therapy; and surrogate endpoints for clinical trials.

Statistical challenges abound in all these areas, ranging from methods to identify suitable biomarkers to optimization of their application. Tight collaboration between statisticians, biologists, surgeons, and physicians, where biological and medical knowledge is incorporated in the statistical modeling whenever possible, will likely increase the chances of biomarkers realizing their full potential impact.

This workshop aims to highlight the statistical challenges involved in the areas of HIV and cancer research and medical practice, present statistical research in progress, and provide a forum for discussing current answers to the statistical challenges and future directions.

Over the past several years, it has become increasingly appreciated that the dynamic properties of enzymes can play a significant role in modulating their catalytic properties. The motions involved can range from the vibration of individual chemical bonds or groups of bonds (taking place on the femtosecond timescale and involving distances of less than 1 A) to large domain motions (taking place on a timescale of milliseconds to seconds and involving distances as great as 10 A or more). With the accumulating experimental evidence attesting to the importance of these motions in catalysis, it has become important to develop appropriate mathematical models for enzyme behavior that provide a conceptual framework within which to understand the influence of this dynamic behavior. The MBI workshop on Enzyme Dynamics and Function will bring together leaders in this emerging field to present their recent work and to participate in discussion groups that will provide a forum for both mathematicians and enzymologists to consider the fundamentals relevant to the field.

Understanding the nature and causes of linkage disequilibrium in the human genome is important for mapping complex disease loci through association studies. The sequencing of the human genome revealed a remarkable haplotype structure and led to the HapMap project whose goal is to understand the patterns of DNA sequence variation. In a parallel development, recent studies have shown that much recombination occurs in hot spots. This workshop will concentrate on mathematical, statistical, and computational approaches to estimating recombination rates and determining the causes of haplotype structure.

This year the program will focus on Microarray Gene Expression Data Analysis. The program leaders are Shili Lin and Joseph Verducci. The first week is spent in a tutorial, which combines morning lectures with active learning laboratories in the afternoon. The following two weeks are spent working on guided team projects and participating in a mini-conference to share project results. The program is meant primarily for graduate students; college instructors and qualified undergraduates will also be considered.

The 2005 Summer Program dates are August 1 - 19.

#### Mentors

*Statistics Mentors*: Shili Lin and Joe Verducci*Computational Mentors*: Victor Jin, Greg Singer, and Ramana Davuluri*Wet Lab Leaders*: Pearlly Yan, Michael Chan, and Alfred Cheng

### 2003-2004

The cell cycle is the sequence of events by which a growing cell replicates all its components and divides them between two daughter cells, so that each daughter receives all the information and machinery necessary to repeat the process. Because cell proliferation underlies all biological growth, development, and reproduction, an understanding of the molecular machinery controlling cell growth and division is a fundamental goal of cell biology. In the past 15 years, there has been an explosion of information about: (1) the genes and proteins that regulate DNA replication, mitosis and cell division (the cell cycle "engine"), and (2) the signal transduction pathways that control the "accelerators and brakes" of the engine. Everyone now agrees that this regulatory network is so complex that rigorous mathematical modeling will be required to understand the intricate relationships among its components, and to derive the observed behavior of proliferating cells to the underlying regulatory system. The purposes of the first workshop of this quarter are to summarize current knowledge about the molecular controls of cell division, to examine the state-of-the-art in computational modeling of these controls, to open a fruitful dialogue between experimental cell biologists and theoreticians, to define the next set of problems to be attacked by mathematical modeling, and to recruit a new generation of collaborative experimentalists and theoreticians to the problem.

The workshop will focus on the cell cycle engine and signal transduction pathways in mammalian cells to set the stage for the next workshop, which will address issues of cancer biology (tumorigenesis, angiogenesis, chemotherapy, drug resistance). The first 2 days will address the mammalian cell cycle engine, as sketched out in a molecular wiring diagram published by Kohn in Molec Biol Cell (10:2703-2734, 1999). Speakers will address the following issues:

- Cyclin-dependent kinases and their partners (cyclins A, B, ...),
- Cyclin-dependent kinase inhibitors (p15, p21, p27),
- Regulation of cell cycle genes expression,
- Cell cycle checkpoints,
- Computational models.

Days 3-5 will focus on the network of signal transduction pathways surrounding the cell cycle engine, as described in a recent review by Hanahan and Weinberg in Cell (100: 57-70, 2000):

- Growth signals (MAP kinase pathway -> cyclin D and pRb),
- Antigrowth signals (TGFb -> Smads -> p15, p21, p27),
- Cell adhesion signals and anoikis (Integrins, Cadherins),
- Survival factors (e.g., IGF1 -> P13K -> NF-kB, FGF -> MEK),
- Cell suicide signals (intrinsic and extrinsic pathways of apoptosis),
- Immortalization (telomerase dynamics),
- Genetic instability (p53 and DNA damage checkpoint).

The mathematical tools that are expected to contribute strongly to these questions are:

- Dynamical systems theory
- Bifurcation theory
- Multiple time scales
- Parameter estimation
- Robust control
- Stochastic differential equations
- Graph theoretic methods

The workshop will bring together experimental cell biologists, theoretical biologists, mathematicians, and computer scientists who are all interested in problems of cell growth, division, and death.

Several dynamic processes play an important role in the response of a cell to therapy. This workshop will focus on the dynamic interplay of biological factors that determine the outcome of chemotherapy of cancer. The key factors are: (a) delivery of therapy to target tumor cells, (b) mechanisms of drug action, (c) growth and differentiation of cell populations, (d) initiation and development of resistance, and (e) optimization of chemotherapy protocols.

- Delivery of therapy to target tumor cells. Over 80% of human cancers are solid tumors. Presentation of a drug to cells in a solid tumor and the accumulation and retention of a drug in tumor cells depend on the drug delivery from the site of administration, the ability of the drug to diffuse through the interstitial space, and the binding of the drug to intracellular macromolecules. Some of these factors are also time- and drug- concentration-dependent. For example, the interstitial space, which determines the porosity and therefore the diffusion coefficient, may be expanded due to drug-induced apoptosis. Mathematical models to depict how these processes affect the drug delivery to tumor cells are useful to identify the treatment regimens that will result in the most effective drug concentration and residence time in the target sites.
- Mechanisms of drug action. Most anticancer drugs act on specific molecular targets that are often involved in the regulation of cell growth, cell differentiation, and cell death. Mathematical models to link the effective drug concentration in the tumor cells with the molecular targets, in a time- and concentration-dependent manner, are needed to improve the understanding of drug-target interaction.
- Mathematical modeling of growth and differentiation of cell populations. This is one of the oldest and best developed topics in biomathematics. It involves modeling of growth and differentiation of laboratory cell populations, of populations of normal cells, and of cell in tumors. Precise mathematical models exist for the processes of haemopoiesis (blood cell production) and self-renewal of colon epithelium. Mathematical tools used vary from stochastic processes (useful when describing small colonies or early stages of cancer) particularly branching processes, to nonlinear ordinary differential equations (useful for modeling feedbacks of cell-production systems), to integral equations and partial differential equations (useful for modeling heterogeneous populations). The challenges involve integrating newly described genetic and molecular mechanisms in the models of proliferation, as well as mathematically modelled geometric growth of tumors in various phases (prevascular, vascular, anoxic), and heterogeneity of tumor populations. Mathematical tools needed involve partial differential equations with free boundary, bifurcation in systems of many nonlinear ordinary differential equations, and branching processes with infinite type space.
- Genetic basis, initiation, and development of resistance. Cancer cells are genetically unstable and can acquire genetic and phenotypic changes that permit them to escape cytotoxic insults. Development of drug resistance is a major problem in cancer chemotherapy, and is usually acquired after exposure to a drug. Development of drug resistance is often a function of the frequency, intensity and duration of drug exposure, as well as the chronological age of the cells. These biological parameters can be described in mathematical terms.
- odeling and optimization of chemotherapy protocols. This is an area of potentially great practical importance. Classical models involve populations of normal and cancer cells described as systems of ordinary differential equations with control terms representing treatment intervention. The most common approach involves defining a performance index, which summarizes efficiency of the therapy and damage done to normal (non-cancer) cells, and using methods of control theory to find the best value of the index. These models had a lot of appeal in the early days of chemotherapy, when the complexity of tumor cell populations was not entirely appreciated. There exist models taking into account emerging resistance (like the Coldman-Goldie clonal resistance model), and heterogeneity (e.g. gene-amplification), but they are based on unrealistic biological hypotheses. Challenges for the field involve more realistic models of drug action and cell proliferation and heterogeneity, as well as new methods for parameter estimation. Mathematical tools needed involve robust optimal control in systems of ordinary differential equations, resonance results for periodic dynamical systems, and control of infinitely-dimensional and distributed systems.

The use of mathematical models to describe these biological processes will improve the understanding of the dynamic interplay between these processes and the ability to translate the basic science findings to clinical application. The challenges involved will undoubtedly lead to new mathematical problems and give rise to the development of new mathematical and computational methods.

In this workshop, we shall study mathematical models for the processes whereby a cell converts an external signal into a signal of a different kind, with particular emphasis upon those transduction mechanisms that rely on the dynamic control of the intracellular calcium concentration. For instance, in response to an external signal such as a neurotransmitter or a hormone, many cell types exhibit oscillations in the concentration of intracellular free calcium, oscillations which themselves control a variety of intracellular processes, including secretion, gene expression, cell movement, or wound repair. In muscle cells, the release of calcium from the sarcoplasmic reticulum controls muscle contraction, while in photoreceptors calcium forms an important negative feedback loop that controls adaptation. In neurosecretory cells, oscillations of the cytoplasmic calcium concentration lead to hormone secretion. Thus, calcium is an integral part of many different transduction processes. It aids in the conversion of an electrical signal to a force (muscle cells), it aids in the conversion of a light signal to an electrical signal (photoreceptors), and it aids in the conversion of one hormonal signal to another hormonal signal or an electrical signal to a hormonal signal (neurosecretory cells).

Mathematical tools: ODEs, PDEs, bifurcation theory, nonlinear traveling waves, excitability, stochastic models, perturbation theory

Communication from cell to cell, or from a neuron to a muscle, is obviously an important physiological process, and one in which calcium plays a crucial role at many points. The release of neurotransmitter at a synapse or neuromuscular junction depends upon a raised calcium concentration in the nerve terminal, while muscle contraction depends on the release of calcium from the sarcoplasmic reticulum leading to contraction of the actin and myosin filaments. Mathematical models have been a part of the long history of the study of both muscles and synapses, with the earliest models being over a century old. In this workshop, we shall begin by studying mathematical models for synapses, and how calcium plays an important role in the secretion of neruotransmitter. We will then continue by considering models of the release of calcium via ryanodine receptors and, finally, consider models of force generation by actin and myosin.

The Blood Oxygen Level Dependent (BOLD) image contrast provides an important mechanism for tissue characterization with Magnetic Resonance Imaging. Among the neuro-functional of applications of BOLD fMRI are fundamental assessments of the processing of motor, visual, auditory, and sensory tasks by the brain, the evaluation of various diseases including neurological disorders, the pre-surgical determination of brain function, and the evaluation of psychiatric diseases. The BOLD effect is also a dominant mechanism for imaging at an ultra-high magnetic field strength and for cardiac imaging.

Currently, the majority of neuro-functional applications use BOLD fMRI in a qualitative fashion and employ statistical analysis to extract the signal changes present in fMRI data. This task is difficult because of the highly spatially and temporally correlated nature of fMRI data and because of the small levels of the signal changes (1-4%).

For a complete understanding of the BOLD effect and its relation to neuronal activation, one must not only understand where signal changes occur but also the physiologic and physical mechanisms causing the signal change. A number of studies have addressed these issues, however many details regarding these physical and physiologic mechanism remain open questions.

The physical modeling of fMRI data involves the description of MRI signal changes due to the diffusion of tissue water molecules in the locally variable magnetic fields produced by paramagnetic deoxyhemoglobin. These spatially variable magnetic fields, on a 10-100 m scale, can be described mathematically; this knowledge can be used to estimate the signal from water proton diffusion in different tissue compartments (intra-, extra-vascular) and in different geometries (of the vascular and micro-vascular network), as well as the amount and distribution of deoxyhemoglobin. Physiological models are needed to explain the altered amount of deoxyhemoglobin during neuronal activation and its dependence on blood oxygenation, cerebral metabolic rate, oxygen extraction fraction, cerebral blood volume, and cerebral blood flow. It needs to account for the interconnectedness of these different factors under normal or pathologically altered physiologic conditions. Using this knowledge, the statistical modeling of BOLD fMRI signal changes can be improved by better descriptions of the spatial and temporal correlations present in such data, and the prior extent of activation for different tasks. This will, in turn, lead to a more accurate understanding of the physiologic and physical mechanisms causing the signal change.

This workshop will bring together researchers from the statistical, imaging, and modeling communities; it seeks to integrate their knowledge to enhance the medical and basic biomedical sciences communities' understanding of the physiologic and physical mechanisms causing BOLD fMRI signal changes.

The general goal of this workshop is to bring together immune system theorists and experimental immunologists with mathematicians who can become stimulated by this exciting and important area, and who may be able to make an impact by contributing new methods and tools of analysis. First, we will consider how cells of the immune system receive and send signals, i.e., how their surface receptors initiate signaling cascades, and how these cells secrete lymphokines that stimulate other cells of the immune system. Next, we will focus on questions concerning cells of the immune system and how these cells respond and communicate with other cells and antigen. Lastly, we will explore the dynamics of interactions among B cells, T cells, and antigen presenting cells, and the regulation of these populations during an immune response. We will examine events occurring during immune responses, including the formation of spatial structures, such as germinal centers, as well as problems dealing with somatic mutation and affinity maturation. The mathematics employed will involve systems of nonlinear ordinary differential equations, partial differential equations, cellular automata, stochastic processes, and computer simulation.

In this workshop, we will focus on modeling the dynamics of pathogens interacting with the immune system. We will do this in three main areas: viral models, bacterial models, and parasitic models. We will then explore chemotherapy treatment strategies and the generation of drug resistant mutants. Treatment will be discussed on the last day of the week.

Large numbers of cells and organisms, and long time scales, make differential equations the appropriate and primary tool used to study these phenomenon. Delay equations, simulations, and stochastic models will also play a role.

This year the program will focus on Cell Processes. The program leader is Professor James Sneyd. After an introductory tutorial and discussion in the first two days, the participants will be divided into teams of five, with each team being led by an MBI postdoc. Teams will work on one project for the first two and a half weeks, and there will be a miniconference in the final two days.

During the three-week period there will also be several general talks on cell cycle and proliferation by active researchers and visits to bioscience labs.

### 2002-2003

Dynamics plays an important role in neural systems at many levels from the subcellular up to the network levels. The time scales range from the submillisecond to many hours and as a consequence there are many different levels of detail reflected in the models. One of the main interests in systems and cellular neuroscience is to understand how the nonlinear properties of neurons and their connections sculpt inputs and change over time. Recent experiments have shown that the connections between neurons are not static and are influenced by the previous history of the neuron, the relative timing of spikes, and the local firing properties of the neuron. This workshop will focus on the temporal dynamics of neurons at the single cell and network levels.

The dendrites of neurons are often modeled as simple passive delay lines. However, experiments have revealed that there are many nonlinear time-dependent currents which can render the neuron sensitive to both the relative timing of inputs as well as their spatial distribution. Back propagation from the soma through the dendrites has been linked to changes in synaptic efficacy between connected neurons. One of the goals of the workshop is to consider the functional roles of these active processes.

As mentioned above, connections between neurons are dynamic even in relatively short time scales. For example, it has experimentally shown that the strength of connections between two neurons can change depending on the relative firing times of the two connected neurons. These dynamic synapses have been shown to alter the gain control in circuits.

Small networks of neurons have been shown to generate a variety of rhythms. Propagating waves appear to play a role both in development and in sensory processing while synchronous rhythms have been implicated in learning and the separation of inputs. Part of this workshop will be devoted to asking what the possible role of these rhythms is, how they are generated, and how they interact to form spatio-temporal patterns of activity such as transient synchrony and waves.

Large scale modeling of cortical networks requires certain simplifications be made in the characterization of individual neurons. One of the goals of this workshop will be to connect the biophysically detailed models of single neurons and dendrites to the simplified units required in large-scale simulations. Several mathematical approaches to this problems have been quite fruitful. These include mean-field methods (population averages), averaging methods (exploiting differences in time scales), and perturbation methods (weak coupling, neurons near a bifurcation point, etc).

The workshop will bring together computational neuroscientists, mathematicians, and experimental biologists who are all working on questions about the role of temporal dynamics in cells and networks of neurons.

The mathematical areas that are expected to be strongly involved in this workshop include dynamical systems (multiscales, bifurcations, perturbation methods), mean field methods, PDE's, integral differential equations, and stochastic equations.

An important set of issues in computational neuroscience centers around bridging scales of modeling and neural system description. Some formulations at the cell and circuit levels are well-developed and experimentally based, and linkages between the two levels are beginning to form - for example, theoreticians are actively seeking derivations of the mean-field population equations for N-cell network models. In contrast, system level descriptions have traditionally been viewed more-or-less as black box formulations, unconstrained in many cases by system-level neurophysiology and without support by neural correlates. We are beginning to see now, the growth and appearance of system level models with closer links to anatomy and physiology. This is partly driven by new methods of system level data collection including imaging (e.g. fMRI) and multielectrode arrays with simultaneous recording in several brain areas. This workshop will bring together neuroscientists and modelers who are developing more neurally-motivated system level treatments. It will also include researchers with cell and circuit modeling experience who seek to step-up to the "higher-level" descriptions.

This higher level modeling addresses significant questions that are difficult to formulate and correlate with neurophysiology at lower levels - for example, questions about cognitive behavioral tasks, reward, attention, adaptive control, neural representation of the environment, learning and planning of motor control. A major goal is to develop formulations that capture the essence of such behaviors and the multi-level feedback loops without confounding one's understanding by excessively detailed models. In this way one hopes to identify some principles of operation. A major challenge is to chose good model systems so that formulations include potentially identifiable variables, say that might be related to imaging data, and parameters. By including some circuit level researchers we also hope to alert system-level modelers to some aspects of lower-level description that could have consequences for or clarify some underlying assumptions of the high-level models. Examples will be drawn from motor-control systems with possible links to Parkinsonism and bio-motivated robotics, language/vocalization, predictive or adaptive sensory/cortical processing, dynamics of interconnected brain areas during cognition such as delayed match-to-sample tasks.

The mathematical areas that are expected to be strongly involved in this workshop are the same as for the first workshop.

How is information about the external world and about animals's internal states represented within their nervous systems? Although a great deal is known about the relationships between the stimulus/response properties of nerve cells in a variety of systems, we are in many cases far from having a detailed understanding of the correspondence between neural activity patterns and the information represented by those patterns. We will not be able to understand the operation of any nervous system rigorously until we decipher the neural code, i.e., the system of symbols used to represent and convey information within that system. A sound, rigorous understanding of neural coding will also be essential from the standpoint of developing sophisticated models of nerve cells and systems. What aspects of neural ensemble activity patterns should be measured experimentally and incorporated into models?

There is probably no such thing as THE neural code, universal across all animals or even between different subsystems in a single animal, in the same sense as there exists a universal genetic code. However, general principles of neural encoding are starting to emerge. Much recent work in this area involves the application of sophisticated statistical approaches to the analysis of neural spike train data, and applied mathematicians have made substantial contributions to this area of research. Numerous approaches to the estimation of information-theoretic quantities from spike trains have been proposed and applied in a variety of systems. However, many of the approaches are based on very different sets of assumptions. Some significant differences have emerged in the interpretations of these information theoretic analyses, and it is unclear how much of these differences can be explained by differences in what is actually being measured, to the biases or hidden assumptions in the methodologies, or to real differences in the biological coding schemes. The whole field is ripe for a rigorous examination, comparison and normalization of the different approaches. Neuroscience would benefit greatly from an increased involvement of mathematicians and statisticians in extending the analytical framework, and from their direct involvement in designing and interpreting the experiments.

Three general aims of the workshop include the following:

- to inspire collaborative interactions between experimentalists, mathematicians and statisticians in the development of more powerful algorithms for the analysis of neural encoding, with a strong focus on refining current hypotheses for ensemble spike train coding;
- to establish a sound, rigorous basis for examining the differences in findings within and across preparations;
- to consider the very challenging problems associated with extending information-theoretic analysis to networks.

Examples of organizing questions to be considered in this workshop are as follows:

- What is a channel, in the Shannon sense, within the neural processing architecture? Are single nerve cells the elemental computational units, or some larger-scale neural ensembles? This may depend on the level of analysis (e.g., whether the system is being studied with respect to the operations being carried out within single-cells, all the way up to systems consisting of millions of neurons distributed between several brain areas.
- What is the nature and quantity of information represented at each processing stage of a neural subsystem? What is being represented? (i.e., what is the relevant stimulus world for the system under study?)
- What is the code with which that information is represented, transmitted and operated upon across those channels? A variety of encoding schemes have been proposed, ranging from simple linear rate codes to complex nonlinear ensemble codes. What are rigorous criteria for identifying linear and non-linear codes? For static vs. dynamic temporal codes? What algorithms should we develop and apply to identify these different schemes?
- Are nerve cells and networks noisy or deterministic? What are the principle sources of noise, from the biophysical level of macromolecules and ion channels to the dynamics of large networks of synaptically interconnected cells? To what extent must stochastic behavior be incorporated into neural models, and at what phenomenological level, in order to insure validity of those models?

The goal of the workshop is to articulate the present and future trends in:

- Modeling the neuronal networks
- Analysis of related mathematical models, and to discuss
- General mathematical techniques for integro-differential equations.

The nonlocal interaction of neurons plays a crucial role in the generation of waves and patterns in the brain. Each neuron may send excitatory or inhibitory synaptic input to other neurons, and the intrinsic and synaptic dynamics may involve multiple time scales. The spatio-temporal properties of patterns, such as whether neurons fire in synchrony or not, typically depend on the type and strength of the neuronal interactions.

The mathematical models that incorporate these effects are often integro-differential equations. These models account for the spatial interactions via convolution integrals whose kernels encode the specific interaction properties of neurons. Not much analytical work has been done for equations of this type, and special properties such as maximum principles or singular perturbation theory need to be exploited.

This workshop focuses on surveying the mathematical techniques used to model and analyze the inherently nonlocal interaction of neurons and on concrete applications in neuroscience.

Olfaction provides an ideal model for a distributed neural code. Unlike other sensory systems, from the receptor level onward, there is no simple spatial organization of the inputs. The output from receptors terminates on the olfactory bulb (or its analogues, the antennal lobe in insects) where it is processed and sent on to the olfactory cortex (mushroom body, in insects) Thus complex processing occurs at the earliest levels of input.

At the first level of processing, the olfactory bulb (and the analogue regions) is characterized by complex oscillations. These oscillations appear to be crucial in order for the animal to discriminate between odors, particularly those which are closely related. Furthermore, animals can learn a new odor with only a single presentation. Thus, part of this workshop will focus on models and experiments for olfactory oscillations and learning.

The mathematical areas that are expected to be strongly involved in this workshop are dynamical systems (oscillations, perturbation methods, bifurcations) and other areas of differential equations.

The timing of firing of auditory neurons carries information used for both localization and interpretation of sound. Psychophysical studies strongly support the existence of a timing code for localization and pitch detection, while broadband transients and gaps are critical features of speech consonants. In order to understand speech, we must understand how sound is processed in the central auditory system. Mathematical modeling and computer simulation already play a significant role in auditory research, but further intensive effort is needed to understand how the spectro-temporal information present in the cochlea nuclei is used for localization and interpretation of sound. The workshop will focus on the following topics:

- ITD coding: Binaural processing has seen a resurgence of interest lately. This is mainly due to the progress in the understanding of the computational mechanisms underlying the representation of interaural time difference (ITD) in small mammals. It now is possible to compare these new results with results from larger mammals (including humans), and from the barn owl that so far have been the most established model systems to study binaural processing.
- Complex sound processing: Real sounds are complex and we do not know how they are coded or decoded. Recent work shows that the auditory signal is divided into parallel streams for information transmission, which may be governed by different mechanisms. Spectral temporal receptive field (STRF) analyses of the auditory signal in higher centers (bird forebrain and mammalian cortex) has provided descriptions of the stimulus-response function of auditory neurons. In songbirds, where salient stimulus is well known, there are successively complex functional stages of song analysis by neurons in the auditory forebrain. Similar results have been obtained in studies of marmoset vocalization. Comparisons of neural responses in A1 of marmosets and cats have shown that the preference for natural marmoset twitter calls in marmoset A1 was absent in cat A1. This differential representation of marmoset vocalizations in two cortices suggests that experience-dependent and possibly species-specific mechanisms are involved in cortical processing of communication sounds.
- Spatial processing: The real world presents a dynamic and complex auditory scene. We want to understand how the brain can build separate perceptual descriptions of sound-generating events despite the mixing of signals at the two ears. All hearing vertebrates carry out auditory scene analysis, where they group such as the call of a particular monkey continuing over time, or the echo of a flying insect. This is a problem of general relevance.

All these have made major advances over the past few years and all present significant theoretical challenges. Therefore it is timely to bring together biologists, engineers, and mathematicians who work on different aspects of the above topics.

The goals of the workshop are to increase the communication and cooperation between experimentalists and modelers and to introduce mathematicians with little previous experience in this area to the wide range of interesting mathematical problems in the auditory science.

The mathematical areas which are expected to be strongly involved in this workshop are information theory, Fourier analysis, statistics, differential equations and real analysis.

In this workshop we will focus on modeling the basal ganglia in both birds and mammals. In mammals the basal ganglia are a group of forebrain nuclei that play an important, perhaps even central, role in the control of movement. They also appear to be involved in cognition, motivation and emotion. Dysfunction of the basal ganglia is associated with movement disorders such as Parkinson's disease and Huntington's chorea. Structures within the basal ganglia have in fact been the target of therapeutic surgical procedures including pallidotomy, lesioning of the subthalamic nuclei and deep brain stimulation.

Recent work has shown just how similar the organization and function of the basal ganglia is in both birds and mammals. Even better, experiments on the song system have provided a window into mammalian basal ganglion function. When a bird is deafened, its song deteriorates. When deafening is paired with lesion of the basal ganglia, however, this deterioration does not take place. This appears to be because the lesion has removed an instructive signal that is produced by the basal ganglia. These results are important for both studies of birdsong and for studies of motor learning, and they need to be discussed by both theoreticians and experimentalists who work on birds and mammals.

There is a rich array of data on basal ganglia physiology and connections in both groups. In mammals, numerous experiments have demonstrated that neurons with the basal ganglia display a variety of dynamic behavior; moreover patterns of neuronal activity, both spatial and temporal, differ between normal and pathological states. Neither the origins of these neural firing patterns nor the neuronal mechanisms that underlie the patterns are understood. Some mathematical models have been introduced recently to describe the various aspects of the basal ganglia, however these have been almost exclusively based on the average firing rates of the neurons, while ignoring their temporal dynamics. As experiments continue to demonstrate the importance of temporal dynamics, the need for more realistic, biophysically based models is becoming increasingly clear. The primary goal of this workshop is stimulate the development of models realistic enough to test hypotheses on the role of neuronal activity within the basal ganglia in both normal and pathological states.

The mathematical areas which are expected to be strongly involved in this workshop are partial and integral differential equations, dynamical systems and probability.

Each summer the MBI hosts a 3-week education program. The first week is spent in a tutorial, which combines morning lectures with active learning laboratories in the afternoon. The following 2 weeks are spent working on guided team projects and participating in a mini-conference to share project results. The 40 participants include 10 undergraduate students, 10 graduate students, 10 college teachers, and 10 high school teachers.

The 2003 summer program in Neuronal Rhythms is scheduled for July 14th to August 1st.