## 2014 Workshop for Young Researchers in Mathematical Biology

### (August 25,2014 - August 28,2014 )

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.

### Accepted Speakers

David Anderson
Mathematics, University of Wisconsin
Ruth Baker
Wolfson Centre for Mathematical Biology, Mathematical Institute, University of Oxford
Amy Buchmann
Applied and Computational Mathematics and Statistics, University of Notre Dame
Andrey Dovzhenok
Mathematical Sciences, University of Cincinnati
Rebecca Everett
Applied Mathematics, Arizona State University
Kenneth Ho
Mathematics, Stanford University
Majid Jaberi-Douraki
Physiology, McGill University
Jaejik Kim
Biostatistics & Epidemiology, Georgia Regents University
Christopher Knowlton
Physics, University of California, San Diego
Peter Kramer
Mathematical Sciences, Rensselaer Polytechnic Institute
Jay Newby
Mathematical Biosciences Institute, The Ohio State University
Calistus Ngonghala
Global Health and Social Medicine, Harvard Medical School
Qing Nie
Biomedical Engineering & Mathematics, University of California, Irvine
Linus Schumacher
Centre for Mathematical Biology, University of Oxford
Peter Thomas
Department of Mathematics, Applied Mathematics, and Statistics, Case Western Reserve University
Henry Tuckwell
Max Planck Institute For Mathematics In The Sciences, Leipzig and Electrical and Electronic Engineering, University of Adelaide
Ryan Waters
Mathematical Sciences, Montana State University
Monday, August 25, 2014
Time Session
08:00 AM

Shuttle to MBI

08:15 AM
08:45 AM

Breakfast

08:45 AM
09:00 AM

Opening remarks

09:00 AM
10:00 AM
Henry Tuckwell - Modeling brainstem neurons and their interactions

Brainstem and lower nuclei contain neurons which are the principal CNS sources of the neurotransmitters serotonin (dorsal and other raphe nuclei) and noradrenaline (locus coeruleus and associated centers). By means of vast ascending and descending tracts with extensive arborizations, these transmitters influence the physiological activity of practically every neuron (and some glia) in the CNS, including the cerebral cortex, hippocampus, cerebellum, spinal cord and the brainstem itself. The noradrenergic and serotonergic systems are intertwined, with reciprocal connections and common afferents so that their properties cannot really be studied independently of each other. Noradrenaline and serotonin are implicated in sleep and many affective and cognitive disorders, as indicated by genetic studies and the therapeutic efficacy of drugs which inhibit their transporters. The neuronal and endocrine circuits involving their actions are numerous and complex. Serotonergic neurons of the DRN, for example, are host to about 17 receptor types (Maejima et al., 2013, Frontiers Int. Neurosci. 7, #40) and there are about 15 neurotransmitters which are known to inhibit noradrenaline release (Kubista & Boehm, 2006, Pharmacology & Therapeutics 112, 213-242). Several groups, including researchers at OSU, have commenced quantitative research on these systems. We will examine some of these studies, including recently published mathematical modeling of spike generation in serotonergic neurons (HCT and NJ Penington, Progress in Neurobiology, 2014) and analysis of the interactions between the noradrenergic and serotonergic systems.

Joint research with BP Guiard (Toulouse) and NJ Penington (New York).

10:00 AM
10:30 AM

Break

10:30 AM
11:00 AM
Christopher Knowlton - Network Identification from Spike Timing Information

Networks of neurons perform functional control in complex organisms. In many systems, such as the HVC in song birds, a lot has been done in characterizing the behavior of individual cells and their synapses in response to external stimulus (1,2) and how the networks interact with each other (3) but little headway has been made into determining the actual neural circuits that comprise these networks (4). While HVC is just a familiar example, the inability to probe network behavior at the many cell level, as opposed to single cell or local mean field level, is a common problem in neural systems.

Network behavior is determined by the types of and distribution of the various types of neurons and the connection architecture of the synaptic connections between them. Determining the connection architecture would allow for a quantitative treatment of the network response to novel stimuli, the changes in network architecture over time due to plasticity, and to create better models of the behavior of the sub-network of interest for describing larger brain functions.

Characterizing the behavior of networks of neurons is complicated by the complexity of the individual elements and the difficulty of measuring their states. Estimating the full state of a network of spiking neurons requires sufficient information from measurement to be able to predict both current and future behavior. 'Sufficient' in this case refers to the amount of information required to both cause model and data to synchronize, and for sufficient resolution into any unmeasured time independent parameters – such as the connection strength.

For many neural systems, this information comes from voltage recordings of one or more cells in the network. While the voltage behavior of single cells can be measured using single electrode recordings, the invasiveness of these procedures prevent large numbers of simultaneous recordings. For large numbers of cells, extracellular recordings allow for a much broader, yet coarser measurement of activity. Whether these coarse measurements are sufficient to estimate both individual neuron and networks states depends heavily on the structure of the model and how it is stimulated.

I will present the use of a path integral method that can exploit some of the regularity in Hodgkin- Huxley type models to estimate the connectivity of small networks of neurons conditioned on extracellular spike time recordings in simulation. (5)

1: Toth BA, Kostuk M, Meliza CD, Margoliash D, Abarbanel HD. (2011) Dynamical estimation of neuron and network properties I: variational methods. Biol Cybern. 105(3-4):217-37

2: Gentner TQ, Margoliash D. (2003) Neuronal populations and single cells representing learned auditory objects. Nature 424: 669–674. 3: Nottebohm F (2005) The neural basis of birdsong. PLoS Biol 3(5): e164.

4: Mooney, R and J Prather (2005) The HVC microcircuit: the synaptic basis for interactions between song motor and vocal plasticity pathways. J Neurosci: 25 (8)

5: Christopher Knowlton, C. Daniel Meliza, Daniel Margoliash, and Henry D.I. Abarbanel, (2014) “Dynamic estimation of neuron and network properties III: Network Analysis Using Neuron Spike Times” Biological Cybernetics 1-13 (2014) link.springer.com/article/10.1007/s00422-014-0601-y

11:00 AM
11:30 AM
Andrey Dovzhenok - Predictive modeling and validation of glucose and temperature compensation of the Neurospora circadian clock

Circadian rhythms play a vital role in an organism’s functions anticipating daily changes in its environment. The period of circadian oscillator is relatively insensitive to changes in physiological temperature and nutrients (e.g. glucose), which are referred to as temperature and glucose compensation, respectively. In this study, we constructed a mathematical model of the Neurospora circadian clock, and investigated molecular mechanisms of glucose and temperature compensation. Our model shows that the glucose compensation is achieved by balancing the expression rates of csp-1 and wc-1. More importantly, we experimentally validated loss of glucose compensation in wc-1 overexpression mutant and maintenance of nuclear abundance of FRQ as predicted in the model. Our work highlights predictive modeling of circadian clock machinery and experimental validations employing the model fungus, Neurospora crassa.

11:30 AM
01:30 PM

Lunch Break

01:30 PM
02:30 PM
Qing Nie - Stem Cells: From Simple Model to Big Data

In developing and renewing tissues, terminally differentiated cell types are typically specified through the actions of multistage cell lineages. Such lineages commonly include a stem cell and multiple progenitor cell stages, which ultimately give rise to terminally differentiated cells. In this talk, I will present several modeling frameworks with different complexity on multistage cell lineages driven by stem cells, which account for diffusive signaling molecules, regulatory networks, individual cells, mechanics, and evolution. Questions of our interest include role of feedbacks in regeneration, stem cell niche for tissue spatial organization, crosstalk between epigenetic and genetic regulations. In addition, I will discuss our recent effort on connecting modeling and big data by integrating prior knowledge and heterogeneous spatial and temporal data for elucidating developing tissues.

02:30 PM
02:45 PM

Break

02:45 PM
03:15 PM
Amy Buchmann - Modeling Cell-Cell Communication and Information Transfer of Social Bacteria

Many bacteria are able to communicate information by getting close to each other and signaling through direct contact between cells. This talk will focus on how information is spread between swarming Myxococcus xanthus cells. In particular, I will focus on how the physical cellular properties of individual cells and local behavioral rules influence and optimize information spread throughout the entire cell population. This study is done using both computational cell-based simulations and cell tracking in experiments.

03:15 PM
03:45 PM
Majid Jaberi-Douraki - Predictive Models of Type I Diabetes Progression

In type 1 diabetes, an autoimmune disease mediated by autoreactive T-cells that attack insulin-secreting pancreatic beta-cells, it has been suggested that disease progression may additionally require protective mechanisms in the target tissue to impede such auto-destructive mechanisms. We hypothesize that the autoimmune attack against beta-cells causes endoplasmic reticulum stress by forcing the remaining beta-cells to synthesize and secrete defective insulin. To rescue beta-cell from the endoplasmic reticulum stress, beta-cells activate the unfolded protein response to restore protein homeostasis and normal insulin synthesis. Here we investigate the compensatory role of unfolded protein response by developing a multi-state model of type 1 diabetes that takes into account beta-cell destruction caused by pathogenic autoreactive T-cells and apoptosis triggered by endoplasmic reticulum stress. We discuss the mechanism of unfolded protein response activation and how it counters beta-cell extinction caused by an autoimmune attack and/or irreversible damage by endoplasmic reticulum stress. Our results reveal important insights about the balance between beta-cell destruction by autoimmune attack (beta-cell homicide) and beta-cell apoptosis by endoplasmic reticulum stress (beta-cell suicide). It also provides an explanation as to why UPR may not be a successful therapeutic target to treat type 1 diabetes.

03:45 PM
04:45 PM

Poster Preview 1

05:00 PM
07:00 PM

Poster Session 1 with Reception

07:00 PM

Shuttle pick-up from MBI

Tuesday, August 26, 2014
Time Session
08:00 AM

Shuttle to MBI

08:15 AM
09:00 AM

Breakfast

09:00 AM
10:00 AM
Peter Thomas - Dimension reduction for stochastic conductance based neural models

Random gating of ion channels is a significant source of variability in the responses of single nerve cells. Finding accurate and effective low-dimensional representations of neural dynamics that incorporate stochastic effects is an important step towards understanding the role of channel noise in network level behavior. Dimension reduction techniques aim to capture the fundamental dynamicsof a system with as few degrees of freedom as possible. For oscillatingsystems, the reduction of a multi-dimensional limit cycle system to a one-dimensional phase oscillator provides a powerful framework for understanding entrainment and synchronization of nerve cells and neural populations. However, this reduction presumes the existence of an "asymptotic phase" variable that is not well defined outside of the deterministic setting. We propose a new definition of the asymptotic phase for a stochastic oscillator in terms of the eigenfunctions of the backward evolution operator of the system density. Time permitting, we will discuss a second example of dimension reduction, the recently introduced heuristic "stochastic shielding" approximation [Schmandt and Galan (2012) Phys. Rev. Lett.]. Rather than simplifying the state space of a random process, Schmandt and Galan reduce the dimension of the "sample space", i.e. the number of independent stochastic processes driving the dynamics. Our analysis of Schmandt and Galan's heuristic leads to a new ranking of edge importance for a random process on an arbitrary graph, with respect to any measurement functional on the graph [Schmidt and Thomas, 2014, J. Math. Neurosci.].

Joint work with Benjamin Lindner and Deena Schmidt.

10:00 AM
10:30 AM

Break

10:30 AM
11:00 AM
Jaejik Kim - Statistical Validation in Dynamic Molecular Systems for Gene Regulatory Networks

The description of network dynamics is an important and fundamental tool to understand gene regulation processes, along with the gene regulatory network. To describe the network dynamics, dynamic molecular systems consisting of a set of ordinary differential equations (ODEs) have been often used. However, since gene experiments cannot observe entire regulation processes and there might be multiple competing sets of ODEs generating similar dynamics, validation for dynamic systems are essential for more accurate inference and prediction for the processes. Moreover, since ODEs are deterministic while mRNA expression data typically have both measurement and instrument uncertainties with heteroscedasticity, they should be evaluated in terms of flexibility and model adequacy for given data. This study proposes statistical validation and selection methods for dynamic molecular systems based on a likelihood method and they are applied to the parotid de-differentiation network obtained from RT-PCR experiments. Although this study focuses on mRNA expression data, the proposed validation method can be extended into various biomedical studies.

11:00 AM
11:30 AM
Jay Newby - Effects of Moderate Noise on a Limit Cycle Oscillator: Counter Rotation and Bistability

The effects of noise on the dynamics of nonlinear systems is known to lead to many counter-intuitive behaviors. Using simple planar limit cycle oscillators, we showthat the addition of moderate noise leads to qualitatively different dynamics. In particular, the system can appear bistable, rotate in the opposite direction of thedeterministic limit cycle, or cease oscillating altogether. Utilizing standard techniques from stochastic calculus and recently developed stochastic phase reductionmethods, we elucidate the mechanisms underlying the different dynamics and verify our analysis with the use of numerical simulations. Lastly, we show that similarbistable behavior is found when moderate noise is applied to the more biologically realistic FitzHugh-Nagumo model.

11:30 AM
02:00 PM

Lunch Break

02:00 PM
03:00 PM
David Anderson - Chemical reaction network theory for stochastic and deterministic models of biochemical reaction systems

I will give a short tutorial on the two most common modeling regimes for biochemical reaction systems: ODE models and stochastic discrete jump models. I will show how the two models are connected through the law of large numbers and will then give basic results relating network topology to qualitative behavior of the underlying system in both modeling regimes. In particular, I will give one set of conditions which guarantees that the long-term behaviors of the ODE and stochastic model are stable, and another set under which the long-term behaviors are quite different. The flavor of results presented fall into the field of Chemical Reaction Network Theory.

03:00 PM
03:15 PM

Break

03:15 PM
03:30 PM

Group photo in front of Jennings Hall

03:30 PM
04:45 PM

Panel Discussion

05:00 PM

Shuttle pick-up from MBI

Wednesday, August 27, 2014
Time Session
08:00 AM

Shuttle to MBI

08:15 AM
09:00 AM

Breakfast

09:00 AM
10:00 AM
Peter Kramer - Stochastic Modeling in Microbiological Systems

I will illustrate, via several examples, how concepts and techniques from the mathematical theory of stochastic processes can be used to help understand the effective behavior of a system of interacting microbiological agents.'' By an agent,'' I refer to a biological entity such as a molecular motor, a neuron, or a swimming bacterium. Each of these have been sufficiently studied that its operating principles at an individual level are by now relatively well understood, at least in a general sense. But several phenomena pertaining to systems of these agents remain difficult to explain in terms of the dynamical rules of the individual agents. What is challenging about these systems is they are fundamentally non-equilibrium, and only involve a moderately large number of agents, so that stochastic fluctuations remain important even on the collective (mesoscopic) level, and mean-field treatments are restricted in their validity. I will describe some remarkable phenomena regarding the tug-of-war dynamics of molecular motors, switching dynamics of sleep and wake states, and pattern formation by suspensions of swimming bacteria, and indicate how ideas from asymptotic analysis, metastability theory, and stochastic partial differential equations can be deployed to obtain some understanding of how these collective phenomena are quantitatively connected to the dynamics of the individual agents.

10:00 AM
10:30 AM

Break

10:30 AM
11:00 AM
Ryan Waters - Analysis of CRISPR Distributions and Mechanisms for Acquisition

An adaptive immune system is important to ensure appropriate, precise, and rapid response to a foreign pathogen. While adaptive immune response has traditionally only be attributed to vertebrates, it has recently been discovered that some bacteria also demonstrate a form of dynamic immunity. The CRISPR (clustered regularly interspaced short palindromic repetitions) system is made up of short phage homologs which, with the help of Cas (CRISPR-associated) genes, work to recognize and silence exogenous genetic material. Additionally, when new foreign genetic material is recognized, the nucleic acid sequence can then be incorporated into the CRISPR gene. The mechanisms for acquisition and recognition are still not well understood. We are interested to look at ‘ideal’ CRISPR distributions and to explore how different acquisition strategies might lead to different CRISPR distributions. Additionally, we are interested in the role of stochastic effects in bacterial CRISPR acquisition and how this diversity may be important to community survival.

11:00 AM
11:30 AM
Sunnie Joshi - Estimating Residual Stresses in Arteries by an Inverse Spectral Technique

It is known that residual stresses play a significant role in determining the overall stress distribution in soft tissues. A mathematical model is studied to estimate residual stress field in the arterial wall by making use of intravascular ultrasound (IVUS) imaging techniques. The arterial wall is modeled as a nonlinear, isotropic, slightly compressible elastic body. A boundary value problem is formulated for the residually stressed arterial wall, the boundary of which is subjected to a quasi-static blood pressure, and then an idealized model for the IVUS interrogation is constructed by superimposing small amplitude time harmonic infinitesimal vibrations on large deformations. The analysis leads to a system of second order differential equations with homogeneous boundary conditions of Sturm-Liouville type. By making use of the classical theory of inverse Sturm-Liouville problems, and root finding and optimization techniques, an inverse spectral algorithm is developed to approximate the residual stress distribution in the arterial wall, given the first few eigenfrequencies of several induced blood pressures.

11:30 AM
02:00 PM

Lunch Break

02:00 PM
03:00 PM
Ruth Baker - Experimental and modelling investigation of monolayer development with clustering

Standard differential equation models of collective cell behaviour, such as the logistic growth model, invoke a mean-field assumption which is equivalent to assuming that individuals within the population interact with each other in proportion to the average population density. Implementing such assumptions implies that the dynamics of the system are unaffected by spatial structure, such as the formation of patches or clusters within the population. Recent theoretical developments have introduced a class of models, known as moment dynamics models, that aim to account for the dynamics of individuals, pairs of individuals, triplets of individuals, and so on. Such models enable us to describe the dynamics of populations with clustering, however, little progress has been made with regard to applying moment dynamics models to experimental data. Here, we report new experimental results describing the formation of a monolayer of cells using two different cell types: 3T3 fibroblast cells and MDA MB 231 breast cancer cells. Our analysis indicates that the 3T3 fibroblast cells are relatively motile and we observe that the 3T3 fibroblast monolayer forms without clustering. Alternatively, the MDA MB 231 cells are less motile and we observe that the MDA MB 231 monolayer formation is associated with significant clustering. We calibrate a moment dynamics model and a standard mean-field model to both data sets. Our results indicate that the mean-field and moment dynamics models provide similar descriptions of the 3T3 fibroblast monolayer formation whereas these two models give very different predictions for the MDA MD 231 monolayer formation. These outcomes indicate that standard mean-field models of collective cell behaviour are not always appropriate and that care ought to be exercised when implementing such a model.

03:00 PM
03:30 PM

Break

03:30 PM
04:00 PM
Rebecca Everett - How Might Mathematical Models Help Improve Personalized Treatment of Prostate Cancer?

Prostate cancer is the most common non-skin cancer in men and second most fatal in the United States. It is often treated by a hormone therapy called androgen suppression therapy since both normal and cancerous prostate cells depend on androgens for growth and survival. Due to the side effects of this treatment, the quality of life decreases for the patients while on the therapy. Thus patients often choose intermittent androgen suppression therapy (IAS), in which the patients alternate between durations of on and off treatment. Using a mathematical model, we propose a novel computational method for predicting the main mechanism for resistance to treatment in individual patients. Using the same mathematical model, we also predict the future prostate specific antigen (PSA) levels, a biomarker for prostate cancer, in individual patients and compare the results to clinical data. Since biological processes take time, we also explore a delayed differential equations cancer model.

04:00 PM
04:30 PM
Linus Schumacher - Unravelling the rules of multicellular migration during development with models and experiments

We study the mechanisms underlying cell migration in the developing embryo, using a computational model developed in close collaboration with in vivo experiments in the chick cranial neural crest. Here, a stream of cells has to invade a target tissue and at the same time distribute along the migratory route. Cranial neural crest cells are known to seek out a chemoattractant (VEGF). However, the chemoattractant is uniformly produced. Our working hypothesis is that a chemotactic gradient is induced by the cells themselves through internalisation of chemoattractant. This is represented computationally within a hybrid model framework (discrete cells off-lattice, continuous chemoattractant) on a growing domain.

Previous work has indicated the need for two subpopulations of cells with different behaviours. The presence of these subpopulations was validated experimentally, both by gene profiling and by confirming model predictions for tissue transplantation experiments. Our focus is now to extend this modelling framework, incorporating realistic cell sensing and differences in cell cohesion recently observed experimentally. The goal is to identify critical cell behaviours that lead to robust multicellular neural crest migration. Together with our collaborators we plan experiments and then conduct them in parallel in vivo, in vitro and computationally. Experimental results parameterise and inform the simulations, which in turn help to interpret existing results and suggest new experiments. We repeat this cycle of hypothesis generation and testing iteratively with the aim of providing a framework generalizable to multicellular migration in different organisms.

04:30 PM
05:00 PM

Poster Preview 2

05:00 PM
07:00 PM

Poster Session 2 with Reception

07:00 PM

Shuttle pick-up from MBI

Thursday, August 28, 2014
Time Session
08:00 AM

Shuttle to MBI

08:15 AM
09:00 AM

Breakfast

09:00 AM
09:30 AM
Calistus Ngonghala - Coupled economic and ecological processes can generate poverty traps

Economic activity is coupled to ecological processes through an array of mechanisms across the spectrum of conceivable scales. In pursuit of general integrated frameworks, here we combine the dominant paradigmatic model of economic growth theory with standard models of disease ecology. Our calibrated model indicates that the structure of these systems can create bistable outcomes, and therefore poverty traps, in both income and disease that do not occur independently in the uncoupled models. The presence of poverty traps is dependent on various biologically-determined parameters, such as the background transmission rate of disease, and the number of pathogens in the system. In particular, our model indicates that the number of pathogens in the system increases the intensity of ecological-economic feedback, making poverty traps inevitable at suf.ciently high numbers of pathogens that prevent the acquisition of human capital. The framework provides a general approach for modeling the dynamics of coupled ecological-economic systems, equally reliant on existing paradigms in both the social and natural sciences. More speci.cally, it offers a model on the relationship between human health and economic growth.

09:30 AM
10:00 AM

Break

10:00 AM
10:30 AM
Kenneth Ho - Progress toward fast algorithms for protein design

The protein design problem is fundamental to understanding biomolecular structure and function: given a rigid backbone and a set of rotamers for each sidechain, determine the rotamer configuration that minimizes the energy. A dominant contribution to the energy at the molecular scale is electrostatics, which historically has also been among the most difficult to compute. An ideal electrostatics solver for protein design would (1) have high accuracy; (2) be geometrically adaptive; (3) have optimal linear complexity; (4) efficiently handle multiple right-hand sides; and (5) rapidly accommodate local geometric perturbations. In this talk, we describe our progress toward meeting these goals by combining classical boundary integral equation techniques with newly developed linear-time fast direct solvers. We will note where conventional iterative methods fail, describe some early missteps, push on to our latest algorithms, and end with a positive outlook for the future. Our main technical achievement consists of linear-complexity direct solvers for elliptic PDEs in both integral and differential form, which should be of significant independent numerical interest.

11:00 AM

Shuttle pick-up from MBI (one to hotel, one to airport)

Name Email Affiliation
Al Omari, Mohammed alomari1050@hotmail.com Department of Mathematics, Department of Mathematics, Faculty of Arts and Science in Qilwah, AlBaha University
Anderson, David anderson@math.wisc.edu Mathematics, University of Wisconsin
Baker, Ruth ruth.baker@maths.ox.ac.uk Wolfson Centre for Mathematical Biology, Mathematical Institute, University of Oxford
Battista, Christina cbattis2@ncsu.edu Department of Mathematics, North Carolina State University
Bhattacharyya, Samit szb16@psu.edu Biology, The PennSylvania State University
Biswas, Md. Haider Ali mhabiswas@yahoo.com Mathematics Discipline, Science, Engineering and Technology School, Khulna University, Bangladesh
Buchmann, Amy abuchman@nd.edu Applied and Computational Mathematics and Statistics, University of Notre Dame
Cezaro, Fabiana fabi.travessini@gmail.com Mathematical Sciences, University of Memphis
Chen, Jing j.chen@math.miami.edu Mathematics, University of Miami
Choi, Boseung cbskust@gmail.com Computer Science and Statistics, Daegu University
De Cezaro, Adriano decezaromtm@gmail.com Mathematics, Statistics and Physics, Federal University of Rio Grande
Dolbniak, Marzena marzena.dolbniak@polsl.pl Automatic Control, Electronic and Computer Science, Silesia University of Technology
Dovzhenok, Andrey andrey.dovzhenok@uc.edu Mathematical Sciences, University of Cincinnati
Everett, Rebecca rarodger@asu.edu Applied Mathematics, Arizona State University
Grigoryan, Viktor vgrigoryan@oxy.edu Mathematics, Simmons College
Ho, Kenneth klho@stanford.edu Mathematics, Stanford University
Jaberi-Douraki, Majid majid.jaberi-douraki@mail.mcgill.ca Physiology, McGill University
Jiang, Shuai jiangs89@gwu.edu Computer Science and Engineering, University of South Carolina
Johnston, Ian ianj@math.bu.edu Mathematics and Statistics, Boston University
Joshi, Sunnie Sjoshi@temple.edu Mathematics, Temple University
Kesir, Mustafa kesirm@gmail.com Department of Animation, Ipek University
Kim, Jaejik jaekim@gru.edu Biostatistics & Epidemiology, Georgia Regents University
Kim, Kibong kbkim@smu.ac.kr Dept. of Biomedical Science, Sangmyung Univ.
Knowlton, Christopher cknowlton@physics.ucsd.edu Physics, University of California, San Diego
Kong, Liang lkong9@uis.edu Mathematical Science, University of Illinois at Springfield
Kramer, Peter kramep@rpi.edu Mathematical Sciences, Rensselaer Polytechnic Institute
Lanz, Aprillya dr.l.lanz@gmail.com Mathematics, Norfolk State University
Machuca, Alicia alicia.machuca@mavs.uta.edu Department of Mathematics, University of St. Thomas
Mashayekhi, Somayeh so_mashayekhi@yahoo.com Mathematics, Mississippi State University
McGee, Reginald mcgee3@purdue.edu Mathematics, Purdue University
Newby, Jay Mathematical Biosciences Institute, The Ohio State University
Ngonghala, Calistus ngonghala@yahoo.com Global Health and Social Medicine, Harvard Medical School
Nie, Qing qnie@math.uci.edu Biomedical Engineering & Mathematics, University of California, Irvine
Oduro, Bismark bo613809@ohio.edu Mathematics, Ohio University
Pantha, Buddhi bpantha@utk.edu Department of Mathematics, University of Tennessee
Phong, Connie cphong@uchicago.edu Institute for Genomics and Systems Biology, University of Chicago
Rezaei Yousefi, Mohammadmahdi rezaeiyousefi.1@osu.edu Electrical and Computer Engineering, The Ohio State University
Schumacher, Linus linus.schumacher@maths.ox.ac.uk Centre for Mathematical Biology, University of Oxford
Selby, Heather hselby@jimmy.harvard.edu Department of Biostatistics and Computational Biology, Dana Farber Cancer Institute
Thomas, Peter pjthomas@case.edu Department of Mathematics, Applied Mathematics, and Statistics, Case Western Reserve University
Tubay, Jerrold jmtubay@uplb.edu.ph Graduate School of Science and Technology, Shizuoka University
Tuckwell, Henry tuckwell@mis.mpg.de Max Planck Institute For Mathematics In The Sciences, Leipzig and Electrical and Electronic Engineering, University of Adelaide
Ueda, Hana hanau@math.umd.edu Mathematics, University of Maryland
Waters, Ryan waters@math.montana.edu Mathematical Sciences, Montana State University
Xia, Jun jxia1@gsu.edu Mathematics and Statistics, Georgia State University
Xu, Qiuping qxu@math.fsu.edu Department of Mathematics, Florida State University
Xu, Huarong hxu2@nd.edu ACMS, Univ. of Notre Dame
Yoo, Yeonjoo yjyoo@iupui.edu Department of Mathematical Sciences, IUPUI(Indiana University-Purdue University Indianapolis)
Zhang, Jie jzhang34@gsu.edu Mathematics and Statistics, Georgia State University
Zou, Lan lanlanpin@gmail.com Department of mathematics, Sichuan University
Chemical reaction network theory for stochastic and deterministic models of biochemical reaction systems

I will give a short tutorial on the two most common modeling regimes for biochemical reaction systems: ODE models and stochastic discrete jump models. I will show how the two models are connected through the law of large numbers and will then give basic results relating network topology to qualitative behavior of the underlying system in both modeling regimes. In particular, I will give one set of conditions which guarantees that the long-term behaviors of the ODE and stochastic model are stable, and another set under which the long-term behaviors are quite different. The flavor of results presented fall into the field of Chemical Reaction Network Theory.

Experimental and modelling investigation of monolayer development with clustering

Standard differential equation models of collective cell behaviour, such as the logistic growth model, invoke a mean-field assumption which is equivalent to assuming that individuals within the population interact with each other in proportion to the average population density. Implementing such assumptions implies that the dynamics of the system are unaffected by spatial structure, such as the formation of patches or clusters within the population. Recent theoretical developments have introduced a class of models, known as moment dynamics models, that aim to account for the dynamics of individuals, pairs of individuals, triplets of individuals, and so on. Such models enable us to describe the dynamics of populations with clustering, however, little progress has been made with regard to applying moment dynamics models to experimental data. Here, we report new experimental results describing the formation of a monolayer of cells using two different cell types: 3T3 fibroblast cells and MDA MB 231 breast cancer cells. Our analysis indicates that the 3T3 fibroblast cells are relatively motile and we observe that the 3T3 fibroblast monolayer forms without clustering. Alternatively, the MDA MB 231 cells are less motile and we observe that the MDA MB 231 monolayer formation is associated with significant clustering. We calibrate a moment dynamics model and a standard mean-field model to both data sets. Our results indicate that the mean-field and moment dynamics models provide similar descriptions of the 3T3 fibroblast monolayer formation whereas these two models give very different predictions for the MDA MD 231 monolayer formation. These outcomes indicate that standard mean-field models of collective cell behaviour are not always appropriate and that care ought to be exercised when implementing such a model.

Seroprevalence of Toxoplasma Gondii in Pregnant Women and Slaughtered Pigs of Chitwan District

Objective: To determine the Seroprevalence of Toxoplasma gondii infection in pregnant women and slaughtered pigs of chitwan district of Nepal and their association with different risk factors to assess the possible zoonotic transmission.

Design:Cross-sectional study

Methodology: Questionnaire survey was conducted on 47 serum samples of pregnant women collected from 5 different health post and 79 slaughtered pig samples from different slaughter houses. Serologic evidence of toxoplasmosis for IgG was conducted by the Enzyme Linked Immunoassay (DSI, Italy). The result was analyzed using chi-square test and Fisher exact test was used when indicated.

Results: 53.19 % serum samples of pregnant women and 1.27% of slaughtered pigs analyzed had serologic evidence of Toxoplasma infection (IgG). 65.96% of the interviewed people had a history of consumption of raw or undercooked meat and 85.1% had contact with cats. Among the different risk factors associated with toxoplasmosis in pregnant women playing habit with cat was found to be statistically significant. (p value<0.05, crude OR =0.02%).

Conclusion and recommendations: The prevalence rate obtained in pregnant women in this study did not differ much from the prevalence reported in previous studies. This suggests that the same degree of risk to this infection exists in the community. Thus significance of toxoplasmosis as a disease of zoonotic importance was demonstrated. In case of the relatively low antibody prevalence in pig, the risk of acquiring this infection from consuming undercooked pork is relatively low. Further survey on larger sample size is needed to validate the observation. Close contact with cat and the consumption of raw or undercooked meat were the major risk factors in the transmission of the disease. Considering the relatively high prevalence as revealed by this study, it would be important to conduct studies on a wider scale. The prevalence rate of T. gondii in other animals should also be determined in order to find the risk of humans to be infected by other animals. It would also be important to increase public awareness and health education in women especially during pregnancy

Modeling Cell-Cell Communication and Information Transfer of Social Bacteria

Many bacteria are able to communicate information by getting close to each other and signaling through direct contact between cells. This talk will focus on how information is spread between swarming Myxococcus xanthus cells. In particular, I will focus on how the physical cellular properties of individual cells and local behavioral rules influence and optimize information spread throughout the entire cell population. This study is done using both computational cell-based simulations and cell tracking in experiments.

TBD

Abstract not submitted

Predictive modeling and validation of glucose and temperature compensation of the Neurospora circadian clock

Circadian rhythms play a vital role in an organism’s functions anticipating daily changes in its environment. The period of circadian oscillator is relatively insensitive to changes in physiological temperature and nutrients (e.g. glucose), which are referred to as temperature and glucose compensation, respectively. In this study, we constructed a mathematical model of the Neurospora circadian clock, and investigated molecular mechanisms of glucose and temperature compensation. Our model shows that the glucose compensation is achieved by balancing the expression rates of csp-1 and wc-1. More importantly, we experimentally validated loss of glucose compensation in wc-1 overexpression mutant and maintenance of nuclear abundance of FRQ as predicted in the model. Our work highlights predictive modeling of circadian clock machinery and experimental validations employing the model fungus, Neurospora crassa.

Benthic O2 uptake

Benthic O2 uptake is the most widely used proxy for estimating organic matter degradation in the ocean floor, which has important implications on global climate, distribution of benthic communities and provides important information on the biogeochemistry of marine sediments. The quantification of diffusive O2 uptake (DOU) across the sediment water interface (SWI) from depth distribution of O2 is a common technique used in estimating the sediment O2 uptake. A critical evaluation of DOU estimation procedures was investigated in two different sediment environments, homogeneous and heterogeneous sediments. In the homogenous environment 1D numerical routines were used to create synthetic “perfect” O2 depth profiles with different OPD’s and subsequently numerically sampled to generate synthetic data O2 profiles by mimicking different sampling procedures of real sensors. In each case a sensitivity analysis was done to estimate the systematic bias between the “true” DOU extracted from the numerical routines and the sample DOU calculated from the linear gradient fit of the first two and first five sample profile O2 concentrations. Typically used microelectrodes (50μ m outer tip diameter and 100μ m step size) sampling under perfect conditions were found to underestimate the sediments “true” DOU by 5-10 %. However this bias was found to become significantly large (up to 40 %) when the step depths were increased (120-1000μ m).

Virtual 2-dimensional (2D) O2 distribution maps with natural spatially dependent hotspots obtained from Sagami Bay (Glud et al., 2009) were created using 2D reactivetransport models and assumed to represent heterogeneous environments. These maps essentially function as a sequence of neighboring O2 micro profiles measured by a real sensor in typical lateral steps the same as the grid geometry of the 2D model. Sample DOU calculated from the extracted 1D microprofiles approximate well to “true” DOU extracted from the. 2D numerical routines. Compared to the experimental in situ DOUdata the sample and model DOU’s did not displayed any scatter trend from the theoreticalhomogenous OPD-DOU relationship. The number of 1D micro profiles necessary to underpin the average DOU within the sediment transects with a 10% error limit varied between 5-35 increasing with the heterogeneity of the transects. Random sampling was found to give a better estimate of the average DOU within each transects than selective sampling. Annual organic carbon mineralization rate in Sagami Bay determined from our 2D model was 7.1 g C m-2 yr-1.

The study concludes that (1) there is inherent bias in the microelectrode profiling procedure in estimating the DOU using the linear gradient fit below the SWI even under perfect conditions. (2) 1D microprofiling works well in a 3D biogeochemical hotspot environment and, (3) spatial heterogeneity in O2 uptake rates along the sediment surface due to lateral mosaic hotspot distribution do not create scatter in theoretical OPD-DOU relationship.

How Might Mathematical Models Help Improve Personalized Treatment of Prostate Cancer?

Prostate cancer is the most common non-skin cancer in men and second most fatal in the United States. It is often treated by a hormone therapy called androgen suppression therapy since both normal and cancerous prostate cells depend on androgens for growth and survival. Due to the side effects of this treatment, the quality of life decreases for the patients while on the therapy. Thus patients often choose intermittent androgen suppression therapy (IAS), in which the patients alternate between durations of on and off treatment. Using a mathematical model, we propose a novel computational method for predicting the main mechanism for resistance to treatment in individual patients. Using the same mathematical model, we also predict the future prostate specific antigen (PSA) levels, a biomarker for prostate cancer, in individual patients and compare the results to clinical data. Since biological processes take time, we also explore a delayed differential equations cancer model.

Progress toward fast algorithms for protein design

The protein design problem is fundamental to understanding biomolecular structure and function: given a rigid backbone and a set of rotamers for each sidechain, determine the rotamer configuration that minimizes the energy. A dominant contribution to the energy at the molecular scale is electrostatics, which historically has also been among the most difficult to compute. An ideal electrostatics solver for protein design would (1) have high accuracy; (2) be geometrically adaptive; (3) have optimal linear complexity; (4) efficiently handle multiple right-hand sides; and (5) rapidly accommodate local geometric perturbations. In this talk, we describe our progress toward meeting these goals by combining classical boundary integral equation techniques with newly developed linear-time fast direct solvers. We will note where conventional iterative methods fail, describe some early missteps, push on to our latest algorithms, and end with a positive outlook for the future. Our main technical achievement consists of linear-complexity direct solvers for elliptic PDEs in both integral and differential form, which should be of significant independent numerical interest.

Predictive Models of Type I Diabetes Progression

In type 1 diabetes, an autoimmune disease mediated by autoreactive T-cells that attack insulin-secreting pancreatic beta-cells, it has been suggested that disease progression may additionally require protective mechanisms in the target tissue to impede such auto-destructive mechanisms. We hypothesize that the autoimmune attack against beta-cells causes endoplasmic reticulum stress by forcing the remaining beta-cells to synthesize and secrete defective insulin. To rescue beta-cell from the endoplasmic reticulum stress, beta-cells activate the unfolded protein response to restore protein homeostasis and normal insulin synthesis. Here we investigate the compensatory role of unfolded protein response by developing a multi-state model of type 1 diabetes that takes into account beta-cell destruction caused by pathogenic autoreactive T-cells and apoptosis triggered by endoplasmic reticulum stress. We discuss the mechanism of unfolded protein response activation and how it counters beta-cell extinction caused by an autoimmune attack and/or irreversible damage by endoplasmic reticulum stress. Our results reveal important insights about the balance between beta-cell destruction by autoimmune attack (beta-cell homicide) and beta-cell apoptosis by endoplasmic reticulum stress (beta-cell suicide). It also provides an explanation as to why UPR may not be a successful therapeutic target to treat type 1 diabetes.

Estimating Residual Stresses in Arteries by an Inverse Spectral Technique

It is known that residual stresses play a significant role in determining the overall stress distribution in soft tissues. A mathematical model is studied to estimate residual stress field in the arterial wall by making use of intravascular ultrasound (IVUS) imaging techniques. The arterial wall is modeled as a nonlinear, isotropic, slightly compressible elastic body. A boundary value problem is formulated for the residually stressed arterial wall, the boundary of which is subjected to a quasi-static blood pressure, and then an idealized model for the IVUS interrogation is constructed by superimposing small amplitude time harmonic infinitesimal vibrations on large deformations. The analysis leads to a system of second order differential equations with homogeneous boundary conditions of Sturm-Liouville type. By making use of the classical theory of inverse Sturm-Liouville problems, and root finding and optimization techniques, an inverse spectral algorithm is developed to approximate the residual stress distribution in the arterial wall, given the first few eigenfrequencies of several induced blood pressures.

Statistical Validation in Dynamic Molecular Systems for Gene Regulatory Networks

The description of network dynamics is an important and fundamental tool to understand gene regulation processes, along with the gene regulatory network. To describe the network dynamics, dynamic molecular systems consisting of a set of ordinary differential equations (ODEs) have been often used. However, since gene experiments cannot observe entire regulation processes and there might be multiple competing sets of ODEs generating similar dynamics, validation for dynamic systems are essential for more accurate inference and prediction for the processes. Moreover, since ODEs are deterministic while mRNA expression data typically have both measurement and instrument uncertainties with heteroscedasticity, they should be evaluated in terms of flexibility and model adequacy for given data. This study proposes statistical validation and selection methods for dynamic molecular systems based on a likelihood method and they are applied to the parotid de-differentiation network obtained from RT-PCR experiments. Although this study focuses on mRNA expression data, the proposed validation method can be extended into various biomedical studies.

Network Identification from Spike Timing Information

Networks of neurons perform functional control in complex organisms. In many systems, such as the HVC in song birds, a lot has been done in characterizing the behavior of individual cells and their synapses in response to external stimulus (1,2) and how the networks interact with each other (3) but little headway has been made into determining the actual neural circuits that comprise these networks (4). While HVC is just a familiar example, the inability to probe network behavior at the many cell level, as opposed to single cell or local mean field level, is a common problem in neural systems.

Network behavior is determined by the types of and distribution of the various types of neurons and the connection architecture of the synaptic connections between them. Determining the connection architecture would allow for a quantitative treatment of the network response to novel stimuli, the changes in network architecture over time due to plasticity, and to create better models of the behavior of the sub-network of interest for describing larger brain functions.

Characterizing the behavior of networks of neurons is complicated by the complexity of the individual elements and the difficulty of measuring their states. Estimating the full state of a network of spiking neurons requires sufficient information from measurement to be able to predict both current and future behavior. 'Sufficient' in this case refers to the amount of information required to both cause model and data to synchronize, and for sufficient resolution into any unmeasured time independent parameters – such as the connection strength.

For many neural systems, this information comes from voltage recordings of one or more cells in the network. While the voltage behavior of single cells can be measured using single electrode recordings, the invasiveness of these procedures prevent large numbers of simultaneous recordings. For large numbers of cells, extracellular recordings allow for a much broader, yet coarser measurement of activity. Whether these coarse measurements are sufficient to estimate both individual neuron and networks states depends heavily on the structure of the model and how it is stimulated.

I will present the use of a path integral method that can exploit some of the regularity in Hodgkin- Huxley type models to estimate the connectivity of small networks of neurons conditioned on extracellular spike time recordings in simulation. (5)

1: Toth BA, Kostuk M, Meliza CD, Margoliash D, Abarbanel HD. (2011) Dynamical estimation of neuron and network properties I: variational methods. Biol Cybern. 105(3-4):217-37

2: Gentner TQ, Margoliash D. (2003) Neuronal populations and single cells representing learned auditory objects. Nature 424: 669–674. 3: Nottebohm F (2005) The neural basis of birdsong. PLoS Biol 3(5): e164.

4: Mooney, R and J Prather (2005) The HVC microcircuit: the synaptic basis for interactions between song motor and vocal plasticity pathways. J Neurosci: 25 (8)

5: Christopher Knowlton, C. Daniel Meliza, Daniel Margoliash, and Henry D.I. Abarbanel, (2014) “Dynamic estimation of neuron and network properties III: Network Analysis Using Neuron Spike Times” Biological Cybernetics 1-13 (2014) link.springer.com/article/10.1007/s00422-014-0601-y

Stochastic Modeling in Microbiological Systems

I will illustrate, via several examples, how concepts and techniques from the mathematical theory of stochastic processes can be used to help understand the effective behavior of a system of interacting microbiological agents.'' By an agent,'' I refer to a biological entity such as a molecular motor, a neuron, or a swimming bacterium. Each of these have been sufficiently studied that its operating principles at an individual level are by now relatively well understood, at least in a general sense. But several phenomena pertaining to systems of these agents remain difficult to explain in terms of the dynamical rules of the individual agents. What is challenging about these systems is they are fundamentally non-equilibrium, and only involve a moderately large number of agents, so that stochastic fluctuations remain important even on the collective (mesoscopic) level, and mean-field treatments are restricted in their validity. I will describe some remarkable phenomena regarding the tug-of-war dynamics of molecular motors, switching dynamics of sleep and wake states, and pattern formation by suspensions of swimming bacteria, and indicate how ideas from asymptotic analysis, metastability theory, and stochastic partial differential equations can be deployed to obtain some understanding of how these collective phenomena are quantitatively connected to the dynamics of the individual agents.

Effects of Moderate Noise on a Limit Cycle Oscillator: Counter Rotation and Bistability

The effects of noise on the dynamics of nonlinear systems is known to lead to many counter-intuitive behaviors. Using simple planar limit cycle oscillators, we showthat the addition of moderate noise leads to qualitatively different dynamics. In particular, the system can appear bistable, rotate in the opposite direction of thedeterministic limit cycle, or cease oscillating altogether. Utilizing standard techniques from stochastic calculus and recently developed stochastic phase reductionmethods, we elucidate the mechanisms underlying the different dynamics and verify our analysis with the use of numerical simulations. Lastly, we show that similarbistable behavior is found when moderate noise is applied to the more biologically realistic FitzHugh-Nagumo model.

Coupled economic and ecological processes can generate poverty traps

Economic activity is coupled to ecological processes through an array of mechanisms across the spectrum of conceivable scales. In pursuit of general integrated frameworks, here we combine the dominant paradigmatic model of economic growth theory with standard models of disease ecology. Our calibrated model indicates that the structure of these systems can create bistable outcomes, and therefore poverty traps, in both income and disease that do not occur independently in the uncoupled models. The presence of poverty traps is dependent on various biologically-determined parameters, such as the background transmission rate of disease, and the number of pathogens in the system. In particular, our model indicates that the number of pathogens in the system increases the inten­sity of ecological-economic feedback, making poverty traps inevitable at suf.ciently high numbers of pathogens that prevent the acquisition of human capital. The framework provides a general ap­proach for modeling the dynamics of coupled ecological-economic systems, equally reliant on ex­isting paradigms in both the social and natural sciences. More speci.cally, it offers a model on the relationship between human health and economic growth.

Stem Cells: From Simple Model to Big Data

In developing and renewing tissues, terminally differentiated cell types are typically specified through the actions of multistage cell lineages. Such lineages commonly include a stem cell and multiple progenitor cell stages, which ultimately give rise to terminally differentiated cells. In this talk, I will present several modeling frameworks with different complexity on multistage cell lineages driven by stem cells, which account for diffusive signaling molecules, regulatory networks, individual cells, mechanics, and evolution. Questions of our interest include role of feedbacks in regeneration, stem cell niche for tissue spatial organization, crosstalk between epigenetic and genetic regulations. In addition, I will discuss our recent effort on connecting modeling and big data by integrating prior knowledge and heterogeneous spatial and temporal data for elucidating developing tissues.

Unravelling the rules of multicellular migration during development with models and experiments

We study the mechanisms underlying cell migration in the developing embryo, using a computational model developed in close collaboration with in vivo experiments in the chick cranial neural crest. Here, a stream of cells has to invade a target tissue and at the same time distribute along the migratory route. Cranial neural crest cells are known to seek out a chemoattractant (VEGF). However, the chemoattractant is uniformly produced. Our working hypothesis is that a chemotactic gradient is induced by the cells themselves through internalisation of chemoattractant. This is represented computationally within a hybrid model framework (discrete cells off-lattice, continuous chemoattractant) on a growing domain.

Previous work has indicated the need for two subpopulations of cells with different behaviours. The presence of these subpopulations was validated experimentally, both by gene profiling and by confirming model predictions for tissue transplantation experiments. Our focus is now to extend this modelling framework, incorporating realistic cell sensing and differences in cell cohesion recently observed experimentally. The goal is to identify critical cell behaviours that lead to robust multicellular neural crest migration. Together with our collaborators we plan experiments and then conduct them in parallel in vivo, in vitro and computationally. Experimental results parameterise and inform the simulations, which in turn help to interpret existing results and suggest new experiments. We repeat this cycle of hypothesis generation and testing iteratively with the aim of providing a framework generalizable to multicellular migration in different organisms.

Dimension reduction for stochastic conductance based neural models

Random gating of ion channels is a significant source of variability in the responses of single nerve cells. Finding accurate and effective low-dimensional representations of neural dynamics that incorporate stochastic effects is an important step towards understanding the role of channel noise in network level behavior. Dimension reduction techniques aim to capture the fundamental dynamicsof a system with as few degrees of freedom as possible. For oscillatingsystems, the reduction of a multi-dimensional limit cycle system to a one-dimensional phase oscillator provides a powerful framework for understanding entrainment and synchronization of nerve cells and neural populations. However, this reduction presumes the existence of an "asymptotic phase" variable that is not well defined outside of the deterministic setting. We propose a new definition of the asymptotic phase for a stochastic oscillator in terms of the eigenfunctions of the backward evolution operator of the system density. Time permitting, we will discuss a second example of dimension reduction, the recently introduced heuristic "stochastic shielding" approximation [Schmandt and Galan (2012) Phys. Rev. Lett.]. Rather than simplifying the state space of a random process, Schmandt and Galan reduce the dimension of the "sample space", i.e. the number of independent stochastic processes driving the dynamics. Our analysis of Schmandt and Galan's heuristic leads to a new ranking of edge importance for a random process on an arbitrary graph, with respect to any measurement functional on the graph [Schmidt and Thomas, 2014, J. Math. Neurosci.].

Joint work with Benjamin Lindner and Deena Schmidt.

Modeling brainstem neurons and their interactions

Brainstem and lower nuclei contain neurons which are the principal CNS sources of the neurotransmitters serotonin (dorsal and other raphe nuclei) and noradrenaline (locus coeruleus and associated centers). By means of vast ascending and descending tracts with extensive arborizations, these transmitters influence the physiological activity of practically every neuron (and some glia) in the CNS, including the cerebral cortex, hippocampus, cerebellum, spinal cord and the brainstem itself. The noradrenergic and serotonergic systems are intertwined, with reciprocal connections and common afferents so that their properties cannot really be studied independently of each other. Noradrenaline and serotonin are implicated in sleep and many affective and cognitive disorders, as indicated by genetic studies and the therapeutic efficacy of drugs which inhibit their transporters. The neuronal and endocrine circuits involving their actions are numerous and complex. Serotonergic neurons of the DRN, for example, are host to about 17 receptor types (Maejima et al., 2013, Frontiers Int. Neurosci. 7, #40) and there are about 15 neurotransmitters which are known to inhibit noradrenaline release (Kubista & Boehm, 2006, Pharmacology & Therapeutics 112, 213-242). Several groups, including researchers at OSU, have commenced quantitative research on these systems. We will examine some of these studies, including recently published mathematical modeling of spike generation in serotonergic neurons (HCT and NJ Penington, Progress in Neurobiology, 2014) and analysis of the interactions between the noradrenergic and serotonergic systems.

Joint research with BP Guiard (Toulouse) and NJ Penington (New York).

Analysis of CRISPR Distributions and Mechanisms for Acquisition

An adaptive immune system is important to ensure appropriate, precise, and rapid response to a foreign pathogen. While adaptive immune response has traditionally only be attributed to vertebrates, it has recently been discovered that some bacteria also demonstrate a form of dynamic immunity. The CRISPR (clustered regularly interspaced short palindromic repetitions) system is made up of short phage homologs which, with the help of Cas (CRISPR-associated) genes, work to recognize and silence exogenous genetic material. Additionally, when new foreign genetic material is recognized, the nucleic acid sequence can then be incorporated into the CRISPR gene. The mechanisms for acquisition and recognition are still not well understood. We are interested to look at ‘ideal’ CRISPR distributions and to explore how different acquisition strategies might lead to different CRISPR distributions. Additionally, we are interested in the role of stochastic effects in bacterial CRISPR acquisition and how this diversity may be important to community survival.

### Posters

On adding viscoelasticity to 1-D fluid dynamics models, and the effect of outflow boundary conditions

Over past decades, wave propagation within the arterial vasculature has attracted much attention. This can be attributed to the interest in understanding how blood flow and pressure waveforms change with aging and hypertension. To properly understand cardiovascular dynamics associated with these changes, all aspects of the system must be considered including the fluid dynamics, the impact of the arterial wall, and the upstream and downstream vasculature. A mathematical model of the aforementioned quantities allows for prediction of pressure and flow waveforms. The biomechanical properties of the vessels change along the axial direction as well as with aging or hypertension. As vessels decrease in size, they become stiffer, an effect that is amplified by the aging process. The stiffening of vessels affects not only the wave propagation speed but also the shape profile of pressure waves as they travel along the vessels. Mathematical modeling can provide an essential tool for investigating how changes in wall properties and outflow boundary conditions impact wave propagation. These models can eventually be rendered into a patient-specific model to demonstrate the changing effects on an individual. This study uses a one-dimensional fluid dynamics model coupled with a viscoelastic wall model that can predict volumetric blood flow, pressure, and vessel areawaveforms in arterial networks. The fluid dynamics model is derived from the Navier-Stokes equations for an incompressible fluid in a cylinder, and the wall model is derived from quasilinear viscoelasticity theory relating pressure and vessel area. The viscoelastic model incorporates an elastic response as well as a creep function in describing the deformation of the arterial wall. A number of wall models are investigated combining linear and nonlinear elastic responses with an exponential creep function to demonstrate how the wall model affects wave propagation. The downstream vasculature is represented by a three-element Windkessel model composed of two resistors and a capacitor whose values are found through comparing the impedance spectrum with that of a structured tree model. Varying the parameters in both the wall model and the Windkessel model allows us to regulate the stiffness along each vessel as well as the upstream effects caused by the downstream vasculature. This study used the one-dimensional model to simulate flow, pressure, and area waveforms in a large network geometry representing the ovine aorta and several of its major branch vessels. Our model has been validated against young ovine data and can be used to help predict the ultimate impact aging has on an arterial network.

Strain interactions and seasonal dynamics of childhood disease incidence: whooping cough revisited

Background/Questions/Methods

Incidence of whooping cough unlike many other childhood infections exhibits variable dynamics across time and space. The periodicity of this disease varies from 2 to 5 years in different geographic regions from developing to developed countries. Many hypotheses have been put forward to explain this variability such as nonlinearity and seasonality, stochasticity, variable recruitment of susceptibles via birth, immunization and immune boosting. In this piece of work, we propose an alternative hypothesis to describe the variability in periodicity – the intricate dynamical variability of whooping cough incidence may arise from interactions of two strains of Bordetella, namely B. pertussis and B. parapertussis. We develop a two-strain age-structured model, where these two pathogens interact via age-dependent convalescence of individuals with severe illness from infections. We numerically analyze the model and characterize the outbreak dynamics under different strength of interactions. We also explore the dynamical response of the model to different perturbations like case importations and noise in transmission.

Results/Conclusion

With moderate strength of interactions, the model exhibits multi-annual coexisting attractors depending on the basic reproduction ratio of the two pathogens. For instance in higher R0, four different stable attractors coexist in a finely structured intertwined basin of attraction. In two attractors, both strains exhibit in-phase dynamics; while in the other two, they oscillate out-of-phase with relatively high fluctuations. It is also seen that perturbation due to movement or case importation and noise in transmission pushes the system from one dynamical regime to another. The coexistence of multi-annual cycles and the behavior of switching between attractors suggest that variable dynamics of whopping cough could be an emergent property of the interacting system, which is not observed earlier.

Optimal Control of Nipah Virus (NiV) Infections

Infectious disease remains the major cause of mortality worldwide (see [1]). Nipah is one of such highly pathogenic zoonotic virus which has posed a great threat causing emerging infectious disease in the public health in the South Asia, specially in Bangladesh. As it has the highly devastating mortality rate (an estimated 100% in some cases), it is not surprising that this emerging disease can be pandemic causing alarming threats for the global public health if effective control strategy is not adopted. It is mentioned that there is no proper drugs or effective vaccine for the treatment of nipah virus (NiV) infections. It is a must to control the spread of NiV infections in absence of proper drugs or effective vaccine. In this paper, we propose a mathematical model which describes the host-pathogen interactions in terms of ordinary differential equations (ODEs). We aim is to investigate the disease propagation and control strategy of NiV infections. We analyze the model numerically and illustrate the resultswith simulation using the optimal control technique in the form of maximum principle in vein of [3].

References

[1] M.H.A. Biswas, L.T. Paiva and M.D.R. de Pinho, A SEIR Model for Control of Infectious Diseases with Constraints, Mathematical Biosciences and Engineering, 11(4), 2014, pp. 761–784.

[2] H.W. Hethcote, The Mathematics of Infectious Diseases, SIAM Review, 42 (4) (2000), pp. 599–653.

[3] R. Vinter, Optimal Control, Birkh¨auser, Boston 2000.

Modeling the Geographic Spread of Rabies in China

Human rabies is one of the major public health problems in China. Dogs are the main infection source, which contributes 85%-95% of human cases in China. In the past few years, due to the dog trade, immigration of dogs became essential to understand the transmission dynamics of rabies in China. For example, some provinces such ad Shaanxi and Shanxi, used to be rabies free, have increasing numbers of human infectious cases. In 2005, the Institute for Viral Disease Control and Prevention of China CDC cooperated with the provincial CDC laboratories and began collecting samples from dog population in regions where human rabies cases had been reported; additionally all the positive samples in DFA and RT-PCR detection were submitted for DNA sequencing. Then a spatial dynamic analysis to identify structure in the geographic diffusion of the rabies virus in China was performed at the provincial level. Based on these scientific results, we propose a multi patch model for transmission of rabies in China, which consists of eight compartments of dogs and humans in each patch. We also simulate the data of three pairs of provinces from Chinese Ministry of Health and a sensitivity analysis of the basic reproduction number is performed in order to understand how the dog movement influence the disease spread. Some disease prevention and control strategies will be given according to the mathematical analysis of the model and simulations. This is a joint work with Lan Zou and Shigui Ruan.

TBD

Abstract not submitted

On an inverse problem in bioconversion of glycerol

The biodiesel synthesis produces a great amount of glycerol as a subproduct. The ever-growing of residual glycerol is becoming of a great environmental and economical concern. Hence, bioconversion glycerol into a valued-added products as 1,3 propanediol (1,3 - PD) and/or ethanol has recently been receiving more and more attention. See [8, 3, 7, 6, 5] and references therein.

Since the early 80’s, microbial synthesis of glycerol into 1,3 PD by Klebsiella pneumoniae has been studied [8, 3, 7, 6, 5]. The advantage of fermentation of glycerol in batch culture relays in the relatively easy and almost toxic-free byproducts compared with the expensive industrial fermentation process [3, 5, 8, 7, 6]. On the other hand, it is hard to obtain a high 1,3 PD concentration in the microbial culture fermentation process as it is using chemical production [8, 5]. Therefore, an interesting problem that comes out it the development and improvement of the productivity of 1,3 - PD from microbial fermentation.

In this work, we concentrate our attention in the mass balances of biomass, substrate and products in batch culture model [8, 7, 6] that can be formulated as the initial valued problem

x?(t) = f(t,x(t))x(0) = x0 ,(1)

where f(t,x(t)) = (µx1(t),−q2x1(t),q3x1(t),q4x1(t),q5x1(t))T and xi(t) for i = 1,••• ,5 are the biomass, glycerol, 1,3 - PD, acetate and ethanol concentration at time t in the reactor, respectively.

The vector x0 is the initial state and we denote by T the termination time of the fermentation process. The parameters in (1) are: µ is the specific growth rate of cells, q2 is the specific consumption rate of substrate and qj for j = 3,4,5 are the specific formulation rate of products.

1

Is well known that there exist critical concentrations outside which the microbial bioconversion is unfulfilled [8]. Hence, it is biologically and economically meaningful to calibrate the parameters in the nonlinear dynamic system (1) such that the maximum bioconversion of glycerol to 1,3-PD is attained.

The main proposal of this work is to study the mathematical analysis of the parameter identification problem in the bioconversion of glycerol to 1,3- PD guide from the nonlinear system (1) from data measurements in the bioconversion process. This problem falls in the class of the so called inverse problems in system biology [1] that are ill-posed. In other words, small perturbations in the measurements can lead into wrong parameters. This means that a regularization strategy is necessary [1].

We prove properties of the parameter-to-solution map that illustrates the illposedness of the parameter identification problem. We also propose an Augmented Lagrangian Tikhonov type regularization approach which we obtain the regularizing properties of approximated solutions [4, 1, 2]. Moreover, we analyze numerical realizations of the parameter identification problem which the intent to guide the practice.

Modeling of different source of cellular noise

Mathematical models of biological systems can provide valuable insights into mechanisms regulating intracellular processes, determining individual cell fate and population dynamics. However, in many cases understanding and incorporating heterogeneity in cellular behavior is key to understanding processes at the population level. Heterogeneity is observed in almost every population of cells. New experimental methods that have been developed for tracking single-cell protein content allow to measure changes of protein levels in response to various stimuli [1]. These measurements provide data for mathematical models that can support experimental work in analysis of complex biological systems. At the same time, they call for development of a coherent modeling framework that would facilitate including heterogeneity of individual cells in models of population dynamics. [2].

One way to take into account cellular heterogeneity is to associate it with cellular noise that can be extrinsic and/or intrinsic. The source of extrinsic noises are factors that do not act uniformly on the population and thus trigger a cellular response in only a fraction of the population. Nongenetic, intrinsic heterogeneity have no straightforward explanation of its source. Intrinsic factors are thought to stem from the random (i.e. stochastic), synthesis and breakdown of individual molecules, such as mRNA and proteins [3].

The methods of modeling both noise types are widely known. Extrinsic variability can be modelled by introducing variability in model parameters and initial conditions [4, 5] or switching transcription processes. Intrinsic variability is generally created using Gillespie algorithm. Also, unequal distribution of cellular mRNA and proteins between two daughter cells after cell division contributes to heterogeneity in cellular responses [5].

The goal of this work is to combine these methods in one model with several aims in mind. The first question to be answered is which source is the contributes the most to the heterogeneity. Second, since including more and more phenomena in any model drastically increases model complexity, it is worth analysing which of them can be neglected.

Furthermore, an efficient method for incorporating the key sources of heterogeneity in population models is developed. And last, but not least, the work is concerned with determining the distribution of initial conditions in a cell population, which is a prerequisite in many modeling approaches. Although usually normal or gamma distributions are recommended, my initial results suggest that it is not always the case. We use several simple mathematic methods to find out when adding to the model complexity is necessary, and which modeling approaches lead to qualitatively different results.

TBD

Abstract Not Submitted

Shortest DCJ Scenarios and Implicit Transpositions

Genome rearrangements are rare evolutionary events that shuffle genomic architectures. The minimal number of such events between two genomes is often used in the phylogenomic studies to measure their evolutionary remoteness. Double-Cut-and-Join (DCJ) operations represent a convenient model of most common genome rearrangements (reversals, translocations, fissions, and fusions), while other genome rearrangements, such as transpositions, can be modeled by pairs of DCJs.

While it is easy to construct a shortest DCJ scenario transforming one genome into the other, there may exist multiple such scenarios, making it difficult to reveal the true evolutionary history. Furthermore, since the DCJ model does not directly account for transposition-like rearrangements, their impact on shortest DCJ scenarios is unclear.

We address the first issue by analyzing the structure of shortest DCJ scenarios between two genomes and showing that they all are connected with simple length-preserving modifications, each affecting only a pair of consecutive DCJs. In other words, all shortest DCJ scenarios are equivalent under these modifications.

We further study implicit appearances of transposition-like rearrangements (represented by pairs of DCJs) in shortest DCJ scenarios and prove that they may be unavoidable and have a large proportion.

Linearization of the Median Genome under DCJ

Reconstruction of the median genome consisting of linear chromosomes from three given genomes is known to be intractable. There exist efficient methods for solving a relaxed version of this problem, where the median genome is allowed to have circular chromosomes. We propose a method for construction of an approximate solution to the original problem from a solution to the relaxed problem and prove a bound on its approximation accuracy. Our method also provides insights into the combinatorial structure of genome transformations with respect to appearance of circular chromosomes.

Hierarchical gene-proximity models for GWAS

Motivated by the important problem of detecting association to traits in genome-wide association studies (GWAS), we present a novel Bayesian model that establishes a hierarchy between single nucleotide polymorphisms (SNPs) and genes by defining weights according to gene lengths and distances from genes to markers. The proposed hierarchical model enables the selection of SNPs that are close in genomic distance to relevant genes and are most likely to be associated with a given trait. To this end we formally conduct posterior inference in the form of variable selection. We compare the performance of our model to the most popular alternative, single association tests, on simulated GWAS data. We conclude with a discussion on results on the Rheumatoid Arthritis dataset from the Wellcome Trust Case Control Consortium (WTCCC).

Concise Functional Enrichmen of Ranked Gene Lists

Advances in molecular biology have led to the broad availability of genome-wide expression data and the development of gene interaction databases like the Gene Ontology. Standard techniques used in genome-wide expression profiling (like RNA-Seq) output long lists of genes, ranked by expression levels. Gene set enrichment methods that simultaneously analyze the expression and the interaction of all genes have been developed to reveal overall trends, previously hidden in the data. Most gene set enrichment methods only work in a binary mode; that is, either a gene is considered differentially expressed or not. This view disregards the various levels of differential expression, which could be used to obtain a better explanation of the data. Other common shortcomings include high redundancy and non-­specificity of the explanatory set, as well as the sole use of the hypergeometric p-value, which favors terms that annotate many genes. To our knowledge, all gene set enrichment methods exhibit at least one of these deficiencies. We present a new enrichment algorithm that neither disregards important information by operating in binary mode, nor shares any of the common shortcomings of gene enrichment methods.

A Mathematical Model of Redox/Methylation Metabolism in Human Neuronal Cells

It is vital for cells to control their state of reduction and oxidation (redox), and the metabolic pathways providing this crucial function intersect with pathways controlling hundreds of methylation reactions. It has been hypothesized that abnormal redox and methylation status contributes to a number of brain disorders, including autism or Alzheimer’s disease (AD) {Deth 2008,Mutter 2010}. Following in the footsteps of Reed et al. {Reed 2008}, who created a mathematical model of these pathways in liver cells, I built a mathematical model of redox and methylation metabolism for human neuronal cells, in order to explore the predictions of this hypothesis and to see if further insights can be gained based on this model. While redox and methylation metabolism exists in all human cells, in many regards the brain compartment provides a unique environment for its many aspects of regulation.

Among other findings, simulations with this neuronal model support the hypothesis that inhibition of selenoenzymes by mercury can alter the redox status of the cell to a significant extent, which can ultimately contribute to autism or AD, depending on age. In addition, inhibition of these enzymes could be essentially irreversible, in the sense that, no other treatment could restore the levels of key metabolites back to normal homeostatic levels. We further use the model to explore the behavior of neuronal cells under different metabolic circumstances.

A Computational Prediction System for Identifying Human microRNA Target Sites

MicroRNAs (miRNAs) are important regulators of gene expression and play crucial roles in many biological processes including apoptosis, differentiation, development, and tumorigenesis. Recent estimates suggest that more than 50% of human protein coding genes may be regulated by miRNAs and that each miRNA may bind to 300-400 target genes. Approximately 1,000 human miRNAs have been identified so far with each having up to hundreds of unique target mRNAs. However, the targets for a majority of these miRNAs have not been identified due to the lack of large-scale experimental detection techniques. Experimental detection of miRNA target sites is a costly and time-consuming process, even though identification of miRNA targets is critical to unraveling their functions in various biological processes. To identify miRNA targets, we developed miRTar Hunter, a novel computational approach for predicting target sites regardless of the presence or absence of a seed match or evolutionary sequence conservation. Our approach is based on a dynamic programming algorithm that incorporates more sequence-specific features and reflects the properties of various types of target sites that determine diverse aspects of complementarities between miRNAs and their targets. We evaluated the performance of our algorithm on 532 known human miRNA:target pairs and 59 experimentally-verified negative miRNA:target pairs, and also compared our method with three popular programs for 481 miRNA:target pairs. miRTar Hunter outperformed three popular existing algorithms in terms of recall and precision, indicating that our unique scheme to quantify the determinants of complementary sites is effective at detecting miRNA targets.

References
1. D.P. Bartel. MicroRNAs: target recognition and regulatory functions. Cell, 136: 215-233, 2009.
2. D. Betel, M. Wilson, A. Gabow, D.S. Marks, C. Sander. The microRNA.org resource: targets and expression. Nucleic Acids Res., 36: D149-153, 2008.
3. I. Hofacker. Vienna RNA secondary structure server. Nucleic Acids Res., 31: 3429-3431, 2003.
4. P. Sethupathy, M. Megraw, A. G. Hatzigeorgiou. A guide through present computational approaches for the identification of mammalizan microRNA targets. Nat. Methods, 3: 881-886, 2006
5. M.S. Waterman, M. Eggert. A new algorithm for best subsequence alignments with application to tRNA-rRNA comparisons. Journal of Mol. Biol., 197: 723-728, 1987.

Spreading speeds of Fisher-KPP Equations in Periodic Media with Localized Spatial Inhomogeneity

Our work is concerned with positive periodic solutions and spatial spreading speeds of KPP type evolution equations with random or nonlocal or discrete dispersal in locally spatially inhomogeneous and temporal periodic media. It is shown that such an equation has a unique globally stable positive periodic solution and has a spreading speed in every direction. Moreover, it is shown that the localized spatial inhomogeneity of the medium neither slows down nor speeds up the spatial spreading in all the directions.

The Dynamics of Methamphetamine Abuse and HIV among Men Seeking Men: a Mathematical Perspective

Methamphetamine is an addictive stimulant that releases high levels of neurotransmitter dopamine. The use of methamphetamine have shown to increase libido and reduces inhibition. As a result, methamphetamine is commonly used among men who have sex with men to to initiate, enhance, and prolong sexual encounters. This, in turns, promotes high risk sexual behavior in this community of methamphetamine users which increases the risk of acquiring an STD. Furthermore, studies have shown that the use of methamphetamine is associated with more frequent risky sexual behaviors among HIV positive men when compared with HIV negative men.

This study will present the dynamics of methamphetamine abuse and HIV incidence in the men seeking men community from a mathematical perspective. A compartmental model is developed to represent a system of nonlinear differential equations. The implications of preventative measures will be discussed.

TBD

Abstract not submitted.

Hybrid functions approach for solving HIV pathogenesis models

This work provide a novel numerical method for solving systems of differential equations modeling HIV pathogenesis. Applying the proposed method, I study the model developed by Perelson et al. (1993), and I investigate the delayed HIV pathogenesis model developed by Hu et al.(2010). Finally, I generalize the model to a partial differential equations system and apply the proposed numerical method to it to investigate the spatiotemporal dynamics of CD4+T cells as well as the impact of the diffusion of CD4+T cells in the population dynamics.

A Computational Study of the Effects of Syk Activity on B Cell Receptor Signaling Dynamics

B cells, a type of white blood cell, are an integral component of the initiation and coordination of immune system responses to antigens, substances foreign to the body. The kinase Syk is intricately in- volved in early intracellular signaling events in B cells, and is required for proper response when antigens bind to B cell receptors (BCRs). Experiments using an analog-sensitive version of Syk (Syk-AQL) have elucidated its role, but have not completely characterized its behavior. We present a computational model for BCR signaling, using dynamical systems, which incorporates both wild-type Syk and Syk- AQL. We investigate how manipulation of Syk-AQL can be used to modulate the downstream response associated with BCR stimulation.

Models of spraying strategies: Continuous vs. Intermittent.

Chagas disease is a major health problem in rural South and Central America where an estimated 8 to 11 million people are infected. The disease is potentially life-threatening, with estimates of the number of deaths caused by it on the order of over 10 000 per year. It is a vector-borne disease caused by the parasite Trypanosoma cruzi, which is transmitted to humans mainly through the bite of insects from several species of so-called “kissing bugs" (vector species).

Current control measures to reduce Chagas disease transmission include treatment of homes with insecticides to control the vector species population. However, reinfestation of homes by vectors has been shown to occur as early as four to six months after insecticide-based control interventions. We develop models and compare the effectiveness of two spraying strategies namely; continuous and intermittent.

Optimal Control Applied in Coupled ODE/PDE model for anthrax Epizootic

Abstract not submitted.

Robust and tunable circadian rhythms: bridging the intrinsic properties of the core oscillator and the output signaling pathway

In prokaryotic systems the adaptive response to an environmental stress is often controlled by two component regulatory systems. In the prototypical two-component system, environmental information is transmitted by a single phosphotransfer event between a sensor histidine kinase and a cognate response regulator that then drives a transcriptional response. Versions of the simple, single-phosphotransfer motif have been shown through a combination of experiments and mathematical modeling to enable a broad range of signaling properties, including graded and hysteric responses (Igoshin et al., Mol Microbiol. 2008) and concentration robustness (Batchelor and Goulian, PNAS 2003; Shinar et al., PNAS 2007). In the cyanobacterium S. elongatus, signaling through the SasA-RpaA simple two-component system transduces information regarding the state of endogenous circadian clock to the transcriptional machinery, effecting a global circadian gene expression program that includes rhythmic expression of the clock genes themselves (Markson et al., Cell 2013).

Given this transcriptional feedback, we are interested in extending our previous deterministic model of the cyanobacterial KaiABC protein circadian oscillator (Phong et al., PNAS 2013) into a stochastic framework that includes output signaling through the SasA-RpaA two-component system. While we have previously shown that delayed negative feedback on the catalytic activity of the core oscillator permits tunable phase and amplitude while maintaining a robust circadian period, the activity state of the core oscillator also determines its associations with the output signaling proteins. Thus our revised model will be informed by our experimental efforts to reconstitute SasA-RpaA signaling and characterize its input-output relationships in vitro. We hope to gain a better understanding of how the intrinsic signaling properties of the prototypical twocomponent system are used to ensure a strong phase relationship between the KaiABC protein clock state and its circadian transcriptional output.

Optimal Control of Gene Regulatory Networks with Uncertain Intervention Effects

Optimal control policies for Markovian gene regulatory networks assume that external intervention is 100% specific to control genes. In practice, however, this effect may be unpredictable in the sense that intervention may also target alternative genes. Our goal is to find an optimal control policy that performs well in such cases. We model this by an uncertainty class of controlled networks corresponding to different affected genes, governed by a probability distribution representing our confidence in the intervention specificity to each gene, and optimize relative to this uncertainty class.

A Binary Gene Pair Model To Discover New Breast Cancer Molecular Subtypes

Comprehensive analyses of genomic profiles have classified breast cancer into four molecular subtypes: Luminal A, Luminal B, HER2-enriched, and Basal-like. The relevance of these molecular breast cancer subtypes for basic and translational research has led to their use in prognostic assessments, prediction of therapeutic efficacy, and retrospective analyses of clinical trials. The translation of genomic profiles such as microarrays into clinical applications, however, is impeded by the reproducibility of microarray experiments at different sites, the compatibility of results on different platforms, and even the variability of microarray results in the same laboratory. In this paper, we propose a novel binary gene pair model to effectively combine microarray data. In the binary gene pair model, if Gene 1 is greater than Gene 2, then Gene1_Gene2 is 1; otherwise Gene1_Gene2 is 0: Gene1_Gene2 = 1, Gene 1 > Gene2, 0, Gene 1 < Gene 2. Now, instead of n genes, each sample has n(n-1)/2 gene pairs. Here, microarray data is transformed to binary data that is independent of microarray platform, and robust to the addition or removal of samples. The binary gene pair model, feature selection, and clustering are used to confirm existing breast cancer subtypes, and discover new breast cancer subtypes in the Molecular Taxonomy of Breast Cancer International Consortium (METABRIC) data. The METABRIC dataset consists of a discovery cohort (997 patients) and validation (995 patients). A preliminary analyzes suggests that the PAM50, a breast cancer signature, binary gene pairs cluster more accurately across molecular subtypes than genes in the METABRIC data.

The paradox of enrichment in phytoplankton by induced competitive interactions

The biodiversity loss in a single trophic level due to high nutrient concentration has been reported in aquatic ecosystems (e.g., red tides, algal blooms). This effect of enrichment to biodiversity seems similar to the paradox of enrichment. We here propose a mechanism that induces the paradox of enrichment in phytoplankton using multiple contact process in a square lattice system called the lattice Lotka-Voltera competition model. Simulation results demonstrate how-high nutrient condition invokes severe competition for space in a lattice ecosystem resulting in the loss of phytoplankton diversity in ecological time. Thus, the paradox appears when high nutrient condition destroys an ecosystem either by elevated interspecific competition within a trophic level and/or destabilization by trophic interactions. In addition, it has been seen that an optimal nutrient condition exists that maximizes biodiversity. These results can help environmental agencies manage the nutrient levels in aquatic ecosystems to preserve biodiversity.

Targeting performances for stochastic models of neural growth with uniform branching and pruning

The highly interconnected and functional circuitry of the nervous system relies on the complex architecture of neuronal networks elaborated during development, which in turn depends on the ability of neurons to branch and establish connections with appropriate targets. Traditional mathematical and computational researches have focused on characterizing arborization patterns of functionally-specific neuronal populations and showing how particular growth dynamics shape their morphological distinctiveness. Less effort, however, has been placed in understanding how the growth rules associated with neuronal morphogenesis translate into effective search/avoid strategies for reaching desirable targets. In this work, we start with a simplified growth model to evaluate the search efficiency of targets by neurons evolving within a stochastic arborization algorithm under a conditional finite resource constraint. Specifically, for a set time interval of evolution t0, each active neurite branches independent of other branches with set probability (p) and prunes with set probability (r), while total tree length is limited to maximal value (L). Targeting effectiveness (number of active branches at a certain distance away from origin) is evaluated as described in Osan et al, PLOS One 2011. We then proceed with a mathematical treatment of the search problem using probability rules and statistics to derive the trends induced by variations in the parameters p, r and L. We use the probability distribution obtained from the analytical treatment to compute the expected performance and variability. These results match the full-fledged numerical simulations of stochastically growing neurons, thus showing that the optimal arborization dynamics associated with target effectiveness can be similarly derived from two separate treatments. The agreement between computational simulations and non-algorithmic statistical analysis, demonstrates the ability of in charta (on paper) approaches to build on standard in silico evaluations of in vivo observations. Future work will examine parameter-based branching and pruning, allowing us to formulate predictions on how changing specific aspects of arborization can fine-tune targeting performances. The in charta work, expanded to include aspects of arbor geometry (i.e. branch angle), can provide insight into phenomena observed during neurogenesis, such as sibling competition, fasciculation, and tiling. This parallel approach to uncovering biological explanations associated with the dynamics of growth, contributes to our understanding of design principles that operate during neural development and regeneration.

A Mathematical Model of Tumor Progression Based on Cancer Cell Metabolic Mechanism

In this work a mathematical model based on cancer cell metabolic mechanism is developed. Over decades of cancer research the characteristics of cancer cells metabolism have been investigated with the aim to understand the behaviors and activities of tumor progressions for successful cancer treatment. In 1920s Warburg found that most cancer cells rely on aerobic glycolysis rather than oxidative phosphorylation. Recently biologists also recognized that cancer cells incorporate glutamine metabolism. Although the molecular mechanism in cancer cells metabolism is not fully understood, biologists proposed that the metabolism of cancer cells facilitates the uptake and incorporation of nutrients into biomass which are essential for cell proliferation and leads to microenviromental acidosis which promotes the invasion[1][2][3]. We introduce a mathematical model based on a set of non-linear reaction-diffusion equations to explain the prevalence of cancer cells metabolism characteristics and the acid-mediated invasion hypothesis. Numerical simulations are used to explore the behaviors of the tumor's progression and verify theoretical analysis, which parameters govern the tumor invasion and how the parameters control the speed of invasion. A better understanding of the roles of cancer cells metabolic mechanism in tumor evolution may lead to better development of efficacy cancer therapy methods.

Ref:

[1] Undertanding the Warburg Effect: The Metabolic Requiremnets of Cell Proliferation, Matthew G.Vander Heiden,Lewis C. Cantley, and Craig B.Thompson, Science, 2009 May 22; 324(5930):1029-1033.

[2] Q's next: The Diverse Functions of Glutamine in Metabolism, Cell Biology and Cancer, Ralph J.DeBerardinis, M.D., Ph.D. and Tzuling Cheng, Ph.D.,Oncogene, 2010 January 21.

[3]Why Do Cancers Have High Aerobic Glycolysis? Robert A.Gatenby and Robert J.Gillies, Nature Reviews/Cancer, November 2004.

Automatic Egg Chamber Stages Identification of Drosophila Oogenesis from DAPI Image

The Drosophila egg chamber is an excellent and well-established model in biological field for studying signaling pathways in development and collective movement of cells. In Drosophila, each female has two ovaries, which is composed of 16-20 ovarioles. Each ovariole is a string of progressively developing egg chambers. The development of egg chamber is divided into 14 stages. Biologists determine the specific stages of the egg chamber in their routine work based on egg chamber morphology and some stage-specific markers. However, the judgment relies heavily on researchers’ own experience. Moreover, even a skilled biologist is hard to distinguish egg chambers at transitional stages, if without further collecting more data. Here, we report that we collect confocal images of egg chamber together with some stage-specific markers by skilled biologist. We extract image features and plan to construct a correlation between the egg chamber stages and image features of the middle-section slice of egg chamber. This correction could be used by scientists to automatically determine specific stages with the same standard. Moreover, with the help of machine learning methods, we hope to identify some hidden features that lead to unknown biological mechanisms.

Modeling core body temperature during exercise

After the 2003 London Marathon, 6 runners were diagnosed with hyperthermia and 13 runners with hypothermia. To understand how opposite conditions developed in the same environment, we created a mathematical model to describe core (body) temperature responses to exercise at different ambient temperatures. Rats were implanted with telemetric probes, which reported core temperature; then allowed to recover and familiarized to run at a treadmill. Core temperature time-series were recorded during 15 min runs with various speeds (0, 6, 12, 18 m/min at 0 incline) in cool (24°C, T1) and hot (32°C, T2) environment. At T1 there was a temperature drop during first 5 min, while at T2 temperature did not change during that period. After 5 min, temperature started rising linearly at both T1 and T2 until the treadmill was stopped. The slope of this linear increase remained constant for all four speeds at T1, whereas at T2 it progressively steepened with the speed increase.

To explain these findings, we have designed a model which consisted of two chambers exchanging heat: the core and muscles. The core dissipated heat proportionally to difference between the core and ambient temperatures. This model was formally described by a system of differential equations. All parameters of the system were subject to fit the average temperature response curves. Changes of the core temperature in rats, which were placed on the treadmill but were not running (0m/min), were considered as a non-specific effect resulting from stress.

Hypothermia during the first 5 min at T1 was interpreted as a result of increased heat dissipation due to changes in the posture of rats caused by their placement onto a treadmill. This drop was not observed at T2 because of much lesser change in dissipation. The linear increase of temperature after 5 min was a result of heat generation in muscles, while the delay in the core temperature response was due to the time required for the heat transfer from muscles to the core. We hypothesize that exercise activates thermoregulatory inhibition of thermogenesis and/or increases heat dissipation, which prevents excessive heat accumulation during exercise in cool environment. However, at high ambient temperature this thermoregulatory compensation is impossible because the core metabolism cannot be reduced any further, while heat dissipation is already at its maximum. Therefore, heat generation by exercise added to heat accumulation and presented itself as an increased rate of the temperature growth. We conclude that compensatory mechanisms in the thermoregulatory system may underlie some controversial results concerned with the role of locomotion in the body temperature dynamics.

Homogeneous and Inhomogeneous Speed Solutions from Traveling Wave Propagation of Activity in Neural Tissues

They study of traveling waves of activity in disinhibited neural slices can provide valuable insights into the normal functions of the brain or during abnormal states such as epilepsy. Large-scale networks containing integrate-and-fire models of the neurons have been successfully used to model these wave phenomena. For these models, a common assumption is that while the strength of the synaptic connections between two neurons changes as a function of distance, this interaction does not depend on other local parameters. Based on our work on homogeneous media, we examine how inhomogeneities affect the dynamics of the activity propagation. In particular, we seek to determine the conditions leading to propagation failure. While an explicit formula for speed modulations for activity propagation is difficult to determine, we established a series of progressively more accurate approximations that we used to compare with results from numerical simulations.?

On the Sexual Transmission Dynamics of Hepatitis B Virus in China

In a previous work, we noticed that there might be co-infections of HBV and HIV by comparing incidence rates of these two diseases in China. The comparisons between the incidence data of HBV and sexually transmitted diseases (including AIDS, HIV, syphilis, gonorrhea) in China demonstrate that sexual transmission is an important route of spread of HBV in China. Based on this fact, we propose a compartmental model including under-aged children, male adults, and female adults. The effect of sexual transmission of the spread and prevalence of HBV in China is studied. The model is used to simulate the HBV incidence rates for under-aged children, adult males, and adult females, respectively. The sensitivity analysis of the basic reproduction number indicates that increasing the immunization rates of both under-aged children and adults are important and crucial to control the transmission of HBV in China; however, immunization of under-aged children only is not enough to reduce the basic reproduction number to be less than one. Our study shows that effective hepatitis B control measures in China include enhancing public education and awareness about hepatitis B virus, in particular about the fact that hepatitis B is a sexual transmitted disease, and increasing the immunization rate of both under-aged children and adults, especially certain high risk groups.

Modeling brainstem neurons and their interactions
Henry Tuckwell

Brainstem and lower nuclei contain neurons which are the principal CNS sources of the neurotransmitters serotonin (dorsal and other raphe nuclei) and noradrenaline (locus coeruleus and associated centers). By means of vast ascending and desc

Predictive Models of Type I Diabetes Progression
Majid Jaberi-Douraki

In type 1 diabetes, an autoimmune disease mediated by autoreactive T-cells that attack insulin-secreting pancreatic beta-cells, it has been suggested that disease progression may additionally require protective mechanisms in the target tissu

Many bacteria are able to communicate information by getting close to each other and signaling through direct contact between cells. This talk will focus on how information is spread between swarming Myxococcus xanthus c

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