April 17th, 2019

Denise Kirschner

Professor, Microbiology, University of Michigan

Building, Analyzing and Calibrating Multi-Scale Models in 2D and 3D: Tuberculosis as a Case Study

Multi-scale models (MSM) are increasingly being used to study complex biological processes. Multi-scale models span a range of both spatial and temporal scales and can also encompass multiple physiological compartments. MSMs are growing more complex and cumbersome and it is necessary to coarse grain model aspects when appropriate. A new approach that we call tuneable resolution can provide that flexibility.  Additionally, analyses of MSMs can be difficult, and we have fine-tuned a global uncertainty and sensitivity analysis approach that can be applied to all MSM types performing both inter- and intra-scale analyses and to assist with model calibration and validation. Finally, we have been exploring optimization, for example of drug treatment regimens, in the context of MSMs and have identified protocols that are computationally efficient. We will explore all of these topics in the context of our extensive work in the area of the host immune-response to infection with the bacterium Mycobacterium tuberculosis.

March 20th, 2019

Franziska Michor

Professor of Computational Biology, Department of Biostatistics, Harvard University

Mathematical Modeling of Cancer Evolution

Cancer represents one of the biggest problems for modern societies. In 2017, the cancer incidence was projected to be around 1.7 million cases with an estimated mortality of roughly 601,000. By 2020, cancer deaths worldwide could reach 10 million. Therefore, an important goal of life science research is to improve tumor diagnostics and anti-cancer treatment options to alleviate cancer-related morbidity and mortality. We are interested in using the tools of theoretical evolutionary biology, applied mathematics, statistics, and computational biology to address important questions in cancer research. In this talk I will present recent work in my lab.

February 20th, 2019

Michael Mackey

Applied Mathematics in Bioscience and Medicine, Physiology, McGill University

Using Mathematics to Understand, Treat and Avoid Hematological Disease

Mathematical modeling of the regulation of blood cell production has reached a level of sophistication where it can be used to help to understand the cellular/molecular basis of some diseases like cyclical neutropenia. Equally, it has been used to suggest ways to treat some of these diseases by suggesting likely targets for drug intervention. And, lastly, the mathematics is now suggesting that there are ways in which we can avoid the hematological side effects of procedures like chemotherapy. In spite of these types of progress, however, we must recognize the very primitive nature of our modeling and that much remains to be done.

January 23rd, 2019

Michael I. Jordan

Pehong Chen Distinguished Professor, Department of Statistics, University of California, Berkeley

Machine Learning: Dynamical, Economic and Stochastic Perspectives

While there has been significant progress in the theory and practice in machine learning in recent years, many fundamental challenges remain. Some are mathematical in nature, such as the challenges associated with optimization and sampling in high-dimensional spaces. Some are statistical in nature, including the challenges associated with multiple decision-making. Others are economic in nature, including the need to price services and provide incentives in learning-based two-way markets. I will present recent progress on each of these fronts.

December 12th, 2018

Mark Lewis

Canada Research Chair in Mathematical Biology, University of Alberta

Using Mathematics to Understand Animal Movement Patterns

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

November 14th, 2018

Gunnar Carlsson

Department of Mathematics, Stanford University

The Shape of Biological Data

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

October 17th, 2018

Avner Friedman

Distinguished University Professor, Department of Mathematics, The Ohio State University

Using Mathematical Models to Conduct Cancer Clinical Trials

Most cancer clinical trials with combination therapy in phase II have failed in phase III. One of the reasons for this failure is that no sufficient forethought was given to the interactions between the two (or more) agents.  Before embarking on a clinical trial with (say) two agents, one should address the following questions:

1. If the two drugs are positively correlated at any dose amounts, how to achieve the same tumor volume reduction with minimal negative side-effects?
2. If the two drugs are antagonistic at certain ranges of the doses, how to avoid these zones of antagonism?
3. What schedule is most effective in reducing tumor burden? e.g. in which order to give the drugs?
4. How to reduce drug resistance by the tumor cells?

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

April 18th, 2018

Marc Suchard

Biomathematics and Human Genetics, University of California, Los Angeles

High-dimensional Phenotypes on Evolutionary Trees: Efficient Algorithms and New Models

March 21st, 2018

Philip Maini

Centre for Mathematical Biology, University of Oxford

Modelling Collective Cell Motion in Biology

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

February 14th, 2018

Alan Hastings

Department of Environmental Science and Policy, University of California, Davis

Dynamics and Control of Spatial Ecological Populations

I will focus on two important themes in contemporary ecology that draw upon mathematical tools: the dynamics of populations in space and management of populations. I will consider both deterministic and stochastic models of spatial population dynamics. For the management questions, I will consider both the issue of controlling invasive species in space and approaches for maintaining endangered species. Mathematical tools will be diverse, ranging from partial differential equations to stochastic models to different optimization approaches. Issues of time scales and the interface between models and data will be emphasized.

January 17th, 2018

Alan Perelson

Theoretical Biology and Biophysics Group, Los Alamos National Laboratory

Modeling Antibodies and HIV Cure

The French VISCONTI study identified 14 HIV+ patients, who received antiretroviral treatment during primary infection for a median duration of 36.5 months and maintained post-treatment control of their virus below the limit of detection for a median of 89 months after stopping therapy. Byrareddy et al., Science 2016, showed that SIV-infected rhesus macaques on ART given a rhesus monoclonal antibody against the integrin 47 could maintain undetectable plasma viremia for over 9 months after all treatment was stopped. These examples provide proof-of-concept that a “functional cure” of HIV-1 infection, i.e. long-term control of HIV without continued treatment, is achievable.

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

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

December 6th, 2017

Lisa Fauci

Department of Mathematics, Tulane University

Biological Fluid Dynamics at the Microscale: Nonlinearities in a Linear World

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

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

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

November 8th, 2017

Kristin Swanson

Neurosurgery, Mayo Clinic

Every Patient Deserves Their Own Equation: Patient-Specific Mathematical NeuroOncology

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

October 18th, 2017

John Tyson

Computational Cell Biology, Virginia Polytechnic Institute and State University

Network Dynamics and Cell Physiology

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

September 20th, 2017

James Collins

Department of Biological Engineering, Massachusetts Institute of Technology

Synthetic Biology: Life Redesigned

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

April 12th, 2017

James Keener

Department of Mathematics, University of Utah

Cell Physiology: Making Diffusion Your Friend

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

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

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

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

March 15th, 2017

Uri Alon

Department of Molecular Cell Biology, Weizmann Institute of Science

Evolutionary Tradeoffs and the Geometry of Phenotype Space

Evolutionary tradeoffs lead to phenotypes that lie in polytopes in trait space, allowing evolutionary tasks to be inferred from data on animal morphology, single cell gene expression and other systems.

February 15th, 2017

Joel Cohen

Laboratory of Populations, Rockefeller & Columbia Universities

The Variation is the Theme: Taylor's Law from Chagas Disease Vector Control to Tornado Outbreaks

Darwin and Mendel discovered key roles of variation in biology. Some useful tools for quantifying, understanding, and exploiting variation are not sufficiently widely known among biologists. Taylor's power law of fluctuation scaling describes a relationship between the variance and the mean of a positive quantity. Examples of Taylor's law include the population density of bacteria, rice, wheat, potatoes, trees, triatomine bugs that transmit Chagas disease, fish, rodents, and humans; the numbers of cells per mammalian organ, parasites per host, cancer metastases, and single nucleotide polymorphisms; and non-biological quantities such as the prime numbers, the number of tornadoes per outbreak, and the volumes of currency exchanges and stock trades. Taylor's law results from a wide variety of processes, so inferences based on Taylor's law require care. This talk will be partly a tutorial addressed to the question: What can Taylor's law do for you?

January 11th, 2017

Leah Edelstein-Keshet

Department of Mathematics, University of British Columbia

Navigating Biochemical Pathways for Cell Polarization and Motility (A Personal Journey)

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

December 7th, 2016

Arthur Lander

Center for Complex Biological Systems, University of California, Irvine

Understanding Growth Control

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

November 9th, 2016

Elizabeth Thompson

Department of Statistics, University of Washington

Finding Genes via Relatedness and the Co-ancestry of Genome

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

October 26th, 2016

Charles Peskin

Courant Institute of Mathematical Sciences, New York University

Fiber Architecture (Differential Geometry) of the Heart and its Valves

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

September 21st, 2016

Simon Levin

Department of Ecology & Evolutionary Biology, Princeton University

Mathematical Ecology: A Century of Progress, and Challenges for the Next Century

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