Mathematical Biology Research in the IAM

Mathematical Biology Group

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General Information

The Mathematical Biology Group is involved in interdisciplinary research applying mathematics in a wide range of biological fields including immunology, epidemiology, cell biology, electrophysiology, ecology, game theory and evolution. Our group is one of the best-established and largest in the field. Opportunities for graduate students and postdocs include lab experience through various collaborators on campus.

We are always interested to hear from potential graduate students and postdoctoral fellows. We recruit from many different backgrounds, including mathematics, physics, chemistry, bioinformatics, engineering and the biological sciences. We often supervise undergraduate thesis projects (for instance, from the Biophysics and Integrated Science programs) and take on summer research undergraduate students.

We are pleased to be part of the new PIMS International Graduate Training Centre (IGTC) in Mathematical Biology, which is a distributed centre including participation of groups from across British Columbia and Alberta. The PIMS IGTC offers scholarships to incoming students at UBC, among other universities. New and continuing students are encouraged to apply.

Please see also the Mathematical Biology at UBC home page.


Reaction-diffusion modelling of cell polarisation (colour depicts concentration of the active form of Rho GTPase): transient stimuli (left, centre-left), random initial conditions (centre), graded stimuli with reversal (centre-right), polarisation change due to geometry (right).

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Core Faculty

The Mathematical Biology Group is composed of several core IAM faculty who are actively involved in the IAM activities and supervise IAM students or postdoctoral fellows. Prospective students interested in a research project in Mathematical Biology in the IAM are encouraged to contact one or more of the core faculty as potential supervisors and let them know of their interests.

Fred Brauer	Fred is a Professor Emeritus in the Mathematics Department, who continues to be active in research and in supervision of graduate students. His research interests include mathematical epidemiology, population biology, and dynamical systems.
Dan Coombs	Dan is predominantly interested in theoretical immunology, especially cell signalling, cell-surface receptor kinetics, T and B cell immune synapse, and biological filament dynamics. Other areas of his research include multiscale modelling of infectious diseases and the development and improvement of techniques for measuring biophysical parameters.
Eric Cytrynbaum	Eric's research focusses on the dynamics of bacterial cell division, including both the regulation of division-site selection and the biophysics of force generation by the FtsZ ring, as well as eukaryotic cytoskeleton pattern formation and its role in cellular organisation and development (specifically plant growth). Eric is also interested in the modelling of wave propagation in excitable media with applications to cardiac electrophysiology.
Michael Doebeli	Michael is a Professor of Zoology and Mathematics. His research area is in ecology and evolution, including topics such as sympatric speciation, game theory, dynamics of spatially structured populations, cultural diversification, and controlling chaos.
Jimmy Feng	Jimmy works on cell and tissue mechanics, with an emphasis on modeling and simulating the feedback between biochemical signaling and mechanical responses on the cytoskeletal, whole-cell and tissue levels. Current projects include particle-based simulation of malaria-infected red cells, multiscale models of cell motility and tissue morphogenesis.
Christoph Hauert	Christoph is interested in computer simulations and models of complex systems with applications in physics, biology and medicine. The main focus of his work is on the evolutionary game theory and on structured populations (cooperation, reward and punishment).
Leah Keshet	Leah has been active in many areas of mathematical biology. Her current work is focussed on cytoskeleton and actin dynamics, and on swarming and aggregation behaviour in animal societies. Leah's book Mathematical Models in Biology has been one of the classic texts in the field.
Yue-Xian Li	Yue-Xian is interested in calcium dynamics, signal transduction in cells, biophysics, and neuroscience. Specific research topics include calcium signalling in neuroendocrine cells, fertilisation calcium waves in oocytes, and neuronal synchrony leading to rhythmogenesis of hormonal signals.

Spatio-temporal oscillations in Min bacterial division

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Recommended Courses

Students interested in the Mathematical Biology research in the IAM are advised to take the following preliminary, core and optional courses.

Preliminary and Foundational Courses
MATH 400: Partial Differential Equations
MATH 401: Green Functions and Variational Methods
MATH 450/550: Perturbation Methods
MATH 521: Numerical Analysis of PDEs
MATH 551: Asymptotic Analysis for PDEs
MATH 552: Dynamical Systems Theory
MATH 607E: Numerical Methods for Differential Equations

Mathematical Biology Courses
MATH 462: Projects in Mathematical Biology
MATH 560: Mathematical Biology
MATH 561: Mathematics of Infectious Diseases and Immunology
MATH 562: Mathematical Electrophysiology
MATH 563: Modelling of Cell-Scale Biology
MATH 564: Evolutionary Dynamics
MATH 612: Topics in Mathematical Biology

Further Options
MATH 554: Symmetries and Differential Equations
MATH 605E: Mathematical Modelling and Analysis of Industrial Problems

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Sample Publications

Listed below are some of the recent theses and journal publications by IAM students, IAM faculty, and IAM postdoctoral fellows in the field of Mathematical Biology. Click on the item of interest to open a thesis file, an article pdf on the author's web page, or an article abstract on the journal site.

Jun Allard, Geoffrey Wasteneys and Eric Cytrynbaum. Mechanisms of Self-Organization of Cortical Microtubules in Plants Revealed by Computational Simulations. Molecular Biology of the Cell, 21, pp. 278-286 (2010).

Christoph Hauert. Replicator Dynamics of Reward and Reputation in Public Goods Games. Journal of Theoretical Biology, 267, pp. 22-28 (2010).

Michael Doebeli and Iaroslav Ispolatov. Complexity and Diversity. Science, 328, pp. 494-497 (2010).

Jennifer Morrison. Deciphering Multi-State Mobility Within Single Particle Trajectories of Proteins on the Plasma Membrane. M.Sc. Thesis, University of British Columbia (2010).

Jun Allard and Eric Cytrynbaum. Force Generation by a Dynamic Z-ring in E. Coli Cell Division. Proceedings of the National Academy of Sciences USA, 106(1), pp. 145-150 (2009).

Eric Cytrynbaum and T. J. Lewis. Global Bifurcations and the Appearance of a One-Dimensional Spiral Wave in Excitable Media. SIAM Journal of Applied Dynamical Systems, 8(1), pp. 348-370 (2009).

Alexandra Jilkine. A Wave-Pinning Mechanism for Eukaryotic Cell Polarization Based on Rho GTPase Dynamics. Ph.D. Thesis, University of British Columbia (2009).

Erin Prosk. The Cofilin Activity Pathway in Metastasizing Mammary Tumour Cells. M.Sc. Thesis, University of British Columbia (2009).

Ryan Lukeman. Modeling Collective Motion in Animal Groups: From Mathematical Analysis to Field Data. Ph.D. Thesis, University of British Columbia (2009).

Omer Dushek, Raibatak Das and Daniel Coombs. A Role for Rebinding in Rapid and Reliable T Cell Responses to Antigen. Public Library of Science – Computational Biology, Vol. 5, Issue 11, pp. 1-12 (November 2009).

Majid Hosseini and Jimmy Feng. A Particle-Based Model for Simulating Erythrocyte Deformation and Transport Through Capillaries. Chemical Engineering Science, 64, pp. 4488-4497 (2009).

Omer Dushek, Raibatak Das and Daniel Coombs. Analysis of Membrane-Localized Binding Kinetics with FRAP. European Biophysics Journal, 37, pp. 627�638 (2008).

Anmar Khadra, Pere Santamaria and Leah Edelstein-Keshet. The Role of Low Avidity T Cells in the Protection Against Type 1 Diabetes: A Modeling Investigation. Journal of Theoretical Biology, 256(1), pp. 126-141 (2008).

Ryan Lukeman, Yue-Xian Li and Leah Edelstein-Keshet. A Conceptual Model for Milling Formations in Biological Aggregates. Bulletin of Mathematical Biology, 71(2), pp. 352-382 (2008).

Yoichiro Mori, Alexandra Jilkine and Leah Edelstein-Keshet. Wave-Pinning and Cell Polarity from a Bistable Reaction-Diffusion System. Biophysical Journal, 94(9), pp. 3684-3697 (2008).

Chunfeng Zhou, Pengtao Yue and Jimmy Feng. Simulation of neutrophil deformation and transport in capillaries using Newtonian and viscoelastic drop models. Annals of Biomedical Engineering, 35, pp. 766-780 (2007).


Molecular-motor force-balance in organelle positioning by microtubule asters; left: motors pull from the edge of the cell only (centered position unstable), right: motors pull from everywhere inside the cell (centered position stable).

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Last Update: 12 Dec 2010