IGTC Graduate Summer School in Mathematical Biology

A PIMS/Accelerate BC sponsored Summer School in Mathematical Biology

University of British Columbia, Vancouver, May 11-June 11, 2008

Abstracts for Talks

This page provides abstracts for many of the lectures and seminars.

For a detailed daily schedule click HERE.

For a list of events by category and/or lecturer(s) click HERE.

For details of the main Course Content click HERE.

For an overview of the month-long schedule click HERE.

Unless otherwise indicated, events will take place at the UBC campus of PIMS. Directions for PIMS can be found HERE.

Sunday May 11, Opening Lecture:

Prof Michael Doebeli

(Depts of Mathematics and Biology, UBC)

Adaptive diversification: theory and experiments

Abstract: Understanding the origin of diversity is a fundamental problem in biology. Traditional evolutionary theory predicts uniformity: natural selection, acting on organisms under given environmental conditions and developmental constraints, produces a unique, optimally adapted phenotype. According to this view, different types only come about through a change in conditions over space or time. In particular, the process of diversification, that is, the split of an ancestral population into distinct descendent lineages, is a by-product of geographical separation. This traditional view misses out on the important perspective that diversification itself can be an adaptive process. In this talk I will review theoretical work showing that diversification as an adaptive response to ecological interactions is a plausible evolutionary process. This work is based on the mathematical framework of adaptive dynamics, and in particular on the phenomenon of evolutionary branching due to frequency-dependent selection. I will describe basic models for evolutionary branching based on resource competition. I will then describe ongoing efforts to test the theory of evolutionary branching in evolving Escherichia coli populations, which provide promising experimental model systems for studying adaptive diversification at the genetic, physiological and ecological level.

Special Mathematical-Biology Guest Lectures

These Seminars will be held at PIMS. Pizza and drinks will be served at 12:30PM.

Friday May 16, 1:00PM

Prof Eirikur Palsson

(Dept. of Biology, SFU)

Excitability of Dictyostelium discoideum is regulated by the ratio of membrane bound to secreted phosphodiesterase

Abstract: After onset of starvation randomly distributed Dictyostelium discoideum cells initiate formation of cooperative aggregation territories over a wide range of initial cells densities. Recruitment of a high number of cells is important, and it appears that formation of large territories has been selected for. Propagating cAMP waves enable the formation of territories larger than 1 cm diameter. These cAMP waves are generated by the means of an elaborate cAMP signaling system that makes the whole field of cells excitable. Dictyostelium cells respond chemotactically to these waves, guiding cell aggregation towards a signaling center. An important component of the signaling system is the PdsA phosphodiesterase (PDE), that breaks down the external cAMP. PdsA can be either membrane bound or secreted. Here I show that by utilizing both of those two forms of PDE and by fine tuning the ratio, Dictyostelium extends the range of cell densities where cAMP waves can propagate and thus where aggregation can be successful. The membrane bound PDE reduces the likelihood that the aggregation territory breaks up into many smaller territories, as the cell density increases, while the secreted PDE is important for wave propagation at low cell densities. An interesting interpretation of these findings is that for some excitable systems, with discrete point sources located far apart, wave propagation is not possible if the sink is in the same location as the source. However, when the source and sink are in a different location wave propagation is possible. An example would be Ca++ propagation in cardiac cells.

Friday May 23, 1:00PM

Prof Daniel Coombs

(Dept. of Mathematics, UBC)

Models of T cell activation

Abstract: T cells are activated via their T cell receptors (TCR) binding to specific antigen on other cells, in the form of antigenic peptide-MHC complexes. T cells can be activated by very few presented peptide-MHC of the right type. The serial engagement hypothesis suggests that each peptide-MHC binds to multiple TCR, amplifying its effect. In this talk, I will talk about serial engagement and related things at an introductory level.

Tuesday May 27, 1:00PM

Prof Yue Xian Li

(Dept. of Mathematics, UBC)

Tango Waves in Inhomogeneous Calcium Excitable Media

Abstract: Oscillations and travelling waves are often observed in intracellular levels of calcium when egg cells are either activated by a sperm or by other kinds of stimuli. This is often due to the existence of calcium stores that are capable of dynamically releasing calcium making the intracellular medium a calcium excitable medium (Li et al, Am J Physiol 296:C1079, 1995). Tango waves are wave fronts that propagate in a back-and-forth manner and was found in a bidomain model of calcium waves in frog eggs (Li, Physica D, 186:27, 2003). We show that such waves can occur in the presence of a time-dependent spatial inhomogeneity in an excitable medium. Analysis of such a phenomenon was carried out using the FitzHugh-Nagumo (F-N) model with a spatially varying but time-independent term, z(x), added to the first equation. Inhomogeneities cause pinning and oscillations of the front. This is best shown when z(x) is a linear ramp. When the slope is large, it stabilizes the front. The front becomes less stable as the slope decreases. At a critical slope, the front becomes unstable through a Hopf bifurcation beyond which oscillations occur (Prat and Li, Physica D, 186:50, 2003). These results were generalized to a wider class of excitable media including systems of PDEs and IDEs (integral-differential equations) (Prat et al, Physica D, 202:177, 2005). In this talk, I will present a summary of these results.

Monday June 2, 1:00PM

Prof Eric Cytrynbaum

(Dept. of Mathematics, UBC)

Finding the center - how to solve simple geometry problems at the cellular scale

Abstract: Fragments of fish melanophore cells can form and center aggregates of pigment granules by dynein-motor-driven transport along a self-organized radial array of microtubules (MTs). This system has been extensively studied recently as a model for cytoskeleton-driven organization of the intracellular space. I will present a quantitative model that describes pigment aggregation and MT-aster self-organization and the subsequent centering of both structures. The model is based on the observations that MTs are immobile and treadmill, while dynein-motor-covered granules have the ability to nucleate MTs. From assumptions based on experimental observations, I'll derive partial integro-differential equations describing the coupled granule-MT interaction. Scaling arguments and perturbation theory allow for analysis in two limiting cases. This analysis explains the mechanism of aster self-organization as a positive feedback loop between motor aggregation at the MT minus ends and MT nucleation by motors. Furthermore, the centering mechanism is explained as a global geometric bias in the cell established by self-nucleated microtubules. Numerical simulations lend additional support to the analysis. The model sheds light on role of polymer dynamics and polymer-motor interactions in cytoskeletal organization.

Student Research Seminars on Thursday May 15, 2:00PM

Student Research Seminars on Thursday May 22, 2:00PM

Student Research Seminars on Tuesday May 27, 2:30PM

Student Research Seminars on Wednesday June 4, 2:00PM