## Tim Elston : Models and methods for studying cell movement

- CGTP Group Meeting Seminar ( 253 Views )Most cells possess the ability to change morphology or migrate in response

to environmental cues. To understand the molecular mechanisms that drive

cell movement requires a systems-level approach that combines computational

approaches, including mathematical modeling and image analysis tools, with

high-resolution microscopy of living cells. Here we present several

examples for how such an integrated research strategy has been

successfully applied. First, we combine stochastic modeling with novel

biosensors for monitoring the spatiotemporal dynamics of Rho GTPase

activity to investigate the role of RhoG in cell polarization and

migration. Next, mathematical modeling and quantitative image analysis

methods are used to establish the role of cerebral cavernous malformation

(CCM) proteins in vascular tube formation. Finally, we present a novel

computational method for tracking and quantifying changes in cell shape.

## Linda Petzold : CANCELED: The Emerging Roles and Computational Challenges of Stochasticity in Biological Systems

- CGTP Group Meeting Seminar ( 241 Views )******* CANCELED ****************** In recent years it has become increasingly clear that stochasticity plays an important role in many biological processes. Examples include bistable genetic switches, noise enhanced robustness of oscillations, and fluctuation enhanced sensitivity or Â?stochastic focusing".. Numerous cellular systems rely on spatial stochastic noise for robust performance. We examine the need for stochastic models, report on the state of the art of algorithms and software for modeling and simulation of stochastic biochemical systems, and identify some computational challenges.

## Marty Golubitsky : Animal Gaits and Symmetries of Periodic Solutions

- CGTP Group Meeting Seminar ( 208 Views )The interface between the mathematical sciences and the biosciences is two-way and may be summarized as "math -> bio" and "bio -> math." This talk will have two parts. First, I will describe previous work on gaits of four-legged animals (based on distinguishing gaits, such as walk, trot, and pace, by their spatio-temporal symmetries). Second, I will discuss how the application to gaits has led to results about phase-shift synchrony in periodic solutions of coupled systems of differential equations.

## Carla Staver : Positive Feedbacks and the Global Distribution of Biomes

- CGTP Group Meeting Seminar ( 195 Views )A mechanistic understanding of biome distributions is a critical issue in

modern ecology, especially in the context of predictive models of past and

future climate change. While we can explain the current distribution of

many biomes accurately, our predictions are less successful in dynamic

systems where vegetation-environment feedbacks are significant. The

challenge is to integrate feedbacks more fundamentally into a coherent

theory of ecological process that determines biome distributions

currently, and that will shape them into the future. This is among the

most urgent questions to be addressed in ecology today. Savannas and

grasslands cover ~40% of the land surface and forests cover another ~30%.

Understanding the dynamics among these biomes will help explain biosphere

dynamics, past, present and into the future. I will combine empirical and

theoretical work for insights into the mechanisms that give rise to the

emergent stability of savanna, despite variability in vegetation structure

within the biome.

## Rick Durrett : Spatial evolutionary games with small selection coefficients

- CGTP Group Meeting Seminar ( 194 Views )We use results of Cox, Durrett, and Perkins for voter model perturbations to study spatial evolutionary games on $\ZZ^d$, $d\ge 3$ when the interaction kernel is finite range, symmetric, and has covariance matrix $\sigma^2I$. The games we consider have matrices of the form ${\bf 1} + wG$ where ${\bf 1}$ is matrix of 1's and $w$ is small and positive. We prove that the effect of space is equivalent to (i) changing the entries of the game matrix and (ii) replacing the replicator ODE by a related PDE. The first idea is due to Ohtsuki and Nowak (for the pair approximation) while the second is well known in the theory of stochastic spatial processes. A remarkable aspect of our result is that the limiting PDE depends on the interaction kernel only through the values of two simple noncoalescence probabilities. Due to results of Aronson and Weinberger, and Fife and McLeod, we can analyze any 2x2 game. However, when there are three strategies the limiting object is a system of reaction diffusion equations, so we only have results for special cases.

## Marc Ryser : HPV and cervical cancer: a stochastic model at tissue level

- CGTP Group Meeting Seminar ( 191 Views )Infection with the Human Papilloma Virus (HPV) is a prerequisite for the development of cervical cancer, the second most common cancer in women in the developing world. While about 80% of women get infected with HPV during their lifetime, most clear the virus within 2 years. However, if the infection persists, further cellular events can lead to high-grade lesions and eventually invasive carcinoma. To date, various aspects of the carcinogenesis remain poorly understood at the cellular level. In this talk, we develop and discuss a stochastic model of the cervical epithelium, coupling the dynamics of HPV infection to a multi-stage model of carcinogenesis.

## Kingshuk Roy Choudury : Statistical modelling and comparison of tumor growth

- CGTP Group Meeting Seminar ( 187 Views )"I will talk about tumor growth modelling in xenograft experiments. It's a statistical approach (see e.g. the ref. below), but I'd like to incorporate more mathematical modelling." Roy Choudhury, K., Kasman, I., Plowman, G., 2010, Analysis of multi-arm tumor growth trials in xenograft animals using phase change adaptive piecewise quadratic models, Statistics in Medicine, 29, 2399-2409