Numerical PDE Bifurcation Analysis of Cell Polarity Reaction Diffusion Models

This is a work in progress talk by a local grad student.

Here I will present some results on the dynamics of cell polarity models. I investigate two different models, one for the concentration of actin in the cytoskeleton of the cell and another for the concentration of nucleation promoting factors (NPF) and filamentous actin along the cell diameter. Both models consist of a three component reaction diffusion equation with mass conservation. I investigate the dynamics of these models using bifurcation analysis to study the emergence of spatial patterns and wave-like solutions. I will go through all the details for generating a bifurcation diagram for the actin cytoskeleton model, including analysis of the spatially homogeneous steady states, identifying some Hopf bifurcations that lead to travelling wave solutions, the numerical continuation of these solutions, and how I determined the stability of these solutions. Then I will outline some preliminary results for the second model, which includes identifying specific model behaviours and a preliminary bifurcation diagram.
I wish to thank Andreas Buttenschön and Arik Yochelis for the assistance with understanding and implementing the analytical and numerical methods used in this work.