A modelling approach to cytoskeleton dynamics

The crawling movement of several types of cells is based on the dynamics of a part of the cytoskeleton, the lamellipodial network of actin polymers. It involves polymerization and depolymerization, branching, crosslinking, the creation and removal of adhesion sites, interaction with myosin motors, the reaction to stresses produced by deformation and by the cell membrane, the transport of monomers, and probably a few other mechanisms. Our aim is to create a framework for the mathematical modelling and simulation of these effects in order to quantify their contribution to cell movement.

A first step in this program will be presented, where a two-dimensional actin network is modelled as a grid of two families of locally parallel filaments (microscopic model), and a continuum (macroscopic) model is derived by a homogenization limit. First numerical simulations of a dynamically stable rotationally symmetric rest state of a lamellipodial fragment (which can be created in the laboratory) will also be shown.