A Computational Model for Eukaryotic Cell Migration and Chemotaxis

A computational framework is presented for the simulation of eukaryotic  cell migration and chemotaxis. A pattern formation model, based on a system of nonlinear reaction-diffusion equations, is approximated in the  evolving cell membrane using an arbitrary Lagrangian Eulerian surface finite  element method (ALE-SFEM). The solution state is used to drive a  mechanical model of the protrusive and retractive forces of the cell  boundary. Movement of the cell is achieved using a parameterised finite  element method. Building on an earlier model of ours, we extend our computational  technique to include the coupling with two-dimensional intra and extra-cellular effects such as surface receptor ligand binding kinetics and cell adhesion. We will discuss the efficient grid generation for two-dimensional evolving domains and the solution of reaction-diffusion equations on the evolving cell membrane coupled to processes in the bulk. The capability of the numerical framework will be demonstrated in a range of biological simulations including chemotaxis.