Integrating Actin and Myosin II in a Viscous Model for Cell Migration

Abstract

This article presents a mathematical and computational model for cell migration that couples a system of reaction-advection-diffusion equations describing the bio-molecular interactions between F-actin and myosin II to a force balance equation describing the structural mechanics of the actin-myosin network. In eukaryotic cells, cell migration is largely powered by a system of actin and myosin dynamics. We formulate the model equations on a two-dimensional cellular migrating evolving domain to take into account the convective and dilution terms for the biochemical reaction-diffusion equations, with hypothetically proposed reaction-kinetics. We employ the evolving finite element method to compute approximate numerical solutions of the coupled biomechanical model in two dimensions. Numerical experiments exhibit cell polarization through symmetry breaking which are driven by the F-actin and myosin II. This conceptual hypothetical proof-of-concept framework set premises for studying experimentally-driven actin-myosin reaction-kinetic network interactions with generalizations to multi-dimensions.