Mass-Conservation Increases Robustness in Stochastic Reaction-Diffusion Models of Cell Crawling

Abstract

The process of polarization determines the head and tail of single cells. A mechanism of this kind frequently precedes the subsequent cell locomotion and it determines the direction of motion. The process of polarization has frequently been described as a reaction-diffusion mechanism combined with a source of stochastic perturbations. We selected a particular model of amoeboid cell crawling for the motion of Dictyostelium discoideum and studied the interplay between pattern formation and locomotion. Next, we integrated the model in a two-dimensional domain considering the shape deformations of the cells in order to characterize the dynamics. We observed that the condition of pattern formation is finely tuned and we propose a modification based on the use of a mass-conservation constraint to substantially increase the robustness of the mathematical model.