Analysis of dynamic and stationary pattern formation in the cell cortex

We study a sol-gel mechanochemical model for cellular cytoplasm. Using conservation equations and a force balance equation, we derive equations for the sol-gel dynamics. Regular perturbation analysis suggests the growth of patterns which may be either dynamic or stationary, depending on parameter values. Nonlinear analysis, which indicates that these patterns remain bounded, is confirmed by numerically solving the mechanochemical equations. We use these analytical and numerical results to model two different biological problems: the dynamic formation of filopodia in nerve growth cones, and the growth of microvilli in epithelial cells.