# Spatio-temporal perturbations as a mechanism of cell repolarization

Published in Submitted, 2021

Abstract: The intrinsic polarity of migrating cells is regulated by spatial distributions of protein activity. Those proteins (small GTPases, such as Rac and Rho) redistribute in response to stimuli, determining the cell front and back. Reaction-diffusion equations with mass conservation and positive feedback have been used to explain initial polarization of a cell. However, the sensitivity of a polar cell to a reversal stimulus has not yet been fully understood. We carry out full PDE bifurcation analysis of two polarity models to investigate routes to repolarization: (1) a single-GTPase (wave-pinning’’) model and (2) a mutually antagonistic Rac-Rho model. We find distinct routes to reversal in (1) vs (2). We show numerical simulations of full PDE solutions for the RD equations, demonstrating agreement of predictions with bifurcation results. Finally, simulations of the polarity models in deforming 1D model cells shows behaviour that is consistent with biological experiments.