We study a minimal model of a crawling eukaryotic cell with a chemical polarity controlled by a reaction-diffusion mechanism describing Rho GTPase dynamics. The size, shape, and speed of the cell emerge from the combination of the chemical polarity, which controls the locations where actin polymerization occurs, and the physical properties of the cell, including its membrane tension. We find in our model both highly persistent trajectories, in which the cell crawls in a straight line, and turning trajectories, where the cell transitions from crawling in a line to crawling in a circle. We discuss the controlling variables for this turning instability, and argue that turning arises from a coupling between the reaction-diffusion mechanism and the shape of the cell. This emphasizes the surprising features that can arise from simple links between cell mechanics and biochemistry. Our results suggest that similar instabilities may be present in a broad class of biochemical descriptions of cell polarity.
Mathematical and Computational Modeling of Amoeboid Cell Crawling
Universitat Politècnica de Catalunya—BarcelonaTech（加泰罗尼亚理工大学）；Institute for Research and Innovation in Health (IRIS), Universitat Politècnica de Catalunya—BarcelonaTech（加泰罗尼亚理工大学健康研究与创新研究所）；Universität Potsdam（波茨坦大学）；Kanazawa University（金泽大学）
