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We study a minimal model of a crawling eukaryotic cell with a chemicalpolarity controlled by a reaction-diffusion mechanism describing Rho GTPasedynamics. The size, shape, and speed of the cell emerge from the combination ofthe chemical polarity, which controls the locations where actin polymerizationoccurs, and the physical properties of the cell, including its membranetension. We find in our model both highly persistent trajectories, in which thecell crawls in a straight line, and turning trajectories, where the celltransitions from crawling in a line to crawling in a circle. We discuss thecontrolling variables for this turning instability, and argue that turningarises from a coupling between the reaction-diffusion mechanism and the shapeof the cell. This emphasizes the surprising features that can arise from simplelinks between cell mechanics and biochemistry. Our results suggest that similarinstabilities may be present in a broad class of biochemical descriptions ofcell polarity.

Crawling and turning in a minimal reaction-diffusion cell motility model: coupling cell shape and biochemistry