Modeling the interplay of mechanosensitive adhesion and membrane tension for polarization and shape determination in crawling cells

The initiation of directional cell motion requires symmetry breaking that can happen both with or without external stimuli. During cell crawling, forces generated by the cytoskeleton and their transmission through mechanosensitive adhesions to the extracellular substrate play a crucial role. In a recently proposed 1D model (Sens, PNAS 2020), a mechanical feedback loop between force-sensitive adhesions and cell tension was shown to be sufficient to explain spontaneous symmetry breaking and multiple motility patterns through stick-slip dynamics, without the need to account for signaling networks or active polar gels. We extend this model to 2D to study the interplay between cell shape and mechanics during crawling. Through a local force balance along the deformable boundary, we show that the membrane tension coupled with shape change can regulate the spatiotemporal evolution of the stochastic binding of mechanosensitive adhesions. Based on this model, we perform a linear stability analysis and determine the unstable parameter regimes where spontaneous symmetry breaking can take place. Using non-linear simulations, we show that starting from a randomly perturbed circular shape, this instability can lead to keratocyte-like shapes that are robust for a wide range of parameters.