Contractility-Driven Cell Motility against a Viscoelastic Resistance

We study a model of contraction-based cell motility inside a microchannel to investigate the regulation of cell polarization and motion by the mechanical resistance of the environment. A positive feedback between the asymmetry of the acto-myosin cortex density and cell motion gives rise to spontaneous symmetry breaking and motility beyond a threshold contractility that depends on the resistance of extracellular medium. In highly viscous environments, we predict bistability under moderate contractility, so that symmetry breaking needs to be activated. In viscoelastic environments, we find the possibility for periodic oscillations in cortex density polarization and velocity. At the boundary between viscous and viscoelastic environments, the cell may cross, bounce back, or become trapped, depending on the viscoelastic relaxation time. These results are summarized in phase diagrams obtained by combining linear stability analysis and numerical simulations.