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 a spontaneous symmetry breaking 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 a viscoelastic environment, we find periodic oscillations in cortex density and velocity polarization. At the boundary between viscous and viscoelastic environments, the cell may either cross into the viscoelastic medium, bounce back into the viscous medium, or become trapped at the boundary. The different scenarios defined different phase diagram that are confirmed by numerical simulations.