Cell crawling on a compliant substrate: A biphasic relation with linear friction

A living cell actively generates traction forces on its environment with its actin cytoskeleton. These forces deform the cell elastic substrate which, in turn, affects the traction forces exerted by the cell and can consequently modify the cell dynamics. By considering a cell constrained to move along a one-dimensional thin track, we take advantage of the problem geometry to explicitly derive the effective law that describes the non-local frictional contact between the cell and the deformable substrate. We then couple such a law with one of the simplest model of the active flow within the cell cytoskeleton. This offers a paradigm that does not invoke any local non-linear friction law to explain that the relation between the cell steady state velocity and the substrate elasticity is non linear as experimentally observed. Additionally, we present an experimental platform to test our theoretical predictions. While our efforts are still not conclusive in this respect as more cell types need to be investigated, our analysis of the coupling between the substrate displacement and the actin flow leads to friction coefficient estimates that are in-line with some previously reported results.

Automated summary

Living cells generate traction forces on their environment through the actin cytoskeleton, which deforms the elastic substrate and in turn affects the cell dynamics. In this study, we derive an effective law for the non-local frictional contact between the cell and the deformable substrate by considering a cell constrained to move along a one-dimensional thin track. By coupling this law with a model of active flow within the cell cytoskeleton, we provide a paradigm to explain the experimentally observed non-linear relationship between cell steady state velocity and substrate elasticity.