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

TL;DR

This paper develops a theoretical model describing how cell traction forces and substrate deformation interact, revealing a biphasic relation between cell velocity and substrate elasticity, supported by preliminary experimental validation.

Contribution

It introduces an explicit non-local friction law coupled with a simple actin flow model to explain nonlinear cell motility behavior on deformable substrates.

Findings

The model predicts a biphasic relation between cell velocity and substrate elasticity.

Experimental estimates of friction coefficients align with previous reports.

Preliminary tests support the theoretical predictions.

Abstract

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.