Stochastic resetting and the mean-field dynamics of focal adhesions

In this paper we investigate the effects of diffusion on the dynamics of a single focal adhesion at the leading edge of a crawling cell by considering a simplified model of sliding friction. Using a mean-field approximation, we derive an effective single-particle system that can be interpreted as an overdamped Brownian particle with spatially dependent stochastic resetting. We then use renewal and path-integral methods from the theory of stochastic resetting to calculate the mean sliding velocity under the combined action of diffusion, active forces, viscous drag, and elastic forces generated by the adhesive bonds. Our analysis suggests that the inclusion of diffusion can sharpen the response to changes in the effective stiffness of the adhesion bonds. This is consistent with the hypothesis that force fluctuations could play a role in mechanosensing of the local microenvironment.