Cellular-scale mechanism of cell crawling responding to substrate stiffness

TL;DR

This study develops a mechanochemical model to understand how cells regulate their migration speed and persistence in response to substrate stiffness, revealing an optimal stiffness for migration and the role of cell deformation and adhesion symmetry breaking.

Contribution

The paper introduces a new theory integrating biochemical reactions, deformation, and adhesion to explain cellular durotaxis and substrate stiffness response.

Findings

Cell migration speed and diffusion vary non-monotonically with substrate stiffness.

An optimal substrate stiffness exists for maximum cell migration.

Memory effects increase persistence time on softer substrates.

Abstract

Biological cells are able to adapt their behaviour in response to environmental cues. Durotaxis is a phenomenon in which cells adjust their migration depending on the mechanical properties of a surrounding substrate. Although durotaxis has been studied more than two decades, basic cellular-scale mechanism of how cells regulate the motility responding to substrate stiffness remains to be elucidated. We address this issue by developing a theory utilising a mechanochemical model that integrates intracellular biochemical reactions with cellular deformation and substrate adhesion. Numerical analysis reveals that the characteristic speed and diffusion constant of cells change non-monotonically with respect to substrate stiffness, indicating the emergence of an optimal stiffness for migration. In addition, by introducing a memory effect that allows feedback from cell mechanics to the intracellular chemical reactions, the persistence time increases with substrate stiffness on a substrate softer than the optimal. We further investigate theoretically the origin of the non-monotonic dependence, that is comparable to the experimental observations, in terms of cell deformation and symmetry breaking in substrate adhesion. We believe that our study provides a unifying framework to understand complex durotactic cell migration.