Switching between optimum substrate rigidity and focal adhesion reinforcement at the cell leading edge

It’s well known that substrate mechanical properties strongly influence cell behaviour and fate. There exists two well documented but contrasting responses of cells to substrate rigidity, namely the biphasic and the monotonic relationship of traction force and retrograde flow velocity with substrate stiffness. We have developed a theoretical model for the dynamics at the leading edge of a cell placed on a viscoelastic substrate, involving a pair of coupled reaction-diffusion equations. Motivated by experiments, the association and dissociation rates of focal adhesions are taken to be force dependent. Our model not only captures the experimentally observed stick-slip dynamics at the cell edge, but also can predict switching between both the biphasic relationship i.e. the presence of an optimum substrate stiffness where the retrograde flow is minimum and traction force is maximum; and the monotonic relationship between retrograde flow, traction force and substrate stiffness. Besides, our theory also elucidates the role played by substrate viscosity, predicts the presence of optimum viscosity as well as states the condition under which cellular rigidity sensing is lost.

Stick-slip dynamics of migrating cells on viscoelastic substrates
P. S. De and R. De
Phys. Rev. E 100, 012409 (2019)