Elastic properties of force-transmitting linkages determine multistable mechanosensitive behaviour of cell adhesion

Cells can sense and respond to their environment. Central to this process is the formation of molecular clutches, which are dynamic linkages between the extracellular matrix and the actin cytoskeleton mediated by integrins and adaptor proteins. Although it is well known that force-dependent interactions between molecular-clutch components are essential for sensing substrate rigidity, the influence of nonlinear adaptor-protein elasticity is poorly understood. Here we show that adaptor-protein elasticity and local interactions between molecular clutches and the extracellular matrix are key to cellular perception of substrate stiffness. We present a semi-analytical theory that integrates experimentally measured force responses of adaptor proteins to describe cell-adhesion sensing. We propose that molecular clutches probe local mechanical substrate properties and collectively function as a differential that allows a retrograde actin flow and substrate movement to occur at different rates while maintaining a stable mechanical coupling between them. Our model reproduces experimentally measured force-loading rates of individual molecular clutches and correctly predicts cell-adhesion behaviour for a range of substrate stiffnesses. The framework presented can be extended to study complex phenomena such as focal-adhesion maturation and cell-type-specific mechanosensing.