Contact stiffness governs cell mechanosensing through molecular clutches.

In cell-extracellular matrix (ECM) interactions, cells apply traction forces to the local ECM through adhesions, in which the local ECM deformation depends on both local and non-local adhesions. Here, we established a nonlocal model based on a contact mechanics-derived parameter-contact stiffness (CS)-to quantify cell-ECM reciprocity. The CS defines the relationship between the local ECM deformation and the total force applied by a cell, integrating the effects of ECM elastic modulus, thickness, cell spreading area, etc. We found that both Yes-associated Protein (YAP) activity and the extent of differentiation in human mesenchymal stem cells scaled with CS in power law relation. To investigate the mechanism underlying the mechanosensing by cells, we proposed a CS-based motor clutch model; The excellent agreement between our model predictions and experimental results suggests that various physical or chemical stimuli affects the forces from the molecular clutches by altering the CS. The CS-based motor clutch model elucidates the contributions of time-dependent cell architecture evolution to stem cell differentiation and the influence of a non-adjacent ECM layer on cell behaviours. These results demonstrate that the CS provides a predictive perspective that allows researchers to address longstanding questions about the effects of cell-ECM interactions on cell behaviors.