Supplementary data1-The source data behind the graphs in the Contact Stiffness Governs Cell Mechanosensing through Molecular Clutche.zip

In cell-extracellular matrix (ECM) interactions, cells apply dynamic traction forces to the local ECM through adhesions, in which the local deformation depends on both local and non-local adhesions. Here, we established a nonlocal model based on a contact mechanics-derived integrative parameter—contact stiffness (CS)—to quantify cell-ECM mechanical 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, ECM 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 concept of CS provides a predictive perspective that allows researchers to address longstanding questions about the effects of cell-ECM interactions on cell behaviors.When cells interact with the extracellular matrix (ECM), they are able to apply physical forces to remodel the surrounding microenvironments, while they can also actively modify their behaviors in respond to the alteration in ECM mechanics. Emerging evidence shows that mechanical variables in the cell-ECM system, including ECM elastic modulus, ECM thickness, and cell spreading area, have profound effects on cell behaviors (e.g., motility, proliferation, apoptosis, and differentiation) that are required for processes such as embryonic development, tissue regeneration, and tumor metastasis. For example, mesoderm stiffening is essential to triggering neural crest cell migration in Xenopus laevis, and stiff matrix promotes tumor metastasis by driving the epithelial-mesenchymal transition of breast tumor cells.Cells sense and response to mechanical stimuli arising from ECMs through cycles of mechanosensing, mechanotransduction, and mechanoresponse. The mechanisms underlying cell mechanosensing have been well-explained with motor clutch framework, suggesting that cells perceive alterations in ECM mechanics through the molecular clutches; the kinetics of molecular clutches is governed by an intricate balance between intracellular forces, generated by stress fibers on focal adhesion (FA) plaques, and extracellular traction in the ECM 22-24. Importantly, previous models mainly discussed the cell mechanosensing of elastic modulus of ECM, which assumed that the local reaction force of the ECM on the cell depends on the local ECM deformation state and ECM modulus. However, contact mechanics theory has established that local ECM deformation depends on both local forces (exerted by local FAs) and non-local forces (imposed by the cell through non-local FAs); i.e., variations in local ECM deformation are induced by changes in the total force, rather than the local force, imposed by the cell on the ECM. During cell-ECM interactions, the deformation-force relationship depends simultaneously on several ECM-associated variables (including ECM modulus and thickness) and variables related to cell-ECM contact geometry (including cell spreading area and shape). Previous studies focusing on these variables individually have advanced our understanding of how ECM mechanosensing and associated cellular processes regulate diverse physiological and pathological processes. However, contact mechanics theory indicates that the effects of these variables are not mutually independent, but rather are coupled in the mechanosensing process.The underlying mechanisms by which these different variables synergistically regulate cell behaviors remain unknown. To address this issue, we here investigated the contact stiffness (CS), which describes the relationship between local ECM deformation and the cell contractility, in the context of the mechanical effects of the ECM on cell behaviors. Based on contact mechanics theory, CS integrates the effects of different individual parameters (including ECM elastic modulus, ECM thickness, cell spreading area, and cell shape) into one variable that impacts cell-ECM interactions. We assessed ECM mechanosensing in human mesenchymal stem cells (hMSCs) with varying CS values by controlling ECM elastic modulus, ECM thickness, or cell spreading area. The results demonstrated that CS outperformed other individual mechanical variables (i.e., ECM elastic modulus, ECM thickness, and cell spreading area) in characterizing mechanoregulation of YAP activation and stem cell differentiation in both confined and unconfined cell spreading area conditions. Using the concept of CS, we develop a cross-scale model based on the classical motor clutch model, which reveals the contributions of cell architecture to stem cell differentiation and predicts cellular mechanosensing of a non-adjacent ECM layer. Our findings demonstrate that CS can provide a unified frame for understanding the mechanosensing processes by which cells respond to various mechanical stimuli from ECMs.