Cells generate mechanical stresses via the action of myosin motors on the actin cytoskeleton. Although the molecular origin of force generation is well understood, we currently lack an understanding of the regulation of force transmission at cellular length scales. Here, using 3T3 fibroblasts, we experimentally decouple the effects of substrate stiffness, focal adhesion density, and cell morphology to show that the total amount of work a cell does against the substrate to which it is adhered is regulated by the cell spread area alone. Surprisingly, the number of focal adhesions and the substrate stiffness have little effect on regulating the work done on the substrate by the cell. For a given spread area, the local curvature along the cell edge regulates the distribution and magnitude of traction stresses to maintain a constant strain energy. A physical model of the adherent cell as a contractile gel under a uniform boundary tension and mechanically coupled to an elastic substrate quantitatively captures the spatial distribution and magnitude of traction stresses. With a single choice of parameters, this model accurately predicts the cell's mechanical output over a wide range of cell geometries.

Cell-cell and cell-matrix adhesions play essential roles in the function of tissues. There is growing evidence for the importance of cross talk between these two adhesion types, yet little is known about the impact of these interactions on the mechanical coupling of cells to the extracellular matrix (ECM). Here, we combine experiment and theory to reveal how intercellular adhesions modulate forces transmitted to the ECM. In the absence of cadherin-based adhesions, primary mouse keratinocytes within a colony appear to act independently, with significant traction forces extending throughout the colony. In contrast, with strong cadherin-based adhesions, keratinocytes in a cohesive colony localize traction forces to the colony periphery. Through genetic or antibody-mediated loss of cadherin expression or function, we show that cadherin-based adhesions are essential for this mechanical cooperativity. A minimal physical model in which cell-cell adhesions modulate the physical cohesion between contractile cells is sufficient to recreate the spatial rearrangement of traction forces observed experimentally with varying strength of cadherin-based adhesions. This work defines the importance of cadherin-based cell-cell adhesions in coordinating mechanical activity of epithelial cells and has implications for the mechanical regulation of epithelial tissues during development, homeostasis, and disease. mechanotransduction | traction force microscopy M echanical interactions of individual cells have a crucial role in the spatial organization of tissues (1, 2) and in embryonic development (3-5). The mechanical cooperation of cells is evident in dynamic processes such as flow-induced alignment of vascular endothelial cells (6) and muscle contraction (7). However, mechanical interactions of cells within a tissue also affect the tissue's static mechanical properties including elastic modulus (8), surface tension (9), and fracture toughness (10). Little is known about how these tissue-scale mechanical phenomena emerge from interactions at the molecular and cellular levels (11).Tissue-scale mechanical phenomena are particularly important in developmental morphogenesis (12), homeostasis (13), and wound healing (14) in epithelial tissues. Cells exert mechanical force on each other at sites of intercellular adhesion, typically through cadherins (15, 16), as well as on the underlying extracellular matrix (ECM) through integrins (17-19). Cadherin-based adhesions can alter physical aspects of cells such as the surface tension of cellular aggregates (20) and the spreading (21) and migration (22) of single cells adherent to cadherin-patterned substrates. Integrity of intercellular adhesions may also contribute to metastatic potential (23). We and others have shown that epithelial cell clusters with strong cell-cell adhesions exhibit coordinated mechanical behavior over length scales much larger than a single cell (24-27). Several studies have implicated cross talk between cell-ECM and cell-cell adhesions (28, 29) that can be modulated by ac...

Coordinated motion of cell monolayers during epithelial wound healing and tissue morphogenesis involves mechanical stress generation. Here we propose a model for the dynamics of epithelial expansion that couples mechanical deformations in the tissue to contractile activity and polarization in the cells. A new ingredient of our model is a feedback between local strain, polarization and contractility that naturally yields a mechanism for viscoelasticity and effective inertia in the cell monolayer. Using a combination of analytical and numerical techniques, we demonstrate that our model quantitatively reproduces many experimental findings [Nat. Phys. 8, 628 (2012)], including the build-up of intercellular stresses, and the existence of traveling mechanical waves guiding the oscillatory monolayer expansion.