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Force localization in contracting cell layers

Epithelial cell layers on soft elastic substrates or pillar arrays are commonly used as model systems for investigating the role of force in tissue growth, maintenance and repair. Here we show analytically that the experimentally observed localization of traction forces to the periphery of the cell layers does not necessarily imply increased local cell activity, but follows naturally from the elastic problem of a finite-sized contractile layer coupled to an elastic foundation. For homogeneous contractility, the force localization is determined by one dimensionless parameter interpolating between linear and exponential force profiles for the extreme cases of very soft and very stiff substrates, respectively. If contractility is sufficiently increased at the periphery, outward directed displacements can occur at intermediate positions, although the edge itself still retracts. We also show that anisotropic extracellular stiffness leads to force localization in the stiffer direction, as observed experimentally.