Elasticity of adherent active cells on a compliant substrate*

We present a continuum mechanical model of rigidity sensing by livings cells adhering to a compliant substrate. The cell or cell colony is modeled as an elastic active gel, adapting recently developed continuum theories of active viscoelastic fluids. The coupling to the substrate enters as a boundary condition that relates the cell's deformation field to local stress gradients. In the presence of activity, the substrate induces spatially inhomogeneous contractile stresses and deformations, with a power law dependence of the total traction forces on cell or colony size. This is in agreement with recent experiments on keratinocyte colonies adhered to fibronectin coated surfaces. In the presence of acto-myosin activity, the substrate also enhances the cell polarization, breaking the cell's front-rear symmetry. Maximal polarization is observed when the substrate stiffness matches that of the cell, in agreement with experiments on stem cells.