Theory of rigidity sensing of biological cells

Recent research at the interface of physics and biology has shown that cellular processes such as proliferation, differentiation and tissue development, are controlled by the mechanical properties of cells and their environment. This talk reviews current experiments on cell mechanics in the context of theoretical models in which cells are treated in terms of active force dipoles. The theory includes non-equilibrium cell activity (related to the fact that the cell is "alive"), local mechanical equilibrium, and random forces to determine cell response to the rigidity of the substrate. To do so, we have generalized the treatment of elastic inclusions in solids to "living" inclusions whose active polarizability, analogous to that of non-living matter, results in feedback in response to matrix stresses. We use this to explain recent observations of the non-monotonic dependence of stem cell cytoskeletal polarization on matrix rigidity. Similar considerations are used to study the nematic or smectic ordering of elastic dipoles and are applied to the dependence of muscle striation on substrate properties. These findings provide a mechanical correlate for experiments that demonstrated the existence of an optimal substrate elasticity for stem cell differentiation.