How cells feel their substrate: spontaneous symmetry breaking of active surface stresses

Adherent cells exert active forces and elastically deform their substrate. We consider a simple model geometry of a spread cell adhered to a thick substrate layer. We show how anisotropic cell shapes and active cell contractility induce cytoskeletal shear within the cell in a substrate-stiffness dependent manner. This cytoskeletal shear represents a possible mechanical guidance cue for cell force polarization, and could, for example, trigger initial nematic alignment of nascent stress fibers at early stages of cytoskeletal organization. Cell induced substrate strains propagate a depth into the substrate that is comparable to the linear dimension of the spread cell. As a consequence, cellular strains depend on the lateral dimensions of the spread cell. We employ Fourier techniques and a mean-field coupling approximation, which allows both for analytical progress and qualitative insight.