Mechanical Stability Determines Stress Fiber and Focal Adhesion Orientation

It is well documented in a variety of adherent cell types that in response to anisotropic signals from the microenvironment cells alter their cytoskeletal organization. Previous theoretical studies of these phenomena were focused primarily on the elasticity of cytoskeletal actin stress fibers (SFs) and of the substrate while the contribution of focal adhesions (FAs) through which the cytoskeleton is linked to the external environment has not been considered. Here we propose a mathematical model comprised of a single linearly elastic SF and two identical linearly elastic FAs of a finite size at the endpoints of the SF to investigate cytoskeletal realignment in response to uniaxial stretching of the substrate. The model also includes the contribution of the chemical potential energies of the SF and the FAs to the total potential energy of the SF-FA assembly. Using the global (Maxwell's) stability criterion, we predict stable configurations of the SF-FA assembly in response to substrate stretching. Model predictions obtained for physiologically feasible values of model parameters are consistent with experimental data from the literature. The model shows that elasticity of SFs alone can not predict their realignment during substrate stretching and that geometrical and elastic properties of SFs and FAs need to be included.