Substrate stretching and reorganization of stress fibers as a finite elasticity problem

It is well known that substrate stretching reorganizes the actin cytoskeleton of an adherent cell. Experiments have proved that the stress fibers are reoriented into one or two distinct directions. It is further pointed out that reorientation of the stress fibers phenomena are observed with quite high strains, where linear elasticity theory is not valid. Therefore, the existing linear theories for mechanics interpretation of those phenomena are not satisfactory. The experimental evidence of the existence of two distinct directions of the reorientation indicates a co-existence of phases non-linear elastic phenomenon. Further that observation is quite strong evidence that the strain energy density function should be non-convex. The reorganization of the stress fibers under uniaxial substrate stretching is studied as a non-linear elastic stability problem. Adapting the global (Maxwell’s) criterion for stability, various phenomena, concerning the reorientation of the stress fibers, are interpreted into the context of finite elasticity. The experiments demonstrate co-existence of phases phenomena that are justified in the present study. The influence of various factors like contractility and extracellular stretching is demonstrated. Furthermore, the non-convexity factor is attributed to the influence of the small GTPase Rho regulating the formation of the actin stress fibers. The predominant final stress fibers placement that is transverse to the extracellular stress direction and appears in long time after the co-existence of phases placement is also justified.