Stress fiber response to mechanics: a free energy dependent statistical model

An experimental observation has been puzzling scientists for years: cells tend to align perpendicular to cyclic uniaxial strain, but parallel to external static strain. Recent experimental results demonstrate that both the magnitude of the external strain and the cell contractility manipulate the cells' orientation under cyclic uniaxial strain. In light of these reports, we introduce a minimum free energy model to explain the different orientation tendencies of cells subjected to external strain, and elucidate the significant role of cell contractility in this issue. With the present model, we successfully explain a series of well-documented phenomena: (1) cells orient nearly parallel to static uniaxial strain; (2) cell alignment depends on the magnitude of the cyclic uniaxial strain; (3) under cyclic uniaxial stretch, a tensioned contractility results in a strengthened perpendicular alignment of the cells, whereas a contractility relaxation results in a nearly parallel alignment. In addition, this model also successfully describes the functional relationship between cell contractility and substrate stiffness.