A mathematical model of cell reorientation in response to substrate stretching

It is well documented that in response to substrate stretching adhering cells alter their orientation. Generally, the cells reorient away from the direction of the maximum substrate strain, depending upon the magnitude of the substrate strain and the state of cell contractility. Theoretical models from the literature can describe only some aspects of this phenomenon. In the present study, we developed a more comprehensive mathematical model of cell reorientation than the current models. Using the framework of theory of non-linear elasticity, we found that the problem of cell reorientation was a stability problem, with the global (Maxwell's) criterion for stability. For the case of uniaxial substrate stretching, we showed that cells would orient away from the direction of substrate strain such that the angle between the cell long axis and the direction of the substrate strain would increase with increasing magnitude of the strain. We also showed that at a given substrate strain this angle would be greater in cells having greater contractile strain. These results are consistent with experimental observations reported in the literature.