Cell morphology and migration linked to substrate rigidity.

Abstract

A mathematical model, based on thermodynamics, was developed to demonstrate how substrate rigidity influences cell morphology and migration. The mechanisms by which substrate rigidity are translated into cell-morphological changes and cell movement are described. The model takes into account the competition between the elastic energies in the cell-substrate system and work of adhesion at the cell periphery. The cell morphology and migration are dictated by the minimum of the total free energy of the cell-substrate system. By using this model, reported experimental observations on cell morphological changes and migration can be better understood with a theoretical basis. In addition, these observations can be more accurately correlated with the variation of substrate rigidity. This study indicates that the activity of the adherent cell is dependent not only on the substrate rigidity but also is correlated with the relative rigidity between the cell and substrate. Moreover, the study suggests that the cell stiffness can be estimated based on the substrate stiffness corresponding to the change of trend in morphological stability.