Influence of substrate stiffness on cell–substrate interfacial adhesion and spreading: A mechano-chemical coupling model

Abstract Cell interactions with extracellular matrix, such as cell adhesion and spreading, are crucial for many biological functions and processes. Recent experimental progresses have demonstrated that substrate rigidities exert a remarkable influence on cell–substrate interfacial adhesion and spreading behaviors. The underlying biophysical mechanism, however, remains elusive. Based on the classical Bell-Dembo’s theory, this paper develops a mechano-chemical coupling model to physically describe cell adhesion and spreading mediated by substrate stiffness. By investigating the competitive nature between cell–substrate specific attraction and non-specific repulsion, the kinetic relation of receptor–ligand interplay is established, in which the influences of receptor–ligand separation, substrate elasticity and non-specific repulsion on cell adhesions are especially addressed. According to mechanical equilibrium conditions between cell membranes and underlying elastic substrates, an analytical expression is then deduced to relate the cell–substrate interfacial adhesion strength to the substrate rigidity. Moreover, by means of the conventional wetting theory, the dependence of steady-state cell spreading on substrate stiffness is also quantitatively studied. Comparisons with the existing experimental data show that the proposed model can be used to explore cell–substrate interactions regulated by substrate rigidities.