Force-driven aggregation of specific bonds on compliant substrates

A thermodynamic model was employed to understand the underlying physics of the force-dependent size of cell's focal adhesions. The model describes the specific adhesion of an elastic membrane to a compliant substrate such that the adhesion site is subjected to the force of a constant pulling traction. The membrane contains mobile adhesion receptors with specific energetic affinities for complimentary ligands on the substrate. The adhesion is resisted by a disjoining pressure induced by a squeezed layer of glycocalyx. The model demonstrates that the enlargement of adhesion area with increasing pulling traction is possible due to a spontaneous response of the adhesion site to attain the state of minimum free energy. The correlation between the force and the adhesion area strongly depends on the rigidity of the substrate.