A quantitative understanding of how cells interact with their extracellular matrix via molecular bonds is fundamental for many important processes in cell biology and engineering. In these interactions, the deformability of cells and matrix are usually comparable with that of the bonds, making their rebinding events globally coupled with the deformation states of whole systems. Unfortunately, this important principle is not realized or adopted in most conventional theoretical models for analyzing cellular adhesions. In this study, we considered a new theoretical model of a cluster of ligand-receptor bonds between two soft elastic bodies, in which the rebinding rates of ligands to receptors are described, by considering the deformation of the overall system under the influence of bond distributions. On the basis of theory of continuum and statistical mechanics, we obtained an elasticity-associated rebinding rate of open bonds in a closed analytical form that highly depends on the binding states and distributions of all other bonds as well as on the overall deformation energy stored in the elastic bodies and all closed bonds. On the basis of this elasticity-associated rebinding rate and by performing Monte Carlo simulations, we uncovered new mechanisms underlying the adhesion stability of molecular-bond clusters associated with deformable elastic bodies. Moreover, we revealed that the rebinding processes of molecular bonds is not only dependent on interfacial separation but is related to overall energy. This newly proposed rebinding rate may substantially improve our understanding of how cells adapt to their microenvironments by adjusting their mechanical properties through cytoskeleton remodeling.
