A Stochastic Description on Adhesion of Molecular Bond Clusters Between Rigid Media with Curved Interfaces

Abstract

Cellular adhesion is mediated by the formation and rupture of specific molecular bonds between ligands and receptors. As an idealized model, based on the Markov process assumption, we present a detailed theoretical analysis of the stochastic dynamics of a cluster of parallel bonds between two rigid bodies with curved interfaces under displacement- and force-controlled loadings, respectively. Regarding the equilibrium cluster size, strength, bond distribution and life time, exact solutions from the corresponding one-step master equations are obtained for the special cases of clusters with fixed separations or clusters with flat interfaces, while the general cases of those with curved interfaces are dealt with numerical techniques. Especially, Monte Carlo simulations are performed to verify the proposed analytical results and to demonstrate interesting differences between stochastic adhesion behaviors of the clusters under loading protocols of fixed separations and fixed forces, respectively.