Mechanics of Molecular Bond Clusters between Elastic Media: Stochastic-Elastic Coupling in Cell-Matrix Adhesion

Abstract

Focal adhesions are clusters of specific receptor-ligand bonds that link an animal cell to an extracellular matrix. A capability to control focal adhesions, for which a quantitative description of the collective behavior of multiple molecular bonds is a critical step, is essential for tissue and cellular engineering. While the behavior of single molecular bonds is governed by statistical mechanics at small scale, continuum mechanics should be valid at large scale. How can this transition be modeled and can this tell us something about the mechanics of cell adhesion? Here we develop a stochastic-elasticity model of a periodic array of adhesion clusters between two dissimilar elastic media subjected to an inclined tensile stress, in which stochastic descriptions of molecular bonds and elastic descriptions of interfacial traction are unified in a single modeling framework. A fundamental scaling law of interfacial traction distribution is established to govern the transition between uniform and cracklike singular distributions of the interfacial traction within molecular bonds. Guided by this scaling law, we perform Monte Carlo simulations to investigate the effects of cluster size, cell/matrix modulus and loading direction on lifetime and strength of the adhesion clusters. The results show that intermediate adhesion size, stiff substrate, cytoskeleton stiffening, and low-angle pulling are factors that contribute to the stability of focal adhesions. The predictions of our model provide feasible explanations for a wide range of experimental observations and suggest possible mechanisms by which cells can modulate adhesion and deadhesion via cytoskeletal contractile machinery.