Stochastic dynamics of substrate non-uniform stiffness affecting molecular adhesion in cell-substrate interface subjected to tensile loading

The mechanically heterogeneous extracellular matrix (ECM) or tissues widely exist in biological systems and are capable of significantly regulating directional cell migration. However, prior to whole cell movement, how the cell senses these cues from mechanical heterogeneities of the ECM or substrate remains unclear at the molecular bond level. To address this issue, we theoretically investigate interface adhesion between a non-uniform stiffness substrate and a rigid plate via a series of receptor-ligand bonds subjected to a tensile loading by integrating substrate surface deformation described by continuum mechanics approach into the stochastic events of bond dissociation and association govern by Markov processes. Interestingly, it is found that, during stretching adhesion interface, due to the large collective contact forces near the stiff edge of the adhesion area, the crack first develops at this stiff edge and then grows to another relatively soft adhesion edge until the completed detachment achieved, which is distinct from the cracks growing from both two edges to center of adhesion area in the case of uniformly elastic solid-solid or solid-fluid interface. Moreover, the lifetime of the bond cluster, interface adhesion strength, and the effect of inter-bond distance are examined, respectively. The corresponding mechanism of dependence of the lifetime and adhesion strength on the non-uniform stiffness of the substrate and inter-bond distance is also analyzed. These findings provide a detailed mechanistic understanding of the adhesion interface responding to the mechanical heterogeneities of the substrate at the molecular bond level.