Why do receptor-ligand bonds in cell adhesion cluster into discrete focal-adhesion sites?

Cell adhesion often exhibits the clustering of the receptor-ligand bonds into discrete focal-adhesion sites near the contact edge, thus resembling a rosette shape or a contracting membrane anchored by a small number of peripheral forces. The ligands on the extracellular matrix are immobile, and the receptors in the cell plasma membrane consist of two types: high-affinity integrins (that bond to the substrate ligands and are immobile) and low-affinity integrins (that are mobile and not bonded to the ligands). Thus the adhesion energy density is proportional to the high-affinity integrin density. This paper provides a mechanistic explanation for the clustering/assembling of the receptor-ligand bonds from two main points: (1) the cellular contractile force leads to the density evolution of these two types of integrins, and results into a large high-affinity integrin density near the contact edge and (2) the front of a propagating crack into a decreasing toughness field will be unstable and wavy. From this fracture mechanics perspective, the chemomechanical equilibrium is reached when a small number of patches with large receptor-ligand bond density are anticipated to form at the cell periphery, as opposed to a uniform distribution of bonds on the entire interface. Cohesive fracture simulations show that the de-adhesion force can be significantly enhanced by this nonuniform bond density field, but the de-adhesion force anisotropy due to the substrate elastic anisotropy is significantly reduced.