Morphology of Cell-substratum Adhesion. Influence of Receptor Heterogeneity and Nonspecific Forces

Many cell types modulate growth, differentiation, and motility through changes in cell substrate adhesion, including regulation of focal contact formation. Clustering of cell surface adhesion receptors is an essential early step in the development of focal contacts, and thus may influence cell physiology. In this paper, we present a theoretical framework to examine how cell surface chemistry affects receptor clustering. Our one-dimensional tape-peeling model couples the equations of mechanical equilibrium for a cell membrane with kinetic receptor-ligand binding relations. We considered two distinct model scenarios: Adhesion mediated by multiple receptor-ligand interactions of different length and specific binding of a single receptor type occurs in the presence of van der Waals attraction and nonspecific repulsion. In each case, nonuniform (wave-like) membrane morphologies are observed in certain parameter ranges that support the clustering of adhesion receptors. The formation of these morphologies is described in terms of a balance of membrane stresses; when cell-surface potential as a function of separation distance is symmetric between two potential energy minima, nonuniform morphologies are obtained. Increases in the chemical binding energy between receptor and ligand (e.g., increases in ligand density) or decreases in the membrane rigidity result in smaller wavelengths for nonuniform interfaces. Additionally, we show wave-like geometries appear only when the mechanical compliance of receptor-ligand bonds is within an intermediate range, and examine how the mobility of "repellers"--glycocalyx molecules that exert a nonspecific repulsive force--influences membrane morphology. We find fully mobile repellers always redistribute to prevent nonuniform morphologies.