Modeling the Adhesive Contact between Cells and a Wavy Extracellular Matrix Mediated by Receptor-Ligand Interactions

In this study, we examine the outstanding issue of how surface topology affects the adhesion between cells and the extracellular matrix (ECM). Specifically, we showed that the adhesive contact can be well described by treating the attraction as continuous along the interface if the wavelength of surface undulations is larger than a few microns. On the other hand, the discrete nature of cell-ECM interactions, i.e., adhesion is achieved through the formation of individual receptor-ligand bonds, must be taken into account for wavy surfaces with a much smaller characteristic length. Interestingly, it was found that, due to the interplay between substrate elasticity and stochastic breakage/reformation of molecular bonds, the strength of cell-ECM adhesion will reach its maximum when the surface roughness is of the order of 20-40 nm, in quantitative agreement with recent experiments. In addition, because of the bonding kinetics involved, the apparent adhesion energy was predicted to be strongly rate-dependent with increasing detaching speed between surfaces leading to a rapidly elevated work of separation, a phenomenon that has been widely observed in bio-adhesion.