Kinetics of cell detachment: effect of ligand density

Cell adhesion to substratum is often mediated by binding between cell surface receptors and substrate ligands. Substrates can be derivatized with different types and densities of ligands, but how substrate chemistry determines cellular function, such as adhesion strength, has not been demonstrated quantitatively. We employ a numerical methodology developed by Dembo and colleagues (9), who investigated membrane peeling under conditions of excess ligand density, to investigate the kinetics and strength of cell peeling from ligand coated surfaces for arbitrary ligand density. We show there are two asymptotic limits to peeling strength, as quantified by the critical tension: a high ligand density limit, where the critical tension is independent of ligand density and depends logarithmically on the receptor density; and a low ligand density limit, in which the critical tension depends logarithmically on the ligand density but is independent of receptor density. In between these limits, we numerically determine the critical tension. The critical tension is always a weak function of the dissociation constant between ligand and receptor. Furthermore, we show how the rate of peeling, for tensions above the critical tension, depends on ligand density and the mechanical properties of the receptor-ligand bonds. Interestingly, we illustrate when small increases in ligand density should alter cellular behavior, inducing a change to spreading onto a substrate from peeling up from a substrate. In total the predictions of this paper provide criteria for the design of ligand-coated substrate that provide for the proper adhesion strength and dynamics of detachment of cells from surfaces.