Physical interpretation of the maximum receptor-ligand bond spacing to ensure cell adhesion in ligand-coated substrates

Recent experiments by Arnold et al. (Arnold, M.; Cavalcanti-Adam, E. A.; Glass, R.; Blummel, J.; Eck, W.; Kantlehner, M.; Kessler, H.; Spatz, J. P. ChemPhysChem 2004, 5, 383) revealed that a distance of less than 58-73 nm between receptor-ligand bonds is necessary to ensure focal adhesion in integrin-mediated cell adhesion on ligand-coated substrates. In this letter, we consider focal adhesion growth to be a process assisted by thermal fluctuations and receptor-ligand binding and resisted by repulsive "bulge pressure" and membrane deformation. By applying balance between these forces, we obtain a critical spacing of receptor-ligand bonds given as 2h[alpha kBT/beta Eh3)1/3(E/p)5]1/14, above which the growth of focal adhesion becomes difficult. Here h and E are the in-plane modulus and thickness of a cell membrane, respectively, p is a repulsive "bulge pressure" between the cell membrane and substrate, and alpha and beta are constants on the order of 1. We use typical values of E and h for cell membranes and obtain the critical spacing of receptor-ligand bonds of around 39-89 nm for a wide range of repulsive bulge pressure.