Two intertwined facets of adherent membranes: membrane roughness and correlations between ligand-receptors bonds

We study equilibrium fluctuations of adherent membranes by means of Langevin simulations in the case when the interaction of the membrane with the substrate is twofold: a non-specific homogeneous harmonic potential is placed at large distances, whereas discrete ligand-receptor interactions occur at short distances from the flat substrate. We analyze the correlations between neighboring ligand-receptor bonds in a regime of relatively strong membrane fluctuations. By comparison with the random distribution of bonds, we find that the correlations between the bonds are always positive, suggesting spontaneous formation of domains. The equilibrium roughness of the membrane is then determined by fluctuations in the number density of bonds within the domains. Furthermore, we show that the excess number of bonds arising due to correlations and the instantaneous roughness of the membrane both follow master curves that depend only on the instantaneous bond density and not on the intrinsic binding strength of the ligand-receptor pair. The master curves show identical trends, further corroborating the link between membrane roughness and bond correlations.