Formation of dilute adhesion domains driven by weak elasticity-mediated interactions

Cell-cell adhesion is established by specific binding of receptor and ligand proteins. The adhesion bonds attract each other and often aggregate into large clusters that are central to many biological processes. One possible origin of attractive interactions between adhesion bonds is the elastic response of the membranes to their deformation by the bonds. Here, we analyze these elasticity-mediated interactions using a novel mean-field approach. Analysis of systems at different densities of bonds, $\phi$, reveals that the phase diagram exhibits a nearly-universal behavior when the temperature $T$ is plotted vs. the scaled density $x=\phi \xi^2$, where $\xi$ is the linear size of the membrane's region affected by a single bond. The critical point $(\phi_c,T_c)$ is located at very low densities and slightly below $T_c$ we identify phase coexistence between two low-density phases. Dense domains are observed only when the height by which the bonds deform the membranes, $h_0$, is much larger than their thermal roughness, $\Delta$, which occurs at very low temperatures $T\ll T_c$. We conclude that the elasticity-mediated interactions are weak and cannot be regarded as responsible for the formation of dense adhesion domains. The weakness of the elasticity-mediated effect and its relevance to dilute systems only can be attributed to the fact that the membrane's elastic energy saturates in the semi-dilute regime, when the typical spacing between the bonds $r\gtrsim \xi$, i.e., for $x\lesssim 1$. Therefore, at higher densities, only the mixing entropy of the bonds (which favors uniform distributions) is thermodynamically relevant. We discuss the implications of our results to the question of immunological synapse formation, and demonstrate the elasticity-mediated interactions may be involved in the aggregation of these semi-dilute membrane domains.