Abstract
Phase separation in biological membranes plays an important role in protein targeting and transmembrane signaling. Its occurrence in both membrane leaflets commonly gives rise to matching liquid or liquid-ordered domains in the opposing monolayers. The underlying mechanism of such co-localization is not fully understood. The decrease of the line tension around the thicker ordered domain constitutes an important driving force. Yet, robust domain coupling requires an additional energy source, which we have now identified as thermal undulations. Our theoretical analysis of elastic deformations in a lipid bilayer shows that stiffer lipid domains tend to distribute into areas with lower fluctuations of monolayer curvature. These areas naturally align in the opposing monolayers. Thus, coupling requires both membrane leafs to display a heterogeneity in splay rigidities. The heterogeneity may either originate from intrinsic lipid properties or be acquired by adsorption of peripheral molecules. Undulations and line tension act synergistically: the gain in energy due a minimized line tension is proportional to domain radius and thus primarily fuels the registration of smaller domains; whereas the energetic contribution of undulations increases with membrane area and thus primarily acts to coalesce larger domains.