A theory is presented for the intermembrane junction separation induced by the adhesion between two biomimetic membranes that contain two different types of anchored intermembrane junctions (receptor-ligand complexes). The analysis shows that several mechanisms contribute to the phase separation of the membrane junctions. These mechanisms include the following. (i) The elasticity of the membranes mediates a short-ranged nonlocal interaction between the junctions due to the height difference between type-1 and type-2 junctions. This is the main factor that drives the phase separation. (ii) When type-1 and type-2 junctions have different flexibilities against stretch and compression, the softer junctions are the favored species, and aggregation of the softer junctions can occur. (iii) The thermally activated shape fluctuations of the membranes also contribute to the phase separation by inducing another nonlocal interaction between the junctions and renormalizing the binding energy of the junctions. The combined effect of these mechanisms is that when phase separation occurs, the system separates into two domains with different relative and total junction densities.
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