  We present theoretical analyses and numerical simulations for the
adhesion-induced phase separation of multi-component membranes with two types
of ligand-receptor complexes (junctions). We show that after integrating all
possible distributions of the junctions, the system can be regarded as a
membrane under an effective external potential. Mean field theory and Gaussian
approximation are used to analyze the effective membrane potential and we find
(i) The height difference of the junctions is the main factor that drives phase
separation at sufficiently large junction height difference. (ii) In the two
phase region far from the mean-field critical point, because of the higher
entropy associated with the softer junctions, phase coexistence occurs when the
effective binding energy of the more rigid junctions is higher. (iii) In the
two phase region near the mean-field critical point, the shape of the effective
potential shows that the phase coexistence occurs when the effective binding
energy of softer junctions is higher. The effect of junction density on the
critical point is studied by Monte Carlo simulations, and the result shows that
phase separation occurs at larger junction height difference as junction
density of the system decreases.
