Adhesion-induced Phase Separation of Biomembranes--Effective Potential   and Simulations
  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. 
Jia-Yuan Wu