我們以理論分析和數值模擬的方法來研究由兩種受體—配體鍵結所引發的生物膜黏著而造成的相分離。在考慮了受體—配體複合體所有可能的分佈後，我們得到了一個等效勢能，因此本系統可以被視為生物膜在一個等效的外加勢能中，我們用平均場論和高斯近似來分析這個等效膜勢，並且發現到：（1）在兩種受體—配體複合體高度差大時，受體—配體複合體高度差是造成相分離的主因；（2）在遠離平均場臨界點的兩相區，當相共存發生時，較硬受體—配體複合體的等效鍵結能是較大的，這是因為較軟受體—配體複合體的熵比較大的關係；（3）在靠近平均場臨界點的兩相區，我們畫出了等效膜勢後發現相共存發生在較軟受體—配體複合體的等效鍵結能較大的地方。受體—配體複合體密度對臨界點位置的影響是利用蒙地卡羅模擬來研究，其結果顯示當系統的受體—配體複合體密度減少時相分離生在受體—配體複合體高度差較大的地方。

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.

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