本論文研究黏著叢集在時變外力下斷裂的過程。此叢集由 Nt 個平行排列的配體–受體的鍵結所組成，並在一個隨著時間線性增加的外力 F = Gamma t 作用下所有鍵結將會全部斷裂， Gamma 為叢集對外力的載荷率。我們選擇了兩種不同的單一配體–受體的結合率與分離率，並且利用蒙地卡羅模擬法來模擬叢集斷裂的過程。研究結果顯示黏著叢集的特性與一特徵力 fc ＝ Fc/Nt 及一特徵載荷率 Gamma c 有關。當 Gamma< Gamma c，叢集的斷裂發生在力為 fr ，其值接近但小於 fc 。在此 Gamma的範圍下，叢集的斷裂行為可比擬為一粒子在一維座標下跨越位能障礙的過程。在將此叢集系統的自由能 G (Nb, F) 近似為配體–受體鍵結數目 Nb 的三次多項式下，理論計算發現 < Fc - Fr > Nt^(-1/3) 正比於 [ln Gamma^(-1)]^(2/3)，此關係式亦在模擬結果中被證實。當 Gamma＝ Gamma c，任何叢集大小都在 fr 等於 fc 時發生斷裂。當 Gamma> Gamma c， fr 大於 fc 且 fr 隨載荷率快速地增大，我們亦發現擁有較多的總鍵結數 Nt 之叢集的反應速率方程式 ( rate equation ) 之數值解與模擬結果吻合。 This thesis studies the dissociation of an adhesion cluster under shared linear loading theoretically. A cluster of ligand-receptor pairs in cell adhesion can be modeled as Nt parallel weak bonds between two surfaces. The cluster dissociates under an applied force F which increases linearly with time t, that is, F = Gamma t, where Gamma is the loading rate. Monte Carlo simulations of master equation are performed with two choices of kon and koff , the rebinding and unbinding rates of a bond, respectively. Our simulations show that there exist a critical force per bond fc = Fc/Nt and a critical loading rate Gamma c, and some universal properties of the clusters are associated with these quantities. At Gamma < Gamma c, the rupture force per bond fr is close to but lower than fc. In this regime, cluster dissociation can be regard as a one-dimensional barrier crossing process. We approximate the free energy of the adhesion cluster G(Nb, F) at given F by a cubic function of Nb, number of closed bonds in the cluster. From analytical solutions we obtained a scaling relation < Fc - Fr >Nt^(-1/3) ~ [ln Gamma^(-1)]^(2/3) + constant. This scaling relation is consistent with the numerical simulations of the master equation. At Gamma = Gamma c, the cluster dissociation occurs at fr = fc for any cluster size. At Gamma > Gamma c, fr > fc and fr increases rapidly with Gamma, especially for small clusters. There is no free energy barrier when the clusters rupture at fr > fc, the numerical solutions of rate equation agree with numerical simulations of the master equation.
