黏著叢集在時變外力下的強度

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梁昕蕙(Hsin-Hui Liang) 查詢紙本館藏

畢業系所

物理學系

論文名稱

黏著叢集在時變外力下的強度
(Strength of adhesion clusters under shared linear loading)

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摘要(中)

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。

摘要(英)

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.

關鍵字(中)

★ 黏著強度

關鍵字(英)

★ ligand-receptor pairs
★ adhesion

論文目次

1 Introduction 1
2 The Model 6
2.1 Escape rate of single bond . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.2 Constant kon model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.3 Nonconstant kon model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
3 Free energy of an adhesion cluster 14
3.1 From master equation to free energy . . . . . . . . . . . . . . . . . . . . 14
3.2 Free energy landscape at different f . . . . . . . . . . . . . . . . . . . . . 15
4 Numerical and analytical solutions for rupture force 20
4.1 Monte Carlo simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
4.1.1 Simulation algorithm . . . . . . . . . . . . . . . . . . . . . . . . . 21
4.1.2 Simulation results . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
4.2 Mean rupture force of an adhesion cluster under low loading rate . . . . . 31
4.2.1 Distribution of rupture force . . . . . . . . . . . . . . . . . . . . . 31
4.2.2 Rupture force for fr < fc . . . . . . . . . . . . . . . . . . . . . . . 34
4.3 Solution of rate equation . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
5 Conclusion 45
Bibliography 48

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指導教授

陳宣毅(Hsuan-Yi Chen)

審核日期

2009-1-5

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