臺灣博碩士論文加值系統

我們提出一個理論模型描述受到外力下的受體-配體叢集，並且修正了在貝爾(Bell) 模型中受體-配體的結合率。藉由研究受體-配體鍵結數目的速率方程式(rate equation)，我們可以估計叢集的穩定度（生命期）。研究結果顯示當一具有N個平行受體-配體鍵結的叢集受到一外力F，叢集的生命期只和作用在一個受體-配體鍵結的力的大小f=F/N 有關。我們定義一臨界力fc：當f小於fc，叢集趨於穩定；當f大於fc，叢集的受體-配體鍵結會全部斷裂；當f等於fc，叢集的受體-配體鍵結會斷裂至一特定的鍵結數目（此時大部分的受體-配體是鍵結的），再經由鍵結受體-配體數的漲落使得叢集繼續斷裂。關於叢集的生命期，我們發現當f-> fc^+時，叢集的生命期小於貝爾模型的預測，並且正比於(f-fc)^(-1/2)。當(f-fc)/fc~O(1)時，叢集的生命期大於貝爾的預測，這主要是由於貝爾和我們的模型的初始受體-配體鍵結數目不同所造成。當f=fc 時，受體-配體鍵結數目的漲落變得重要，我們發現叢集的生命期正比於N^(1/3)。

We present a theoretical model that describes ligand-receptor cluster under external force. We modify the model of Bell [1] by considering the rebinding of broken bonds in a consistent way. The stability of the cluster is studied by the rate equation of Nb, the number of connected bonds. Our study reveals that for a cluster with N parallel bonds under external force F, the lifetime of the cluster depends only on the force acting on each bond f = F/N. There exists a critical force Fc = Nfc below which the cluster is stable and above which the cluster dissociates. When f = fc, the number of rupture events per unit time is equal to that of rebinding at Nb^* = Nnb^*. We find nb^*~1, i.e., the effect of rebinding is important when most of the bonds are connected. When f approaches fc from above, the cluster spends most of the time near nb^*, the true lifetime of the cluster is shorter than Bell’s prediction and has a power law behavior T ~(f − fc)^(−1/2). We also show that the true lifetime of the cluster is longer than Bell’s prediction when f is significantly greater than fc due to different number of connected bonds predicted by both theories in the absence of force. When f =fc, for a finite size cluster, the bond number fluctuation is important, the lifetime of the cluster is related to the cluster size by T ~N^(1/3).

Contents
1 Introduction 1
2 Background 6
2.1 Langevin equation . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.2 Smoluchowski equation . . . . . . .. . . . . . . . . . . . . . . . . 7
2.3 Kramers’ escape rate theory . . . . . . . . . . . . . . . . . . . . 9
3 The model 13
3.1 Bell’s model . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
3.2 Linker elasticity and rebinding rate . . . . . . . . . . . . . . . . 19
3.3 Extended cubic theory for koff at large f . . . . . . . . . . . . . 26
4 Numerical and analytical solution of cluster lifetime 28
4.1 Numerical solution . . . . . . . . . . . . . . . . . . . . . . . . . 28
4.1.1 nb(t) for (f − fc)/fc ∼ O(1) . . . . . . . . . . . . . . . . . . 29
4.1.2 nb(t) for (f − fc)/fc << 1 . . . . . . . . . . . . . . . . . . . 29
4.2 Cluster lifetime near fc . . . . . . . . . . . . . . . . . . . . . . 33

5 Conclusion 38
A Lifetime near critical force: Finite-size effect 40
B Adhesion cluster under constant loading rate 45
References 52

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