我們提出了一個理論模型來描述配體-受體叢集的生命期
T( f , Nt )與叢集大小Nt、外力F 的關係，這裡f = F/Nt 為每
一配體-受體對所受之力。此叢集是由Nt 個平行的配體受體
對所組成。由反應速率方程式我們找到一個叢集的特徵力
fc ，我們由不同外力下的蒙地卡羅模擬發現(1)當f >fc 時,
叢集生命期與叢集大小無關。這是由於在反應速率方程式
中，鍵結數目在叢集中所佔比例的衰變與叢集大小無關，而
與f 有關。(2)當f =fc 時，生命期與叢集大小有冪次關係
lnT~lnNt。為了解釋此結果我們引入等效自由能G，則一叢
集的斷裂過程可以用一假想粒子在位能G 下的運動來描
述。在f =fc 時，G 有個反曲點，且叢集生命期大多都花在反
曲點附近的區域上，由標度分析可得lnT~lnNt。(3)當f <fc 時
我們得到lnT~Nt，此時G 在Nb 空間中有一個井，所以叢集
生命期大約是此粒子跨越此井所需要的時間，利用Kramers
粒子脫離率定律可得lnT~ Nt。我們的研究證明了只要配體受
體對的斷裂率以及重新鍵結率是f 與叢集鍵結比例的函數，
則都可以得到以上的三種關係。

We present a theoretical model to study the lifetime T(Nt, f) of an adhesion
cluster under external force F, where Nt is the cluster size and f = F/Nt. The
cluster is composed of Nt parallel ligand-receptor pairs. We find a character-
istic force fc predicted by the rate equation. By Monte Carlo simulation, we
show (i) When f > fc, T is independent of Nt. This can be explained by the
rate equation which predicts that the fraction of connected ligand-receptor
pairs nb(t) depends on f, but not on Nt. (ii)When f = fc, lnT(Nt, f) ∼ lnNt.
To explain the result we construct the effective free energy G and treat the
force pulling process as a particle moving under G in Nb space. G(f = fc)
has a flat region where the particle spends most of its lifetime to cross it.
By estimating the width of the flat region with dimensional analysis, we find
lnT(Nt, f) ∼ lnNt. (iii) When f < fc regime, lnT(Nt, f) ∼ Nt because
G(f < fc) has a barrier with barrier height ∼ Nt and lifetime T comes from
the barrier crossing time of the particle, as a result lnT(Nt, f) ∼ Nt. Finally
we show that the above three relations exist as long as the rebinding and
unbinding rates are functions of f and nb.

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