受體檢測外部刺激並作出適當反應的能力對於生物適應環境變化是相當必要的。許多理論模型都指出，受體單元之間的合作現象(cooperativity)在信號檢測中扮演著舉足輕重的角色。在本篇論文中，我們的理論將解釋受體間的交互作用是如何影響他們最外界刺激的反應與靈敏度(sensitivity)。首先，我們建構一個多單元受體（或N個耦合的一單元受體）的一般模型，其各單元間可以發生交互作用。透過這個模型，系統的能量得以確立，至於各微觀狀態的躍遷率之間的關係則依照細節平衡推導之。接下來，受體的平衡態分佈顯示，通過構象或鄰近單元對配體之親和力的耦合可以提高整個系統的靈敏度。前者使系統表現出類似MWC模型的行為；後者則對應Pauling模型。當外界環境具有高濃度的配體時，比起吻合Pauling模型的受體，類MWC模型的受體表現出更高的受體活化率。緊接著，我們使用Gillespie 演算法模擬受體的動力學。在受體的時間演化中，選擇被活化或是鍵結配體的路徑與各狀態所對應的能量有密不可分的關係。例如:高濃度配體下的活化與鍵結路徑不同於低配體濃度下的路徑。另一方面，隨著耦合強度增加和配體濃度降低，一個受體從沒有被活化且無鍵結配體的狀態演化至被活化同時鍵結著配體平均需要的時間也隨之增加。從定量的結果來看，我們發現高靈敏度且反應快速的受體可以通過其亞基之間的適度耦合來實現。最後，我們發現在平均場理論理一個含有許多單元的受體，一如我們預期，在單元間耦合強度超過一臨界值時，其受體活化率與配體濃度之間的關係如相變般產生出不連續的變化;The ability of a receptor to detect external stimuli and make appropriate responses is necessary for organisms to adapt environmental changes. It has been proposed in many models that cooperativity between receptors plays an important role in signal detection. In this thesis we present our theoretical investigation for the effects of interactions between the receptors on their response and sensitivity. First of all, we build a general model for a multi-unit receptor (or N coupled single-unit receptors) whose units interact with each other. The energy landscape is established and the transition rates between microstates are related to each other by the law of detailed balance. Next, equilibrium distributions of the receptor show that the sensitivity of the system can be improved by couplings through conformation or ligand binding affinity of nearby units. The former leads to behavior similar to the celebrated MWC model; the latter corresponds to Pauling model. The MWC-like receptor have higher activation level than Pauling receptor at high ligand concentration. Then we use Gillespie algorithm to simulate receptor dynamics. The kinetic pathway during receptor binding and activation depends strongly on the energy landscape. For example the kinetic pathways at high ligand concentration is different from that at low ligand concentration. On the other hand, the average time for a free, inactivate receptor to evolve to a fully bound and active state increases as the coupling increases and the ligand concentration decreases. Finally, we show that for a receptor with N >> 1 units, mean field analysis predicts a discontinuous jump in receptor activity under a change of ligand concentration. From our quantitative results, we find that a receptor with high sensitivity and rapid response can be achieved by moderate couplings between its subunits.
