摘要
本文利用布朗動力學模擬法，來研究生物複合分子的非共價鍵結，在有外力作用下斷裂的現象，其中外力是以固定的拉力、等速的拉力和周期性的拉力等三種方式來探討。結果顯示，當外力處於F/Fc<<1的情況下，Bell的表示式成功地描述生物非共價鍵結的斷裂速率，其中Fc是在拉力作用方向的鍵結位能的最大最大斜率值；而當外力處於1-F/Fc<<1的時候，則是Garg所提出的表示式較能正確地描述斷裂速率。在文章中，我們也展示出當外力為固定的拉力時，適合用來萃取生物非共價鍵結的斷裂位能；而當外力為等速的拉力時，則適合用來萃取Fc的值；當外力為周期性的力時，則可用來提取Fc和在沒有外力時斷裂的速率值。 在利用外力來研究生物非共價鍵結斷裂的現象時，生物分子通常使用一段高分子當作連接體連接至外力施加的裝置(如AFM的探針)，因此我們亦利用overdamped Langevin dynamics來研究生物分子與探針的彈性複合系統，藉此來探討在固定的拉力下，連接體的軟硬度對於鍵結斷裂速率的影響。結果顯示鍵結斷裂速率的影響因素，包涵了生物分子本身的熱擾動、拉力的震動以及違反adiabatic condition等。鍵結斷裂的速率會隨著連接體硬度的增加而減少。對於軟的連接體而言，連接體與探針的影響可以被忽略，因此可以量測到真實的斷裂速率；而對於較硬的連接體而言，探針的熱擾動必須考慮進來，因此會造成量測到較小的斷裂速率，而這速率與生物分子和探針兩者的擴散系數比值有關。不過，不管連接體的軟硬度為何，作用的位能大小在固定的拉力試驗下仍然是可以被萃取出來的。 在生物細胞進行作用時，通常不只形成一根鍵結，而是形成多根的鍵結。對於N根藉由彈簧(連接體)連接至固定表面的平行共同作用分子非共價鍵結的系統，我們利用固定位移的方法來分析建構其位能的形狀。在文章中我們顯示N根平行作用鍵結的斷裂動力學，可以用一個具有NEa位能的有效單根鍵結模型來描述，其中Ea為單根鍵結的位能大小，在這模擬中我們發現其臨界拉力Fc正比於N(ksEa)^0.5，而在較軟的連接體時其Fc/N值總是比單一根時的臨界拉力小，藉由這個方法所建構的位能形狀，我們可以計算這個由N根鍵結所形成的黏著叢集在固定拉力或是等速拉力下的斷裂速率，而這理論分析的結果與由Langevin dynamic的結果相符合。本研究結果可供實驗學者在分析實驗數據時，可透過此方法來獲得必要的動力學相關資訊。
並列摘要
The dissociation of a biomolecular complex under the action of constant force, constant loading rate, and periodic force is studied theoretically by Brownian dynamic simulation. We show that the celebrated Bell’s expression provides a good approximation for the bond dissociation rate when F/Fc<<1, where Fc is the maxima slope of the binding potential along the reaction coordinate. When 1-F/Fc<<1 the dissociation rate is better described by a generalized Garg’s form in which the potential derivative is expanded near Fc. We also show that a constant-force experiment is suitable for extracting the activation energy of the bond, a constant loading experiment is suitable to extract Fc, while time-periodic force can be applied to extract both bond dissociation rates at zero force and Fc. In the dissociation of a noncovalent biomolecular bond by external pulling, the bonded site is often connected to the force-acting site by a linkage. The role of the linkage stiffness on the rupture of a ligand-receptor complex under constant force is investigated by overdamped Langevin dynamics for the elastically coupled ligand and probe. The effects on the bond lifetime include effective ligand diffusivity, force fluctuations, and violation of adiabatic condition. The rupture rate declines with increasing linkage stiffness. For soft linkage, the effect associated with spring and probe can be ignored and the true rupture rate can be extracted. On the other hand, for stiff linkage, the diffusivity of the probe has to be accounted for and thus leads to a smaller rupture rate, dependent on the diffusivity ratio between probe and ligand. Nevertheless, the energy barrier height can be reasonably extracted by constant pulling experiments regardless of the linkage stiffness. The free energy landscape of a cooperative cluster of N parallel bonds, confined to the anchoring surface by springs of stiffness ks, is analytically constructed by the constant displacement method. We show that the dissociation kinetics of N parallel bonds can be modeled as an effective single bond with the activation energy being NEa essentially, where Ea is the intrinsic energy barrier of a single bond. The critical force Fc is shown to be proportional to N(ksEa)^0.5 and Fc/N is always small compared to the critical force associated with a single bond for soft springs. On the basis of the free energy landscape, the lifetime of adhesion clusters under constant force or loading rate can be obtained. Our theoretical analyses have been confirmed by Langevin dynamic simulations and demonstrate a new experimental method to obtain kinetic information. The influence of matrix elasticity on the critical force might be relevant to the preference of focal adhesion on rigid surfaces.