運用於蛋白質與蛋白質交互作用之新穎普適性曲線路徑自由能計算方法

Abstract

分子相互作用能量學的計算表徵是分子生物物理學的研究核心，也是迄今為止能彌合相互作用自由能與基礎力學分析之間差距的唯一途徑。分子模擬;如分子動力學（MD）（或蒙特卡羅（MC））;用於計算熱力學明確定義的終態之間的自由能差異。例如，一個公認的位能平均力（PMF）計算為物理上可實現的反應過程提供自由能量分佈，例如分子締合和/或解離，二面角變化，區塊/環的構型上的翻轉等。通常，這些分子反應需跨越幾個能量障礙，在無施加任何額外能量的MD模擬，是不能在如此短的時間尺度中模擬出該有的時間尺度上的運動和空間上的變化 。因此在這種情況下，為了此方法在所需配置的空間中做有效的採樣，施加傘狀位能採樣模擬變成一種廣泛使用於增加採樣的方法， 。 傘狀位能採樣通常以沿著定義好的反應坐標做採樣。然而， 任何微小變化都會影響PMF，因此使用任何隨機選擇的路徑所計算出的能量可能會產生誤導。有效的替代方案則是選擇非預定並自然選取的曲線路徑做採樣。但是，這方面應用在蛋白質 - 蛋白質交互作用系統的研究相對較少。本論文則是透過在傘式採樣模擬找到了廣義的曲線路徑選取方法，對barnase-barstar蛋白複合物的解離進行研究。 由於，沿反應坐標存在著多種可能的反應路徑，因此我們利用多個路徑分析，進行傘式採樣模擬以探索沿不同路徑間的自由能差異。分析所有採樣數據，並為每一條路徑構建PMF。由於起始結構為相同的晶體結構，所以一開始我們預期所有PMF會收斂到相類似的值。然而，令我們驚訝的是，並非所有PMF都收斂在一起，我們觀察到有幾個不同路徑並找到不同的收斂值。利用最小作用力的原理（即變分原理）模擬解離反應，計算出ＰＭＦ的下限的。有趣的是，我們發現PMF輪廓有三個不同路徑收斂到一個雷同的下界。這種結合曲線路徑方法與基於變分原理的方法是新穎的研究方法，其理論框架是優化校準ＰＭＦ使其趨近標準的結合自由能。 此外，利用群聚採樣數據來找出反應路徑，也觀察到在具有穩健下界的物理軌跡彼此不見得一定相同。 這種曲線路徑傘狀採樣以更自然的方式模擬解離反應，計算出的結合自由能與實驗值非常一致。此外，找到的物理軌跡與兩個主要的解離途徑一致，依據最近報導的barnase-barstar關聯的毫秒長MD模擬，這兩個都是主要解離途徑， 詳細的討論皆在內文中。

Computational characterization of molecular interaction energetics is central to molecular biophysics and is so far the only way to bridge the gap between free energies of interaction and underlying mechanistic details. The molecular simulations; such as molecular dynamic (MD) (or Monte-Carlo (MC)); are used to compute free energy difference between thermodynamically well-defined end-states. For example, a well-established potential of mean force (PMF) calculation gives free energy profile for physically achievable processes such as molecular association and/or dissociation, dihedral angle fluctuations, conformational flipping of domains/loops, etc. Usually, these molecular reactions involve crossing over several energy barriers and the unbiased MD simulations cannot sample wider configurational space in shorter time-scaled simulations. In such situations the umbrella sampling simulation, a widely-used sampling enhancement method, is an effective way to sample the desired configurational space. Umbrella sampling was often implemented in such a way that the samplings were enhanced along a predefined vector as a reaction coordinate. However, any slight change in the predefined vector significantly varies the PMF, and therefore the energetics using any such random choice of vector may mislead. A non-predefined curvilinear path-based sampling enhancement approach is a natural alternative, but was relatively less explored for protein-protein systems. In this thesis, dissociation of the barnase-barstar protein complex is rigorously studied by implementing generalized curvilinear-path approach in umbrella sampling simulations. There can be multiple reaction channels along the reaction coordinate. Therefore, umbrella sampling simulations are conducted with multiple-walkers to explore free energy difference along different channels. The sampling data is analyzed and PMFs are constructed for each walker. Since the starting conformation is the same crystal pose, all the PMFs are expected to converge to around same value. However, to our surprise, not all but a subset of PMFs converged. There were several such subsets observed that converged to different values. Since the reaction was simulated for dissociation, as per the principle of least action, i.e. variational principle, a PMF that constitute a lower bound is chosen. Interestingly, we found that not just PMF but one but there profiles constitute a robust lower-bound. The theoretical framework is optimized for correcting the PMF to the standard free energy of binding. Combining curvilinear-path approach with variational principle based optimized corrections to standard free energy of binding is a novel implementation. Further, the pathways are traced using clustering of the sampled data. The traced physical trajectories for the robust lower-bound are observed to be different. The curvilinear-path umbrella sampling approach is highly generalized to simulate dissociation reaction in more natural manner. The estimated free energy of binding is in good agreement with the experimental values. Further, the traced physical trajectories are consistent with the two major dissociation pathways, which are reported recently from milliseconds-long unbiased adaptive MD simulations of barnase-barstar association. Several aspects of implementation of the approach are discussed in detail.