利用加權蛋白質接觸數目推導蛋白質動力學特性

Abstract

最近的研究顯示了蛋白質上的原子的平均平方位移(或稱之為B因子, B-factor)與該原子周圍接觸的原子數目(contact number)以及其到蛋白質的質量重心(center of mass)的平方距離有關。這樣的關係允許我們可以直接的藉由原子接觸數目和原子與質量重心的平方距離去計算B因子側寫(B-factor profile)。這兩種方法我們稱之為蛋白質接觸數目模型(contact number model)和蛋白質固定點模型(protein fixed-point model)，因為此兩種方法不僅不需要使用分子模擬來獲得原子軌跡整合，也不需要針對矩陣去做對角化，而使得這兩種方法變得相當具有吸引力。因此，蛋白質接觸數目模型和蛋白質固定點模型能夠應用在大體積且結構複雜的蛋白質，並且可作為一種高通量(high throughput)的計算工具去計算蛋白質內原子的擾動。在這個研究裡，我們展示藉由融合這兩種模型的特性所產生的加權蛋白質接觸數目模型，來使得計算蛋白質內部的原子運動的準確性能夠被更進一步的提昇。我們藉由除以兩個原子接觸的平方距離來作為加權的方法，並且分析將蛋白質的接觸距離加上不同的切斷半徑(cut-off radius)之後的計算結果。此外我們也展示了這樣的模型也可以被用來計算原子運動的交互相關性(cross-correlation)。實際上，B因子就是原子運動的自我相關性(auto-correlation)。我們使用了一個序列相關性小於25%的非同源性的資料組，其包含了972條具有解析度小於2.0 Å的高解析度X射線結晶結構。針對這樣的資料組，經由X射線所得到的B因子與藉由加權蛋白質接觸數目模型去計算所得到的B因子，兩者之間的平均相關係數可達0.61，比起原始的蛋白質接觸數目模型(0.51)或是其他的方法要來得更好。針對一些例子，我們的研究結果也顯示了經由加權蛋白質接觸數目模型計算所得到的交互關係圖像以及特徵值和特徵向量，與藉由正模分析法(normal mode analysis)和高斯網路模型(Gaussian Network Model)所得到結果，具有全面性的相似度。我們的結果不僅強調了蛋白質的動力特性與蛋白質集結特性有關之外，我們也相信這樣的方法對於研究蛋白質的結構和動力學之間的相關性有相當大的幫助。

It has recently been shown that in proteins the atomic mean-square displacement (or B-factor) can be related to the number of the neighboring atoms (or protein contact number) and the square distance from the center of mass of a protein. This relationship allows one to compute the B-factor profiles directly from protein contact number and the square distance from center of mass. The two methods, referred to as the protein contact number model and the protein fixed-point model, are appealing, since they require neither trajectory integration nor matrix diagonalization. As a result, the protein contact number model and the protein fixed-point model can be applied to very large proteins and can be implemented as a high-throughput computational tool to compute atomic fluctuations in proteins. Here, we show that the properties of the two models can be integrated and further refined to that between the atomic mean-square displacement and the weighted protein contact-number, the weight being the square of the reciprocal distance between the contacting pair. In addition, we show that this relationship can be utilized to compute the cross-correlation of atomic motion (the B-factor is essentially the auto-correlation of atomic motion). For a nonhomologous dataset comprising 972 high-resolution X-ray protein structures (resolution < 2.0 Å and sequence identity < 25%), the mean correlation coefficient between the experimental and computed B-factors based on the weighted protein contact-number model is 0.61, which is better than those of the original contact-number model (0.51) and other methods. We also show that the computed cross-correlation maps, eigenvalues and eigenvectors based on the weighted contact-number model are globally similar to those computed through Gaussian Network Model and normal model analysis for some selected cases. Our results underscore the relationship between protein dynamics and protein packing. We believe that our method will be useful in the study of the protein structure-dynamics relationship.