On the Dielectric “Constant” of Proteins: Smooth Dielectric Function for Macromolecular Modeling and Its Implementation in DelPhi

Implicit methods for modeling protein electrostatics require dielectric properties of the system to be known, in particular, the value of the dielectric constant of protein. While numerous values of the internal protein dielectric constant were reported in the literature, still there is no consensus of what the optimal value is. Perhaps this is due to the fact that the protein dielectric constant is not a “constant” but is a complex function reflecting the properties of the protein’s structure and sequence. Here, we report an implementation of a Gaussian-based approach to deliver the dielectric constant distribution throughout the protein and surrounding water phase by utilizing the 3D structure of the corresponding macromolecule. In contrast to previous reports, we construct a smooth dielectric function throughout the space of the system to be modeled rather than just constructing a “Gaussian surface” or smoothing molecule–water boundary. Analysis on a large set of proteins shows that (a) the average dielectric constant inside the protein is relatively low, about 6–7, and reaches a value of about 20–30 at the protein’s surface, and (b) high average local dielectric constant values are associated with charged residues while low dielectric constant values are automatically assigned to the regions occupied by hydrophobic residues. In terms of energetics, a benchmarking test was carried out against the experimental pKa’s of 89 residues in staphylococcal nuclease (SNase) and showed that it results in a much better RMSD (= 1.77 pK) than the corresponding calculations done with a homogeneous high dielectric constant with an optimal value of 10 (RMSD = 2.43 pK).用于蛋白质静电建模的隐式方法，需要知晓体系的介电性质，尤其是蛋白质的介电常数数值。尽管已有诸多文献报道了蛋白质内部介电常数的不同取值，但学界尚未就最优值达成共识。这一现象的成因或许在于，蛋白质介电常数并非真正的“常数”，而是反映蛋白质结构与序列特性的复杂函数。本研究提出一种基于高斯（Gaussian）的方法实现方案，通过利用对应大分子的三维结构，获取蛋白质及其周围水相的全域介电常数分布。与既往研究不同，本工作并非仅构建“高斯曲面”或平滑分子-水界面，而是在待建模体系的全域空间内构建平滑介电函数。对大量蛋白质的分析结果表明：(a) 蛋白质内部的平均介电常数相对较低，约为6~7，而在蛋白质表面处介电常数可达20~30；(b) 局部平均介电常数较高的区域与带电残基相关联，而疏水残基占据的区域则会自动被赋予较低的介电常数。在能量学方面，本研究以葡萄球菌核酸酶（staphylococcal nuclease, SNase）中89个残基的实验pKa值为基准开展测试，结果显示，相较于采用最优值为10的均匀高介电常数进行的对应计算（均方根偏差RMSD=2.43 pK），本方法得到的均方根偏差仅为1.77 pK，性能更优。