Traditional implicit methods for modeling electrostatics in biomolecules use a two-dielectric approach: a biomolecule is assigned low dielectric constant while the water phase is considered as a high dielectric constant medium. However, such an approach treats the biomolecule–water interface as a sharp dielectric border between two homogeneous dielectric media and does not account for inhomogeneous dielectric properties of the macromolecule as well. Recently we reported a new development, a smooth Gaussian-based dielectric function which treats the entire system, the solute and the water phase, as inhomogeneous dielectric medium (Li L, Li C, Zhang Z, Alexor E, On the dielectric constant of proteins: Smooth dielectric function for macromolecular modeling and its implementation in Delphi, J Chem Theory Comput9(4):2126–2136, 2013). Here we examine various aspects of the modeling of polar solvation energy in such inhomogeneous systems in terms of the solute–water boundary and the inhomogeneity of the solute in the absence of water surrounding. The smooth Gaussian-based dielectric function is implemented in the DelPhi finite-difference program, and therefore the sensitivity of the results with respect to the grid parameters is investigated, and it is shown that the calculated polar solvation energy is almost grid independent. Furthermore, the results are compared with the standard two-media model and it is demonstrated that on average, the standard method overestimates the magnitude of the polar solvation energy by a factor 2.5. Lastly, the possibility of the solute to have local dielectric constant larger than of a bulk water is investigated in a benchmarking test against experimentally determined set of pKa's and it is speculated that side chain rearrangements could result in local dielectric constant larger than 80.

中文翻译：

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基于平滑高斯介电函数的溶剂化能量极性分量建模

用于模拟生物分子中的静电的传统隐式方法使用双电介质方法：生物分子被指定为低介电常数，而水相被认为是高介电常数介质。然而，这种方法将生物分子 - 水界面视为两个均匀介电介质之间的尖锐介电边界，并且不考虑大分子的不均匀介电特性。最近我们报道了一个新的发展，一种基于平滑高斯的介电函数，它将整个系统、溶质和水相视为非均匀介电介质（Li L、Li C、Zhang Z、Alexor E，关于蛋白质的介电常数: 用于大分子建模的平滑介电函数及其在 Delphi 中的实现，J Chem Theory Comput9(4):2126–2136, 2013)。在这里，我们根据溶质 - 水边界和在没有水的环境下溶质的不均匀性检查了这种不均匀系统中极性溶剂化能量建模的各个方面。在DelPhi有限差分程序中实现了基于平滑高斯的介电函数，因此研究了结果对网格参数的敏感性，结果表明计算的极性溶剂化能量几乎与网格无关。此外，将结果与标准的双介质模型进行比较，结果表明，标准方法平均高估了极性溶剂化能量的大小 2.5 倍。最后，