Department of Molecular Biophysics and Physiology, Rush University Medical Center, Chicago, Illinois 60612, USA.
J Chem Phys. 2011 Sep 14;135(10):104113. doi: 10.1063/1.3632995.
We study the energetics of burying charges, ion pairs, and ionizable groups in a simple protein model using nonlocal continuum electrostatics. Our primary finding is that the nonlocal response leads to markedly reduced solvent screening, comparable to the use of application-specific protein dielectric constants. Employing the same parameters as used in other nonlocal studies, we find that for a sphere of radius 13.4 Å containing a single +1e charge, the nonlocal solvation free energy varies less than 18 kcal/mol as the charge moves from the surface to the center, whereas the difference in the local Poisson model is ∼35 kcal/mol. Because an ion pair (salt bridge) generates a comparatively more rapidly varying Coulomb potential, energetics for salt bridges are even more significantly reduced in the nonlocal model. By varying the central parameter in nonlocal theory, which is an effective length scale associated with correlations between solvent molecules, nonlocal-model energetics can be varied from the standard local results to essentially zero; however, the existence of the reduction in charge-burial penalties is quite robust to variations in the protein dielectric constant and the correlation length. Finally, as a simple exploratory test of the implications of nonlocal response, we calculate glutamate pK(a) shifts and find that using standard protein parameters (ε(protein) = 2-4), nonlocal results match local-model predictions with much higher dielectric constants. Nonlocality may, therefore, be one factor in resolving discrepancies between measured protein dielectric constants and the model parameters often used to match titration experiments. Nonlocal models may hold significant promise to deepen our understanding of macromolecular electrostatics without substantially increasing computational complexity.
我们使用非局部连续静电学研究了将电荷、离子对和可电离基团埋入简单蛋白质模型中的能量学。我们的主要发现是非局部响应导致溶剂屏蔽显著降低，与使用特定于蛋白质的介电常数相当。采用与其他非局部研究相同的参数，我们发现对于半径为 13.4Å 的包含单个+1e 电荷的球体，当电荷从表面移动到中心时，非局部溶剂化自由能的变化小于 18 kcal/mol，而局部泊松模型的差异约为 35 kcal/mol。由于离子对（盐桥）产生了相对变化更快的库仑势，因此非局部模型中盐桥的能量学甚至更显著降低。通过改变非局部理论中的中心参数，该参数是与溶剂分子之间相关性相关的有效长度尺度，可以将非局部模型的能量学从标准的局部结果变化到基本上为零；然而，电荷埋藏惩罚减少的存在对蛋白质介电常数和相关长度的变化非常稳健。最后，作为非局部响应影响的简单探索性测试，我们计算了谷氨酸 pKa 位移，发现使用标准蛋白质参数（ε（protein）= 2-4），非局部结果与具有更高介电常数的局部模型预测相匹配。因此，非局部性可能是解决测量蛋白质介电常数与通常用于匹配滴定实验的模型参数之间差异的一个因素。非局部模型可能具有很大的潜力，可以在不大大增加计算复杂性的情况下，加深我们对大分子静电学的理解。
