Department of Biomedical Engineering, University of California, Irvine, California 92697, USA.
J Chem Phys. 2013 Sep 7;139(9):094106. doi: 10.1063/1.4819471.
Continuum modeling of electrostatic interactions based upon numerical solutions of the Poisson-Boltzmann equation has been widely used in structural and functional analyses of biomolecules. A limitation of the numerical strategies is that it is conceptually difficult to incorporate these types of models into molecular mechanics simulations, mainly because of the issue in assigning atomic forces. In this theoretical study, we first derived the Maxwell stress tensor for molecular systems obeying the full nonlinear Poisson-Boltzmann equation. We further derived formulations of analytical electrostatic forces given the Maxwell stress tensor and discussed the relations of the formulations with those published in the literature. We showed that the formulations derived from the Maxwell stress tensor require a weaker condition for its validity, applicable to nonlinear Poisson-Boltzmann systems with a finite number of singularities such as atomic point charges and the existence of discontinuous dielectric as in the widely used classical piece-wise constant dielectric models.
基于泊松-玻尔兹曼方程数值解的静电相互作用连续体建模在生物分子的结构和功能分析中得到了广泛应用。数值策略的一个局限性在于，从概念上讲，将这些类型的模型纳入分子力学模拟是困难的，主要是因为原子力的分配问题。在这项理论研究中，我们首先为服从全非线性泊松-玻尔兹曼方程的分子系统推导出了麦克斯韦应力张量。我们进一步推导出了给定麦克斯韦应力张量的解析静电力公式，并讨论了这些公式与文献中发表的公式之间的关系。我们表明，从麦克斯韦应力张量推导出的公式需要一个较弱的有效性条件，适用于具有有限数量奇点的非线性泊松-玻尔兹曼系统，例如原子点电荷，以及在广泛使用的经典分段常数介电模型中存在不连续介电。
