Department of Molecular Biophysics and Physiology, Rush University Medical Center, Chicago, Illinois 60612, USA.
J Chem Phys. 2011 Sep 28;135(12):124107. doi: 10.1063/1.3641485.
We analyze the mathematically rigorous BIBEE (boundary-integral based electrostatics estimation) approximation of the mixed-dielectric continuum model of molecular electrostatics, using the analytically solvable case of a spherical solute containing an arbitrary charge distribution. Our analysis, which builds on Kirkwood's solution using spherical harmonics, clarifies important aspects of the approximation and its relationship to generalized Born models. First, our results suggest a new perspective for analyzing fast electrostatic models: the separation of variables between material properties (the dielectric constants) and geometry (the solute dielectric boundary and charge distribution). Second, we find that the eigenfunctions of the reaction-potential operator are exactly preserved in the BIBEE model for the sphere, which supports the use of this approximation for analyzing charge-charge interactions in molecular binding. Third, a comparison of BIBEE to the recent GBε theory suggests a modified BIBEE model capable of predicting electrostatic solvation free energies to within 4% of a full numerical Poisson calculation. This modified model leads to a projection-framework understanding of BIBEE and suggests opportunities for future improvements.
我们分析了分子静电学混合介电连续体模型的数学严谨 BIBEE（基于边界积分的静电估算）逼近，使用球形溶质中任意电荷分布的解析可解情况。我们的分析基于 Kirkwood 的使用球谐函数的解，澄清了逼近的重要方面及其与广义 Born 模型的关系。首先，我们的结果为分析快速静电模型提供了一个新的视角：将变量分离为材料性质（介电常数）和几何形状（溶质介电边界和电荷分布）。其次，我们发现反应势算子的本征函数在球体的 BIBEE 模型中得到了精确的保留，这支持了使用该逼近来分析分子结合中的电荷-电荷相互作用。第三，BIBEE 与最近的 GBε理论的比较表明，一个改进的 BIBEE 模型能够将静电溶剂化自由能预测到与全数值泊松计算相差 4%以内。这个改进的模型导致了对 BIBEE 的投影框架理解，并为未来的改进提供了机会。
