MINIMIZATION OF ELECTROSTATIC FREE ENERGY AND THE POISSON-BOLTZMANN EQUATION FOR MOLECULAR SOLVATION WITH IMPLICIT SOLVENT
MINIMIZATION OF ELECTROSTATIC FREE ENERGY AND THE POISSON-BOLTZMANN EQUATION FOR MOLECULAR SOLVATION WITH IMPLICIT SOLVENT
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DOI：
10.1137/080712350
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发表时间：
2009-01-01
影响因子：
2
通讯作者：
Li, Bo
中科院分区：
文献类型：
--
作者：
Li, Bo
在带电分子（溶质）溶剂化的隐式溶剂描述中，静电自由能是溶剂中离子浓度的函数。电荷密度由溶质原子的点电荷和浓度决定，静电势由具有可变介电系数的泊松方程决定。这样的自由能功能被认为是在这项工作中的点离子和离子的情况下，具有均匀的有限尺寸。它被证明为每种情况下，存在一个独特的一组平衡浓度，最大限度地减少自由能，并通过平衡静电势给出相应的玻尔兹曼分布。这样的分布被发现依赖于泊松方程的边界数据。点态上限和下限的自由能最小化浓度。证明了由此产生的Poisson-Boltzmann方程的边值问题的存在性和唯一性，该方程决定了平衡静电势。最后，证明了两种不同形式的边值问题的等价性。
In an implicit-solvent description of the solvation of charged molecules (solutes), the electrostatic free energy is a functional of concentrations of ions in the solvent. The charge density is determined by such concentrations together with the point charges of the solute atoms, and the electrostatic potential is determined by the Poisson equation with a variable dielectric coefficient. Such a free-energy functional is considered in this work for both the case of point ions and that of ions with a uniform finite size. It is proved for each case that there exists a unique set of equilibrium concentrations that minimize the free energy and that are given by the corresponding Boltzmann distributions through the equilibrium electrostatic potential. Such distributions are found to depend on the boundary data for the Poisson equation. Pointwise upper and lower bounds are obtained for the free-energy minimizing concentrations. Proofs are also given for the existence and uniqueness of the boundary-value problem of the resulting Poisson-Boltzmann equation that determines the equilibrium electrostatic potential. Finally, the equivalence of two different forms of such a boundary-value problem is proved.