用 Legendre 变换的泊松-玻尔兹曼静电进行变量隐式求解

IF 2.9 3区 综合性期刊 Q1 MULTIDISCIPLINARY SCIENCES
Zunding Huang, Bo Li
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引用次数: 0

摘要

变分隐含溶剂模型(VISM)是一种高效的生物分子相互作用方法,其中静电相互作用至关重要。介质边界(即溶质-溶剂界面)的总 VISM 自由能由界面能、溶质-溶剂相互作用能和介质静电能组成。最后一部分是静电势的经典凹面泊松-波尔兹曼(PB)能量函数的最大值,最大值是受 PB 方程支配的平衡静电势。为了保证能量最小化的一致性和计算的稳定性,我们在此提出另一种方法,即最小化溶质区域内受高斯定律约束的所有介电位移的凸勒根变换泊松-玻尔兹曼(LTPB)静电能量函数。对可积分和离散的溶质电荷密度都进行了处理,并建立了 LTPB 和 PB 函数的对偶性。为 LTPB 函数的约束最小化设计了一种惩罚方法。在应用于生物分子相互作用时,我们以迭代方式最小化总 VISM 自由能,同时在迭代的每一步中最小化 LTPB 能量。结果表明了这种最小化算法的收敛性。我们对单个离子溶解的数值结果表明,LTPB 的性能优于 PB 公式,为高效生物分子模拟提供了可能。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Variational implicit solvation with Legendre-transformed Poisson–Boltzmann electrostatics

The variational implicit-solvent model (VISM) is an efficient approach to biomolecular interactions, where electrostatic interactions are crucial. The total VISM free energy of a dielectric boundary (i.e. solute–solvent interface) consists of the interfacial energy, solute–solvent interaction energy and dielectric electrostatic energy. The last part is the maximum value of the classical and concave Poisson–Boltzmann (PB) energy functional of electrostatic potentials, with the maximizer being the equilibrium electrostatic potential governed by the PB equation. For the consistency of energy minimization and computational stability, here we propose alternatively to minimize the convex Legendre-transformed Poisson–Boltzmann (LTPB) electrostatic energy functional of all dielectric displacements constrained by Gauss’ Law in the solute region. Both integrable and discrete solute charge densities are treated, and the duality of the LTPB and PB functionals is established. A penalty method is designed for the constrained minimization of the LTPB functional. In application to biomolecular interactions, we minimize the total VISM free energy iteratively, while in each step of such iteration, minimize the LTPB energy. Convergence of such a min–min algorithm is shown. Our numerical results on the solvation of a single ion indicate that the LTPB performs better than the PB formulation, providing possibilities for efficient biomolecular simulations.

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来源期刊
CiteScore
6.40
自引率
5.70%
发文量
227
审稿时长
3.0 months
期刊介绍: Proceedings A has an illustrious history of publishing pioneering and influential research articles across the entire range of the physical and mathematical sciences. These have included Maxwell"s electromagnetic theory, the Braggs" first account of X-ray crystallography, Dirac"s relativistic theory of the electron, and Watson and Crick"s detailed description of the structure of DNA.
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