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首页> 外文期刊>Journal of chemical theory and computation: JCTC >Using Correlated Monte Carlo Sampling for Efficiently Solving the Linearized Poisson-Boltzmann Equation Over a Broad Range of Salt Concentration
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Using Correlated Monte Carlo Sampling for Efficiently Solving the Linearized Poisson-Boltzmann Equation Over a Broad Range of Salt Concentration

机译：使用相关的蒙特卡洛采样有效地求解宽盐浓度范围内的线性化Poisson-Boltzmann方程

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摘要

Dielectric continuum or implicit solvent models provide a significant reduction in computational cost when accounting for the salt-mediated electrostatic interactions of biomolecules immersed in an ionic environment. These models, in which the solvent and ions are replaced by a dielectric continuum, seek to capture the average statistical effects of the ionic solvent, while the solute is treated at the atomic level of detail. For decades, the solution of the three-dimensional Poisson-Boltzmann equation (PBE), which has become a standard implicit-solvent tool for assessing electrostatic effects in biomolecular systems, has been based on various deterministic numerical methods. Some deterministic PBE algorithms have drawbacks, which include a lack of properly assessing their accuracy, geometrical difficulties caused by discretization, and for some problems their cost in both memory and computation time. Our original stochastic method resolves some of these difficulties by solving the PBE using the Monte Carlo method (MCM). This new approach to the PBE is capable of efficiently solving complex, multidomain, and salt-dependent problems in biomolecular continuum electrostatics to high precision. Here, we improve upon our novel stochastic approach by simultaneouly computing electrostatic potential and solvation free energies at different ionic concentrations through correlated Monte Carlo (MC) sampling. By using carefully constructed correlated random walks in our algorithm, we can actually compute the solution to a standard system including the linearized PBE (LPBE) at all salt concentrations of interest, simultaneously. This approach not only accelerates our MCPBE algorithm, but seems to have cost and accuracy advantages over deterministic methods as well. We verify the effectiveness of this technique by applying it to two common electrostatic computations: the electrostatic potential and polar solvation free energy for calcium binding proteins that are compared to similar results obtained using mature deterministic PBE methods.
机译：当考虑到浸没在离子环境中的生物分子的盐介导的静电相互作用时，介电连续体或隐式溶剂模型可显着降低计算成本。这些模型（其中溶剂和离子被电介质连续体代替）试图捕获离子溶剂的平均统计效果，而溶质则在原子的详细水平上得到处理。数十年来，基于各种确定性数值方法的三维Poisson-Boltzmann方程（PBE）的解决方案已成为评估生物分子系统中静电效应的标准隐式溶剂工具。一些确定性的PBE算法有一些缺点，包括缺乏正确评估其准确性，因离散而导致的几何困难以及某些问题的存储和计算时间成本。我们最初的随机方法通过使用蒙特卡洛方法（MCM）解决PBE，解决了其中一些难题。这种新的PBE方法能够高效地解决生物分子连续体静电中复杂，多域和盐依赖性的问题。在这里，我们通过相关的蒙特卡洛（MC）采样同时计算不同离子浓度下的静电势和溶剂化自由能，从而改进了我们的新型随机方法。通过在我们的算法中使用精心构造的相关随机游动，我们实际上可以同时计算包括所有感兴趣的盐浓度下的线性化PBE（LPBE）在内的标准系统的解。这种方法不仅加速了我们的MCPBE算法，而且似乎比确定性方法具有成本和准确性方面的优势。我们通过将其应用于两种常见的静电计算来验证该技术的有效性：钙结合蛋白的静电势和极性溶剂化自由能与使用成熟确定性PBE方法获得的相似结果进行比较。

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