Nonlocal Electrostatics in Spherical Geometries Using Eigenfunction Expansions of Boundary-Integral Operators.
Nonlocal Electrostatics in Spherical Geometries Using Eigenfunction Expansions of Boundary-Integral Operators.
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DOI：
10.1515/mlbmb-2015-0001
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发表时间：
2015-01
影响因子：
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通讯作者：
Brune P
中科院分区：
文献类型：
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作者：
Bardhan JP;Knepley MG;Brune P
在本文中，我们提出了一个精确的，无限级数解的洛伦兹非局部连续静电场的任意电荷分布在一个球形溶质。我们的方法依赖于两个关键步骤：（1）使用边界积分方程重新制定的PDE问题，和（2）对角化的边界积分算子使用的事实，他们的本征函数是表面球谐函数。为了介绍这种不常见的方法在可分离的几何形状的计算，我们首先重新推导柯克伍德的经典结果，蛋白质包围同心的纯水离子排斥（斯特恩）层，然后稀电解质，这是建模与线性化的泊松-玻尔兹曼方程。本征函数展开方法提供了一种计算有效的方法来测试非局部模型的一些含义，包括估计非局部长度尺度参数λ的合理范围。我们的研究结果表明，非局部溶剂响应可能有助于减少需要非常高的介电常数在计算pH值依赖的蛋白质的行为，虽然需要更复杂的非局部模型来解决这个问题。我们的方法的开源MATLAB实现可以在网上免费获得。
In this paper, we present an exact, infinite-series solution to Lorentz nonlocal continuum electrostatics for an arbitrary charge distribution in a spherical solute. Our approach relies on two key steps: (1) re-formulating the PDE problem using boundary-integral equations, and (2) diagonalizing the boundary-integral operators using the fact that their eigenfunctions are the surface spherical harmonics. To introduce this uncommon approach for calculations in separable geometries, we first re-derive Kirkwood’s classic results for a protein surrounded concentrically by a pure-water ion-exclusion (Stern) layer and then a dilute electrolyte, which is modeled with the linearized Poisson–Boltzmann equation. The eigenfunction-expansion approach provides a computationally efficient way to test some implications of nonlocal models, including estimating the reasonable range of the nonlocal length-scale parameter λ. Our results suggest that nonlocal solvent response may help to reduce the need for very high dielectric constants in calculating pH-dependent protein behavior, though more sophisticated nonlocal models are needed to resolve this question in full. An open-source MATLAB implementation of our approach is freely available online.