On regularization of charge singularities in solving the Poisson-Boltzmann equation with a smooth solute-solvent boundary.
On regularization of charge singularities in solving the Poisson-Boltzmann equation with a smooth solute-solvent boundary.
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在用平滑的溶质 - 溶剂边界求解泊松玻尔兹曼方程时，电荷奇点的正规化。
DOI：
10.3934/mbe.2021072
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发表时间：
2021-01-21
期刊：
影响因子：
--
通讯作者：
Zhao S
中科院分区：
文献类型：
--
作者：
Wang S;Alexov E;Zhao S
在求解Poisson-Boltzmann(PB)方程以分析溶质生物分子与周围溶剂与离子之间的静电相互作用时，奇异电荷的数值处理是一个巨大的挑战。众所周知，对奇异电荷的直接离散化会产生显著的误差，因此经常采用间接的方法。然而，对于溶质和溶剂被光滑边界分开的扩散界面PB模型，由于具有空间相关介电函数的基本解是难以处理的，因此还没有发展出间接的方法。在这项工作中，提出了一种新的正则化公式来解析地捕捉奇异性，这在扩散界面PB模型中是第一次。成功之处在于双重分解--除了将电势分解为库仑分量和反应场分量外，介电函数还被分成恒定的基加空间变化的部分。利用恒介电基，库仑势通过格林函数进行解析表示。去掉奇异性后，反应场势满足具有光滑源的正则化PB方程，因此数值离散简单明了。为了验证所提出的正则化方法，还引入了一个高斯卷积面(GCS)，它有效地生成了复杂蛋白质系统的扩散界面。通过考虑解析界面和GCS扩散界面，检验了所提正则化方法的性能，并与三线性方法进行了比较。所提出的GCS正则化算法在计算蛋白质的静电自由能和估计蛋白质络合物的盐亲和力方面取得了令人满意的结果。
Numerical treatment of singular charges is a grand challenge in solving the Poisson-Boltzmann (PB) equation for analyzing electrostatic interactions between the solute biomolecules and the surrounding solvent with ions. A direct discretization of singular charges is known to produce significant errors, and thus indirect approaches are often applied. However, for diffuse interface PB models in which solute and solvent are separated by a smooth boundary, no indirect approach has been developed, because the fundamental solution with a space dependent dielectric function is intractable. In this work, a novel regularization formulation is proposed to capture the singularity analytically, which is the first of its kind for diffuse interface PB models. The success lies in a dual decomposition – besides decomposing the potential into Coulomb and reaction field components, the dielectric function is also split into a constant base plus space changing part. Using the constant dielectric base, the Coulomb potential is represented analytically via Green’s functions. After removing the singularity, the reaction field potential satisfies a regularized PB equation with a smooth source, so that the numerical discretization is straightforward. To validate the proposed regularization, a Gaussian convolution surface (GCS) is also introduced, which efficiently generates a diffuse interface for complex protein systems. The performance of the proposed regularization is examined by considering both analytical and GCS diffuse interfaces, and compared with the trilinear method. The proposed GCS-regularization algorithm produces decent results in calculating electrostatic free energies of proteins and estimating salt affinities for protein complexes.
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影响因子：
5.5
作者：
Chakravorty, Arghya;Jia, Zhe;Li, Lin;Zhao, Shan;Alexov, Emil
通讯作者：
Alexov, Emil
影响因子：
5.5
作者：
Li, Lin;Li, Chuan;Zhang, Zhe;Alexov, Emil
通讯作者：
Alexov, Emil
影响因子：
5.6
作者：
LEE, B;RICHARDS, FM
通讯作者：
RICHARDS, FM
影响因子：
4.1
作者：
Egan, Raphael;Gibou, Frederic
通讯作者：
Gibou, Frederic
影响因子：
3
作者：
NICHOLLS, A;HONIG, B
通讯作者：
HONIG, B