A new outer boundary formulation and energy corrections for the nonlinear Poisson-Boltzmann equation
A new outer boundary formulation and energy corrections for the nonlinear Poisson-Boltzmann equation
复制标题
DOI：
10.1002/jcc.20565
复制
发表时间：
2007-04-15
影响因子：
3
通讯作者：
Fenley, Marcia O.
中科院分区：
文献类型：
--
作者：
Boschitsch, Alexander H.;Fenley, Marcia O.
非线性Poisson-Boltzmann方程（PBE）已成功地用于预测浸没在盐水溶液中的高电荷生物聚电解质的许多静电性质。虽然已经开发了许多三维PBE的数值求解器，但在这些方法中使用的外边界处理的制定仅被松散地处理，特别是在非线性情况下。目前非线性PBE实现中的事实标准是将外边界处的电势设置为零或使用（线性）Debye-Huckel（DH）近似来估计它。然而，评估这些外边界处理如何影响整体解决方案的准确性似乎没有以前作出。正如这里将要证明的那样，在某些条件下，这两种近似都可能产生对势能和能量盐依赖性的完全错误的估计。一个相关的问题是在有限范围的网格上进行计算（例如，所有当前的有限差分和有限元实现）是来自计算网格外部的外部区域对能量和盐依赖性的贡献。这也被证明是显着的，特别是在低盐浓度下，基本上所有的贡献，过量的渗透压和离子应力能量来自这个外部区域。在本文中，作者介绍了一种新的外边界处理，是有效的线性和非线性PBE。作者还制定了能量修正，以考虑来自计算域之外的贡献。最后，作者还考虑了一般离子排斥层对生物分子静电的影响。结果表明，虽然这些层往往会增加表面的静电势，在生理盐的条件下和高净电荷的影响，对过量渗透压项，这是一个衡量盐的依赖性的总静电自由能，是弱的。为了便于演示，并允许非常精细的分辨率和/或大的计算域被认为是，注意力被限制到一维球对称非线性PBE。虽然几何上的限制，建模的原则，但扩展到一般PBE求解器中讨论的附录。一维模型也可用于基准测试和验证现有PBE求解器的盐效应预测能力。(C)2007 Wiley Periodicals，Inc.
The nonlinear Poisson-Boltzmann equation (PBE) has been successfully used for the prediction of numerous electrostatic properties of highly charged biopolyelectrolytes immersed in aqueous salt solutions. While numerous numerical solvers for the 3D PBE have been developed, the formulation of the outer boundary treatments used in these methods has only been loosely addressed, especially in the nonlinear case. The de facto standard in current nonlinear PBE implementations is to either set the potential at the outer boundaries to zero or estimate it using the (linear) Debye-Huckel (DH) approximation. However, an assessment of how these outer boundary treatments affect the overall solution accuracy does not appear to have been previously made. As will be demonstrated here, both approximations can, under certain conditions, produce completely erroneous estimates of the potential and energy salt dependencies. A related concern for calculations carried out on grids of finite extent (e.g., all current finite difference and finite element implementations) is the contribution to the energy and salt dependence from the exterior region outside the computational grid. This too is shown to be significant, especially at low salt concentration where essentially all of the contributions to the excess osmotic pressure and ion stress energies originate from this exterior region. In this paper the authors introduce a new outer boundary treatment that is valid for both the linear and nonlinear PBE. The authors also formulate energy corrections to account for contributions from outside the computational domain. Finally, the authors also consider the effects of general ion exclusion layers upon biomolecular electrostatics. It is shown that while these layers tend to increase the surface electrostatic potential, under physiological salt conditions and high net charges their effect on the excess osmotic pressure term, which is a measure of the salt dependence of the total electrostatic free energy, is weak. To facilitate presentation and allow very fine resolutions and/or large computational domains to be considered, attention is restricted to the 1D spherically symmetric nonlinear PBE. Though geometrically limited, the modeling principles nevertheless extend to general PBE solvers as discussed in the Appendix. The 1D model can also be used to benchmark and validate the salt effect prediction capabilities of existing PBE solvers. (C) 2007 Wiley Periodicals, Inc.