A Fast and Robust Poisson-Boltzmann Solver Based on Adaptive Cartesian Grids.
A Fast and Robust Poisson-Boltzmann Solver Based on Adaptive Cartesian Grids.
复制标题
DOI：
10.1021/ct1006983
复制
发表时间：
2011-05-10
影响因子：
5.5
通讯作者：
Fenley, Marcia O.
中科院分区：
文献类型：
--
作者：
Boschitsch, Alexander H.;Fenley, Marcia O.
提出了一种自适应笛卡尔网格(ACG)的概念，用于快速、稳健地数值求解三维Poisson-Boltzmann方程(PBE)，该方程控制大规模生物分子和高电荷多生物分子组件(如核糖体和病毒)的静电相互作用。与常规3D网格和非结构化网格等竞争网格拓扑相比，ACG具有许多优势。对于非常大的生物分子和多个生物分子组件，网格点的总数比当前PBE解算器中使用的传统晶格网格少几个数量级，从而允许最终用户在台式计算机上获得准确和稳定的非线性PBE解。与基于四面体的非结构网格相比，ACG提供了一种更简单的层次网格结构，这种结构自然适合于多重网格，减少了间接寻址要求，并在有限差分模板中使用了较少的相邻节点。ACG的构建和介电/离子图的确定是直接、快速的，并且需要最少的用户干预。通过将问题重新表述为分子内部的反应场电势和外部离子溶剂区的总静电势，消除了电荷奇异性。这种方法最大限度地减少了对网格的依赖，并减少了对原子电荷点附近精细网格间距的需求。本文的技术部分包括三个部分。首先，描述了ACG及其一般生物分子几何构型。其次，推导出了该网格上PBE的离散近似。最后总结了整个解决方案的流程和多重网格的实现。给出了用基于ACG的PBE求解器得到的结果：(I)嵌入高介电性离子溶剂中的含有内点电荷的低介电球形腔--可用于这种情况的解析解，从而允许对解的精度进行严格评估；(Ii)嵌入离子溶剂中的一对低介电荷电球体以计算静电相互作用自由能作为球中心之间距离的函数；(Iii)蛋白质、核酸及其更大规模组件(如核糖体)的表面势；以及(Iv)大量蛋白质的静电溶剂化自由能及其盐敏感性--由线性和非线性Poisson-Boltzmann方程获得。后一种结果与计时一起可以作为比较不同PBE解算器的性能的基准。
An adaptive Cartesian grid (ACG) concept is presented for the fast and robust numerical solution of the 3D Poisson-Boltzmann Equation (PBE) governing the electrostatic interactions of large-scale biomolecules and highly charged multi-biomolecular assemblies such as ribosomes and viruses. The ACG offers numerous advantages over competing grid topologies such as regular 3D lattices and unstructured grids. For very large biological molecules and multi-biomolecule assemblies, the total number of grid-points is several orders of magnitude less than that required in a conventional lattice grid used in the current PBE solvers thus allowing the end user to obtain accurate and stable nonlinear PBE solutions on a desktop computer. Compared to tetrahedral-based unstructured grids, ACG offers a simpler hierarchical grid structure, which is naturally suited to multigrid, relieves indirect addressing requirements and uses fewer neighboring nodes in the finite difference stencils. Construction of the ACG and determination of the dielectric/ionic maps are straightforward, fast and require minimal user intervention. Charge singularities are eliminated by reformulating the problem to produce the reaction field potential in the molecular interior and the total electrostatic potential in the exterior ionic solvent region. This approach minimizes grid-dependency and alleviates the need for fine grid spacing near atomic charge sites. The technical portion of this paper contains three parts. First, the ACG and its construction for general biomolecular geometries are described. Next, a discrete approximation to the PBE upon this mesh is derived. Finally, the overall solution procedure and multigrid implementation are summarized. Results obtained with the ACG-based PBE solver are presented for: (i) a low dielectric spherical cavity, containing interior point charges, embedded in a high dielectric ionic solvent – analytical solutions are available for this case, thus allowing rigorous assessment of the solution accuracy; (ii) a pair of low dielectric charged spheres embedded in a ionic solvent to compute electrostatic interaction free energies as a function of the distance between sphere centers; (iii) surface potentials of proteins, nucleic acids and their larger-scale assemblies such as ribosomes; and (iv) electrostatic solvation free energies and their salt sensitivities – obtained with both linear and nonlinear Poisson-Boltzmann equation – for a large set of proteins. These latter results along with timings can serve as benchmarks for comparing the performance of different PBE solvers.
登录
查看更多内容
影响因子：
3
作者：
Boschitsch, Alexander H.;Fenley, Marcia O.
通讯作者：
Fenley, Marcia O.
影响因子：
5.5
作者：
Cai, Qin;Hsieh, Meng-Juei;Wang, Jun;Luo, Ray
通讯作者：
Luo, Ray
影响因子：
2.9
作者：
Devkota, Batsal;Petrov, Anton S.;Harvey, Stephen C.
通讯作者：
Harvey, Stephen C.
影响因子：
2.5
作者：
Aftosmis, MJ;Berger, MJ;Melton, JE
通讯作者：
Melton, JE
影响因子：
--
作者：
BONDI, A
通讯作者：
BONDI, A