A treecode-accelerated boundary integral Poisson-Boltzmann solver for electrostatics of solvated biomolecules
A treecode-accelerated boundary integral Poisson-Boltzmann solver for electrostatics of solvated biomolecules
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DOI：
10.1016/j.jcp.2013.03.056
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发表时间：
2013-08-15
影响因子：
4.1
通讯作者：
Krasny，Robert
中科院分区：
文献类型：
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作者：
Geng，Weihua;Krasny，Robert
我们提出了一种树代码加速边界积分（TABI）求解器，用于由线性泊松-玻尔兹曼方程描述的溶剂化生物分子的静电。该方法对分子表面上的静电势及其法向导数采用良好条件的边界积分公式。对表面进行三角剖分，并通过质心配置对积分方程进行离散化。线性系统通过 GMRES 迭代求解，矩阵向量乘积通过笛卡尔树代码执行，这将成本从 O(N2) 降低到 O(NlogN)，其中 N 是三角剖分中的面数。 TABI 求解器用于计算柯克伍德球和溶剂化蛋白质两种情况下的静电溶剂化能。我们展示了错误、CPU 时间和内存使用情况，并比较了 Poisson-Boltzmann 和 Poisson 方程的结果。我们证明了树代码近似误差可以小于离散化误差，并且我们比较了树代码的两个版本，一种具有均匀簇，一种具有适应分子表面的非均匀簇。对于蛋白质测试案例，我们将 TABI 结果与使用基于网格的 APBS 代码获得的结果进行比较，并且我们还使用最多八个处理器进行并行 TABI 模拟。我们发现 TABI 求解器表现出良好的串行和并行性能，并且具有相对简单的实现、高效的内存使用和几何适应性。
We present a treecode-accelerated boundary integral (TABI) solver for electrostatics of solvated biomolecules described by the linear Poisson–Boltzmann equation. The method employs a well-conditioned boundary integral formulation for the electrostatic potential and its normal derivative on the molecular surface. The surface is triangulated and the integral equations are discretized by centroid collocation. The linear system is solved by GMRES iteration and the matrix–vector product is carried out by a Cartesian treecode which reduces the cost from O(N2) to O(NlogN), where N is the number of faces in the triangulation. The TABI solver is applied to compute the electrostatic solvation energy in two cases, the Kirkwood sphere and a solvated protein. We present the error, CPU time, and memory usage, and compare results for the Poisson–Boltzmann and Poisson equations. We show that the treecode approximation error can be made smaller than the discretization error, and we compare two versions of the treecode, one with uniform clusters and one with non-uniform clusters adapted to the molecular surface. For the protein test case, we compare TABI results with those obtained using the grid-based APBS code, and we also present parallel TABI simulations using up to eight processors. We find that the TABI solver exhibits good serial and parallel performance combined with relatively simple implementation, efficient memory usage, and geometric adaptability.