Biomolecular electrostatics is key in protein function and the chemical processes affecting it.Implicit-solvent models expressed by the Poisson-Boltzmann (PB) equation can provide insights with less computational power than full atomistic models, making large-system studies -- at the scale of viruses, for example -- accessible to more researchers. This paper presents a high-productivity and high-performance computational workflow combining Exafmm, a fast multipole method (FMM) library, and Bempp, a Galerkin boundary element method (BEM) package. It integrates an easy-to-use Python interface with well-optimized computational kernels that are written in compiled languages. Researchers can run PB simulations interactively via Jupyter notebooks, enabling faster prototyping and analyzing. We provide results that showcase the capability of the software, confirm correctness, and evaluate its performance with problem sizes between 8,000 and 2 million boundary elements. A study comparing two variants of the boundary integral formulation in regards to algebraic conditioning showcases the power of this interactive computing platform to give useful answers with just a few lines of code. As a form of solution verification, mesh refinement studies with a spherical geometry as well as with a real biological structure (5PTI) confirm convergence at the expected $1/N$ rate, for $N$ boundary elements. Performance results include timings, breakdowns, and computational complexity. Exafmm offers evaluation speeds of just a few seconds for tens of millions of points, and $\mathcal{O}(N)$ scaling. This allowed computing the solvation free energy of a Zika virus, represented by 1.6 million atoms and 10 million boundary elements, at 80-min runtime on a single compute node (dual 20-core Intel Xeon Gold 6148). All results in the paper are presented with utmost care for reproducibility.
翻译:生物分子电流是蛋白质功能和影响它的化学过程的关键。 Poisson- Boltzmann (PB) 等方程式所展示的“ 溶解” 模型可以提供比完整原子模型更低的计算能力洞察力, 使大型系统研究 -- -- 例如病毒规模的研究 -- -- 可供更多的研究人员使用。 本文展示了一个高生产率和高性能的计算工作流程, 包括Exafmm( 快速多极方法( FMM) 库) 和 Bempp( 一个 Galerkin 边界要素( BEM) 软件包 。 它将一个简单到用Nython( Python) 方程式界面的简单解析解析。 研究人员可以通过 Jupypyter 笔记( 快速解析) 进行PBBM模拟, 我们提供的结果展示软件的能力, 证实正确性, 评估其问题大小在8,000万到200万个边界元素之间。 一项研究比较边界组合的两种变量, 用来在数值- 平价值内展示这个精确的解算值的解算结果。