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 PB solver based on Exafmm, a fast multipole method (FMM) library, and Bempp, a Galerkin boundary element method (BEM) package.Bempp-Exafmm tightly integrates an easy-to-use Python interface with well-optimized computational kernels that are written in compiled languages. Thanks to Python's rich ecosystem in scientific computing, users can perform PB simulations interactively via Jupyter notebooks, which opens up the possibility for faster prototyping and analyzing. We provide results showcasing the capability of our software, confirming correctness, and evaluating its performance with problem sizes between 8,000 and 2 million boundary elements. A small 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).

中文翻译：

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使用Bempp-Exafmm进行病毒级静电仿真的高生产率，高性能工作流程

生物分子静电是蛋白质功能以及影响蛋白质功能的化学过程的关键。由Poisson-Boltzmann（PB）方程式表示的隐式溶剂模型可以提供比完全原子模型更少的计算能力的洞察力，从而使更多的研究人员可以进行大型系统研究（例如病毒规模）。本文基于快速多极方法（FMM）库Exafmm和Galerkin边界元方法（BEM）软件包Bempp提出了一种高生产率，高性能的PB求解器.Bempp-Exafmm紧密集成了易于使用的功能Python与以编译语言编写的经过优化的计算内核相接口。由于Python具有丰富的科学计算生态系统，因此用户可以通过Jupyter笔记本交互地执行PB仿真，这为更快的原型设计和分析开辟了可能性。我们提供的结果展示了我们软件的功能，确认了正确性并评估了问题容量在8,000到200万个边界元素之间的软件的性能。一项针对代数条件对边界积分公式的两个变体进行比较的小型研究表明，此交互式计算平台的功能仅需几行代码即可给出有用的答案。作为解决方案验证的一种形式，具有球形几何图形和真实生物结构（5PTI）的网格细化研究确认，对于$ N $边界元素，会以预期的$ 1 / N $速率收敛。性能结果包括计时，故障和计算复杂度。Exafmm的评估速度只有几秒钟，可获取数千万个点，和$ \ mathcal {O}（N）$缩放比例。这样就可以在单个计算节点（双20核Intel Xeon Gold 6148）上以80分钟的运行时间来计算Zika病毒的溶剂化自由能，该自由能由160万个原子和1000万个边界元素表示。