High-productivity, high-performance workflow for virus-scale electrostatic simulations with Bempp-Exafmm

Abstract

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 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. Readers can find input data (meshes and pqr files) in a Zenodo archive, Jupyter notebooks and secondary data necessary to reproduce all the figures in the paper's GitHub repository at https://github.com/barbagroup/bempp_exafmm_paper/, and all the software in version-controlled repositories under permissive standard licenses.

TABI-PB 2.0: An Improved Version of the Treecode-Accelerated Boundary Integral Poisson-Boltzmann Solver

“…These results compare favorably with another recent computation of the Zika solvation energy on a dual 20-core CPU node using a Galerkin boundary integral discretization and an alternative version of the fast multipole method. 55 The H1N1 viral capsid has about nine times as many atoms as the Zika capsid and the ΔG solv is about 30 times lower. As mentioned, valid H1N1 triangulations could not be obtained for larger scale s, so we are unable to estimate the error at this time.…”

Towards optimal boundary integral formulations of the Poisson–Boltzmann equation for molecular electrostatics

“…The algorithm was implemented in the open-source software Bemppcl 28 for the Galerkin BEM, which interfaces with the kernel-independent FMM code ExaFMM, 19,60 and SciPy's 61 implementation of the GMRES linear solver. The tolerance of the solver was set to 10 À5 without restart.…”

“…These formulations yield a better conditioned linear system of equations and, therefore, faster convergence of the linear solver. Researchers usually choose one of these formulations, which were compared recently by Wang et al, 19 but there is no systematic study of the different formulations. Moreover, other possible BEM formulations have not been explored at all.…”

Towards optimal boundary integral formulations of the Poisson-Boltzmann equation for molecular electrostatics

“…Hence, the number of degrees of freedom in the model is the number of vertices in the surface mesh. Furthermore, the dense matrix arithmetic was accelerated with the fast multipole method (FMM) 19,25 for large problems.…”