A biomolecular electrostatics solver using Python, GPUs and boundary elements that can handle solvent-filled cavities and Stern layers

Abstract

The continuum theory applied to bimolecular electrostatics leads to an implicit-solvent model governed by the Poisson-Boltzmann equation. Solvers relying on a boundary integral representation typically do not consider features like solvent-filled cavities or ion-exclusion (Stern) layers, due to the added difficulty of treating multiple boundary surfaces. This has hindered meaningful comparisons with volume-based methods, and the effects on accuracy of including these features has remained unknown. This work presents a solver called PyGBe that uses a boundary-element formulation and can handle multiple interacting surfaces. It was used to study the effects of solvent-filled cavities and Stern layers on the accuracy of calculating solvation energy and binding energy of proteins, using the well-known APBS finite-difference code for comparison. The results suggest that if required accuracy for an application allows errors larger than about 2%, then the simpler, single-surface model can be used. When calculating binding energies, the need for a multi-surface model is problem-dependent, becoming more critical when ligand and receptor are of comparable size. Comparing with the APBS solver, the boundary-element solver is faster when the accuracy requirements are higher. The cross-over point for the PyGBe code is in the order of 1-2% error, when running on one GPU card (NVIDIA Tesla C2075), compared with APBS running on six Intel Xeon CPU cores. PyGBe achieves algorithmic acceleration of the boundary element method using a treecode, and hardware acceleration using GPUs via PyCuda from a user-visible code that is all Python. The code is open-source under MIT license.