Accepted: Biomolecular electrostatics solver using Python and GPUs
Surface charge plot on a lysozyme molecule, obtained using the PyGBe code.
Submitted: 20 September, 2013. Accepted: 24 October, 2013.
This paper presents a study of the effect of solvent-filled cavities and Stern layers in a biomolecular electrostatics solver based on a boundary integral formulation. The tool for this study was the PyGBe code: a solver for biomolecular electrostatics using Python, GPUs and boundary elements. To determine the impact on accuracy of including or not features like cavities and Stern layers, we compared with a community code based on finite-difference solution of the Poisson-Boltzmann equation. Rigorous comparisons like the one we offer are scarce and we bring to bear in this work our experience with verification and convergence analysis of numerical methods.
- "A biomolecular electrostatics solver using Python, GPUs and boundary elements that can handle solvent-filled cavities and Stern layers", Christopher D. Cooper, Jaydeep P. Bardhan, L. A. Barba. Comput. Phys. Comm., 185(3):720–729 (March 2014). 10.1016/j.cpc.2013.10.028 // Preprint arXiv:1309.4018 // figshare: convergence with sphere // figshare: lysozyme // figshare: trypsin-BPTI complex // figshare: peptide-RNA complex // code repository //
Published online 4 November, 2013.
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.
Open data
- "Binding energy of peptide-RNA complex with PyGBe and APBS", Christopher D. Cooper, Jaydeep P. Bardhan, L. A. Barba. (September 2013). 10.6084/m9.figshare.799704 // Preprint arXiv:1309.4018
File bundle including data, figures and plotting scripts of solvation energy and binding energy calculations for peptide-RNA complex using PyGBe and APBS. On figshare under CC-BY.
- "Binding energy of trypsin-BPTI complex with PyGBe and APBS", Christopher D. Cooper, Jaydeep P. Bardhan, L. A. Barba. (September 2013). 10.6084/m9.figshare.799703 // Preprint arXiv:1309.4018
File bundle including data, figures and plotting scripts of solvation energy and binding energy calculations for trypsin-BPTI complex using PyGBe and APBS. On figshare under CC-BY.
- "Convergence and time to solution of PyGBe with lysozyme molecule", Christopher D. Cooper, Jaydeep P. Bardhan, L. A. Barba, . (September 2013). 10.6084/m9.figshare.799702 // Preprint arXiv:1309.4018
File bundle including data, figures and plotting scripts of convergence and time-to-solution versus error for PyGBe and APBS using a lysozyme molecule. On figshare under CC-BY.
- "Convergence of PyGBE with Kirkwood sphere", Christopher D. Cooper, Jaydeep P. Bardhan, L. A. Barba. (September 2013). 10.6084/m9.figshare.799692 // Preprint arXiv:1309.4018
File bundle including data, figures and plotting scripts of convergence results for PyGBe and APBS using a spherical molecule. On figshare under CC-BY.
Links
Acknowledgements
This research is made possible by support from the Office of Naval Research, Applied Computational Analysis Program, N00014-11-1-0356. LAB also acknowledges support from NSF CAREER award OCI-1149784.