Acceleration of Linear Finite-Difference Poisson–Boltzmann Methods on Graphics Processing Units

Abstract

Electrostatic interactions play crucial roles in biophysical processes such as protein folding and molecular recognition. Poisson-Boltzmann equation (PBE)-based models have emerged as widely used in modeling these important processes. Though great efforts have been put into developing efficient PBE numerical models, challenges still remain due to the high dimensionality of typical biomolecular systems. In this study, we implemented and analyzed commonly used linear PBE solvers for the ever-improving graphics processing units (GPU) for biomolecular simulations, including both standard and preconditioned conjugate gradient (CG) solvers with several alternative preconditioners. Our implementation utilizes standard Nvidia® CUDA libraries cuSPARSE, cuBLAS, and CUSP. Extensive tests show that good numerical accuracy can be achieved given that the single precision is often used for numerical applications on GPU platforms. The optimal GPU performance was observed with the Jacobi-preconditioned CG solver, with a significant speedup over standard CG solver on CPU in our diversified test cases. Our analysis further shows that different matrix storage formats also considerably affect the efficiency of different linear PBE solvers on GPU, with the diagonal format best suited for our standard finite-difference linear systems. Further efficiency may be possible with matrix-free operations and integrated grid stencil setup specifically tailored for the banded matrices in PBE-specific linear systems.

Water models for biomolecular simulations

“…A number of numerical PB solvers are available for solving the PB equation to obtain solvation energy for biomolecules of any shape, including web servers, as well as recent GPU‐accelerated implementations and fast solvers designed for restricted geometries . Some of these implementations are available in major modeling packages such as AMBER or CHARMM .…”

Recent Developments and Applications of the MMPBSA Method

“…Their results demonstrate the potential for the NMPBE to be a better predictor of electrostatic solvation and binding free energies compared to the standard PBE. It is worth noting that there has been a community wide push to explore alternative hardware for biomolecular simulations, such as the graphics processing units (GPU), which have a parallel architecture and are suited for high-performance computation with dense data parallelism (Colmenares et al, 2014a , b ; Qi R. et al, 2017 ). A finite difference scheme with the successive over-relaxation method was implemented on the CUDA-based GPUs in the DelPhi package, which achieved a speedup of ~10 times in the linear and non-linear cases (Colmenares et al, 2014b ).…”

“…A finite difference scheme with the successive over-relaxation method was implemented on the CUDA-based GPUs in the DelPhi package, which achieved a speedup of ~10 times in the linear and non-linear cases (Colmenares et al, 2014b ). More recently, Qi et al implemented and analyzed commonly used linear PBE solvers on CUDA GPUs for biomolecular simulations, including both standard and preconditioned conjugate gradient (CG) solvers with several alternative preconditioners (Qi R. et al, 2017 ). After extensive testing, the optimal GPU performance was observed using the Jacobi-preconditioned CG solver with a significant speedup that was up to 50 times faster than the standard CG solver on CPU.…”

An efficient second‐order poisson–boltzmann method

“…A BiCG linear system solver for GPUs was also implemented using the Nvidia CUDA Sparse Matrix (cuSPARSE) library, which provides basic linear algebra procedures for sparse matrix operations . The CSR matrix format was used for the nonsymmetric coefficient matrix as in our previous publication . All GPU and CPU tests were conducted on a dedicated compute node with two NVIDIA TITAN Xp GPU cards, one Intel Xeon E5‐1620 v3 CPU, and 16GB main memory.…”

“…89 The CSR matrix format was used for the non-symmetric coefficient matrix as in our previous publication. 90 All GPU and CPU tests were conducted on a dedicated compute node with two NVIDIA TITAN Xp GPU cards, one Intel Xeon E5–1620 v3 CPU, and 16GB main memory. Our time measurements for both solvers include all execution time of the solver routines, i.e.…”