Robustness and Efficiency of Poisson-Boltzmann Modeling on Graphics Processing Units

Area of Science:

• Computational biology
• Biophysics
• Scientific computing

Background:

• Poisson-Boltzmann equation (PBE) models are vital for electrostatic interactions in biochemistry, especially protein-ligand binding affinity estimation.
• Efficient PBE solvers are critical for processing numerous snapshots in binding affinity calculations.
• Existing graphics processing unit (GPU) PBE solvers use limited methods (SOR, CG) with suboptimal convergence and scaling for large biomolecules.

Purpose of the Study:

• To implement and analyze geometric multigrid (MG) solvers for PBE on GPUs for biomolecular applications.
• To evaluate the robustness and efficiency of MG on GPUs compared to existing methods.
• To develop a hybrid GPU solver balancing robustness and efficiency for PBE calculations.

Main Methods:

• Implementation of a geometric multigrid (MG) solver for the Poisson-Boltzmann equation (PBE) on GPUs.
• Analysis of MG solver performance, focusing on robustness and efficiency for complex biomolecules.
• Comparison of MG with successive over-relaxation (SOR) and conjugate gradient (CG) methods.
• Development of a hybrid solver combining MG efficiency with CG robustness.

Main Results:

• Robustness, not efficiency, is a key challenge for MG and other solvers using single precision with complex biomolecules.
• Geometric multigrid (MG) demonstrates potential for optimal PBE solving on GPUs.
• A hybrid GPU solver combining MG and CG offers a balance of efficiency and accuracy.

Conclusions:

• The developed hybrid GPU PBE solver significantly enhances computational throughput for biomolecular modeling.
• This work addresses the need for efficient and robust PBE solvers on GPUs for biochemical applications.
• The findings pave the way for improved computational efficiency in drug discovery and molecular simulations.