CUDA-accelerated protein electrostatics in linear space

Abstract

Protein interactions are a key for understanding biological function and processes. Among interaction terms, molecular electrostatics is the dominant influencing factor on the long-range visibility of interaction partners. However, accurate electrostatic models are often computationally expensive or require unsatisfiable amounts of memory. Here we present implicit, yet exact representations for the notoriously dense and asymmetric system matrices of boundary element methods (BEM), exemplified on the case of nonlocal protein electrostatics. Our representations only require a small and constant number of floating-point values per surface element and, thus, yield BEM systems for protein surface meshes with hundreds of millions of elements even in strictly memory-limited environments such as hardware accelerators. We provide reference implementations for the Julia and Impala programming languages, including CUDA-accelerated matrix–vector products for our implicit systems. Additionally, we provide CUDA-accelerated BEM solvers for local and nonlocal protein electrostatics that can process real-world biomolecular systems previously inaccessible with exact BEM systems in a matter of minutes.