Exact analytical algorithm for solvent accessible surface area and derivatives in implicit solvent molecular simulations on GPUs

In this paper, we present dSASA (differentiable SASA), an exact geometric method to calculate solvent accessible surface area (SASA) analytically along with atomic derivatives on GPUs. The atoms in a molecule are first assigned to tetrahedra in groups of four atoms by Delaunay tetrahedrization adapted for efficient GPU implementation and the SASA values for atoms and molecules are calculated based on the tetrahedrization information and inclusion-exclusion method. The SASA values from the numerical icosahedral-based method can be reproduced with more than 98% accuracy for both proteins and RNAs. Having been implemented on GPUs and incorporated into the software Amber, we can apply dSASA to implicit solvent molecular dynamics simulations with inclusion of this nonpolar term. The current GPU version of GB/SA simulations has been accelerated up to nearly 20-fold compared to the CPU version, outperforming LCPO, a commonly used, fast algorithm for calculating SASA, as the system size increases. While we focus on the accuracy of the SASA calculations for proteins and nucleic acids, we also demonstrate stable GB/SA MD mini-protein simulations.