  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.
