Performance of a GPU-based Direct Summation Algorithm for Computation of Small Angle Scattering Profile

Small Angle Scattering (SAS) of X-rays or neutrons is an experimental technique that provides valuable structural information for biological macromolecules under physiological conditions and with no limitation on the molecular size. In order to refine molecular structure against experimental SAS data, ab initio prediction of the scattering profile must be recomputed hundreds of thousands of times, which involves the computation of the sinc kernel over all pairs of atoms in a molecule. The quadratic computational complexity of predicting the SAS profile limits the size of the molecules and and has been a major impediment for integration of SAS data into structure refinement protocols. In order to significantly speed up prediction of the SAS profile we present a general purpose graphical processing unit (GPU) algorithm, written in OpenCL, for the summation of the sinc kernel (Debye summation) over all pairs of atoms. This program is an order of magnitude faster than a parallel CPU algorithm, and faster than an FMM-like approximation method for certain input domains. We show that our algorithm is currently the fastest method for performing SAS computation for small and medium size molecules (around 50000 atoms or less). This algorithm is critical for quick and accurate SAS profile computation of elongated structures, such as DNA, RNA, and sparsely spaced pseudo-atom molecules.