Treecode-based generalized Born method

We have developed a treecode-based O(Nlog N) algorithm for the generalized Born (GB) implicit solvation model. Our treecode-based GB (tGB) is based on the GBr6 [J. Phys. Chem. B 111, 3055 (2007)], an analytical GB method with a pairwise descreening approximation for the R6 volume integral expression. The algorithm is composed of a cutoff scheme for the effective Born radii calculation, and a treecode implementation of the GB charge–charge pair interactions. Test results demonstrate that the tGB algorithm can reproduce the vdW surface based Poisson solvation energy with an average relative error less than 0.6% while providing an almost linear-scaling calculation for a representative set of 25 proteins with different sizes (from 2815 atoms to 65456 atoms). For a typical system of 10k atoms, the tGB calculation is three times faster than the direct summation as implemented in the original GBr6 model. Thus, our tGB method provides an efficient way for performing implicit solvent GB simulations of larger biomolecular systems at longer time scales.