Grid Inhomogeneous Solvation Theory (GIST) maps out solvation thermodynamic properties on a
fine meshed grid and provides a statistical mechanical formalism for thermodynamic end-state
calculations. However, differences in how long-range non-bonded interactions are calculated in
molecular dynamics engines and in the current implementation of GIST have prevented precise
comparisons between free energies estimated using GIST and those from other free energy methods
such as thermodynamic integration (TI). Here, we address this by presenting PME-GIST, a
formalism by which particle mesh Ewald (PME) based electrostatic energies and long-range
Lennard-Jones (LJ) energies are decomposed and assigned to individual atoms and the
corresponding voxels they occupy in a manner consistent with the GIST approach. PME-GIST yields
potential energy calculations that are precisely consistent with modern simulation engines and
performs these calculations at a dramatically faster speed than prior implementations. Here, we
apply PME-GIST end-states analyses to 32 small molecules whose solvation free energies are close
to evenly distributed from 2 kcal/mol to -17 kcal/mol and obtain solvation energies consistent with TI
calculations (R2 = 0.99, mean unsigned difference 0.8 kcal/mol). We also estimate the entropy
contribution from the 2nd and higher order entropy terms that are truncated in GIST by the differences
between entropies calculated in TI and GIST. With a simple correction for the high order entropy
terms, PME-GIST obtains solvation free energies that are highly consistent with TI calculations (R2
= 0.99, mean unsigned difference = 0.4 kcal/mol) and experimental results (R2 = 0.88, mean
unsigned difference = 1.4 kcal/mol). The precision of PME-GIST also enables us to show that the
solvation free energy of small hydrophobic and hydrophilic molecules can be largely understood
based on perturbations of the solvent in a region extending a few solvation shells from the solute.
We have integrated PME-GIST into the open-source molecular dynamics analysis software
CPPTRAJ.
Particle Mesh Ewald for Molecular Dynamics in OpenCL on an FPGA Cluster
