Thermodynamic Decomposition of Solvation Free Energies with Particle Mesh Ewald and Long-Range Lennard-Jones Interactions in Grid Inhomogeneous Solvation Theory

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 nonbonded 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-state 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 second 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.