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

Lieyang Chen; Anthony Cruz; Daniel R Roe; Andrew C Simmonett; Lauren Wickstrom; Nanjie Deng; Tom Kurtzman

doi:10.1021/acs.jctc.0c01185

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

J Chem Theory Comput. 2021 May 11;17(5):2714-2724. doi: 10.1021/acs.jctc.0c01185. Epub 2021 Apr 8.

Authors

Lieyang Chen^{1

2}, Anthony Cruz^{1

3}, Daniel R Roe⁴, Andrew C Simmonett⁴, Lauren Wickstrom⁵, Nanjie Deng⁶, Tom Kurtzman^{1

2

3}

Affiliations

¹ Department of Chemistry, Lehman College, The City University of New York, 250 Bedford Park Boulevard West, Bronx, New York 10468, United States.
² Ph.D. Program in Biochemistry, The Graduate Center of The City University of New York, New York, New York 10016, United States.
³ Ph.D. Program in Chemistry, The Graduate Center of The City University of New York, New York, New York 10016, United States.
⁴ Laboratory of Computational Biology, National Institutes of Health - National Heart, Lung and Blood Institute, Bethesda, Maryland 20892, United States.
⁵ Department of Science, Borough of Manhattan Community College, The City University of New York, New York, New York 10007, United States.
⁶ Department of Chemistry and Physical Sciences, Pace University, New York, New York 10038, United States.

Abstract

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.

Grants and funding

R01 GM100946/GM/NIGMS NIH HHS/United States