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

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 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.Thermodynamic decomposition of solvation free energies with particle mesh Ewald and long-range Lennard-Jones interactions in Grid Inhomogeneous Solvation Theory

Developing end-point methods for absolute binding free energy calculation using the Boltzmann-quasiharmonic model

“…More studies are needed to examine this further by comparing with more accurate explicit solvent based solvation free energy methods. 79–82 The main advantage of the EE-BQH approach outlined is that with this method, the different thermodynamic contributions to the free energy of binding can be decomposed into their physical contributions (translational, rotational, and torsional entropies, correlation entropies, etc. ).…”

Characterizing Protein Protonation Microstates Using Monte Carlo Sampling

“…The changes in enthalpy and entropy give insight into the nature of what changes in the reaction. Measurements of the equilibrium constant, K eq , Δ H , and Δ S are common, and there are methods to calculate these parameters from MD trajectories. − However, calculating Δ G , Δ H , and especially Δ S for complex biological molecules often leads to large uncertainty as it can be hard to sample enough states. − Here we analyze the accepted microstates in MCCE to determine the thermodynamic properties of the coupled protonation reactions of Glu35 and Asp52 in lysozyme (Figure ).…”

Characterizing protein protonation microstates using Monte Carlo sampling

“…Measurements of the equilibrium constant, Keq, ∆H and ∆S are common, and there are methods to calculate these parameters from MD trajectories. [55][56][57] However, calculating ∆G, ∆H and especially ∆S for complex biological molecules often leads to large uncertainty as it can be hard to sample enough states. [58][59][60][61][62] Here we analyze the accepted microstates in MCCE to determine the thermodynamic properties of the coupled protonation reactions of Glu35 and Asp52 in lysozyme (Figure 3).…”