Polarizable Simulations with Second-Order Interaction Model—Force Field and Software for Fast Polarizable Calculations: Parameters for Small Model Systems and Free Energy Calculations

Abstract

We are presenting POSSIM (POlarizable Simulations with Second order Interaction Model) – a software package and a set of parameters designed for molecular simulations. The key feature of POSSIM is that the electrostatic polarization is taken into account using a previously introduced fast formalism. This permits cutting computational cost of using the explicit polarization by about an order of magnitude. In this article, parameters for water, methane, ethane, propane, butane, methanol and NMA are introduced. These molecules are viewed as model systems for protein simulations. We have achieved our goal of ca. 0.5 kcal/mol accuracy for gas-phase dimerization energies and no more than 2% deviations in liquid state heats of vaporization and densities. Moreover, free energies of hydration of the polarizable methane, ethane and methanol have been calculated using the statistical perturbation theory. These calculations are a model for calculating protein pKa shifts and ligand binding affinities. The free energies of hydration were found to be 2.12 kcal/mol, 1.80 kcal/mol and −4.95 kcal/mol for methane, ethane and methanol, respectively. The experimentally determined literature values are 1.91 kcal/mol, 1.83 kcal/mol and −5.11 kcal/mol. The POSSIM average error in these absolute free energies of hydration is only about 0.13 kcal/mol. Using the statistical perturbation theory with polarizable force fields is not widespread, and we believe that this work opens road to further development of the POSSIM force field and its applications for obtaining accurate energies in protein-related computer modeling.

Calculating pKa values for substituted phenols and hydration energies for other compounds with the first‐order fuzzy‐border continuum solvation model

“…The calculations were carried out with the POSSIM software 8a modified to include the Fuzzy-Border (FB) continuum solvent model. The solvation energies were found as: $$\mathrm{\Delta }G(\mathit{solv},\mathit{calculated})=E(\mathit{solvated})-E(\mathit{gas}),$$ where E ( solvated ) and E ( gas ) are the computed energies of the system in the aqueous solution and in gas-phase, respectively.…”

“…All the geometry optimizations were carried out with our POSSIM software suite 8a,18 which was modified to permit the calculations with the continuum solvent.…”

“…Second, we propose an approximation to the full-scale Poisson-Boltzmann procedure which is similar to our previously developed fast second-order polarization technique for solutes and explicit solutions and pure liquids. 7,8a It truncates the self-consistent procedure of solving the complete Poisson-Boltzmann equation at either the first or the second iteration. While this method increases the computational speed as compared to the full-scale Poisson-Boltzmann formalism, its main advantage in the case of applying it to a continuum solvent is in reducing the self-consistent problem to an analytical one.…”

“…This truncation is consistent in spirit with our fast polarization technique for explicit all-atom simulations of solutes and solvents. 7,8a And the differences from the standard Poisson-Boltzmann technique have been outline above.…”

“…We have applied the first-order version of the FB method, implemented by augmenting our POSSIM software suite, 8a to calculating pKa values of substituted phenols and to finding hydration energies of 40 other molecules simulated with the OPLS-AA force field. 14,15 We have achieved an accuracy of 0.37 pH units and ca.…”