Estimating Translational and Orientational Entropies Using the k-Nearest Neighbors Algorithm.

David J Huggins

doi:10.1021/ct500415g

Abstract

Inhomogeneous fluid solvation theory (IFST) and free energy perturbation (FEP) calculations were performed for a set of 20 solutes to compute the hydration free energies. We identify the weakness of histogram methods in computing the IFST hydration entropy by showing that previously employed histogram methods overestimate the translational and orientational entropies and thus underestimate their contribution to the free energy by a significant amount. Conversely, we demonstrate the accuracy of the k-nearest neighbors (KNN) algorithm in computing these translational and orientational entropies. Implementing the KNN algorithm within the IFST framework produces a powerful method that can be used to calculate free-energy changes for large perturbations. We introduce a new KNN approach to compute the total solute-water entropy with six degrees of freedom, as well as the translational and orientational contributions. However, results suggest that both the solute-water and water-water entropy terms are significant and must be included. When they are combined, the IFST and FEP hydration free energies are highly correlated, with an R(2) of 0.999 and a mean unsigned difference of 0.9 kcal/mol. IFST predictions are also highly correlated with experimental hydration free energies, with an R(2) of 0.997 and a mean unsigned error of 1.2 kcal/mol. In summary, the KNN algorithm is shown to yield accurate estimates of the combined translational-orientational entropy and the novel approach of combining distance metrics that is developed here could be extended to provide a powerful method for entropy estimation in numerous contexts.

Highlights

Inhomogeneous fluid solvation theory (IFST) is a statistical mechanical framework for calculating solvation free energies
The correlation between ΔGIFST and ΔGExperimental is excellent (R2 = 0.997), with a mean unsigned error (MUE) of 1.2 kcal/ mol. These results suggest that the TIP4P-2005 water model in combination with the CHARMM forcefield is suitable for quantitative application using IFST
This study addresses the quantitative accuracy of IFST by comparing hydration free energies from IFST with hydration free energies from free-energy perturbation (FEP)

Summary

Introduction

Inhomogeneous fluid solvation theory (IFST) is a statistical mechanical framework for calculating solvation free energies. This work identified the problem with using a histogram method to calculate the IFST correlation functions This problem is that the histogram bin sizes must be sufficiently small to capture the complexity of the probability density function but sufficiently large to avoid convergence issues. This is a well-known concern with histogram methods and has been addressed previously by a number of approaches.[15,16] In the previous study, the amount of data from a 100 ns simulation was insufficient to yield converged entropy estimates for the required histogram bin sizes.[10] The necessary use of inadequate histogram bin sizes led to underestimation of the entropy terms, as evidenced by the inability of the Cartesian coordinate system to recapitulate the radial distribution function of bulk water and the underestimate of the orientational entropy of bulk water. A cancellation of errors is expected to yield a reasonable estimate

Methods

Results

Conclusion