The impact of surface area, volume, curvature, and Lennard–Jones potential to solvation modeling

Abstract

This article explores the impact of surface area, volume, curvature, and Lennard-Jones (LJ) potential on solvation free energy predictions. Rigidity surfaces are utilized to generate robust analytical expressions for maximum, minimum, mean, and Gaussian curvatures of solvent-solute interfaces, and define a generalized Poisson-Boltzmann (GPB) equation with a smooth dielectric profile. Extensive correlation analysis is performed to examine the linear dependence of surface area, surface enclosed volume, maximum curvature, minimum curvature, mean curvature, and Gaussian curvature for solvation modeling. It is found that surface area and surfaces enclosed volumes are highly correlated to each other's, and poorly correlated to various curvatures for six test sets of molecules. Different curvatures are weakly correlated to each other for six test sets of molecules, but are strongly correlated to each other within each test set of molecules. Based on correlation analysis, we construct twenty six nontrivial nonpolar solvation models. Our numerical results reveal that the LJ potential plays a vital role in nonpolar solvation modeling, especially for molecules involving strong van der Waals interactions. It is found that curvatures are at least as important as surface area or surface enclosed volume in nonpolar solvation modeling. In conjugation with the GPB model, various curvature-based nonpolar solvation models are shown to offer some of the best solvation free energy predictions for a wide range of test sets. For example, root mean square errors from a model constituting surface area, volume, mean curvature, and LJ potential are less than 0.42 kcal/mol for all test sets. © 2016 Wiley Periodicals, Inc.

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“…Our earlier work indicates that although molecular manifolds and associated geometric properties are able to provide a low-dimensional description of molecules and biomolecules, they have very limited predictive power for large molecular datasets. 39 In particular, the potential role of differential geometry for drug design and discovery is essentially unknown. This work introduces differential geometry-based geometric learning (DG-GL) as an accurate, efficient, and robust strategy for analyzing large, diverse, and complex molecular and biomolecular datasets.…”

“…45 However, differential geometry properties computed from ρ ( r , { η j }, { w j }) have a very limited predictive power. 39…”

“…17,36 Most recently, the use of molecular curvature for quantitative analysis and the prediction of solvation free energies of small molecules have been explored. 39 However, the predictive power of this approach is limited due to the use of whole molecular curvatures. Essentially, chemical and biological information in the complex biomolecule is mostly neglected in this low-dimensional representation.…”

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