Description of hydration free energy density as a function of molecular physical properties

Water dynamics in the hydration shell of hyper-branched poly-ethylenimine

We performed THz and GHz dielectric relaxation spectroscopy to investigate the reorientational dynamics of water molecules in the hydration shell of amphiphilic hyper-branched poly-ethylenimine (HPEI). Four Debye equations were employed to describe four types of water in the hydration shell, including bulk-like water, under-coordinated water, slow water (water molecules hydrating the hydrophobic groups and water molecules accepting hydrogen bonds from the NH₂ groups) and super slow water (water molecules donating hydrogen bonds to and accepting hydrogen bonds from NH groups). The time scales of undercoordinated and bulk-like water show a slight decline from 0.4 to 0.1 ps and from 8 to 2 ps, respectively. Because of hydrophilic amino groups, HPEI molecules exhibit a strong retardation effect, where the time scales of slow and super slow water increase with concentration from 17 to 39.9 ps and from 88 to 225 ps, respectively.

A minireview on the perturbation effects of polar groups to direct nanoscale hydrophobic interaction and amphiphilic peptide assembly

Hydrophobic interaction provides the essential driving force for creating diverse native and artificial supramolecular architectures. Accumulating evidence leads to a hypothesis that the hydrophobicity of a nonpolar patch of a molecule is non-additive and susceptible to the chemical context of a judicious polar patch. However, the quantification of the hydrophobic interaction at the nanoscale remains a central challenge to validate the hypothesis. In this review, we aim to outline the recent efforts made to determine the hydrophobic interaction at a nanoscopic length scale. The advances achieved in the understanding of proximal polar groups perturbing the magnitude of hydrophobic interaction generated by the nonpolar patch are introduced. We will also discuss the influence of chemical heterogeneity on the modulation of amphiphilic peptide/protein assembly and molecular recognition.

Hydrophobic interaction provides the essential driving force for creating diverse native and artificial supramolecular architectures.

Incorporation of Hydrogen Bond Angle Dependency into the Generalized Solvation Free Energy Density Model

To describe the physically realistic solvation free energy surface of a molecule in a solvent, a generalized version of the solvation free energy density (G-SFED) calculation method has been developed. In the G-SFED model, the contribution from the hydrogen bond (HB) between a solute and a solvent to the solvation free energy was calculated as the product of the acidity of the donor and the basicity of the acceptor of an HB pair. The acidity and basicity parameters of a solute were derived using the summation of acidities and basicities of the respective acidic and basic functional groups of the solute, and that of the solvent was experimentally determined. Although the contribution of HBs to the solvation free energy could be evenly distributed to grid points on the surface of a molecule, the G-SFED model was still inadequate to describe the angle dependency of the HB of a solute with a polarizable continuum solvent. To overcome this shortcoming of the G-SFED model, the contribution of HBs was formulated using the geometric parameters of the grid points described in the HB coordinate system of the solute. We propose an HB angle dependency incorporated into the G-SFED model, i.e., the G-SFED-HB model, where the angular-dependent acidity and basicity densities are defined and parametrized with experimental data. The G-SFED-HB model was then applied to calculate the solvation free energies of organic molecules in water, various alcohols and ethers, and the log P values of diverse organic molecules, including peptides and a protein. Both the G-SFED model and the G-SFED-HB model reproduced the experimental solvation free energies with similar accuracy, whereas the distributions of the SFED on the molecular surface calculated by the G-SFED and G-SFED-HB models were quite different, especially for molecules having HB donors or acceptors. Since the angle dependency of HBs was included in the G-SFED-HB model, the SFED distribution of the G-SFED-HB model is well described as compared to that of the G-SFED model.

A generalized G-SFED continuum solvation free energy calculation model

An empirical continuum solvation model, solvation free energy density (SFED), has been developed to calculate solvation free energies of a molecule in the most frequently used solvents. A generalized version of the SFED model, generalized-SFED (G-SFED), is proposed here to calculate molecular solvation free energies in virtually any solvent. G-SFED provides an accurate and fast generalized framework without a complicated description of a solution. In the model, the solvation free energy of a solute is represented as a linear combination of empirical functions of the solute properties representing the effects of solute on various solute-solvent interactions, and the complementary solvent effects on these interactions were reflected in the linear expansion coefficients with a few solvent properties. G-SFED works well for a wide range of sizes and polarities of solute molecules in various solvents as shown by a set of 5,753 solvation free energies of diverse combinations of 103 solvents and 890 solutes. Octanol-water partition coefficients of small organic compounds and peptides were calculated with G-SFED with accuracy within 0.4 log unit for each group. The G-SFED computation time depends linearly on the number of nonhydrogen atoms (n) in a molecule, O(n).

PXR ligand classification model with SFED-weighted WHIM and CoMMA descriptors

Understanding which type of endogenous and exogenous compounds serve as agonists for the nuclear pregnane X receptor (PXR) would be valuable for drug discovery and development, because PXR regulates a large number of genes related to xenobiotic metabolism. Although several models have been proposed to classify human PXR activators and non-activators, models with better predictability are necessary for practical purposes in drug discovery. Grid-weighted holistic invariant molecular (G-WHIM) and comparative molecular moment analysis (G-CoMMA) type 3D descriptors that contain information about the solvation free energy of target molecules were developed. With these descriptors, prediction models built using decision tree (DT)-, support vector machine (SVM)-, and Kohonen neural network (KNN)-based models exhibited better predictability than previously proposed models. Solvation free energy density-weighted G-WHIM and G-CoMMA descriptors reveal new insights into PXR ligand classification, and incorporation with machine learning methods (DT, SVM, KNN) exhibits promising results, especially SVM and KNN. SVM- and KNN-based models exhibit accuracy around 0.90, and DT-based models exhibit accuracy around 0.8 for both the training and test sets.

Calculation of the solvation free energy of neutral and ionic molecules in diverse solvents

The solvation free energy density (SFED) model was modified to extend its applicability and predictability. The parametrization process was performed with a large, diverse set of solvation free energies that included highly polar and ionic molecules. The mean absolute error for 1200 solvation free energies of the 379 neutral molecules in 9 organic solvents and water was 0.40 kcal/mol, and for 90 hydration free energies of ions was 1.7 kcal/mol. Overall, the calculated solvation free energies of a wide range of solute functional groups in diverse solvents were consistent with experimental data.

Fast prediction of hydration free energies from molecular interaction fields

A novel empirical model is presented that allows the fast computation of hydration free energies with high accuracy. The linear model is based upon the separation of the free energy of hydration into a cavity and an interaction term. The cavity contribution is modeled as a linear combination of molecular volume and surface terms. The interaction part is derived from the statistical three-dimensional (3D) free energy density and is modeled approximately as a molecular interaction field using the program GRID. A compression scheme is employed to represent this 3D information on the molecular surface by means of a linear combination of surface functions. A set of 81 small organic molecules with known experimental hydration free energies is used to determine the coefficients of the linear model by least squares regression. The fit is statistically significant yielding a correlation coefficient of 0.99, a root mean square error of 0.27 kcal/mol for the 81 molecules belonging to the training set, and 0.63 kcal/mol for an independent test set of 10 molecules.

Molecular simulation study of cooperativity in hydrophobic association

To investigate the cooperativity of hydrophobic interactions, the potential of mean force of two- and three-molecule methane clusters in water was determined by molecular dynamics simulations using two methods: umbrella-sampling with the weighted histogram analysis method and thermodynamic integration. Two water models, TIP3P and TIP4P, were used, while each methane molecule was modeled as a united atom. It was found that the three-body potential of mean force is not additive, i.e., it cannot be calculated as a sum of two-body contributions, but requires an additional three-body cooperative term. The cooperative term, which amounts to only about 10% of the total hydrophobic association free energy, was found to increase the strength of hydrophobic association; this finding differs from the results of earlier Monte Carlo studies with the free energy perturbation method of Rank and Baker (1997). As in the work of Rank and Baker, the solvent contribution to the potential of mean force was found to be well approximated by the molecular surface of two methane molecules. Moreover, we also found that the cooperative term is well represented by the difference between the molecular surface of the three-methane cluster and those of all three pairs of methane molecules. In addition, it was found that, while there is a cooperative contribution to the hydrophobic association free energy albeit a small one, the errors associated with the use of pairwise potentials are comparable to or larger than this contribution.