Rapid prediction of solvation free energy. 3. Application to the SAMPL2 challenge

The SAMPL2 hydration free energy blind prediction challenge consisted of a data set of 41 molecules divided into three subsets: explanatory, obscure and investigatory, where experimental hydration free energies were given for the explanatory, withheld for the obscure, and not known for the investigatory molecules. We employed two solvation models for this challenge, a linear interaction energy (LIE) model based on explicit-water molecular dynamics simulations, and the first-shell hydration (FiSH) continuum model previously calibrated to mimic LIE data. On the 23 compounds from the obscure (blind) dataset, the prospectively submitted LIE and FiSH models provided predictions highly correlated with experimental hydration free energy data, with mean-unsigned-errors of 1.69 and 1.71 kcal/mol, respectively. We investigated several parameters that may affect the performance of these models, namely, the solute flexibility for the LIE explicit-solvent model, the solute partial charging method, and the incorporation of the difference in intramolecular energy between gas and solution phases for both models. We extended this analysis to the various chemical classes that can be formed within the SAMPL2 dataset. Our results strengthen previous findings on the excellent accuracy and transferability of the LIE explicit-solvent approach to predict transfer free energies across a wide spectrum of functional classes. Further, the current results on the SAMPL2 test dataset provide additional support for the FiSH continuum model as a fast yet accurate alternative to the LIE explicit-solvent model. Overall, both the LIE explicit-solvent model and the FiSH continuum solvation model show considerable improvement on the SAMPL2 data set over our previous continuum electrostatics-dispersion solvation model used in the SAMPL1 blind challenge.     

Anisotropic solvent model of the lipid bilayer. 1. Parameterization of long-range electrostatics and first solvation shell effects

A new implicit solvation model was developed for calculating free energies of transfer of molecules from water to any solvent with defined bulk properties. The transfer energy was calculated as a sum of the first solvation shell energy and the long-range electrostatic contribution. The first term was proportional to solvent accessible surface area and solvation parameters (σ(i)) for different atom types. The electrostatic term was computed as a product of group dipole moments and dipolar solvation parameter (η) for neutral molecules or using a modified Born equation for ions. The regression coefficients in linear dependencies of solvation parameters σ(i) and η on dielectric constant, solvatochromic polarizability parameter π*, and hydrogen-bonding donor and acceptor capacities of solvents were optimized using 1269 experimental transfer energies from 19 organic solvents to water. The root-mean-square errors for neutral compounds and ions were 0.82 and 1.61 kcal/mol, respectively. Quantification of energy components demonstrates the dominant roles of hydrophobic effect for nonpolar atoms and of hydrogen-bonding for polar atoms. The estimated first solvation shell energy outweighs the long-range electrostatics for most compounds including ions. The simplicity and computational efficiency of the model allows its application for modeling of macromolecules in anisotropic environments, such as biological membranes.     

Comparative assessment of computational methods for the determination of solvation free energies in alcohol‐based molecules

The determination of differences in solvation free energies between related drug molecules remains an important challenge in computational drug optimization, when fast and accurate calculation of differences in binding free energy are required. In this study, we have evaluated the performance of five commonly used polarized continuum model (PCM) methodologies in the determination of solvation free energies for 53 typical alcohol and alkane small molecules. In addition, the performance of these PCM methods, of a thermodynamic integration (TI) protocol and of the Poisson–Boltzmann (PB) and generalized Born (GB) methods, were tested in the determination of solvation free energies changes for 28 common alkane‐alcohol transformations, by the substitution of an hydrogen atom for a hydroxyl substituent. The results show that the solvation model D (SMD) performs better among the PCM‐based approaches in estimating solvation free energies for alcohol molecules, and solvation free energy changes for alkane‐alcohol transformations, with an average error below 1 kcal/mol for both quantities. However, for the determination of solvation free energy changes on alkane‐alcohol transformation, PB and TI yielded better results. TI was particularly accurate in the treatment of hydroxyl groups additions to aromatic rings (0.53 kcal/mol), a common transformation when optimizing drug‐binding in computer‐aided drug design. © 2013 Wiley Periodicals, Inc.     

Prediction of molecular solvation free energy based on the optimization of atomic solvation parameters with genetic algorithm

We propose an improved solvent contact model to estimate the solvation free energy of an organic molecule from individual atomic contributions. The modification of the solvation model involves the optimization of three kinds of parameters in the solvation free energy function: atomic fragmental volume, maximum atomic occupancy, and atomic solvation parameters. All of these atomic parameters for 24 atom types are developed by the operation of a standard genetic algorithm in such a way as to minimize the difference between experimental and calculated solvation free energies. The data set for experimental solvation free energies is divided into a training set of 131 compounds and a test set of 24 compounds. Linear regressions with the optimized atomic parameters yield fits with the squared correlation coefficients (r2) of 0.89 and 0.86 for the training set and for the test set, respectively. Overall, the results indicate that the improved solvent contact model with the newly developed atomic parameters would be a useful tool for rapid calculation of molecular solvation free energies in aqueous solution.     

Modeling the pharmacodynamics of passive membrane permeability

Small molecule permeability through cellular membranes is critical to a better understanding of pharmacodynamics and the drug discovery endeavor. Such permeability may be estimated as a function of the free energy change of barrier crossing by invoking the barrier domain model, which posits that permeation is limited by passage through a single “barrier domain” and assumes diffusivity differences among compounds of similar structure are negligible. Inspired by the work of Rezai and co-workers (JACS 128:14073–14080, 2006), we estimate this free energy change as the difference in implicit solvation free energies in chloroform and water, but extend their model to include solute conformational affects. Using a set of eleven structurally diverse FDA approved compounds and a set of thirteen congeneric molecules, we show that the solvation free energies are dominated by the global minima, which allows solute conformational distributions to be effectively neglected. For the set of tested compounds, the best correlation with experiment is obtained when the implicit chloroform global minimum is used to evaluate the solvation free energy difference.     

Breaking the polar‐nonpolar division in solvation free energy prediction

Implicit solvent models divide solvation free energies into polar and nonpolar additive contributions, whereas polar and nonpolar interactions are inseparable and nonadditive. We present a feature functional theory (FFT) framework to break this ad hoc division. The essential ideas of FFT are as follows: (i) representability assumption: there exists a microscopic feature vector that can uniquely characterize and distinguish one molecule from another; (ii) feature‐function relationship assumption: the macroscopic features, including solvation free energy, of a molecule is a functional of microscopic feature vectors; and (iii) similarity assumption: molecules with similar microscopic features have similar macroscopic properties, such as solvation free energies. Based on these assumptions, solvation free energy prediction is carried out in the following protocol. First, we construct a molecular microscopic feature vector that is efficient in characterizing the solvation process using quantum mechanics and Poisson–Boltzmann theory. Microscopic feature vectors are combined with macroscopic features, that is, physical observable, to form extended feature vectors. Additionally, we partition a solvation dataset into queries according to molecular compositions. Moreover, for each target molecule, we adopt a machine learning algorithm for its nearest neighbor search, based on the selected microscopic feature vectors. Finally, from the extended feature vectors of obtained nearest neighbors, we construct a functional of solvation free energy, which is employed to predict the solvation free energy of the target molecule. The proposed FFT model has been extensively validated via a large dataset of 668 molecules. The leave‐one‐out test gives an optimal root‐mean‐square error (RMSE) of 1.05 kcal/mol. FFT predictions of SAMPL0, SAMPL1, SAMPL2, SAMPL3, and SAMPL4 challenge sets deliver the RMSEs of 0.61, 1.86, 1.64, 0.86, and 1.14 kcal/mol, respectively. Using a test set of 94 molecules and its associated training set, the present approach was carefully compared with a classic solvation model based on weighted solvent accessible surface area. © 2017 Wiley Periodicals, Inc.     

Prediction of SAMPL2 aqueous solvation free energies and tautomeric ratios using the SM8, SM8AD,and SMD solvation models

We applied the solvation models SM8, SM8AD, and SMD in combination with the Minnesota M06-2X density functional to predict vacuum-water transfer free energies (Task 1) and tautomeric ratios in aqueous solution (Task 2) for the SAMPL2 test set. The bulk-electrostatic contribution to the free energy of solvation is treated as follows: SM8 employs the generalized Born model with the Coulomb field approximation, SM8AD employs the generalized Born approximation with asymmetric descreening, and SMD solves the nonhomogeneous Poisson equation. The non-bulk-electrostatic contribution arising from short-range interactions between the solute and solvent molecules in the first solvation shell is treated as a sum of terms that are products of geometry-dependent atomic surface tensions and solvent-accessible surface areas of the individual atoms of the solute. On average, three models tested in the present work perform similarly. In particular, we achieved mean unsigned errors of 1.3 (SM8), 2.0 (SM8AD), and 2.6 kcal/mol (SMD) for the aqueous free energies of 30 out of 31 compounds with known reference data involved in Task 1 and mean unsigned errors of 2.7 (SM8), 1.8 (SM8AD), and 2.4 kcal/mol (SMD) in the free energy differences (tautomeric ratios) for 21 tautomeric pairs in aqueous solution involved in Task 2.     

High accuracy quantum-chemistry-based calculation and blind prediction of macroscopic pKa values in the context of the SAMPL6 challenge

Recent advances in the development of low-cost quantum chemical methods have made the prediction of conformational preferences and physicochemical properties of medium-sized drug-like molecules routinely feasible, with significant potential to advance drug discovery. In the context of the SAMPL6 challenge, macroscopic pKa values were blindly predicted for a set of 24 of such molecules. In this paper we present two similar quantum chemical based approaches based on the high accuracy calculation of standard reaction free energies and the subsequent determination of those pKa values via a linear free energy relationship. Both approaches use extensive conformational sampling and apply hybrid and double-hybrid density functional theory with continuum solvation to calculate free energies. The blindly calculated macroscopic pKa values were in excellent agreement with the experiment.     

Free energy of solvation from molecular dynamics simulation applying Voronoi-Delaunay triangulation to the cavity creation

The free energy of solvation for a large number of representative solutes in various solvents has been calculated from the polarizable continuum model coupled to molecular dynamics computer simulation. A new algorithm based on the Voronoi-Delaunay triangulation of atom-atom contact points between the solute and the solvent molecules is presented for the estimation of the solvent-accessible surface surrounding the solute. The volume of the inscribed cavity is used to rescale the cavitational contribution to the solvation free energy for each atom of the solute atom within scaled particle theory. The computation of the electrostatic free energy of solvation is performed using the Voronoi-Delaunay surface around the solute as the boundary for the polarizable continuum model. Additional short-range contributions to the solvation free energy are included directly from the solute-solvent force field for the van der Waals-type interactions. Calculated solvation free energies for neutral molecules dissolved in benzene, water, CCl4, and octanol are compared with experimental data. We found an excellent correlation between the experimental and computed free energies of solvation for all the solvents. In addition, the employed algorithm for the cavity creation by Voronoi-Delaunay triangulation is compared with the GEPOL algorithm and is shown to predict more accurate free energies of solvation, especially in solvents composed by molecules with nonspherical molecular shapes.     

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.     

SLICK--scoring and energy functions for protein-carbohydrate interactions

Protein-carbohydrate interactions are increasingly being recognized as essential for many important biomolecular recognition processes. From these, numerous biomedical applications arise in areas as diverse as drug design, immunology, or drug transport. We introduce SLICK, a package containing a scoring and an energy function, which were specifically designed to predict binding modes and free energies of sugars and sugarlike compounds to proteins. SLICK accounts for van der Waals interactions, solvation effects, electrostatics, hydrogen bonds, and CH...pi interactions, the latter being a particular feature of most protein-carbohydrate interactions. Parameters for the empirical energy function were calibrated on a set of high-resolution crystal structures of protein-sugar complexes with known experimental binding free energies. We show that SLICK predicts the binding free energies of predicted complexes (through molecular docking) with high accuracy. SLICK is available as part of our molecular modeling package BALL (www.ball-project.org).     

SAMPL4, a blind challenge for computational solvation free energies: the compounds considered

For the fifth time I have provided a set of solvation energies (1 M gas to 1 M aqueous) for a SAMPL challenge. In this set there are 23 blind compounds and 30 supplementary compounds of related structure to one of the blind sets, but for which the solvation energy is readily available. The best current values of each compound are presented along with complete documentation of the experimental origins of the solvation energies. The calculations needed to go from reported data to solvation energies are presented, with particular attention to aspects which are new to this set. For some compounds the vapor pressures (VP) were reported for the liquid compound, which is solid at room temperature. To correct from VP_{subcooled liquid} to VP_sublimation requires ΔS_fusion, which is only known for mannitol. Estimated values were used for the others, all but one of which were benzene derivatives and expected to have very similar values. The final compound for which ΔS_fusion was estimated was menthol, which melts at 42 °C so that modest errors in ΔS_fusion will have little effect. It was also necessary to look into the effects of including estimated values of ΔCp on this correction. The approximate sizes of the effects of inclusion of ΔCp in the correction from VP_{subcooled liquid} to VP_sublimation were estimated and it was noted that inclusion of ΔCp invariably makes ΔG_S more positive. To extend the set of compounds for which the solvation energy could be calculated we explored the use of boiling point (b.p.) data from Reaxys/Beilstein as a substitute for studies of the VP as a function of temperature. B.p. data are not always reliable so it was necessary to develop a criterion for rejecting outliers. For two compounds (chlorinated guaiacols) it became clear that inclusion represented overreach; for each there were only two independent pressure, temperature points, which is too little for a trustworthy extrapolation. For a number of compounds the extrapolation from lowest temperature at which the VP was reported to 25 °C was long (sometimes over 100°) so that it was necessary to consider whether ΔCp might have significant effects. The problem is that there are no experimental values and possible intramolecular hydrogen bonds make estimation uncertain in some cases. The approximate sizes of the effects of ΔCp were estimated, and it was noted that inclusion of ΔCp in the extrapolation of VP down to room temperature invariably makes ΔGs more negative.     

Hybrid Solvation Model with First Solvation Shell for Calculation of Solvation Free Energy

We present a hybrid solvation model with first solvation shell to calculate solvation free energies. This hybrid model combines the quantum mechanics and molecular mechanics methods with the analytical expression based on the Born solvation model to calculate solvation free energies. Based on calculated free energies of solvation and reaction profiles in gas phase, we set up a unified scheme to predict reaction profiles in solution. The predicted solvation free energies and reaction barriers are compared with experimental results for twenty bimolecular nucleophilic substitution reactions. These comparisons show that our hybrid solvation model can predict reliable solvation free energies and reaction barriers for chemical reactions of small molecules in aqueous solution.     

Predicting hydration free energies with a hybrid QM/MM approach: an evaluation of implicit and explicit solvation models in SAMPL4

The correct representation of solute-water interactions is essential for the accurate simulation of most biological phenomena. Several highly accurate quantum methods are available to deal with solvation by using both implicit and explicit solvents. So far, however, most evaluations of those methods were based on a single conformation, which neglects solute entropy. Here, we present the first test of a novel approach to determine hydration free energies that uses molecular mechanics (MM) to sample phase space and quantum mechanics (QM) to evaluate the potential energies. Free energies are determined by using re-weighting with the Non-Boltzmann Bennett (NBB) method. In this context, the method is referred to as QM-NBB. Based on snapshots from MM sampling and accounting for their correct Boltzmann weight, it is possible to obtain hydration free energies that incorporate the effect of solute entropy. We evaluate the performance of several QM implicit solvent models, as well as explicit solvent QM/MM for the blind subset of the SAMPL4 hydration free energy challenge. While classical free energy simulations with molecular dynamics give root mean square deviations (RMSD) of 2.8 and 2.3 kcal/mol, the hybrid approach yields an improved RMSD of 1.6 kcal/mol. By selecting an appropriate functional and basis set, the RMSD can be reduced to 1 kcal/mol for calculations based on a single conformation. Results for a selected set of challenging molecules imply that this RMSD can be further reduced by using NBB to reweight MM trajectories with the SMD implicit solvent model.     

Microscopic models for quantum mechanical calculations of chemical processes in solutions: LD/AMPAC and SCAAS/AMPAC calculations of solvation energies

Our previously developed approaches for integrating quantum mechanical molecular orbital methods with microscopic solvent models are refined and examined. These approaches consider the nonlinear solute–solvent coupling in a self-consistent way by incorporating the potential from the solvent dipoles in the solute Hamiltonian, while considering the polarization of the solvent by the potential from the solute charges. The solvent models used include the simplified Langevin Dipoles (LD) model and the much more expensive surface constrained All Atom Solvent (SCAAS) model, which is combined with a free energy pertubation (FEP) approach. Both methods are effectively integrated with the quantum mechanical AMPAC package and can be easily combined with other quantum mechanical programs. The advantages of the present approaches and their earlier versions over macroscopic reaction field models and supermolecular approaches are considered. A LD/MNDO study of solvated organic ions demonstrates that this model can yield reliable solvation energies, provided the quantum mechanical charges are scaled to have similar magnitudes to those obtained by high level ab initio methods. The incorporation of a field-dependent hydrophobic term in the LD free energy makes the present approach capable of evaluating the free energy of transfer of polar molecules from non polar solvents to aqueous solutions. The reliability of the LD approach is examined not only by evaluating a rather standard set of solvation energies of organic ions and polar molecules, but also by considering the stringent test case of sterically hindered hydrophobic ions. In this case, we compare the LD/MNDO solvation energies to the more rigorous FEP/SCAAS/MNDO solvation energies. Both methods are found to give similar results even in this challenging test case. The FEP/SCAAS/AMPAC method is incorporated into the current version of the program ENZYMIX. This option allows one to study chemical reactions in enzymes and in solutions using the MNDO and AM1 approximations. A special procedure that uses the EVB method as a reference potential for SCF MO calculations should help in improving the reliability of such studies.     

All-atom/coarse-grained hybrid predictions of distribution coefficients in SAMPL5

We present blind predictions submitted to the SAMPL5 challenge on calculating distribution coefficients. The predictions were based on estimating the solvation free energies in water and cyclohexane of the 53 compounds in the challenge. These free energies were computed using alchemical free energy simulations based on a hybrid all-atom/coarse-grained model. The compounds were treated with the general Amber force field, whereas the solvent molecules were treated with the Elba coarse-grained model. Considering the simplicity of the solvent model and that we approximate the distribution coefficient with the partition coefficient of the neutral species, the predictions are of good accuracy. The correlation coefficient, R is 0.64, 82 % of the predictions have the correct sign and the mean absolute deviation is 1.8 log units. This is on a par with or better than the other simulation-based predictions in the challenge. We present an analysis of the deviations to experiments and compare the predictions to another submission that used all-atom solvent.     

Comparative study of free energies of solvation of phenylimidazole inhibitors of cytochrome P450cam by free energy simulation,AMSOL, and Poisson Boltzmann methods

Free energies of solvation of phenylimidazole inhibitors of cytochrome P450cam were determined using (1) free energy simulation, (2) AMSOL-SM2 semiempirical methods, and (3) Poisson-Boltzmann methods. The goals of this study were threefold: (1) to compare the results obtained from the three different methods, (2) to investigate the effect of inclusion of intraperturbed group interactions on free energy simulation estimates of solvation free energy differences, and (3) to investigate to what extent differences in free energies of solvation among three of these inhibitors could account for observed differences in their enzyme binding free energies. In general, relative solvation free energies obtained from the free energy simulations and AMSOL-SM2 methods give comparable results (i.e., the same rank ordering and similar quantitative results, differing significantly from results obtained using Poisson-Boltzmann methods). The free energy simulation studies suggest that the neglect of intraperturbed group interactions had little effect on rank order of free energies of solvation of the polar phenylimidazoles. The relative desolvation free energies of the three inhibitors of P450cam—1-phenylimidazole (1-PI), 2-phenylimidazole (2-PI), and 4-phenylimidazole (4-PI)—with known enzyme bound X-ray structures parallel that of their known binding affinities and could account for most of the differences in the free energies of binding of these three inhibitors to P450cam. The origin of the difference of the free energies of solution of these three inhibitors is primarily the additional interaction between solvent and N(SINGLE BOND)H group in the imidazole ring of 2- and 4-phenylimidazole that is absent in the 1-phenylimidazole isomer. This hypothesis is substantiated by a second comparison of the relative solvation free energies of 4-phenylimidazole with its methylated derivative, 3-methyl-4-phenylimidazole, also lacking an N(SINGLE BOND)H group. © 1996 by John Wiley & Sons, Inc.     

The treatment of solvation by a generalized Born model and a self-consistent charge-density functional theory-based tight-binding method

We present a model to calculate the free energies of solvation of small organic compounds as well as large biomolecules. This model is based on a generalized Born (GB) model and a self-consistent charge-density functional theory-based tight-binding (SCC-DFTB) method with the nonelectrostatic contributions to the free energy of solvation modeled in terms of solvent-accessible surface areas (SA). The parametrization of the SCC-DFTB/GBSA model has been based on 60 neutral and six ionic molecules composed of H, C, N, O, and S, and spanning a wide range of chemical groups. Effective atomic radii as parameters have been obtained through Monte Carlo Simulated Annealing optimization in the parameter space to minimize the differences between the calculated and experimental free energies of solvation. The standard error in the free energies of solvation calculated by the final model is 1.11 kcal mol(-1). We also calculated the free energies of solvation for these molecules using a conductor-like screening model (COSMO) in combination with different levels of theory (AM1, SCC-DFTB, and B3LYP/6-31G*) and compared the results with SCC-DFTB/GBSA. To assess the efficiency of our model for large biomolecules, we calculated the free energy of solvation for a HIV protease-inhibitor complex containing 3,204 atoms using the SCC-DFTB/GBSA and the SCC-DFTB/COSMO models, separately. The computed relative free energies of solvation are comparable, while the SCC-DFTB/GBSA model is three to four times more efficient, in terms of computational cost.     

Partition coefficients of methylated DNA bases obtained from free energy calculations with molecular electron density derived atomic charges

Partition coefficients serve in various areas as pharmacology and environmental sciences to predict the hydrophobicity of different substances. Recently, they have also been used to address the accuracy of force fields for various organic compounds and specifically the methylated DNA bases. In this study, atomic charges were derived by different partitioning methods (Hirshfeld and Minimal Basis Iterative Stockholder) directly from the electron density obtained by electronic structure calculations in a vacuum, with an implicit solvation model or with explicit solvation taking the dynamics of the solute and the solvent into account. To test the ability of these charges to describe electrostatic interactions in force fields for condensed phases, the original atomic charges of the AMBER99 force field were replaced with the new atomic charges and combined with different solvent models to obtain the hydration and chloroform solvation free energies by molecular dynamics simulations. Chloroform–water partition coefficients derived from the obtained free energies were compared to experimental and previously reported values obtained with the GAFF or the AMBER‐99 force field. The results show that good agreement with experimental data is obtained when the polarization of the electron density by the solvent has been taken into account, and when the energy needed to polarize the electron density of the solute has been considered in the transfer free energy. These results were further confirmed by hydration free energies of polar and aromatic amino acid side chain analogs. Comparison of the two partitioning methods, Hirshfeld‐I and Minimal Basis Iterative Stockholder (MBIS), revealed some deficiencies in the Hirshfeld‐I method related to the unstable isolated anionic nitrogen pro‐atom used in the method. Hydration free energies and partitioning coefficients obtained with atomic charges from the MBIS partitioning method accounting for polarization by the implicit solvation model are in good agreement with the experimental values. © 2018 Wiley Periodicals, Inc.