Predicting hydration free energies of neutral compounds by a parametrization of the polarizable continuum model

A parametrization of the polarizable continuum model (PCM) is presented having the experimental hydration free energies of 215 neutral molecules as target. The cavitation and dispersion contributions were based on the Tu?on-Silla-Pascual-Ahuir (Tu?on; et al. Chem. Phys. Lett. 1993, 203, 289) and Floris-Tomasi (Floris, F.; Tomasi, J. J. Comput. Chem. 1989, 10, 616) expressions, respectively. Both the polar and nonpolar contributions were evaluated on the same solvent-excluding molecular surface that used unscaled Bondi atomic radii. The parametrization was provided for the HF, Xalpha, LSDA, B3LYP, and mPW1PW91 methods at the 6-31G(d) basis set, and the results are in fair agreement with the experimental data. For the sake of comparison, the PCM(UAHF) and our parametrization (PCM2), both at HF level, have produced DeltaG(PCM(UAHF)) = aDeltaGexp (a = 1.02 +/- 0.02, r = 0.945, sd = 0.987, Ftest = 1778) and DeltaG(PCM2) = aDeltaGexp (a = 0.95 +/- 0.02, r = 0.952, sd = 0.843, Ftest = 2070), respectively. The mean absolute deviations from experimental data were 0.67 and 0.68 kcal/mol for PCM(UAHF) and PCM2, respectively.     

Predictions of hydration free energies from continuum solvent with solute polarizable models: the SAMPL2 blind challenge

This paper reports the results of our attempt to predict hydration free energies on the SAMPL2 blind challenge dataset. We mostly examine the effects of the solute electrostatic component on the accuracy of the predictions. The usefulness of electronic polarization in predicting hydration free energies is assessed by comparing the Electronic Polarization from Internal Continuum model and the self consistent reaction field IEF-PCM to standard non-polarizable charge models such as RESP and AM1-BCC. We also determine an optimal restraint weight for Dielectric-RESP atomic charges fitting. Statistical analysis of the results could not distinguish the methods from one another. The smallest average unsigned error obtained is 1.9 ± 0.6 kcal/mol (95% confidence level). A class of outliers led us to investigate the importance of the solute–solvent instantaneous induction energy, a missing term in PB continuum models. We estimated values between −1.5 and −6 kcal/mol for a series of halo-benzenes which can explain why some predicted hydration energies of non-polar molecules significantly disagreed with experiment.     

Interfacial free energies of ionic crystals

Minimum values of the liquid-crystal interfacial free energy have been obtained from data on the maximum supercooling of small droplets of solutions of ionic crystals.     

Computation of methodology-independent ionic solvation free energies from molecular simulations. II. The hydration free energy of the sodium cation

The raw ionic solvation free energies computed from atomistic (explicit-solvent) simulations are extremely sensitive to the boundary conditions (finite or periodic system, system shape, and size) and treatment of electrostatic interactions (Coulombic, lattice sum, or cutoff based) used during these simulations. In the present article, it is shown that correction terms can be derived for the effect of (A) an incorrect solvent polarization around the ion due to the use of an approximate (not strictly Coulombic) electrostatic scheme; (B) the finite size or artificial periodicity of the simulated system; (C) an improper summation scheme to evaluate the potential at the ion site and the possible presence of a liquid-vacuum interface in the simulated system. Taking the hydration free energy of the sodium cation as a test case, it is shown that the raw solvation free energies obtained using seven different types of boundary conditions and electrostatic schemes commonly used in explicit-solvent simulations (for a total of 72 simulations differing in the corresponding simulation parameters) can be corrected so as to obtain a consistent value for this quantity.     

Alchemical prediction of hydration free energies for SAMPL

Hydration free energy calculations have become important tests of force fields. Alchemical free energy calculations based on molecular dynamics simulations provide a rigorous way to calculate these free energies for a particular force field, given sufficient sampling. Here, we report results of alchemical hydration free energy calculations for the set of small molecules comprising the 2011 Statistical Assessment of Modeling of Proteins and Ligands challenge. Our calculations are largely based on the Generalized Amber Force Field with several different charge models, and we achieved RMS errors in the 1.4-2.2 kcal/mol range depending on charge model, marginally higher than what we typically observed in previous studies (Mobley et al. in J Phys Chem B 111(9):2242-2254, 2007, J Chem Theory Comput 5(2):350-358, 2009, J Phys Chem B 115:1329-1332, 2011; Nicholls et al. in J Med Chem 51:769-779, 2008; Klimovich and Mobley in J Comput Aided Mol Design 24(4):307-316, 2010). The test set consists of ethane, biphenyl, and a dibenzyl dioxin, as well as a series of chlorinated derivatives of each. We found that, for this set, using high-quality partial charges from MP2/cc-PVTZ SCRF RESP fits provided marginally improved agreement with experiment over using AM1-BCC partial charges as we have more typically done, in keeping with our recent findings (Mobley et al. in J Phys Chem B 115:1329-1332, 2011). Switching to OPLS Lennard-Jones parameters with AM1-BCC charges also improves agreement with experiment. We also find a number of chemical trends within each molecular series which we can explain, but there are also some surprises, including some that are captured by the calculations and some that are not.     

Solvation free energies and hydration structure of N-methyl-p-nitroaniline

Solvation Gibbs energies of N-methyl-p-nitroaniline (MNA) in water and 1-octanol are calculated using the expanded ensemble molecular dynamics method with a force field taken from the literature. The accuracy of the free energy calculations is verified with the experimental Gibbs free energy data and found to reproduce the experimental 1-octanol∕water partition coefficient to within ±0.1 in log unit. To investigate the hydration structure around N-methyl-p-nitroaniline, an independent NVT molecular dynamics simulation was performed at ambient conditions. The local organization of water molecules around the solute MNA molecule was investigated using the radial distribution function (RDF), the coordination number, and the extent of hydrogen bonding. The spatial distribution functions (SDFs) show that the water molecules are distributed above and below the nitrogen atoms parallel to the plane of aromatic ring for both the methylamino and nitro functional groups. It is found that these groups have a significant effect on the hydration of MNA with water molecules forming two weak hydrogen bonds with both the methylamino and nitro groups. The hydration structures around the functional groups in MNA in water are different from those that have been found for methylamine, nitrobenzene, and benzene in aqueous solutions, and these differences together with weak hydrogen bonds explain the lower solubility of MNA in water. The RDFs together with SDFs provide a tool for the understanding the hydration of MNA (and other molecules) and therefore their solubility.     

Comparison of 6-31G*-based MST/SCRF and FEP evaluations of the free energies of hydration for small neutral molecules

A comparison between Miertus–Scrocco–Tomasi (MST) SCRF and free energy perturbation (FEP) estimates of the free energy of hydration of eight small neutral molecules is presented. In both cases, the 6-31G* molecular electrostatic potential is used to describe the electrostatic properties of the molecules. The results demonstrate the ability of both methodologies to provide useful theoretical estimates of the total free energy of hydration; the average errors are only 1.5 kcal/mol (FEP) and 0.8 kcal/mol (MST/SCRF). The largest errors in the FEP and MST/SCRF results are less than 1.5 kcal/mol for all molecules except acetic acid, where the FEP method overestimates the free energy of hydration by 3.3 kcal/mol. © John Wiley & Sons, Inc.     

Blind prediction test of free energies of hydration with COSMO-RS

The COSMO-RS method, a combination of the quantum chemical dielectric continuum solvation model COSMO with COSMO-RS, a statistical thermodynamics treatment of surface interactions, simulations, has been used for the direct, blind prediction of free energies of hydration within the SAMPL challenge. Straight application of the latest version of the COSMOtherm implementation in combination with a rigorous conformational sampling yielded a predictive accuracy of 1.56 kcal/mol (RMSE) for the 23 compounds of the blind prediction dataset. Due to the uncertainties of the extrapolations and assumptions involved in the derivation of the experimental data, the accuracy of the predicted data may be considered to be within the noise level of the experimental data.     

Computation of hydration free energies using a parameterized continuum model: Study of equilibrium geometries and reactive processes in water solution

A parameterized self-consistent reaction field model allowing computation of the total free energy of hydration of organic molecules at the ab initio level is presented. The approach uses electrostatic plus polarization energies calculated with the help of a continuum model. The remaining solvation free energy terms are obtained by a simple formula based on atomic parameters and atomic accessible surface areas (ASAs), which are determined with the ASA analytical algorithm. Analytical derivatives of the atomic surfaces areas have been implemented. The atomic parameters have been obtained by a linear regression fit of the calculated and experimental free energies of solution in water for a set of 35 molecules, leading to a standard deviation of 0.75 kcal/mol. Effects of nonelectrostatic terms on solute geometries, association energies, and activation barriers are illustrated. © 1996 by John Wiley & Sons, Inc.     

Predicting hydration free energies with chemical accuracy: the SAMPL4 challenge

An implicit solvent model described by a non-simple dielectric medium is used for the prediction of hydration free energies on the dataset of 47 molecules in the SAMPL4 challenge. The solute is represented by a minimal parameter set model based on a new all atom force-field, named the liquid simulation force-field. The importance of a first solvation shell correction to the hydration free energy prediction is discussed and two different approaches are introduced to address it: either with an empirical correction to a few functional groups (alcohol, ether, ester, amines and aromatic nitrogen), or an ab initio correction based on the formation of a solute/explicit water complex. Both approaches give equally good predictions with an average unsigned error <1 kcal/mol. Chemical accuracy is obtained.     

The importance of excluded solvent volume effects in computing hydration free energies

Continuum dielectric methods such as the Born equation have been widely used to compute the electrostatic component of the solvation free energy, DeltaG(solv)(elec), because they do not need to include solvent molecules explicitly and are thus far less costly compared to molecular simulations. All of these methods can be derived from Gauss Law of Maxwell's equations, which yields an analytical solution for the solvation free energy, DeltaG(Born), when the solute is spherical. However, in Maxwell's equations, the solvent is assumed to be a structureless continuum, whereas in reality, the near-solute solvent molecules are highly structured unlike far-solute bulk solvent. Since we have recently reformulated Gauss Law of Maxwell's equations to incorporate the near-solute solvent structure by considering excluded solvent volume effects, we have used it in this work to derive an analytical solution for the hydration free energy of an ion. In contrast to continuum solvent models, which assume that the normalized induced solvent electric dipole density P(n) is constant, P(n) mimics that observed from simulations. The analytical formula for the ionic hydration free energy shows that the Born radius, which has been used as an adjustable parameter to fit experimental hydration free energies, is no longer ill defined but is related to the radius and polarizability of the water molecule, the hydration number, and the first peak position of the solute-solvent radial distribution function. The resulting DeltaG(solv)(elec) values are shown to be close to the respective experimental numbers.     

Prediction of free energies of hydration with COSMO-RS on the SAMPL3 data set

The COSMO-RS method has been used for the prediction of free energies of hydration on the dataset of 36 chlorinated ethanes, biphenyls and dioxins considered in the SAMPL3 challenge. Straight application of the latest version of the COSMOtherm software yields an overall predictive accuracy of 1.05 kcal/mol (RMSE). The predictions for the chlorinated ethanes and dioxins are much better with 0.40 and 0.49 kcal/mol RMSE, respectively. The predictions for the chlorinated biphenyls show a systematic shift of approximately 1 kcal/mol, but the large RMSE of 1.59 kcal/mol mainly arises from two exceptional outliers. Possible reasons for this observation are discussed.     

Prediction of free energies of hydration with COSMO-RS on the SAMPL4 data set

The COSMO-RS method has been used for the prediction of free energies of hydration on a dataset of 47 complex multifunctional compounds considered in the SAMPL4 challenge. Straight application of the COSMOtherm software with the parameterization C21_0108 yields a predictive accuracy of 1.46 kcal/mol root mean square error overall and 1.18 kcal/mol if a single dominant outlier is removed.     

Surveying implicit solvent models for estimating small molecule absolute hydration free energies

Implicit solvent models are powerful tools in accounting for the aqueous environment at a fraction of the computational expense of explicit solvent representations. Here, we compare the ability of common implicit solvent models (TC, OBC, OBC2, GBMV, GBMV2, GBSW, GBSW/MS, GBSW/MS2 and FACTS) to reproduce experimental absolute hydration free energies for a series of 499 small neutral molecules that are modeled using AMBER/GAFF parameters and AM1-BCC charges. Given optimized surface tension coefficients for scaling the surface area term in the nonpolar contribution, most implicit solvent models demonstrate reasonable agreement with extensive explicit solvent simulations (average difference 1.0-1.7 kcal/mol and R(2)=0.81-0.91) and with experimental hydration free energies (average unsigned errors=1.1-1.4 kcal/mol and R(2)=0.66-0.81). Chemical classes of compounds are identified that need further optimization of their ligand force field parameters and others that require improvement in the physical parameters of the implicit solvent models themselves. More sophisticated nonpolar models are also likely necessary to more effectively represent the underlying physics of solvation and take the quality of hydration free energies estimated from implicit solvent models to the next level.     

Computation of hydration free energies of organic solutes with an implicit water model

A new approach for computing hydration free energies DeltaG(solv) of organic solutes is formulated and parameterized. The method combines a conventional PCM (polarizable continuum model) computation for the electrostatic component DeltaG(el) of DeltaG(solv) and a specially detailed algorithm for treating the complementary nonelectrostatic contributions (DeltaG(nel)). The novel features include the following: (a) two different cavities are used for treating DeltaG(el) and DeltaG(nel). For the latter case the cavity is larger and based on thermal atomic radii (i.e., slightly reduced van der Waals radii). (b) The cavitation component of DeltaG(nel) is taken to be proportional to the volume of the large cavity. (c) In the treatment of van der Waals interactions, all solute atoms are counted explicitly. The corresponding interaction energies are computed as integrals over the surface of the larger cavity; they are based on Lennard Jones (LJ) type potentials for individual solute atoms. The weighting coefficients of these LJ terms are considered as fitting parameters. Testing this method on a collection of 278 uncharged organic solutes gave satisfactory results. The average error (RMSD) between calculated and experimental free energy values varies between 0.15 and 0.5 kcal/mol for different classes of solutes. The larger deviations found for the case of oxygen compounds are probably due to a poor approximation of H-bonding in terms of LJ potentials. For the seven compounds with poorest fit to experiment, the error exceeds 1.5 kcal/mol; these outlier points were not included in the parameterization procedure. Several possible origins of these errors are discussed.     

Accurate predictions of nonpolar solvation free energies require explicit consideration of binding-site hydration

Continuum solvation methods are frequently used to increase the efficiency of computational methods to estimate free energies. In this paper, we have evaluated how well such methods estimate the nonpolar solvation free-energy change when a ligand binds to a protein. Three different continuum methods at various levels of approximation were considered, viz., the polarized continuum model (PCM), a method based on cavity and dispersion terms (CD), and a method based on a linear relation to the solvent-accessible surface area (SASA). Formally rigorous double-decoupling thermodynamic integration was used as a benchmark for the continuum methods. We have studied four protein-ligand complexes with binding sites of varying solvent exposure, namely the binding of phenol to ferritin, a biotin analogue to avidin, 2-aminobenzimidazole to trypsin, and a substituted galactoside to galectin-3. For ferritin and avidin, which have relatively hidden binding sites, rather accurate nonpolar solvation free energies could be obtained with the continuum methods if the binding site is prohibited to be filled by continuum water in the unbound state, even though the simulations and experiments show that the ligand replaces several water molecules upon binding. For the more solvent exposed binding sites of trypsin and galectin-3, no accurate continuum estimates could be obtained, even if the binding site was allowed or prohibited to be filled by continuum water. This shows that continuum methods fail to give accurate free energies on a wide range of systems with varying solvent exposure because they lack a microscopic picture of binding-site hydration as well as information about the entropy of water molecules that are in the binding site before the ligand binds. Consequently, binding affinity estimates based upon continuum solvation methods will give absolute binding energies that may differ by up to 200 kJ/mol depending on the method used. Moreover, even relative energies between ligands with the same scaffold may differ by up to 75 kJ/mol. We have tried to improve the continuum solvation methods by adding information about the solvent exposure of the binding site or the hydration of the binding site, and the results are promising at least for this small set of complexes.     

Solvation in octanol: parametrization of the continuum MST model

This study reports the parametrization of the HF/6‐31G(d) version of the MST continuum model for n‐octanol. Following our previous studies related to the MST parametrization for water, chloroform, and carbon tetrachloride, a detailed exploration of the definition of the solute/solvent interface has been performed. To this end, we have exploited the results obtained from free energy calculations coupled to Monte Carlo simulations, and those derived from the QM/MM analysis of solvent‐induced dipoles for selected solutes. The atomic hardness parameters have been determined by fitting to the experimental free energies of solvation in octanol. The final MST model is able to reproduce the experimental free energy of solvation for 62 compounds and the octanol/water partition coefficient (log P_ow) for 75 compounds with a root‐mean‐square deviation of 0.6 kcal/mol and 0.4 (in units of log P), respectively. The model has been further verified by calculating the octanol/water partition coefficient for a set of 27 drugs, which were not considered in the parametrization set. A good agreement is found between predicted and experimental values of log P_o/w, as noted in a root‐mean‐square deviation of 0.75 units of log P. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 1180–1193, 2001     

Predicting hydration free energies using all-atom molecular dynamics simulations and multiple starting conformations

Molecular dynamics simulations in explicit solvent were applied to predict the hydration free energies for 23 small organic molecules in blind SAMPL2 test. We found good agreement with experimental results, with an RMS error of 2.82 kcal/mol over the whole set and 1.86 kcal/mol over all the molecules except several hydroxyl-rich compounds where we find evidence for a systematic error in the force field. We tested two different solvent models, TIP3P and TIP4P-Ew, and obtained very similar hydration free energies for these two models; the RMS difference was 0.64 kcal/mol. We found that preferred conformation of the carboxylic acids in water differs from that in vacuum. Surprisingly, this conformational change is not adequately sampled on simulation timescales, so we apply an umbrella sampling technique to include free energies associated with the conformational change. Overall, the results of this test reveal that the force field parameters for some groups of molecules (such as hydroxyl-rich compounds) still need to be improved, but for most compounds, accuracy was consistent with that seen in our previous tests.     

Calculation of solvation free energies of charged solutes using mixed cluster/continuum models

We derive a consistent approach for predicting the solvation free energies of charged solutes in the presence of implicit and explicit solvents. We find that some published methodologies make systematic errors in the computed free energies because of the incorrect accounting of the standard state corrections for water molecules or water clusters present in the thermodynamic cycle. This problem can be avoided by using the same standard state for each species involved in the reaction under consideration. We analyze two different thermodynamic cycles for calculating the solvation free energies of ionic solutes: (1) the cluster cycle with an n water cluster as a reagent and (2) the monomer cycle with n distinct water molecules as reagents. The use of the cluster cycle gives solvation free energies that are in excellent agreement with the experimental values obtained from studies of ion-water clusters. The mean absolute errors are 0.8 kcal/mol for H(+) and 2.0 kcal/mol for Cu(2+). Conversely, calculations using the monomer cycle lead to mean absolute errors that are >10 kcal/mol for H(+) and >30 kcal/mol for Cu(2+). The presence of hydrogen-bonded clusters of similar size on the left- and right-hand sides of the reaction cycle results in the cancellation of the systematic errors in the calculated free energies. Using the cluster cycle with 1 solvation shell leads to errors of 5 kcal/mol for H(+) (6 waters) and 27 kcal/mol for Cu(2+) (6 waters), whereas using 2 solvation shells leads to accuracies of 2 kcal/mol for Cu(2+) (18 waters) and 1 kcal/mol for H(+) (10 waters).