Blind prediction of cyclohexane–water distribution coefficients from the SAMPL5 challenge

In the recent SAMPL5 challenge, participants submitted predictions for cyclohexane/water distribution coefficients for a set of 53 small molecules. Distribution coefficients (log D) replace the hydration free energies that were a central part of the past five SAMPL challenges. A wide variety of computational methods were represented by the 76 submissions from 18 participating groups. Here, we analyze submissions by a variety of error metrics and provide details for a number of reference calculations we performed. As in the SAMPL4 challenge, we assessed the ability of participants to evaluate not just their statistical uncertainty, but their model uncertainty—how well they can predict the magnitude of their model or force field error for specific predictions. Unfortunately, this remains an area where prediction and analysis need improvement. In SAMPL4 the top performing submissions achieved a root-mean-squared error (RMSE) around 1.5 kcal/mol. If we anticipate accuracy in log D predictions to be similar to the hydration free energy predictions in SAMPL4, the expected error here would be around 1.54 log units. Only a few submissions had an RMSE below 2.5 log units in their predicted log D values. However, distribution coefficients introduced complexities not present in past SAMPL challenges, including tautomer enumeration, that are likely to be important in predicting biomolecular properties of interest to drug discovery, therefore some decrease in accuracy would be expected. Overall, the SAMPL5 distribution coefficient challenge provided great insight into the importance of modeling a variety of physical effects. We believe these types of measurements will be a promising source of data for future blind challenges, especially in view of the relatively straightforward nature of the experiments and the level of insight provided.     

Prediction of cyclohexane-water distribution coefficients for the SAMPL5 data set using molecular dynamics simulations with the OPLS-AA force field

All-atom molecular dynamics simulations were used to predict water-cyclohexane distribution coefficients \(D_{cw}\) of a range of small molecules as part of the SAMPL5 blind prediction challenge. Molecules were parameterized with the transferable all-atom OPLS-AA force field, which required the derivation of new parameters for sulfamides and heterocycles and validation of cyclohexane parameters as a solvent. The distribution coefficient was calculated from the solvation free energies of the compound in water and cyclohexane. Absolute solvation free energies were computed by an established protocol using windowed alchemical free energy perturbation with thermodynamic integration. This protocol resulted in an overall root mean square error in \(\log D_{cw}\) of almost 4 log units and an overall signed error of ?3 compared to experimental data. There was no substantial overall difference in accuracy between simulating in NVT and NPT ensembles. The signed error suggests a systematic error but the experimental \(D_{cw}\) data on their own are insufficient to uncover the source of this error. Preliminary work suggests that the major source of error lies in the hydration free energy calculations.     

Prediction of cyclohexane-water distribution coefficient for SAMPL5 drug-like compounds with the QMPFF3 and ARROW polarizable force fields

We present the performance of blind predictions of water—cyclohexane distribution coefficients for 53 drug-like compounds in the SAMPL5 challenge by three methods currently in use within our group. Two of them utilize QMPFF3 and ARROW, polarizable force-fields of varying complexity, and the third uses the General Amber Force-Field (GAFF). The polarizable FF’s are implemented in an in-house MD package, Arbalest. We find that when we had time to parametrize the functional groups with care (batch 0), the polarizable force-fields outperformed the non-polarizable one. Conversely, on the full set of 53 compounds, GAFF performed better than both QMPFF3 and ARROW. We also describe the torsion-restrain method we used to improve sampling of molecular conformational space and thus the overall accuracy of prediction. The SAMPL5 challenge highlighted several drawbacks of our force-fields, such as our significant systematic over-estimation of hydrophobic interactions, specifically for alkanes and aromatic rings.     

Blind prediction of distribution in the SAMPL5 challenge with QM based protomer and p<Emphasis Type="Italic">K</Emphasis><Subscript>a</Subscript> corrections

The computation of distribution coefficients between polar and apolar phases requires both an accurate characterization of transfer free energies between phases and proper accounting of ionization and protomerization. We present a protocol for accurately predicting partition coefficients between two immiscible phases, and then apply it to 53 drug-like molecules in the SAMPL5 blind prediction challenge. Our results combine implicit solvent QM calculations with classical MD simulations using the non-Boltzmann Bennett free energy estimator. The OLYP/DZP/SMD method yields predictions that have a small deviation from experiment (RMSD = 2.3 \(\log\) D units), relative to other participants in the challenge. Our free energy corrections based on QM protomer and \({\text{p}}K_{\text{a}}\) calculations increase the correlation between predicted and experimental distribution coefficients, for all methods used. Unfortunately, these corrections are overly hydrophilic, and fail to account for additional effects such as aggregation, water dragging and the presence of polar impurities in the apolar phase. We show that, although expensive, QM-NBB free energy calculations offer an accurate and robust method that is superior to standard MM and QM techniques alone.     

Extended solvent-contact model approach to blind SAMPL5 prediction challenge for the distribution coefficients of drug-like molecules

The performance of the extended solvent-contact model has been addressed in the SAMPL5 blind prediction challenge for distribution coefficient (LogD) of drug-like molecules with respect to the cyclohexane/water partitioning system. All the atomic parameters defined for 41 atom types in the solvation free energy function were optimized by operating a standard genetic algorithm with respect to water and cyclohexane solvents. In the parameterizations for cyclohexane, the experimental solvation free energy (ΔG _sol ) data of 15 molecules for 1-octanol were combined with those of 77 molecules for cyclohexane to construct a training set because ΔG _sol values of the former were unavailable for cyclohexane in publicly accessible databases. Using this hybrid training set, we established the LogD prediction model with the correlation coefficient (R), average error (AE), and root mean square error (RMSE) of 0.55, 1.53, and 3.03, respectively, for the comparison of experimental and computational results for 53 SAMPL5 molecules. The modest accuracy in LogD prediction could be attributed to the incomplete optimization of atomic solvation parameters for cyclohexane. With respect to 31 SAMPL5 molecules containing the atom types for which experimental reference data for ΔG _sol were available for both water and cyclohexane, the accuracy in LogD prediction increased remarkably with the R, AE, and RMSE values of 0.82, 0.89, and 1.60, respectively. This significant enhancement in performance stemmed from the better optimization of atomic solvation parameters by limiting the element of training set to the molecules with experimental ΔG _sol data for cyclohexane. Due to the simplicity in model building and to low computational cost for parameterizations, the extended solvent-contact model is anticipated to serve as a valuable computational tool for LogD prediction upon the enrichment of experimental ΔG _sol data for organic solvents.     

Predicting cyclohexane/water distribution coefficients for the SAMPL5 challenge using MOSCED and the SMD solvation model

We present blind predictions using the solubility parameter based method MOSCED submitted for the SAMPL5 challenge on calculating cyclohexane/water distribution coefficients at 298 K. Reference data to parameterize MOSCED was generated with knowledge only of chemical structure by performing solvation free energy calculations using electronic structure calculations in the SMD continuum solvent. To maintain simplicity and use only a single method, we approximate the distribution coefficient with the partition coefficient of the neutral species. Over the final SAMPL5 set of 53 compounds, we achieved an average unsigned error of \(2.2\pm 0.2\) log units (ranking 15 out of 62 entries), the correlation coefficient (R) was \(0.6\pm 0.1\) (ranking 35), and \(72\pm 6\,\%\) of the predictions had the correct sign (ranking 30). While used here to predict cyclohexane/water distribution coefficients at 298 K, MOSCED is broadly applicable, allowing one to predict temperature dependent infinite dilution activity coefficients in any solvent for which parameters exist, and provides a means by which an excess Gibbs free energy model may be parameterized to predict composition dependent phase-equilibrium.     

SAMPL5: 3D-RISM partition coefficient calculations with partial molar volume corrections and solute conformational sampling

Implicit solvent methods for classical molecular modeling are frequently used to provide fast, physics-based hydration free energies of macromolecules. Less commonly considered is the transferability of these methods to other solvents. The Statistical Assessment of Modeling of Proteins and Ligands 5 (SAMPL5) distribution coefficient dataset and the accompanying explicit solvent partition coefficient reference calculations provide a direct test of solvent model transferability. Here we use the 3D reference interaction site model (3D-RISM) statistical-mechanical solvation theory, with a well tested water model and a new united atom cyclohexane model, to calculate partition coefficients for the SAMPL5 dataset. The cyclohexane model performed well in training and testing (\(R=0.98\) for amino acid neutral side chain analogues) but only if a parameterized solvation free energy correction was used. In contrast, the same protocol, using single solute conformations, performed poorly on the SAMPL5 dataset, obtaining \(R=0.73\) compared to the reference partition coefficients, likely due to the much larger solute sizes. Including solute conformational sampling through molecular dynamics coupled with 3D-RISM (MD/3D-RISM) improved agreement with the reference calculation to \(R=0.93\). Since our initial calculations only considered partition coefficients and not distribution coefficients, solute sampling provided little benefit comparing against experiment, where ionized and tautomer states are more important. Applying a simple \(\hbox {p}K_{\text {a}}\) correction improved agreement with experiment from \(R=0.54\) to \(R=0.66\), despite a small number of outliers. Better agreement is possible by accounting for tautomers and improving the ionization correction.     

Calculating distribution coefficients based on multi-scale free energy simulations: an evaluation of MM and QM/MM explicit solvent simulations of water-cyclohexane transfer in the SAMPL5 challenge

One of the central aspects of biomolecular recognition is the hydrophobic effect, which is experimentally evaluated by measuring the distribution coefficients of compounds between polar and apolar phases. We use our predictions of the distribution coefficients between water and cyclohexane from the SAMPL5 challenge to estimate the hydrophobicity of different explicit solvent simulation techniques. Based on molecular dynamics trajectories with the CHARMM General Force Field, we compare pure molecular mechanics (MM) with quantum-mechanical (QM) calculations based on QM/MM schemes that treat the solvent at the MM level. We perform QM/MM with both density functional theory (BLYP) and semi-empirical methods (OM1, OM2, OM3, PM3). The calculations also serve to test the sensitivity of partition coefficients to solute polarizability as well as the interplay of the quantum-mechanical region with the fixed-charge molecular mechanics environment. Our results indicate that QM/MM with both BLYP and OM2 outperforms pure MM. However, this observation is limited to a subset of cases where convergence of the free energy can be achieved.     

The SAMPL5 challenge for embedded-cluster integral equation theory: solvation free energies,aqueous p<Emphasis Type="Italic">K</Emphasis><Subscript>a</Subscript>, and cyclohexane–water log <Emphasis Type="Italic">D</Emphasis>

We predict cyclohexane–water distribution coefficients (log D _7.4) for drug-like molecules taken from the SAMPL5 blind prediction challenge by the “embedded cluster reference interaction site model” (EC-RISM) integral equation theory. This task involves the coupled problem of predicting both partition coefficients (log P) of neutral species between the solvents and aqueous acidity constants (pK _a) in order to account for a change of protonation states. The first issue is addressed by calibrating an EC-RISM-based model for solvation free energies derived from the “Minnesota Solvation Database” (MNSOL) for both water and cyclohexane utilizing a correction based on the partial molar volume, yielding a root mean square error (RMSE) of 2.4 kcal mol^?1 for water and 0.8–0.9 kcal mol^?1 for cyclohexane depending on the parametrization. The second one is treated by employing on one hand an empirical pK _a model (MoKa) and, on the other hand, an EC-RISM-derived regression of published acidity constants (RMSE of 1.5 for a single model covering acids and bases). In total, at most 8 adjustable parameters are necessary (2–3 for each solvent and two for the pK _a) for training solvation and acidity models. Applying the final models to the log D _7.4 dataset corresponds to evaluating an independent test set comprising other, composite observables, yielding, for different cyclohexane parametrizations, 2.0–2.1 for the RMSE with the first and 2.2–2.8 with the combined first and second SAMPL5 data set batches. Notably, a pure log P model (assuming neutral species only) performs statistically similarly for these particular compounds. The nature of the approximations and possible perspectives for future developments are discussed.     

Étude d'équilibres en solution à l'aide des échangeurs d'ions: II Détermination des constantes de dissociation des perchlorates alcalins dans les mélanges eau—acide acétique—acide perchlorique

The thermodynamic dissociation constants of lithium, sodium, potassium, rubidium and cesium perchlorates in water—acetic acid—perchloric acid mixtures have been determined by an ion-exchange method. The distribution coefficients of alkaline elements have been measured in water—acetic acid—perchloric acid mixtures containing a variable quantity of water (4–100 % by weight) and a constant amount of perchloric acid. The variation of these distribution coefficients with perchloric acid concentration has been studied in various mixtures containing a constant amount of water (less than 20 % $\text{w}\text{w}$). The results have been used to determine the dissociation constants of alkaline perchlorates and the selectivity coefficients of alkaline ions and hydrogen ion in the aqueous organic mixtures studied.     

Solubility of naproxen in several organic solvents at different temperatures

By using the van’t Hoff and Gibbs equations the thermodynamic functions Gibbs free energy, enthalpy, and entropy of solution, were evaluated from solubility data of naproxen (NAP) determined at several temperatures in octanol, isopropyl myristate, chloroform, and cyclohexane, as pure solvents. The water-saturated organic solvents also were studied except cyclohexane. The excess free energy and the activity coefficients of the solutes, and the mixing and solvation thermodynamic quantities were also determined. The NAP solubilities were higher in chloroform and octanol with respect to those obtained in cyclohexane. In addition, by using literature values for NAP aqueous solubility, the thermodynamic functions relative to transfer of this drug from water to organic solvents were also estimated.     

Determination of Diffusion Coefficients for Binary Nonelectrolyte Mixtures. A Free-Volume Predictive Approach

A diaphragm cell has been used to measure mutual diffusion coefficients at 25°C for four binary nonelectrolyte mixtures: ethylbenzene + n-hexane, carbon tetrachloride + ethylbenzene, cyclohexane + p-xylene, and 1,2-dichloroethane + cyclohexane. A free-volume predictive approach for binary mutual diffusion coefficients was developed and tested. Only infinite dilution diffusion coefficients, some readily available pure substance data, and UNIFAC group contribution parameters are used in the model. No binary equilibrium thermodynamic information is required. For 73 binary systems with an overall average absolute deviation of 5.2%, it has been shown that the developed method is better than two commonly available reference methods for the prediction of liquid diffusion coefficients.     

Prediction of cyclohexane-water distribution coefficients with COSMO-RS on the SAMPL5 data set

The Conductor-Like-Screening-Model for Real Solvents (COSMO-RS) method has been used for the blind prediction of cyclohexane-water distribution coefficients logD within the SAMPL challenge. The partition coefficient logP of the neutral species was calculated first and then corrected for dissociation or protonation, as appropriate for acidic or basic solutes, to obtain the cyclohexane-water logD. Using the latest version of the COSMOtherm implementation, this approach in combination with a rigorous conformational sampling yielded a predictive accuracy of 2.11 log units (RMSD) for the 53 compounds of the blind prediction dataset. By that it was the most accurate of all contest submissions and it also achieved the best rank order. The RMSD mainly arises from a group of outliers in the negative logD range, which at least partly may arise from dimerization or other experimental problems coming up for very polar molecules in very non-polar solvents.     

Partition coefficients for the SAMPL5 challenge using transfer free energies

SAMPL challenges (Mobley et al. in J Comput Aided Mol Des 28:135–150, 2014; Skillman in J Comput Aided Mol Des 26:473–474, 2012; Geballe in J Comput Aided Mol Des 24:259–279, 2010; Guthrie in J Phys Chem B 113:4501–4507, 2009) provide excellent opportunities to assess theoretical approaches on new data sets with a goal of gaining greater insight towards protein and ligand modeling. In the SAMPL5 experiment, cyclohexane–water partition coefficients were determined using a vertical solvation scheme in conjunction with the SMD continuum solvent model. Several DFT functionals partnered with correlation consistent basis sets were evaluated for the prediction of the partition coefficients. The approach chosen for the competition, a B3PW91 vertical solvation scheme, yields a mean absolute deviation of 1.9 logP units and performs well at estimating the correct hydrophilicity and hydrophobicity for the full SAMPL5 molecule set.     

Temperature Dependence of Solubility for Ibuprofen in Some Organic and Aqueous Solvents

The thermodynamic functions—Gibbs energy, enthalpy, and entropy of solution—were evaluated from the solubilities of ibuprofen determined at several temperatures in the pure solvents: octanol, isopropyl myristate, chloroform, cyclohexane, and water. The organic solvent-saturated aqueous media and water-saturated organic solvents were also studied, except for cyclohexane. In aqueous media, the solubility was determined at pH = 7.4 and an ionic strength 0.15 mol-L^–1 (physiological values). The excess Gibbs energy and the activity coefficients of the solutes were also determined. The solubilities are higher in organic media such as chloroform and octanol than in aqueous media and cyclohexane.     

Thermodynamic Study of the Solubility of Benzocaine in some Organic and Aqueous Solvents

The thermodynamic functions free energy, enthalpy, and entropy of solution, were evaluated from solubility data of benzocaine determined at several temperatures in octanol, water, and the mutually saturated solvents, in isopropyl myristate, water, and the mutually saturated solvents, and in cyclohexane. In aqueous media the solubility was determined at pH 7.4 and ionic strength 0.15 mol-L^–1. The excess free energy and the activity coefficients of the solutes also were determined. The solubility was higher in organic media, such as octanol and isopropyl myristate, than in aqueous media and cyclohexane.     

An explicit-solvent hybrid QM and MM approach for predicting pKa of small molecules in SAMPL6 challenge

In this work we have developed a hybrid QM and MM approach to predict pKa of small drug-like molecules in explicit solvent. The gas phase free energy of deprotonation is calculated using the M06-2X density functional theory level with Pople basis sets. The solvation free energy difference of the acid and its conjugate base is calculated at MD level using thermodynamic integration. We applied this method to the 24 drug-like molecules in the SAMPL6 blind pKa prediction challenge. We achieved an overall RMSE of 2.4 pKa units in our prediction. Our results show that further optimization of the protocol needs to be done before this method can be used as an alternative approach to the well established approaches of a full quantum level or empirical pKa prediction methods.     

Solubility of 1-Butene in Water and in a Medium for Cultivation of a Bacterial Strain

Solubility measurements of 1-butene in water, from 20 to 50°C and at atmospheric pressure, were carried out using a Ben-Naim/Baer-type apparatus. The experimental results have a precision of about ±0.3%. Using accurate thermodynamic relations, the Ostwald coefficients at the experimental conditions and at infinite dilution, the mole fractions of the dissolved gas at the gas partial pressure of 101.325 kPa and the Henry coefficients at the water vapor pressure were calculated. The mole fraction of dissolved gas were fitted to the Clarke, Glew, and Weiss equation and thermodynamic quantities, standard molar Gibbs energy, entropy, and enthalpy changes, for the process of transferring the 1-butene molecules from the gaseous to the water phase, were computed. Moreover, solubility measurements of 1-butene in an aqueous medium for the cultivation of Xanthobacter Py2 in the same temperature range were also performed at atmospheric pressure. These solubility data are approximately 2.6% lower than those observed in pure water.     

p, T, x, y data of benzene + n-hexane and cyclohexane + n-heptane systems

The isothermal vapour—liquid equilibria of the benzene + n-hexane and cyclohexane + n-heptane systems have been studied using a dynamic method. The thermodynamic consistency of the data has been tested and the prediction from several empirical and semitheoretical models have been compared with the experimental values of different excess properties.