A new set of solute descriptors to calculate solubility of drugs in mono-solvents.

A new set of solute parameters derived from a correlation model using Catalan parameters. The parameters represent the interaction of the solute with the mono-solvents at 298.15K. The computational procedure was adopted from Abraham's solvation model and the obtained results are promising. In this work, the calculated parameters were used to back-calculate the drugs solubility in various mono-solvents at different temperatures employing the van't Hoff's model as the skeleton on the derived model. The obtained mean percentage deviations (MPDs) were in the range of 3.1 to 88.5% with the overall MPD of 29.1%. (1) Derivation of a new set of solute parameters from a correlation model using Catalan parameters; (2) adoption of the calculation method of Abraham's solvation model with the skeleton of van't Hoff's equation; (3) using the achieved parameters for back-calculation of drugs solubility in various mono-solvents; (4) obtaining an overall acceptable mean percentage deviation of 29.1% from calculations.

Machine Learning Quantitative Structure-Property Relationships as a Function of Ionic Liquid Cations for the Gas-Ionic Liquid Partition Coefficient of Hydrocarbons.

Ionic liquids (ILs) are known for their unique characteristics as solvents and electrolytes. Therefore, new ILs are being developed and adapted as innovative chemical environments for different applications in which their properties need to be understood on a molecular level. Computational data-driven methods provide means for understanding of properties at molecular level, and quantitative structure-property relationships (QSPRs) provide the framework for this. This framework is commonly used to study the properties of molecules in ILs as an environment. The opposite situation where the property is considered as a function of the ionic liquid does not exist. The aim of the present study was to supplement this perspective with new knowledge and to develop QSPRs that would allow the understanding of molecular interactions in ionic liquids based on the structure of the cationic moiety. A wide range of applications in electrochemistry, separation and extraction chemistry depends on the partitioning of solutes between the ionic liquid and the surrounding environment that is characterized by the gas-ionic liquid partition coefficient. To model this property as a function of the structure of a cationic counterpart, a series of ionic liquids was selected with a common bis-(trifluoromethylsulfonyl)-imide anion, [Tf2N]-, for benzene, hexane and cyclohexane. MLR, SVR and GPR machine learning approaches were used to derive data-driven models and their performance was compared. The cross-validation coefficients of determination in the range 0.71-0.93 along with other performance statistics indicated a strong accuracy of models for all data series and machine learning methods. The analysis and interpretation of descriptors revealed that generally higher lipophilicity and dispersion interaction capability, and lower polarity in the cations induces a higher partition coefficient for benzene, hexane, cyclohexane and hydrocarbons in general. The applicability domain analysis of models concluded that there were no highly influential outliers and the models are applicable to a wide selection of cation families with variable size, polarity and aliphatic or aromatic nature.

Drug Solubility Correlation Using the Jouyban-Acree Model: Effects of Concentration Units and Error Criteria.

An important factor affecting the model accuracy is the unit expression type for solute and solvent concentrations. One can report the solute and solvent concentration in various units and compare them with various error scales. In order to investigate the unit and error scale expression effects on the accuracy of the Jouyban-Acree model, in the current study, seventy-nine solubility data sets were collected randomly from the published articles and solute and solvent concentrations in the investigated systems were expressed in various units. Mass fraction, mole fraction, and volume fraction were the employed concentration units for the solvent compositions, and mole fraction, molar, and gram/liter were the investigated concentration units for the solutes. The solubility data, with various solute/solvent concentration units, were correlated using the Jouyban-Acree model, and the accuracy of each model for correlating the data was investigated by calculating different error scales and discussed.

Reference Materials for Phase Equilibrium Studies. 1. Liquid-Liquid Equilibria (IUPAC Technical Report).

This article is the first of three projected IUPAC Technical Reports resulting from IUPAC Project 2011-037-2-100 (Reference Materials for Phase Equilibrium Studies). The goal of that project was to select reference systems with critically evaluated property values for the validation of instruments and techniques used in phase equilibrium studies for mixtures. This Report proposes seven systems for liquid-liquid equilibrium studies, covering the four most common categories of binary mixtures: aqueous systems of moderate solubility, non-aqueous systems, systems with low solubility, and systems with ionic liquids. For each system, the available literature sources, accepted data, smoothing equations, and estimated uncertainties are given.

Evaluation of nine condensed-phase force fields of the GROMOS, CHARMM, OPLS, AMBER, and OpenFF families against experimental cross-solvation free energies.

Experimental solvation free energies are nowadays commonly included as target properties in the validation of condensed-phase force fields, sometimes even in their calibration. In a previous article [Kashefolgheta et al., J. Chem. Theory. Comput., 2020, 16, 7556-7580], we showed how the involved comparison between experimental and simulation results could be made more systematic by considering a full matrix of cross-solvation free energies . For a set of N molecules that are all in the liquid state under ambient conditions, such a matrix encompasses N×N entries for considering each of the N molecules either as solute (A) or as solvent (B). In the quoted study, a cross-solvation matrix of 25 × 25 experimental value was introduced, considering 25 small molecules representative for alkanes, chloroalkanes, ethers, ketones, esters, alcohols, amines, and amides. This experimental data was used to compare the relative accuracies of four popular condensed-phase force fields, namely GROMOS-2016H66, OPLS-AA, AMBER-GAFF, and CHARMM-CGenFF. In the present work, the comparison is extended to five additional force fields, namely GROMOS-54A7, GROMOS-ATB, OPLS-LBCC, AMBER-GAFF2, and OpenFF. Considering these nine force fields, the correlation coefficients between experimental values and simulation results range from 0.76 to 0.88, the root-mean-square errors (RMSEs) from 2.9 to 4.8 kJ mol-1, and average errors (AVEEs) from -1.5 to +1.0 kJ mol-1. In terms of RMSEs, GROMOS-2016H66 and OPLS-AA present the best accuracy (2.9 kJ mol-1), followed by OPLS-LBCC, AMBER-GAFF2, AMBER-GAFF, and OpenFF (3.3 to 3.6 kJ mol-1), and then by GROMOS-54A7, CHARM-CGenFF, and GROMOS-ATB (4.0 to 4.8 kJ mol-1). These differences are statistically significant but not very pronounced, and are distributed rather heterogeneously over the set of compounds within the different force fields.

Revision and Extension of a Generally Applicable Group-Additivity Method for the Calculation of the Standard Heat of Combustion and Formation of Organic Molecules.

The calculation of the heats of combustion ΔH°c and formation ΔH°f of organic molecules at standard conditions is presented using a commonly applicable computer algorithm based on the group-additivity method. This work is a continuation and extension of an earlier publication. The method rests on the complete breakdown of the molecules into their constituting atoms, these being further characterized by their immediate neighbor atoms. The group contributions are calculated by means of a fast Gauss-Seidel fitting calculus using the experimental data of 5030 molecules from literature. The applicability of this method has been tested by a subsequent ten-fold cross-validation procedure, which confirmed the extraordinary accuracy of the prediction of ΔH°c with a correlation coefficient R2 and a cross-validated correlation coefficient Q2 of 1, a standard deviation σ of 18.12 kJ/mol, a cross-validated standard deviation S of 19.16 kJ/mol, and a mean absolute deviation of 0.4%. The heat of formation ΔH°f has been calculated from ΔH°c using the standard enthalpies of combustion for the elements, yielding a correlation coefficient R2 for ΔH°f of 0.9979 and a corresponding standard deviation σ of 18.14 kJ/mol.

Calculation of the Vapour Pressure of Organic Molecules by Means of a Group-Additivity Method and Their Resultant Gibbs Free Energy and Entropy of Vaporization at 298.15 K.

The calculation of the vapour pressure of organic molecules at 298.15 K is presented using a commonly applicable computer algorithm based on the group-additivity method. The basic principle of this method rests on the complete breakdown of the molecules into their constituting atoms, further characterized by their immediate neighbour atoms. The group contributions are calculated by means of a fast Gauss-Seidel fitting algorithm using the experimental data of 2036 molecules from literature. A ten-fold cross-validation procedure has been carried out to test the applicability of this method, which confirmed excellent quality for the prediction of the vapour pressure, expressed in log(pa), with a cross-validated correlation coefficient Q2 of 0.9938 and a standard deviation σ of 0.26. Based on these data, the molecules' standard Gibbs free energy ΔG°vap has been calculated. Furthermore, using their enthalpies of vaporization, predicted by an analogous group-additivity approach published earlier, the standard entropy of vaporization ΔS°vap has been determined and compared with experimental data of 1129 molecules, exhibiting excellent conformance with a correlation coefficient R2 of 0.9598, a standard error σ of 8.14 J/mol/K and a medium absolute deviation of 4.68%.

Generalized molecular solvation in non-aqueous solutions by a single parameter implicit solvation scheme.

In computer simulations of solvation effects on chemical reactions, continuum modeling techniques regain popularity as a way to efficiently circumvent an otherwise costly sampling of solvent degrees of freedom. As effective techniques, such implicit solvation models always depend on a number of parameters that need to be determined earlier. In the past, the focus lay mostly on an accurate parametrization of water models. Yet, non-aqueous solvents have recently attracted increasing attention, in particular, for the design of battery materials. To this end, we present a systematic parametrization protocol for the Self-Consistent Continuum Solvation (SCCS) model resulting in optimized parameters for 67 non-aqueous solvents. Our parametrization is based on a collection of ≈6000 experimentally measured partition coefficients, which we collected in the Solv@TUM database presented here. The accuracy of our optimized SCCS model is comparable to the well-known universal continuum solvation model (SMx) family of methods, while relying on only a single fit parameter and thereby largely reducing statistical noise. Furthermore, slightly modifying the non-electrostatic terms of the model, we present the SCCS-P solvation model as a more accurate alternative, in particular, for aromatic solutes. Finally, we show that SCCS parameters can, to a good degree of accuracy, also be predicted for solvents outside the database using merely the dielectric bulk permittivity of the solvent of choice.

Smart systems for determination of drug's solubility.

The solubility of drugs is a crucial physicochemical property in the drug discovery or development process and for improving the bioavailability of drugs. There are various methods for evaluating the solubility of drugs including manual measurement methods, mathematical methods, and smart methods. Manual measurement and mathematical methods have some defects which make the smart systems more reliable and important in this field. In this review, various instruments used for the solubility determination, along with the smart systems, have been discussed. Mechanism and applications of each method have been elaborated in detail. Moreover, unique characteristics as well as some limitations of discussed methods are also described.

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.

Calculation of the Surface Tension of Ordinary Organic and Ionic Liquids by Means of a Generally Applicable Computer Algorithm Based on the Group-Additivity Method.

The calculation of the surface tension of ordinary organic and ionic liquids, based on a computer algorithm applying a refined group-additivity method, is presented. The refinement consists of the complete breakdown of the molecules into their constituting atoms, further distinguishing them by their immediate neighbour atoms and bond constitution. The evaluation of the atom-groups' contributions was carried out by means of a fast Gauss-Seidel fitting method, founded upon the experimental data of 1893 compounds from literature. The result has been tested for plausibility using a 10-fold cross-validation (cv) procedure. The direct calculation and the cv test proved the applicability of the present method by the close similarity and excellent goodness of fit R² and Q² of 0.9039 and 0.8823, respectively. The respective standard deviations are ±1.99 and ±2.16 dyn/cm. Some correlation peculiarities have been observed in a series of ordinary and ionic liquids with homologous alkyl chains, as well as with di- and trihydroxy-groups-containing liquids, which have been discussed in detail, exhibiting the limit of the present method.

Solubility Prediction of Drugs in Binary Solvent Mixtures at Various Temperatures Using a Minimum Number of Experimental Data Points.

This study aimed to provide a rational experimental design to collect a minimum number of experimental data points for a drug dissolved in a given binary solvent mixture at various temperatures, and to describe a computational procedure to predict the solubility of the drugs in any solvent composition and temperature of interest. We gathered available solubility data sets from papers published from 2012 to 2016 (56 data sets, 3488 data points totally). The mean percentage deviations (MPD) used to check the accuracy of predictions was calculated by Eq. 10. Fifty-six datasets were analyzed using 8 training data points which the overall MPD was calculated to be 15.5% ± 15.1%, and for 52 datasets after excluding 5 outlier sets was 12.1% ± 8.9%. The paired t test was conducted to compare the MPD values obtained from the models trained by 7 and 8 training data points and the reduction in prediction overall MPD (from 17.7% to 15.5%) was statistically significant (p < 0.04). To further reduction in MPD values, the computations were also conducted using 9 training data points, which did not reveal any significant difference comparing to the predictions using 8 training data points (p > 0.88). This observation revealed that the model adequately trained using 8 data points and could be used as a practical strategy for predicting the solubility of drugs in binary solvent mixtures at various temperatures with acceptable prediction error and using minimum experimental efforts. These sorts of predictions are highly in demand in the pharmaceutical industry.

Application of a General Computer Algorithm Based on the Group-Additivity Method for the Calculation of Two Molecular Descriptors at Both Ends of Dilution: Liquid Viscosity and Activity Coefficient in Water at Infinite Dilution.

The application of a commonly used computer algorithm based on the group-additivity method for the calculation of the liquid viscosity coefficient at 293.15 K and the activity coefficient at infinite dilution in water at 298.15 K of organic molecules is presented. The method is based on the complete breakdown of the molecules into their constituting atoms, further subdividing them by their immediate neighborhood. A fast Gauss-Seidel fitting method using experimental data from literature is applied for the calculation of the atom groups' contributions. Plausibility tests have been carried out on each of the calculations using a ten-fold cross-validation procedure which confirms the excellent predictive quality of the method. The goodness of fit (Q²) and the standard deviation (σ) of the cross-validation calculations for the viscosity coefficient, expressed as log(η), was 0.9728 and 0.11, respectively, for 413 test molecules, and for the activity coefficient log(γ)∞ the corresponding values were 0.9736 and 0.31, respectively, for 621 test compounds. The present approach has proven its versatility in that it enabled the simultaneous evaluation of the liquid viscosity of normal organic compounds as well as of ionic liquids.

Calculation of Five Thermodynamic Molecular Descriptors by Means of a General Computer Algorithm Based on the Group-Additivity Method: Standard Enthalpies of Vaporization, Sublimation and Solvation, and Entropy of Fusion of Ordinary Organic Molecules and Total Phase-Change Entropy of Liquid Crystals.

The calculation of the standard enthalpies of vaporization, sublimation and solvation of organic molecules is presented using a common computer algorithm on the basis of a group-additivity method. The same algorithm is also shown to enable the calculation of their entropy of fusion as well as the total phase-change entropy of liquid crystals. The present method is based on the complete breakdown of the molecules into their constituting atoms and their immediate neighbourhood; the respective calculations of the contribution of the atomic groups by means of the Gauss-Seidel fitting method is based on experimental data collected from literature. The feasibility of the calculations for each of the mentioned descriptors was verified by means of a 10-fold cross-validation procedure proving the good to high quality of the predicted values for the three mentioned enthalpies and for the entropy of fusion, whereas the predictive quality for the total phase-change entropy of liquid crystals was poor. The goodness of fit (Q²) and the standard deviation (σ) of the cross-validation calculations for the five descriptors was as follows: 0.9641 and 4.56 kJ/mol (N = 3386 test molecules) for the enthalpy of vaporization, 0.8657 and 11.39 kJ/mol (N = 1791) for the enthalpy of sublimation, 0.9546 and 4.34 kJ/mol (N = 373) for the enthalpy of solvation, 0.8727 and 17.93 J/mol/K (N = 2637) for the entropy of fusion and 0.5804 and 32.79 J/mol/K (N = 2643) for the total phase-change entropy of liquid crystals. The large discrepancy between the results of the two closely related entropies is discussed in detail. Molecules for which both the standard enthalpies of vaporization and sublimation were calculable, enabled the estimation of their standard enthalpy of fusion by simple subtraction of the former from the latter enthalpy. For 990 of them the experimental enthalpy-of-fusion values are also known, allowing their comparison with predictions, yielding a correlation coefficient R² of 0.6066.

Comment on "structural determinants of drug partitioning in surrogates of phosphatidylcholine bilayer strata".

The Abraham model correlation for describing the partitioning behavior of solutes between water and hexadecane was redetermined using the measured partition coefficient data and solute descriptors derived from experimental data. The newly derived correlation provides a much better mathematical description of the observed partition coefficient data than the correlation given in the published paper.

An NMR method for the quantitative assessment of intramolecular hydrogen bonding; application to physicochemical, environmental, and biochemical properties.

(1)H NMR chemical shifts have been obtained in the solvents deuterochloroform and dimethyl sulfoxide. The difference in the chemical shifts of an OH or NH group in these two solvents, Δδ = δ(DMSO) - δ(CDCl3), can be converted into the hydrogen bond acidity, A, of the group using the equation A = 0.0065 + 0.133Δδ. The NMR A value, ANMR, can be used as a quantitative assessment of intramolecular hydrogen bonding. We list values of Δδ and ANMR for 55 compounds containing an OH group and 60 compounds with an NH group. For the hydroxy compounds, if A > 0.5 then the OH group is not part of an intramolecular hydrogen bond, but if A < 0.1 then the OH group forms part of an intramolecular hydrogen bond. For NH compounds, if A > 0.16 the NH group is not part of an intramolecular hydrogen bond, and if A < 0.05 the NH group is part of an intramolecular hydrogen bond. No comparison compounds are needed, and the method is extremely simple. We further show how it is possible to relate intramolecular hydrogen bonding to the actual effect on values of a number of physicochemical, environmental, and biochemical properties.

Comments Regarding "Solubility determination and thermodynamic model analysis of L-α-glyceryl phosphorylcholine in different organic solvents of 278.15-323.15 K".

A polemic is given regarding several of the calculated curve-fit parameters that Zhou and coworkers reported in their published paper. The calculated curve-fit parameters for the Combined Nearly Ideal Binary Solvent/Redlich-Kister, Jouyban-Acree-van't Hoff, Sun and modified Apelblat models were found to give mole fraction solubilities that exceeded unity. Our analysis also found that the mean relative absolute percent deviations provided by the authors were significantly underestimated.

Preferential Solvation Study of Rosuvastatin in the {PEG400 (1) + Water (2)} Cosolvent Mixture and GastroPlus Software-Based In Vivo Predictions.

Rosuvastatin (RST) is a poorly water-soluble drug responsible for limited in vivo dissolution and subsequently low oral systemic absorption (poor bioavailability). The mole fraction solubility values of RST in various ratios of binary mixtures "{PEG400 (1) + water (2)}" at 298.15 K were employed to investigate the preferential solvation (PS) of RST (3) by the binary components. Moreover, the GastroPlus program predicted the drug dissolution/absorption rates, plasma drug concentration, and compartmental regional drug absorbed from a conventional tablet as compared to the RST-loaded (PEG400 + water) mixture (at x 1 = 0.5) in healthy subjects (considering the fast condition). Fedors' method was adopted to estimate the values of molar volume (314.8 cm3·mol-1) and Hildebrand solubility parameter (28.08 MPa1/2) of RST. The results of inverse Kirkwood-Buff integrals showed the PS of RST by PEG400 as observed in all studied ratios of the binary mixture. The highest PS value (δx 1,3 = 1.65 × 10-2) for RST by PEG400 was attained at x 1 = 0.5. Finally, the GastroPlus program predicted the maximum dissolution rate [20 mg within 15 min as compared to pure RST (1.5 mg within 15 min)]. Moreover, the program predicted increased in vivo oral absorption (1.2 µg/mL) and enhanced regional absorption (95.3%) of RST from upper segments of the gastrointestinal tract for the RST-loaded PEG400 + water mixture in humans as compared to conventional tablets (87.5% as total regional absorption and 0.88 µg/mL as in vivo absorption). Hence, the present binary system ferrying RST can be a promising strategy to control systemic dyslipidemia after oral or subcutaneous administration.

Development of surface-SFED models for polar solvents.

We developed surface grid-based solvation free energy density (Surface-SFED) models for 36 commonly used polar solvents. The parametrization was performed with a large and diverse set of experimental solvation free energies mainly consisting of combinations of polar solvent and multipolar solute. Therefore, the contribution of hydrogen bonds was dominant in the model. In order to increase the accuracy of the model, an elaborate version of a previous hydrogen bond acidity and basicity prediction model was introduced. We present two parametrizations for use with experimentally determined (Surface-SFED/HB(exp)) and empirical (Surface-SFED/HB(cal)) hydrogen bond acidity and basicity values. Our computational results agreed well with experimental results, and inaccuracy of empirical hydrogen bond acidity and basicity values was the main source of error in Surface-SFED/HB(cal). The mean absolute errors of Surface-SFED/HB(exp) and Surface-SFED/HB(cal) were 0.49 and 0.54 kcal/mol, respectively.

The hydrogen bond properties of water from 273 K to 573 K; equations for the prediction of gas-water partition coefficients.

An equation due to Plyasunov and Shock for the calculation of gas to water partition coefficients, as log K(w), at high temperature requires knowledge of experimental values of log K, ΔH the standard enthalpy of hydration at 298 K, ΔCp the heat capacity of hydration at 298 K and b' that is a constant that refers to the variation of ΔCp(w) with temperature. Linear free energy relationships based on Abraham descriptors for solutes have been constructed for all of these four input quantities, so that log K(w), ΔH, ΔCp and b' can be estimated. Known values of the four input quantities, where available, together with estimated values enabled values of log K(w) from 273 to 573 K to be calculated for 555 solutes. At various fixed temperatures LFERs again based on Abraham descriptors were constructed from the obtained log K(w) values for the 555 solutes. These LFERs can then be used to estimate further values of log K(w) between 273 and 573 K for any solute with already determined descriptors, so that knowledge of experimental values of log K, ΔH, ΔCp and b' is no longer necessary. The obtained LFERs show how the solvation properties of water vary with temperature. Both water hydrogen bond acidity and hydrogen bond basicity towards solutes decrease substantially with increase of temperature until at 573 K the hydrogen bond properties of water resemble those for solvents such as nitrobenzene and acetonitrile at 298 K. A characteristic property of water at ambient temperatures is that water will not solvate non-polar solutes, thus leading to large Henry's law constants and small values of K(w). Although this property also decreases with increase of temperature, our results indicate that it still remains to some extent even at 573 K, so that the general solvation properties of water at 573 K do not resemble the solvation properties of organic solvents at 298 K.