Mathematical representation of solubility of amino acids in binary aqueous-organic solvent mixtures at various temperatures using the Jouyban-Acree model

Applicability of a solution model for calculating solubility of amino acids in binary aqueous-organic solvent mixtures at various temperatures was shown. The accuracy of the proposed model was evaluated by computing mean percentage deviation (MPD) employing available solubility data of amino acids in binary solvents at various temperatures from the literature. The overall MPD (+/- SD) for correlation of solubility data was 16.5 +/- 8.8%. In addition, the equations calculating solubility of amino acids in binary solvent mixtures at a fixed temperature was revisited.     

Modeling drug solubility in water-cosolvent mixtures using an artificial neural network

Application of the artificial neural network (ANN) to calculate the solubility of drugs in water-cosolvent mixtures was shown using 35 experimental data sets. The networks employed were feedforward backpropagation errors with one hidden layer. The topology of neural network was optimized and the optimum topology achieved was a 6-5-1 architecture. All data points in each set were used to train the ANN and the solubilities were back-calculated employing the trained networks. The differences between calculated solubilities and experimental values was used as an accuracy criterion and defined as mean percentage deviation (MPD). The overall MPD (OMPD) and its S.D. obtained for 35 data sets was 0.90 +/- 0.65%. To assess the prediction capability of the method, five data points in each set were used as training set and the solubility at other solvent compositions were predicted using trained ANNs whereby the OMPD (+/-S.D.) for this analysis was 9.04 +/- 3.84%. All 496 data points from 35 data sets were used to train a general ANN model, then the solubilities were back-calculated using the trained network and MPD (+/-S.D.) was 24.76 +/- 14.76%. To test the prediction capability of the general ANN model, all data points with odd set numbers from 35 data sets were employed to train the ANN model, the solubility for the even data set numbers were predicted and the OMPD (+/-S.D.) was 55.97 +/- 57.88%. To provide a general ANN model for a given cosolvent, the experimental data points from each binary solvent were used to train ANN and back-calculated solubilities were used to calculate MPD values. The OMPD (+/-S.D.) for five cosolvent systems studied was 2.02 +/- 1.05%. A similar numerical analysis was used to calculate the solubility of structurally related drugs in a given binary solvent and the OMPD (+/-S.D.) was 4.70 +/- 2.02%. ANN model also trained using solubility data from a given drug in different cosolvent mixtures and the OMPD (+/-S.D.) obtained was 3.36 +/- 1.66%. The results for different numerical analyses using ANN were compared with those obtained from the most accurate multiple linear regression model, namely the combined nearly ideal binary solvent/Redlich-Kister equation, and the ANN model showed excellent superiority to the regression model.     

Solubility prediction of solutes in aqueous mixtures of ethylene glycols

The applicability of a trained version of the Jouyban-Acree model, for predicting the solubility of solutes in aqueous mixtures of ethylene glycol and its polymerized forms was shown. The solubilities of 8 drugs in binary mixtures were determined and the mean percentage deviation (MPD) was calculated as a prediction accuracy criterion and the overall MPD (+/- SD) was 23.2 (+/- 13.1)%.     

Prediction of drug solubility in water-propylene glycol mixtures using Jouyban-Acree model

A trained version of the Jouyban-Acree model was presented to predict drug solubility in water-propylene glycol mixtures at various temperatures. The model is able to predict the solubility in various solubility units and requires the experimental solubility of a solute in mono-solvent systems. The mean percentage deviation (MPD) of predicted solubilities was computed to show the accuracy of the predicted data and 24% was found as the average MPD for 27 data sets studied. The proposed model enables the researchers to predict solubiliy in water-propylene glycol mixtures at various temperatures and reduces the number of required experimental data from five to two points.     

Solubility prediction of clonazepam in aqueous mixtures of ethanol,polyethylene glycol 200 and propylene glycol at 30 °C

Solubility of clonazepam in aqueous binary mixtures of ethanol, polyethylene glycol 200 and propylene glycol was determined at 30 °C using the shake flask method. The maximum solubility of clonazepam was observed at volume fraction of 0.90 of ethanol, whereas for aqueous mixtures of polyethylene glycol 200 and propylene glycol, the maximum values were observed in the neat cosolvents. The generated data was fitted to the Jouyban-Acree model and its constants were computed, then the back-calculated solubilities were compared with the corresponding experimental values by calculating the mean percentage deviation (MPD) in which the overall MPD for three cosolvent systems was 7.0 %. The solubility data in cosolvent + water mixtures was predicted using previously trained versions of the Jouyban-Acree model and the prediction MPDs were 13.4, 54.2 and 24.9 %, respectively for ethanol, polyethylene glycol 200 and propylene glycol mixtures and the overall MPD was 30.8 %.     

Solubility of pioglitazone hydrochloride in ethanol,N-methyl pyrrolidone,polyethylene glycols and water mixtures at 298.20 °K

Background and the purpose of the study

Solubility of pharmaceuticals is still a challenging subject and solubilization using cosolvents is the most common technique used in the pharmaceutical industry. The purpose of this study was reporting and modeling the experimental molar solubility of pioglitazone hydrochloride (PGZ-HCl) in binary and ternary mixtures of ethanol (EtOH), N-methyl pyrrolidone (NMP), polyethylene glycols (PEGs) 200, 400, 600 and water along with the density of saturated solutions at 298.2 °K.

Methods

To provide a computational method, the Jouyban-Acree model was fitted to the solubilities of the binary solvents, and solubilities of the ternary solvents were back-calculated by employing the solubility data in mono-solvents. In the next step, the ternary interaction terms were added to the model and the prediction overall mean percentage deviation (MPD) of the ternary data was reduced. Also a previously proposed version of the model was used to predict the solubility of PGZ-HCl in binary and ternary mixtures employing the experimental solubility data in mono-solvents.

Results

The overall MPD of the model for fitting the binary data and predicted data of ternary solvents were 2.0 % and 50.5 %, respectively. The overall MPD of the predicted solubilities in ternary solvents using the ternary interaction terms in the model was 34.2 %, and by using the proposed version of the Jouyban-Acree model for binary and ternary data the overall correlation and prediction errors were 18.0 and 15.0 %, respectively.

Conclusion

The solubility of PGZ-HCl was increased by addition of EtOH, NMP, PEGs 200, 400 and 600 to aqueous solutions. The reported data extended the available solubility data of pharmaceuticals which are crucial in formulation of liquid dosage forms. The constants of the Jouyban-Acree model using the generated data are also reported which provides the possibility of solubility prediction in other solvent mixtures and temperatures.     

A model to represent solvent effects on the chemical stability of solutes in mixed solvent systems

The applicability of the combined nearly ideal binary solvent/Redlich-Kister (CNIBS/R-K) equation for quantification of solvent effects on the stability of a solute is shown employing the experimental data of three solutes in different aqueous binary solvents. The proposed model provides a simple computational method to correlate/predict the instability rate constant of a drug in mixed solvent systems. The accuracy of the model is compared with that of a model proposed by Connors and co-workers employing various methods including mean percentage deviation (MPD) as comparison criteria. The obtained overall MPD values for the proposed model to correlate and predict the instability rate constants are 2.05 +/- 1.44 and 4.41 +/- 3.21%, respectively, where the corresponding values for Connors' model are 4.34 +/- 3.28 and 10.74 +/- 9.86%. The results suggest that by using only five experimental instability rate constants at different concentrations of the cosolvent in a binary mixture, it is possible to predict unmeasured values falling between data points within an acceptable error range.     

Modeling the electrophoretic mobility of beta-blockers in capillary electrophoresis using artificial neural networks

Artificial neural networks were used for modeling the mobility of five beta-blockers (i.e., labetalol atenolol, practolol, timolol and propranolol) in running buffer with ternary solvent background electrolyte systems containing 80 mM acetate buffer dissolved in water, methanol, ethanol and their ternary mixtures. The volume fractions of two solvents (f(2), f(3)) and cologarithm of electrophoretic mobilities in pure solvents (i.e., -Lnmu(1), -Lnmu(2) and -Lnmu(3)) were used as inputs and cologarithm of the mobility in mixed solvents was the output of the networks. The number of neurons in hidden layer, learning rate, momentum and the number of epochs were optimized, in which two neurons in hidden layer, 0.2, 0.9 and 20000 were found the optimized values for learning rate, momentum and number of epochs, respectively. Mean percentage deviations (MPD) between calculated and experimental mobilities were computed as an accuracy criterion. To assess the correlative ability of the model, all data points in each set were used as training set and the mobilities were back-calculated by the trained networks, in which the overall MPD (OMPD)+/- standard deviation (SD) for correlative study was 3.1+/- 2.3. To evaluate the prediction capability of the proposed ANN model, the network was trained using 15 data points for each analyte and the remaining data points were predicted. The obtained OMPD (+/-SD) for this analysis was 3.6+/-3.0. To further investigate on the applicability of ANN, a generalized network was trained with 10 data points from each beta-blocker and then the network was employed to predict the mobilities of the analytes in ternary solvent electrolyte systems. The MPDs for predicted mobilities were 3.6%, 3.6%, 3.9%, 3.7% and 2.9% respectively for labetalol, atenolol, practolol, timolol and propranolol.     

Mathematical representation of apparent dissociation constants in aqueous-organic solvent mixtures

A mathematical model for calculating apparent acid dissociation constants (pK(a)) in hydroorganic mixtures with respect to the concentration of organic solvent in a binary mixture is proposed. The correlation ability of the proposed model is evaluated by employing pK(a) value of 75 different weak acids in 13 water-cosolvent systems. The results show that the equation is able to correlate the pK(a) values with an overall mean percentage differences (MPD) of 0.52+/-0.43%. In order to test the prediction capability of the model, four experimental pK(a) values for each data set have been employed to train the model, then the pK(a) values at other solvent compositions predicted and the overall MPD obtained is 1.41+/-1.15%. The applicability of the model to correlate/predict pK(a) values of structurally related drugs in a given binary solvent has been shown. The obtained overall MPD for correlation and prediction capabilities are 1.60+/-2.16 and 2.89+/-3.22%, respectively.     

Electrophoretic behavior of alprenolol in mixed solvent electrolyte systems

The electrophoretic mobilities of alprenolol have been determined in a mixed solvent background electrolyte system containing sodium acetate (40 mM)+acetic acid (40 mM) as buffering agent and different volume fractions of water, methanol and ethanol using capillary electrophoresis. The mobility of alprenolol has been used to test the prediction capability of a model trained by previously reported mobility data of five beta-blocker drugs at the same electrophoretic conditions. The average percentage mean deviations (APMD) between experimental and predicted values were used as an accuracy criterion. The APMD (+/-SD) obtained for alprenolol data in binary/ternary solvent electrolyte system employing the mobility values in mono-solvent buffers was 4.37 (+/-3.50)% and the corresponding value for an ab initio prediction method was 7.65 (+/-4.30)%.     

Solubility of drugs in aqueous solutions. Part 4. Drug solubility by the dilute approximation

As in our previous publications in this journal [Int. J. Pharm. 258 (2003a) 193; Int. J. Pharm. 260 (2003b) 283; Int. J. Pharm. 267 (2003c) 121], this paper is concerned with the solubility of poorly soluble drugs in aqueous mixed solvents. In the previous publications, the solubilities of drugs were assumed to be low enough for the so-called infinite dilution approximation to be applicable. In contrast, in the present paper, the solubilities are considered to be finite and the dilute solution approximation is employed. As before, the fluctuation theory of solutions is used to express the derivatives of the activity coefficient of a solute in a ternary solution (dilute solute concentrations in a binary solvent) with respect to the concentrations of the solvent and cosolvent. The expressions obtained are combined with a theoretical equation for the activity coefficient of the solute. As a result, the activity coefficient of the solute was expressed through the activity coefficients of the solute at infinite dilution, solute mole fraction, some properties of the binary solvent (composition, molar volume and activity coefficients of the components) and parameters reflecting the nonidealities of binary species. The expression thus obtained was used to derive an equation for the solubility of poorly soluble drugs in aqueous binary solvents which was applied in two different ways. First, the nonideality parameters were considered as adjustable parameters, determined from experimental solubility data. Second, the obtained equation was used to correct the solubilities of drugs calculated via the infinite dilution approximation. It was shown that both procedures provide accurate correlations for the drug solubility.     

In silico prediction of drug solubility in water-dioxane mixtures using the Jouyban-Acree model

A numerical method based on the Jouyban-Acree model was presented for prediction of drug solubility in water-dioxane mixtures at various temperatures. The method requires drug solubility in monosolvent systems, i.e. two data points for each temperature of interest. The mean percentage deviation (MPD) of predicted solubilities was calculated to show the accuracy of the predicted data and 27% was found as the average MPD for 36 data sets studied. The proposed numerical method reduced the number of required experimental data from five to two points and could also be extended to predict solubility at various temperatures.     

Excess free energy approach to the estimation of solubility in mixed solvent systems I: Theory

An approach is developed by which the solubility of an organic compound in mixed solvents may be estimated. In this approach, an expression for the excess Gibbs free energy of mixing for multicomponent solvent systems was used to obtain parameters characteristic of the interaction between the solvents. A fairly simple equation which predicts the solubility of a solute in a binary solvent system over the entire solvent composition range was then derived. The equation may be partitioned into terms that contain (a) pure solvent solubilities, (b) solvent-solvent interaction contributions, and (c) contributions from the solute-mixed solvent interactions. The required data are the molar volume of the solute, the pure solvent solubilities, and, theoretically, one experimentally determined solubility in a solvent mixture. The equation can be easily extended for systems with three or more solvents.     

Investigation of the solubility relationships of polar,semi-polar and non-polar drugs in mixed co-solvent systems

The solubility relationships of a non-polar (tioconazole), polar (oxfenieine) and semi-polar (caffeine) drug have been investigated in aqueous ethanol, propylene glycol and polyethylene glycol 400 (PEG 400) binary co-solvent systems. A semi-empirical equation was deduced to describe the relationship between the amount of drug dissolved and the volume fraction of co-solvent employed. The data for tioconazole and oxfenicine followed the expected semi-logarithmic relationship between solubility and fraction co-solvent. However, the semi-polar drug, caffeine followed this relationship only with PEG 400; the other two co-solvents yielded parabolic relationships.Using the binary solubility data, multiple linear regression was used to deduce an equation for the solubility of tioconazole in ternary ethanol, propylene glycol and PEG 400 co-solvent systems. The derived relationship gave excellent prediction of the drug solubility throughout the complete volume fraction range. This allowed a graphical representation of the drug solubility-co-solvent fraction relationship to be established. This visualization of are drug solubility relationship was then used to demonstrate its utility to optimize drug solubility within the competing constraints of the pharmaceutical system.     

Thermodynamic modeling of activity coefficient and prediction of solubility: Part 1. Predictive models

A new activity coefficient model was developed from excess Gibbs free energy in the form G(ex) = cA(a) x(1)(b)...x(n)(b). The constants of the proposed model were considered to be function of solute and solvent dielectric constants, Hildebrand solubility parameters and specific volumes of solute and solvent molecules. The proposed model obeys the Gibbs-Duhem condition for activity coefficient models. To generalize the model and make it as a purely predictive model without any adjustable parameters, its constants were found using the experimental activity coefficient and physical properties of 20 vapor-liquid systems. The predictive capability of the proposed model was tested by calculating the activity coefficients of 41 binary vapor-liquid equilibrium systems and showed good agreement with the experimental data in comparison with two other predictive models, the UNIFAC and Hildebrand models. The only data used for the prediction of activity coefficients, were dielectric constants, Hildebrand solubility parameters, and specific volumes of the solute and solvent molecules. Furthermore, the proposed model was used to predict the activity coefficient of an organic compound, stearic acid, whose physical properties were available in methanol and 2-butanone. The predicted activity coefficient along with the thermal properties of the stearic acid were used to calculate the solubility of stearic acid in these two solvents and resulted in a better agreement with the experimental data compared to the UNIFAC and Hildebrand predictive models.     

Extended Hildebrand solubility approach: sulfonamides in binary and ternary solvents

The extended Hildebrand solubility approach is used to estimate the solubility of sulfonamides in binary and ternary solvent systems. The solubility of sulfisomidine in the binary solvent, dioxane-water, shows a bell-shaped profile with a solubility maximum well above the ideal solubility of the drug. This is attributed to solvation of the drug with the dioxane-water solvent, and indicates that the solute-solvent interaction energy (W) is larger than the geometric mean (delta 1 delta 2) of regular solution theory. The solubilities of sulfadiazine, sulfisomidine, sulfathiazole, and sulfamethoxazole were determined in mixtures of dimethylacetamide, glycerol, and water, and the solubility profiles were well reproduced by use of the extended Hildebrand solubility approach. Since the solubility parameter (delta 1 = 11) of the solvent (dimethylacetamide) was approximately equal to the solubility parameters of the sulfonamides, and because of the powerful solvating power of dimethylacetamide, the solubility profiles did not exhibit peaks as observed for sulfisomidine in dioxane-water. When sulfisomidine was dissolved in a ternary mixture, i.e., butyl acetate (delta 1 = 8.5), dimethylacetamide (delta 1 congruent to 11), and methanol (delta 1 = 14.5), a spike was produced in the solubility profile at the solubility parameter of dimethylacetamide. This sharply peaked profile suggests that the two branches be treated as separate solubility curves, which are then independently well reproduced by the extended Hildebrand solubility approach. None of the four sulfonamides yielded log-linear relationships in the ternary mixtures.     

Solubility of drugs in aqueous solutions. Part 3: multicomponent mixed solvent

The results obtained previously by Ruckenstein and Shulgin [Int. J. Pharm. 258 (2003a) 193; Int. J. Pharm. 260 (2003b) 283] via the fluctuation theory of solutions regarding the solubility of drugs in binary aqueous mixed solvents were extended in the present paper to multicomponent aqueous solvents. The multicomponent mixed solvent was considered to behave as an ideal solution and the solubility of the drug was assumed small enough to satisfy the infinite dilution approximation.An expression derived for the activity coefficient of a solid solute in a multicomponent solvent was used to obtain an equation for the solubility of a drug in terms of its solubilities in two subsystems of the multicomponent solvent and their molar volumes. Ultimately the solubility can be expressed in terms of those in binary or even in individual solvents and their molar volumes.The method was applied to the solubility of tioconazole and 19-Nor-1alpha,25-dihydrovitamin D(2) in several ternary and in a quaternary aqueous mixed solvents. The predicted solubilities were compared with experimental data and good agreement was found.     

Modeling the electrophoretic mobility of analytes in binary solvent electrolyte systems in capillary electrophoresis using an artificial neural network

An artificial neural network (ANN) methodology was used to model the electrophoretic mobility of basic analytes in binary solvent electrolyte systems. The electrophoretic mobilities in pure solvent electrolytes, and the volume fractions of the solvents in mixtures were used as input. The electrophoretic mobilities in mixed solvent buffers were employed as the output of the network. The optimized topology of the network was 3-3-1. 32 experimental mobility data sets collected from the literature were employed to test the correlation ability and prediction capability of the proposed method. The mean percentage deviation (MPD) between the experimental and calculated values was used as an accuracy criterion. The MPDs obtained for different numerical analyses varied between 0.21% and 13.74%. The results were also compared with similar calculated mobilities which were derived from the best multiple linear model from the literature. From these results it was found that the ANN methodology is superior to the multiple linear model.