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.     

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 %.     

Mathematical representation of solute solubility in binary mixture of supercritical fluids by the Jouyban-Acree model

Applicability of a solution model for calculating the solute solubility in binary mixtures of supercritical fluids at different SCF compositions and pressures was shown using phenanthrene solubility data in supercritical carbon dioxide and supercritical ethane at 313 K and a pressure range of 100-350 bar. The correlation ability of the proposed model was evaluated by fitting all data points and computing error term employing back-calculated solubilities. The prediction capability of the model was assessed by dividing each data set to two subsets, namely training and test subsets. The predicted solubilities using trained models were used to calculate the prediction error term. The results show that both correlative and predictive error terms were less than the experimentally obtained RSD values.     

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 salicylic acid in water-ethanol-propylene glycol mixtures using the Jouyban-Acree model

To show the applicability of a solution model, i.e. the Jouyban-Acree model, for predicting the solubility of a solute in ternary solvent systems based on model constants computed using solubility data of the solute in binary solvent systems, the solubility of salicylic acid in water-ethanol, water-propylene glycol, ethanol-propylene glycol mixtures was determined. A minimum number of three data points from each binary system was used to calculate the binary interaction parameters of the model. Then the solubility in other binary solvent compositions and also in a number of ternary solvents was predicted, and the mean percentage deviation (MPD) was calculated as an accuracy criterion. The overall MPD (+/-SD) was 7.3 (+/-7.3)% and those of a similar predictive model was 15.7 (+/-11.5)%. The mean difference between the proposed and a previous model was statistically significant (paired t-test, p < 0.004).     

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.     

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.     

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.     

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.     

The effects of pH and mixed solvent systems on the solubility of oxytetracycline

The solubility of oxytetracycline (OTC) in aqueous and mixed solvent systems was studied. The effects of pH and cosolvent composition on the solubility and apparent dissociation constants (pKa') of OTC were determined by a solubility method. The pKa' values of OTC in each mixed solvent system were estimated and used to generate expressions for predicting drug solubility in each cosolvent as a function of pH. Cosolvent systems of PEG 400, propylene glycol, glycerin, and 2-pyrrolidone were studied in the pH range of 2.5-9. Solubility results showed increased solubility with increased cosolvent concentration, especially in 2-pyrrolidone solvent systems. These results also showed that cosolvents enhanced drug solubility through either their effects on polarity of the solvent medium or complex formation with OTC. Aqueous and mixed solvent systems at lower pH values resulted in higher OTC solubilization because the drug existed primarily in its cationic form. A mass balance equation including all ionic species of OTC allowed for estimation of the intrinsic solubilities and pKa' values in each solvent system. pKa' values and intrinsic solubility of the OTC zwitterion increased with increasing cosolvent content. These parameters allowed prediction of drug solubility within the pH range and cosolvent concentrations used in this study.     

Solubility prediction in water-ethanol mixtures based on the excess free energy approach using a minimum number of experimental data

The solubility of nalidixic acid in water-ethanol mixtures has been determined at 25 degrees C. The generated solubility data sets have been used to assess the accuracy of different numerical analyses for the excess free energy model and a new numerical method for solubility prediction in water-ethanol mixtures based on four experimental determinations is proposed. The accuracy of a previously presented numerical method to fit all data points is compared with that of a proposed analysis using average percentage deviation (APD). The APD obtained are 14.6 (+/- 8.0) and 8.4 (+/- 4.1), respectively for previous and proposed methods. A minimum number of three and four data points employed to train the original forms of the excess free energy model and the solubility at other solvent compositions were predicted. The APDs obtained were 61.4 and 23.0%, respectively. The APD produced for the proposed numerical method was 16.1%.     

Influence of solute structure on deviations from the log-linear solubility equation in propylene glycol:water mixtures

The solubilities of the methyl, ethyl, propyl, and butyl esters of p-hydroxy- and p-aminobenzoates have been determined in propylene glycol:water mixtures. The log of the observed solubility data in propylene glycol:water mixtures was examined for deviations from the following equation: In Xi = f In (Xc) + (1 - f) In (Xw), where Xi is the calculated mole fractional solubility of the solute, f is the volume fraction of cosolvent, Xc is the observed mole fractional solubility in the neat cosolvent, and Xw is the solubility in water. In each case, the deviations from the predicted solubilities demonstrated a characteristic pattern. Positive deviations were observed at high volume fractions of cosolvent, while negative deviations were observed at low volume fractions. The magnitude of the deviations at low volume fractions of cosolvent was related to the carbon chain length within each group of esters. A similar phenomenon was not observed at high volume fractions of cosolvent; however, the magnitude of the deviations was dependent on the nature of the polar group on the ester. The data are interpreted in terms of the possible effects of solvent structure on the solubility of the solutes.     

Solubility prediction in supercritical CO(2) using minimum number of experiments

The correlation ability and solubility prediction in supercritical carbon dioxide of a proposed equation were studied. The work involved the solubilities of nicotinic acid and p-acetoxyacetanilide in supercritical carbon dioxide using a dynamic flow solubility system at 35-75 degrees C and 100-200 bar. The generated experimental solubility data together with 21 data sets collected from the literature were used to evaluate the correlation ability of available empirical equations. The average absolute relative deviations (AARD) for the empirical equations are 12.6-24.8%. The prediction capability of the modified empirical relationship was studied with six experimental data points as a training set. Then, solubility at other temperatures and pressures were predicted. The AARD between predicted solubilities and observed values is 17%.     

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.     

The Effects of pH and Mixed Solvent Systems on the Solubility of Oxytetracycline

The solubility of oxytetracycline (OTC) in aqueous and mixed solvent systems was studied. The effects of pH and cosolvent composition on the solubility and apparent dissociation constants (pK′_a) of OTC were determined by a solubility method. The pK′_a values of OTC in each mixed solvent system were estimated and used to generate expressions for predicting drug solubility in each cosolvent as a function of pH. Cosolvent systems of PEG 400, propylene glycol, glycerin, and 2-pyrrolidone were studied in the pH range of 2.5–9. Solubility results showed increased solubility with increased cosolvent concentration, especially in 2-pyrrolidone solvent systems. These results also showed that cosolvents enhanced drug solubility through either their effects on polarity of the solvent medium or complex formation with OTC. Aqueous and mixed solvent systems at lower pH values resulted in higher OTC solubilization because the drug existed primarily in its cationic form. A mass balance equation including all ionic species of OTC allowed for estimation of the intrinsic solubilities and pK′_a values in each solvent system. pK′_a values and intrinsic solubility of the OTC zwitterion increased with increasing cosolvent content. These parameters allowed prediction of drug solubility within the pH range and cosolvent concentrations used in this study.     

Aqueous and cosolvent solubility data for drug-like organic compounds

Recently 2 QSPR-based in silico models were developed in our laboratories to predict the aqueous and non-aqueous solubility of drug-like organic compounds. For the intrinsic aqueous solubility model, a set of 321 structurally diverse drugs was collected from literature for the analysis. For the PEG 400 cosolvent model, experimental data for 122 drugs were obtained by a uniform experimental procedure at 4 volume fractions of PEG 400 in water, 0%, 25%, 50%, and 75%. The drugs used in both models represent a wide range of compounds, with log P values from -5 to 7.5, and molecular weights from 100 to >600 g/mol. Because of the standardized procedure used to collect the cosolvent data and the careful assessment of quality used in obtaining literature data, both data sets have potential value for the scientific community for use in building various models that require experimental solubility data.     

Solubility in amide-water cosolvent systems II: Cosolvent excess at solute surface.

The solubility of methylparaben was determined at 25 degrees in a series of amide-water cosolvent systems. The data were used to demonstrate the possibility of an amide excess at or near the ester solute over that in the bulk solvent. The analysis, stemming from an interfacial tension-solute area solubility model proposed by earlier workers, involved data obtained as a function of amide concentration and as a function of amide alkylation. Both sets of data support the basic contention of the paper.     

人工神经网络预测HPMC缓释片中易溶性药物的释放

目的应用BP人工神经网络模型预测水溶性药物从HPMC缓释片中的释放。方法以6种不同溶解性的水溶性药物(对乙酰氨基酚、氧氟沙星、盐酸环丙沙星、乳酸左氧氟沙星、多索茶碱、氯苯那敏、维拉帕米)为模型药物,设计62个处方,其中前面55个处方作为训练处方,另外7个处方作为验证处方,压制HPMC缓释片,进行释放度检查。以溶解度、载药量、HPMC的量、HPMC的固有黏度、MCC的量、PVP的浓度和药物溶出仪的转速作为自变量,药物在各个取样时间点的累积释放量作为输出,建立BP人工神经网络模型,并与响应面法进行对照,通过线性回归法和相似因子法比较人工神经网络和响应面法的预测能力,借助三维图说明各个变量对药物释放的影响。结果线性回归和相似因子法表明人工神经网络较响应面法的预测值与实际测定值更吻合,更能充分地说明单因素对药物释放的影响规律。结论人工神经网络可以代替响应面法处理HPMC缓释片处方设计中的不同溶解度的水溶性药物的多因素多响应的非线性问题而且可以推广到别的制剂设计中。