Prediction of the pharmaceutical solubility in water and organic solvents via different soft computing models

Document Type: Research note


Faculty of Chemical Engineering, Babol Noushiravani University of Technology, Babol, Iran


Solubility data of solid in aqueous and different organic solvents are very important physicochemical properties considered in the design of the industrial processes and the theoretical studies. In this study, experimental solubility data of 666 pharmaceutical compounds in water and 712 pharmaceutical compounds in organic solvents were collected from different sources. Three different artificial neural networks including multilayer perceptron, radial basis function and support vector machine were constructed to predict the solubility of these different pharmaceutical compounds in water and different solvents. Molecular weight, melting point, temperature and the number of each functional group in the pharmaceutical compound and organic solvents were selected as the input variables of these three different neural network models. The neural network predictions were compared with the experimental data and the SVR-PSO model with the Average Absolute Relative Deviation equal to 0.0166 for the solubility in water and 0.0707 for solubility in organic compounds was selected as the most accurate model.


Main Subjects

[1]      Siepmann, J. and Siepmann, F., “Mathematical modeling of drug dissolution”, Int. J. Pharm., 453, 12 (2013).

[2]      Inczedy, J., Lengyel, T. and Ure, A. M., Compendium of analytical nomenclature, 3rd edition, Blackwell Science, USA, (1998).

[3]      Prausnitz, J. M., Lichtenthaler, R. N., de Azevedo, E. G. and Rowlinson, J., Molecular thermodynamics of fluid-phase equilibria, Pearson Education, USA, (1998).

[4]      Delaney, J. S., “Predicting aqueous solubility from structure”, Drug Discov. Today, 10, 289 (2005).

[5]      Babu, V. R., Areefulla, S. H. and Mallikarjun, V., “Solubility and dissolution enhancement: An  overview”, J. Pharm. Res., 3, 141 (2010).

[6]      Savjani, K. T., Gajjar, A. K. and Savjani, J. K., “Drug solubility: Importance and enhancement techniques”, ISRN Pharm., 2012, 195727 (2012).

[7]      Feng, L., van Hullebusch, E. D., Rodrigo, M. A., Esposito, G. and Oturan, M. A., “Removal of residual anti-inflammatory and analgesic pharmaceuticals from aqueous systems by electrochemical advanced oxidation processes: A review”, Chem. Eng. J., 228, 944 (2013).

[8]      Lindenberg, C., Kråttli, M., Cornel, J. and Mazzotti, M., “Design and optimization of a combined cooling/antisolvent crystallization process”, Cryst. Growth Des., 9, 1124 (2009).

[9]      Blanchard, L. a. and Brennecke, J. F., “Recovery of organic products from ionic liquids using supercritical carbon dioxide”, Ind. Eng. Chem. Res., 40, 2550 (2001).

[10]  Crerar, D. A. and Anderson, G. M., “Solubility and solvation reactions of quartz in dilute hydrothermal solutions”, Chem. Geol., 8, 107 (1971).

[11]  Gmehling, J. G., Anderson, T. F. and Prausnitz, J. M., “Solid-liquid equilibria using UNIFAC”, Ind. Eng. Chem. Fundam., 17, 269 (1978).

[12]  Feelly Ruether, G. S., “Modeling the solubility of pharmaceuticals in pure solvents and solvent mixtures for drug process design”, J. Pharm. Sci., 98, 4205 (2009).

[14]  Zhao, Y., Wu, Z., Liu, W. and Pei, X., “A new theoretical model for predicting the solubility of solid solutes in different solvents”, Fluid Phase Equilib., 412, 123 (2016).

[15]  Gharagheizi, F., “Representation/ prediction of solubilities of pure compounds in water using artificial neural network-group contribution method”, J. Chem. Eng. Data, 56, 720 (2011).

[16]  Yalkowsky, S. H. and Valvani, S. C., “Solubility and partitioning, I: Solubility of nonelectrolytes in water”, J. Pharm. Sci., 69, 912 (1980).

[17]  Ruelle, P. and Kesselring, U. W., “Solubility predictions for solid nitriles and tertiary amides based on the mobile order theory”, Pharm. Res., 11, 201 (1994).

[18]  Abraham, M. H. and Le, J., “The correlation and prediction of the solubility of compounds in water using an amended solvation energy relationship”, J. Pharm. Sci., 88, 868 (1999).

[19]  Klamt, A., Eckert, F., Hornig, M., Beck, M. E. and Brger, T., “Prediction of aqueous solubility of drugs and pesticides with COSMO-RS”, J. Comput. Chem., 23, 275 (2002).

[20]  Wang, J., Krudy, G., Hou, T., Zhang, W., Holland, G. and Xu, X. J., “Development of reliable aqueous solubility models and their application in druglike analysis”, J. Chem. Inf. Model., 47, 1395 (2007).

[21]  Huuskonen, J., “Estimation of aqueous solubility for a diverse set of organic compounds based on molecular topology”, J. Chem. Inf. Comput. Sci., 40, 773 (2000).

[22]  Hou, T. J., Xia, K., Zhang, W. and Xu, X. J., “ADME evaluation in drug discovery: 4. Prediction of aqueous solubility based on atom contribution approach”, J. Chem. Inf. Comput. Sci., 44, 266 (2004).

[23]  Gharagheizi, F., Eslamimanesh, A., Mohammadi, A. H. and Richon, D., “Determination of critical properties and acentric factors of pure compounds using the artificial neural network group contribution algorithm”, J. Chem. Eng. Data., 56, 2460 (2011).

[24]  Chen, G., Luo, X., Zhang, H., Fu, K., Liang, Z., Rongwong, W., Tontiwachwuthikul, P. and Idem, R., “Artificial neural network models for the prediction of CO2 solubility in aqueous amine solutions”, Int. J. Greenh. Gas Control., 39, 174 (2015).

[25]  Tatar, A., Naseri, S., Bahadori, M., Hezave, A. Z., Kashiwao, T., Bahadori, A. and Darvish, H., “Prediction of carbon dioxide solubility in ionic liquids using MLP and radial basis function (RBF) neural networks”, J. Taiwan Inst. Chem. Eng., 60, 151 (2016).

[26]  Mehdizadeh, B. and Movagharnejad, K., “A comparison between neural network method and semi empirical equations to predict the solubility of different compounds in supercritical carbon dioxide”, Fluid Phase Equilib., 303, 40 (2011).

[27]  Graupe, D., Principles of artificial neural networks, World Scientific, Singapore, (2013).

[28]  Kennedy, J. and Eberhart, R., “Particle swarm optimization”, Proceedings of IEEE Int. Conf. Neural Networks, Perth, WA, Australia, 4, pp. 1942–1948 (2002).

[29]  Haykin, S. S., Neural networks and learning machines, 3rd Edition, USA, (2009).

[30]  Broomhead, D. S. and Lowe, D., “Radial basis functions, multi-variable functional interpolation and adaptive networks”, DTIC Document, (1988).

[31]  Mustafa, M. R., Rezaur, R. B., Rahardjo, H. and Isa, M. H., “Prediction of pore-water pressure using radial basis function neural network”, Eng. Geol., 135–136, 40 (2012).

[32]  Shen, W., Guo, X., Wu, C. and Wu, D., “Forecasting stock indices using radial basis function neural networks optimized by artificial fish swarm algorithm”, Knowledge-Based Syst., 24, 378 (2011).

[33]  Vladimir, V. N. and Vapnik, V., The nature of statistical learning theory, Springer-Verlag, Berlin, Germany, (1995).

[34]  Kazem, A., Sharifi, E., Hussain, F. K., Saberi, M. and Hussain, O. K., “Support vector regression with chaos-based firefly algorithm for stock market price forecasting”, Appl. Soft Comput., 13, 947 (2013).

[35]  Yu, P. S., Chen, S. T. and Chang, I. F., “Support vector regression for real-time flood stage forecasting”, J. Hydrol., 328, 704 (2006).

[36]  Smola, A. J. and Schölkopf, B., “A tutorial on support vector regression”, Stat. Comput., 14, 199 (2004).

[37]  Yalkowsky, S. H., He, Y. and Jain, P., Handbook of aqueous solubility data, 2nd ed., CRC Press, USA, (2010).

[38]  Ribeiro Neto, A. C., Pires, R. F., Malagoni, R. A. and Franco, M. R., “Solubility of vitamin C in water, ethanol, propan-1-ol, water + ethanol, and water + propan-1-ol at (298.15 and 308.15) K”, J. Chem. Eng. Data, 55, 1718 (2010).

[39]  Pobudkowska, A., DomaƄska, U. and Jurkowska, B. A., “Solubility of pharmaceuticals in water and alcohols”, Fluid Phase Equilib., 392, 56 (2015).

[40]  Wenju, L., Leping, D., Black, S. and Hongyuan, W., “Solubility of carbamazepine (form III) in different solvents from (275 to 343) K”, J. Chem. Eng. Data, 53, 2204 (2008).

[41]  Li, Q. S., Li, Z. and Wang, S., “Solubility of trimethoprim (TMP) in different organic solvents from (278 to 333) K”, J. Chem. Eng. Data, 53, 286 (2008).

[42]  Jouyban, A., Handbook of solubility data for pharmaceuticals, CRC Press, USA, (2009).

[43]  Wang, L., Du, C., Wang, X., Zeng, H., Yao, J. and Chen, B., “Solubilities of phosphoramidic acid, N-(phenylmethyl)-, diphenyl ester in selected solvents”, J. Chem. Eng. Data, 60, 1814 (2015).

[44]  Marrero, J. and Gani, R., “Group-contribution based estimation of pure component properties”, Fluid Phase Equilib., 183–184, 183 (2001).

[45]  Agirre-Basurko, E., Ibarra-Berastegi, G. and Madariaga, I., “Regression and multilayer perceptron-based models to forecast hourly O3 and NO2 levels in the Bilbao area”, Environ. Model. Softw., 21, 430 (2006).