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Cenci F, Diab S, Ferrini P, Harabajiu C, Barolo M, Bezzo F, Facco P. Predicting drug solubility in organic solvents mixtures: A machine-learning approach supported by high-throughput experimentation. Int J Pharm 2024:124233. [PMID: 38763309 DOI: 10.1016/j.ijpharm.2024.124233] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/20/2024] [Revised: 05/14/2024] [Accepted: 05/14/2024] [Indexed: 05/21/2024]
Abstract
A novel approach based on supervised machine-learning is proposed to predict the solubility of drugs and drug-like molecules in mixtures of organic solvents. Similar to quantitative structure-property relationship (QSPR) models, different solvent types are identified by molecular descriptors, which, in this study, are considered as UNIFAC subgroups. To overcome the potential lack of UNIFAC subgroups for the complex Active Pharmaceutical Ingredients (APIs) currently developed in the pharmaceutical industry, the API molecule is considered as a unique entity in the proposed modelling approach. Therefore, API solubility is predicted as a function of temperature, functional subgroups of the solvents and composition of the solvent mixture; in turn, regressors' correlation is handled through Partial Least-Squares (PLS) regression. The method is developed and tested with experimental data of a real API and 14 organic solvents that are industrially employed for crystallisation. Solubility predictions are accurate and precise for single solvents, binary mixtures and ternary mixtures of organic solvents at different compositions and temperatures, with a determination coefficient R2 ≥ 0.90. To further test the applicability of the model, the proposed approach is applied to 9 literature organic solubility datasets of drugs and drug-like compounds and compared to benchmark solubility models in the literature. Results show that the proposed approach provides satisfactory predictions: the majority of validation and calibration data have R2 = 0.95-0.99; the ratio between RMSE (root mean squared error) of the proposed method and the range of measured solubility values is from 1 to 3 orders of magnitude smaller than the RMSE ratio obtained by the benchmark models.
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Affiliation(s)
- Francesca Cenci
- GSK, Park Road, Ware SG12 0DP, United Kingdom; CAPE-Lab - Computer-Aided Process Engineering Laboratory, Department of Industrial Engineering, University of Padovavia, Marzolo 9, 35131 Padova, Italy
| | - Samir Diab
- GSK, Park Road, Ware SG12 0DP, United Kingdom
| | - Paola Ferrini
- GSK, Gunnels Wood Road, Stevenage SG1 2NY, United Kingdom
| | | | - Massimiliano Barolo
- CAPE-Lab - Computer-Aided Process Engineering Laboratory, Department of Industrial Engineering, University of Padovavia, Marzolo 9, 35131 Padova, Italy
| | - Fabrizio Bezzo
- CAPE-Lab - Computer-Aided Process Engineering Laboratory, Department of Industrial Engineering, University of Padovavia, Marzolo 9, 35131 Padova, Italy
| | - Pierantonio Facco
- CAPE-Lab - Computer-Aided Process Engineering Laboratory, Department of Industrial Engineering, University of Padovavia, Marzolo 9, 35131 Padova, Italy.
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Cysewski P, Jeliński T, Przybyłek M. Experimental and Theoretical Insights into the Intermolecular Interactions in Saturated Systems of Dapsone in Conventional and Deep Eutectic Solvents. Molecules 2024; 29:1743. [PMID: 38675562 PMCID: PMC11051893 DOI: 10.3390/molecules29081743] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/14/2024] [Revised: 04/05/2024] [Accepted: 04/10/2024] [Indexed: 04/28/2024] Open
Abstract
Solubility is not only a crucial physicochemical property for laboratory practice but also provides valuable insight into the mechanism of saturated system organization, as a measure of the interplay between various intermolecular interactions. The importance of these data cannot be overstated, particularly when dealing with active pharmaceutical ingredients (APIs), such as dapsone. It is a commonly used anti-inflammatory and antimicrobial agent. However, its low solubility hampers its efficient applications. In this project, deep eutectic solvents (DESs) were used as solubilizing agents for dapsone as an alternative to traditional solvents. DESs were composed of choline chloride and one of six polyols. Additionally, water-DES mixtures were studied as a type of ternary solvents. The solubility of dapsone in these systems was determined spectrophotometrically. This study also analyzed the intermolecular interactions, not only in the studied eutectic systems, but also in a wide range of systems found in the literature, determined using the COSMO-RS framework. The intermolecular interactions were quantified as affinity values, which correspond to the Gibbs free energy of pair formation of dapsone molecules with constituents of regular solvents and choline chloride-based deep eutectic solvents. The patterns of solute-solute, solute-solvent, and solvent-solvent interactions that affect solubility were recognized using Orange data mining software (version 3.36.2). Finally, the computed affinity values were used to provide useful descriptors for machine learning purposes. The impact of intermolecular interactions on dapsone solubility in neat solvents, binary organic solvent mixtures, and deep eutectic solvents was analyzed and highlighted, underscoring the crucial role of dapsone self-association and providing valuable insights into complex solubility phenomena. Also the importance of solvent-solvent diversity was highlighted as a factor determining dapsone solubility. The Non-Linear Support Vector Regression (NuSVR) model, in conjunction with unique molecular descriptors, revealed exceptional predictive accuracy. Overall, this study underscores the potency of computed molecular characteristics and machine learning models in unraveling complex molecular interactions, thereby advancing our understanding of solubility phenomena within the scientific community.
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Affiliation(s)
- Piotr Cysewski
- Department of Physical Chemistry, Pharmacy Faculty, Collegium Medicum of Bydgoszcz, Nicolaus Copernicus University in Toruń, Kurpińskiego 5, 85-096 Bydgoszcz, Poland; (T.J.); (M.P.)
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Sokolov AA, Yagofarov MI, Balakhontsev IS, Nizamov II, Mukhametzyanov TA, Solomonov BN, Yurkshtovich YN, Stepurko EN. Thermodynamic Properties of 3- and 4-Ethoxyacetanilides between 80 and 480 K. Molecules 2023; 28:7027. [PMID: 37894506 PMCID: PMC10609036 DOI: 10.3390/molecules28207027] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/04/2023] [Revised: 10/06/2023] [Accepted: 10/09/2023] [Indexed: 10/29/2023] Open
Abstract
In this work, we present a comprehensive study of the thermodynamic properties of 3-and 4-ethoxyacetanilides. The heat capacities in crystalline, liquid, and supercooled liquid states from 80 to 475 K were obtained using adiabatic, differential scanning (DSC), and fast scanning (FSC) calorimetries. The fusion enthalpies at Tm were combined from DSC measurement results and the literature data. The fusion enthalpies at 298.15 K were evaluated in two independent ways: adjusted according to Kirchhoff's law of thermochemistry, and using Hess' law. For the latter approach, the enthalpies of the solution in DMF in crystalline and supercooled liquid states were derived. The values obtained by the two methods are consistent with each other. The standard thermodynamic functions (entropy, enthalpy, and Gibbs energy) between 80 and 470 K were calculated.
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Affiliation(s)
- Andrey A Sokolov
- Department of Physical Chemistry, Kazan Federal University, Kremlevskaya Str. 18, 420008 Kazan, Russia
| | - Mikhail I Yagofarov
- Department of Physical Chemistry, Kazan Federal University, Kremlevskaya Str. 18, 420008 Kazan, Russia
| | - Ilya S Balakhontsev
- Department of Physical Chemistry, Kazan Federal University, Kremlevskaya Str. 18, 420008 Kazan, Russia
| | - Ilyas I Nizamov
- Department of Physical Chemistry, Kazan Federal University, Kremlevskaya Str. 18, 420008 Kazan, Russia
| | - Timur A Mukhametzyanov
- Department of Physical Chemistry, Kazan Federal University, Kremlevskaya Str. 18, 420008 Kazan, Russia
| | - Boris N Solomonov
- Department of Physical Chemistry, Kazan Federal University, Kremlevskaya Str. 18, 420008 Kazan, Russia
| | | | - Elena N Stepurko
- Chemistry Department, Belarusian State University, 220030 Minsk, Belarus
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Przybyłek M, Jeliński T, Mianowana M, Misiak K, Cysewski P. Exploring the Solubility Limits of Edaravone in Neat Solvents and Binary Mixtures: Experimental and Machine Learning Study. Molecules 2023; 28:6877. [PMID: 37836720 PMCID: PMC10574143 DOI: 10.3390/molecules28196877] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/22/2023] [Revised: 09/25/2023] [Accepted: 09/27/2023] [Indexed: 10/15/2023] Open
Abstract
This study explores the edaravone solubility space encompassing both neat and binary dissolution media. Efforts were made to reveal the inherent concentration limits of common pure and mixed solvents. For this purpose, the published solubility data of the title drug were scrupulously inspected and cured, which made the dataset consistent and coherent. However, the lack of some important types of solvents in the collection called for an extension of the available pool of edaravone solubility data. Hence, new measurements were performed to collect edaravone solubility values in polar non-protic and diprotic media. Such an extended set of data was used in the machine learning process for tuning the parameters of regressor models and formulating the ensemble for predicting new data. In both phases, namely the model training and ensemble formulation, close attention was paid not only to minimizing the deviation of computed values from the experimental ones but also to ensuring high predictive power and accurate solubility computations for new systems. Furthermore, the environmental friendliness characteristics determined based on the common green solvent selection criteria, were included in the analysis. Our applied protocol led to the conclusion that the solubility space defined by ordinary solvents is limited, and it is unlikely to find solvents that are better suited for edaravone dissolution than those described in this manuscript. The theoretical framework presented in this study provides a precise guideline for conducting experiments, as well as saving time and resources in the pursuit of new findings.
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Affiliation(s)
- Maciej Przybyłek
- Department of Physical Chemistry, Pharmacy Faculty, Collegium Medicum of Bydgoszcz, Nicolaus Copernicus University in Toruń, Kurpińskiego 5, 85-096 Bydgoszcz, Poland; (T.J.); (M.M.); (K.M.)
| | | | | | | | - Piotr Cysewski
- Department of Physical Chemistry, Pharmacy Faculty, Collegium Medicum of Bydgoszcz, Nicolaus Copernicus University in Toruń, Kurpińskiego 5, 85-096 Bydgoszcz, Poland; (T.J.); (M.M.); (K.M.)
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Cysewski P, Przybyłek M, Jeliński T. Intermolecular Interactions as a Measure of Dapsone Solubility in Neat Solvents and Binary Solvent Mixtures. MATERIALS (BASEL, SWITZERLAND) 2023; 16:6336. [PMID: 37763610 PMCID: PMC10532775 DOI: 10.3390/ma16186336] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/07/2023] [Revised: 09/19/2023] [Accepted: 09/20/2023] [Indexed: 09/29/2023]
Abstract
Dapsone is an effective antibacterial drug used to treat a variety of conditions. However, the aqueous solubility of this drug is limited, as is its permeability. This study expands the available solubility data pool for dapsone by measuring its solubility in several pure organic solvents: N-methyl-2-pyrrolidone (CAS: 872-50-4), dimethyl sulfoxide (CAS: 67-68-5), 4-formylmorpholine (CAS: 4394-85-8), tetraethylene pentamine (CAS: 112-57-2), and diethylene glycol bis(3-aminopropyl) ether (CAS: 4246-51-9). Furthermore, the study proposes the use of intermolecular interactions as molecular descriptors to predict the solubility of dapsone in neat solvents and binary mixtures using machine learning models. An ensemble of regressors was used, including support vector machines, random forests, gradient boosting, and neural networks. Affinities of dapsone to solvent molecules were calculated using COSMO-RS and used as input for model training. Due to the polymorphic nature of dapsone, fusion data are not available, which prohibits the direct use of COSMO-RS for solubility calculations. Therefore, a consonance solvent approach was tested, which allows an indirect estimation of the fusion properties. Unfortunately, the resulting accuracy is unsatisfactory. In contrast, the developed regressors showed high predictive potential. This work documents that intermolecular interactions characterized by solute-solvent contacts can be considered valuable molecular descriptors for solubility modeling and that the wealth of encoded information is sufficient for solubility predictions for new systems, including those for which experimental measurements of thermodynamic properties are unavailable.
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Affiliation(s)
- Piotr Cysewski
- Department of Physical Chemistry, Pharmacy Faculty, Collegium Medicum of Bydgoszcz, Nicolaus Copernicus University in Toruń, Kurpińskiego 5, 85-096 Bydgoszcz, Poland; (M.P.); (T.J.)
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Cysewski P, Jeliński T, Przybyłek M. Finding the Right Solvent: A Novel Screening Protocol for Identifying Environmentally Friendly and Cost-Effective Options for Benzenesulfonamide. Molecules 2023; 28:5008. [PMID: 37446671 DOI: 10.3390/molecules28135008] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/31/2023] [Revised: 06/23/2023] [Accepted: 06/24/2023] [Indexed: 07/15/2023] Open
Abstract
This study investigated the solubility of benzenesulfonamide (BSA) as a model compound using experimental and computational methods. New experimental solubility data were collected in the solvents DMSO, DMF, 4FM, and their binary mixtures with water. The predictive model was constructed based on the best-performing regression models trained on available experimental data, and their hyperparameters were optimized using a newly developed Python code. To evaluate the models, a novel scoring function was formulated, considering not only the accuracy but also the bias-variance tradeoff through a learning curve analysis. An ensemble approach was adopted by selecting the top-performing regression models for test and validation subsets. The obtained model accurately back-calculated the experimental data and was used to predict the solubility of BSA in 2067 potential solvents. The analysis of the entire solvent space focused on the identification of solvents with high solubility, a low environmental impact, and affordability, leading to a refined list of potential candidates that meet all three requirements. The proposed procedure has general applicability and can significantly improve the quality and speed of experimental solvent screening.
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Affiliation(s)
- Piotr Cysewski
- Department of Physical Chemistry, Pharmacy Faculty, Collegium Medicum of Bydgoszcz, Nicolaus Copernicus University in Toruń, Kurpińskiego 5, 85-096 Bydgoszcz, Poland
| | - Tomasz Jeliński
- Department of Physical Chemistry, Pharmacy Faculty, Collegium Medicum of Bydgoszcz, Nicolaus Copernicus University in Toruń, Kurpińskiego 5, 85-096 Bydgoszcz, Poland
| | - Maciej Przybyłek
- Department of Physical Chemistry, Pharmacy Faculty, Collegium Medicum of Bydgoszcz, Nicolaus Copernicus University in Toruń, Kurpińskiego 5, 85-096 Bydgoszcz, Poland
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Cysewski P, Jeliński T, Przybyłek M, Nowak W, Olczak M. Solubility Characteristics of Acetaminophen and Phenacetin in Binary Mixtures of Aqueous Organic Solvents: Experimental and Deep Machine Learning Screening of Green Dissolution Media. Pharmaceutics 2022; 14:pharmaceutics14122828. [PMID: 36559321 PMCID: PMC9781932 DOI: 10.3390/pharmaceutics14122828] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/26/2022] [Revised: 12/10/2022] [Accepted: 12/12/2022] [Indexed: 12/23/2022] Open
Abstract
The solubility of active pharmaceutical ingredients is a mandatory physicochemical characteristic in pharmaceutical practice. However, the number of potential solvents and their mixtures prevents direct measurements of all possible combinations for finding environmentally friendly, operational and cost-effective solubilizers. That is why support from theoretical screening seems to be valuable. Here, a collection of acetaminophen and phenacetin solubility data in neat and binary solvent mixtures was used for the development of a nonlinear deep machine learning model using new intuitive molecular descriptors derived from COSMO-RS computations. The literature dataset was augmented with results of new measurements in aqueous binary mixtures of 4-formylmorpholine, DMSO and DMF. The solubility values back-computed with the developed ensemble of neural networks are in perfect agreement with the experimental data, which enables the extensive screening of many combinations of solvents not studied experimentally within the applicability domain of the trained model. The final predictions were presented not only in the form of the set of optimal hyperparameters but also in a more intuitive way by the set of parameters of the Jouyban-Acree equation often used in the co-solvency domain. This new and effective approach is easily extendible to other systems, enabling the fast and reliable selection of candidates for new solvents and directing the experimental solubility screening of active pharmaceutical ingredients.
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New Insights into Thermodynamics of Solutes in Neat and Complex Solvents. MOLECULES (BASEL, SWITZERLAND) 2022; 27:molecules27186131. [PMID: 36144864 PMCID: PMC9503935 DOI: 10.3390/molecules27186131] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 09/05/2022] [Accepted: 09/13/2022] [Indexed: 11/17/2022]
Abstract
Solubility is one of the most important physicochemical properties, both from a practical and theoretical perspective [...].
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Application of COSMO-RS-DARE as a Tool for Testing Consistency of Solubility Data: Case of Coumarin in Neat Alcohols. Molecules 2022; 27:molecules27165274. [PMID: 36014510 PMCID: PMC9413568 DOI: 10.3390/molecules27165274] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/21/2022] [Revised: 08/11/2022] [Accepted: 08/15/2022] [Indexed: 11/17/2022] Open
Abstract
Coumarin is a naturally occurring lactone-type benzopyrone with various applications in the pharmaceutical, food, perfume, and cosmetics industries. This hydrophobic compound is poorly soluble in water but dissolves well in protic organic solvents such as alcohols. Despite the extensive use of coumarin, there are only a few reports documenting its solubility in organic solvents, and some reported data are incongruent, which was the direct impulse for this study. To resolve this problem, a theoretical congruency test was formulated using COSMO-RS-DARE for the determination of intermolecular interaction parameters, which allowed for the identification of outliers as suspicious datasets. The perfect match between back-computed values of coumarin solubility and the experimental ones confirms the reliability of the formulated theoretical approach and its adequacy for testing solubility data consistency. As the final approval, the temperature-related coumarin solubility in seven neat alcohols was determined experimentally. Four solvents (methanol, ethanol, 1-propanol, and 2-propanol) were used for reproducibility purposes, and an additional three (1-butanol, 1-pentanol, and 1-octanol) were used to extend the information on the homologous series. The consistency of this extended solubility dataset is discussed in terms of the comparison of remeasured solubility values with the ones already published and within the series of structurally similar solvents. The proposed procedure extends the range of applicability of COSMO-RS-DARE and provides a real and useful tool for consistency tests of already published solubility data, allowing for the approval/disapproval of existing data and filling gaps in datasets. Linear regressions utilizing a 2D molecular descriptor, SpMin2_Bhm, or the distance between solute and solvent in the Hansen solubility space, Ra, were formulated for the estimation of COMSO-RS-DARE integration parameters.
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Przybyłek M, Miernicka A, Nowak M, Cysewski P. New Screening Protocol for Effective Green Solvents Selection of Benzamide, Salicylamide and Ethenzamide. Molecules 2022; 27:molecules27103323. [PMID: 35630800 PMCID: PMC9144492 DOI: 10.3390/molecules27103323] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/27/2022] [Revised: 05/18/2022] [Accepted: 05/20/2022] [Indexed: 02/06/2023] Open
Abstract
New protocol for screening efficient and environmentally friendly solvents was proposed and experimentally verified. The guidance for solvent selection comes from computed solubility via COSMO-RS approach. Furthermore, solute-solvent affinities computed using advanced quantum chemistry level were used as a rationale for observed solvents ranking. The screening protocol pointed out that 4-formylomorpholine (4FM) is an attractive solubilizer compared to commonly used aprotic solvents such as DMSO and DMF. This was tested experimentally by measuring the solubility of the title compounds in aqueous binary mixtures in the temperature range between 298.15 K and 313.15 K. Additional measurements were also performed for aqueous binary mixtures of DMSO and DMF. It has been found that the solubility of studied aromatic amides is very high and quite similar in all three aprotic solvents. For most aqueous binary mixtures, a significant decrease in solubility with a decrease in the organic fraction is observed, indicating that all systems can be regarded as efficient solvent-anti-solvent pairs. In the case of salicylamide dissolved in aqueous-4FM binary mixtures, a strong synergistic effect has been found leading to the highest solubility for 0.6 mole fraction of 4-FM.
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Lv J, Yao L, Li S, Dong J, Ye M, Fan D, Li C, Tian F, Li Y. New aniline derivatives from the volva of Phallus rubrovolvatus and their anti-inflammatory activity. Bioorg Chem 2022; 119:105577. [DOI: 10.1016/j.bioorg.2021.105577] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/11/2021] [Revised: 12/15/2021] [Accepted: 12/17/2021] [Indexed: 11/25/2022]
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Cysewski P, Przybyłek M, Rozalski R. Experimental and Theoretical Screening for Green Solvents Improving Sulfamethizole Solubility. MATERIALS (BASEL, SWITZERLAND) 2021; 14:5915. [PMID: 34683507 PMCID: PMC8539550 DOI: 10.3390/ma14205915] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 09/03/2021] [Revised: 09/30/2021] [Accepted: 10/05/2021] [Indexed: 01/22/2023]
Abstract
Solubility enhancement of poorly soluble active pharmaceutical ingredients is of crucial importance for drug development and processing. Extensive experimental screening is limited due to the vast number of potential solvent combinations. Hence, theoretical models can offer valuable hints for guiding experiments aimed at providing solubility data. In this paper, we explore the possibility of applying quantum-chemistry-derived molecular descriptors, adequate for development of an ensemble of neural networks model (ENNM), for solubility computations of sulfamethizole (SMT) in neat and aqueous binary solvent mixtures. The machine learning procedure utilized information encoded in σ-potential profiles computed using the COSMO-RS approach. The resulting nonlinear model is accurate in backcomputing SMT solubility and allowed for extensive screening of green solvents. Since the experimental characteristics of SMT solubility are limited, the data pool was extended by new solubility measurements in water, five neat organic solvents (acetonitrile, N,N-dimethylformamide, dimethyl sulfoxide, 1,4-dioxane, and methanol), and their aqueous binary mixtures at 298.15, 303.15, 308.15, and 313.15 K. Experimentally determined order of decreasing SMT solubility in neat solvents is the following: N,N-dimethylformamide > dimethyl sulfoxide > methanol > acetonitrile > 1,4dioxane >> water, in all studied temperatures. Similar trends are observed for aqueous binary mixtures. Since N,N-dimethylformamide is not considered as a green solvent, the more acceptable replacers were searched for using the developed model. This step led to the conclusion that 4-formylmorpholine is a real alternative to N,N-dimethylformamide, fulfilling all requirements of both high dissolution potential and environmental friendliness.
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Affiliation(s)
- Piotr Cysewski
- Department of Physical Chemistry, Faculty of Pharmacy, Collegium Medicum in Bydgoszcz, Nicolaus Copernicus University in Toruń, Kurpińskiego 5, 85-950 Bydgoszcz, Poland;
| | - Maciej Przybyłek
- Department of Physical Chemistry, Faculty of Pharmacy, Collegium Medicum in Bydgoszcz, Nicolaus Copernicus University in Toruń, Kurpińskiego 5, 85-950 Bydgoszcz, Poland;
| | - Rafal Rozalski
- Department of Clinical Biochemistry, Faculty of Pharmacy, Collegium Medicum in Bydgoszcz, Nicolaus Copernicus University in Toruń, Karłowicza 24, 85-950 Bydgoszcz, Poland;
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