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 Table of Contents  
Year : 2022  |  Volume : 11  |  Issue : 2  |  Page : 182-191

Prediction of cocrystal formation between drug and coformer by simple structural parameters

1 Student Research Committee, Tabriz University of Medical Sciences, Tabriz, Iran
2 Pharmaceutical Analysis Research Center, Tabriz University of Medical Sciences, Tabriz, Iran
3 Pharmaceutical Engineering Group, Department of Health Sciences, Lulea University of Technology, Lulea, Sweden
4 Drug Applied Research Center, Tabriz University of Medical Sciences, Tabriz, Iran; Editorial Office of Pharmaceutical Sciences Journal, Faculty of Pharmacy, Tabriz University of Medical Sciences, Tabriz, Iran

Date of Submission08-Dec-2021
Date of Acceptance18-Jun-2022
Date of Web Publication23-Dec-2022

Correspondence Address:
Dr. Ali Shayanfar
Editorial Office of Pharmaceutical Sciences Journal, Faculty of Pharmacy, Tabriz University of Medical Sciences, Tabriz
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Source of Support: None, Conflict of Interest: None

DOI: 10.4103/jrptps.JRPTPS_172_21

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Background: Cocrystal formation between an active pharmaceutical ingredient (API) and coformer is an applicable technique to change the physicochemical and pharmacokinetic properties. Computational methods can overcome the need for extensive experiments and improve the chances of success in the coformer selection. In this method, two compounds connect by non-covalent interactions that form a unique crystalline structure. Prediction of a cocrystal formation between API and coformer can help in the screening and design of new cocrystals. Methods: In this study, available data in the literature were applied to develop a prediction method based on binary logistic regression to screen cocrystal formation by sum and absolute difference of structural parameters (the number of rotatable bonds, Abraham solvation parameters, and topological polar surface area) of the two involved compounds. Results: The results showed various factors (eight structural parameters of the two compounds) could affect cocrystal formation, and the developed model can predict cocrystallization with a probability of about 90%. Conclusion: The related parameter to hydrogen bonding basicity and volume of compounds has the most significant effect on cocrystal formation.

Keywords: Abraham solvation parameters, cocrystal, prediction

How to cite this article:
Shayanfar S, Jouyban A, Velaga S, Shayanfar A. Prediction of cocrystal formation between drug and coformer by simple structural parameters. J Rep Pharma Sci 2022;11:182-91

How to cite this URL:
Shayanfar S, Jouyban A, Velaga S, Shayanfar A. Prediction of cocrystal formation between drug and coformer by simple structural parameters. J Rep Pharma Sci [serial online] 2022 [cited 2023 Sep 21];11:182-91. Available from: https://www.jrpsjournal.com/text.asp?2022/11/2/182/364997

  Introduction Top

Physicochemical properties of active pharmaceutical ingredients (API), such as hygroscopicity, thermal stability, solubility, dissolution rate, and bioavailability, have an essential part in drug discovery and development.[1] Unfortunately, most of the candidate APIs have low solubility leading to poor bioavailability. To overcome this limitation, numerous methods have been recommended to increase solubility, such as cocrystal formation.[2] Cocrystallization technology has caught much attention in the pharmaceutical industry, and it can improve the properties of an API, such as solubility, bioavailability, storage stability, and manufacturability.[3],[4] It allows better products to be produced for the marketplace by improving the physical and chemical properties of API without any change in structure, contrary to the situation that happened during salt formation.[5],[6],[7] The advantage of cocrystallization is that non-ionizable API molecules can form cocrystal against the salt formation, so the list of acceptable crystal coformers is more comprehensive than salt formation.[8]

Cocrystals are structurally homogeneous crystalline materials consisting of two molecules that are present in definite stoichiometric ratios, interacting with each other via a non-covalent bond, especially hydrogen bonding. The coformers are usually selected from Everything Added to Food in the United States (EAFUS) and the Generally Recognized As Safe (GRAS) lists. The fundamental rule of selecting coformers is based on the possibility of forming supramolecular synthons via intermolecular interactions.[9]

Based on the FDA guidance, cocrystals are a kind of solvates, whereas the second component is non-volatile. Some functional groups would form strong and directional hydrogen bonds, such as amides, heterocyclic bases, and carboxylic acids. These groups in the structures of APIs and coformers could lead to the formation of cocrystals.[1]

Experimental cocrystal preparation and characterization are time-consuming, and it needs relatively expensive instrumental methods such as powder X-ray diffraction and differential scanning calorimetry (DSC).[10]

Cocrystal screening and the possibility of cocrystal formation between API and coformer have become an increasingly important part of crystal engineering over the recent years. It can reduce required experiments to find out an appropriate coformer for an API.[11] There are many reports in the literature in which the attempts of researchers to prepare a cocrystal were unsuccessful and binary eutectic compositions obtained.[12],[13],[14],[15],[16] Investigation of factors affecting crystallization, computational approaches by various structural parameters for predicting cocrystal formation, and screening by different methods have been advanced in recent years to predict cocrystal formation. Structural parameters such as shape and polarity, Hansen solubility parameters of API[17] and coformer, ab initio molecular dynamics method,[18] conductor-like screening model for real solvents,[19],[20] molecular electrostatic potential surfaces to assess molecular complementarity between two cocrystal components,[21] and realistic lattice energy landscapes[22] were suggested as essential parameters in cocrystal formation. In some cases, new statistical methods, e.g., multivariate adaptive regression splines methodology, were used for developing a prediction model.[23] In the majority of the in silico methods, a few compounds have been applied. Recently, descriptors based on fingerprint vectors and molecular graphs were applied for developing a model by artificial neural networks for a data set extracted from the Cambridge Structural Database.[24]

Valid and comprehensive experimental data are necessary to predict new cocrystal formation. One of the main reasons why this method is not mature and accurate to provide the acceptable prediction model is inaccessibility of comprehensive and uniform data sets (true positive/true negative cocrystal formation data). Przybyłek and Cysewski[25] have reported a data set comprising 226 binary mixtures (drug and phenolic acids as potential pharmaceutical coformers) classified as cocrystals or simple eutectics. They applied a multi-parameter model comprising 1D and 2D descriptors for cocrystal prediction with a probability of about 80%.

Simple statistical models to develop a mechanistic model, e.g., based on logistic regression and descriptors [i.e., topological polar surface area (TPSA), number of rotatable bonds (NRBs), and Abraham solvation parameters of components], are more acceptable in modeling studies[26] and could be useful in the future in cocrystal screening and formation. In this study, a virtual cocrystal screening process was reported on the basis of the structural parameters and logistic regression, and the prediction validity of the method was checked by leave-many-out cross-validation.

  Computational Method Top

A cocrystal formation data set (true positive/true negative) comprising 226 data points was taken from a published article [Table 1].[25] SMILES (Simplified Molecular-Input Line-Entry System Codes) of compounds, a chemical notation that can be used by the computer that represents a chemical structure in a way,[27] were collected by searching their chemical names in PubChem (https://pubchem.ncbi.nlm.nih.gov). The numerical values for TPSA, NRB, and Abraham solvation parameters were computed by ACD/Labs software (https://ilab.acdlabs.com). Abraham solvation parameters are independent variables with the following solute properties: E is the excess molar refraction, S indicates dipolarity/polarizability descriptors of the solute, A is hydrogen-bond acidity, B is the solute hydrogen-bond acidity and basicity, and V is the McGowan volume of the solute.[28] Moreover, A×B was computed as another parameter which dealt with solute–solute interactions.[29] Then, sum and absolute difference of compounds 1 and 2’s parameters were calculated.
Table 1: Experimental cocrystal formation (true positive=1, true negative=0) between compounds 1 and 2[18] and probability (P) of a binary response by Eq. () (P>0.5: cocrystal formation, P<0.5: no cocrystal formation) and prediction cocrystal formation

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The binary classification carried out using experimental true positive/true negative cocrystal formation was set as a dependent variable and sum and absolute difference of compounds 1 and 2’s descriptors, i.e., TPSA, NRB, and Abraham solvation parameters, set as independent variables to develop a model based on logistic regression[30] to predict cocrystal formation. Logistic regression models compute the probabilities (P) for classification problems with two possible outcomes, i.e., P>0.5, class I (cocrystal formation) and P<0.5 (no cocrystal formation).

Statistically significant descriptors were selected for the logistic regression model based on probability values (P-value) associated with each descriptor whenever they were statistically significant at the 90% level (P<0.1). It displays the probability that the descriptor is by chance less than 10%.[26] The validity of the developed model was checked by the leave-10-out cross-validation method. In modeling studies, training a model by linear and non-linear models is not enough to confirm the prediction capability. The developed model should be applied to other data sets which did not include in the training of the model. On the way, whenever we can say a model is acceptable, it could predict the outcome of other compounds with reasonable accuracy. Therefore, external validation (test set) is essential. However, because of a small sample of available data, cross-validation was used. Cross-validation analysis, e.g., leave-many-out, is recommended in quantitative structure–activity studies, especially when the sample size is small, and some reports showed its superiority in external validation.[31],[32] Therefore, a type of leave-many-out cross-validation (10 out) was applied. It evaluates the prediction capability of the model in which 10 compounds are left out from the training set, and the trained model was used to predict the removed data points. [Figure 1] illustrated a schematic representation of computational methods for the calculation of parameters and logistic regression for predicting cocrystal formation in this study.
Figure 1: A schematic representation of computational methods for the calculation of parameters and logistic regression for predicting cocrystal formation in this study

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  Results and Discussion Top

Based on the preliminary analysis, reported data of cocrystal formation between carboximide and carboxylic acid behave as outliers (17 data). Geometric disposition of hydroxyl functionality on benzoic acid that can drive the formation of cocrystals[33] is a possible reason to act as outliers, and structural parameters cannot estimate cocrystal formation. Therefore, remained data points (210 data) were applied to develop a model by sum and absolute difference of compounds 1 and 2’s descriptors, i.e., TPSA, NRB, and Abraham solvation parameters based, on binary logistic regression, in which the obtained model is:

where P is the probability of binary responses (class 0: P<0.5 or 1 P>0.5) based on the true positive/true negative cocrystal formation and e is Euler’s number (e=2.718). In addition, probability values (P-value) associated with each descriptor were less than 0.1. The model [Eq. ()] estimated 94% and 75% of true positive and true negative cocrystal formation in the correct group, respectively [Table 1]. Leave-many-out cross-validation was performed to evaluate the prediction capability of the model, and the results were listed in [Table 2]. No significant difference in accuracy after leave-10-out cross-validation confirms the prediction capability of the developed model. Besides, receiver-operating characteristic (ROC) curves were used to evaluate the classification abilities of the logistic-regression-based models. ROC of Eq. () was illustrated in [Figure 2], and the area under the curve is 0.943. It confirms the validity of the developed model for predicting cocrystal formation between the two compounds.
Table 2: Percentage of correct prediction of cocrystal formation between compounds 1 and 2 by Eq. () and leave-10-out cross-validation

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Figure 2: Receiver-operating characteristic (ROC) curve of the model (Eq. ) for predicting cocrystal formation

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Evaluation of the selected parameters shows that the hydrogen bonding parameters have the most significant effect on cocrystal formation. Feature selection with a forward method using SPSS software indicated that the most crucial parameter for the classification of data is the sum of the hydrogen-bond basicity (B1+B2) and volume of compounds (V1V2). With these two parameters [Eq. ()], 60% and 95% of true positive and true negative cocrystal formations are classified in the correct group, respectively:

Based on the developed model, high numerical values correspond to hydrogen bond donor of drug and coformer and similar volume between the two compounds gives a P higher than 0.5, which indicates cocrystal formation. Further analyses showed that all of the true positive cocrystal formation data between compounds 1 and 2 have B1+B2>1 [Figure 3]. In contrast, this value for No cocrystal formation data is 66% and only three data have B1+B2>2. The cocrystal can be formed using non-covalent interaction, which is often hydrogen bond.[34],[35] It has a critical effect on the cocrystal formation between the two compounds. Typical hydrogen bonds utilized in crystal engineering are bonds among carboxylic acids, amides, and N-heterocyclic hydrogen-bond acceptor with carboxylic acid.[36] According to the studied parameters, A and B belong to the hydrogen bonding group of compounds, and they represent hydrogen bonding donor and acceptor groups, respectively. These results indicate that although “A” could have a proper role in cocrystal formation based on the obtained model [Eq. ()], “B” in comparison with “A” is a more critical parameter affecting cocrystal formation. Some compounds with A=0 such as caffeine [Figure 4] which do not have hydrogen bond donor groups can form cocrystal with some of the coformers. Moreover, these results confirm the previous findings, in which supramolecular heterosynthons (i.e., non-covalent bonds between different functional groups composed of a hydrogen bond acceptor and a hydrogen bond donor group such as carboxylic acid–aromatic nitrogen) favor for cocrystal formation than supramolecular homosynthon.[37] Although the developed model [(Eq. ()] with only two parameters predicts cocrystal formation with 86% accuracy, nevertheless, the prediction for No cocrystal formation is not acceptable (60%) because it is only 10% close to the chance probability value (50%). Other parameters were used to improve the accuracy values of true positive and true negative cocrystal formation to 94% and 75%, respectively [(Eq. ()]. Based on the mentioned descriptors, the model did not have satisfying results unless the sum and absolute difference of another descriptor (sum and absolute difference of A×B) dealt with acidity and basicity hydrogen bond descriptors of compounds included in the model yielded much better correlations. The obtained results verify the importance of hydrogen bonding in cocrystal formation. Similar outcomes to including A×B in developing quantitative structure–property relationship (QSPR) models have been reported by Abraham and Acree[29] for the solubility prediction of solutes in octanol and water by Abraham solvation parameters.
Figure 3: Cocrystal formation vs. B1+B2 of compounds 1 and 2. All of the true positive cocrystal formation between compounds 1 and 2 has B1+B2>1, whereas this value for no cocrystal formation data is 66% and only three data have B1+B2>2

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Figure 4: Structure of caffeine. It has no hydrogen bond donor functional group (A=0); however, they could form cocrystal with various coformers

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The results of this study approve the capability of Abraham solvation parameters for predicting cocrystal formation. These parameters have been extensively used in QSPR models to predict physicochemical and pharmacokinetic properties.[38],[39],[40],[41] Moreover, the established models based on logistic regression using Abraham solvation parameters as structural descriptors have been applied to estimate Biopharmaceutics Drug Disposition Classification System (BDDCS)[42] and the oral bioavailability correlation between humans and preclinical animals.[43]

In this study, for the first time, Abraham solvation parameters and some other simple descriptors were used for the prediction of non-covalent interaction between API and coformer, i.e., cocrystal formation. The results indicate the importance of related parameters to hydrogen binding basicity and volume of API and conformer, which is the most common interaction in cocrystal formation. Mechanistic interpretation for the developed model means that it is potentially helpful in the regulatory context.[26]

The limitation of this study is a relatively small data set (only 52 NO cocrystal formation data). The applied descriptors and the developed model on a large uniform data set composed of true positive and true negative cocrystal formation could improve the prediction accuracy of the model. Other structural descriptors, i.e., intermolecular descriptors and 1D, 2D, and even 3D descriptors, could have more positive effects on the accuracy of cocrystal formation prediction between drug and coformer. However, the developed models with them are complex, and mechanistic interpretation sometimes is not possible.

  Conclusion Top

Prediction of cocrystal formation of a drug with different coformers helps to design the cocrystal in drug development, and it could speed up the process of cocrystal formation studies. Hydrogen bonding parameters and the molecules’ volume are the most important in cocrystal formation between the two compounds. The molecules with similar volumes and more functional groups involved in hydrogen bonding are positive structural chemical factors in cocrystal formation. However, other parameters are necessary to propose an applicable model with good accuracy to predict cocrystal formation. The results of this study can help the mechanistic evaluation of cocrystal formation and cocrystal screening without time-consuming and costly experiment methods with only computational structural descriptors. However, finalization of cocrystal formation requires other standard methods such as DSC, X-ray diffractions, and so on.

Financial support and sponsorship

The authors would like to thank the Tabriz University of Medical Sciences for the financial support (60049) of the project.

Conflicts of interest

There are no conflicts of interest.

Authors’ contribution

SS and AS performed data analysis and manuscript writing. SV contributed in data analysis and AJ contributed in manuscript preparation. All authors read and approved the final manuscript.

Ethics approval

Not applicable.

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  [Figure 1], [Figure 2], [Figure 3], [Figure 4]

  [Table 1], [Table 2]


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