Molecular Drivers of Crystallization Kinetics for Drugs in Supersaturated Aqueous Solutions

Journal of Pharmaceutical Sciences 108 (2019) 252-259

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Journal of Pharmaceutical Sciences

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Pharmaceutics, Drug Delivery and Pharmaceutical Technology Molecular Drivers of Crystallization Kinetics for Drugs in Supersaturated Aqueous Solutions

* Amjad Alhalaweh 1, Ahmad Alzghoul 2, Christel A.S. Bergstrom€ 1,

1 Department of Pharmacy, Uppsala University, Uppsala Biomedical Centre, P.O. Box 580, Uppsala SE-751 23, Sweden 2 Department of Information Technology, Uppsala University, Lagerhyddsv.€ 2, hus 1, Box 337, Uppsala SE- 751 05, Sweden article info abstract

Article history: In this study, we explore molecular properties of importance in solution-mediated crystallization Received 21 August 2018 occurring in supersaturated aqueous drug solutions. Furthermore, we contrast the identified molecular Revised 23 October 2018 properties with those of importance for crystallization occurring in the solid state. A literature data set of Accepted 1 November 2018 54 structurally diverse compounds, for which crystallization kinetics from supersaturated aqueous so- Available online 10 November 2018 lutions and in melt-quenched solids were reported, was used to identify molecular drivers for crystallization kinetics observed in solution and contrast these to those observed for solids. The compounds Keywords: fi crystallization were divided into fast, moderate, and slow crystallizers, and in silico classi cation was developed using a glass molecular K-nearest neighbor model. The topological equivalent of Grav3 (related to molecular size and in silico modeling shape) was identified as the most important molecular descriptor for solution crystallization kinetics; the supersaturation larger this descriptor, the slower the crystallization. Two electrotopological descriptors (the atom-type E- physicochemical properties þ precipitation state index for -Caa groups and the sum of absolute values of pi Fukui( ) indices on C) were found to separate the moderate and slow crystallizers in the solution. The larger these descriptors, the slower the crystallization. With these 3 descriptors, the computational model correctly sorted the crystallization tendencies from solutions with an overall classification accuracy of 77% (test set). ® © 2019 The Authors. Published by Elsevier Inc. on behalf of the American Pharmacists Association . This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/ 4.0/).

Introduction The precipitating phasedand the kinetics by which compounds precipitatedalso depends on the crystallization environment.11 The large number of poorly soluble discovery compounds has Figure 1 illustrates the possible scenarios for crystallization from resulted in an increased interest in making use of formulation a highly supersaturated solution. A fast kinetic pathway leads to strategies that produce supersaturated solutions in the quest to precipitation of the drug in crystalline form(s), whereas slower increase absorption of such drugs.1,2 The supersaturated solution of kinetics result in a supercooled liquid or glass.12,13 A supercooled the drug is metastable, a state that favors the conversion of the drug liquid results when the operating temperature is above the wet 3 to its most stable crystalline form. This process is kinetically driven glass transition temperature (Tg) and becomes a glass below this and depends on among others the solvent, pH, temperature, temperature. These different forms are the result of liquid-liquid agitation, degree of supersaturation, and the inherent properties of phase separation, or glass-liquid phase separation, if below 4-6 the drug (e.g., size, polarity, rigidity). How the compound in- the Tg. The phase separation occurs at a compound-speciﬁc teracts with, for example, micelles or excipients present in the so- concentration.12 lution is critical for the stability of supersaturated solutions.7-10 To date, the maximum supersaturation level of a compound has mostly been determined in simple water-based systems rather than more complex solvents such as intestinal ﬂuids.

Abbreviations used: DSC, differential scanning calorimetry; GF, glass former; Taylor et al, looked at the effects of some molecular properties for GLPS, glass-liquid phase separation; KNN, K nearest neighbor; LLPS, liquid-liquid a group of structurally related drugs (calcium channel blockers) e phase separation; nGF, non glass former; Tg, glass transition temperature; on their precipitation rate/crystallization from supersaturated T_Grav3, topological equivalent of Grav3. solutions.7 No strong correlations were found for the rather This article contains supplementary material available from the authors by request limited number of molecular descriptors they explored, but or via the Internet at https://doi.org/10.1016/j.xphs.2018.11.006. * Correspondence to: Christel Bergstrom€ (Telephone: þ46 18 471 4118). increased structural complexity tended to reduce the crystalli- 7 E-mail address: [email protected] (C.A.S. Bergstrom).€ zation rate. In another study, they studied the crystallization of https://doi.org/10.1016/j.xphs.2018.11.006 ® 0022-3549/© 2019 The Authors. Published by Elsevier Inc. on behalf of the American Pharmacists Association . This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). A. Alhalaweh et al. / Journal of Pharmaceutical Sciences 108 (2019) 252-259 253

Experimental Section

Crystallization Kinetics

Experimental data for 54 compounds were compiled from literature sources.6-8,12 Figure 2 summarizes the criteria defining crystallization from undercooled melts and from supersaturated solutions. In brief, supersaturated solutions were obtained by a solvent shift method in which a DMSO stock solution of the compound was mixed with aqueous buffer. The crystallization kinetics in the resulting supersaturated solutions was monitored by synchrotron radiation to identify the onset of turbidity. On the basis of the time required for precipitation, the compounds were sorted into fast, moderate, and slow crystallizers (Fig. 2). For this set of 54 compounds, we experimentally determined the glass-forming ability for the 4 compounds not studied earlier Figure 1. Possible scenarios for crystallization from supersaturated solutions. by our group. This was compiled then with the data from previous publications on the other 50 compounds.14,15 The crystallization tendency in the solid amorphous form was determined 54 compounds from supersaturated aqueous solutions8 and through in situ melt-quenching in a DSC Q2000 calorimeter (TA classified them as fast (150 s), moderate (60 min), and slow Instruments, New Castle, DE). The DSC instrument was equipped crystallizers (>60 min). Based on this data set, they concluded with a refrigerated cooling system and was calibrated for tem- that the drug properties rather than the methods to produce the perature and enthalpy using indium. The melting point was amorphous material tend to dictate the crystallization kinetics. determined using nonhermetic aluminum pans into which 1-3 However, no predictive models for crystallization kinetics were mg of the compound was weighed. The pans were exposed to a presented. heating rate of 10C/min under a continuously purged dry ni- Taylor et al. have also studied crystallization tendency in trogen atmosphere (50 mL/min). Glass formation was investi- undercooled melts.14 These experiments were carried out in situ gated by performing a heat-cool-heat cycle during which the using differential scanning calorimetry (DSC), and hence, explored compound was heated in the pans to around 2C above the crystallization processes occurring in the solid material. On the melting point for 2 min to ensure complete melting, and there- basis of the DSC, the compounds were classified as noneglass after cooled to e70C at a ramp rate of 20C/min. The formation formers (nGF) or glass formers (GF) as a result of their behavior of a glass state was then investigated by heating the system again, in the DSC. Thereafter, the GF group was further classified based immediately after cooling, using a heating rate of 20C/min. The on crystallization tendency, where compounds that crystallize presence of the amorphous form was confirmed by detection of fi from the glass upon heating were identi ed as non-stable GFs. the Tg on heating. The compounds were sorted into the 3 classes The stability of these GFs can be identified by the Hückel pi suggested by Taylor et al.14 We then matched the solid GF classes atomic charges for their C atoms and the number of hydrogen with crystallization kinetics from solution: class I in solid form bonds. When these values are low, the compounds crystallize corresponded to rapid crystallization from solution; class II to rapidly, that is, they are non-stable GFs, whereas high values moderate crystallization from solution; and class III to slow mean the amorphous form is stable.15 The crystallization tendency crystallization rate in solution (Fig. 1). (and hence, physical stability) has also been explored through storage of amorphous drugs in relation to their respective Tg. The Computational Model Development amorphous material was stored in situ in a DSC at 20C above the Tg for 24 h. These studies looked at inherent molecular properties The ADMET Predictor software v7.1 (SimulationsPlus, Lancaster, important for physical stability in undercooled melts and CA) was used to calculate the chemical descriptors (n ¼ 404) of the aromaticity was found as a molecular driver for more rapid compounds. To explore the chemical diversity of the compounds, a crystallization.16 principal component analysis was performed using the MATLAB Another way of studying the crystallization tendency is to use software. The first 2 principal components were used to plot the solvent evaporation to produce the amorphous form.6 Solvent data in 2 dimensions (Fig. 3) and to explore possible clusters of fast, evaporation takes longer than melt-quenching by DSC, but there is moderate, and slow crystallizers. good agreement between the capacity of these 2 methods to pro- A computational model to differentiate the 3 classes of crystal- duce the amorphous form.15,17 Solvent evaporation results in the lization kinetics was developed using the KNN algorithm and production of amorphous material via the formation of supersat- MATLAB software. KNN is a supervised learning algorithm that urated solutions. In this study, we wanted to better understand and classifies new data by a majority vote on the K-nearest training predict the crystallization kinetics of drug compounds from samples. The algorithm is nonparametric; thus, it makes no as- aqueous supersaturated solutions. To what extent do the molecular sumptions about the underlying data distribution. The algorithm properties of the drug drive nucleationdand hence crystallization has shown good performance in applications with multiclass data kineticsdin amorphous solids compared to nucleation in super- sets and has been used to model biological and medical data.18-21 saturated solutions? Using the experimental data from a large and The experimental data set was divided into a training set (n ¼ 41) structurally diverse data set, we linked the molecular properties to develop the model and a test set (n ¼ 13) to validate the obtained using K-nearest neighbor (KNN) algorithms. The models enable a model. In each of the sub data sets, the distribution of the classes deeper understanding of crystallization occurring in water and also was equal, as described by the fraction of compounds representing provide an early assessment of the risk for a rapid loss of super- each class (fast, moderate, and slow). Feature selection was used to saturation, for example, after oral administration of an amorphous reduce the number of chemical descriptors (n ¼ 404) and avoid the dosage form. effects in dimensionality in the KNN algorithm. Therefore, two- 254 A. Alhalaweh et al. / Journal of Pharmaceutical Sciences 108 (2019) 252-259

Figure 2. Classification systems used to define crystallization tendency in solids and crystallization rate from supersaturated solutions. The solids were sorted in accordance with observations of recrystallization kinetics during melt-quenching using a heat-cool-heat cycle in a differential scanning calorimeter. Crystallization from the solution was observed from the time when precipitation occurred as identified by a decrease in concentration.

sample t-test was applied to select the most relevant descriptors for Results model prediction. The data set was also normalized to prevent large-scale descriptors from dominating the distance measure. The Data on the crystallization form and precipitation rate from leave-one-out cross-validation was used to determine the value of supersaturated aqueous solution were compiled for 54 compounds K parameter for the KNN algorithm.19,20 The ﬁnal model was from the literature (Table 1).6-8,12 Table 1 also shows the crystalli- thereafter validated with the test set. zation tendencies in the amorphous solid material. Of the 54

Figure 3. Distribution of the data set divided into training and test sets. The data set (n ¼ 54) is presented in the chemical space described by the ﬁrst 2 principal components in the principal component analysis. The ellipse shows the 95% CI of the presented principal components. The training data set is presented in blue circles and the test data set in green circles. Compounds are numbered as in Table 1. A. Alhalaweh et al. / Journal of Pharmaceutical Sciences 108 (2019) 252-259 255

Table 1 Calculated Molecular Properties for the Data Set Studied

ID Compound Solution Solid MW T_Grav3 SaasC Pi_AFPlc Tr/Te

1 4-Biphenylcarboxylic acid Fast I 198.2 13.8 2.4 13.6 Tr 2 4-Biphenylmethanol Fast I 184.2 13.6 3.3 12.0 Tr 3 4-Phenylphenol Fast I 170.2 13.2 2.6 12.6 Te 4 Benzamide Fast I 121.1 11.5 0.6 7.4 Tr 5 Caffeine Fast I 194.2 13.9 0.0 7.1 Te 6 Carbamazepine Fast I 236.3 14.9 3.6 18.0 Te 7 Felbinac Fast I 212.3 14.1 3.1 13.9 Tr 8 Indoprofen Fast I 281.3 15.7 3.3 14.6 Tr 9 Lidocaine Fast I 234.3 14.5 3.2 8.0 Tr 10 Naproxen Fast I 230.3 14.5 1.6 12.7 Tr 11 Phenacetin Fast I 179.2 13.2 1.6 10.0 Te 12 Tolfenamic acid Fast I 261.7 15.1 3.1 14.4 Tr 13 Loviride Fast II 351.2 16.5 2.9 16.8 Tr 14 Piroxicam Fast II 331.4 17.5 0.3 15.5 Tr 15 Tolazamide Fast II 311.4 17.3 1.0 8.4 Tr 16 Acetaminophen Moderate II 151.2 12.4 0.8 8.8 Te 17 Anthranilic acid Moderate I 137.1 11.9 0.5 8.4 Tr 18 Chlorzoxazone Moderate I 169.6 13.2 0.2 10.0 Tr 19 Dibucaine Moderate II 343.5 16.8 1.1 10.7 Tr 20 Dipyridamole Moderate I 504.6 19.4 2.3 6.8 Tr 21 Flufenamic acid Moderate I 281.2 15.4 -0.4 13.5 Tr 22 Flurbiprofen Moderate II 244.3 14.7 1.3 14.9 Tr 23 Haloperidol Moderate I 375.9 17.3 1.8 13.9 Tr 24 Nilutamide Moderate III 317.2 16.1 -3.1 5.8 Tr 25 Tolbutamide Moderate I 270.4 16.4 1.1 8.2 Tr 26 Chlorpropamide Moderate I 276.7 16.4 0.5 9.0 Te 27 Fenoﬁbrate Moderate III 360.8 16.8 2.1 14.3 Te 28 Griseofulvin Moderate I 352.8 16.9 1.2 12.2 Tr 29 Nimesulide Moderate III 308.3 17.2 0.4 5.7 Tr 30 Nimodipine Moderate II 418.5 17.8 0.3 12.0 Te 31 Nifedipine Moderate II 346.3 16.6 0.0 12.0 Tr 32 Aceclofenac Moderate III 354.2 16.7 2.7 18.6 Tr 33 Celecoxib Moderate II 381.4 18.2 0.9 14.5 Tr 34 Felodipine Moderate III 384.3 17.1 1.2 16.1 Tr 35 Nisoldipine Moderate III 388.4 17.3 0.0 12.0 Tr 36 Nitrendipine Moderate III 360.4 16.9 0.3 12.0 Te 37 Ibuprofen Slow III 206.3 13.8 2.1 7.9 Tr 38 Procaine Slow III 236.3 14.6 1.2 7.7 Te 39 Bifonazole Slow II 310.4 16.5 5.0 21.6 Te 40 Carvedilol Slow III 406.5 18 2.2 21.2 Tr 41 Cinnarizine Slow II 368.5 17.5 4.0 20.0 Tr 42 Clotrimazole Slow III 344.9 17 4.0 22.4 Tr 43 Clozapine Slow III 326.8 16.8 4.8 14.7 Tr 44 Efavirenz Slow III 315.7 16.2 -0.3 14.1 Tr 45 Indomethacin Slow III 357.8 16.9 2.8 17.3 Tr 46 Ketoconazole Slow III 531.4 19.7 3.6 21.0 Tr 47 Ketoprofen Slow III 254.3 14.9 1.7 13.2 Tr 48 Loratadine Slow III 382.9 17.6 5.6 16.2 Tr 49 Miconazole Slow III 416.1 17.8 4.0 18.8 Tr 50 Probucol Slow III 516.9 19 7.1 16.0 Tr 51 Ritonavir Slow III 721.0 21.8 4.5 25.6 Te 52 Atazanavir Slow III 704.9 21.2 3.4 25.3 Te 53 Lopinavir Slow III 628.8 20.6 4.5 25.0 Tr 54 Cilnidipine Slow III 492.5 18.9 1.2 20.0 Tr

Compounds are listed based on their classes in solution experiments.a Slow, moderate, and fast refer to crystallization kinetics from solution. Classes I, II, and III refer to the crystallization tendency class in amorphous solids. a The following abbreviations are used: molecular weight (MW); topological equivalent of Grav3_3D (T_Grav3); Atom-type E-state index for -Caa groups (SaasC); Sum of absolute values of pi Fukui(þ) indices on C (Pi_AFPlc); training ad test sets (Tr and Te, respectively).

compounds, 28%, 39%, and 33% were fast, moderate, and slow melt (i.e., the solid form). The topological equivalent of Grav3 crystallizers, respectively. The data set was structurally diverse and (T_Grav3) is a chemical descriptor for differentiating GF and nGF15 had no clear trends of clustering in the standard principal and was therefore the ﬁrst descriptor we evaluated for its impor- component analysis. However, it was noticed that slow crystallizers tance on crystallization rate from aqueous solutions. The same differed to some extent from the other 2 classes (Supporting cutoff value was used as for the T_Grav3 identiﬁed for crystalliza- Information, Fig. 1s). tion from undercooled melt. The descriptor T_Grav3 has previously been related to nGFs when the value is below 15.5. If the same Computational Models for Prediction of Rate of Crystallization molecular property is of importance in the solution as in the solid form, compounds with T_Grav3 <15.5 should then be rapid crys- At the start of this project, we used the model that we had tallizers from the solution. In contrast, when T_Grav3 is > 15.5, the previously developed for describing crystallization tendency from a compound is a GF, which should mean it is a moderate or slow 256 A. Alhalaweh et al. / Journal of Pharmaceutical Sciences 108 (2019) 252-259

Figure 4. Prediction of compound crystallization behavior from undercooled melt for reference (a) and supersaturated aqueous solution (b) using the topological equivalent of Grav3 (T_Grav3).

crystallizer from the solution. These cutoff values for T_Grav3 classes from each other. These descriptors were the atom-type E- resulted in a classification accuracy for fast crystallizers of 58% and state index for -Caa groups and the Sum of absolute values of pi 89% for moderate or slow (Fig. 4). Hence, although this descriptor Fukui (þ) indices on C. Figure 6 shows the prediction of the 2 cutoff value accurately identified the slow to moderate crystallizers, classes by each chemical descriptor separately, and Figure 7 shows it did not work as well for the fast crystallizers. We then continued the distribution of the moderate and slow classes using the 2 de- to explore the role of molecular weight (MW) in crystallization scriptors together. Four compounds (ibuprofen, procaine, efavirenz, from solution. Our previous studies have shown that compounds ketoprofen) were experimentally determined to be slow crystal- with MW >300 g/mol typically belong to the GF group, whereas lizers but falsely predicted to belong to the moderate group when compounds below 200 g/mol belong to the nGF group.15,22 Using using the two-descriptor prediction. the same argument as for T_Grav3, compounds >300 g/mol would therefore be expected to be moderate to slow crystallizers from the Prediction of Crystallization From Supersaturated Solution Using a solution, whereas <200 g/mol would be fast crystallizers making KNN Algorithm the assumption that the same descriptors can predict the crystallization rate in amorphous solids and from solutions. For com- On the basis of the results from the two-sample t-test, 3 pounds with MW >300 g/mol, this was indeed the case for the data chemical descriptorsdthe T_Grav3, the Atom-type E-state index set in this article; the moderate to slow crystallizers were predicted for -Caa groups, and a Fukui(þ) indexdwere selected for devel- with an accuracy of 90.3% using this descriptor alone (Fig. 5). opment of the KNN-based model for the 3 classes (slow, moderate, However, for compound with MW <300 g/mol, the predictions fast). The K parameter of the KNN algorithm was set to 9 because failed. Compounds with MW between 200 and 300 g/mol were this value achieved the lowest training and leave-one-out cross- found to belong to all 3 classes, and in addition, MW <200 was not a validation errors. The performance of the KNN algorithm on the good predictor for compounds that are fast crystallizers. Thus, these training and test data sets is presented in the confusion matrix in molecular properties, T_Grav3 and MW, were both good predictors the Supporting Information (Table 1s). of slow to moderate crystallizers but were not successful in the The overall classification accuracy of the KNN model was 78% for prediction of fast crystallization. Hence, they could not be used in the training set and 77% for the test set. The 2 data sets are plotted isolation to accurately predict all 3 classes. in Figure 8 in 2 dimensions, using the 2 principal analysis components to illustrate the KNN classification. As the figure shows, the Prediction of Crystallization of Moderate and Slow Crystallization data are noticeably separated into 3 areas representing the slow, Compounds From Aqueous Solutions moderate, and fast crystallizers. Because T_Grav3 and MW are closely related, we also explored the accuracy when MW was used The two-sample t-test method was then applied to see if instead of T_Grav3. This resulted in a slightly lower accuracy of the moderate and slow crystallizers could be distinguished from each test set predictions (74%) indicating that this simpler molecular other on the basis of molecular structure. Two chemical descriptors descriptor may be an alternative input parameter to T_Grav3 for the were found that could significantly distinguish the 2 different modeling of crystallization kinetics from supersaturated solutions.

Figure 5. Prediction of drug crystallization tendency (classes), using molecular weight as the only descriptor for (a) undercooled melt (for reference) and (b) supersaturated solution. A. Alhalaweh et al. / Journal of Pharmaceutical Sciences 108 (2019) 252-259 257

Figure 6. Prediction of compound crystallization behavior using (a) atom-type E-state index for -Caa groups and (b) sum of absolute values of pi Fukui(þ) indices for under-cooled melt (class II and class III) and supersaturated solution (slow and moderate).

Discussion water solubility among others properties.24-29 In our study, the value of this descriptor was related to the rate of crystallization; the Two molecular descriptors were identified in this work that can larger the descriptor, the slower the crystallization from supersat- separate the slow from moderate crystallization rate from the so- urated aqueous solution. The other important descriptor is the sum lution. The atom-type E-state index for -Caa groups is a chemical of absolute values of pi Fukui(þ) indices on carbon atoms. This descriptor related to the general principle of atom-type Electro- descriptor is derived from the absolute electron charge and has pological State Indices.23 These indices provide information on been previously used to separate GF molecules from nGF com- intrinsic electronic and topological properties of the atoms in a pounds within the small size range of 200-300 g/mol. In this work, molecule with a numerical value that describes the availability of a the effective electron reactivity (transfer and sharing) associated certain atom to interact with other atoms or, for example, func- with high values for the Fukui indices increases the rate of crys- tional groups. They have been previously used in predictions of tallization. These results are in agreement with our previous find- octanol-water partition coefficients, toxicity, boiling point, and ings for crystallization of amorphous solids, where high Fukui index

Figure 7. Moderate and slow crystallizing compounds distributed in the chemical space deﬁned by atom-type E-state index for -Caa groups and sum of absolute values of pi Fukui(þ) indices. Circle numbers refer to compound numbering in Table 1. Moderate: ﬁlled circle ( ) and slow: empty circle (B). 258 A. Alhalaweh et al. / Journal of Pharmaceutical Sciences 108 (2019) 252-259

Figure 8. Prediction of the solution crystallization classes using the KNN algorithm. Fast (C), moderate ( ), and slow (B). Double circles indicate compounds from the test set. The red x indicates misclassified compounds. Circle numbers refer to compound numbering in Table 1. values were associated with greater tendency to crystallize in the water-based solvents, given its structurally diverse training set. In amorphous form. other words, the model predicts the expected life span of super- In a recent study by Rades et al., the link between glass-forming saturated delivery systems that are not stabilized by, for example, ability and supersaturation propensity was explored.30 They used a inhibitors of precipitation. The model may therefore facilitate slightly different DSC methodology to classify the glass-forming predictions of formulation challenges for each compound. The ability than that used herein, and furthermore, they measured model is a fast screening approach to obtain early information the maximum apparent degree of supersaturation and time to about formulation strategies, especially during the transition stage precipitation in fasted-state simulated intestinal fluid. Interest- between discovery and early drug development. For example, the ingly, they identified that the good GFs also were the compounds model can rapidly identify slow crystallizing compounds, which are with the highest maximum degree of supersaturation. However, better candidates for amorphous formulations than fast ones, for they were not able to identify any relationship between glass- which, another strategy should be targeted. In addition, it may forming ability and the time to precipitation. In our work, we guide drug synthesis methods to facilitate, for example, drug decided to make use of a categorization approach of the time to crystallization in the medicinal chemistry laboratory. precipitation, which may be one factor that resulted in that it was possible to predict this property and link it to the glass-forming Conclusion ability. It should be noted that other differences between the 2 studies may contribute to the differences observed (data set size, This study presents a molecular understanding of the driving compound types, complexity of solvent). force for crystallization of small molecular compounds from highly Interestingly, the atom-type E-state index for -Caa groups and supersaturated aqueous solutions. Fast crystallizers could be the sum of absolute values of pi Fukui(þ) indices on carbon atoms differentiated from moderate to slow crystallizers on the basis of were successful in separating compounds that have small molec- descriptors related to the size and shape of the molecule, whereas ular differences. The data set included a series of calcium antagonist moderate and slow crystallizers were recognizable by descriptors analogues. These compounds (felodipine, cilnidipine, nifedipine, related to electronic and topological characterization. A computa- nimodipine, nisoldipine, and nitrendipine) were studied for their tional model based on these descriptors was developed, and this crystallization behavior as they are compounds with related model sorted the drugs within the 3 classes (fast, moderate, slow) structure. Using the two-chemical descriptor model, cilnidipine with an acceptable accuracy for the screening stage (78% and 77% was predicted to be the slowest crystallizer from the solution (Fig. 7, for training and test sets, respectively). The developed model does numbers 30, 31, 34, 35, 36, and 54), which was what was also not require any experimental input to sort the compounds ac- experimentally observed. The following order was experimentally cording to their crystallization kinetics and hence, the computa- observed cilnidipine < felodipine ¼ nisoldipine < nitrendipine ¼ tional model is a rapid method that can be implemented already nimodipine < nifedipine. Using our model based on only 2 chemical before compound synthesis. The classification system and under- descriptors, the order was as follow cilnidipine < felodipine < standing of the related molecular properties of each class can help nitrendipine ¼ nimodipine < nisoldipine ¼ nifedipine. Only nisol- in formulation design and provide a way to efficiently explore dipine was predicted faster than it should be although it was performance of supersaturating drug delivery systems. correctly predicted to be within the moderate class. Hence, for the data set explored, the computational model captured small struc- Acknowledgments tural changes and allowed correct classification of analogues. In this work, we established a KNN model that enabled the This work was supported by the Swedish Research Council identification of slow, moderate, and fast crystallizers (from Grants 621-2011-2445 and 621-2014-3309. The authors are grate- aqueous supersaturated solutions) based on rapidly calculated ful to Simulations Plus (Lancaster, CA) for providing the Drug De- molecular descriptors. We expect this model to be generally livery Group at the Department of Pharmacy, Uppsala University applicable for the prediction of crystallization tendency from with a reference site license for the software ADMET Predictor™. A. Alhalaweh et al. / Journal of Pharmaceutical Sciences 108 (2019) 252-259 259

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