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Reliability of the Hansen solubility parameters as co-crystal formation prediction tool
International Journal of Pharmaceutics 558 (2019) 319–327
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International Journal of Pharmaceutics journal homepage: www.elsevier.com/locate/ijpharm
Reliability of the Hansen solubility parameters as co-crystal formation prediction tool Ala' Salem, Sándor Nagy, Szilárd Pál, Aleksandar Széchenyi
T
⁎
University of Pécs, Institute of Pharmaceutical Technology and Biopharmacy, Pécs, Hungary
A R T I C LE I N FO
A B S T R A C T
Keywords: Hansen solubility parameters (HSPs) Predicting co-crystal formation Group contribution method Pharmaceutical co-crystals Miscibility Eutectics Screening
Pharmaceutical co-crystals present an opportunity to improve the solubility of conventional active pharmaceutical ingredients (APIs). Despite advances in co-crystal screening, the rational design of even the chemically simplest co-crystals remains challenging. Hansen solubility parameters (HSPs) have previously been used as a tool to predict co-crystal formation using only the chemical structure. The aim of this study was to validate the use of HSPs as a tool to predict co-crystal formation, analyse its limitations and examine the previously set Δδ inclusion cut-off value. A total of 109 co-formers of carbamazepine, caffeine and theophylline were used as a training set. Sixteen different descriptors were examined. An additional 72 co-formers of piroxicam and nicotinamide were used to test the methods and new cut-off values. The established cut-off value (8.18 MPa0.5) despite being similar to the previously reported value (7 MPa0.5), offered no real advantage over the previously reported value. Our results suggest the use of the modified radius (Ra) method of calculating the solubility difference, which had higher sensitivity of 90% compared to 86% for the previously reported method and cut-off value to indicate co-crystal formation as well as a lower miss and false omission rates.
1. Introduction Co-crystallization is among the most powerful pharmaceutical development strategies to improve the active pharmaceutical ingredients (APIs) aqueous solubility (Cao et al., 2018). Other advantages of cocrystallization include improved in-vitro drug activity (Shete et al., 2015), stability (Liu et al., 2012), mechanical properties (Karki et al., 2009; Ainurofiq et al., 2018) and bioavailability (Childs et al., 2013). Co-crystals are formed through a non-covalent bond, mostly hydrogen bonding between a neutral API molecule and a hydrophilic co-former (Vishweshwar et al., 2006; Douroumis et al., 2017) or between two APIs (drug-drug co-crystals) (Nechipadappu et al., 2017). The most challenging step in co-crystal design is the selection of a co-former likely to form a co-crystal as well as improve the API properties. Several strategies and methods have been developed to aid in the co-former selection. The simplest, however most time consuming method, is based on the trial–error approach, where co-formers are arbitrary chosen from a list of pharmaceutically acceptable materials. Sophisticated methods are based on the detailed knowledge of the molecular structure and properties of the API and co-former. Such methods require complex software and high computational capacity for the calculations (Cheney et al., 2011). Another approach arises from the definition of co-crystals which are homogeneous molecular mixtures of the API and co-former. ⁎
This is where miscibility fits into the prediction of co-crystal formation. The use of theoretical miscibility determination tools based on the calculation of solubility parameters can be employed in the selection of co-formers (Gaikwad et al., 2017). As co-formers with solubility parameters closer to the API are more likely to be mixable and form cocrystals (Desai and Patravale, 2018). The use of solubility parameters in co-crystal screening was reported in a number of articles. In a recent study, Desai and Patravale (2018) used the Hildebrand solubility parameter as part of a theoretical co-former selection method for curcumin. The Hildebrand solubility parameter (Hδ) (Eq. (1)) (Hildebrand and Scott, 1950) is calculated from the energy of vaporization (ΔEV), and molar volume (Vm).
Hδ = √
ΔEv Vm
(1)
Hansen solubility parameters (HSPs) established in 1967 by Hansen (1967) represents a step forward from the Hildebrand solubility parameter. HSPs is an approach where the liquids total cohesion energy is split into contributions from atomic dispersion (δd), dipole–dipole/ polar interactions (δp) and hydrogen bonding (δh) (Eq. (2)). The δh contribution in the HSPs is divided into hydrogen-bond donor (δhDon) and acceptor (δhAcc) values. For a given liquid pair, the closer are the HSP values in the three dimensional HSP space, the greater is their
Corresponding author at: Institute of Pharmaceutical Technology and Biopharmacy, Faculty of Pharmacy, University of Pécs, H-7624, 2 Rókus u, Pécs Hungary. E-mail address: [email protected] (A. Széchenyi).
https://doi.org/10.1016/j.ijpharm.2019.01.007 Received 18 October 2018; Received in revised form 15 December 2018; Accepted 3 January 2019 Available online 14 January 2019 0378-5173/ © 2019 Elsevier B.V. All rights reserved.
International Journal of Pharmaceutics 558 (2019) 319–327
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The three parameters δp, δd and δh can be treated as coordinates of a point in three-dimensions, known as the Hansen space. The following equation is used to calculate the modified radius (Ra) between Hansen parameters in Hansen space (Eq. (4)). Ra represents the distance between two molecules in the Hansen sapce. The value “4” in Eq. (3) is a theoretically justified constant for convenient visualization of spherical rather than ellipsoidal regions of the solubility plot (Cañete et al., 2014; Hansen, 2007).
requiring knowledge of a molecules chemical structure only (Subrahmanyam et al., 1996). The use of HSPs as co-crystals screening method has been reported in several review articles (Fukte et al., 2014; Cysewski, 2016; Abramov et al., 2012; Brittain, 2012; Panzade and Shendarkar, 2017). It has even been described as a better highthroughput method than lattice energy first-principles calculations (Grecu et al., 2014), while another review describe it as a method of limited use (Gadade and Pekamwar, 2016). The use of HSPs in cocrystal screening can be a promising method once validated using a scope of APIs and co-formers as well as investigating other preparation methods and conditions to confirm miscibility as co-crystallization prerequisite. Finally cut-off values need reassessment and refinement before this method become routine in pharmaceutical co-crystal screening. The aim of this study is to evaluate the reliability of HSPs to predict the formation of published co-crystals of different APIs, compare simple absolute difference in solubility (Eq. (5)) to more accurate calculations (Eq. (6)) and Ra (Eq. (4)) as well as identify its limitations. Examine and refine the established cut-off values for accurate co-crystal formation prediction using a set of test co-formers. Moreover, compare co-crystals to eutectics to examine the possibility of differentiating these two closely related pharmaceutical forms using HSPs.
Ra = {(4 ∗ Δδd )2 + (Δδ p )2 + (Δδ h )2}0.5
2. Methods
similarity, and consequently their affinity is stronger. This analysis is particularly useful in polymer dissolution. The concept has been stretched from polymer mixing to mixing of a wide range of materials including nano-structures (Wang et al., 2013; Gardebjer et al., 2016) and pharmaceutical co-crystals (Mohammad et al., 2011). The volume dependent solubility parameter (δv) (Eq. (3)) was introduced by Bagley et al. (Bagley et al., 1971). The Bagley diagram, a two-dimensional plot of δv against δh, has applications in various fields including the prediction of drug intestinal absorption and miscibility (Breitkreutz, 1998).
δ = (δ2d + δ2p + δ2h )0.5
(2)
δ V = (δ2d + δ2p )0.5
(3)
(4)
A paper published by Mohammad et al. in 2011, titled “Hansen solubility parameter as a tool to predict cocrystal formation”, investigated whether HSPs predicted miscibility could be a tool to predict co-crystal formation, taking advantage of that co-crystals could form by eutectic melt. In this study the HSPs miscibility of indomethacin with 33 different co-formers were calculated. If the difference of solubility between the API and co-former is less than 7 MPa0.5, they were considered as miscible and therefore likely to form a co-crystal. With the exception of glycine, all pairs that were predicted as miscible were confirmed to be miscible experimentally. However, only four out of twenty one miscible co-formers resulted in co-crystals. The study concluded that HSPs can be used to short list potential co-formers before laboratory screening. The authors of the study speculated that the failure of miscible systems to form co-crystals may be attributed to reasons like complementarity, conformational flexibility, preferred packing patterns, molecular shape and size, stability as well as the lack of hydrogen bonding. Suggesting also that miscibility is necessary for the formation of co-crystals. The authors also pointed out the need for further studies including APIs of different physicochemical properties and many co-formers to generalize the observations reported. An important aspect of the study published by Mohammad et al. (2011) is the use of cut off value of less than 7 MPa0.5 in the difference of total solubility parameter (Δδ) (Eq. (5)) to predict miscibility and therefore co-crystal formation. This value has been adapted from a paper published by Greenhalgh et al. in 1999 that used Hildebrand solubility parameters as an indication of ibuprofen-carrier incompatibilities in solid dispersions. As a general observed trend classified miscibility according to the ΔHδ into three different categories, those having ΔHδ value (MPa0.5) from 1.6 to 7.5 in molten exhibited complete miscibility, values from 7.4 to 15.0 in liquid showed a degree of immiscibility, lastly a value above 15 had total immiscibility. The fact that Hildebrand parameters represent the overall cohesive energy but offer less information on the relative strengths of forces present such as polar, hydrogen bonding and dispersion, should necessitate Δδ value investigations to predict co-crystal formation when using HSPs. A more accurate method of measuring the difference in solubility parameters is the use of Eq. (6), which allows proper three dimensional point representation.
Δδ = |δAPI − δco-former|
(5)
Δδt = {(Δδd )2 + (Δδ p )2 + (Δδ h )2}0.5
(6)
2.1. Training set of co-formers To evaluate co-crystal formation prediction by HSPs, 109 reported co-formers of carbamazepine, theophylline and caffeine, of different preparation methods, solvents and molar ratios were used as a training set. The list is comprised of 87 successful and 22 failed co-crystals. It includes twelve successful and two failed drug-drug co-crystals. The list of the co-formers used in this study, organized by their HSPs, is provided in the supplementary material (Table S1). It should be noted that some pairs have been reported as both successful and failed co-crystals in different studies, due to preparation factors such as the method and solvent. In such cases, pairs were regarded as successful if reported in a publication, even if they have been reported as unsuccessful by a different study. This was done to avoid data misinterpretation. 2.2. Assessment and refinement of prediction and molecular descriptors Hansen Solubility Parameters in Practice (HSPiP) software version 5.0.11 was used to calculate the different HSP values, experimental data from the software database were used whenever available (Hansen, 2007). PubChem, an open chemistry database, was used to obtain the SMILES (simplified molecular-input line-entry system) format of APIs and co-formers. The SMILES format is a linear text that describes the connectivity and chirality of a molecule. A total of 16 descriptors were calculated. Definitions and equations representing the different descriptors used in this study are shown in Table S2 of the supplementary material. Correlation plots were constructed between the different approaches (Δδ, Δδt and Ra) and differences in δd, δp, δh, and δv. Other tested descriptors tested were the HSP distance (obtained by the software), molecular weight and volume, density, ovality and components of δh. Statistical analysis was performed to conclude effectiveness and cut-off values. Results were presented as average ± SD. Differences were considered significant at p-value ≤0.05 after performing Levene’s test of variance homogeneity and one-way analysis of the variance (ANOVA) using SPSS (Software package version 25). Finally, the parameters ability to predict co-crystal formation was described in terms of statistical measures of performance; sensitivity, specificity, miss and fall-out rates, accuracy and precision. 2.3. Eutectics and test set of co-formers As mentioned previously the HSPs relies on co-crystals forming from
One advantage of HSPs is that it is a simple theoretical approach, 320
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Table 1 HSPs and descriptors of carbamazepine, caffeine and theophylline. API
Carbamazepine
Caffeine
Theophylline
20.92 8.06 22.42 4.47 8.70 3.10 22.86 1.60 187.5 236.3 1.26
19.5 10.1 21.96 13 6.60 7.10 25.52 1.66 155.1 194.2 1.25
19.72 15.42 25.03 10.5 8.40 5.70 27.15 1.72 130.8 180.2 1.38
Structure
δd δp δv δh δhDon. δhAcc. δt Ovality M Vol. M Wt. Ρ
crystal formation prediction, H-bonding is a key factor to consider. Both Δδt and Ra correlate with Δδh. New cut-off values for both Δδ, Δδt and Ra were obtained statistically using the mean value obtained for positive co-crystals of the three APIs. The selection of these three descriptors was based on their ability to statistically differentiate formed and failed co-crystals. Both Δδt and Δδ exhibited a p-value of 0.001, while Ra had a p-value < 0.001. Positive co-formers had Δδ values ranging from 0.50 to 8.18 MPa0.5. The Δδt values for positively formed co-crystals ranged from 3.95 to 16.87 MPa0.5. While the Ra value range for positive co-crystals was between 4.76 and 17.64 MPa0.5. Therefore values of Δδ, Δδt or Ra above 8.18, 16.87 and 17.64 MPa0.5 respectively would correspond to failed co-crystal formation. This newly established cut-off value (8.18 MPa0.5) is similar to the previous 7 MPa0.5 cut-off value. These statistically obtained cut-off values were used to classify the co-formers (Table 2). As shown in the classified co-formers according to Greenhalgh et al. observations (Table S3), only 5 (11.4%) of the carbamazepine co-formers reported to form co-crystals had a Δδ value above 10 MPa0.5. However none had a value above 15 MPa0.5, which is the proposed limit for some miscibility. Co-formers of both theophylline and caffeine have also been under the 15 MPa0.5 cut-off value. Considering 7 MPa0.5 as the cut-off value, 12 (13.8%) of the co-formers reported to form co-crystals had a Δδ values above the cut-off value. However, 11 (12.6) of the coformers reported to form co-crystals had Δδ above the newly established cut-off of 8.18 MPa0.5. Moreover 9 (10.3%) co-formers reported to form co-crystals were above the 16.87 MPa0.5 and 17.64 MPa0.5 cutoff values of Δδt and Ra respectively. To establish the effectiveness of the HSPs as a co-crystal formation prediction tool, the statistical measures of performance were calculated for each method as well as for the previously reported cut-off value to allow comparison (Table 3). Sensitivity (a measure of the proportion of true positives that was correctly identified) and specificity (accounting for the percentage of true negatives that was correctly identified) were calculated. The improvements brought about by the new cut-off value (8.18 MPa0.5); higher sensitivity and lower miss and false omission rates were complicated by low specificity and precision on one hand and higher fall-out rate on the other. Therefore the use of either cut-off values cannot be favoured. When conducting co-former screening, it is particularly useful to utilize a method of high sensitivity and low false omission and miss rates. On the other hand using Δδt or Ra with the established cut-off values resulted in a greater sensitivity, precision and accuracy while maintaining the same levels of specificity and fall-out rate. It also led to lower miss and false omission rates. As a limited number of failed co-crystals are reported in the literature and co-
eutectic melts (Mohammad et al., 2011). However failed co-crystallization experiments have resulted in eutectics (Chadha et al., 2017). The eutectic form might give a result similar to co-crystals when screened with the HSPs. This seems to complicate the use of HSPs as an accurate tool. In this study we have also looked on literature reported eutectics as failed co-crystallization products. Nine eutectic pairs were used to evaluate the possibility of distinguishing co-crystals from eutectics using HSPs. Finally, a total of forty-four published co-formers of piroxicam and twenty seven co-formers of nicotinamide were used as a test set to examine the cut-off values and compare the different approaches.
3. Results and discussion 3.1. Selection of appropriate parameter and cut-off value The HSPs and other molecular parameters of carbamazepine, caffeine and theophylline are shown in Table 1. The HSPs distributions of the APIs co-formers are shown in Bagley (2-D) and Hansen (3-D) diagrams in Fig. 1. Co-formers for each of the APIs were classified according to Greenhalgh et al. observations (Table S3). Values reported in (MPa0.5) for δ, (cc/mol) for molecular volume (M Vol), (g/mol) for molecular weight (M Wt) and (g/cc) for density (ρ) After performing Levene’s test of variance homogeneity, the variances of the parameters were not significantly different statistically. Therefore Pearson’s correlation coefficient was calculated to find correlations between the different parameters. As reported by Mohammad et al. (2011) Δδ showed a correlation with Δδh. It was also found that Δδt correlated well with Ra (R2 value = 0.97), and Δδh (R2 = 0.94). Table S4 in the supplementary material shows correlation values of the different approaches, as well as their ability to differentiate formed and failed co-crystals. ANOVA was conducted to evaluate differences between each of the approaches. More correlation calculations were done to evaluate the H-bond component relations to the different methods. Pearson’s correlation coefficient of the ΔδhDon and ΔδhAcc, the difference in the solubility parameters between the co-former δhDon and API δhAcc (Δδh CDor-AAcc) as well as co-former δhAcc and API δhDon (Δδh CAcc-ADor) with the different approaches are also shown in the table. It is particularly obvious that the ΔδhAcc correlates with the parameters much more than ΔδhDon. The correlation between Δδt and ΔδhAcc was the greatest (R2 = 0.83). Interestingly, the Δδh CDor − AAcc value correlates far more to the approaches that the Δδh CAcc − ADor value. The mean values of each of the approaches for the co-crystals are shown in Table S5. In an aim to establish an ideal approach for co321
International Journal of Pharmaceutics 558 (2019) 319–327
A. Salem et al.
Fig. 1. Position of the API co-formers with the i. Bagley diagram and ii. Hansen diagram. a. carbamazepine co-formers: 0: Carbamazepine, 1: saccharin, 2: indomethacin, 3: benzamide, 4: nifedipine, 5: nicotinamide, 6: 4-aminosalicylic acid, 7: glutaric acid, 8: hydroquinone, 9: succinic acid, 10: acridinium, 11: cinnamic acid, 12: fumaric acid, 13: citric acid, 14: L-tartaric acid, 15: benzoic acid, 16: salicylic acid, 17: gentisic acid, 18: glycolamide, 19: lactamide, 20: tromethamine, 21: megluimine, 22: L-arginine, 23; l-lysine, 24: urea, 25: ethylmaltol, 26: stearic acid, 27: 4-aminobenzoic acid, 28: aspirin, 29: oxalic acid, 30: pterostilbene, 31: ketoglutaric acid, 32: maleic acid, 33: adipic acid, 34: (+)-camphoric acid, 35: 4-hydroxybenzoic acid, 36: 1-hydroxy-2-naphthoic acid, 37: dl-tartaric acid, 38: glycolic acid, 39: L/DL-malic acid, 40: dimethyl sulfoxide, 41: benzoquinone, 42: terephthalaldehyde, 43: acetic acid, 44: formic acid, 45: butyric acid, 46: trimesic acid, 47: 5-nitroisophthalic acid, 48: adamantane-1,3,5,7-tetracarboxylic acid, 49: formamide, 50: malonic acid, 51: 2,3-dihydroxy benzoic acid, 52: 1-naphthoic acid, 53: anthracene-9-carboxylic acid, 54: vanillic acid, 55: 4-nitropyridine N-oxide, 56: picric acid, 57: 2-aminopyrimidine, 58: 2,4-diamino-6-phenyl-1,3,5-triazine, 59: anthranilic acid, 60: ibuprofen. b. caffeine co-formers: 0: caffeine, 1:glutaric acid, 2: oxalic acid, 3: L-malic acid, 4:dimethylsuccinic, 5: mesaconic acid, 6: 2,4dihydroxybenzoic acid, 7: malonic acid, 8: maleic acid, 9: adipic acid, 10: anthranilic acid, 11: theophylline, 12: salicylic acid, 13: pterostilbene, 14: ethylene diamine, 15: acetic acid, 16: formic acid, 17: trifluoroacetic acid, 18: citric acid, 19: L-lactic acid, 20: 4-aminosalicylic acid, 21: paracetamol, 22: p-coumaric acid, 23: 4-hydroxybenzoic acid, 24: phenobarbital , 25: 2-hydroxybenzoic acid, 26: 3-hydroxybenzoic acid, 27: 4-aminobenzoic acid, 28: myricetin, 29: dapsone. c. theophylline co-formers: 0: theophylline, 1: acesulfame, 2: saccharin, 3: oxalic acid, 4: citric acid, 5: L/DL-malic acid, 6: L/DL-tartaric acid, 7: glutaric acid, 8: nicotinamide, 9: p-coumaric acid, 10: sorbic acid, 11: salicylic acid, 12: malonic acid, 13: maleic acid, 14: anthranilic acid, 15: phenobarbital , 16: 5-fluorouracil, 17: gentisic acid, 18: L-lactic acid, 19: sulfamethazine, 20: dapsone. 322
323
Theophylline
Caffeine
> 8.18 < 16.87
> 16.87 < 17.64
> 17.64 < 8.18
> 8.18 < 16.87
> 16.87 < 17.64
Δδt
Ra
Δδ
Δδt
Ra
> 17.64
< 8.18
> 17.64
< 17.64
> 16.87
< 16.87
> 8.18
Δδ
Ra
Δδt
Glutaric acid, dimethylsuccinic acid, mesaconic acid, 2,4-dihydroxybenzoic acid, malonic acid, maleic acid, adipic acid, anthranilic acid, theophylline, salicylic acid, pterostilbene, ethylene diamine, citric acid, 4-aminosalicylic acid, paracetamol, p-coumaric acid, 4-hydroxybenzoic acid, phenobarbital, 2hydroxybenzoic acid, 3-hydroxybenzoic acid, 4-aminobenzoic acid, myricetin, dapsone Oxalic acid, L-malic acid Glutaric acid, oxalic acid, l-malic acid, dimethylsuccinic acid, mesaconic acid, 2,4-dihydroxybenzoic acid, malonic acid, maleic acid, adipic acid, anthranilic acid, theophylline, salicylic acid, pterostilbene, ethylene diamine, citric acid, 4-aminosalicylic acid, paracetamol, p-coumaric acid, 4-hydroxybenzoic acid, phenobarbital, 2-hydroxybenzoic acid, 3-hydroxybenzoic acid, 4-aminobenzoic acid, myricetin, dapsone – Glutaric acid, oxalic acid, l-malic acid, dimethylsuccinic acid, mesaconic acid, 2,4-dihydroxybenzoic acid, malonic acid, maleic acid, adipic acid, anthranilic acid, theophylline, salicylic acid, pterostilbene, ethylene diamine, citric acid, 4-aminosalicylic acid, paracetamol, p-coumaric acid, 4-hydroxybenzoic acid, phenobarbital, 2-hydroxybenzoic acid, 3-hydroxybenzoic acid, 4-aminobenzoic acid, myricetin, dapsone – Acesulfame, saccharin, citric acid, L/DL-malic acid, glutaric acid, nicotinamide, p-coumaric acid, sorbic acid, salicylic acid, malonic acid, maleic acid, anthranilic acid, phenobarbital, 5-fluorouracil, gentisic acid, sulfamethazine Oxalic acid, L/DL-tartaric acid Acesulfame, saccharin, oxalic acid, citric acid, L/DL-malic acid, glutaric acid, nicotinamide, p-coumaric acid, sorbic acid, salicylic acid, malonic acid, maleic acid, anthranilic acid, phenobarbital, 5-fluorouracil, gentisic acid, sulfamethazine L/DL-tartaric acid Acesulfame, saccharin, oxalic acid, citric acid, L/DL-malic acid, glutaric acid, nicotinamide, p-coumaric acid, sorbic acid, salicylic acid, malonic acid, maleic acid, anthranilic acid, phenobarbital, 5-fluorouracil, gentisic acid, sulfamethazine L/DL-tartaric acid
Saccharin, indomethacin, benzamide, nifedipine, nicotinamide, 4-aminosalicylic acid, glutaric acid, acridinium, cinnamic acid, benzoic acid, salicylic acid, gentisic acid, 4-aminobenzoic acid, aspirin, pterostilbene, (+)-camphoric acid, 4-hydroxybenzoic acid, 1-hydroxy-2-naphthoic acid, dimethyl sulfoxide, benzoquinone, terephthalaldehyde, acetic acid, formic acid, butyric acid, trimesic acid, 5nitroisophthalic acid, adamantane-1,3,5,7-tetracarboxylic acid, 2,3-dihydroxy benzoic acid, 1-naphthoic acid, anthracene-9-carboxylic acid, vanillic acid, 4-nitropyridine N-oxide, picric acid, 2-aminopyrimidine, 2,4-diamino-6-phenyl-1,3,5-triazine, anthranilic acid Hydroquinone, succinic acid, fumaric acid, L-tartaric acid, urea, oxalic acid, formamide, malonic acid
Saccharin, indomethacin, benzamide, nifedipine, nicotinamide, 4-aminosalicylic acid, glutaric acid, acridinium, cinnamic acid, benzoic acid, salicylic acid, gentisic acid, 4-aminobenzoic acid, aspirin, pterostilbene, (+)-camphoric acid, 4-hydroxybenzoic acid, 1-hydroxy-2-naphthoic acid, dimethyl sulfoxide, benzoquinone, terephthalaldehyde, acetic acid, formic acid, butyric acid, trimesic acid, 5nitroisophthalic acid, adamantane-1,3,5,7-tetracarboxylic acid, 2,3-dihydroxy benzoic acid, 1-naphthoic acid, anthracene-9-carboxylic acid, vanillic acid, 4-nitropyridine N-oxide, picric acid, 2-aminopyrimidine, 2,4-diamino-6-phenyl-1,3,5-triazine, anthranilic acid Hydroquinone, succinic acid, fumaric acid, L-tartaric acid, urea, oxalic acid, formamide, malonic acid
Saccharin, indomethacin, benzamide, nifedipine, nicotinamide, 4-aminosalicylic acid, glutaric acid, succinic acid, acridinium, cinnamic acid, benzoic acid, salicylic acid, gentisic acid, 4-aminobenzoic acid, aspirin, pterostilbene, (+)-camphoric acid, 4-hydroxybenzoic acid, 1-hydroxy-2-naphthoic acid, dimethyl sulfoxide, benzoquinone, terephthalaldehyde, acetic acid, formic acid, butyric acid, trimesic acid, 5nitroisophthalic acid, adamantane-1,3,5,7-tetracarboxylic acid, 2,3-dihydroxy benzoic acid, 1-naphthoic acid, anthracene-9-carboxylic acid, vanillic acid, 4-nitropyridine N-oxide, picric acid, 2-aminopyrimidine, 2,4-diamino-6-phenyl-1,3,5-triazine, anthranilic acid Hydroquinone, fumaric acid, L-tartaric acid, urea, oxalic acid, formamide, malonic acid
Δδ
Carbamazepine
< 8.18
Co-former of formed co-crystals
Miscibility criteria (MPa0.5)
API
Table 2 Classification of API co-formers according to the miscibility criteria Δδ, Δδt and Ra.
L-lactic acid
L-lactic acid Dapsone
– Dapsone
– L-lactic acid, dapsone
– Acetic acid, formic acid, trifluoroacetic acid, L-lactic acid
L-lactic acid Acetic acid, formic acid, trifluoroacetic acid, L-lactic acid
Citric acid, glycolamide, lactamide, tromethamine, megluimine, ketoglutaric acid, maleic acid, DL-tartaric acid, glycolic acid, L/DL-malic acid Acetic acid, formic acid, trifluoroacetic acid
Citric acid, glycolamide, lactamide, tromethamine, megluimine, ketoglutaric acid, maleic acid, DL-tartaric acid, glycolic acid, L/DL-malic acid L-arginine, L-lysine, ethylmaltol, stearic acid, adipic acid, ibuprofen
Citric acid, glycolamide, lactamide, tromethamine, megluimine, maleic acid, DLtartaric acid, glycolic acid, L/DL-malic acid L-arginine, L-lysine, ethylmaltol, stearic acid, adipic acid, ibuprofen
L-arginine, L-lysine, ethylmaltol, stearic acid, ketoglutaric acid, adipic acid, ibuprofen
Co-former of failed co-crystals
A. Salem et al.
International Journal of Pharmaceutics 558 (2019) 319–327
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A. Salem et al.
Table 3 Statistical measures of the performance of the different methods and cut-off values. Method
Previously reported*
Established in this study
Δδ
Δδ
Δδt
Ra
7 86.21 50.00 13.79 50.00 54.54 87.21 78.90
8.18 87.36 45.45 12.64 54.54 50.00 86.36 78.90
16.87 89.65 50.00 10.34 50.00 40.91 87.64 81.65
17.64 89.65 50.00 10.34 50.00 40.91 87.64 81.65
Table 4 HSPs and descriptors of piroxicam and nicotinamide. API
Piroxicam
Nicotinamide
21.13 17.86 26.67 12.48 7.6 10.8 30.35 1.896 220.7 331.4 1.501
19.89 15.07 24.95 12.8 7.5 9.6 28.04 1.379 100.4 122.1 1.217
Structure
Cut-off (MPa0.5) Sensitivity (%) Specificity (%) Miss rate (%) Fall-out rate (%) False omission rate (%) Precision (%) Accuracy (%)
δd δp δv δh δhDon δhAcc δt Ovality M Vol. M Wt. ρ
* Cut-off value as previously reported by Greenhalgh et al. (1999) and employed by Mohammad et al. (2011).
crystallization experiments have to be exhausted before a pair be termed failed, a larger set of failed co-formers is needed to accurately determine the specificity of this method. The HSPs are able to predict miscibility; however in some cases the co-crystal formation is independent of miscibility. It is rather challenging to explain both the formation of co-crystals at higher values and the failure to form co-crystals when the difference in solubility parameters is within the range of miscibility. Possible reasons for the failure of co-formers to form co-crystals may be due to thermodynamic considerations, structure incompatibility or that the preparation method did not favour the formation of co-crystals. The fall-out (false positive) rate was further analysed. Co-formers that failed to form co-crystals but were identified by this method as having a Δδt/ Ra value below the set cut-off are shown in Table 2. The reasons for their failure to co-crystallize with the APIs were further examined in one case. Theophylline did not form a co-crystal with dapsone as reported by Jiang et al. (2014), nor did dapsone form a co-crystal with theobromine. However the authors have reported a formation of two types of co-crystals with caffeine. The crystal structure have been determined for both co-crystal forms, and it has been found that the two methyl groups play crucial roles in the architecture of the corresponding cocrystal by forming a nonclassic auxiliary H-bonding. The structure of Theophylline differs from Caffeine in one methyl group, in the position that was crucial for co-crystal formation with Dapsone which could explain the failure to form a theophylline-dapsone co-crystal. Furthermore the lack of methyl group in theophylline structure provides one more H donor group that strengths the intermolecular bonding in pure theophylline crystal. This can be seen in the difference between melting points for these three structurally similar molecules. The melting point for caffeine is 235 °C, theophylline 273 °C and 375 °C for theobromine which could indicate the thermodynamic favourable formation of separate phase crystals.
interactions to form a 2 or 3 dimensional lattice. The experimentally determined HSPs do differ for the three isomers, but the difference is not significant and cannot be used to distinguish the specific interaction for formation of co-crystal. On the other hand it could be argued that with appropriate parameters, co-crystals could be formed for these pairs. The ideal approach of co-crystal formation prediction should be strict enough to minimize the inclusion of pairs that are unlikely to form co-crystals, yet broad enough to limit the exclusion of pairs able to co-crystallize.
3.3. Prediction of piroxicam and nicotinamide co-crystal formation HSPs of piroxicam and nicotinamide are shown in Table 4. Mean values for the Piroxicam and Nicotinamide co-formers are shown in Table S8. A total of 31 co-crystals of piroxicam and 13 failed co-crystals as well as 21 formed and 7 failed co-crystals of nicotinamide were used to test the cut-off values and best method to predict co-crystal formation. Table 5 represents the classification of piroxicam and nicotinamide co-formers according to the new cut-off values established by the training set using Δδ and Δδt. The percentage represents the portion of the co-formers actually able to form co-crystals within the inclusion value. While Fig. 2 represents the Hansen diagram of the piroxicam and nicotinamide co-formers. Utilizing Δδ with the newly established cut-off value was able to predict co-crystal formation in 63.6 and 79.2% of the cases in piroxicam and nicotinamide respectively, having a weighted average of 69.7%. Ra seemed to be slightly superior as it predicted co-crystal formation in 72.1 and 78.6% of cases in the same test set of piroxicam and nicotinamide, having a weighted average of 74.6%. These values were higher than the reported 70% inclusion using lipoaffinity index (Cysewski and Przybyłek, 2017). This miss rate using Δδ was the highest (6.5–13.6%) followed by Δδt (0–9.1%). The miss rate of Ra in the test set (0%) makes this method of co-former screening ideal compared to the other methods tested in this study. Both Ra and Δδt are similar by definition, and found to be correlated. The advantage of Ra over Δδt can be explained due to the importance of dispersive interactions in co-crystal formation (Peng-Yuan Chen et al., 2015). Therefore multiplying the dispersive component of the HSP in the calculation of Ra not only improved the visual representation (Cañete et al., 2014) but also give a greater role of this type of interaction in co-crystal formation. Reporting of failed cocrystallization experiments is encouraged, to improve the quality of the statistical analysis. As out of the 31 formed co-crystals of piroxicam, 9 were reported as failed co-crystallization in either other publications or using different preparation methods or parameters. A larger set of data is required to better understand the limitations of this simple method in
3.2. Eutectics As shown in Tables S6 and S7, all eutectic pairs published by Kaur et al. (2015) had values of Δδ and Δδt lower than 15 MPa0.5 suggestive of co-crystal formation except benzoic acid-succinimide. This may indicate that the use of HSPs is unable to differentiate between co-crystals and eutectics. Particularly because Δδt values were within the average range of 10.45 MPa0.5, despite the fact that Δδ showed statistical difference between formed co-crystals and eutectics (p-value = 0.001). The authors have given the structural explanation for the formation of co-crystal or eutectic. It considers the isomers of hydroxybenzoic acid. The position of –OH group within the hydroxybenzoic acid determines whether co-crystal or eutectic will be formed. The carboxylic group forms a primary molecular syntonic unit, but only the isomer that have –OH in para positon can provide an extension through auxiliary 324
325
> 16.87 < 17.64
Ra
> 17.64
> 8.18 < 16.87
Δδt
> 16.87 < 17.64
Ra
> 17.64 < 8.18
> 8.18 < 16.87
Δδt
Δδ
Azelaic acid, 3-hydroxybenzoic acid, phenylsuccinic acid, isophthalic acid, trimesic acid, hydrocaffeic acid, gentisic acid, furosemide, benzoic acid, adipic acid , succinic acid, L/DLmalic acid, ketoglutaric acid, 4-hydroxybenzoic acid, glutaric acid, malonic acid, salicylic acid, 1-hydroxy-2-naphthoic acid, hippuric acid, resorcinol, methylparaben Sebacic acid, (+)-camphoric acid Saccharine sodium, urea, nicotinamide, oxalic acid, maleic acid, fumaric acid, pimelic acid, suberic acid, azelaic acid, sebacic acid, 3-hydroxybenzoic acid, phenylsuccinic acid, isophthalic acid, trimesic acid, hydrocaffeic acid, gentisic acid, furosemide, benzoic acid, adipic acid , succinic acid, (+)-camphoric acid, L/DL-malic acid, ketoglutaric acid, 4hydroxybenzoic acid, glutaric acid, malonic acid, salicylic acid, 1-hydroxy-2-naphthoic acid, hippuric acid, resorcinol, methylparaben – Saccharine sodium, urea, nicotinamide, oxalic acid, maleic acid, fumaric acid, pimelic acid, suberic acid, azelaic acid, sebacic acid, 3-hydroxybenzoic acid, phenylsuccinic acid, isophthalic acid, trimesic acid, hydrocaffeic acid, gentisic acid, furosemide, benzoic acid, adipic acid, succinic acid, (+)-camphoric acid, L/DL-malic acid, ketoglutaric acid, 4hydroxybenzoic acid, glutaric acid, malonic acid, salicylic acid, 1-hydroxy-2-naphthoic acid, hippuric acid, resorcinol, methylparaben – Ketoprofen, carbamazepine, 4-aminosalicylic acid, furosemide, indomethacin, nitrofurantoin, piroxicam, naproxen, AMG 517, theophylline, ketoconazole, myricetin, mefenamic acid, lamotrigine, flufenamic acid, fenofibrate, ascorbic acid, succinic acid, oxalate Acetazolamide, adefovir dipivoxil, R/S ibuprofen Ketoprofen, carbamazepine, 4-aminosalicylic acid, acetazolamide, furosemide, indomethacin, nitrofurantoin, piroxicam, naproxen, AMG 517, theophylline, ketoconazole, myricetin, mefenamic acid, lamotrigine, flufenamic acid, R/S ibuprofen, fenofibrate, ascorbic acid, succinic acid, oxalate Adefovir dipivoxil Ketoprofen, carbamazepine, 4-aminosalicylic acid, acetazolamide, furosemide, indomethacin, nitrofurantoin, piroxicam, naproxen, AMG 517, adefovir dipivoxil, theophylline, ketoconazole, myricetin, mefenamic acid, lamotrigine, flufenamic acid, R/S ibuprofen, fenofibrate, ascorbic acid, succinic acid, oxalate –
< 8.18
Δδ
Piroxicam
Nicotinamide
Co-former of successfully prepared co-crystals
Miscibility criteria (MPa0.5)
API
Table 5 Classification of piroxicam and Nicotinamide co-formers according to the criteria of Δδ, Δδt and Ra.
78.6
– Nitazoxanide, spironolactone, artemisinin, compound 1, ivabradine hydrochloride, βlapachone
–
75.0
79.2
72.1
72.1
63.6
%
Artemisinin Nitazoxanide, spironolactone, artemisinin, compound 1, ivabradine hydrochloride, βlapachone
L/DL-tartaric acid Nitazoxanide, spironolactone, compound 1, ivabradine hydrochloride, β-lapachone
L/DL-tartaric acid Cinnamic acid, catechol, ferulic acid, para amino benzoic acid, anthranilic acid, terephthalic acid, 3-(4-Hydroxyphenyl)-propionic acid, citric acid, glycolic acid, caprylic acid, Lpyroglutamic, vanillin
Caprylic acid Cinnamic acid, catechol, ferulic acid, para amino benzoic acid, anthranilic acid, terephthalic acid, 3-(4-Hydroxyphenyl)-propionic acid, citric acid, glycolic acid, caprylic acid, Lpyroglutamic, vanillin
Cinnamic acid, catechol, ferulic acid, para amino benzoic acid, anthranilic acid, terephthalic acid, 3-(4-Hydroxyphenyl)-propionic acid, L/DL-tartaric acid, citric acid, glycolic acid, Lpyroglutamic, vanillin
Co-former of failed co-crystals
A. Salem et al.
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Fig. 2. Position of a. piroxicam and b. nicotinamide co-formers with the i. Bagley diagram and ii. Hansen diagram. a. 0: piroxicam, 1: saccharine sodium, 2: urea, 3: nicotinamide, 4: cinnamic acid, 5: catechol, 6: ferulic acid, 7: p-amino benzoic acid, 8: anthranilic acid, 9: oxalic acid, 10: maleic acid, 11: fumaric acid, 12: pimelic acid, 13: suberic acid, 14: azelaic acid, 15: sebacic acid, 16: 3-hydroxybenzoic acid, 17: phenylsuccinic acid, 18: isophthalic acid, 19: terephthalic acid, 20: trimesic acid, 21: hydrocaffeic acid, 22: 3-(4-hydroxyphenyl)-propionic acid, 23: gentisic acid, 24: furosemide, 25: benzoic acid, 26: adipic acid, 27: succinic acid, 28: (+)-camphoric acid, 29: L/DL-malic acid, 30: ketoglutaric acid, 31: 4-hydroxybenzoic acid, 32: glutaric acid, 33: malonic acid, 34: salicylic acid, 35: 1-hydroxy-2naphthoic acid, 36: hippuric acid, 37: L/DL-tartaric acid, 38: citric acid, 39: glycolic acid, 40: caprylic acid, 41: l-pyroglutamic, 42: resorcinol, 43: methylparaben, 44: vanillin. b. 0: nicotinamide, 1: ketoprofen, 2: carbamazepine, 3: 4-aminosalicylic acid, 4: acetazolamide, 5: furosemide, 6: indomethacin, 7: nitrofurantoin, 8: piroxicam, 9: Nitazoxanide, 10: naproxen, 11: AMG 517, 12: adefovir dipivoxil, 13: spironolactone, 14: artemisinin, 15: compound 1*, 16: theophylline, 17: ivabradine hydrochloride, 18: ketoconazole, 19: myricetin, 20: mefenamic acid, 21: lamotrigine, 22: β-lapachone, 23: flufenamic acid, 24: ibuprofen and R/S ibuprofen, 25: fenofibrate, 26: ascorbic acid, 27: succinic acid, 28: oxalate. *Compound 1 structure is available in the supplementary material Fig. S1.
solids, was developed by Just et al. (2013). The polar parameter of this method has been used as an indicator of the caffeine-glutaric acid cocrystallization microenvironment (Hasa et al., 2016). Once this method is fully developed, it could offer promising improvements to the use of HSPs as a co-former screening tool. The general rules guiding co-crystal formation remains challenging to establish. Continuous efforts are needed for computational methods able to predict the formation of such complex systems (Taylor and Day, 2018).
the prediction of co-crystal formation. One limitation of this method is its inability to account for parameters of preparation or solvent. The methods low specificity makes it likely to discard otherwise plausible co-formers. This has been represented here in terms of miss rate, expressed as a percentage of the co-formers that would have been dismissed as possible co-formers when using this method as a screening tool. The percent miss rate of co-formers is shown in Fig. 3. This reported percentage should only be viewed as a means of representing limitations to the use of HSPs as co-crystal screening method. A larger data size is required to give statistical meaning to these results. The miss rate for both piroxicam and nicotinamide was lower than that established for the test set of co-formers particularly when using Δδt and Ra. An improved group contribution method, based on pharmaceutical
4. Conclusions HSPs as a tool to predict pharmaceutical co-crystal formation has been evaluated using co-formers of three different APIs and further tested using co-formers of two other APIs. The previously set cut-off 326
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Grecu, T., Adams, H., Hunter, C.A., McCabe, J.F., Portell, A., Prohens, R., 2014. Virtual screening identifies new cocrystals of nalidixic acid. Cryst. Growth Des. 14, 1749–1755. Greenhalgh, D.J., Williams, A.C., Timmins, P., York, P., 1999. Solubility parameters as predictors of miscibility in solid dispersions. J. Pharm. Sci. 88, 1182–1190. Hansen, C.M., 1967. The Three Dimensional Solubility Parameter and Solvent Diffusion Coefficient. Danish Technical Press, Copenhagen. Hansen, C., 2007. Hansen Solubility Parameters: A User’s Handbook. CRC Press, Boca Raton, FL, USA. Hasa, D., Carlino, E., Jones, W., 2016. Polymer-assisted grinding, a versatile method for polymorph control of cocrystallization. Cryst. Growth Des. 16, 1772–1779. Hildebrand, J.H., Scott, R.S., 1950. The Solubility of Nonelectrolytes, 3rd ed. Reinhold, New York. Jiang, L., Huang, Y., Zhang, Q., He, H., Xu, Y., Mei, X., 2014. Preparation and solid-state characterization of dapsone drug-drug co-crystals. Cryst. 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Fig. 3. Percent miss rate for each of the methods.
value of Δδ at 7 MPa0.5 was validated, as the cut-off value found in this study is 8.18 MPa0.5 had no statistical difference in terms of sensitivity and specificity compared to the previous value. From the data of 16 descriptors calculated with group contribution method and their statistical analysis we suggest a usage of Δδt and Ra with cut of values of 16.87 and 17.64 MPa0.5 respectively. With these approaches a simple yet efficient selection of plausible co-formers is obtained with 73.8–85% efficiency as obtained for the test set, without major loss of plausible co-formers with limited miscibility. Unfortunately this method excludes plausible co-formers that are predicted as immiscible. These do form co-crystals with the examined API. It was found that the miss rate using Δδ was 13.64% while using Δδt, the miss rate was lower (9.09%) and even lower (0%) using Ra for test group co-formers. This fact limits the use of HSP as a tool to predict co-crystal formation, yet it may be useful when screening sufficiently large numbers of co-formers. The quality of statistical data obtained in this study is influenced by insufficient number of all experiments, especially the failed co-crystallization. The quality of the results was further influenced by the fact that in most reported experiments, the co-former selection are done on chemical intuitive or synthon basis. Conflict of interest Authors declare no conflict of interests. Acknowledgments The project has been supported by the European Union, co-financed by the European Social Fund (grant No. EFOP-3.6.1.-16-2016-00004, grant title: Comprehensive Development for Implementing Smart Specialization Strategies at the University of Pécs). The authors appreciate Stipendium Hungaricum scholarship programme – Tempus Public Foundation and the support of the academic and technical staff at the University of Pécs, department of Pharmaceutical technology and Biopharmacy. Appendix A. Supplementary data Supplementary data to this article can be found online at https:// doi.org/10.1016/j.ijpharm.2019.01.007. References Abramov, Y.A., Loschen, C., Klamt, A., 2012. Rational coformer or solvent selection for pharmaceutical cocrystallization or desolvation. J. Pharm. Sci. 101, 3687–3697. Ainurofiq, A., Mauludin, R., Mudhakir, D., Umeda, D., Soewandhi, S.N., Putra, O.D., Yonemochi, E., 2018. Improving mechanical properties of desloratadine via multicomponent crystal formation. Eur. J. Pharm. Sci. 111, 65–72.
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Reliability of the Hansen solubility parameters as co-crystal formation prediction tool Ala' Salem, Sándor Nagy, Szilárd Pál, Aleksandar Széchenyi
T
⁎
University of Pécs, Institute of Pharmaceutical Technology and Biopharmacy, Pécs, Hungary
A R T I C LE I N FO
A B S T R A C T
Keywords: Hansen solubility parameters (HSPs) Predicting co-crystal formation Group contribution method Pharmaceutical co-crystals Miscibility Eutectics Screening
Pharmaceutical co-crystals present an opportunity to improve the solubility of conventional active pharmaceutical ingredients (APIs). Despite advances in co-crystal screening, the rational design of even the chemically simplest co-crystals remains challenging. Hansen solubility parameters (HSPs) have previously been used as a tool to predict co-crystal formation using only the chemical structure. The aim of this study was to validate the use of HSPs as a tool to predict co-crystal formation, analyse its limitations and examine the previously set Δδ inclusion cut-off value. A total of 109 co-formers of carbamazepine, caffeine and theophylline were used as a training set. Sixteen different descriptors were examined. An additional 72 co-formers of piroxicam and nicotinamide were used to test the methods and new cut-off values. The established cut-off value (8.18 MPa0.5) despite being similar to the previously reported value (7 MPa0.5), offered no real advantage over the previously reported value. Our results suggest the use of the modified radius (Ra) method of calculating the solubility difference, which had higher sensitivity of 90% compared to 86% for the previously reported method and cut-off value to indicate co-crystal formation as well as a lower miss and false omission rates.
1. Introduction Co-crystallization is among the most powerful pharmaceutical development strategies to improve the active pharmaceutical ingredients (APIs) aqueous solubility (Cao et al., 2018). Other advantages of cocrystallization include improved in-vitro drug activity (Shete et al., 2015), stability (Liu et al., 2012), mechanical properties (Karki et al., 2009; Ainurofiq et al., 2018) and bioavailability (Childs et al., 2013). Co-crystals are formed through a non-covalent bond, mostly hydrogen bonding between a neutral API molecule and a hydrophilic co-former (Vishweshwar et al., 2006; Douroumis et al., 2017) or between two APIs (drug-drug co-crystals) (Nechipadappu et al., 2017). The most challenging step in co-crystal design is the selection of a co-former likely to form a co-crystal as well as improve the API properties. Several strategies and methods have been developed to aid in the co-former selection. The simplest, however most time consuming method, is based on the trial–error approach, where co-formers are arbitrary chosen from a list of pharmaceutically acceptable materials. Sophisticated methods are based on the detailed knowledge of the molecular structure and properties of the API and co-former. Such methods require complex software and high computational capacity for the calculations (Cheney et al., 2011). Another approach arises from the definition of co-crystals which are homogeneous molecular mixtures of the API and co-former. ⁎
This is where miscibility fits into the prediction of co-crystal formation. The use of theoretical miscibility determination tools based on the calculation of solubility parameters can be employed in the selection of co-formers (Gaikwad et al., 2017). As co-formers with solubility parameters closer to the API are more likely to be mixable and form cocrystals (Desai and Patravale, 2018). The use of solubility parameters in co-crystal screening was reported in a number of articles. In a recent study, Desai and Patravale (2018) used the Hildebrand solubility parameter as part of a theoretical co-former selection method for curcumin. The Hildebrand solubility parameter (Hδ) (Eq. (1)) (Hildebrand and Scott, 1950) is calculated from the energy of vaporization (ΔEV), and molar volume (Vm).
Hδ = √
ΔEv Vm
(1)
Hansen solubility parameters (HSPs) established in 1967 by Hansen (1967) represents a step forward from the Hildebrand solubility parameter. HSPs is an approach where the liquids total cohesion energy is split into contributions from atomic dispersion (δd), dipole–dipole/ polar interactions (δp) and hydrogen bonding (δh) (Eq. (2)). The δh contribution in the HSPs is divided into hydrogen-bond donor (δhDon) and acceptor (δhAcc) values. For a given liquid pair, the closer are the HSP values in the three dimensional HSP space, the greater is their
Corresponding author at: Institute of Pharmaceutical Technology and Biopharmacy, Faculty of Pharmacy, University of Pécs, H-7624, 2 Rókus u, Pécs Hungary. E-mail address: [email protected] (A. Széchenyi).
https://doi.org/10.1016/j.ijpharm.2019.01.007 Received 18 October 2018; Received in revised form 15 December 2018; Accepted 3 January 2019 Available online 14 January 2019 0378-5173/ © 2019 Elsevier B.V. All rights reserved.
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The three parameters δp, δd and δh can be treated as coordinates of a point in three-dimensions, known as the Hansen space. The following equation is used to calculate the modified radius (Ra) between Hansen parameters in Hansen space (Eq. (4)). Ra represents the distance between two molecules in the Hansen sapce. The value “4” in Eq. (3) is a theoretically justified constant for convenient visualization of spherical rather than ellipsoidal regions of the solubility plot (Cañete et al., 2014; Hansen, 2007).
requiring knowledge of a molecules chemical structure only (Subrahmanyam et al., 1996). The use of HSPs as co-crystals screening method has been reported in several review articles (Fukte et al., 2014; Cysewski, 2016; Abramov et al., 2012; Brittain, 2012; Panzade and Shendarkar, 2017). It has even been described as a better highthroughput method than lattice energy first-principles calculations (Grecu et al., 2014), while another review describe it as a method of limited use (Gadade and Pekamwar, 2016). The use of HSPs in cocrystal screening can be a promising method once validated using a scope of APIs and co-formers as well as investigating other preparation methods and conditions to confirm miscibility as co-crystallization prerequisite. Finally cut-off values need reassessment and refinement before this method become routine in pharmaceutical co-crystal screening. The aim of this study is to evaluate the reliability of HSPs to predict the formation of published co-crystals of different APIs, compare simple absolute difference in solubility (Eq. (5)) to more accurate calculations (Eq. (6)) and Ra (Eq. (4)) as well as identify its limitations. Examine and refine the established cut-off values for accurate co-crystal formation prediction using a set of test co-formers. Moreover, compare co-crystals to eutectics to examine the possibility of differentiating these two closely related pharmaceutical forms using HSPs.
Ra = {(4 ∗ Δδd )2 + (Δδ p )2 + (Δδ h )2}0.5
2. Methods
similarity, and consequently their affinity is stronger. This analysis is particularly useful in polymer dissolution. The concept has been stretched from polymer mixing to mixing of a wide range of materials including nano-structures (Wang et al., 2013; Gardebjer et al., 2016) and pharmaceutical co-crystals (Mohammad et al., 2011). The volume dependent solubility parameter (δv) (Eq. (3)) was introduced by Bagley et al. (Bagley et al., 1971). The Bagley diagram, a two-dimensional plot of δv against δh, has applications in various fields including the prediction of drug intestinal absorption and miscibility (Breitkreutz, 1998).
δ = (δ2d + δ2p + δ2h )0.5
(2)
δ V = (δ2d + δ2p )0.5
(3)
(4)
A paper published by Mohammad et al. in 2011, titled “Hansen solubility parameter as a tool to predict cocrystal formation”, investigated whether HSPs predicted miscibility could be a tool to predict co-crystal formation, taking advantage of that co-crystals could form by eutectic melt. In this study the HSPs miscibility of indomethacin with 33 different co-formers were calculated. If the difference of solubility between the API and co-former is less than 7 MPa0.5, they were considered as miscible and therefore likely to form a co-crystal. With the exception of glycine, all pairs that were predicted as miscible were confirmed to be miscible experimentally. However, only four out of twenty one miscible co-formers resulted in co-crystals. The study concluded that HSPs can be used to short list potential co-formers before laboratory screening. The authors of the study speculated that the failure of miscible systems to form co-crystals may be attributed to reasons like complementarity, conformational flexibility, preferred packing patterns, molecular shape and size, stability as well as the lack of hydrogen bonding. Suggesting also that miscibility is necessary for the formation of co-crystals. The authors also pointed out the need for further studies including APIs of different physicochemical properties and many co-formers to generalize the observations reported. An important aspect of the study published by Mohammad et al. (2011) is the use of cut off value of less than 7 MPa0.5 in the difference of total solubility parameter (Δδ) (Eq. (5)) to predict miscibility and therefore co-crystal formation. This value has been adapted from a paper published by Greenhalgh et al. in 1999 that used Hildebrand solubility parameters as an indication of ibuprofen-carrier incompatibilities in solid dispersions. As a general observed trend classified miscibility according to the ΔHδ into three different categories, those having ΔHδ value (MPa0.5) from 1.6 to 7.5 in molten exhibited complete miscibility, values from 7.4 to 15.0 in liquid showed a degree of immiscibility, lastly a value above 15 had total immiscibility. The fact that Hildebrand parameters represent the overall cohesive energy but offer less information on the relative strengths of forces present such as polar, hydrogen bonding and dispersion, should necessitate Δδ value investigations to predict co-crystal formation when using HSPs. A more accurate method of measuring the difference in solubility parameters is the use of Eq. (6), which allows proper three dimensional point representation.
Δδ = |δAPI − δco-former|
(5)
Δδt = {(Δδd )2 + (Δδ p )2 + (Δδ h )2}0.5
(6)
2.1. Training set of co-formers To evaluate co-crystal formation prediction by HSPs, 109 reported co-formers of carbamazepine, theophylline and caffeine, of different preparation methods, solvents and molar ratios were used as a training set. The list is comprised of 87 successful and 22 failed co-crystals. It includes twelve successful and two failed drug-drug co-crystals. The list of the co-formers used in this study, organized by their HSPs, is provided in the supplementary material (Table S1). It should be noted that some pairs have been reported as both successful and failed co-crystals in different studies, due to preparation factors such as the method and solvent. In such cases, pairs were regarded as successful if reported in a publication, even if they have been reported as unsuccessful by a different study. This was done to avoid data misinterpretation. 2.2. Assessment and refinement of prediction and molecular descriptors Hansen Solubility Parameters in Practice (HSPiP) software version 5.0.11 was used to calculate the different HSP values, experimental data from the software database were used whenever available (Hansen, 2007). PubChem, an open chemistry database, was used to obtain the SMILES (simplified molecular-input line-entry system) format of APIs and co-formers. The SMILES format is a linear text that describes the connectivity and chirality of a molecule. A total of 16 descriptors were calculated. Definitions and equations representing the different descriptors used in this study are shown in Table S2 of the supplementary material. Correlation plots were constructed between the different approaches (Δδ, Δδt and Ra) and differences in δd, δp, δh, and δv. Other tested descriptors tested were the HSP distance (obtained by the software), molecular weight and volume, density, ovality and components of δh. Statistical analysis was performed to conclude effectiveness and cut-off values. Results were presented as average ± SD. Differences were considered significant at p-value ≤0.05 after performing Levene’s test of variance homogeneity and one-way analysis of the variance (ANOVA) using SPSS (Software package version 25). Finally, the parameters ability to predict co-crystal formation was described in terms of statistical measures of performance; sensitivity, specificity, miss and fall-out rates, accuracy and precision. 2.3. Eutectics and test set of co-formers As mentioned previously the HSPs relies on co-crystals forming from
One advantage of HSPs is that it is a simple theoretical approach, 320
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Table 1 HSPs and descriptors of carbamazepine, caffeine and theophylline. API
Carbamazepine
Caffeine
Theophylline
20.92 8.06 22.42 4.47 8.70 3.10 22.86 1.60 187.5 236.3 1.26
19.5 10.1 21.96 13 6.60 7.10 25.52 1.66 155.1 194.2 1.25
19.72 15.42 25.03 10.5 8.40 5.70 27.15 1.72 130.8 180.2 1.38
Structure
δd δp δv δh δhDon. δhAcc. δt Ovality M Vol. M Wt. Ρ
crystal formation prediction, H-bonding is a key factor to consider. Both Δδt and Ra correlate with Δδh. New cut-off values for both Δδ, Δδt and Ra were obtained statistically using the mean value obtained for positive co-crystals of the three APIs. The selection of these three descriptors was based on their ability to statistically differentiate formed and failed co-crystals. Both Δδt and Δδ exhibited a p-value of 0.001, while Ra had a p-value < 0.001. Positive co-formers had Δδ values ranging from 0.50 to 8.18 MPa0.5. The Δδt values for positively formed co-crystals ranged from 3.95 to 16.87 MPa0.5. While the Ra value range for positive co-crystals was between 4.76 and 17.64 MPa0.5. Therefore values of Δδ, Δδt or Ra above 8.18, 16.87 and 17.64 MPa0.5 respectively would correspond to failed co-crystal formation. This newly established cut-off value (8.18 MPa0.5) is similar to the previous 7 MPa0.5 cut-off value. These statistically obtained cut-off values were used to classify the co-formers (Table 2). As shown in the classified co-formers according to Greenhalgh et al. observations (Table S3), only 5 (11.4%) of the carbamazepine co-formers reported to form co-crystals had a Δδ value above 10 MPa0.5. However none had a value above 15 MPa0.5, which is the proposed limit for some miscibility. Co-formers of both theophylline and caffeine have also been under the 15 MPa0.5 cut-off value. Considering 7 MPa0.5 as the cut-off value, 12 (13.8%) of the co-formers reported to form co-crystals had a Δδ values above the cut-off value. However, 11 (12.6) of the coformers reported to form co-crystals had Δδ above the newly established cut-off of 8.18 MPa0.5. Moreover 9 (10.3%) co-formers reported to form co-crystals were above the 16.87 MPa0.5 and 17.64 MPa0.5 cutoff values of Δδt and Ra respectively. To establish the effectiveness of the HSPs as a co-crystal formation prediction tool, the statistical measures of performance were calculated for each method as well as for the previously reported cut-off value to allow comparison (Table 3). Sensitivity (a measure of the proportion of true positives that was correctly identified) and specificity (accounting for the percentage of true negatives that was correctly identified) were calculated. The improvements brought about by the new cut-off value (8.18 MPa0.5); higher sensitivity and lower miss and false omission rates were complicated by low specificity and precision on one hand and higher fall-out rate on the other. Therefore the use of either cut-off values cannot be favoured. When conducting co-former screening, it is particularly useful to utilize a method of high sensitivity and low false omission and miss rates. On the other hand using Δδt or Ra with the established cut-off values resulted in a greater sensitivity, precision and accuracy while maintaining the same levels of specificity and fall-out rate. It also led to lower miss and false omission rates. As a limited number of failed co-crystals are reported in the literature and co-
eutectic melts (Mohammad et al., 2011). However failed co-crystallization experiments have resulted in eutectics (Chadha et al., 2017). The eutectic form might give a result similar to co-crystals when screened with the HSPs. This seems to complicate the use of HSPs as an accurate tool. In this study we have also looked on literature reported eutectics as failed co-crystallization products. Nine eutectic pairs were used to evaluate the possibility of distinguishing co-crystals from eutectics using HSPs. Finally, a total of forty-four published co-formers of piroxicam and twenty seven co-formers of nicotinamide were used as a test set to examine the cut-off values and compare the different approaches.
3. Results and discussion 3.1. Selection of appropriate parameter and cut-off value The HSPs and other molecular parameters of carbamazepine, caffeine and theophylline are shown in Table 1. The HSPs distributions of the APIs co-formers are shown in Bagley (2-D) and Hansen (3-D) diagrams in Fig. 1. Co-formers for each of the APIs were classified according to Greenhalgh et al. observations (Table S3). Values reported in (MPa0.5) for δ, (cc/mol) for molecular volume (M Vol), (g/mol) for molecular weight (M Wt) and (g/cc) for density (ρ) After performing Levene’s test of variance homogeneity, the variances of the parameters were not significantly different statistically. Therefore Pearson’s correlation coefficient was calculated to find correlations between the different parameters. As reported by Mohammad et al. (2011) Δδ showed a correlation with Δδh. It was also found that Δδt correlated well with Ra (R2 value = 0.97), and Δδh (R2 = 0.94). Table S4 in the supplementary material shows correlation values of the different approaches, as well as their ability to differentiate formed and failed co-crystals. ANOVA was conducted to evaluate differences between each of the approaches. More correlation calculations were done to evaluate the H-bond component relations to the different methods. Pearson’s correlation coefficient of the ΔδhDon and ΔδhAcc, the difference in the solubility parameters between the co-former δhDon and API δhAcc (Δδh CDor-AAcc) as well as co-former δhAcc and API δhDon (Δδh CAcc-ADor) with the different approaches are also shown in the table. It is particularly obvious that the ΔδhAcc correlates with the parameters much more than ΔδhDon. The correlation between Δδt and ΔδhAcc was the greatest (R2 = 0.83). Interestingly, the Δδh CDor − AAcc value correlates far more to the approaches that the Δδh CAcc − ADor value. The mean values of each of the approaches for the co-crystals are shown in Table S5. In an aim to establish an ideal approach for co321
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Fig. 1. Position of the API co-formers with the i. Bagley diagram and ii. Hansen diagram. a. carbamazepine co-formers: 0: Carbamazepine, 1: saccharin, 2: indomethacin, 3: benzamide, 4: nifedipine, 5: nicotinamide, 6: 4-aminosalicylic acid, 7: glutaric acid, 8: hydroquinone, 9: succinic acid, 10: acridinium, 11: cinnamic acid, 12: fumaric acid, 13: citric acid, 14: L-tartaric acid, 15: benzoic acid, 16: salicylic acid, 17: gentisic acid, 18: glycolamide, 19: lactamide, 20: tromethamine, 21: megluimine, 22: L-arginine, 23; l-lysine, 24: urea, 25: ethylmaltol, 26: stearic acid, 27: 4-aminobenzoic acid, 28: aspirin, 29: oxalic acid, 30: pterostilbene, 31: ketoglutaric acid, 32: maleic acid, 33: adipic acid, 34: (+)-camphoric acid, 35: 4-hydroxybenzoic acid, 36: 1-hydroxy-2-naphthoic acid, 37: dl-tartaric acid, 38: glycolic acid, 39: L/DL-malic acid, 40: dimethyl sulfoxide, 41: benzoquinone, 42: terephthalaldehyde, 43: acetic acid, 44: formic acid, 45: butyric acid, 46: trimesic acid, 47: 5-nitroisophthalic acid, 48: adamantane-1,3,5,7-tetracarboxylic acid, 49: formamide, 50: malonic acid, 51: 2,3-dihydroxy benzoic acid, 52: 1-naphthoic acid, 53: anthracene-9-carboxylic acid, 54: vanillic acid, 55: 4-nitropyridine N-oxide, 56: picric acid, 57: 2-aminopyrimidine, 58: 2,4-diamino-6-phenyl-1,3,5-triazine, 59: anthranilic acid, 60: ibuprofen. b. caffeine co-formers: 0: caffeine, 1:glutaric acid, 2: oxalic acid, 3: L-malic acid, 4:dimethylsuccinic, 5: mesaconic acid, 6: 2,4dihydroxybenzoic acid, 7: malonic acid, 8: maleic acid, 9: adipic acid, 10: anthranilic acid, 11: theophylline, 12: salicylic acid, 13: pterostilbene, 14: ethylene diamine, 15: acetic acid, 16: formic acid, 17: trifluoroacetic acid, 18: citric acid, 19: L-lactic acid, 20: 4-aminosalicylic acid, 21: paracetamol, 22: p-coumaric acid, 23: 4-hydroxybenzoic acid, 24: phenobarbital , 25: 2-hydroxybenzoic acid, 26: 3-hydroxybenzoic acid, 27: 4-aminobenzoic acid, 28: myricetin, 29: dapsone. c. theophylline co-formers: 0: theophylline, 1: acesulfame, 2: saccharin, 3: oxalic acid, 4: citric acid, 5: L/DL-malic acid, 6: L/DL-tartaric acid, 7: glutaric acid, 8: nicotinamide, 9: p-coumaric acid, 10: sorbic acid, 11: salicylic acid, 12: malonic acid, 13: maleic acid, 14: anthranilic acid, 15: phenobarbital , 16: 5-fluorouracil, 17: gentisic acid, 18: L-lactic acid, 19: sulfamethazine, 20: dapsone. 322
323
Theophylline
Caffeine
> 8.18 < 16.87
> 16.87 < 17.64
> 17.64 < 8.18
> 8.18 < 16.87
> 16.87 < 17.64
Δδt
Ra
Δδ
Δδt
Ra
> 17.64
< 8.18
> 17.64
< 17.64
> 16.87
< 16.87
> 8.18
Δδ
Ra
Δδt
Glutaric acid, dimethylsuccinic acid, mesaconic acid, 2,4-dihydroxybenzoic acid, malonic acid, maleic acid, adipic acid, anthranilic acid, theophylline, salicylic acid, pterostilbene, ethylene diamine, citric acid, 4-aminosalicylic acid, paracetamol, p-coumaric acid, 4-hydroxybenzoic acid, phenobarbital, 2hydroxybenzoic acid, 3-hydroxybenzoic acid, 4-aminobenzoic acid, myricetin, dapsone Oxalic acid, L-malic acid Glutaric acid, oxalic acid, l-malic acid, dimethylsuccinic acid, mesaconic acid, 2,4-dihydroxybenzoic acid, malonic acid, maleic acid, adipic acid, anthranilic acid, theophylline, salicylic acid, pterostilbene, ethylene diamine, citric acid, 4-aminosalicylic acid, paracetamol, p-coumaric acid, 4-hydroxybenzoic acid, phenobarbital, 2-hydroxybenzoic acid, 3-hydroxybenzoic acid, 4-aminobenzoic acid, myricetin, dapsone – Glutaric acid, oxalic acid, l-malic acid, dimethylsuccinic acid, mesaconic acid, 2,4-dihydroxybenzoic acid, malonic acid, maleic acid, adipic acid, anthranilic acid, theophylline, salicylic acid, pterostilbene, ethylene diamine, citric acid, 4-aminosalicylic acid, paracetamol, p-coumaric acid, 4-hydroxybenzoic acid, phenobarbital, 2-hydroxybenzoic acid, 3-hydroxybenzoic acid, 4-aminobenzoic acid, myricetin, dapsone – Acesulfame, saccharin, citric acid, L/DL-malic acid, glutaric acid, nicotinamide, p-coumaric acid, sorbic acid, salicylic acid, malonic acid, maleic acid, anthranilic acid, phenobarbital, 5-fluorouracil, gentisic acid, sulfamethazine Oxalic acid, L/DL-tartaric acid Acesulfame, saccharin, oxalic acid, citric acid, L/DL-malic acid, glutaric acid, nicotinamide, p-coumaric acid, sorbic acid, salicylic acid, malonic acid, maleic acid, anthranilic acid, phenobarbital, 5-fluorouracil, gentisic acid, sulfamethazine L/DL-tartaric acid Acesulfame, saccharin, oxalic acid, citric acid, L/DL-malic acid, glutaric acid, nicotinamide, p-coumaric acid, sorbic acid, salicylic acid, malonic acid, maleic acid, anthranilic acid, phenobarbital, 5-fluorouracil, gentisic acid, sulfamethazine L/DL-tartaric acid
Saccharin, indomethacin, benzamide, nifedipine, nicotinamide, 4-aminosalicylic acid, glutaric acid, acridinium, cinnamic acid, benzoic acid, salicylic acid, gentisic acid, 4-aminobenzoic acid, aspirin, pterostilbene, (+)-camphoric acid, 4-hydroxybenzoic acid, 1-hydroxy-2-naphthoic acid, dimethyl sulfoxide, benzoquinone, terephthalaldehyde, acetic acid, formic acid, butyric acid, trimesic acid, 5nitroisophthalic acid, adamantane-1,3,5,7-tetracarboxylic acid, 2,3-dihydroxy benzoic acid, 1-naphthoic acid, anthracene-9-carboxylic acid, vanillic acid, 4-nitropyridine N-oxide, picric acid, 2-aminopyrimidine, 2,4-diamino-6-phenyl-1,3,5-triazine, anthranilic acid Hydroquinone, succinic acid, fumaric acid, L-tartaric acid, urea, oxalic acid, formamide, malonic acid
Saccharin, indomethacin, benzamide, nifedipine, nicotinamide, 4-aminosalicylic acid, glutaric acid, acridinium, cinnamic acid, benzoic acid, salicylic acid, gentisic acid, 4-aminobenzoic acid, aspirin, pterostilbene, (+)-camphoric acid, 4-hydroxybenzoic acid, 1-hydroxy-2-naphthoic acid, dimethyl sulfoxide, benzoquinone, terephthalaldehyde, acetic acid, formic acid, butyric acid, trimesic acid, 5nitroisophthalic acid, adamantane-1,3,5,7-tetracarboxylic acid, 2,3-dihydroxy benzoic acid, 1-naphthoic acid, anthracene-9-carboxylic acid, vanillic acid, 4-nitropyridine N-oxide, picric acid, 2-aminopyrimidine, 2,4-diamino-6-phenyl-1,3,5-triazine, anthranilic acid Hydroquinone, succinic acid, fumaric acid, L-tartaric acid, urea, oxalic acid, formamide, malonic acid
Saccharin, indomethacin, benzamide, nifedipine, nicotinamide, 4-aminosalicylic acid, glutaric acid, succinic acid, acridinium, cinnamic acid, benzoic acid, salicylic acid, gentisic acid, 4-aminobenzoic acid, aspirin, pterostilbene, (+)-camphoric acid, 4-hydroxybenzoic acid, 1-hydroxy-2-naphthoic acid, dimethyl sulfoxide, benzoquinone, terephthalaldehyde, acetic acid, formic acid, butyric acid, trimesic acid, 5nitroisophthalic acid, adamantane-1,3,5,7-tetracarboxylic acid, 2,3-dihydroxy benzoic acid, 1-naphthoic acid, anthracene-9-carboxylic acid, vanillic acid, 4-nitropyridine N-oxide, picric acid, 2-aminopyrimidine, 2,4-diamino-6-phenyl-1,3,5-triazine, anthranilic acid Hydroquinone, fumaric acid, L-tartaric acid, urea, oxalic acid, formamide, malonic acid
Δδ
Carbamazepine
< 8.18
Co-former of formed co-crystals
Miscibility criteria (MPa0.5)
API
Table 2 Classification of API co-formers according to the miscibility criteria Δδ, Δδt and Ra.
L-lactic acid
L-lactic acid Dapsone
– Dapsone
– L-lactic acid, dapsone
– Acetic acid, formic acid, trifluoroacetic acid, L-lactic acid
L-lactic acid Acetic acid, formic acid, trifluoroacetic acid, L-lactic acid
Citric acid, glycolamide, lactamide, tromethamine, megluimine, ketoglutaric acid, maleic acid, DL-tartaric acid, glycolic acid, L/DL-malic acid Acetic acid, formic acid, trifluoroacetic acid
Citric acid, glycolamide, lactamide, tromethamine, megluimine, ketoglutaric acid, maleic acid, DL-tartaric acid, glycolic acid, L/DL-malic acid L-arginine, L-lysine, ethylmaltol, stearic acid, adipic acid, ibuprofen
Citric acid, glycolamide, lactamide, tromethamine, megluimine, maleic acid, DLtartaric acid, glycolic acid, L/DL-malic acid L-arginine, L-lysine, ethylmaltol, stearic acid, adipic acid, ibuprofen
L-arginine, L-lysine, ethylmaltol, stearic acid, ketoglutaric acid, adipic acid, ibuprofen
Co-former of failed co-crystals
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Table 3 Statistical measures of the performance of the different methods and cut-off values. Method
Previously reported*
Established in this study
Δδ
Δδ
Δδt
Ra
7 86.21 50.00 13.79 50.00 54.54 87.21 78.90
8.18 87.36 45.45 12.64 54.54 50.00 86.36 78.90
16.87 89.65 50.00 10.34 50.00 40.91 87.64 81.65
17.64 89.65 50.00 10.34 50.00 40.91 87.64 81.65
Table 4 HSPs and descriptors of piroxicam and nicotinamide. API
Piroxicam
Nicotinamide
21.13 17.86 26.67 12.48 7.6 10.8 30.35 1.896 220.7 331.4 1.501
19.89 15.07 24.95 12.8 7.5 9.6 28.04 1.379 100.4 122.1 1.217
Structure
Cut-off (MPa0.5) Sensitivity (%) Specificity (%) Miss rate (%) Fall-out rate (%) False omission rate (%) Precision (%) Accuracy (%)
δd δp δv δh δhDon δhAcc δt Ovality M Vol. M Wt. ρ
* Cut-off value as previously reported by Greenhalgh et al. (1999) and employed by Mohammad et al. (2011).
crystallization experiments have to be exhausted before a pair be termed failed, a larger set of failed co-formers is needed to accurately determine the specificity of this method. The HSPs are able to predict miscibility; however in some cases the co-crystal formation is independent of miscibility. It is rather challenging to explain both the formation of co-crystals at higher values and the failure to form co-crystals when the difference in solubility parameters is within the range of miscibility. Possible reasons for the failure of co-formers to form co-crystals may be due to thermodynamic considerations, structure incompatibility or that the preparation method did not favour the formation of co-crystals. The fall-out (false positive) rate was further analysed. Co-formers that failed to form co-crystals but were identified by this method as having a Δδt/ Ra value below the set cut-off are shown in Table 2. The reasons for their failure to co-crystallize with the APIs were further examined in one case. Theophylline did not form a co-crystal with dapsone as reported by Jiang et al. (2014), nor did dapsone form a co-crystal with theobromine. However the authors have reported a formation of two types of co-crystals with caffeine. The crystal structure have been determined for both co-crystal forms, and it has been found that the two methyl groups play crucial roles in the architecture of the corresponding cocrystal by forming a nonclassic auxiliary H-bonding. The structure of Theophylline differs from Caffeine in one methyl group, in the position that was crucial for co-crystal formation with Dapsone which could explain the failure to form a theophylline-dapsone co-crystal. Furthermore the lack of methyl group in theophylline structure provides one more H donor group that strengths the intermolecular bonding in pure theophylline crystal. This can be seen in the difference between melting points for these three structurally similar molecules. The melting point for caffeine is 235 °C, theophylline 273 °C and 375 °C for theobromine which could indicate the thermodynamic favourable formation of separate phase crystals.
interactions to form a 2 or 3 dimensional lattice. The experimentally determined HSPs do differ for the three isomers, but the difference is not significant and cannot be used to distinguish the specific interaction for formation of co-crystal. On the other hand it could be argued that with appropriate parameters, co-crystals could be formed for these pairs. The ideal approach of co-crystal formation prediction should be strict enough to minimize the inclusion of pairs that are unlikely to form co-crystals, yet broad enough to limit the exclusion of pairs able to co-crystallize.
3.3. Prediction of piroxicam and nicotinamide co-crystal formation HSPs of piroxicam and nicotinamide are shown in Table 4. Mean values for the Piroxicam and Nicotinamide co-formers are shown in Table S8. A total of 31 co-crystals of piroxicam and 13 failed co-crystals as well as 21 formed and 7 failed co-crystals of nicotinamide were used to test the cut-off values and best method to predict co-crystal formation. Table 5 represents the classification of piroxicam and nicotinamide co-formers according to the new cut-off values established by the training set using Δδ and Δδt. The percentage represents the portion of the co-formers actually able to form co-crystals within the inclusion value. While Fig. 2 represents the Hansen diagram of the piroxicam and nicotinamide co-formers. Utilizing Δδ with the newly established cut-off value was able to predict co-crystal formation in 63.6 and 79.2% of the cases in piroxicam and nicotinamide respectively, having a weighted average of 69.7%. Ra seemed to be slightly superior as it predicted co-crystal formation in 72.1 and 78.6% of cases in the same test set of piroxicam and nicotinamide, having a weighted average of 74.6%. These values were higher than the reported 70% inclusion using lipoaffinity index (Cysewski and Przybyłek, 2017). This miss rate using Δδ was the highest (6.5–13.6%) followed by Δδt (0–9.1%). The miss rate of Ra in the test set (0%) makes this method of co-former screening ideal compared to the other methods tested in this study. Both Ra and Δδt are similar by definition, and found to be correlated. The advantage of Ra over Δδt can be explained due to the importance of dispersive interactions in co-crystal formation (Peng-Yuan Chen et al., 2015). Therefore multiplying the dispersive component of the HSP in the calculation of Ra not only improved the visual representation (Cañete et al., 2014) but also give a greater role of this type of interaction in co-crystal formation. Reporting of failed cocrystallization experiments is encouraged, to improve the quality of the statistical analysis. As out of the 31 formed co-crystals of piroxicam, 9 were reported as failed co-crystallization in either other publications or using different preparation methods or parameters. A larger set of data is required to better understand the limitations of this simple method in
3.2. Eutectics As shown in Tables S6 and S7, all eutectic pairs published by Kaur et al. (2015) had values of Δδ and Δδt lower than 15 MPa0.5 suggestive of co-crystal formation except benzoic acid-succinimide. This may indicate that the use of HSPs is unable to differentiate between co-crystals and eutectics. Particularly because Δδt values were within the average range of 10.45 MPa0.5, despite the fact that Δδ showed statistical difference between formed co-crystals and eutectics (p-value = 0.001). The authors have given the structural explanation for the formation of co-crystal or eutectic. It considers the isomers of hydroxybenzoic acid. The position of –OH group within the hydroxybenzoic acid determines whether co-crystal or eutectic will be formed. The carboxylic group forms a primary molecular syntonic unit, but only the isomer that have –OH in para positon can provide an extension through auxiliary 324
325
> 16.87 < 17.64
Ra
> 17.64
> 8.18 < 16.87
Δδt
> 16.87 < 17.64
Ra
> 17.64 < 8.18
> 8.18 < 16.87
Δδt
Δδ
Azelaic acid, 3-hydroxybenzoic acid, phenylsuccinic acid, isophthalic acid, trimesic acid, hydrocaffeic acid, gentisic acid, furosemide, benzoic acid, adipic acid , succinic acid, L/DLmalic acid, ketoglutaric acid, 4-hydroxybenzoic acid, glutaric acid, malonic acid, salicylic acid, 1-hydroxy-2-naphthoic acid, hippuric acid, resorcinol, methylparaben Sebacic acid, (+)-camphoric acid Saccharine sodium, urea, nicotinamide, oxalic acid, maleic acid, fumaric acid, pimelic acid, suberic acid, azelaic acid, sebacic acid, 3-hydroxybenzoic acid, phenylsuccinic acid, isophthalic acid, trimesic acid, hydrocaffeic acid, gentisic acid, furosemide, benzoic acid, adipic acid , succinic acid, (+)-camphoric acid, L/DL-malic acid, ketoglutaric acid, 4hydroxybenzoic acid, glutaric acid, malonic acid, salicylic acid, 1-hydroxy-2-naphthoic acid, hippuric acid, resorcinol, methylparaben – Saccharine sodium, urea, nicotinamide, oxalic acid, maleic acid, fumaric acid, pimelic acid, suberic acid, azelaic acid, sebacic acid, 3-hydroxybenzoic acid, phenylsuccinic acid, isophthalic acid, trimesic acid, hydrocaffeic acid, gentisic acid, furosemide, benzoic acid, adipic acid, succinic acid, (+)-camphoric acid, L/DL-malic acid, ketoglutaric acid, 4hydroxybenzoic acid, glutaric acid, malonic acid, salicylic acid, 1-hydroxy-2-naphthoic acid, hippuric acid, resorcinol, methylparaben – Ketoprofen, carbamazepine, 4-aminosalicylic acid, furosemide, indomethacin, nitrofurantoin, piroxicam, naproxen, AMG 517, theophylline, ketoconazole, myricetin, mefenamic acid, lamotrigine, flufenamic acid, fenofibrate, ascorbic acid, succinic acid, oxalate Acetazolamide, adefovir dipivoxil, R/S ibuprofen Ketoprofen, carbamazepine, 4-aminosalicylic acid, acetazolamide, furosemide, indomethacin, nitrofurantoin, piroxicam, naproxen, AMG 517, theophylline, ketoconazole, myricetin, mefenamic acid, lamotrigine, flufenamic acid, R/S ibuprofen, fenofibrate, ascorbic acid, succinic acid, oxalate Adefovir dipivoxil Ketoprofen, carbamazepine, 4-aminosalicylic acid, acetazolamide, furosemide, indomethacin, nitrofurantoin, piroxicam, naproxen, AMG 517, adefovir dipivoxil, theophylline, ketoconazole, myricetin, mefenamic acid, lamotrigine, flufenamic acid, R/S ibuprofen, fenofibrate, ascorbic acid, succinic acid, oxalate –
< 8.18
Δδ
Piroxicam
Nicotinamide
Co-former of successfully prepared co-crystals
Miscibility criteria (MPa0.5)
API
Table 5 Classification of piroxicam and Nicotinamide co-formers according to the criteria of Δδ, Δδt and Ra.
78.6
– Nitazoxanide, spironolactone, artemisinin, compound 1, ivabradine hydrochloride, βlapachone
–
75.0
79.2
72.1
72.1
63.6
%
Artemisinin Nitazoxanide, spironolactone, artemisinin, compound 1, ivabradine hydrochloride, βlapachone
L/DL-tartaric acid Nitazoxanide, spironolactone, compound 1, ivabradine hydrochloride, β-lapachone
L/DL-tartaric acid Cinnamic acid, catechol, ferulic acid, para amino benzoic acid, anthranilic acid, terephthalic acid, 3-(4-Hydroxyphenyl)-propionic acid, citric acid, glycolic acid, caprylic acid, Lpyroglutamic, vanillin
Caprylic acid Cinnamic acid, catechol, ferulic acid, para amino benzoic acid, anthranilic acid, terephthalic acid, 3-(4-Hydroxyphenyl)-propionic acid, citric acid, glycolic acid, caprylic acid, Lpyroglutamic, vanillin
Cinnamic acid, catechol, ferulic acid, para amino benzoic acid, anthranilic acid, terephthalic acid, 3-(4-Hydroxyphenyl)-propionic acid, L/DL-tartaric acid, citric acid, glycolic acid, Lpyroglutamic, vanillin
Co-former of failed co-crystals
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Fig. 2. Position of a. piroxicam and b. nicotinamide co-formers with the i. Bagley diagram and ii. Hansen diagram. a. 0: piroxicam, 1: saccharine sodium, 2: urea, 3: nicotinamide, 4: cinnamic acid, 5: catechol, 6: ferulic acid, 7: p-amino benzoic acid, 8: anthranilic acid, 9: oxalic acid, 10: maleic acid, 11: fumaric acid, 12: pimelic acid, 13: suberic acid, 14: azelaic acid, 15: sebacic acid, 16: 3-hydroxybenzoic acid, 17: phenylsuccinic acid, 18: isophthalic acid, 19: terephthalic acid, 20: trimesic acid, 21: hydrocaffeic acid, 22: 3-(4-hydroxyphenyl)-propionic acid, 23: gentisic acid, 24: furosemide, 25: benzoic acid, 26: adipic acid, 27: succinic acid, 28: (+)-camphoric acid, 29: L/DL-malic acid, 30: ketoglutaric acid, 31: 4-hydroxybenzoic acid, 32: glutaric acid, 33: malonic acid, 34: salicylic acid, 35: 1-hydroxy-2naphthoic acid, 36: hippuric acid, 37: L/DL-tartaric acid, 38: citric acid, 39: glycolic acid, 40: caprylic acid, 41: l-pyroglutamic, 42: resorcinol, 43: methylparaben, 44: vanillin. b. 0: nicotinamide, 1: ketoprofen, 2: carbamazepine, 3: 4-aminosalicylic acid, 4: acetazolamide, 5: furosemide, 6: indomethacin, 7: nitrofurantoin, 8: piroxicam, 9: Nitazoxanide, 10: naproxen, 11: AMG 517, 12: adefovir dipivoxil, 13: spironolactone, 14: artemisinin, 15: compound 1*, 16: theophylline, 17: ivabradine hydrochloride, 18: ketoconazole, 19: myricetin, 20: mefenamic acid, 21: lamotrigine, 22: β-lapachone, 23: flufenamic acid, 24: ibuprofen and R/S ibuprofen, 25: fenofibrate, 26: ascorbic acid, 27: succinic acid, 28: oxalate. *Compound 1 structure is available in the supplementary material Fig. S1.
solids, was developed by Just et al. (2013). The polar parameter of this method has been used as an indicator of the caffeine-glutaric acid cocrystallization microenvironment (Hasa et al., 2016). Once this method is fully developed, it could offer promising improvements to the use of HSPs as a co-former screening tool. The general rules guiding co-crystal formation remains challenging to establish. Continuous efforts are needed for computational methods able to predict the formation of such complex systems (Taylor and Day, 2018).
the prediction of co-crystal formation. One limitation of this method is its inability to account for parameters of preparation or solvent. The methods low specificity makes it likely to discard otherwise plausible co-formers. This has been represented here in terms of miss rate, expressed as a percentage of the co-formers that would have been dismissed as possible co-formers when using this method as a screening tool. The percent miss rate of co-formers is shown in Fig. 3. This reported percentage should only be viewed as a means of representing limitations to the use of HSPs as co-crystal screening method. A larger data size is required to give statistical meaning to these results. The miss rate for both piroxicam and nicotinamide was lower than that established for the test set of co-formers particularly when using Δδt and Ra. An improved group contribution method, based on pharmaceutical
4. Conclusions HSPs as a tool to predict pharmaceutical co-crystal formation has been evaluated using co-formers of three different APIs and further tested using co-formers of two other APIs. The previously set cut-off 326
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Fig. 3. Percent miss rate for each of the methods.
value of Δδ at 7 MPa0.5 was validated, as the cut-off value found in this study is 8.18 MPa0.5 had no statistical difference in terms of sensitivity and specificity compared to the previous value. From the data of 16 descriptors calculated with group contribution method and their statistical analysis we suggest a usage of Δδt and Ra with cut of values of 16.87 and 17.64 MPa0.5 respectively. With these approaches a simple yet efficient selection of plausible co-formers is obtained with 73.8–85% efficiency as obtained for the test set, without major loss of plausible co-formers with limited miscibility. Unfortunately this method excludes plausible co-formers that are predicted as immiscible. These do form co-crystals with the examined API. It was found that the miss rate using Δδ was 13.64% while using Δδt, the miss rate was lower (9.09%) and even lower (0%) using Ra for test group co-formers. This fact limits the use of HSP as a tool to predict co-crystal formation, yet it may be useful when screening sufficiently large numbers of co-formers. The quality of statistical data obtained in this study is influenced by insufficient number of all experiments, especially the failed co-crystallization. The quality of the results was further influenced by the fact that in most reported experiments, the co-former selection are done on chemical intuitive or synthon basis. Conflict of interest Authors declare no conflict of interests. Acknowledgments The project has been supported by the European Union, co-financed by the European Social Fund (grant No. EFOP-3.6.1.-16-2016-00004, grant title: Comprehensive Development for Implementing Smart Specialization Strategies at the University of Pécs). The authors appreciate Stipendium Hungaricum scholarship programme – Tempus Public Foundation and the support of the academic and technical staff at the University of Pécs, department of Pharmaceutical technology and Biopharmacy. Appendix A. Supplementary data Supplementary data to this article can be found online at https:// doi.org/10.1016/j.ijpharm.2019.01.007. References Abramov, Y.A., Loschen, C., Klamt, A., 2012. Rational coformer or solvent selection for pharmaceutical cocrystallization or desolvation. J. Pharm. Sci. 101, 3687–3697. Ainurofiq, A., Mauludin, R., Mudhakir, D., Umeda, D., Soewandhi, S.N., Putra, O.D., Yonemochi, E., 2018. Improving mechanical properties of desloratadine via multicomponent crystal formation. Eur. J. Pharm. Sci. 111, 65–72.
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