Structure-based in silico model profiles the binding constant of poorly soluble drugs with β-cyclodextrin

European Journal of Pharmaceutical Sciences 42 (2011) 55–64

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European Journal of Pharmaceutical Sciences journal homepage: www.elsevier.com/locate/ejps

Structure-based in silico model profiles the binding constant of poorly soluble drugs with ␤-cyclodextrin Haiyan Li a,b , Jin Sun b,∗ , Yongjun Wang b , Xiaofan Sui c , Le Sun b , Jiwen Zhang a,∗∗ , Zhonggui He b,∗ a

Center for Drug Delivery System, Shanghai Institute of Materia Medica, State Key Laboratory of Drug Research, Chinese Academy of Sciences, Shanghai 201203, China Department of Biopharmaceutics, School of Pharmacy, Shenyang Pharmaceutical University, Shenyang 110016, China c Liaoning Provincial Institute for Drug and Food Control, Shenyang 110023, China b

a r t i c l e

i n f o

Article history: Received 8 August 2010 Received in revised form 26 September 2010 Accepted 19 October 2010 Available online 25 October 2010 Keywords: Poorly soluble drugs ␤-Cyclodextrin inclusion complex Binding constant In silico model

a b s t r a c t Cyclodextrin inclusion complexation technique is the key method to enhance the solubility and absorption of poorly soluble drugs in the early development stage, and thus it is essential to predict the binding constant between drug molecules and cyclodextrin. Structure-based in silico model was constructed for a data set of 86 poorly soluble drugs and used to profile the binding constant of drug-␤-cyclodextrin inclusion complex. The stepwise regression was employed to select the optimum subset of the independent variables. The in silico model was built by the multiple linear regression method and validated by the residual analysis, the normal Probability–Probability plot and Williams plot. For the entire data set, the R2 and Q2 of the model were 0.78 and 0.67, respectively. The results indicated that the fitted model is robust, stable and satisfies all the prerequisites of the regression models. The chemical space position and important contributors were compared between selected drug molecules and organic compounds available in the literature. It was suggested that the binding behavior of drug molecules with ␤-CD should differ from that of the common organic compounds. Focusing on structurally diverse drugs, the in silico model can be used as an efficient tool to rapidly screen the drug-␤-cyclodextrin inclusion complex stability and to rationally design the new drug delivery system of poorly soluble drugs. © 2010 Elsevier B.V. All rights reserved.

1. Introduction Cyclodextrins (CDs) have been extensively utilized to modify physical and chemical properties of guest molecules in food, cosmetic, textile industrial, chemical, agricultural and pharmaceutical fields. For drug delivery, cyclodextrins can overcome various undesirable properties of drug molecules via inclusion complexation, such as improved solubility (Brewster and Loftsson, 2007), good solid properties (Uekama and Otagiri, 1987) and stability (Loftsson and Brewster, 1996), modified release kinetics of drugs (Uekama, 2004a), enhanced absorption performance (Davis and Brewster, 2004) and reduced side-effects (Uekama et al., 1998). Furthermore, the cyclodextrins inclusion complexes can also be

∗ Corresponding authors at: No. 59 Mailbox, Department of Biopharmaceutics, School of Pharmacy, Shenyang Pharmaceutical University, No. 103 of Wenhua Road, Shenyang 110016, China. Tel.: +86 24 23986321; fax: +86 24 23986321. ∗∗ Corresponding author at: Room 3518, Center for Drug Delivery System, Shanghai Institute of Materia Medica, State Key Laboratory of Drug Research, Chinese Academy of Sciences, No. 555 of Zuchongzhi Road, Shanghai 201203, China. Tel.: +86 21 50805901; fax: +86 21 50805901. E-mail addresses: [email protected] (J. Sun), [email protected] (J. Zhang), [email protected] (Z. He). 0928-0987/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.ejps.2010.10.006

used in site-specific drug delivery (Uekama, 2004b; Uekama et al., 2006). In practical applications of cyclodextrin complexation, attention should be paid to the dissociation equilibrium of the complexation process and the binding constant (K) of the complex (Carrier et al., 2007). The binding constant is a useful index to estimate the binding strength between the guest and the host molecules and the disassociation/association stability of the complex, and is also essential for evaluating the influence of cyclodextrins on in vivo absorption and bioavailability of drugs (Gamsiz et al., 2010a,b). Many approaches have been used to determine the cyclodextrin binding constants of guest molecules (Dodziuk, 2006), such as spectroscopic methods, surface tension methods, nuclear magnetic resonance, phase-solubility technique, fluorometry, high-pressure liquid chromatography and electrochemistry. However, these experimental methods are often tedious and time-consuming because of the low aqueous solubility of the guest molecules. The QSAR technique seems to be a useful alternative tool to estimate the binding constant and thermodynamic stability of cyclodextrin inclusion complexes. There are some published studies exploring the QSAR model for the estimation of the binding constant between organic compounds and cyclodextrin (PérezGarrido et al., 2009a,b; Chari et al., 2009). However, there is no

56

H. Li et al. / European Journal of Pharmaceutical Sciences 42 (2011) 55–64

QSAR model focusing on the structurally diverse drug molecules, although there are many researches reporting the determination of the binding constants of poorly soluble drugs with ␤-cyclodextrin. The drug molecules occupy a special domain in the chemical space (Petit-Zeman, 2004; Lajiness et al., 2004). Due to the differences in chemical structure, the binding behavior of drug molecules with cyclodextirns should differ from that of organic compounds. With the extensive application of cyclodextrins in improving drug solubility and oral absorption, there is an urgent need for a QSAR model to predict the binding constants for the drug molecules. In this study, focusing on structurally diverse drug molecules with poor solubility, a QSAR model was constructed to estimate the ␤-CD binding constant of 86 drugs based on structural parameters. The feature selection was performed by stepwise regression and the QSAR model was established with multiple linear regression (MLR) method. The principal objectives of the study were therefore (i) to develop a quantitative relationship between the molecular structure parameters and log K values of drugs; (ii) to estimate the predictive accuracy of the QSAR model and to assess the applicability domain assuring the reliable predictions by the QSAR model; (iii) to elucidate the most important factors influencing the interactions between drug molecules and ␤-CD and to compare the ␤-CD binding behavior between the selected drug molecules and organic compounds reported in the literature. 2. Materials and methods 2.1. Data collection The entire set was composed of 86 structurally diverse drugs with poor solubility. The dependent variable was the ␤-CD binding constant (K) collected from the scientific literature with drugs as guest molecules. For one drug with many K values from different laboratories, the values determined at the following conditions were selected, the availability of the experimental K values derived with the solvents of water or the buffer with the pH close to 7.0, the study performed at 25 ◦ C and with the inclusion formation ratio of 1:1. If the K values from different laboratories all followed the above criteria and were close to each other, the average value was chosen. Otherwise, the K value with least error or determined by phase solubility method was selected. The stereoisomers, the structural parameters of which could not be distinguished, had nevertheless different K values (such as methamphetamine and amphetamine). Thus, one of the isomers was discarded, being only the other one considered in our study with an averaged value of K. Moreover, K value of each drug was log-transformed (log K) to normalize the data and to reduce unequal error variances. A complete list of the observed log K values for 86 drugs was displayed in Table 1. 2.2. Calculation of structural parameters The 2D structures of 86 drugs were searched in SciFinder Scholar database (O’Reilly et al., 2002) and the saved mol files were imported into TSAR 3.3. Finally, the corresponding relationship between the name and the structure of each drug was manually inspected and, when needed, corrected. The 3D structures and the partial charges of drugs were derived using CORINA 3D and Charge-2 packages in TSAR 3.3, respectively. The geometries of the molecules were optimized using the Cosmic module of TSAR. The calculations were terminated if the energy difference or the energy gradient were smaller than 1e−005 and 1e−010 kcal/mol, respectively. Then, a set of 110 structural parameters was calculated with TSAR 3.3, including: molecular surface area and volume, moments

of inertia, ellipsoidal volume, dipole moments, lipole moments, molecular mass, Wiener index, molecular connectivity indices, molecular shape indices, electrotopological state indices, log P, rings (aromatic and aliphatic), and groups (methyl, hydroxyl, etc.). Vamp, a semi-empirical molecular orbital package in TSAR 3.3, was used to calculate the electrostatic properties like total energy, electronic energy, nuclear repulsion energy, accessible surface area, atomic charge, mean polarizability, heat of formation, HOMO (highest occupied molecular orbital energy) and LUMO (lowest unoccupied molecular orbital energy), ionization potential, total dipole, and dipole components and perform structural optimizations in vacuum with default parameters using Hamiltonian method AM1 and formalism type of restricted Hartree–Fock (RHF). Then, the logarithm of distribution coefficient at pH 7.0 (log D7.0 ) and the logarithm of mass solubility (g/mL) at pH = 7.0 (S7.0 ) were obtained from the SciFinder Scholar database (O’Reilly et al., 2002).

2.3. Feature selection Nine parameters with the same values for ≥90% drugs were discarded and the number of variables was filtered to 103. The subjective feature selection method, the stepwise regression was used to select the subset of independent variables that were highly correlated with the observed log K (␣-to-enter and ␣-to-remove both set to 0.10). Then, the correlation matrix of the independent variables was established to investigate the mutual correlations among the selected descriptors.

2.4. Model development and validation Multiple linear regression analysis was applied to develop the QSAR model. In order to examine the predictive power and robustness of the model, the entire dataset was subdivided into training set (n = 64) and test set (n = 22) by the cluster analysis of observed log K. The whole range of the observed log K was divided into bins, and compounds belonging to each bin were randomly assigned to the training or test sets. Meanwhile, leave-one-out (LOO) crossvalidation and test set validation procedures were performed. Then R2 , RMSE (the root mean square error) and Q2 resulted from LOO were calculated to evaluate the model predictability. The regression diagnosis was also carried out to examine the normality, independence and homocedasticity of the residuals.

2.5. Model applicability domain The main objective for our QSAR model building was to accurately predict the dependent variable for alien drugs. And its use within the model applicability domain was one of the conditions that would assure reliable predictions by the model. The definition of the applicability domain of the model was important constitutes for the QSAR model validation. There are four major approaches to define interpolation regions in a multivariate space: range based, distance based, geometrical and probability density distribution based (Jaworska et al., 2005). In this study, the leverage approach, using the Williams plot of standardized residuals versus leverage values, was used to define the applicability domain (Eriksson et al., 2003). The applicability domain was defined inside a squared area within ±x standard deviations and a leverage threshold h* (h* was defined as 3m/n, where m is the number of the independent variables and n is the number of observations, whereas x = 3), lying outside this area (vertical lines) the outliers and (horizontal lines) influential observations.

Table 1 Data for the observed binding constant (K) and selected 15 structural parameters of 86 drugs. Name

Set

log Ka

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

5-Methoxypsoralen Adenine Albendazole Amphetamine Amylobarbitone Atenolol Brompheniramine Caffeine Catechin Ciprofloxacin Cloprostenol Cloxacillin Codeine Curcumin Danazol Diethylstilbestrol

Test Train Train Test Train Test Train Test Train Train Train Train Test Train Test Train

2.6021 2.0253 1.8382 1.7959 2.7372 2.0414 2.2625 2.2341 3.9912 2.4440 2.9859 3.2380 2.7400 3.6251 2.9877 4.4624

17 18 19 20

Diflunisal Doxylamine Enalapril Estradiol

Train Test Train Train

3.5902 1.7160 2.5617 4.5119

21 22 23 24 25 26

Ethyl salicylate Famotidine Fenbufen Fenoprofen Fisetin Fluconazole

Train Train Train Test Train Train

2.2201 −3.9702 2.7308 −151.7900 3.9792 −26.3190 2.9930 −19.3130 2.9345 −1.8533 1.8370 −14.7670

27 28 29 30 31 32 33 34 35

Fluorouracil Fluoxetine Flurbiprofen Flutamide Furnidipine Furosemide Gemfibrozil Glipizide Ibuprofen

Train Train Test Train Train Test Test Train Train

1.2304 3.8402 3.2304 2.5514 2.1931 2.9157 2.1728 2.6168 3.9370

36 37

Indomethacin Irbesartan

Train Train

38 39 40 41 42 43 44 45 46 47 48 49 50

Ketoconazole Lamotrigine l-Isoleucine l-Leucine l-Methionine l-Norleucine Mebendazole Melatonin Meloxicam Methamphetamine Methyl salicylate Midazolam Myricetin

Train Train Train Test Train Train Train Train Train Train Train Train Train

X1

X2

X3

X4

−9.3269 −47.6880 −48.1240 −7.5428 −74.5120 −27.3320 −3.5876 −20.4010 −10.7400 −32.3500 −24.9840 −39.6320 7.6679 −14.2240 −6.0929 −13.8240

4.1957 2.8142 2.6028 2.3065 3.6278 2.6940 4.9662 3.5610 3.7364 4.8584 6.2460 4.6259 4.8191 4.6038 3.4406 3.6908

−2.6482 1.5177 7.2674 −0.3800 4.6404 2.2034 −0.7331 1.8286 0.2417 1.8628 −4.7517 0.5608 1.7541 3.9359 0.0284 −0.6031 −0.5844 2.1127 8.9991 0.6420 1.8117 3.2357 3.8694 2.1003 2.2222 1.3906 1.3377 2.4793 0.2326 3.5163 −0.4288 4.7940

−29.7360 4.7499 11.6330 −9.3318

3.2248 2.3607 5.1843 −1.1828 6.2530 0.0954 3.5250 1.4792

X5

X6

X7

X8

X9

X10

X11

X12

X13

X14

X15

−4.5310 12.6650 78.4430 −1.2090 6.9830 15.5430 0.2700 29.6870 −8.2310 −1.2210 −5.8500 11.1470 0.9720 −11.0220 −77.5540 4.8030 16.2040 −157.6400 −3.1450 5.2950 −4.2310 −2.9270 9.6050 31.0810 2.4610 −9.5850 60.0980 −2.6800 −8.6820 68.9550 3.9930 10.8010 −137.1000 −2.0620 15.5480 78.3710 0.2120 −6.0400 −38.3940 −0.5520 −29.9450 9.2210 5.2490 10.7600 −166.8200 0.0520 −1.2330 −3.9430

0.6698 −2.7648 3.9543 4.2321 0.2601 −2.4862 10.6630 0.1084 −0.2801 0.2592 12.9080 −4.9247 1.8248 −1.7102 1.7472 0.0621

1.6813 −0.0075 −0.0332 1.0463 −0.3448 −3.5462 2.5642 0.0769 −0.8271 −0.3428 −2.7881 −4.6100 −1.5795 2.4210 0.1930 −0.2759

1.7713 1.9965 1.7590 2.1313 2.7428 2.0858 1.9156 2.1778 1.6703 1.5315 1.6405 1.4359 1.6183 1.6029 1.4401 1.9577

0 0 0 0 0 1 0 0 5 1 4 1 1 2 1 2

0 6 2 0 0 0 2 2 0 0 0 1 0 0 1 0

1 1 0 0 1 0 0 1 1 2 0 0 3 0 3 0

−2.2066 0.3975 1.5725 −0.3362 5.1890 −3.0520 1.4271 −0.0484 −3.0576 0.0995 −0.8850 −0.1993 −0.9411 −2.8460 1.4096 10.5330

37.0110 19.2050 38.8780 24.8440 26.8720 35.4190 42.8810 29.8390 38.4710 46.1190 50.3990 45.6520 43.4860 43.2880 52.9140 42.7160

3.4240 1.6008 2.7813 6.1116 2.1010 −10.7650 4.0079 −0.2381

−2.8256 2.1096 −0.2246 −3.3981

1.9661 1.9958 1.9079 1.5342

2 0 1 2

0 2 0 0

0 0 0 2

−0.1676 −1.3397 −1.1374 −1.2687

27.9740 0.3940 34.5060 −0.4890 49.6580 −1.5400 37.1420 -0.4510

3.1476 2.8126 2.7702 3.1622 3.4040 4.9589

−2.4362 1.8348 1.9164 −1.5156 −0.6588 −11.4670 −0.2920 2.8314 9.7624 0.8828 3.6689 7.3241 −4.3170 0.5640 −3.3139 −3.2841 1.2158 1.5884

0.2196 4.3126 0.1139 1.2091 −0.0573 6.0299

2.3603 2.0473 1.6888 1.7843 1.7035 1.7069

1 0 1 1 4 1

0 4 0 0 0 6

0 0 0 0 1 0

1.3577 0.9673 2.5780 −2.6480 1.0469 7.8759

25.1150 36.5590 39.0670 33.3860 41.4640 28.1640

−2.6110 −6.0060 21.2560 3.4410 −5.7260 −212.6300 −0.4030 −7.5420 −8.3370 −0.7240 −10.2150 20.1900 2.6980 21.4360 −54.4380 −0.7430 0.1510 80.4610

−45.2500 12.4220 −14.3990 −7.7093 −29.4920 −56.2240 −16.9170 −48.7100 −18.4860

2.5842 5.4420 2.8936 3.5564 5.3095 4.4151 3.5490 5.6115 2.8386

5.3273 −1.3177 2.6768 4.1937 0.1558 4.0638 −0.6637 2.9225 3.6907 0.4737 −4.9160 0.9383 −0.0310 4.3269 −1.6759 2.1228 0.7851 3.8302

0.1222 −3.1934 −6.5118 1.4319 −8.2832 5.7671 6.2794 −2.3997 2.1072

−0.0158 4.9104 −1.0038 −2.5365 −3.7927 −0.3159 0.0288 5.9995 −1.1915

2.3462 1.8222 1.8729 2.6868 1.8664 1.9588 2.2094 1.3042 2.2909

0 0 1 0 0 1 1 0 1

0 0 0 0 0 0 0 4 0

1 0 0 0 1 0 0 1 0

−2.6857 0.3755 0.6816 1.7914 −5.2432 0.5160 0.4228 −1.7925 −1.4819

12.5240 27.3320 36.9490 31.0750 54.4910 38.6420 38.5120 56.6540 31.1970

3.7490 5.8090 −0.0950 1.9070 0.2210 17.0740 −2.5250 −26.1410 −5.4740 −8.1300 1.9150 5.8450 −0.8260 4.2600 −4.9930 39.5050 −1.4900 9.3810

−19.8820 30.2870 53.6970 −0.7450 183.8400 −78.1210 38.2900 81.2300 46.1870

2.8808 2.0187

−23.2710 −2.8898

5.1473 5.4520

3.6415 5.0254

−0.5634 4.6342

2.9376 5.6329

1.7516 1.1567

1 0

0 2

0 0

−8.5185 −2.4919

50.9660 −0.5170 −10.9130 58.0310 −0.4230 12.3250

−72.9570 −72.2330

0.6335 2.5682 0.6902 0.5185 0.3979 0.5185 3.0111 2.0000 2.3578 1.8921 2.3598 2.0334 2.0700

−20.7610 −48.6750 3.7189 −0.1492 1.7897 2.5785 −38.5890 −23.2080 −22.3340 0.1539 −2.7929 −4.3634 −6.7657

5.7855 3.7120 2.6153 2.4469 2.3313 2.3951 4.0579 3.9423 3.3040 3.0017 2.9314 5.3795 3.9585

5.6922 4.2682 4.8820 2.3937 0.2642 0.7342 −0.3978 0.6619 1.8063 −0.5462 −0.2402 0.7277 5.7545 2.5231 3.0348 0.7626 1.2783 −0.1615 −0.5163 2.2369 −2.2001 1.4923 0.5791 4.6312 3.7212 −0.0048

13.2140 1.4575 −4.4116 −4.3284 2.8645 4.5471 −6.3387 3.9576 1.0976 4.6577 1.9424 0.2719 3.6355

18.6380 −0.9062 −2.4237 −2.3856 −1.8539 −1.6940 1.7558 1.9727 −0.8850 1.4430 0.0014 7.1018 0.2612

1.0877 1.9993 3.5758 3.3766 3.1553 3.1553 1.4989 1.7766 1.7400 2.1325 2.4020 1.5898 1.7582

0 0 1 1 1 1 0 0 1 0 1 0 6

2 4 0 0 0 0 2 0 2 0 0 3 0

1 0 0 0 0 0 0 0 1 0 0 0 1

1.7570 4.7683 −0.3851 −0.5461 −0.2137 −0.1229 −1.7418 3.3599 −1.1099 0.3026 1.3402 6.0290 0.4973

68.8200 33.5090 15.1470 14.9790 12.9230 13.8440 42.5920 37.8400 44.7580 27.9600 22.9470 42.8260 40.2370

0.7636 4.3309

−0.7000 −1.3040 0.3590 −0.1740 0.3050 0.9350 −2.0090 −0.1720 1.8270 −0.2600 −2.2780 −3.6900 −1.3270

3.5790 4.6470 −2.3670 5.0990

−20.5600 14.3410 −0.3270 1.9560 1.1990 0.5320 −9.8360 −21.0530 −33.3140 0.9310 −4.5330 −13.8260 −2.6070

9.0000 −62.5480 −52.4750 −55.9630

77.0750 −58.4610 7.0190 −16.7550 −19.0900 −10.1340 37.9580 1.6490 −18.8250 7.9210 18.3900 69.4740 66.1220

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57

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H. Li et al. / European Journal of Pharmaceutical Sciences 42 (2011) 55–64

No

58

Table 1 (Continued ) Name

Set

log Ka

51 52

Naproxen Nifedipine

Train Train

2.3222 2.0860

−18.8150 −26.0380

2.8827 6.0723

1.2734 4.8607

2.9894 0.2423

1.3761 −7.0963

53

Nimesulide

Train

2.2013

−13.2850

5.0237

1.2329

2.1954

54 55 56 57 58 59 60 61 62 63

Omeprazole Paroxetine Phenacetin Pheniramine Phenytoin Pilocarpine Piroxicam Praziquantel Procaine Progesterone

Test Train Train Train Train Test Train Train Test Train

1.7559 3.3058 2.2355 1.7709 2.7924 1.9800 1.4592 2.5987 2.0766 4.3928

−11.9090 −1.1033 -24.4390 −2.2638 −42.0720 4.9453 −17.4360 0.4958 −14.2130 −14.8840

4.5062 4.9781 2.4890 4.9794 4.5853 3.2033 3.3830 4.6293 3.7575 3.1711

−2.3121 −0.4822 −4.6791 1.5375 2.0467 0.0639 1.7401 5.0470 −0.8194 −0.4993

64 65 66 67 68 69 70 71 72 73 74 75 76 77

Psoralen Quercetin Quinine Rhein Riboflavin Ricobendazole Robinetin Rofecoxib Rubidate Rutin Salicylic acid Sildenafil Spironolactone Sulindac

Train Train Train Train Train Test Train Train Train Test Train Train Test Train

2.8215 2.3617 3.0900 2.5441 3.3247 2.0346 2.2900 2.8859 2.6532 2.4232 2.4713 2.1761 3.9973 2.1430

−9.4796 −11.4600 0.3189 −26.7100 −30.6350 −48.7200 3.3846 −5.5330 0.6143 20.2090 −22.7380 −23.9830 −26.4620 −30.5460

2.8200 3.8074 4.8895 3.3335 5.7002 2.9978 3.5697 4.6364 6.4753 7.1020 2.7488 5.1582 5.7979 4.3088

78

Sulphaguanidine

Test

2.6532

−91.6530

79 80 81 82 83

Tamoxifen Tenoxicam Theobromine Theophylline Thioctic acid

Test Train Train Train Test

4.0792 1.6721 2.8603 2.1139 3.5328

84 85

Tolbutamide Triamterene

Train Train

86

Warfarin

Test

a

X1

X2

X3

X7

X8

X9

X10

0.1590 −3.4421

1.8857 2.4343

1 0

0 0

0 1

4.5229

1.3647

1.9677

0

0

2.0742 2.8988 0.9853 3.1441 2.2587 1.0184 −0.3903 2.1569 1.6576 3.6889

−0.7092 1.8562 1.0761 8.8095 −1.0259 2.7380 0.6286 9.0087 1.0170 1.8734

1.1192 −7.4992 −0.7922 −2.7795 1.1465 −0.6745 −2.1988 −1.9935 −0.6775 0.9810

1.5296 1.2717 2.1471 1.9093 1.8263 1.8682 1.7357 1.4595 2.1373 1.5992

0 0 0 0 0 0 1 0 0 0

5.5590 6.8386 0.0537 −0.4637 1.0337 0.7314 −2.6941 2.2981 2.3134 3.2385 −1.9853 −3.4569 −0.0493 0.5796

1.7704 0.2796 2.6192 1.5724 0.5454 1.0667 0.2796 2.2409 2.6252 −1.6148 1.4606 1.6005 2.3927 2.6837

2.5439 4.2406 0.4945 0.4990 7.8069 −2.9405 −3.6165 −6.4669 3.2386 −5.3966 0.7763 −9.4780 −0.1003 −2.1510

0.0154 −0.1270 −1.2063 0.1272 −10.8970 2.1955 0.0061 1.5470 −3.8818 −0.1814 0.0206 −0.7527 0.5577 1.6454

3.3493

−4.0580

−0.1470

2.5398

0.0189 −20.0470 −45.8780 −16.8570 25.5500

5.7732 3.3391 3.0981 3.6361 2.6457

−0.4178 1.8327 −0.0961 8.4677 18.6260

5.9101 −1.0986 −0.8496 −0.9706 1.7823

2.2909 2.2245

−50.2210 −80.3930

4.2903 3.6282

−3.6610 2.0807

2.1728

−20.3130

5.1027

−5.1300

The log-transformation of the observed binding constant values.

X4

X5

X6

X11

X12

X13

X14

X15

1.8515 3.0399

37.9750 46.3080

−2.9250 4.7550

6.0370 24.0940

58.8810 −58.2570

0

−3.1573

33.0190

1.3290

−30.3300

−16.0790

4 0 0 2 0 2 2 0 0 0

0 1 0 0 0 0 1 3 0 3

0.7135 1.2080 0.1749 2.4723 −4.9343 −4.5113 −4.4965 −1.5630 1.4650 4.0762

43.6160 45.0970 28.3750 37.8550 36.7190 28.7920 41.7480 48.2680 36.0210 49.6780

−1.4220 0.9070 3.1080 −0.2870 −1.9410 −0.1560 0.3660 3.4010 −0.6920 −0.4910

25.0880 −3.4670 11.5980 11.4330 −0.1970 19.9980 −31.8410 16.6790 −6.4190 −46.2480

7.8040 9.4200 −21.8550 −30.9640 −22.2010 −51.8760 6.1620 −73.4990 −34.2630 −2.5750

1.6777 0 1.7353 5 1.4597 1 1.8666 3 1.8268 4 1.8088 0 1.7294 5 1.6052 0 2.2661 2 1.3220 10 2.3960 2 1.4934 0 1.4727 0 1.6340 1

0 0 2 0 4 2 0 0 0 0 0 3 0 0

1 1 2 1 2 0 1 0 0 3 0 2 3 0

2.2238 0.5004 −5.7258 −4.9135 −1.1247 −0.3201 1.1085 −5.9283 −0.1152 1.6055 1.5888 4.5983 −4.9067 −2.7105

35.7000 40.5980 46.5080 43.3810 53.4510 41.0990 40.8780 43.4210 41.7790 69.7660 20.2790 63.8910 56.9300 52.2470

−3.4990 0.1440 −1.3610 0.9680 5.4100 0.8110 1.7170 −0.6830 −4.1350 −0.9820 −1.9610 −0.0820 1.6080 0.8450

−12.8440 −1.7020 −13.0810 27.5540 −25.9020 43.9540 24.6280 −4.8190 0.2840 44.8360 −2.9200 −10.1630 26.9480 14.0020

69.2370 39.5200 −8.1150 −3.8200 −94.7010 25.6200 −41.0400 8.6130 71.4140 34.9640 14.4180 43.8020 −373.5000 −40.3600

1.7370

2.4613

0

1

0

2.4788

26.1580

0.1830

−2.2940

−40.4140

−12.5720 1.1992 0.7041 0.8176 1.0797

−1.4534 −3.0907 −0.1415 0.0035 0.0978

1.6020 1.7194 2.1365 2.1550 1.8732

0 1 0 0 1

0 2 2 2 0

0 1 1 1 0

3.9121 −4.5755 1.8796 1.3177 0.0000

67.2430 39.3980 23.9900 24.4110 0.0000

−1.4330 1.5410 −3.9120 −6.0900 −1.6570

11.6650 −31.9000 9.3960 −16.8780 −12.9070

−3.3710 4.3000 41.6830 48.1290 −79.5410

2.2143 1.3677

2.2827 3.8617

4.7893 −2.6702

2.3307 1.6767

0 0

0 8

0 0

1.9809 8.0321

36.1900 42.1940

0.4380 −2.3720

−8.4830 17.3650

−52.2950 −34.6180

2.7275

2.5304

−4.6968

1.7782

1

0

1

−4.3939

54.3740

7.1650

0.4690

2.6510

Reference Cirri et al. (2006) Chowdary and Reddy (2002) Chowdary and Nalluri (2000) Figueiras et al. (2007) Bernini et al. (2004) Ono et al. (1999) Kwaterczak et al. (2009) Chen et al. (2004) Csernák et al. (2006) Junquera et al. (1999) Becket et al. (1999) Li et al. (2002) Lahiani-Skiba et al. (2006) Vincieri et al. (1995) Borghetti et al. (2009) Csernák et al. (2006) Petralito et al. (2009) Loukas et al. (1997) Castillo et al. (1999) Banerjee et al. (2007) Rawat and Jain (2003) Tang et al. (2002) Haiyun et al. (2003) Junquera et al. (1999) Al Omari et al. (2006) Jarho et al. (2000) Tros de Ilarduya et al. (1998) ˜ de la Pena ˜ et al. Munoz (2007) Chen et al. (2004) Larrucea et al. (2002) Wei et al. (2003) Wei et al. (2003) Junquera and Aicart (1999) Veiga et al. (2001) Mukne and Nagarsenker (2004) Lin and Yang (1986)

H. Li et al. / European Journal of Pharmaceutical Sciences 42 (2011) 55–64

No

H. Li et al. / European Journal of Pharmaceutical Sciences 42 (2011) 55–64

59

Table 2 The correlation matrix of the fifteen selected parameters.

X1 X2 X3 X4 X5 X6 X7 X8 X9 X10 X11 X12 X13 X14 X15

X1

X2

X3

X4

X5

X6

X7

X8

X9

X10

X11

X12

X13

X14

X15

0.18 0.13 0.24 0.12 −0.10 −0.03 0.26 −0.39 0.12 −0.14 0.00 −0.13 −0.05 0.21

1 0.05 0.26 −0.05 0.11 −0.49 0.16 0.07 0.24 −0.08 0.71 −0.04 0.08 −0.02

1 −0.07 0.08 0.04 −0.16 0.02 0.05 0.12 −0.04 −0.12 −0.25 −0.12 0.13

1 0.18 0.23 −0.30 −0.22 −0.15 −0.20 0.11 0.32 −0.09 −0.02 −0.01

1 0.11 −0.04 0.01 0.01 −0.02 0.05 −0.10 0.08 −0.17 −0.06

1 −0.24 −0.20 0.15 −0.16 0.12 0.12 −0.25 −0.03 0.12

1 −0.13 −0.22 −0.37 0.11 −0.72 0.02 −0.08 −0.02

1 −0.21 0.26 −0.04 0.20 0.19 0.16 0.05

1 −0.03 0.29 0.08 −0.14 0.09 0.02

1 −0.10 0.42 0.19 −0.01 −0.17

1 −0.08 −0.15 0.03 0.13

1 0.10 0.12 −0.04

1 0.07 −0.58

1 −0.14

1

Fig. 1. Correlation between the predicted and the observed log K for a dataset of 86 drugs from the QSAR model (y = 1.00x + 0.00, R2 = 0.78).

3. Results and discussion 3.1. Quantitative structure–binding constant relationship For the dataset of 86 drugs and 103 structural parameters, fifteen parameters were obtained via the variable selection to develop the model (Table 1). As seen from the correlation matrix (Table 2), no significant correlations were found among the fifteen descriptors. The QSAR models for the entire dataset and the training set were represented by Eqs. (1) and (2), respectively. In Eq. (1), all of the selected descriptors were auto-scaled to a mean value of zero and a variance of one to ensure that all parameters had equal determinant strength to affect log K. The correlations between the predicted and the observed log K (entire dataset and training set) were shown in Figs. 1 and 2. Obviously, the QSAR models exhibited 2 relative desire predictive performance, with R2 > 0.75, QLOO ≥ 0.60, significant p values (<0.0001). log K

log K

=

=

Fig. 2. Correlation between the predicted and the observed log K for a dataset of 86 drugs from the QSAR model (training set: n = 64, y = 0.78x + 0.55, R2 = 0.78; test set: n = 22, R2 = 0.71; : training set, : test set).

where X1 is the cosmic electrostatic energy; X2 is the inertia moment 2 length; X3 is the dipole moment Y component; X4 is log P; X5 is the lipole Y component; X6 is the lipole Z component; X7 is the Balaban topological index; X8 is the group count for hydroxyl; X9 is the group count for chain c = n; X10 is the 6membered aliphatic rings; X11 is the VAMP polarization XY; X12 is the VAMP polarization YY; X13 is the VAMP dipole Y component; X14 is the VAMP quadpole XY; X15 is the VAMP octupole ZZY. 3.2. Regression diagnosis and applicability domain The multiple linear regression technique is based on four assumptions, which justify the rational use of linear regression for model development. They are (i) linear relationship between

−0.3882X1∗ + 0.1294X2∗ − 0.1236X3∗ + 0.5711X4∗ − 0.2232X5∗ − 0.3086X6∗ −0.6468X7∗ + 0.2656X8∗ − 0.2586X9∗ + 0.2321X10∗ + 0.1022X11∗ −0.6103X12∗ − 0.2204X13∗ − 0.1314X14∗ − 0.0024X15∗ + 2.4838 2 (N = 86, R2 = 0.78, QLOO = 0.67, RMSE = 0.44, F = 16.78, p < 0.0001)

(1)

−0.0148X1 + 0.0801X2 − 0.0384X3 + 0.4067X4 − 0.0452X5 − 0.0921X6 −1.2504X7 + 0.1718X8 − 0.1334X9 + 0.2914X10 + 0.0249X11 −0.0439X12 − 0.0583X13 − 0.0090X14 − 0.0012X15 + 5.0530 2 (N = 64, R2 = 0.78, QLOO = 0.60, RMSE = 0.47, F = 11.38, p < 0.0001)

(2)

60

H. Li et al. / European Journal of Pharmaceutical Sciences 42 (2011) 55–64

Fig. 3. Plot of residuals versus fitted values of log K.

dependent and independent variables, (ii) independence of the errors, (iii) homoscedasticity of the errors (constant variance) and (iv) normality of the error distribution. The points in Figs. 1 and 2 were randomly distributed around the diagonal line in the correlation plot, indicating the linearity between log K and independent variables. The Durbin–Watson coefficient of 2.025 was in the range of 1.5–2.5, meaning the data met the assumption of independent errors. In the plots of studentized residuals versus standardized predicted values (Fig. 3), the points seemed to be fluctuating randomly around zero in an un-patterned fashion, indicating the errors in the model were homoscedastic. As to the normal P–P plot (Probability–Probability plot, Fig. 4), the points clustered around a straight line, suggesting the error matched the normal distribution.

Fig. 4. Normal P–P plot of regression standardized residual for the QRAR model.

As shown in the Williams plot (Fig. 5), most of the drugs in the data set are within the applicable domain covered by ±3 times the standard residual and the leverage threshold (h* = 0.52), except for ketoconazole with hi value of 0.72. It is suggested that ketoconazole is structurally influential in the data set, probably because of the groups of dichlorophenyl in its structure. The standardized residuals of drugs in the data set are all smaller than three standard deviation units. Thus there are no outliers in the QSAR model for log K prediction.

Fig. 5. Williams plot of the QSAR model for log K prediction (the horizontal lines are the three standard deviation units and the vertical dotted line is the warning value of hat, h* = 0.52).

H. Li et al. / European Journal of Pharmaceutical Sciences 42 (2011) 55–64

Fig. 6. Coefficients plot of the fifteen selected molecular descriptors.

3.3. Important contributors affecting the drug-ˇ-cyclodextrin inclusion A set of fifteen parameters was chosen by feature selection to establish the QSAR model. This result suggested that these parameters have significant effects on the binding constant between drug and ␤-cyclodextrin, allowing for mechanistic interpretation of the model in part (Fig. 6). In general, these structural parameters of drugs represented the hydrophobicity, the van der Waals interaction, the capability to form hydrogen bonds and molecular shape, which were considered as the major types of interactions between drugs and ␤-cyclodextrins (Pérez-Garrido et al., 2009a). Drug ␤-cyclodextrin complexation usually involved the interaction between the hydrophobic moieties of drugs and the pocket of the cyclic cyclodextrin molecules. The hydrophobic effect played major role in the association of drugs and ␤-cyclodextrin. As expected, the stronger the hydrophobicity of drugs, the larger the binding constant. Especially, the coefficient of log P was 0.5711, the third largest and was positively correlated with log K (Eq. (1)), in a good agreement with the above considerations. The van der Waals interaction, the attractive forces of one transient dipole for another, was also an important interaction for the inclusion of drugs into cyclodextrins. The probability of forming substantial transient dipole interactions in the drug molecule would facilitate their complexation by ␤-CD. The parameters of the dipole moment Y component, the lipole Y component, the lipole Z component, the VAMP polarization XY, the VAMP polarization YY, the VAMP dipole Y component and the VAMP quadpole XY, the

61

VAMP octupole ZZY were also identified as significant descriptors in our model. For the capability to form hydrogen bonds, the drugs might be stabilized within the cavity by hydrogen bonding between drugs and cyclodextrins. The group count number of hydroxyl was selected in our model, positively correlated with log K, which was consistent with the expectation above. As for the molecular shape and flexibility, a certain degree of branching might be optimal for the inclusion. However, the excess branching would have a negative effect on the entrance of drugs into the cyclodextrin interior cavity. The connective index of Balaban topological index and the inertia moment 2 length were also chosen in the QSAR model. Moreover, cosmic electrostatic energy, 6-membered aliphatic rings and the group count for chain c = n were also selected simultaneously as contributors in the QSAR model to log K prediction. As described above, the QSAR model in our study is useful not only in predicting the binding constants of drug molecules with ␤cyclodextrin, but also in elucidating the important driving forces for cyclodextrin complexation of drug molecules. In summary, the driving forces include the hydrophobic interaction, the electrostatic interaction, van der Waals interaction and hydrogen bonding. It is reported that the van der Waals interaction and hydrophobic interaction are major driving forces for cyclodextrin complex formation, and electrostatic interaction and hydrogen bonding can significantly affect the conformation of a particular inclusion complex (Liu and Guo, 2002). According to the QSAR model, the process of complex formation is hypothesized and divided into two stages, which is helpful in understanding the complexation mechanism (Fig. 7). Firstly, high-energy water molecules in the cavity of the cyclodextrins were displaced by the hydrophobic drug molecules with suitable shape and flexibility prompted by the hydrophobic interaction and van der Waals interaction, named as complex formation stage. Then, the binding and dissociation equilibrium of the complexation is established and maintained by the electrostatic interaction and hydrogen bonding, named as the complex stabilization stage. Consequently, the binding constants of drug molecules with ␤-cyclodextrins are determined by all of these forces. And the hypothesis proposed above is needed to validate by the molecular simulation technique in our further work. 3.4. The ˇ-CD binding behavior comparison between drug molecules and organic compounds A data set of 233 molecules from the published model (Pérez-Garrido et al., 2009a) was built with the method

Fig. 7. Hypothetical complexation process of drug molecules with cyclodextrins.

62

H. Li et al. / European Journal of Pharmaceutical Sciences 42 (2011) 55–64

Fig. 8. The score plot of principal component analysis with 86 drugs in our model and 229 compounds in the literature (the black triangle: dataset of 86 drugs; the red square: dataset of 229 compounds). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.)

described in Section 2.1. The CAS register numbers of three compounds (2-Norbornaneacetate, 3-n-propylphenyl acetate and 3-n-butylphenyl acetate) were not given in the paper. The calculated information of 1-Adamantaneacetate could not be found in SciFinder Scholar database. Therefore, the comparison was carried out between the 86 drug molecules and the 229 organic compounds in the literature. Then, the position of these two datasets in the chemical space was compared through the score plot of the principal component analysis (PCA). Finally, the QSAR models of these two datasets were also developed and compared. In the score plot of the PCA (Fig. 8), the datasets of 86 drugs in our model and 229 organic compounds in the literature were obviously clustered into two categories. The positions of these two datasets in the chemical space were quite different, indicating the structural characteristics of them were distinct. The interactions of guest molecules with ␤-CD were sourced to the structural characteristics of the guest molecule themselves. Therefore, the binding behavior of drug molecules with ␤-CD should differ from that of organic compounds. The QSAR models of the dataset with 229 compounds were built by the method described in Section 2. 22 structural parameters were selected. The R2 and Q2 values were 0.79 and 0.74, respectively. For the model of 229 compounds, the most important parameters were log P, 5-membered aliphatic rings, VAMP HOMO, number of H-bond acceptors and 6-membered rings, representing the hydrophobicity, molecular shape, molecular reactivity and the capability to form hydrogen bonds, respectively. The most important parameters in our model based on 86 drugs were balaban topological index, VAMP polarization YY, log P, cosmic electrostatic energy and lipole Z component, representing the molecular shape, the van der Waals interaction, the hydrophobicity and the electrostatic interaction, respectively. Therefore, the important contributors for these two QSAR models were different. When the independent variables were exchanged for the two QSAR models, the results got worse. The R2 and Q2 values of the QSAR model based on 229 organic compounds and 15 structural parameters were 0.68 and 0.62, respectively. The R2 and Q2 values of the QSAR model based on 86 drugs and 22 structural parameters were 0.50 and 0.11, respectively. In summary, not only the chemical space position, but also the important contributors of the QSAR models for 86 drugs and 229 organic compounds were different. It was suggested that the bind-

ing behavior of the drug molecules with ␤-CD should differ from that of the organic compounds. 3.5. Model limitation One obvious weakness of the present model is the scarcity of the data used in the study. The size of dataset (64 for training set and 22 for test set) may not be large enough to evaluate the generalization ability of the predictive model. Therefore, the leave-one-out and test set validation procedures have been employed. A furthermore shortcoming of the study lies in the skew distribution of the observed log K values in the entire dataset. As shown in Table 1, the binding constant values of 81 drugs in the dataset (94%) were above ten (log K > 1). However, only five drugs (6%) have the binding constant below ten (log K < 1), which result in the relative lower values of R2 compared to the QSAR models for organic compounds in the literature (Pérez-Garrido et al., 2009a,b; Chari et al., 2009). The reason may be that the reported binding constant values are derived from the poorly soluble drugs, which are always hydrophobic and with strong binding tendency to be included into the hydrophobic cavity of ␤-CD. Thus, most of the binding constants collected from the reported literature are large as described above. A larger dataset, composed of drugs with uniform distribution of log K, is necessary for further validating the QSAR approach in the prediction of the binding constant between drugs and cyclodextrins. 4. Conclusions Focused on the specific domain of drug molecules in the chemical space, the QSAR model for a data set of 86 poorly soluble drugs was developed successfully to predict the binding constant between drugs and ␤-cyclodextrin. The exhaustive statistical diagnoses demonstrated the QSAR model was robust and satisfied the prerequisites of regression models. The parameters of log P, Balaban topological index, cosmic electrostatic energy, VAMP polarization YY and VAMP dipole Y component were identified as the five important structural parameters influencing the binding constant between drugs and ␤-cyclodextrin. In addition, the chemical space position and important contributors were compared between drug molecules and organic compounds. It was suggested that the binding behavior of the drug

H. Li et al. / European Journal of Pharmaceutical Sciences 42 (2011) 55–64

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