characterization of the interaction of 2-hydroxypropyl-β-cyclodextrin with itraconazole at ph 2, 4,...

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Characterization of the Interaction of 2-Hydroxypropyl-b- cyclodextrin With Itraconazole at pH 2, 4, and 7 JEF PEETERS, 1 PETER NEESKENS, 1 JAN P. TOLLENAERE, 2 PIETER VAN REMOORTERE, 1 MARCUS E. BREWSTER 1 1 Department of Drug Delivery Research, Johnson & Johnson Pharmaceutical Research and Development, Beerse 2340, Belgium 2 Department of Molecular Design & Chemoinformatics, Johnson & Johnson Pharmaceutical Research and Development, Beerse 2340, Belgium Received 28 August 2001; revised 13 December 2001; accepted 16 January 2002 ABSTRACT: Phase-solubility techniques were used to assess the effect of pH on itraco- nazole complexation with 2-hydroxypropyl-b-cyclodextrin (HPbCD). In addition, molecular modeling using b-cyclodextrin as a surrogate for HPbCD was completed. Data suggested A p -type solubility relationships, indicating higher order complexation at higher HPbCD concentrations. Stability constants were derived from the solubility isotherms using a simplex optimization procedure. At pH 2 (2 units below the pK a4 ), a 1:2 complex formation was observed, whereas at pH 4 (i.e., the pK a4 for itraconazole) and at pH 7, 1:3 complexation occurred. The lower order of complexation observed at lower pH may be related to substructure protonation which reduced HPbCD interaction. Molecular mechanics also suggest 1:3 complex formation for the neutral species, indicating that possible interaction sites may include (in order of binding) triazole > 1,4- diaminophenyl > 2-butyl piperazine. ß 2002 Wiley-Liss, Inc. and the American Pharma- ceutical Association J Pharm Sci 91:1414–1422, 2002 Keywords: itraconazole; solubility; cyclodextrin; complexation; calculation or stabil- ity constants INTRODUCTION Itraconazole (Sporanox 1 ) is a useful broad- spectrum triazole antifungal agent that has gained widespread acceptance. 1 The antimycotic agent has demonstrated in vitro activity aga- inst Candida albicans, as well as nonalbicans Candida sp., Cryptococcus neoformans, a number of dimorphic fungi, and several molds such as Aspergillus sp. This broad spectrum in activity is noteworthy because itraconazole is the only orally bioavailable antifungal agent to be useful in both the treatment of Candida sp. and Asper- gillus sp., the two most commonly occurring fungal pathogens. 2 Physicochemically, itraconazole can be charac- terized as a very poorly water soluble, weak base. The aqueous solubility of the compound is esti- mated at 1 ng/mL at neutral pH and 4 mg/mL at pH 1. The pK a4 was determined to be 4 using both potentiometric and spectrophotometric ap- proaches. Determination were made in aqueous methanol and extrapolated to 100% water to pro- vide the reported value. The pK a3 has not been measured but is estimated at 1.5–2, and the other 1414 JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 91, NO. 6, JUNE 2002 Correspondence to: Marcus E. Brewster (Telephone: 32-14- 603157; Fax: 32-14-607083; E-mail: [email protected]) Journal of Pharmaceutical Sciences, Vol. 91, 1414–1422 (2002) ß 2002 Wiley-Liss, Inc. and the American Pharmaceutical Association

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Characterization of the Interaction of 2-Hydroxypropyl-b-cyclodextrin With Itraconazole at pH 2, 4, and 7

JEF PEETERS,1 PETER NEESKENS,1 JAN P. TOLLENAERE,2 PIETER VAN REMOORTERE,1 MARCUS E. BREWSTER1

1Department of Drug Delivery Research, Johnson & Johnson Pharmaceutical Research and Development,Beerse 2340, Belgium

2Department of Molecular Design & Chemoinformatics, Johnson & Johnson Pharmaceutical Researchand Development, Beerse 2340, Belgium

Received 28 August 2001; revised 13 December 2001; accepted 16 January 2002

ABSTRACT: Phase-solubility techniques were used to assess the effect of pH on itraco-nazole complexation with 2-hydroxypropyl-b-cyclodextrin (HPbCD). In addition,molecular modeling using b-cyclodextrin as a surrogate for HPbCD was completed.Data suggested Ap-type solubility relationships, indicating higher order complexationat higher HPbCD concentrations. Stability constants were derived from the solubilityisotherms using a simplex optimization procedure. At pH 2 (2 units below the pKa4),a 1:2 complex formation was observed, whereas at pH 4 (i.e., the pKa4 for itraconazole)and at pH 7, 1:3 complexation occurred. The lower order of complexation observed atlower pH may be related to substructure protonation which reduced HPbCD interaction.Molecular mechanics also suggest 1:3 complex formation for the neutral species,indicating that possible interaction sites may include (in order of binding) triazole > 1,4-diaminophenyl > 2-butyl �� piperazine. � 2002 Wiley-Liss, Inc. and the American Pharma-

ceutical Association J Pharm Sci 91:1414–1422, 2002

Keywords: itraconazole; solubility; cyclodextrin; complexation; calculation or stabil-ity constants

INTRODUCTION

Itraconazole (Sporanox1) is a useful broad-spectrum triazole antifungal agent that hasgained widespread acceptance.1 The antimycoticagent has demonstrated in vitro activity aga-inst Candida albicans, as well as nonalbicansCandida sp., Cryptococcus neoformans, a numberof dimorphic fungi, and several molds such asAspergillus sp. This broad spectrum in activity isnoteworthy because itraconazole is the only orallybioavailable antifungal agent to be useful inboth the treatment of Candida sp. and Asper-gillus sp., the two most commonly occurringfungal pathogens.2

Physicochemically, itraconazole can be charac-terized as a very poorly water soluble, weak base.The aqueous solubility of the compound is esti-mated at �1 ng/mL at neutral pH and �4 mg/mLat pH 1. The pKa4 was determined to be 4 usingboth potentiometric and spectrophotometric ap-proaches. Determination were made in aqueousmethanol and extrapolated to 100% water to pro-vide the reported value. The pKa3 has not beenmeasured but is estimated at 1.5–2, and the other

1414 JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 91, NO. 6, JUNE 2002

Correspondence to: Marcus E. Brewster (Telephone: 32-14-603157; Fax: 32-14-607083; E-mail: [email protected])

Journal of Pharmaceutical Sciences, Vol. 91, 1414–1422 (2002)� 2002 Wiley-Liss, Inc. and the American Pharmaceutical Association

ionizable nitrogens are not protonated (i.e., thepKa1 and pKa2) in the 2–10 pH range. Otherrelevant data include the melting point, whichis 165–1698C, and the log P, which could not bemeasured using a simple shake flask method(i.e., > 5). The calculated log P (C log P) is 6.2. Thisinformation as well as permeability and oralbioavailability data confirmed that itraconazolecould be classified as a BCS (SUPAC) type IIcompound (i.e., poorly soluble but gastrointestinal[GI] permeable).3–5 This classification is con-sistent with the absence of significant exposurewhen itraconazole is dosed orally in simple cap-sules and non-optimized formulations.

The first commercialized oral dosage form wasdeveloped using a novel solid solution technologyin which the drug and hydroxypropylmethylcel-lulose in a solvent are sprayed on an inert sugarsphere in a closed Wurster process.6 After dryingand capsule filling of the beads, itraconazole ispresent in a molecularly dispersed solid solutionthat dissolves to give a supersaturated solution ofthe drug in the stomach.7 The supersaturatedsolution is sufficiently stable to allow for signifi-cant absorption and bioavailability. This formula-tion has become the mainstay for treatment ofonychomycosis and tinea infections.1

Although the bead-based capsules are highlyuseful, especially for the treatment of superficialfungal maladies and disseminated infections, thetreatment of certain subpopulations necessitat-ed the development of improved dosage forms.8,9

Given the solubility and pKa of the itraconazole,the pH of the stomach must be sufficiently lowto allow for drug dissolution; that is, those con-ditions that favor low pH in the stomach willimprove bioavailability.10 Thus, administration ofan itraconazole capsule with food (where gastricsecretion is stimulated) or with an acidic bever-age (cola) favor good absorption.11,12 In patientssuffering from AIDS, hypochlorhydria is a com-mon complication.13 The reduced acid secretionis correlated with poorer oral bioavailability ofitraconazole from the marketed capsule formula-tion.14,15 In cancer patients, the use of chemother-apeutic agents often damages the GI tract,causing mucositis and thereby possibly affect-ing drug absorption. Similarly, patients receivingautologous bone marrow transplants can expe-rience graft-versus-host gut disease.1 Finally,patients may be cachexic and not able to takesolid food. To address these and other issues, twoaqueous formulations for itraconazole (an oralsolution and intravenous [iv] product) were devel-

oped through the use of cyclodextrin complexationwith 2-hydroxypropyl-b-cyclodextrin (HPbCD),which was chosen as the functional excipi-ent.1,2,8,9,16 Cyclodextrin solutions offer severaladvantages. Because itraconazole is effectivelysolubilized, it is immediately available, and thephase-to-phase transition, which limits bioavail-ability, is eliminated.16 In addition, the acidity ofthe stomach should not affect the oral bioavail-ability and, in fact, the dosage form should bemore effective on an empty stomach.17 Finallycyclodextrin solutions allow for safe iv treatment,which is desired in a number of situations in-cluding the treatment of life-threatening disse-minated fungal infection as well as in therapyinitiation (i.e., in dose loading) to reduce the timeto steady state.1,8,9 The selected cyclodextrin,HPbCD, is a safe and well tolerated excipient andeffects drug solubilization through the formationof dynamic (noncovalent) complex formation.18–21

Itraconazole solubilized in an HPbCD aqueoussolution was found to be effective in both precli-nical pharmacology studies as well as in numer-ous clinical trials.1,8,9 Formulations designedalong these lines were developed, approved bythe Food and Drug Administration and variousEuropean agencies, and have been marketed. Theoral product was approved in the United Statesin February of 1997 and the iv product in Marchof 1999.

To design in vitro models to study the in vitroand in vivo behavior of these HPbCD -basedsolutions, the phase solubility relationship of cry-stalline itraconazole was examined at three pHvalues (2, 4, and 7). In addition to information ondilution behavior and physical solution stability,

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this pH range was intended to give insight tochanges that occurred to the formulation on GItransit as well as the effect of ionization oncomplexation.

EXPERIMENTAL SECTION

Materials

2-Hydroxypropyl-b-cyclodextrin (HPbCD) was ob-tained from Roquette (France) and was character-ized by a degree of substitution of 4.2 based on aFourier transform infrared spectroscopy (FTIR)method. Crystalline itraconazole was obtainedfrom the Janssen Research Foundation (JRF).

Phase-Solubility Experiments

Complexes were prepared by first sonicating anexcess of itraconazole in various concentrationsof aqueous HPbCD ranging from 0 to 35–40% w/vprepared in three unbuffered system (pH 7, pH 4,and pH 2 [pH was adjusted with HCl]). After10 min of sonication, the systems were shakenfor 2 days, at which time the pH was checked andadjusted as necessary. The samples were thenequilibrated for 3–6 months at 258C with itra-conazole concentrations measured at 6 days,2 weeks, 4 weeks, 3 months, and/or 6 months.At the appropriate time point, a small volumeof the supernatant was withdrawn and filteredthrough a 0.45 mm polyvinylidene difluoridemembrane (Nihon Millipore). Samples were thendiluted with 0.01 N HCl and analyzed by ultra-violet (UV) spectrophotometry (at 254 nm) with aHewlett Packard 8451B diode array spectrophot-ometer. The chemical stability of itraconazole wasconfirmed over the storage time by high-perfor-mance liquid chromatography (HPLC). The sys-tems configuration included a Varian LC 9010solvent pump, a Varian 9096 autosampler fittedwith a 10-mL sample loop, and a Varian 9065Polychrom diode array detector (for itraconazole,l¼ 268 nm) connected to a Compac Descpro PC.Samples were eluted on an RP 18 Hypersil ODScolumn (10 cm� 4.0 mm i.d., 3-mm particle size)using a flow rate of 1.6 mL/min and a mobilephase composition of ammonium acetate (0.5%):methanol:acetonitrile (35:14:51). Dibutyl phtha-late served as the internal standard. Under theseconditions, the retention time of itraconazole was4.0 min and that for the internal standard was4.62 min.

Determination of Stability Constants

The relationship between solubilizer and drugwas analyzed using the phase-solubility approachdescribed by Higuchi and Connors.22 In thisapproach, the total concentration of cyclodextrinis the sum of the free cyclodextrin concentrationplus all cyclodextrin associated with drug com-plexes such that for 1:1, 1:2, and 1:3 complexes,[CD]TOTAL is, respectively,

½CD�TOTAL ¼ ½CD� þ SoK1:1½CD� ð1Þ

½CD�TOTAL ¼ ½CD� þ SoK1:1½CD�þ 2SoK1:1K1:2½CD�2 ð2Þ

½CD�TOTAL ¼ ½CD� þ SoK1:1½CD� þ 2SoK1:1K1:2½CD�2

þ 3SoK1:1K1:2K1:3½CD�3 ð3Þ

The total drug concentration for the threerespective drug complexes is given by the follow-ing three expressions:

STOTAL ¼ Soð1 þ K1:1½CD�Þ ð4Þ

STOTAL ¼ Soð1 þ K1:1½CD� þ K1:1K1:2½CD�2Þ ð5Þ

STOTAL ¼ Soð1 þ K1:1½CD� þ K1:1K1:2½CD�2

þ K1:1K1:2K1:3½CD�3Þ ð6Þ

where K1:1, K1:2, and K1:3 are the stabilityconstants associated with drug–cyclodextrincomplex, the drug–2(cyclodextrin), and drug–3(cyclodextrin) species, and So is the solubilityof the drug in the absence of cyclodextrin. Thecalculation of the free [CD] concentration isstraightforward for 1:1 complexes and can bederived from the quadratic relationship developedby Higuchi and Kristiansen for 1:2 complexes.23

For 1:3 and higher order systems, a simplexoptimization procedure was applied.24 In theapproach used, trial values of the stabilityconstants (Ks) are first obtained by numericallyfitting a third-order polynomial using the totalHPbCD concentration as the independent vari-able. The rough estimates are then used to calcu-late the solubility of itraconazole as a function ofHPbCD concentration as well as the concentra-tion of free cyclodextrin at each solubility pointusing an exact solution to the equation. Thedifferences between the calculated solubility andthe experimentally derived data were then mini-mized by varying the values of the three stability

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constants using a nonlinear optimization tech-nique (the iterative approach of Nelder–Meadbased on an IBM-implemented APL program)based on least-square regression.24 Analysis ofthe residuals between calculated and experimen-tal solubility data were then used to assess modelfitness.

Molecular Mechanics

The X-ray crystal structures of itraconazole andb-cyclodextrin (the model compound for HPbCD)were used as input structures for the molecularmechanics minimization calculations. The Bio-sym CVFF force field (Insight version 2.3.5) wasused without cross-terms and with a dielectricconstant of e¼ 1. All structures were minimizedusing a conjugate gradient optimization proce-dure until a root mean square (rms) value of 0.001kcal/AA was obtained.25 The starting structuresof the complex were constructed manually in sucha way that the centers of mass of the cyclodextrinand itraconazole were separated by 6 A, therebyallowing an unbiased approach during the mini-mization. The interaction energy between the

cyclodextrin and itraconazole molecules werecalculated based on the following equation:

��E ¼ �Ecomplex � ð�Ecyclodextrin þ �EitraconazoleÞð7Þ

where �Ecomplex, �Ecyclodextrin, and �Eitraconazole

are the energies for the complex of b-cyclodextrinand itraconazole, respectively. �Eitraconazole wascalculated as 215.8 kcal/mol and �Ecyclodextrin as198.6 kcal/mol.

RESULTS AND DISCUSSION

Itraconazole is a weak base with four possibleionizable nitrogens in its structure. In solution,protonated forms are in equilibrium with non-protonated structures, with the relative fractionsof each species dependent on the pKa of theionizable nitrogens and the ambient pH. Itraco-nazole or its various protonated forms can inter-act with cyclodextrins giving rise to complexationof various orders (i.e., 1:1, 1:2, 1:3, etc.). Thesepossibilities can give rise to complicated equili-bria, as illustrated in Scheme 1.26–28 In addition,it is possible that cyclodextrins may interact at

Scheme 1. Equilibrium constants for the complexation of HP-b-CD with variousunprotonated and protonated forms of itraconazole.

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various binding sites in the itraconazole molecule,producing a large number of microconstants.The interaction of itraconazole with HPbCDat three pH values and at various equilibrationtimes was evaluated using phase-solubilityanalysis (Figures 1–3). Qualitative assessmentof relationships indicate a curvilinear dependenceof solubility on solubilizer concentration indicat-ing Ap type behavior for all systems studied.22

This result suggests higher order cyclodextrincomplexation at higher cyclodextrin concentra-tions, which is consistent with Scheme 1. Inaddition, the synergistic manner in which cyclo-dextrins and pH adjustment affect solubility isevident. In the absence of HPbCD, the solubilityof itraconazole is very low (< 1 mg/mL) at pHvalues> 1. In the presence of HPbCD (e.g., 35%w/v), solubility increases with decreasing pH,such that at pH 7, 4, and 2, concentrations of

1.45, 2.21, and 4.00 mg/mL itraconazole, respec-tively, were obtained. These interaction are wellrecognized, and a theoretical basis for thesesynergies has recently been suggested.29–31

Analysis of the phase-solubility data requiredextraction of stability constant information. Assuggested by Higuchi and Connors, the totalamount of drug (STOTAL) in a cyclodextrin-containing solution can be described by eqs. 8and 9 for second and third order complexes,respectively:22

STOTAL ¼ So þ K1:1So½CD� þ K1:1K1:2So½CD�2

ð8Þ

STOTAL ¼So þ K1:1So½CD� þ K1:1K1:2So½CD�2

þ K1:1K1:2K1:3So½CD�3 ð9Þ

Initial curve fitting used simple polynomials tosuggest the order of complexation as a function ofpH; that is, [CDTOTAL] was used as an estimate of[CD]. This approach indicated that a second-orderequation best fit the pH 2 data, whereas third-order models most appropriately described the pH4 and 7 data. Use of the simple polynomial toestimate the stability constants was not possible,however, because plotting total [CD] concentra-tion as a function of total drug concentrationsignificantly overestimated the concentration offree [CD] in solution, leading to systematic errorsin the calculated stability constants (Figure 4).Higuchi and Kristiansen calculated free ligandconcentrations with a modified quadratic equa-tion based on known values of the total drug

Figure 1. Solubility of crystalline itraconazole atpH 2 as a function of HPbCD concentration after vari-ous storage times at 258C.

Figure 2. Solubility of crystalline itraconazole atpH 4 as a function of HPbCD concentration after vari-ous storage times at 258C.

Figure 3. Solubility of crystalline itraconazole atpH 7 as a function of HPbCD concentration after vari-ous storage times at 258C.

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and total ligand concentration.23 Using theseestimates as new trial values, the K values wereobtained by a least-squares optimization ap-proach. This approach has been widely used forthe estimation of stability constants, includingthose related to cyclosporin A and other materi-als.32,33 Although these paradigms allowed for thecalculation of K1:1 and K1:2 values, the determina-tion of higher order complexes is not possible withthis formalism. To overcome these limitations, aNelder–Mead nonlinear optimization approachwas developed to fit the phase-solubility data (seeExperimental Section). This procedure as well asthe approach of Higuchi and Kristiansen wereapplied to the phase-solubility data presented inFigures 1–3. As suggested by simple polynomialcurve fitting, the quadratic model (which assumessecond-order complexation) was applicable tophase-solubility data obtained at pH 2 with datacollected in Table 1. This result is consistent withthe finding published by Miyake et al.33,34 On theother hand, use of this model for the higher pH

systems was not appropriate and gave rise tonegative stability constants. Data derived fromthe third-order model for the pH 4 and pH 7equilibration media are given in Tables 2 and 3,respectively. Assessment of higher order comple-xation processes gave rise to poorer correlations.

The data obtained at pH 2 (Table 1) indicatedthat equilibrium was established by week 4,as suggested by the stability of the calculatedconstants. Deviation of predicted and experimen-tal data was small, with errors < 0.3 mg/mL. Forthe pH 4 data (Table 2), equilibrium was rapidlyestablished and the model fit the data well, assuggested by a plot of the residuals derived fromcalculated and determined solubility values (witha range of 0 to 0.12 mg/mL). Finally, equilibrationof the pH 7 system (Table 3) was also more rapidthan the pH 2 samples, with good reproducibilityobserved after 2 weeks, and with stability con-stants at 4 weeks, 3 months, and 6 months beingessentially the same. Residuals obtained fromexperimentally derived and calculated drug solu-bilities were small and within the range of 0 to0.06 mg/mL, suggesting that the model describedthe data well.

The data also suggest that the nature of thecomplex may change as a function of ionization.At pH 7, the compound is essentially un-ionized,indicating that only the first line of Scheme 1should apply (Figure 5). In this instance, the K1:1

term seems to dominate for the 1:3 complex. At pH4, half of the species in solution should representun-ionized itraconazole and half the singly proto-nated compound. At this pH, a 1:3 complex is

Table 3. Calculated Stability Constants forCrystalline Itraconazole/HPbCD (pH 7)

Time K1:1 (M�1) K1:2 (M�1) K1:3 (M�1)

6 Days 1926 1 2612 Weeks 1654 13 124 Weeks 2105 9 163 Months 2318 6 216 Months 2035 8 19

Table 2. Calculated Stability Constants forCrystalline Itraconazole/HPbCD (pH 4)

Time K1:1 (M�1) K1:2 (M�1) K1:3 (M�1)

7 Days 15 2504 1216 Days 20 910 346 Days 16 1064 333 Months 20 2659 7

Figure 4. Error associated with the prediction ofdrug concentration based on the use of total HPbCDconcentration ([CD]TOTAL) versus the use of the freeHPbCD concentration ([CD]). These differences givesystemic errors of �20–30% in the calculation ofstability constants.

Table 1. Calculated Stability Constants forCrystalline Itraconazole/HPbCD (pH 2)

Time K1:1 (M�1) K1:2 (M�1)

6 Days 5280 382 Weeks 10354 204 Weeks 9895 233 Months 8744 276 Months 8929 27

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favored, with the K1:2 being the dominant term.At pH 2, itraconazole exists as roughly equalportions of the singly and doubly protonated form.At this pH, a 1:2 complex is preferably formedand, similar to the pH 7 data, the K1:1 is thedominant term. The decrease in complex orderfor a weak base as the pH is reduced has beenobserved in other systems. Johnson et al., forexample, found that for the protease inhibitorkynostatin, the order of complexation was re-duced from 1:2 to 1:1 as the pH dropped.35 In thatcase, the protonation of an accessible isoquinolinefunction eliminated a binding site on the moleculebecause cyclodextrin interaction is far less favor-able for ionized groups than neutral species. Inaddition, the increased importance of the K1:2

term at pHs> 2 was suggested by the work ofMiyake et al.33 In their study on the interaction ofHPbCD with cyclodextrin at pH 2, an increasingpH was associated with a decrease in the K1:1

term and an increase in the K1:2 value. This resultwas interpreted as a stronger binding of itraco-nazole to a second HPbCD molecule subsequentto deprotonation of the singly protonated species.

These experimental results were also viewedin a theoretical framework in which molecularmechanics were used to assess complex order. Theinteraction of b-cyclodextrin (which was used as amodel for HPbCD) with itraconazole was investi-gated to determine the energy of binding as wellas the favored interaction sites. Calculations on1:1 complexes indicated that the most stable

species was one in which the triazole interactedwith the wider surface of the b-cyclodextrin torus(��E¼ 45.4 kcal/mol). Interaction with the oppo-site end of the molecule and particularly withthe 2-butyl moiety is energetically less favorableby about 9 kcal/mol. For the 1:2 complex, theinteraction between b-cyclodextrin and the tria-zole function remained and a second cyclodextrinwas found to interact with the 1,4-diaminophenylring adjacent to the triazolone function (��E¼90.63 kcal/mol). In addition to the hydrophobicinteraction between the phenyl group and thecyclodextrin cavity, this complex is also stabilizedby a hydrogen bond between the two cyclodextrinrings. Optimization of a 1:3 complex gave rise totwo complexes that were almost degenerate. Inthese two systems, the cyclodextrin nuclei wereassociated with both the triazole and the phenylfunction as in the 1:2 complex. The third cyclo-dextrin interacted with either the 2-butyl group(Figure 6, ��E¼ 129.9 kcal/mol) of the triazoloneor with the piperazine (��E¼ 133.9 kcal/mol). Inthe case of the 2-butyl interaction, five hydrogenbonds to the adjacent cyclodextrin stabilize thecomplex, whereas for the piperazine systems, thecomplex is stabilized by hydrogen bonding tothe piperazine nitrogen as well as the adjacentcyclodextrin. Higher order complexes (1:4 and 1:5)gave negative ��E values, indicating that thesesystems were not stable, presumably due to stericinteraction. Given the usual caveats for gasphase-based calculations and the hyperdimen-sionality of the minimization problem,25 thesedata are useful in the interpretation of the phase-solubility data. At low pH, the triazole functionis at least partially protonated, reducing thetendency of this substructure to interact withHPbCD and reducing the total number of bind-ing sites on the itraconazole scaffold. As the pHincrease, the triazole deprotonates, allowing this

Figure 5. Relative proportions of itraconazole, singlyprotonated itraconazole, and doubly protonated itra-conazole as a function of pH.

Figure 6. Representation of a 1:3 complex betweenitraconazole and b-cyclodextrin.

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moiety to participate in complexation and in-creasing the complex order. As noted, the fact thatdeprotonation allows CD interaction with theenergetically most favorable binding site (basedon the molecular mechanics simulation), the mag-nitude of the K1:2 term is larger at pH 4 than atpH 2. At pH 7, itraconazole is essentially unchar-ged and forms 1:3 complexes with a dominate K1:1

term (because there is no competition betweenprotonation and complexation and because thetriazole is the most stable binding site).

CONCLUSIONS

The solubility of itraconazole as a function ofHPbCD concentration at pH 4 and 7 was bestdescribed by a third-order complexation model,whereas data obtained in pH 2 media could bestbe fitted to a second-order equation. Importantly,the equilibria for such systems is complex, withnumerous interactions. Ionization affects cyclo-dextrin complexation, but cyclodextrin comple-xation also affects ionization. For example, a500-fold molar excess of HPbCD reduces thepKa4 of itraconazole from 4.0 to 3.0 (i.e., thepKa4, in Scheme 1). Furthermore, stability con-stants obtained by simplex optimization are notunique mathematical solutions because they arethe result of the minimization of the square ofthe residuals. Other solutions, and hence othervalues, for the stability constants are indeedpossible. It is therefore better to use these datasemiempirically to describe and predict behaviorof cyclodextrin complexes in solution and changesderived there from. Also, the stability constantsshould be evaluated as composite values becausea number of processes are included in their mag-nitude. From the data presented, pH is clearlyan important factor. Solubility of itraconazoleincreases with decreasing pH, as would be expec-ted from the pKa of the compound, and the natureof the interaction changes in different pH media(such that K1:1 term predominates at neutralpH and at pH 2, whereas the K1:2 term dominatesat a pH of 4). These factors argue for strict appli-cation of stability constants to those conditionsfrom which they were derived.

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