Preparation and Characterization of Inclusion Complexes of a Hemisuccinate Ester Prodrug of Δ<Superscript>9</Superscript>-Tetrahydrocannabinol with Modified Beta-Cyclodextrins

Δ⁹-Tetrahydrocannabinol hemisuccinate (THC-HS), an ester prodrug of Δ⁹-tetrahydrocannabinol (THC) has been investigated for its potential to form inclusion complexes with modified synthetic beta-cyclodextrins (CDs). Phase solubility studies were performed to determine the stoichiometric ratio of complexation of THC-HS with random methylated beta-cyclodextrin (RAMEB) and 2-hydroxypropyl beta-cyclodextrin (HPBCD). THC-HS/RAMEB and THC-HS/HPBCD solid systems were prepared by lyophilization and the lyophilized complexes were characterized by Fourier transform infrared (FT-IR) spectroscopy, proton nuclear magnetic spectroscopy, and molecular modeling techniques. The formation of inclusion complexes of THC-HS/RAMEB and THC-HS/HPBCD was demonstrated by an A_L type curve with the slopes less than unity by the phase solubility method. The association constants for THC-HS/RAMEB and THC-HS/HPBCD were found to be 562.48 and 238.83 M⁻¹, respectively. The stoichiometry of both of the complexes was found to be 1:1 as determined from the Job's plot. This was confirmed by ¹H NMR and FT-IR techniques. The results obtained from the molecular modeling studies were in accordance with the data obtained from nuclear magnetic resonance and FT-IR. The docking studies revealed the most probable mode of binding of THC-HS with RAMEB in which the alkyl chain was submerged in the hydrophobic pocket of the CD molecule and hydrogen bonding interactions were observed between the hemisuccinate ester side chain of THC-HS and the rim hydroxy groups of RAMEB. The solubility of THC-HS was significantly higher in RAMEB compared to HPBCD. Solid dispersions of THC-HS with CDs will be further utilized to develop oral formulations of THC-HS with enhanced bioavailability.     

Solubility of cyclomaltooligosaccharides (cyclodextrins) in H2O and D2O: a comparative study

Cyclomaltooligosaccharides (cyclodextrins, CDs) are cyclic oligomers having six, seven, or eight units of alpha-D-glucose, named as cyclomaltohexaose (alpha-CD), cyclomaltoheptaose (beta-CD) and cyclomaltooctaose (gamma-CD), respectively. The molecule of CD has a cavity in which the interior is hydrophobic relative to its outer surface. The solubility of cyclodextrins in water is unusual, as an irregular trend is observed in the series of the cyclic oligomers of glucose. beta-CD is at least nine times less soluble than the others CDs. This intriguing behavior has been investigated, and some interesting explanations in terms of the effect caused by CD on the water lattice structure have been proposed. In this work a comparative study on the solubility of alpha, beta, and gamma-cyclodextrins was carried out in H2O and D2O and reveals a much lower solubility of the three CDs in D2O. The solid-phase structure of the CDs in equilibrium with the solution is quite similar with both solvents. The results are discussed in terms of the CD molecular structure and the differences in the hydrogen bonds formed between H2O and D2O.     

Enhanced Solubilisation of Six PAHs by Three Synthetic Cyclodextrins for Remediation Applications: Molecular Modelling of the Inclusion Complexes

Solubilisation of six polycyclic aromatic hydrocarbons (PAHs) (acenaphthene, anthracene, fluoranthene, fluorene, phenanthrene and pyrene) by three synthetic cyclodextrins (CDs) (2-hydroxypropyl-β-CD, hydroxypropyl-γ-CD and ramdomly methylated-β-CD) was investigated in order to select the CD which presents the greatest increase in solubility and better complexation parameters for its use in contaminated scenarios. The presence of the three cyclodextrins greatly enhanced the apparent water solubility of all the PAHs through the formation of inclusion complexes of 1∶1 stoichiometry. Anthracene, fluoranthene, fluorene and phenanthrene clearly presented a higher solubility when β-CD derivatives were used, and especially the complexes with the ramdomly methylated-β-CD were favoured. On the contrary, pyrene presented its best solubility results when using 2-hydroxypropyl-γ-CD, but for acenaphthene the use of any of the three CDs gave the same results. Complementary to experimental phase-solubility studies, a more in-depth estimation of the inclusion process for the different complexes was carried out using molecular modelling in order to find a correlation between the degree of solubilisation and the fit of PAH molecules within the cavity of the different CDs and to know the predominant driving forces of the complexation.     

Beta-cyclodextrin inhibits the sweet taste suppressing activity of gurmarin by the formation of an inclusion complex with aromatic residues in gurmarin.

Our recent study in mice revealed that the inhibitory activity of gurmarin on the sweet taste responses was reduced significantly by the presence of beta-cyclodextrin (beta-CD). To investigate the mechanism involved in the action of beta-CD, physicochemical experiments were performed on the interaction of CDs with gurmarin examining the effect of CDs on the UV absorption spectrum of gurmarin and on the elution behavior in gel filtration (or exclusion) chromatography. Among the three kinds of cyclodextrins tested, beta-CD induced significant changes in the UV absorption spectrum of gurmarin that were characteristic of those found in the inclusion complex formation of tyrosine and tryptophan with beta-CD. The abnormal retention behavior of gurmarin in gel filtration resulting from hydrophobic interaction with the gel matrix reverted to normal in the presence of beta-CD in the elution buffer. These results suggest that the unique domain of gurmarin, in which five aromatic amino acid residues are all directed outwardly and form a hydrophobic cluster, is a possible site of interaction with the gurmarin-sensitive sweet taste receptor molecules in rodents.     

Evidence for the 2:1 molecular recognition and inclusion behaviour between beta- and gamma-cyclodextrins and cinchonine

Cinchonine (Cin) is the primary drug of choice in the treatment of malaria, but its poor solubility has restricted its use via the oral route. Cyclodextrins (CDs) form inclusion complexes with cinchonine to form soluble complexes. This interaction was investigated by solubility studies, electrospray ionization mass spectrometry (ESI-MS), and molecular modeling. ESI-MS evaluated successfully the nature of the solution-phase inclusion complexes. The experimental results showed that not only 1:1, but also stable 2:1 inclusion complexes can be formed between CDs and Cin. Multi-component complexes of beta-CD-Cin-beta-CD (1:1:1), gamma-CD-Cin-gamma-CD (1:1:1), and beta-CD-Cin-gamma-CD (1:1:1) were found in equimolar beta- and gamma-CD mixtures with Cin. The formation of 2:1 and multi-component 1:1:1 non-covalent CD-Cin complexes indicates that beta- and gamma-CD are able to form sandwich-type inclusion complexes with Cin in high concentrations. The phase-solubility diagram showed non-linear type A(p) profile, indicating that more than one cyclodextrin molecule is involved in the complexation of one guest molecule. Molecular modeling calculations have been carried out to rationalize the experimental findings and predict the lowest energy molecular structure of inclusion complex.     

Inclusion complexes of azadirachtin with native and methylated cyclodextrins: solubilization and binding ability

The inclusion complexation behavior of azadirachtin with several cyclodextrins and their methylated derivatives has been investigated in both solution and the solid state by means of XRD, TG-DTA, DSC, NMR, and UV-vis spectroscopy. The results show that the water solubility of azadirachtin was obviously increased after resulting inclusion complex with cyclodextrins. Typically, beta-cyclodextrin (beta-CD), dimethyl-beta-cyclodextrin (DMbetaCD), permethyl-beta-cyclodextrin (TMbetaCD), and hydroxypropyl-beta-cyclodextrin (HPbetaCD) are found to be able to solubilize azadirachtin to high levels up to 2.7, 1.3, 3.5, and 1.6 mg/mL (calculated as azadirachtin), respectively. This satisfactory water solubility and high thermal stability of the cyclodextrin-azadirachtin complexes, will be potentially useful for their application as herbal medicine or healthcare products.     

Enhanced bioavailability of soy isoflavones by complexation with beta-cyclodextrin in rats

In order to improve the solubility and bioavailability of a soy isoflavone extract (IFE), inclusion complexes (IFE-beta-CD) of the isoflavone extract with beta-cyclodextrin (beta-CD) were prepared and studied for their solubility and bioavailability. The aqueous solubility of the complexes of IFE with beta-CD (2.0 mg/ml) was about 26 times that of IFE itself (0.076 mg/ml). The same dosages of IFE and IFE-beta-CD were orally administered to SD rats (Sprague-Dawley) on an isoflavone glycoside (IFG) basis (daidzin, genistin and glycitin), and the plasma concentrations of daidzein, genistein and glycitein were measured over time to estimate the average AUC (area under the plasma concentration versus time curve) of the isoflavones. After the oral administration, the AUC values for daidzein, genistein and glycitein were 340, 11 and 28 microg x min/ml, respectively. In contrast, the respective AUC values after the administration of IFE-beta-CD were 430, 20 and 48 microg x min/ml. The bioavailability of daidzein in IFE-beta-CD was increased to 126% by the formation of inclusion complexes with beta-CD, compared with that in IFE. Furthermore, the bioavailability of genistein and glycitein in IFE-beta-CD formulation was significantly higher by up to 180% and 170%, respectively, compared with that of IFE p=0.008 and p=0.028, respectively). These results show that the absorption of IFE could be improved by the complexation of IFE with beta-CD (IFE-beta-CD).     

The unexpected increase of clotrimazole apparent solubility using randomly methylated β‐cyclodextrin

Clotrimazole (CTZ) and cyclodextrin (CD) inclusion complexes having improved apparent water solubility were obtained from phase solubility diagrams. β‐CD (1.5% w/w) and hydroxypropyl‐β‐CD (40% w/w) offered poor CTZ solubility enhancements (12 and 384 times, respectively). Unexpectedly, the apparent solubility of CTZ was 9980 times increased from 0.4 µg.mL^?1 (1.42 μM) without CD to 4.89 mg.mL^?1 (14.9 mM) using randomly‐methylated β‐CD (Me‐β‐CD) (40% w/w). This is the highest apparent CTZ solubility improvement ever reported in the literature using conventional CDs. Quantitative nuclear magnetic resonance (¹H‐NMR) coupled with two‐dimensional nuclear Overhauser effect (NOESY) experiments and molecular docking calculations showed that the highest interactions with Me‐β‐CD were reported for CTZ two phenyl groups. A lower interaction was reported for chlorophenyl, while imidazole had the weakest interaction with Me‐β‐CD. Copyright © 2015 John Wiley & Sons, Ltd.     

SN-38-Cyclodextrin Complexation and Its Influence on the Solubility,Stability, and In Vitro Anticancer Activity Against Ovarian Cancer

SN-38, an active metabolite of irinotecan, is up to 1,000-fold more potent than irinotecan. But the clinical use of SN-38 is limited by its extreme hydrophobicity and instability at physiological pH. To enhance solubility and stability, SN-38 was complexed with different cyclodextrins (CDs), namely, sodium sulfobutylether β-cyclodextrin (SBEβCD), hydroxypropyl β-cyclodextrin, randomly methylated β-cyclodextrin, and methyl β-cyclodextrin, and their influence on SN-38 solubility, stability, and in vitro cytotoxicity was studied against ovarian cancer cell lines (A2780 and 2008). Phase solubility studies were conducted to understand the pattern of SN-38 solubilization. SN-38-βCD complexes were characterized by differential scanning calorimetry (DSC), X-ray powder diffraction analysis (XRPD), and Fourier transform infrared (FTIR). Stability of SN-38-SBEβCD complex in pH 7.4 phosphate-buffered saline was evaluated and compared against free SN-38. Phase solubility studies revealed that SN-38 solubility increased linearly as a function of CD concentration and the linearity was characteristic of an A_P-type system. Aqueous solubility of SN-38 was enhanced by about 30–1,400 times by CD complexation. DSC, XRPD, and FTIR studies confirmed the formation of inclusion complexes, and stability studies revealed that cyclodextrin complexation significantly increased the hydrolytic stability of SN-38 at physiological pH 7.4. Cytotoxicity of SN-38-SBEβCD complex was significantly higher than SN-38 and irinotecan in both A2780 and 2008 cell lines. Results suggest that SBEβCD encapsulated SN-38 deep into the cavity forming stable inclusion complex and as a result increased the solubility, stability, and cytotoxicity of SN-38. It may be concluded that preparation of inclusion complexes with SBEβCD is a suitable approach to overcome the solubility and stability problems of SN-38 for future clinical applications.     

Physicochemical Characterization of Efavirenz–Cyclodextrin Inclusion Complexes

Efavirenz (EFV) is an oral antihuman immunodeficiency virus type 1 drug with extremely poor aqueous solubility. Thus, its gastrointestinal absorption is limited by the dissolution rate of the drug. The objective of this study was to characterize the inclusion complexes of EFV with β-cyclodextrin (β-CD), hydroxypropyl β-CD (HPβCD), and randomly methylated β-CD (RMβCD) to improve the solubility and dissolution of EFV. The inclusion complexation of EFV with cyclodextrins in the liquid state was characterized by phase solubility studies. The solid-state characterization of various EFV and CD systems was performed by X-ray diffraction, differential scanning calorimetry, and scanning electron microscopy analyses. Dissolution studies were carried out in distilled water using US Pharmacopeia dissolution rate testing equipment. Phase solubility studies provided an A_L-type solubility diagram for β-CD and A_P-type solubility diagram for HPβCD and RMβCD. The phase solubility data enabled calculating stability constants (K _s) for EFV-βCD, EFV-HPβCD, and EFV-RMβCD systems which were 288, 469, and 1,073 M⁻¹, respectively. The physical and kneaded mixtures of EFV with CDs generally provided higher dissolution of EFV as expected. The dissolution of EFV was substantially higher with HPβCD and RMβCD inclusion complexes prepared by the freeze drying method. Thus, complexation with HPβCD and RMβCD could possibly improve the dissolution rate-limited absorption of EFV.     

Stereoselectivity in β-cyclodextrin complexation of 1,4-dihydropyridine derivatives

Structure–interaction relationships, stereoselectivity, and solubility enhancement in inclusion compexation of β-cyclodextrins (CDs) with some racemic and enantiomerically pure 1,4-dihydropyridine derivatives (DHPs) were investigated. 1:1 and 1:2 (mole ratio) complexes were prepared and characterized by X-ray powder diffraction, differential scanning calorimetry (DSC), MS-FAB spectrometry, ¹H-NMR spectroscopy, water and phase solubility. The solubility studies have revealed different complexation equilibria for optically pure DHP enantiomers, and corresponding racemic mixtures in water solutions. By means of ¹H-NMR chemical shift measurements, the inclusion of aromatic fragments of racemic and enantiomerically pure DHP molecules within the cavities of different CDs was elucidated. Considerable stereoselectivity in complexation interactions was observed. The results indicate the potential use of cyclodextrins as chiral selectors for enantiomeric resolution of 1,4-DHP calcium antagonists. © 1993 Wiley-Liss, Inc.     

Reduction of the suppressive effects of gurmarin on sweet taste responses by addition of beta-cyclodextrin

Cyclodextrins (CDs) have the remarkable ability to form inclusion complexes with a wide variety of guest molecules. In the present study, possible influences of CDs on gurmarin inhibition of the chorda tympani responses to sucrose were examined in C57BL mice. Responses to sucrose were suppressed to approximately 50% of control by treatment of the tongue with 30 micrograms/ml (approximately 7.1 microM) gurmarin. Rinsing the tongue with 15 mM beta-CD after gurmarin gave rapid recovery of the suppressed sucrose responses to approximately 85% of control, whereas 15 mM alpha- or gamma-CD did not. When gurmarin was mixed with beta-CD, the suppressive effects of gurmarin on sucrose responses were largely reduced. No such reduction was observed for mixtures with alpha- and gamma-CD. Gurmarin includes tyrosine and tryptophan residues whose aromatic rings are directed outward and can probably form inclusion complexes with beta-CD. Therefore, the observed reduction of the effects of gurmarin may be due to steric hindrances in inclusion complexes of gurmarin with beta-CD that may interfere with gurmarin binding to sweet taste receptors.      

Kinetic and thermodynamic analysis of the cyclodextrin-allyl isothiocyanate inclusion complex in an aqueous solution

The decomposition of allyl isothiocyanate (AITC) in an aqueous solution was depressed in the presence of cyclodextrin (CD), it's suppression effect increasing in the order of none < beta-CD < alpha-CD. The results of kinetic and thermodynamic analysis of the CD-AITC inclusion complexes showed that the inclusion process was mostly governed by an enthalpy change (delta H degree) rather than by an entrophy change (delta S degree), and that Van der Waals forces played a primary role int he inclusion. Steric factors were important for the reaction activity of AITC inclusion into the CD cavity, especially significant being the stereospecificity between the size of the CD cavity and the AITC molecule which is the main factor concerning it's activity. Our results suggest that the association stability and activity of the included AITC molecule are important factors in the suppression mechanism for CDs. Therefore, both these factors would make an alpha-CD-AITC system more advantageous than a beta-CD-AITC system, and the marked suppression effect of alpha-CD on the decomposition of AITC can be attributed to the formation of inclusion complexes in an aqueous solution.     

Effect of Cyclodextrin Complexation on the Aqueous Solubility and Solubility/Dose Ratio of Praziquantel

Praziquantel (PZQ), the primary drug of choice in the treatment of schistosomiasis, is a highly lipophilic drug that possesses high permeability and low aqueous solubility and is, therefore, classified as a Class II drug according to the Biopharmaceutics Classification System (BCS). In this work, β-cyclodextrin (β-CD) and hydroxypropyl-β-cyclodextrin (HP-β-CD) were used in order to determine whether increasing the aqueous solubility of a drug by complexation with CDs, a BCS-Class II compound like PZQ could behave as BCS-Class I (highly soluble/highly permeable) drug. Phase solubility and the kneading and lyophilization techniques were used for inclusion complex preparation; solubility was determined by UV spectroscopy. The ability of the water soluble polymer polyvinylpyrolidone (PVP) to increase the complexation and solubilization efficiency of β-CD and HP-β-CD for PZQ was examined. Results showed significant improvement of PZQ solubility in the presence of both cyclodextrins but no additional effect in the presence of PVP. The solubility/dose ratios values of PZQ-cyclodextrin complexes calculated considering the low (150 mg) and the high dose (600 mg) of PZQ, used in practice, indicate that PZQ complexation with CDs may result in drug dosage forms that would behave as a BCS-Class I depending on the administered dose.     

Enantioselective toxicity of metolachlor to Scenedesmus obliquus in the presence of cyclodextrins

Cyclodextrins (CDs) possess a variety of chiral centers and are capable of recognizing enantiomeric molecules through the formation of inclusion complexes. Two types of CDs, α-cyclodextrin (α-CD) and β-cyclodextrin (β-CD), were selected to evaluate the effects of the enantioselective ecotoxicity of racemic metolachlor (Rac-metolachlor) and its S-enantiomer (S-metolachlor) on the freshwater algae Scenedesmus obliquus (S. obliquus) by acute toxicity test. The results showed that the aquatic toxicity of S-metolachlor was higher than Rac-metolachlor and that CDs enhanced the toxicity of metolachlor enantioselectively by increasing the aquatic toxicity of Rac-metolachlor rather than that of S-metolachlor to S. obliquus. The equilibrium constant for Rac-metolachlor-CD complexes was higher than that of S-metolachlor-CDs, which was responsible for the greater aquatic toxicity shift effect of Rac-metolachlor. Thermodynamic studies of CD complexes showed that inclusion for all of the complexes was primarily a spontaneous, enthalpy-driven process. These results will help to understand the preliminary mechanism of shifting aquatic toxicity of metolachlor by CDs and the CDs mediated environmental processes of metolachlor, to correctly apply CDs to chiral pesticides formulation and environmental remediation of chiral contaminants.     

Spectrofluorometric analytical applications of cyclodextrins

Cyclodextrins (CDs) are a family of cyclic oligosaccharides composed of α‐(1,4)‐linked glucopyranose subunits. The most important feature of CDs is their ability to form inclusion complexes (host–guest complexes) with a very wide range of solid, liquid and gaseous compounds by a molecular complexation. During the last decade, a considerable number of research papers has been focused on the use of CDs to enhance fluorescence intensity of different analytes and to develop CD‐induced spectrofluorimetric method. In this review, the various spectrofluorimetric methods based on host–inclusion complex are presented. Copyright © 2013 John Wiley & Sons, Ltd.     

Enantiomeric separation of chiral ruthenium(II) complexes using capillary electrophoresis

Capillary zone electrophoresis (CZE) and micellar capillary electrophoresis (MCE) were applied for the enantiomeric separation of nine mononuclear tris(diimine)ruthenium(II) complexes as well as the separation of all stereoisomers of a dinuclear tris(diimine)ruthenium(II) complex. Nine cyclodextrin (CD) based chiral selectors were examined as run buffer additives to evaluate their effectiveness in the enantiomeric separation of tris(diimine)ruthenium(II) complexes. Seven showed enantioselectivity. Sulfated gamma-cyclodextrin (SGC), with four baseline and three partial separations, was found to be the most useful chiral selector. In CZE mode, the derivatized gamma-CDs were more effective than beta-CDs while sulfated CDs work better than carboxymethyl CDs. In MCE mode, hydroxypropyl beta-CD separated the greatest number of tris(diimine) ruthenium(II) complexes. The effects of chiral selector concentration, run buffer pH and concentration, the concentration ratio between chiral selector and other factors were investigated.     

Molecular Modeling and Physicochemical Properties of Supramolecular Complexes of Limonene with α- and β-Cyclodextrins

This study evaluated three different methods for the formation of an inclusion complex between alpha- and beta-cyclodextrin (α- and β-CD) and limonene (LIM) with the goal of improving the physicochemical properties of limonene. The study samples were prepared through physical mixing (PM), paste complexation (PC), and slurry complexation (SC) methods in the molar ratio of 1:1 (cyclodextrin:limonene). The complexes prepared were evaluated with thermogravimetry/derivate thermogravimetry, infrared spectroscopy, X-ray diffraction, complexation efficiency through gas chromatography/mass spectrometry analyses, molecular modeling, and nuclear magnetic resonance. The results showed that the physical mixing procedure did not produce complexation, but the paste and slurry methods produced inclusion complexes, which demonstrated interactions outside of the cavity of the CDs. However, the paste obtained with β-cyclodextrin did not demonstrate complexation in the gas chromatographic technique because, after extraction, most of the limonene was either surface-adsorbed by β-cyclodextrin or volatilized during the procedure. We conclude that paste complexation and slurry complexation are effective and economic methods to improve the physicochemical character of limonene and could have important applications in pharmacological activities in terms of an increase in solubility.     

Structural and physicochemical characterization of the inclusion complexes of cyclomaltooligosaccharides (cyclodextrins) with melatonin

The stoichiometry, geometry, stability, and solubility of the inclusion complexes of melatonin (MLT) with native cyclomaltooligosaccharides (alpha-, beta- or gamma-cyclodextrins, CDs) are determined experimentally by high-resolution NMR spectroscopy, calorimetric and solubility measurements, and mass spectrometry. The observed differences are discussed in terms of molecular recognition expression of the host-guest (h-g) interactions within the hydrophobic CDs cavities of different size. The 1:1 h-g stoichiometry in water solution prevails at low CD concentrations; the trend to form higher order associations is observed at increasing CD concentrations. The stability order beta-CD>gamma-CD>alpha-CD for the complexes in water solution and beta-CD>alpha-CD>gamma-CD for the protonated or alkali-cationated complexes in the gas phase are rationalized on the grounds of the structural data from NMR spectroscopy and of the thermodynamic parameters from calorimetric measurements.     

Modeling the influence of cyclodextrins on oral absorption of low‐solubility drugs: I. Model development

The ability to quantitatively predict the influence of a solubilization technology on oral absorption would be highly beneficial in rational selection of drug delivery technology and formulation design. Cyclodextrins (CDs) are cyclic oligosaccharides which form inclusion complexes with a large variety of compounds including drugs. There are many studies in the literature showing that complexation between CD and drug enhances oral bioavailability and some demonstrating failure of CD in bioavailability enhancement, but relatively little guidance regarding when CD can be used to enhance bioavailability. A model was developed based upon mass transport expressions for drug dissolution and absorption and a pseudo‐equilibrium assumption for the complexation reaction with CD. The model considers neutral compound delivered as a physical mixture with CD in both immediate release (IR) and controlled release (CR) formulations. Simulation results demonstrated that cyclodextrins can enhance, have no effect, or hurt drug absorption when delivered as a physical mixture with drug. The predicted influence depends on interacting parameter values, including solubility, drug absorption constant, binding constant, CD:drug molar ratio, dose, and assumed volume of the intestinal lumen. In general, the predicted positive influence of dosing as a physical mixture with CD was minimal, alluding to the significance of dosing as a preformed complex. The model developed enabled examination of which physical and chemical properties result in oral absorption enhancement for neutral drug administered as a physical mixture with CD, demonstrating the utility of modeling the influence of a drug delivery agent (e.g., CD) on absorption for rational dosage form design. Biotechnol. Bioeng. 2010; 105: 409–420. © 2009 Wiley Periodicals, Inc.