Behavior of Tricyclic Antidepressants in Aqueous Solution - American

three tricyclic antidepressant drugs (TCAs), imipramine, desipramine, and amitriptyline hydrochlorides, in the absence and in the presence of β-cyclo...
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Behavior of Tricyclic Antidepressants in Aqueous Solution: Self-Aggregation and Association with β-Cyclodextrin E. Junquera, J. C. Romero, and E. Aicart* Departamento de Quı´mica Fı´sica I, Facultad de Ciencias Quı´micas, Universidad Complutense, 28040-Madrid, Spain Received June 13, 2000. In Final Form: December 27, 2000 Conductivity measurements have been carried out to study the behavior of the aqueous solutions of three tricyclic antidepressant drugs (TCAs), imipramine, desipramine, and amitriptyline hydrochlorides, in the absence and in the presence of β-cyclodextrin (β-CD) at 25 °C. The TCAs studied herein have been found to show an aggregation behavior in aqueous solution. A model has been proposed to determine the aggregation number of small aggregates from conductivity measurements. Several parameters, such as the aggregation number, Nag, the critical aggregation concentration, cac, and the dissociation degree of the aggregates, β, have been determined. In the presence of β-CD, the TCAs form inclusion complexes with 1:1 stoichiometries and binding constants in the range of 1500-3000 M-1. The ionic molar conductivities 0 0 0 of the TCA+ ion, free in solution, λTCA +, associated with the β-CD, λCD/TCA+, and self-aggregated, λag, have been calculated as well. The effect of β-CD on the aggregation behavior of the drugs has been evaluated by determining the apparent critical aggregation concentration, cac* (the cac for the ternary β-CD/TCA/ H2O systems), and the dissociation degree. Complementary measurements of pH, UV-vis, and fluorescence as well as a preliminary simulation of the complexes from manual docking studies were done to support some evidence.

Introduction Imipramine (IPR), desipramine (DIPR), and amitriptyline (AMYTP) are tricyclic antidepressants (TCAs) belonging to the first generation of antidepressant drugs.1,2 These substances share a basic chemical structure comprising a three-ring core and an alkylamine side chain (see Chart 1). The value of the angle between the two phenyl rings of these molecules is important: the more nearly planar, the greater the neuroleptic activity, whereas the more the phenyl rings are inclined toward each other, the more antidepressive activity predominates. However, TCAs suffer from several drawbacks such as anticholinergic, cardiovascular, and antiarrhythmic side effects.1,2 The presence of the alkylamine side chain on TCA molecules confers on them a “surfactant-like” behavior which may be manifested in the formation of aggregates in aqueous solution. Despite the interest in characterizing this aggregation and its possible consequences on the drug properties, it has not been analyzed in the literature. Thus, one of the objectives of this work is the study of this phenomenon, with the determination of parameters such as the concentration at which the aggregation takes place, that we have called critical aggregation concentration, cac, the dissociation degree of the aggregate, β, and the aggregation number, Nag. For the latest purpose, we have proposed a model which allows for the determination of small aggregation numbers from conductivity measurements, of great interest given the well-known difficulty in this respect with the techniques normally used on these studies, that is, light scattering and fluorescence, either static or dynamic.3 * Corresponding author. Phone: 34-91-3944208. Fax: 34-913944135. E-mail: [email protected]. (1) Hall, C. M.; Nugent, R. A. Encyclopedia of Chemical Technology, Vol. 2; Kroschwitcz, J. I., Howe-Grant, M., Eds.; John Wiley & Sons: New York, 1992. (2) Bowman, W. C.; Rand, M. J. Textbook of Pharmacology; Blackwell Science Pub.: London, 1992.

Chart 1

Furthermore, the undesirable side effects of TCAs abovementioned may be avoided, or at least reduced, if the drugs are properly vectored in the organism. Among the different artificial receptors known to overcome these problems, cyclodextrins (CDs) are considered the most suitable host molecules for the vectorization in aqueous media of guest molecules with hydrophobic parts (i.e., drugs, surfactants, dyes, pesticides, etc.).4-6 The parent cyclodextrins are wellknown nontoxic macrocyclic sugars, with doughnutshaped structures, consisting of R(1f4) joined glucopyranose units.4 Their hydrophobic inner surfaces make them the most important simple organic compounds capable of forming noncovalently bonded inclusion com(3) Zana, R. Surfactant Solutions: New Methods of Investigation; Marcel Dekker Inc.: New York, 1987. (4) Szejtli, J.; Osa, T. Comprehensive Supramolecular Chemistry, Vol. 3, Cyclodextrins; Elsevier: Oxford, 1996. (5) D’Souza, V. T.; Lipkowitz, K. B. Chem. Rev. 1998, 98, 1741. (6) Connors, K. A. Chem. Rev. 1997, 97, 1325.

10.1021/la000819q CCC: $20.00 © 2001 American Chemical Society Published on Web 02/15/2001

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plexes with a variety of drug molecules in aqueous solution. This encapsulation may dramatically alter the physical, chemical, and biological properties of either the parent drug or the cyclodextrin. Actually, the use of cyclodextrins as a new family of pharmaceutical excipients and drug carriers4-8 has become increasingly a successful method to improve the general bioavailability of drugs with serious problems of side effects, limited aqueous solubilities, or instabilities. In this work, we have also focused our attention on the characterization of the inclusion complexes formed by β-CD, dimension-wise the most interesting CD for drug encapsulation, and the three TCAs previously mentioned. This analysis has been carried out mainly through conductivity measurements and determination of the stoichiometry, A, and the association constant, KCD/TCA, of the complexes, of crucial importance to the bioavailability of the drug. An estimation of the structure of the complex, through molecular modeling simulations, has helped in understanding and confirming some of the experimental evidence. Materials and Methods Materials. β-Cyclodextrin and hydrochlorides of AMYTP, IPR, and DIPR were purchased from Sigma. All of them, with purities higher than 99%, were used without further purification. A thermogravimetric analysis showed that β-CD consists of eight water molecules per molecule, which were considered in the calculations of solute concentrations. All the solutions were prepared with distilled and deionized water (taken from a Millipore Super-Q system, with a conductivity lower than 18 µS cm-1). The homogeneity of the initial solutions was assured by sonicating them in an ultrasonic bath for 1 h. Conductivity Measurements. Conductivity data were collected with a Hewlett-Packard 4263A LCR meter, using a Metrohm electrode, calibrated with a KCl standard solution. Mixtures were prepared from a digital buret, whose cylinder was kept at the same constant temperature as the measuring cell. Details of the apparatuses and the experimental procedure of the fully computerized technique were described earlier.9 The reproducibility of the specific conductivity, κ, obtained as an average of 2400 measurements for each concentration, is believed to be better than 0.03%. The accuracy of the molarity of the solutions is better than 1 × 10-5 M, and the temperature is held constant at 25.000 ( 0.001 °C. The conductivity measurements were made (i) as a function of [drug] for the binary drug/water systems; (ii) as a function of [cyclodextrin], keeping constant the concentration of the drug, for the ternary cyclodextrin/drug/water systems; (iii) as a function of [drug] in the presence of a constant cyclodextrin concentration, the range of [drug] going from the pre- to postaggregate region, for the ternary cyclodextrin/drug/ water systems. Spectroscopic Measurements. The UV-vis spectra were recorded with a Varian Cary 5G double beam UV-vis-NIR spectrophotometer from 200 to 280 nm with 1 nm intervals. Two 10 mm stoppered rectangular silica UV cells (sample and reference cells) were placed in a stirred cuvette holder, whose temperature was kept constant at 25.00 ( 0.05 °C. The scan rate was selected in all the cases as 300 nm/min. The equipment and the experimental procedure were fully described elsewhere.10 Steady-state fluorescence experiments were performed with a Perkin-Elmer LS-50B luminiscence spectrometer. Details of the experimental procedure were fully described earlier.11 A 10 mm stoppered rectangular silica cell was placed in a stirred cuvette holder whose temperature was kept constant at 25.00 ( 0.01 °C. During the experiments, the excitation and emission slits were fixed at 5 and 5 nm, respectively, the excitation (7) Thompson, D. O. Crit. Rev. Ther. Drug Carrier Syst. 1997, 14, 1. (8) Rajewski, R. A.; Stella, V. J. J. Pharm. Sci. 1996, 85, 1142. (9) Junquera, E.; Aicart, E. Rev. Sci. Instrum. 1994, 65, 2672. (10) Merino, C.; Junquera, E.; Jime´nez-Barbero, J.; Aicart, E. Langmuir 2000, 16, 1557. (11) Junquera, E.; Aicart, E. J. Inclusion Phenom. 1997, 29, 119.

Figure 1. pH values of aqueous solutions of amitriptyline hydrochloride as a function of concentration, at 25 °C. wavelength was set at 260 nm, and the emission spectra were collected from 300 to 450 nm. In all the measurements, the scan rate was selected at 240 nm/min.

Results and Discussion Monomer Behavior. The pH of the aqueous solutions of amitriptyline hydrochloride in pure water has been measured at 25 °C in order to confirm whether the amytriptylinate cation (AMYTP+), arising from the dissociation of the salt, hydrolyzes in aqueous solution (Figure 1). Data were collected with a Metrohm 713 ion meter, using a combined glass electrode. The equipment and the experimental procedure, fully computerized, have been previously described in detail.12 Negligible changes in the pH can be observed in the dilute range, indicating that the amitriptyline is in the solution as the cation AMYTP+, with no contribution of the neutral species. This experimental evidence confirms the utility of unbuffered solutions in the following studies at low drug concentrations. Moreover, a clear change of the pH is found at a higher concentration of the drug, pointing to a possible aggregation phenomenon which will be confirmed and fully analyzed later. A similar behavior is expected for the other TCAs studied in this work. In Figure 2, the values of the specific conductivity, κ, for the binary TCA/water solutions are plotted as a function of [TCA] at 25 °C. It can be observed in the figure that the experimental κ values show a clear change at a drug concentration which ranges from ∼40 to ∼55 mM depending on the TCA, confirming pH evidence. This change, ascribable to the formation of an aggregate, is shown more clearly in Figure 3, where the molar conductance is plotted as a function of drug concentration. The concentration at which the change in the slope of the conductivity takes place has been called in this work critical aggregate concentration, cac, and it has been determined as a minimum in the second derivative of the specific conductivity data (see inset at the bottom of Figure 2). The values obtained for the three TCAs studied herein are reported in Table 1. The more polar character of desipramine and imipramine molecules, with a nitrogen on the aliphatic (12) Junquera, E.; Aicart, E. J. Phys. Chem. B 1997, 101, 7163.

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0 Table 1. Values of Ionic Molar Conductivities at Infinite Dilution of TCA+ Cation, Both in the Free, λTCA +, and 0 Aggregated, λag, Forms, and Values of the Critical Aggregate Concentration, cac, Dissociation Degree, β, and Aggregation Number, Nag, of the TCA Aggregates, at 25 °C

TCA

cac (mM)

β

Nag

0 a 2 -1) λTCA + (S cm mol

λ0ag (S cm2 mol-1)

AMYTP+

43.7 ( 0.2 56.3 ( 0.2 56.7 ( 0.2

0.58 ( 0.02 0.63 ( 0.02 0.56 ( 0.02

5(1 5(1 5(1

18.5 ( 0.8 20.3 ( 0.9 17.5 ( 0.8

84 ( 3 80 ( 3 102 ( 4

DIPR+ IPR+ a

Calculated from the preaggregate data of the binary TCA/water systems.

presence of either one or two methyl groups at the end of the aliphatic residue seems to have a lesser importance in this respect, as previously found for other surfactant systems.14-19 Moreover, the conductivity of the solution in the preaggregate region can be expressed as a function of the ionic molar conductivities, λi, and the concentration of the charged species as follows:

κ ) λCl- [Cl-] + λTCA+ [TCA+]

(1)

where the species OH- and H+ have been excluded, because at the pH of the aqueous drug solution their contribution to the conductivity is negligible compared with that of TCA+ and Cl-. The λi values at low concentrations can be estimated by the Onsager relation:20

(

| |

30.32zi + 0.7852 z+z-

λi ) λ0i Figure 2. Values of specific conductivity, κ, of aqueous solutions of the hydrochlorides of amitriptyline, desipramine, and imipramine as a function of [drug], at 25 °C. The inset at the bottom shows the plot of the second derivative of κ with respect to the concentration (the solid line is the smoothing of the points).

Figure 3. Values of molar conductivity, Λ, of aqueous solutions of the hydrochlorides of amitriptyline, desipramine, and imipramine as a function of [drug], at 25 °C.

cycle, may be responsible for a higher cac value. In any case, the three cac values are surprisingly comparable with those of surfactants with an ammonium head but with a clearly longer tail of 10-11 carbon atoms.13,14 The

1/2

1 + BanI

)

q λ0 I1/2 1/2 i 1+q

(2)

where λ0i represents the ionic molar conductivity at infinite dilution, an is the effective size of the hydrated ion, I is the ionic strength, q is a parameter related to the charges and the ionic molar conductivities of the ions,20 and B is a constant whose value is taken from the 0 - were literature.20 The values of λCl - at 25 °C and aCl taken from the literature as well.20,21 The parameter an of the three TCA cations studied herein has been 0 22 The estimated from λTCA + with an empirical relation. 0 values of λTCA+ have been calculated by fitting the experimental κ data below cac to eqs 1 and 2 with a nonlinear regression (NLR) method14 and are reported in Table 1. The two methyl groups on the cationic head of amitriptyline and imipramine, as compared to one methyl group on desipramine, justify their lower ionic conductivity. These conductivities are comparable to those previously found for surfactants of similar molecular weight.14,19,23 Association Behavior. (1) Self-Aggregation. The aggregation phenomenon presented above is characterized not only by the cac value but also by other parameters (13) Junquera, E.; Aicart, E.; Tardajos, G. J. Phys. Chem. 1992, 96, 4533. (14) Junquera, E.; Pen˜a, L.; Aicart, E. Langmuir 1995, 11, 4685. (15) Tanford, C. The Hydrophobic Effect: Formation of Micelles and Biological Membranes; Wiley & Sons, Inc.: New York, 1980. (16) Fendler, J. H. Membrane Mimetic Chemistry; John Wiley & Sons: New York, 1982. (17) Atwood, D.; Florence, A. T. Surfactant Systems. Their Chemistry, Pharmacy and Biology; Chapman and Hall: London, 1983. (18) Mukerjee, P.; Mysels, K. J. Critical Micelle Concentrations of Aqueous Surfactant Systems; NSRDS-NBS 36; U.S. Government Printing Office: Washington, DC, 1971. (19) Junquera, E.; Pen˜a, L.; Aicart, E. Langmuir 1997, 13, 219. (20) Robinson, R. A.; Stokes, R. H. Electrolyte Solutions; Butterworth: London, 1965. (21) Tinner, U. Electrodes in Potentiometry; Metrohm, AG: Herisau, Switzerland, 1989. (22) Bru¨ll, L. Gazz. Chim. Ital. 1934, 64, 624. (23) Junquera, E.; Mendicuti, F.; Aicart, E. Langmuir 1999, 15, 4472.

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such as the dissociation degree of the aggregate, β, and the aggregation number, Nag. The dissociation degree of an ionic micelle can be estimated from the ratio between the post- and premicellar slopes of the κ versus concentration plot. The β values for the aggregates of amitriptyline, imipramine, and desipramine hydrochlorides are reported in Table 1. The desipramine aggregate shows the higher dissociation degree (63%), whereas the amitriptyline and imipramine aggregates show a comparable β value of ∼57%. These differences point to the presence of one or two methyl groups at the end of the polar head: two methyl groups seem to stabilize the charge of the aggregate to a lesser extent than one methyl group does. In this work, we propose a model to determine the aggregation number of small aggregates from conductivity measurements. In addition, the molar conductivity values at infinite dilution of the ionic aggregates, λ0ag, are also calculated by the model. Basically, the model is based on the fact that the specific conductivity of the solution in the postaggregate region is given by

κ ) κcac + λCl- [Cl-]diss + λag [TCA+]ag

(3)

where κcac is the specific conductivity at the cac, λag and [TCA+]ag are the ionic molar conductivity and concentration of the TCA+ aggregates, and [Cl-]diss is the concentration of Cl- dissociated from the aggregates. Given that the concentrations of free Cl- and free TCA+ before the cac are equal, the [Cl-]diss magnitude can be expressed in terms of the aggregation number, Nag, and the dissociation degree of the aggregate, β, as follows:

[Cl-]diss ) Nagβ [TCA+]ag

Figure 4. UV-vis spectra of aqueous solutions of AMYTP‚ HCl at different concentrations, at 25 °C: (1) 2.9 × 10-6 M, (2) 8.9 × 10-6 M, (3) 1.4 × 10-5 M, (4) 1.9 × 10-5 M, (5) 2.4 × 10-5 M, (6) 3.3 × 10-5 M, (7) 4.3 × 10-5 M, (8) 5.4 × 10-5 M, (9) 6.6 × 10-5 M, (10) 8.0 × 10-5 M, (11) 9.4 × 10-5 M, and (12) 10.7 × 10-5 M. The inset at the top shows the Lambert-Beer linear plot.

(4)

The concentration dependence of ionic molar conductivities on eq 3 is given by eq 2, the ionic strength of the aggregate solution being

1 I ) cac + [(β + Nagβ2)([TCA+]tot - cac)] 2

(5)

[TCA+]tot ) cac + Nag [TCA+]ag

(6)

with

The values of λ0ag and Nag for the aggregates have been calculated by fitting the experimental κ data in the postaggregate region of Figure 1 to eqs 3-6 with a NLR method and are reported in Table 1. In all of the cases, around five molecules of drug take part in the aggregates, which have λ0ag values of 80-100 S cm2 mol-1, less than 0 the product of (NagλTCA +), as expected. It is evident that whatever the structure of the aggregates may be, it seems to be similar in the three cases, given that the aggregate parameters are almost the same irrespective of the drug molecules. (2) Association with β-Cyclodextrin. The association process between the β-CD and the TCA molecules was first approached from UV-vis and static fluorescence measurements. Figure 4 shows the UV-vis spectra of the aqueous solution of AMYTP at different drug concentrations at 25 °C. It can be observed that the spectra show two peaks centered at 210 and 240 nm, with absorbance values increasing with drug concentration, following a typical Lambert-Beer behavior. From the linear regression of the values of the absorbances at λ ) 240 nm as a function of drug concentration (see inset at the top of Figure 4), the molar absorption coefficient, , was deter-

Figure 5. Emission fluorescence spectra of an aqueous solution of AMYTP‚HCl at constant concentration (1.3 × 10-4 M) at 25 °C, in the absence and presence of different concentrations of β-CD: (0) 0 M, (1) 0.36 × 10-4 M, (2) 0.73 × 10-4 M, (3) 1.04 × 10-4 M, (4) 2.85 × 10-4 M, (5) 5.55 × 10-4 M, and (6) 10.6 × 10-4 M.

mined as (12 730 ( 170) M-1 cm-1. The second peak, corresponding to the πfπ* transition (k band), at 240 nm, is the one used to follow the emission fluorescence spectra of AMYTP, as a result of the excitation on the tail of the absorption band, in order to avoid an undesirable inner filter effect. The curve labeled with 0 in Figure 5 shows the emission fluorescence spectrum of a 1.3 × 10-4 M aqueous solution of amitriptyline hydrochloride, characterized by a very low fluorescence intensity. However, no significant variations in either the absorption spectra or the intensity of fluorescence emission (curves 1-6 in

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0 Table 2. Values of Ionic Molar Conductivities at Infinite Dilution of TCA+ Cation, Both in the Free, λTCA +, and 0 + Complexed, λCD/TCA+, Forms, and Values of the Association Constant, KCD/TCA , and Stoichiometries, A, of the CD/TCA+ Inclusion Complexes, at 25 °C

complex

[TCA] (mM)

A

0 a 2 -1) λTCA + (S cm mol

KCD/TCA+ (M-1)

0 2 -1) λCD/TCA + (S cm mol

β-CD/AMYTP+

4.980 4.967 4.974

1.03 ( 0.02 1.00 ( 0.02 1.01 ( 0.02

22.6 ( 1.5 22.5 ( 1.5 22.8 ( 1.5

3185 ( 300 2035 ( 200 1495 ( 150

9.3 ( 1.3 9.0 ( 1.3 8.6 ( 1.3

β-CD/DIPR+ β-CD/IPR+ a

Calculated from the data of the ternary β-CD/TCA/water systems.

Considering these 1:1 stoichiometries, the encapsulation of the drug into the β-CD follows the equilibrium

TCA+ + CD a CD/TCA+

(7)

governed by the binding constant

KCD/TCA+ )

aCD/TCA+ aCDaTCA+

(8)

We have previously reported a model24 to obtain the binding constant of the inclusion complex from conductivity data, which can be expressed in terms of the complex concentration as follows:

κ ) λCl-[Cl-] + λTCA+[TCA+] + λCD/TCA+[CD/TCA+] (9)

Figure 6. Values of specific conductivity, κ, of aqueous solutions of the hydrochlorides of amitriptyline, desipramine, and imipramine at constant [drug] ∼ 5 mM as a function of [β-CD], at 25 °C. The inset at the top shows the determination of the stoichiometry of the complex in the case of β-CD/IPR+.

Figure 5) of the drugs were observed with the addition of cyclodextrin. These results could be indicating that the groups responsible for the spectroscopic responses, presumably the system of three cycles (saturated and nonsaturated), are not included within the CD cavity, although this conclusion needs structural studies to be confirmed. Moreover, it implies that if the inclusion takes place it has to involve the other part of the drug molecule, that is, the charged alkylamine side chain. In such a case, the conductivity technique is a good choice to analyze this process. The formation of the inclusion complex β-CD/ TCA+ can be observed in Figure 6, which shows the plot of the specific conductivity of the drug aqueous solutions in the presence of β-cyclodextrin as a function of [β-CD]. In all of the cases, the drug concentration is kept constant (∼5 mM), well below its cac. The decrease in κ when β-CD is added points to the inclusion of the TCA+ cation into the β-CD cavity, because the mobility of the associated cation is expected to be less than that of the free cation. The stoichiometry of this inclusion complex can be determined as the ratio between [β-CD] and [TCA+], [β-CD] being the concentration at which two straight lines intercept and [TCA+] being the initial drug concentration, kept constant in the experiment. The inset at the top of Figure 6 shows, as an example, this determination in the case of the β-CD/IPR+ complex, and Table 2 reports the values obtained for the three complexes. It can be observed that all the stoichiometries are 1:1, indicating that the complexes are formed by the association of a molecule of β-CD per each molecule of TCA+, as usually found for most cyclodextrin/drug complexes.4-6,10,12,23

The model is based upon the following main points, fully detailed elsewhere: (a) the activity coefficients of the charged species are obtained through the extended Debye-Hu¨ckel theory; (b) the ionic molar conductivities of the charged species, λi, are related to the corresponding values at infinite dilution, λ0i , through the Debye-Hu¨ckel-Onsager theory; (c) the ionic molar 0 conductivity at infinite dilution of TCA+, λTCA +, may be either fixed to the value determined from the conductivity data of the binary system (Table 1) or left as a fit coefficient. We have chosen the second option because 0 the λTCA + values thus obtained may be compared with those previously determined on the binary systems, as a control test of the model. As widely explained elsewhere,24 eqs 2, 8, and 9 and the mass and charge balances have been used to fit the experimental κ data as a function of β-CD concentration with a nonlinear regression method, based on a nonlinear Newton-Raphson and a Marquardt algorithm. The fit coefficients, that is, the binding constant, KCD/TCA+, and the ionic molar conductivities at infinite dilution 0 0 of the complex, λCD/TCA +, and the free drug, λTCA+, are 0 reported in Table 2. It can be observed that (i) λTCA + values are in agreement with those previously reported in Table 1, proving the goodness of the model; (ii) the ionic molar conductivities of the associated drug molecules, 0 λCD/TCA +, decrease more than 50% with respect to their 0 unassociated state, λTCA +. This fact is indicative of a decreased mobility of the cationic drug when it is encapsulated within the CD cavity, as could be expected. The reduction of the conductivity as a consequence of the inclusion found for the drugs studied in this work is comparably higher than that obtained for CD/surfactant systems with long tails,14,19 pointing to a tighter localization of the charge on the complex in the present case; (iii) the values obtained for the association constants of the β-CD/TCA+ complexes are of the same order of magnitude as those of other CD/surfactant systems14,19 and decrease in the order KCD/AMYTP+ > KCD/DIPR+ > KCD/IPR+. These (24) Junquera, E.; Pen˜a, L.; Aicart, E. J. Pharm. Sci. 1997, 87, 86.

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Figure 8. Values of molar conductivity, Λ, of aqueous solutions of the hydrochlorides of amitriptyline, desipramine, and imipramine at constant [β-CD] ∼ 10 mM as a function of [TCA], at 25 °C.

Figure 7. Preliminary geometry of the complex β-CD/AMYTP minimized with the MM+ force field of MM (HyperChem version 5.1).

moderate values are favorable from a pharmaceutical point of view, because it is known4-6 that a high affinity between the drug and the β-CD implies a difficult delivery of the active principle to the organism, whereas on the contrary there are no significant differences between the administration of the CD/drug complex and of the drug alone. The association constants for the complexes R-CD/AMYTP+ (K ) 113 ( 7 M-1) and R-CD/IPR+ (K ) 130 ( 20 M-1), determined from competitive spectroscopic studies,25 are consistent with the values reported in this work given the well-known reduction of the affinity of the encapsulation process when β-CD is replaced by R-CD. It is known14,19,26,27 that CD/ionic surfactant complexes are slightly associated (∼1%) to the surfactant counterions, but this circumstance does not occur when the inclusate is a globular molecule. Because the drugs studied herein have in their molecules a globular part (the three cycles) and a kind of surfactant tail with a cationic polar head, and in fact they show a typical surfactant behavior, we have checked whether in the present case the Cl- anion is associated with the CD/TCA+ complex to some extent. For that purpose, the model reported in this work has been extended to include a fourth fit coefficient, KCD/TCA+Cl, which takes into account this possible association. However, the results confirm that this association does not exist (KCD/TCA+Cl- ∼ 0). Figure 7 shows, as an example, a stereoview of a preliminary molecular modeling simulation of the inclusion complex formed by β-CD and the amitriptilynate cation, minimized with the MM+ force field of molecular (25) Georgiou, M. E.; Georgiou, C. A.; Koupparis, M. A. Analyst 1999, 124, 391. (26) Palepu, R.; Reinsborough, V. C. Can. J. Chem. 1989, 67, 1550. (27) McPherson, Y.; Palepu, R.; Reinsborough, V. C. J. Inclusion Phenom. 1990, 9, 137.

mechanics,28 as integrated in Hyperchem version 5.1. The atomic coordinates of the crystal structure of β-CD were used to obtain a conformational minimum for the receptor. The substrate, previously minimized, was docked manually into the cavity by both faces of the receptor and then minimized. It can be noticed that the three cycles of the drug molecule seem to reside out of the apolar cavity, whereas the tail with the polar head is encapsulated within it. This possible geometry is consistent with the evidence found in the UV-vis and fluorescence experiments. The spectroscopic properties of the drug are not appreciably affected in the presence of CD because the part of the molecule which is mainly responsible for these properties is outside the cavity. Anyway, the mobility and the conductivity of the drug does decrease as it is included within the cavity, irrespective of the structure of the complex. (3) Effect of CD on the Self-Aggregation. Figure 8 shows the plot of molar conductivity of aqueous solutions of β-CD at a constant concentration of around 10 mM as a function of TCA concentration. As can be seen in the figure, the curves are similar to those shown in Figure 3 for the pure TCAs with two important differences: (i) a minimum in the curves at a certain [TCA] (prior to the aggregate formation), not present in Figure 3, reveals the complex formation and (ii) the change in the slope of the conductivity (once the complex is formed), resulting from the formation of the aggregates, is shifted toward a higher drug concentration with respect to the values obtained from Figure 3. From the [TCA] at the minima in Figure 8 and the constant [β-CD] in each case, the stoichiometries of the complexes, A, have been determined and reported in Table 3. The results show a very good agreement with those reported in Table 2. The change in the slope of the conductivity data versus [TCA] allows determination of the apparent critical aggregation concentration, cac*, defined as the cac in the presence of CD, and the dissociation degree of the (28) Burkett, U.; Allinger, N. L. Molecular Mechanics; American Chemical Society: Washington, DC, 1982.

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Table 3. Values of Apparent Critical Aggregate Concentration, cac*, Free Drug Concentration, [TCA]free, and Dissociation Degree, β, of the TCA Aggregates in the Presence of β-CD and the Stoichiometry of the β-CD/TCA+ Complexes at 25 °C TCA

[β-CD] (mM)

cac* (mM)

β

Α

[TCA+]free (mM)

AMYTP+ DIPR+ IPR+

9.618 9.779 10.115

52.5 ( 0.2 66.0 ( 0.2 66.3 ( 0.2

0.58 ( 0.02 0.61 ( 0.02 0.57 ( 0.02

1.03 ( 0.02 0.98 ( 0.02 0.99 ( 0.02

43.2 ( 0.4 56.0 ( 0.4 56.1 ( 0.4

aggregates, following the same procedures previously used for the pure drugs. The values thus calculated are reported in Table 3. In analogy with the formation of micelles in the presence of cyclodextrin,14 the cac* can be expressed as

cac* ) [TCA]free + [TCA]assoc ) [TCA]free + [β-CD]/A (10) where [TCA]free is the drug concentration available for the aggregation process in the presence of CD, [TCA]assoc is the concentration of the drug forming the complex, and [β-CD] is the cyclodextrin concentration kept constant. The values of [TCA]free, calculated by using eq 10, are also

reported in Table 3. These results reveal several important features of the TCA aggregation process in the presence of cyclodextrin: (i) the drug concentration available for the aggregation, [TCA]free, coincides with the cac values reported in Table 1, within the experimental error; (ii) this fact justifies that the concentration at which TCAs aggregate, cac*, is raised by the quantity [β-CD]/A from cac values; (iii) the dissociation degree of the TCA aggregates is not affected by the presence of β-CD. Acknowledgment. This research was supported by the Ministerio de Educacio´n y Cultura of Spain through the DGES Grant PB98-0755. LA000819Q