Kinetics of Inclusion Reactions ofâ-Cyclodextrin with Several Dihydroxycholate IonsStudied by NMR Spectroscopy

C. T. Yim*Department of Chemistry, Dawson College, 3040 Sherbrooke Street West,Westmount, Quebe´c, Canada H3Z 1A4

X. X. ZhuDepartement de Chimie, UniVersitede Montreal, C.P. 6128, succursale Centre-Ville,Montreal, Quebe´c, Canada H3C 3J7

G. R. Brown†

Department of Chemistry, McGill UniVersity, 801 Sherbrooke Street West,Montreal, Quebe´c, Canada H3A 2K6

ReceiVed: August 18, 1998

The1H NMR spectra of some aqueous dihydroxycholate-â-cyclodextrin systems show separate 18-CH3 signalsfor complexed and free dihydroxycholate ions. The observed variations in line shapes with concentration andtemperature were investigated, and kinetic data were derived for both the formation and decomplexationprocesses. Analysis of the results indicates that, within the concentration range studied, the dominant exchangemechanism involves a unimolecular decomplexation step (dihydroxycholate,â-cyclodextrin)f dihydroxy-cholate+ â-cyclodextrin. For the chenodeoxycholate system the enthalpies of activation are 43( 5 and 45( 2 kJ/mol, the entropies of activation are-5 ( 10 and -66 ( 7 J/(K mol) for the formation anddecomplexation reactions, respectively, and its decomplexation rate constant is 34( 1 s-1 at 300 K. Otherdihydroxycholate-cyclodextrin systems show similar activation parameters but slightly lower reaction ratesat 300 K. Dehydration plays a major role in the formation process, while the decomplexation rates appear tobe controlled by the conformation of the dihydroxycholates.

Introduction

Cyclodextrins (CDs) are macrocyclic oligosaccharides capableof forming inclusion complexes with a variety of organic andinorganic molecules in aqueous solutions. The CD moleculestake the shape of a truncated cone, with cavities of differentsizes depending on the number of glycosidic units. The interiorof the cavities is rather hydrophobic, while the exterior remainshydrophilic. The cavities can be used to trap molecules ofcomparable size, a feature that is of special interest in molecularrecognition studies.1,2 The inclusion processes also lead toimportant modifications of the properties of the guest com-pounds, and inclusion complexes have found applications insolving numerous practical problems.3-5

The molecular recognition by cyclodextrins has been inves-tigated from theoretical, thermodynamic, and kinetic aspects.Primarily on the basis of thermodynamic and stability data, thedriving force for inclusion has been attributed to hydrogenbonding, van der Waals forces, hydrophobic interactions,relaxation of the conformational strain in the CD, and releaseof hydrogen-bonded water molecules from the cavity.5 Crameret al.6 reported the first kinetic measurements performed on aseries of naphthylazobenzene-R-CD complexes. They found

that the dissociation rate constants for eight of these complexesvaried from 0.01 to 1.3× 105 s-1, in marked contrast with theirbinding constants, which ranged only from 270 to 1010 M-1.They attributed the observed kinetic specificity to the involve-ment of the desolvation of the guest molecules in the rate-determining step. Their results illustrate the importance of kineticmeasurements, which provide valuable dynamic and mechanisticinformation that is indispensable for understanding the natureof interactions involved in inclusion reactions. Since then,interesting kinetic data have been accumulated for reactionsinvolving CD complexes using a variety of methods such astemperature jump, stopped flow, fluorescence lifetime, andultrasonic absorption techniques.6-16

For most cyclodextrin inclusion complexes, the exchangebetween complexed and free species is rapid on the NMR timescale, allowing only average, relatively narrow NMR signalsto be observed.17 Although these spectra are valuable forstudying structure and properties of inclusion complexes, theycontain little information concerning the kinetics of complex-ation processes. However, in the early 1990s Matsuo et al.reported the observation of distinct1H NMR signals due tobound and free species in several through-ringR-CD complexesformed by guest molecules possessing a polymethylene chainterminated with charged groups.18,19Reaction rates and activa-tion parameters were extracted from the observed temperatureeffect on these signals. On the other hand NMR methods,particularly23Na NMR, have been used extensively by several

* To whom correspondence should be addressed. E-mail: cyyi@Musica.McGill.ca. Fax: 514-931-3567.

† Present address: University of Northern British Columbia, ChemistryProgram, 3333 University Way, Prince George, British Columbia, CanadaV2N 4Z9.

597J. Phys. Chem. B1999,103,597-602

10.1021/jp9833909 CCC: $18.00 © 1999 American Chemical SocietyPublished on Web 01/05/1999

authors to investigate the kinetics of the complexation of alkalimetal cations by crown ethers, also a system of considerableinterest in molecular recognition studies.20-22 Detailed resultson reaction mechanism, activation parameters, and solventeffects were obtained by performing relaxation rate measure-ments or line shape simulations. These studies illustrate theunique character of the NMR method in its capacity to probereactions without perturbing the system and provide usefulkinetic information about reactions occurring in equilibriummixtures.

It has been demonstrated previously thatâ- andγ-cyclodex-trins form inclusion complexes with bile salts anions.23 Thepossibility of using cross-linked cyclodextrin resins as bile saltbinding agents has also been explored.24 To further probe the“host-guest” interaction in bile salt-CD systems we haveexamined the kinetics of complexation ofâ-cyclodextrin withthree dihydroxycholate anions: chenodeoxycholate, glycocheno-deoxycholate, and ursodeoxycholate. The1H NMR spectra ofthese three aqueous dihydroxycholate-â-cyclodextrin systemsshow separate 18-CH3 signals for complexed and free dihy-droxycholate ions. The observed variations in line shape withconcentration and temperature were investigated and kinetic datawere derived for both the formation and decomplexationprocesses.

Experimental Section

The â-cyclodextrin (â-CD), sodium chenodeoxycholate(NaCDC), and sodium glycochenodeoxycholate (NaGCDC)were purchased from Aldrich and used as received. The sodiumursodeoxycholate (NaUDC) was prepared by neutralizing thecorresponding acid, also purchased from Aldrich. The chemicalstructures of these three dihydroxycholates with the correspond-ing abbreviations are shown in Figure 1. D2O solutions of thedihydroxycholates containing varying amounts ofâ-CD wereprepared. The concentration of chenodeoxycholate was keptbetween 3.88 and 3.99 mM, glycochenodeoxycholate between4.03 and 4.30 mM, and ursodeoxycholate between 3.17 and 3.33mM. These concentrations, which are well below the reported

critical micelle concentrations (cmc) values, were selected tominimize possible interference from micelle formation.25,26Theconcentration ofâ-CD was in the range of 0.5-3.2 mM.

The1H NMR spectra were acquired with a Varian Unity 500spectrometer operating at 499.84 MHz for protons. The probetemperature was calibrated with standard samples of ethyleneglycol and methanol.

Results and Discussion

In our experiments the attention was focused on the signalsfrom 18-CH3 group. For samples containing dihydroxycholatealone, it is a well-separated sharp singlet at the upfield end ofthe spectrum.27 The addition ofâ-CD results in the appearanceof a new 18-CH3 peak, located approximately 75 Hz (0.15 ppm)downfield from the original peak. Obviously, this peak can beattributed to the complexed dihydroxycholate ions, whichundergo moderately slow exchange with the free ions, asevidenced by the considerable broadening of both signals. Thearea intensity of the complexed species increased withâ-CDconcentration at the expense of that of the free dihydroxycholate.Shown in Figure 2 is a representative plot for the CDC-â-CDat 300 K showing the normalized total area of the two signalsand the area fraction of the signal due to the complexed ion, asa function of theâ-CD/CDC molar ratio. The formation of stable1:1 complexes is clearly confirmed by the plot. In addition, theconstant total area indicatesthat these two signals are the onlyones from the 18-CH3 group. There have been reports ofadditional signals attributable to reaction intermediates in theproton NMR spectra of severalR-CD complexes.15 We did notobserve these signals in any of our samples, and any reactionintermediate, if it exists, certainly does not bring about a separatesignal. Therefore, the C18 methyl protons will be treated asuncoupled spin systems undergoing two-site exchange.

Figure 3 shows the effect of initial concentration ofâ-CD,[â-CD]0, on the spectra of CDC-â-CD at 300 K. To extractthe exchange rates from these spectra, a complete line-shapesimulation was performed using the Bloch equation modifiedfor an uncoupled spin system undergoing chemical exchangebetween two nonequivalent sites,28 site A and site B for thefree and complexed dihydroxycholate anion, respectively. Thesimulation requires the inputs of the chemical shift differencebetween the two sites (∆ν), the line width in the absence of

Figure 1. Structure of the dihydroxycholates.

Figure 2. Normalized total area of C18 methyl signals (0) and areafraction of the complexation induced C18 peak (∆) as a function ofmolar ratio,â-CD/CDC, for CDC-â-CD at 300 K. The total area wasnormalized to an initial concentration of CDC) 3.80× 10-3 M.

598 J. Phys. Chem. B, Vol. 103, No. 3, 1999 Yim et al.

exchange (T2), the lifetime (τA and τB), and the relativepopulation (pA and pB) of each site. The populations andlifetimes are related by

For each system the values of∆ν andT2 were first chosenby careful inspection of the spectra and by trial simulation. Theywere then kept constant for the simulation of spectra at differenttemperatures and concentrations. The values ofpA andτA werevaried until the simulated and experimental spectra could besuperimposed. The simulated spectra for the same system, withthe values ofpA andτA used in the simulation, are also shownin Figure 3.

Two possible mechanisms may affect the exchange of boundand free “guest” in inclusion complexes. They are (a) theunimolecular decomplexation

and (b) the bimolecular anion interchange mechanism20-22

where Cpx and DHOC- represent the inclusion complex andthe free dihydroxycholate anion, respectively. It can be shownthat τA andτB are related to the rate constants by

whereR ) (pB/pA) and [DHOC]0 is the initial concentration ofthe dihydroxycholate. Equation 3 shows that a plot of((1/τA)+ (1/τB))/[DHOC]0 as a function of (1+ R)/[DHOC]0 shouldyield a straight line with slopek-1 and interceptk2. Plots ofseveral representative data sets are shown in Figure 4. In allcases, the intercepts have relatively small positive or negativevalues, which, within experimental error, can be taken as zero.Thus we conclude that, within the concentration range studied,the contribution of the bimolecular mechanism to the overallexchange is negligible.

The occurrence of both unimolecular decomplexation andbimolecular interchange processes has been demonstrated forother guest-host systems with the latter becoming, as expected,more dominant at higher concentrations.21,22Unfortunately, theformation of micelles by dihydroxycholates compelled us toconfine this study within a low concentration range. Further-more, it seems reasonable to expect that the bimolecularinterchange process would occur more readily with guestmolecules capable of passingthroughtheâ-CD cavity. There-fore, in view of the size and the rigidity of the cyclopen-taphenanthrene unit, it is doubtful that the bimolecular mech-anism would become significant in our systems even at higherconcentrations. In this respect, it would be of interest to examinethe kinetics of cyclodextrin inclusion complexes having proper-ties more amenable to the bimolecular interchange process.

The rate constants at several temperatures are listed in Table1. Of the three systems studied, the complexation with cheno-deoxycholate has the highest rate constants while that forursodeoxycholate has the lowest, illustrating the importance ofthe configuration of the 7-hydroxy group. The listed rateconstants for the formation reaction,k1’s, show relatively largeuncertainties; this reflects the fact that calculation ofk1 valuesinvolves the equilibrium concentration ofâ-CD, [â-CD]. In ourapproach [â-CD] is obtained by

where subscript “0” indicates the initial concentration of thespecies, and AFcpx is the area fraction of the signal due thecomplexed species as plotted in Figure 2. The equilibriumconcentrations, calculated by eq 4 as the difference betweentwo relatively large numbers, are very sensitive to possibleerrors in area measurements, leading to large uncertainties in

Figure 3. Experimental (left) and simulated (right) NMR spectra ofCDC-â-CD at 308 K. [â-CD]0 is the initial concentration ofâ-CD inmillimolar. pA and τA are the relative population and lifetime (inmilliseconds) of free anions, respectively.

pA + pB ) 1 (1)

pA

τA)

pB

τB(2)

â-CD + DHOC- y\zk1

k-1Cpx

Cpx + DHOC-* y\zk2

Cpx + DHOC-

Figure 4. Representative plots for determining rate constantsk-1 andk2: CDC at 283 K (O); GCDC at 300 K (0); UDC at 315 K (4).

1τA

+ 1τB

) k-1(1 + R) + k2[DHOC]0 (3)

[â-CD] ) [â-CD]0 - AFcpx [DHOC]0 (4)

Inclusion Reactions ofâ-Cyclodextrin J. Phys. Chem. B, Vol. 103, No. 3, 1999599

the derivedk1 values. Since [â-CD] is also utilized for evaluatingthe formation constants (Kf), similar error consideration can beapplied to ourKf values. At 300 K they are (2.5( 0.4)× 103,(3.7( 0.5)× 103, and (4.0( 0.7)× 103 mol/L, for the CDC-,GCDC-, and UDC-â-CD complexes, respectively. The largeuncertainties inKf values prevent us from obtaining quantitativeinformation on their temperature dependence. Here we can onlyreport that, at all temperatures studied, UDC forms the moststable inclusion complex and CDC the least stable. TheKf valuesdecrease with temperature, indicating a small negative∆Hf ofabout-5 to -10 kJ/mol.

On the basis of steric considerations and NMR evidence ithas been suggested that the hydrophilic side chain enters andprotrudes through the â-CD cavity and that formation ofinclusion complexes predominantly involves interactions withthe bulky hydrophobic steroid skeleton of the bile salt anions.23

In this regard, it is interesting to note that the presence of theglycine unit at theextreme endof the side chain induces a smallbut significant decrease in the observed rate constants, support-ing the view that the bile salt anions penetrate theâ-CD cavityvia the hydrophilic end.

As reported earlier23 the proton NMR spectra of other systemscontainingâ-CD and cholate or glycocholate anions do not showseparate C18, C19, or C21 methyl peaks for the complexed andfree anions. However, a more careful examination of the spectraobtained with samples containing sodium cholate revealed asmall but significant broadening of the C18 methyl peak. Arough estimate yielded an approximate rate constant (k-1) of800 s-1 for its decomplexation process at 295 K. Thus, we canconclude that the exchange rates are much faster for bile-saltanions containing the 12R-hydroxyl group. The absence of the12R-hydroxyl group not only leads to a more stable complexwith â-CD, as evidenced by the magnitude of theKf values,but also significantly slows down the formation and decom-plexation processes. Usually, a downfield shift in the proton

NMR signals is observed with the formation of CD complexes.15

Interestingly, with the dihydroxycholate samples a much largershift was observed for C19 methyl (about 0.06 ppm) than forC21 methyl (e0.02 ppm), while the opposite was true for thecholate and glycocholate systems.23 These results suggest thatdihydroxycholate anions penetrate theâ-CD cavities to a greaterextent (see Figure 1). Therefore, we attribute the observeddifferences in stability and in rates to stronger interactions withthe bulky steroid skeleton caused by deeper penetration of thedihydroxycholate anions into the cavities.

The rate constants listed in Table 1 were used to constructEyring plots, shown in Figures 5 and 6. The derived activationparameters (∆G‡, ∆H‡, and∆S‡) for these three systems, givenin Table 2, show quite similar trends, with little difference inboth enthalpy and entropy of activation. Furthermore, both theformation and decomplexation reactions have similar activationenthalpies. However, the three decomplexation reactions haverelatively large, negative∆S‡ values, while the∆S‡ values forformation processes are much smaller and can be of either sign.The contribution of the negative activation entropy leads to alarger, positive∆G‡ for the decomplexation reactions and thusmuch smaller rate constants.

Several authors have considered various contributions to thefree energy change for bimolecular associations in solution, andin some cases their values have been estimated for specificsystems for semiquantitative prediction of binding constants.29-32

Following Williams et al.31 and retaining only the important

TABLE 1: Rate Constants for the Formation (k1) and Decomplexation (k-1) Reactions at Several Temperatures

CDC GCDC UDC

T (K)k1/104

(M-1 s-1)k-1

(s-1)k1/104

(M-1 s-1)k-1

(s-1)k1/104

(M-1 s-1)k-1

(s-1)

283 3.5( 0.6 11.9( 0.3291 6.3( 0.7 22.0( 1.1 4.6( 0.7 11.1( 0.9 4.0( 0.7 7.9( 0.6300 9.1( 1.0 34.0( 1.2 7.5( 1.4 18.4( 0.6 7.4( 1.3 15.4( 0.6308 17( 2.7 63.6( 1.1 12( 1.5 32.8( 0.6 11( 2.0 24.2( 1.8315 19( 3.0 52.1( 1.6 19( 3.0 40.5( 0.9

Figure 5. Plots of ln(k1/T) vs (1/T) for the formation reactions: CDC(O); GCDC (0); UDC (∆). To avoid overlap, the points for CDC andUDC have been moved by 0.05× 10-3 deg K-1, to the right and left,respectively.

Figure 6. Plots of ln(k-1/T) vs (1/T) for the decomplexation reac-tions: CDC (O); GCDC (0); UDC (4).

TABLE 2: Activation Parameters for SeveralDihydroxycholate-â-Cyclodextrin Inclusion Complexes

formation decomplexation

∆H‡

(kJ/mol)

∆S‡

[J/(Kmol)]

∆G‡

(kJ/mol)at 300 K

∆H‡

(kJ/mol)

∆S‡

[J/(Kmol)]

∆G‡

(kJ/mol)at 300 K

CDC 43( 5 -5 ( 10 45( 7 44.6( 2.0 -66 ( 7 65( 5GCDC 42( 6 -10 ( 6 45( 7 47.1( 2.0 -63 ( 7 66( 4UDC 46( 6 2 ( 7 46( 7 48.2( 2.0 -62 ( 5 67( 4

600 J. Phys. Chem. B, Vol. 103, No. 3, 1999 Yim et al.

terms relevant to relatively nonpolar guests such as dihydroxy-cholates and to binding in aqueous medium, the free energychange (∆G) upon bimolecular associations can be expressedas:

The first term, ∆G(trans+rot), relates to the freezing of thetranslational and rotational freedoms of the guest molecules.The term∆Gconformaccounts for possible conformational changesnecessary for the formation of complexes. The third term,∆GvdW, arises because of the increase in the van der Waalsinteractions due to the efficient packing achieved in thecomplexes. The last term,∆Gdehyd, represents the contributionfrom the dehydration of the reaction species; this includes the“classical” hydrophobic interaction, a mainly entropic phenom-enon involving the dehydration of nonpolar solutes and therearrangement of H-bond configurations around the solutemolecules.33 Only the last two terms,∆GvdW and∆Gdehyd, arefavorable for association processes. Since similar forces shouldbe involved in the formation of activated complexes, one couldrationalize the observed activation parameters in terms of thesecontributions.

The formation of an associative activation complex occurswith at least partial loss of translational, rotational, andconformational freedoms, resulting in an unfavorable, negativeentropy contribution. The small activation entropy for theformation reaction in our systems clearly indicates that theentropically favorable dehydration process, involving bothhydrophilic and hydrophobic moieties, must be involved in theformation of activated complexes. The rate of complexation isthus predominantly determined by its∆H‡ value, the energybarrier for the deep penetration of dihydroxycholate anions intothe â-CD cavity.

The large negative∆S‡ for the decomplexation processes canbe partly ascribed to the conformation of the side chain in theactivated complex. It can be argued that in order to retrieve thebile salt anion from the cavity the side chain must adopt a ratherstraight conformation, thus resulting in a negative entropy.However, this proposition cannot account for the large ratechange rendered by the 12R-hydroxyl group, nor for thenegligible effect of the glycine unit on the values of activationentropy. Therefore the large negative∆S‡ might also indicatethat, in the activated complex, the steroid skeleton of thedihydroxycholate anions experiences a very restricted environ-ment created by the tight fit of the bulky skeleton into theâ-CDcavity.

We visualize the inclusion process as consisting of thefollowing steps: (a) Dihydroxycholate ions approach theâ-cyclodextrin and adopt an appropriate orientation. (b) Someof the hydrating water molecules are removed from thedihydroxycholate side chain and from theâ-CD cavity. The sidechain inserts into the cavity via the secondary hydroxy rim, themore open side of the conical cyclodextrin. (c) Dehydration ofthe steroid skeleton takes place. The skeleton enters the cavityand adopts a more restrictive orientation with respect to thegroups lining the interior of the cavity. It is at this stage thatthe activated state is reached. (d) With deeper penetration ofthe steroid skeleton a final, stable inclusion complex is formed.The deeper penetration and tight fit ensure stronger van derWaals interactions with theâ-cyclodextrin. (e) The dihydroxy-cholate side chain adopts a more relaxed conformation andrehydration of its protruding moieties may also occur.

Conclusions

We first demonstrate that the exchange rates for the inclusionreaction of several bile salt-cyclodextrin complexes can beextracted by line shape simulation of the observed NMR signals.The results reveal that, in the concentration ranges studied, thebimolecular mechanism does not make a measurable contribu-tion to the observed exchange rate. Thus, the decomplexationproceeds via a unimolecular mechanism. The first-order rateconstants were derived for decomplexation reaction of the threedihydroxycholate-â-CD complexes; they vary from 7 to 63 s-1

in the temperature range studied. Our kinetic results for thecomplexation of CDC and GCDC strongly support the sugges-tion that the dihydroxycholate anions enter theâ-CD cavity viathe hydrophilic side chain.

Similar ∆H‡ and ∆S‡ values were obtained for both theformation and decomplexation of these three inclusion com-plexes. The small∆S‡ values for the complexation reactionclearly indicate the involvement of dehydration of the reactionspecies in the formation of activated complexes. We also notedthe relatively larger negative activation entropy for the decom-plexation process. It was argued that, for the three dihydroxy-cholate systems, the high stability of the inclusion complexesand their slow reaction rates can be attributed to the deeppenetration of the corresponding anions into theâ-CD cavity.This leads to strong hydrophobic and van der Waals interactions,and also brings about a rather restricted environment for theactivated complex, as indicated by the large negative activationentropy of the decomplexation reaction.

Acknowledgment. Financial support from Fonds FCAR(EÄ quipe) of Quebec and from the Natural Sciences andEngineering Research Council (NSERC) of Canada is gratefullyacknowledged.

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