Site-Specific Interaction between 2-Dibenzofuran Carboxylate andâ- and γ-CyclodextrinsDetermined by Intermolecular NOE and Molecular Modeling

Gustavo Gonzalez-Gaitano,*,† Pablo R. Sainz-Rozas,† JoseRamon Isasi,†Andres Guerrero-Martı nez,‡ and Gloria Tardajos‡

Departamento de Quı´mica y Edafologı´a, UniVersidad de NaVarra, 31080 Pamplona, NaVarra, Spain, andDepartamento de Quı´mica-Fısica I, Facultad de Ciencias Quı´micas, UniVersidad Complutense,28040 Madrid, Spain

ReceiVed: April 9, 2004; In Final Form: June 5, 2004

The topologies of the complexes between 2-dibenzofuran carboxylate (DBFC) andâ- and γ-cyclodextrins(CDs) have been studied by NMR methods (1H NMR and 2D ROESY) and by molecular modeling strategies.The analysis of the spectra and the molar ratio plots reveal the formation of complexes of 1:1 stoichiometrywith â-CD. The stability constants have been calculated by multivariable nonlinear least-squares regressionfrom the changes in the chemical shifts of the protons of both host and guest molecules. For theâ-CD complex,the interproton distances between the host and guest have been deduced from the NOE enhancements. Rigiddocking calculations using the geometrical restraints given by the NMR experiments, together with moleculardynamics simulations assuming a continuum solvent model, indicate that DBFC is oriented with the carboxylategroup at the narrow rim of the CD. The radial distribution functions obtained by considering explicit watermolecules with periodic boundary conditions indicate that the solvation degree of the charged group of DBFCin its free or bound form is the same. In the case ofγ-CD, the NMR data indicate the presence of 1:1 and2:1 complexes [(DBFC)2/γ-CD], with a constant for the second binding step higher than that of the first. Thestoichiometry and binding constants, apparently in disagreement with previously reported fluorescenceexperiments, are satisfactorily explained by considering the range of working concentrations.

Introduction

Cyclodextrins (CDs) are cyclic oligosaccharides built up fromR-D-glucopyranose residues linked by glycosidic bonds, withthe most common being those formed by six, seven, or eightglucose units (R-, â-, andγ-CD, respectively). Because of thelack of free rotation about the glycosidic bonds, CDs display atorus-like or hollow truncated cone shape, with a hydrophobiccavity and two hydrophilic rims in which the primary andsecondary OH groups are inserted (Chart 1). The main featurethat makes CDs of interest is their ability to form inclusioncomplexes with a variety of guest molecules, in solution or inthe solid phase. This quality offers many interesting applications,which have been described extensively in the literature.1 Thefirst condition required for a molecule to form an inclusioncomplex with CD is that it fits in the cavity, either completelyor partially. In addition, a favorable energetic balance is required,which depends on the nature of the guest, the inner diameter ofthe CD, and the CD’s substitution degree.2

In a previous work,3 we investigated the photophysics (mainlyby absorption and steady-state fluorescence) of a dibenzofuran(DBF) derivative, 2-dibenzofuran carboxylic acid (DBFCA), inseveral solvents and in the presence of CDs. DBFCA formsinclusion complexes withR-, â-, andγ-cyclodextrins, with thespectral behavior being highly dependent on the type of CDand pH. Yet, the information that such techniques can provide

about the complexes in solution is usually limited to thestoichiometry and the evaluation of the association constantsand thermodynamic parameters that can be extracted from this(i.e., enthalpy and entropy, from the temperature dependenceof K).

From the structural point of view, nuclear Overhauserspectroscopy is considered one of the most definitive methodsfor the study of complexes with cyclodextrins,4 because thedipolar interactions that are detected as NOE enhancementsreflect the spatial proximity between protons. For medium-sizedsystems, such as those studied here, the appropriate techniqueis rotating frame Overhauser effect spectroscopy (ROESY),because the NOESY signals are too weak for a reliableevaluation of distances.5 This technique, used jointly withmolecular modeling calculations, can provide detailed informa-tion on the structure of the complexes, always keeping in mindthe dynamic character of these systems, in which a fastequilibrium between complex and free molecules is taking place.It is precisely due to this dynamic nature, and to the highsymmetry of CDs, that the information about interprotondistances is usually considered only from the qualitative pointof view, thus losing the most important potentiality of ROESY.

* Corresponding author. Address: Departamento de Quı´mica y Edafo-logıa, Universidad de Navarra, 31080 Pamplona, Navarra, Spain. E-mail:gaitano@unav.es.

† Universidad de Navarra.‡ Universidad Complutense.

CHART 1

14154 J. Phys. Chem. B2004,108,14154-14162

10.1021/jp0484231 CCC: $27.50 © 2004 American Chemical SocietyPublished on Web 08/20/2004

In this framework, we have investigated the topology of theinclusion complexes formed between 2-dibenzofuran carboxylate(DBFC) andâ-CD andγ-CD. An exhaustive analysis of theNOE volumes, together with different strategies of molecularmodeling (mainly rigid docking and molecular dynamics), hasbeen performed to achieve a full concordance between all setsof experimental data. The results complete the previous onesobtained by fluorescence measurements and shed light onaspects that emission spectroscopy cannot ascertain.

Materials and Methods

NMR Experiments. â-CD was obtained from Roquette andγ-CD from Wacker, having water contents of 10.6% and 7.91%,respectively, as determined by thermal analysis. 2-Dibenzofurancarboxylic acid (DBFCA) was manufactured by Aldrich (RareChemicals Library). The solutions were prepared in D2O(Aldrich Chemical Co., 99.9% minimum in D), with thenecessary amount of NaOD (Merck, 40% solution of NaOD inD2O, 99.5% in D) to reach pH 10. All reactants were usedwithout further purification.

For the1H NMR experiments, a stock solution of 2-diben-zofuran carboxylate (DBFC) was added to vials containingweighed amounts of CD, and the mixtures were sonicated andtransferred to NMR tubes (final volumes of ca. 0.5 mL). Thespectra were recorded at 300 K in a Bruker Avance 400Ultrashield spectrometer (9.36 T) by averaging 600 scans, witha digital resolution of 0.15 Hz. The HDO signal was used asthe reference. The resonances of DBFC were assigned with theaid of the 1D and COSY spectra. No dependence of the chemicalshifts of DBFC on the concentration was detected. For thecalculation of the binding constants from the chemical shifts,the actual concentration of DBFC was obtained by the ratiobetween the area of the H1 signal of the CD (integrating forseven or eight protons forâ-CD or γ-CD, respectively) andthat of proton a (Chart 1), after a fine baseline correction of thespectrum. The H1 signal is the narrowest of all of the CDresonances and is free of overlapping. The concentration of theCD, well-known by weighing, is taken as the reference. Theconcentrations thus calculated were 7.5× 10-4 and 1.05× 10-3

M for the studies withâ-CD andγ-CD, respectively.For the 2D ROESY experiments, the sample concentrations

were 9.98× 10-3 M â-CD + 4.11× 10-3 M DBFC and 9.82× 10-3 M γ-CD + 6.10× 10-3 M DBFC prepared by addingalkaline solutions ofâ- and γ-CD to weighed amounts ofDBFCA. The concentration of DBFC was calculated asmentioned above, and the temperature was kept constant in theseexperiments at 298 K. A Bruker Avance DPX-300 spectrometer(7.05 T) was used, by applying the pulse sequence defined inthe literature.6 The power level for the spin-lock pulse wasγB1/2π ) 2500 Hz. Different spin-lock mixing times (rangingbetween 400 and 800 ms) were applied to ensure the validityof the linear approximation for the NOE peak intensities andto obtain the best signal-to-noise ratio, which was achieved with600 ms for both CD/DBFC systems. Thirty-two scans werecollected in each spectrum, which consisted of a matrix with512× 1024 data points covering a spectral width of 3307 Hz.The treatment of the free induction decays (FIDs) was carriedout with MestRe-C software.7 Before the Fourier transformationand the subsequent 2D phase tuning were executed, linearprediction in F1 and cosine square apodization in both dimen-sions were applied to the FIDs. The resulting spectra werebaseline corrected in each dimension with third-order polynomi-als prior to the integration of the NOEs.

The interproton distances have been calculated from the NOEpeaks by the equation5,8

whereaij is the NOE cross-peak volume andrref is a referencedistance between two protons yielding an NOE volume,aref.The coefficientscij are introduced to account for the offsetdependence of the cross-peak intensities relative to the transmit-ter center, according to the equations described by A¨ mmalahtiet al., i.e.

and

In these expressions,ωR - ω0 is the difference between thechemical shift of the peak and the center of the spectral window(1426 Hz in our experiments), andγB1 is the spin-lock power,expressed in Hz.

Computational Studies and Methodology.Computationswere performed with Insight II software,9 on an SGI-Cray Origin2000 computer at the CSC (Centro de Supercomputacio´nComplutense, Madrid, Spain), employing the AMBER10,11forcefield, which is included in the software.

Energy minimization of the isolated host and guest moleculeswas performed with the Discover module, employing differentalgorithms (beginning with steepest descents and finishing witha modified Newton-Raphson to refine the structures) until theroot-mean squares of the derivatives were less than 0.0001 kcalÅ-1. Afterward, short molecular dynamics (MD) simulationswere run at 298 K, and the process of minimization was repeatedto reach a stable conformation. For the rigid docking experi-ments, anxyplane was defined by the glycosidic oxygen atomsof the CD, and the coordinate origin as the center of mass ofthese seven O4s. Thez axis is perpendicular to this plane, withpositive orientation toward the wider rim. The coordinate originof DBFC is its center of mass, and the axes are defined by theprincipal axes of inertia of the molecule. The centers of thehost and guest are separated by 2.5 Å, and the DBFC approachesthe CD along thez direction. DBFC is allowed to rotate freelyaround its three axes at eachz value, in steps of 20°. For eachpoint, defined by (z, R, â, γ), the distances between the H atomsthat give rise to significant NOE intensities are measured toobtain the effective interproton distances (see the Results andDiscussion section). To avoid atomic overlap, only thosecomputed geometries that yield reasonable values of theintermolecular van der Waals energy of interaction (as calculatedwith the Docking module of the software) are recorded. Thesevalues are compared with the experimental distances obtainedby eq 1, and the root-mean-square (rms) values calculated. Allof these tasks are executed with a program written in the BiosymCommand Language.

For the MD calculations, we accounted for the solvent bothexplicitly and implicitly. In the first case, a periodic cubic boxof 26-Å length, containing 514 water molecules was defined,whereas in the second, the solvent was a continuous mediumwith bulk ε ) 80 and distance-dependent. All of the simulationswere carried out at 300 K, in the NVT ensemble.

rij ) rref(crefaref

cijaij)1/6

(1)

cij ) 1

sin2 θi sin2 θj

tanθR )γB1

ωR - ω0, R ) i or j

Site-Specific Interaction between DBFC andâ- andγ-CDs J. Phys. Chem. B, Vol. 108, No. 37, 200414155

In the former case, the starting points of the MD were thefour structures with lowest rms value for each orientation(carboxylate group either by the wider or narrower CD rims),deduced from the rigid docking experiments. The system waspreviously minimized by the conjugate gradients method untila derivative of 2 kcal Å-1 was reached. Afterward, a 10-psequilibration run was performed, followed by the collection ofthe trajectory for 1.2 ns. No significant variation of the energywas observed during the last 700 ps. Geometrical restraints areimposed between the a and a′ protons of DBFC (Chart 1) andH3 and H5 of CD, which are within 4 Å of each other, accordingto the NOE data. In the case of the continuum solvent model,the preceding minimization proceeded until a gradient of 0.1kcal Å-1 was reached. Ten structures were used for each relativeorientation ofâ-CD to DBFC, with a simulation time of 800ps each. The additional energy contribution due to the geo-metrical constraints was included in the energy terms. Thetrajectories were analyzed with the Analysis module of theprogram.

Results and Discussion

1D NMR Spectroscopy. Estimation of the Binding Con-stants.Upon addition of an alkaline solution of 7.5× 10-4 MDBFC to variable amounts ofâ-CD, the resonances of allprotons of the guest (see Chart 1 for notation) undergo shiftingwith the exception of d and d′. However, b′, c, and c′ movedownfield, whereas a and a′ shift upfield. At the same time, allprotons ofâ-CD, and especially H3 and H5, located in the innerpart of the CD, move upfield (Figure 1). H6, at the rim madeup of the primary hydroxyls, also shift to high fields, to an extentsimilar to that of H3. The maximum changes in some of theseresonances reach-0.215 ppm in the case of H5 and-0.123ppm for a′. The external protons H1, H2, and H4 are the leastaltered (-0.042,-0.045, and-0.032 ppm, respectively). Thechemical shifts for the protons of bothâ-CD and DFBC areplotted versus the molar ratio in Figure 2.

In the case ofγ-CD (fixed DBFC concentration of 1.05×10-3 M), the effect on the chemical shifts of the host and guestis much more notable (Figure 3). First, all of the resonances ofthe DBFC protons are shielded upon addition ofγ-CD, withoverall changes that reach values of-0.609 ppm for a′. Thesame happens with the protons ofγ-CD, with H5 shifting, forexample, by 0.296 ppm. Even the external protons, H1,

Figure 1. Expansion of the1H NMR spectra for DBFC+ â-CDmixtures at different molar ratios R) [DBFC]/[â-CD], with [DBFC]) 7.5 × 10-4 M (left, DBFC protons; right,â-CD protons).

Figure 2. Molar ratio plots for representative protons of the systemDBFC + â-CD. Solid lines are obtained by a multivariable fit to a 1:1binding.

Figure 3. Expansion of the1H NMR spectra for DBFC+ γ-CDmixtures at different molar ratios [DBFC]/[γ-CD], with [DBFC] ) 1.05× 10-3 M (left, DBFC protons; right,γ-CD protons).

14156 J. Phys. Chem. B, Vol. 108, No. 37, 2004 Gonzalez-Gaitano et al.

H2, and H4, change almost twice as much as those inâ-CD(-0.118,-0.103, and-0.094 ppm, respectively).

The molar ratio plots (Figure 4) indicate a 2:1 stoichiometry,i.e., two molecules of DBFC perγ-CD, as deduced from theintersections between the extrapolations from high and lowmolar ratios. This result is, apparently, different from thatobtained by us by steady-state fluorescence, in which a 1:1complex was determined.3

The binding constants can be obtained from the molar ratioplots, provided that the exchange between the free and boundforms of the molecule (host or guest) is fast in the NMR timescale.12 If such is the case, the chemical shifts are the weightedaverages of all of the species present. In the case of a 1:1complex, the measured chemical shift,δ, is

that is, the sum of the contributions of the chemical shifts dueto the free host (i ) CD) or substrate (i ) S), δi, and thecomplex, δ1

i , each weighted by its mole fraction. In thisequation,X is calculated with respect to the molecule whosechemical shifts are being observed. The concentrations of allof the components in solution are connected by the correspond-ing mass balance and mass action law. The development interms of the concentration of free substrate,|S|, leads to aquadratic equation in the form

where S0 is the fixed DBFC concentration and CD0 is theconcentration of the cyclodextrin added. The positive root ofthis polynomial is introduced into eq 2 andδ is expressed as afunction of the parametersδi, δ1

i , andK1.

In the case of a 2:1 stoichiometry (S2/CD complex) theequation that must be fulfilled is

whereδ2i andX2

i stand for the chemical shift and mole fractionof the 2:1 complex, respectively, andn is a stoichiometric factorequal to 1 for the CD and 2 otherwise. In this case, a cubicpolynomial in |S| is obtained

whereK2 is the association constant for the second binding step.Note that any of the above equations can also be expressed asa function of|CD|.

From the numerical point of view, the problem reduces tofinding a vector (K1, K2, δi, δ1

i , δ2i ) that minimizes the sum of

the squares of the residuals at each point. In the case of 1:1binding, eq 2 can be linearized if one component is in largeexcess with respect to the other, which is the basis of graphicalmethods such as the Benesi-Hildebrand or Scatchard, amongothers. However, this experimental condition is not alwaysattainable in NMR titrations with cyclodextrins, for example,because of limitations on the solubility of the components oron the sensitivity of the spectrometers, so the amounts of CDand host are nearly comparable. Moreover, the linearization isnot applicable to more complex binding models.13

The common procedure for obtaining the association constantsby NMR spectroscopy is the nonlinear least-squares fitting(NLSF) of the chemical shifts versus the concentration of thehost, the guest, or their molar ratio, given by equations such as2 and 4, provided that the stoichiometry is known.13 Any ofthe above equations must be fulfilled for all of the protons inthe system that shift with the concentration. At this point, apossible strategy is to deal only with the protons, either of thehost or the guest, that undergo the greatest changes anddetermineK from the average of values obtained independentlyfrom each proton.14 Another procedure is to use multivariableanalysis by fitting the whole set of protons under study, imposingthe condition that the binding constant or constants must bethe same for each proton. The main advantage of the multi-variable analysis versus the individual one arises from theincrease in the number of data accompanied by the reductionof the number of parameters to be estimated, and it has beenused frequently in the literature.15 In this case, an extension ofeq 4 can be written as

where thej subindex refers to protonj of the ith molecule (CDor S). Nowø2 becomes

wherem is the number of protons,n is the number of pointsper isotherm, andδj,k

exp is the measured chemical shift. Giventhat the protons of both the CD and DBFC change in the systemunder study, we have treated our experimental data accordingto eq 6 by using multivariable analysis. To this end, we havewritten a MATLAB16 function that performs this analysis, based

Figure 4. Molar ratio plots for all of the protons of the system DBFC+ γ-CD. Solid lines are obtained by a multivariable fit to a 2:1 binding.

δ ) Xiδi + X1i δ1

i + nX2i δ2

i (4)

|S|3 + (2CD0 - S0 + 1K2

)|S|2 + 1K2

(CD0 - S0 + 1K1

)|S| -

S0

K1K2) 0 (5)

δj ) Xiδji + X1

i δ1,ji + nX2

i δ2,ji (6)

ø2 ) ∑j)1

m

∑k)1

n

(δj,kexp - δj,k)

2 (7)

δ ) Xiδi + X1i δ1

i (2)

|S|2 + (CD0 - S0 + 1K1

)|S| -S0

K1) 0 (3)

Site-Specific Interaction between DBFC andâ- andγ-CDs J. Phys. Chem. B, Vol. 108, No. 37, 200414157

on the Newton-Raphson algorithm, although it automaticallychanges to the Levenberg-Marquardt method in the case ofpoor convergence. The input parameter is a vector that containsthe initial guess for the binding constants and chemical shiftsof each proton in its free and complexed states. The output isthe estimation of the parameters together with their error bounds,defined as the confidence intervals corresponding to onestandard deviation (significance level,R ) 0.16). As an additionto the described procedure, we have introduced a weight factorfor each proton,wj, that is included in eq 7, defined as theabsolute value of the difference between the chemical shift inthe free form and the maximum value reached in the bindingisotherm. In this way, the protons that are more affected by theinclusion make a more significant contribution to the calculatedbinding constant.

The molar ratio plot in Figure 2 forâ-CD + DBFC points toa 1:1 stoichiometry, in accordance to the Benesi-Hildebrandplots reported for this same system by steady-state fluorescenceexperiments.3 For the regression analysis, we have excluded theprotons d and d′ of DBFC, whose chemical shifts do not changealong the binding isotherm, and c′, which is poorly resolvedbecause of overlap at high molar ratios. The fitted parametersare compiled in Table 1. The binding constant, measured at 300K, is (1.84 ( 0.09) × 103 M-1. This value is in very goodagreement with (2.12( 0.05)× 103 M-1 at 298 K obtained byfluorescence, considering that they were measured through verydifferent spectroscopic techniques.

For theγ-CD + DBFC system, the data in Figure 3 indicatethat more than one molecule of DBFC perγ-CD form thecomplex. The chemical shifts were thus fitted to eq 4. In thiscase, we have used the whole proton set of both moleculesbecause they all change substantially and their resonances arewell-resolved. The results are collected in Table 1, yieldingassociation constantsK1 ) (6 ( 2) × 102 M-1 andK2 ) (7 (2) × 103 M-1. As always happens when dealing with multipleequilibria, the standard deviations of the parameters are higherwhen compared to a 1:1 binding, because of the increasednumber of variables. The explanation of the fact that thefluorescence experiments yield a 1:1 stoichiometry instead ofthe 2:1 deduced by NMR experiments lies in the different rangesof concentration used in the two experiments. In fluorescencespectroscopy, it is compulsory to work at low concentrationsof fluorophore to keep the conditions within the interval oflinearity and to avoid complications due to self-absorption orquenching. The experiments for this system were carried out at

|DBFC|0 ) 4.6 × 10-6 M. Under these conditions, theparticipation of a 2:1 complex is negligible, specially at highγ-CD concentration, so only the presence of the 1:1 complexcan be perceived, which was the reported stoichiometry. In NMRexperiments, on the other hand, the working concentrations arenecessarily higher to detect the signals of the protons of eitherthe host or the guest that shift upon inclusion. The aforemen-tioned fluorescence study yielded a 1:1 stoichiometry with abinding constant at pH 10 and 298 K of 450 M-1, not verydifferent from theK1 value obtained by the NMR experiments,within the experimental error. The relatively low value for thisconstant, compared to that ofâ-CD, is reasonable according tothe wider cavity size ofγ-CD, in which the first DBFC moleculethat enters must fit loosely. The higher value ofK2 reveals thatthe inclusion of a second guest molecule is more favorable thanthe inclusion of the first one. In this way, the cavity ofγ-CD iswide enough to lodge two molecules of DBFC. This alsohappens with the guest in its acid form, DBFCA, which givesexcimer emission in fluorescence, although at concentrationsthat are 3 orders of magnitude lower than for the guest in itsionized form.3

Structure of the Complexes (2D ROESY and MolecularModeling). â-CD/DBFC.Figure 5 shows an expanded regionof the 2D ROESY spectrum of a mixture 9.98× 10-3 M â-CDand 4.11× 10-3 M DBFC obtained according to the proceduredescribed in the the NMR Experiments section. The inspectionof this bidimensional spectrum reveals intense cross-peaksbetween the inner protons ofâ-CD and some of the DBFCmoiety, namely, between H5 and a and H3 and a′. Thesefindings are consistent with the changes in the 1D spectra andconfirm the intracavity binding. Following in intensity are thecross-peaks between H5 and a′ and H3 and b′. The resonancescorresponding to d, d′, and c′ correlate also with H5 and H3,although it is not possible to resolve each contribution becauseof signal overlap. H2 and H4 give weaker and overlapping cross-peaks with a and a′. Finally, H6 displays a small but significantcorrelation with a and c, and also with the band composed ofc′, d, and d′. All of the NOE intensities are gathered in Table2.

The fact that the most intense NOE signals are paired asH5-a and H3-a′ suggests a preferred orientation of the DBFCinside the cavity, with the part that contains the carboxylategroup pointing toward the narrower rim ofâ-CD. This isconsistent with the smaller dipolar correlations for the pairsH3-a and H5-a′ and also with the weaker ones between H3and b′ and between H6 and a and c.

TABLE 1: Parameters Fitted by Multivariable Analysis for the Complexes of DBFC with â-CD and γ-CD

â-CD γ-CD

δi δ1i δi δ1

i δ2i

H1 4.970( 0.004 4.877( 0.008 5.00( 0.02 5.0( 0.2 4.84( 0.02H3 3.890( 0.002 3.655( 0.006 3.846( 0.012 3.85( 0.14 3.57( 0.02H6 3.777( 0.002 3.534( 0.006 3.755( 0.0012 3.75( 0.13 3.47( 0.02H5 3.761( 0.002 3.299( 0.011 3.729( 0.008 3.89( 0.12 3.283( 0.018H2 3.561( 0.004 3.460( 0.007 3.56( 0.023 3.5( 0.3 3.42( 0.04H4 3.459( 0.005 3.388( 0.010 3.46( 0.02 3.5( 0.3 3.31( 0.04a 8.468( 0.002 8.372( 0.002 8.464( 0.004 7.94( 0.05 7.741( 0.017a′ 8.081( 0.002 7.946( 0.002 8.080( 0.004 7.53( 0.05 7.313( 0.018c 7.937( 0.002 8.033( 0.002 7.931( 0.008 7.73( 0.04 7.644( 0.016b′ 7.366( 0.003 7.426( 0.003 7.358( 0.005 7.05( 0.04 6.918( 0.014c′ 7.469( 0.004 7.04( 0.03 6.936( 0.014d 7.566( 0.005 7.25( 0.04 7.134( 0.014d′ 7.605( 0.004 7.06( 0.05 6.840( 0.018

K1 ) (1.84( 0.09)× 103 L mol-1 K1 ) (6 ( 2) × 102 L mol-1

K2 ) (7 ( 2) × 103 L mol-1

14158 J. Phys. Chem. B, Vol. 108, No. 37, 2004 Gonzalez-Gaitano et al.

At this point, molecular modeling experiments can providea more tangible idea about the structure of the complexes, takinginto account the quantitative information about the interprotondistances obtained from ROESY experiments. To this end, wesimulated different orientations of the guest within the cavityby rigid docking and measured, for each conformation, thedistances between the proton pairs H3-a, H3-a′, H5-a, H5-a′, H3-b′, and H5-c, the most intense and well-resolved cross-peaks. Because of the 7-fold symmetry ofâ-CD there are sevenequivalent protons, and each NOE peak reflects the dipolarinteractions due to all of them. It is possible to define an“effective distance”17 as an average that considers all of theequivalent protons giving rise to one NOE signal. This effectivedistance,reff, is calculated from the relationship

wheren is the number of equivalent protons. The experimentaldistances can be extracted from the NOEs, provided a referenceis defined. This signal can be taken, for example, from any

proton pair of the host or guest whose distance is known.Another possibility, suitable in systems with a high symmetrysuch as this, is instead to compare the ratios between distances,thus avoiding the use of a reference.18-20 This procedure hasthe advantage that it does not produce biased results in thegeometry if the reference is not well assigned. We have usedthis latter method, by comparing the experimental ratios withthe quotients of the NOEs to obtain the corresponding root-mean-square deviation for the distance

Figure 6 shows the rms value obtained with eq 9 as a functionof the distance between the center ofâ-CD and the center ofmass of the DBFC. For a certainz value, there is a set ofstructures given by the combination of three angles that varyin 20° steps, so each point in Figure 6 represents the coordinates(z, R, â, γ). In this calculation, the angleR corresponds to thegyration around the main inertia axis, whereasâ and γ, therotations around the other inertia axes, are related to the extentof tilting within the CD. The absolute minimum is obtained atz ) 0.6 Å, and the rms value at this point is plotted as a clustergraph in Figure 7 for these two angles (R essentially does notaffect the rms values, because of symmetry of the system andthe choice of the coordinates).

The 3D plot shows that the combination of angles thatrepresents the structures with the lowest deviations are clusteredaroundâ ) γ ) 0° (note thatâ ) γ ) 180° represents thesame family of structures by symmetry). This combinationimplies that DBFC has its charged group at the narrow borderof the cavity (orientation A, hereafter). The other family of

Figure 5. Partial view of the 2D ROESY spectrum for the DBFC/â-CD system (9.98× 10-3 M â-CD, 4.11× 10-3 M DBFC).

TABLE 2: Relative NOE Intensities for SelectedCross-Peaks from the 2D ROESY Spectruma,b

â-CD + DBFC

a a′ c b′ c′, d′,dc

H3 23 100 -d 33 38H4, H2c 23 22 - - 17H5 78 37 23 - 50H6 13 - 8 - 17

γ-CD + DBFC

a a′ c d b′, c′,d′c

H3 63 73 - 100 96H5 46 63 - 31 15H6 32 21 - 34 48

a Values normalized to the most intense signal.b Intensities used forthe assignment of distances are given in bold font.c Signals overlapfor these protons.d - ) weak, nonintegrable.

1

reff6

)1

n∑i)1

n 1

ri6

(8)

Figure 6. Root-mean-square deviations as a function of the distancebetween the centers of DBFC andâ-CD.

rms) 1

x3

x[reff5a

reff3a

- (a3a

a5a)1/6]2

+ [reff5a′

reff3a′ - (a3a′

a5a′)1/6]2

+ [reff5c

reff3b′ - (a3b′

a5c)1/6]2

(9)

Site-Specific Interaction between DBFC andâ- andγ-CDs J. Phys. Chem. B, Vol. 108, No. 37, 200414159

structures, with higher rms values, is clustered aroundâ ) 0°,γ ) 180° (or â ) 180°, γ ) 0°), i.e., with the COO- pointingtoward the wider rim (orientation B). This second arrangementcorresponds to the band of points that appear at higher rmsvalues in Figure 6, whereas orientation A produces the lowerband. The docked geometry giving the minimum rms valueaccording to these calculations is drawn in Figure 8.

These results, obtained from the NMR data and rigid docking,must agree with the relative potential energies of the complexes.Therefore, we used MD simulations choosing, as the startingpoints of the dynamics, the docked structures with the lowestrms values for orientations A and B, according to the methodol-ogy described in the Computational Studies and Methodologysection. With the continuum solvent model, by averaging theenergies during the last 500 ps, the potential energy of the typeA complex is found to be 186.9 kcal, whereas that of B is 188.2kcal, signifying a more stable situation for the former. Thedifference between the two energy values is not large, a commonsituation in complexes in which the guest can enter both sidesof the CD without steric hindrance, but the results are reproduc-ible and in accordance with the experimental evidence. Suchsmall differences in energy, and even lower, are responsiblefor effects such as enantiomeric separations in chromatographyusing chiral stationary phases with CDs, for example.21,22

When the MD calculations are carried out with explicit watermolecules in a periodic box, it is not possible to distinguishbetween the potential energies of the two orientations. Althoughthe model is formally more rigorous (and the computationaltime is demanding), the resulting potential energies are virtuallythe same. In this case, the system is composed of the complexplus an ensemble of 514 water molecules. The fluctuations ofthe potential energy due to the solvent mask the smalldifferences between the two orientations, making the resultingenergies indistinguishable. Either more trajectories or longersimulation times might be necessary to discern which is themost stable geometry. Yet, the calculation under periodicboundary conditions with the solvent treated explicitly allowsother interesting structural information to be obtained via theradial distribution function,g(r), which gives the probabilityof finding a pair of atoms a distancer apart relative to theprobability expected for a completely random distribution atthe same density. This function is calculated for each frame ofthe trajectory and averaged along the productive time of thesimulation. The radial distribution function between the carbonatom of the COO- group and the water oxygen atoms is plottedin Figure 9 for both geometries, together with the dynamics ofa DBFC molecule in a periodic box with the same number ofwater molecules. Theg(r) functions have one maximum in localdensity that corresponds to the first hydration shell, followedby a depression and a second maximum having a density almostequal to that of the bulk. The interesting point of these resultsis that the functions for orientations A and B are practically thesame, with the maximum atr ) 3.5 Å. In addition, the twofunctions match that of the DBFC in the absence ofâ-CD, i.e.,the hydration state of the charged group is the same whetherthe guest is forming the complex or is free. This undoubtedlyindicates that the carboxylate group must remain outside thecavity and hydrated by the solvent and that it does not interact,or barely does so, with the OHs ofâ-CD. This conclusion hadbeen suggested in the aforementioned fluorescence study bythermodynamic arguments. In that work, the enthalpy andentropy of the binding process were calculated from thetemperature dependence of the binding constants through the

Figure 7. Cluster plot for the rms deviations as a function of the extentof tilting of DBFC within â-CD cavity (given as anglesâ andγ).

Figure 8. Structure of minimum rms value in the docking process,corresponding to the coordinatesz ) 0.6 Å, R ) 120°, â ) 200°, γ )180°.

Figure 9. Radial distribution functions between the carboxyl C atomof DBFC and the water oxygen atoms for (a) DBFC in water (dottedline), (b) complex with A orientation (dashed line), (c) complex withB orientation (solid line).

14160 J. Phys. Chem. B, Vol. 108, No. 37, 2004 Gonzalez-Gaitano et al.

van’t Hoff equation. The binding enthalpy for this system is-19.1( 0.4 kJ mol-1, the same as that for dibenzofuran withâ-CD within the experimental uncertainty (-22 ( 3 kJ mol-1,ref. 23). Considering that the only difference between the twois the extra COO- group, the results suggest that the carboxylatewould be preferentially hydrated by the solvent, having only asmall effect on the binding. The present MD results seem toreinforce these experimental findings.24

γ-CD/DBFC.An enlarged view of the ROESY spectrum isshown in Figure 10. As a difference from the case of theâ-CD/DBFC complex, the cross-peaks of protons a, a′, and d withH3 are higher than those with H5. The NOEs of b′, c′, and d′appear overlapped, whereas c does not correlate with any oftheγ-CD protons. The structural interpretation of these facts iscomplicated, because of the coexistence of two stoichiometrieswith this CD. According to the calculated binding constants,K1 and K2, and the experimental conditions (6.10× 10-3 MDBFC and 9.82× 10-3 M γ-CD), the concentrations of thetwo complexes in solution are|DBFC/γ-CD| ) 1.1 × 10-3 Mand|(DBFC)2/γ-CD| ) 2.4× 10-3 M, i.e, the concentration ofthe 2:1 complex is twice that of the 1:1 complex, and they bothcontribute to the measured NOE intensity. To separate the twocontributions, it would be necessary to work at concentrationswhere either the 1:1 or 2:1 stoichiometry is dominant. At a lowDBFC concentration, the prevailing stoichiometry would be 1:1,but under these conditions, the sensitivity of the spectrometeris poor. The other case, i.e., production of the 2:1 complex,would imply an excess ofγ-CD, but in this case, the contributionof the free CD makes H5 overlap H6, and the signals appearindistinguishable. Little can be said, then, about the structurefrom the NMR data, except that both molecules must beincluded in the cavity. If we are to consider the negative chargeof the carboxylate group, it does not seem feasible to have thetwo molecules packed face-to-face. In fact, it has been shownby theoretical studies25 that DBF dimers are arranged with themolecules packed oppositely, keeping an interplanar distanceof ca. 3.5 Å. This range of distances can be attained with twoDBFC molecules within theγ-CD cavity. The most reasonablestructure of the complex would have the two guest molecules

aligned along the main axis ofγ-CD but with their respectivecharged groups at the two borders of the cavity. The fact thatall of the chemical shifts of the guest move to high field indicatesa sort of homogeneous magnetic environment, which is notobserved for the complex withâ-CD, and which seems moreconsistent with a more symmetrical arrangement, such as theone suggested. In addition, all of the NOE cross-peaks aresimilar in value (Table 2), showing no special preference forthe orientation inside the cavity, which seems to confirm thehypothesis about the structure.

Conclusions

The structure and binding of the inclusion complexes between2-dibenzofuran carboxylate anion (DBFC) andâ- andγ-cyclo-dextrins (CDs) have been studied by 1D proton NMR and 2DROESY spectroscopies together with molecular modeling. Thestoichiometry for the complex withâ-CD is 1:1, with anassociation constant, obtained by multivariable nonlinear regres-sion analysis, that matches that obtained by steady-statefluorescence methods. For theâ-CD complex, the DBFCmolecule is oriented inside the CD cavity with the carboxylategroup at the narrow rim of the cavity, as deduced from theinterpretation, with the aid of rigid docking strategies, of theNOE enhancements. Molecular dynamics simulations assuminga continuum solvent model confirm these findings. The con-sideration of more accurate models for the solvent (formal watermolecules under periodic boundary conditions) does not helpin the discernment of the most stable conformation, but allowsfor the calculation of the radial distribution function that, forthe complex withâ-CD, indicates that the hydration state ofthe charged group is the same upon complexation and that thisgroup does not take part in the formation of the complex,confirming the thermodynamic data previously reported. Forthe case of the association withγ-CD, the stoichiometry is 2:1[(DBFC)2/γ-CD], with a constant for the second binding stephigher than that for the first. The 1:1 stoichiometry reported bysteady-state fluorescence is adequately explained in terms ofthe range of concentration used in each case. The current NMRresults suggest an axial inclusion of two DBFC molecules withinthe cavity, with the carboxylate groups pointing to the two sidesof the CD.

Acknowledgment. This work has been carried out with thefinancial support from the Ministerio de Ciencia y Tecnologı´a(Project BQU2001-1426-C02-02) and from the Gobierno deNavarra. The authors acknowledge the services of the “Centrode Supercomputacio´n Complutense (CSC)” and the “Centro deResonancia Magne´tica Nuclear” of the UCM. They alsoacknowledge Prof. M. Font and M. Romero for their valuablehelp with the computational calculations.

References and Notes

(1) Szejtli, J.Cyclodextrins and Their Inclusion Complexes; KluwerAcademic Publishers: Dordrecht, The Netherlands, 1988. (b) Duchene, D.Cyclodextrins and Their Industrial Uses; Editions de Sante´: Paris, 1987.(c) Duchene, D.New Trends in Cyclodextrins and DeriVatiVes; Editionsde Sante´: Paris, 1991. (d) Hedges, A. R.Chem. ReV. 1998, 98, 2035.

(2) Connors, K. A.Chem. ReV. 1997, 97, 1325. (b) Rekharsky, M. V.;Inoue, Y.Chem. ReV. 1998, 98, 1875.

(3) Sainz-Rozas, P. R.; Isasi, J. R.; Sa´nchez, M.; Tardajos, G.;Gonzalez-Gaitano, G.J. Phys. Chem. A.2004, 108, 392.

(4) Schneider, H. J.; Hacket, F.; Ru¨diger, V. Chem. ReV. 1998, 98,1755.

(5) Neuhaus, D.; Williamsom, M. P.The Nuclear OVerhauser Effectin Structural and Conformational Analysis; VCH: New York, 1989.

(6) Bax, A.; Davis, D. G.J. Magn. Reson. 1985, 63, 207.

Figure 10. Partial view of the 2D ROESY spectrum for the DBFC/γ-CD system (9.82× 10-3 M γ-CD, 6.10× 10-3 M DBFC).

Site-Specific Interaction between DBFC andâ- andγ-CDs J. Phys. Chem. B, Vol. 108, No. 37, 200414161

(7) MestRe-C, version 3.5.1; Departamento de Quı´mica Organica,Universidad de Santiago de Compostela: Santiago de Compostela, Spain,2003.

(8) Ammalahti, E.; Bardet, M.; Molko, D.; Cadet, J.J. Magn. Reson.A. 1996, 122, 230.

(9) Insight II, version 2000: Accelrys Inc.: San Diego, CA, 2000.(10) Weiner, S. J.; Kollman, P. A.; Nguyen, D. T.; Case, D. A.J.

Comput. Chem.1986, 7, 230.(11) Homans, S. W.Biochemistry1990, 29, 9110.(12) Connors, K. A.Binding Constants. The Measurement of Molecular

Complex Stability; John Wiley & Sons: New York, 1987; pp 189-192.(13) For a review of binding constants by NMR spectroscopy, see

Fielding, L. Tetrahedron2000, 56, 6151 and references therein.(14) Gonza´lez-Gaitano, G.; Guerrero-Martı´nez, A.; Nunez-Barriocanal,

J. L.; Tardajos, G.J. Phys. Chem. B.2002, 106, 6096.(15) See, for example: Gelb, R. I.; Schwartz, L. M.; Laufer, D. A.J.

Am. Chem. Soc.1978, 100, 5875. Salvatierra, D.; Dı´ez, C.; Jaime, C.J.Inclusion Phenom. Macrocyclic Chem.1997, 27, 215. Al-Soufi, W.; RamosCabrer, P.; Jover, A.; Budal, R. M.; Va´zquez Tato, J.Steroids2003, 68,43.

(16) MATLAB, version 5.2, The MathWorks, Inc.: Natick, MA, 1998.(17) Funasaki, N.; Ishikawa, S.; Neya, S.J. Phys. Chem. B2002, 106,

6431.(18) Salvatierra, D.; Jaime, C.; Virgili, A.; Sa´nchez-Ferrando, F.J. Org.

Chem.1996, 61, 9578.(19) Salvatierra, D.; Sa´nchez-Ruiz, X.; Gardun˜o, R.; Cervello´, E.; Jaime,

C.; Virgili, A.; Sanchez-Ferrando, F.Tetrahedron2000, 56, 3035.(20) Zubiaur, M.; Jaime, C.J. Org. Chem.2000, 65, 8139.(21) Kim, H.; Jeong, K.; Lee, S.; Jung, S.Bull. Korean Chem. Soc.

2003, 24, 95.(22) Dodziuk, H.; Lukin, O.Chem. Phys. Lett.2000, 327, 18.(23) Rodrı´guez, P.; Sa´nchez, M.; Isasi, J. R.; Gonza´lez-Gaitano, G.Appl.

Spectrosc.2002, 56, 1490.(24) FTIR measurements of DBFC andâ-CD in D2O at basic pH (not

shown) point to the same conclusion: the stretching of the COO- group isnot affected by the complexation.

(25) Minn, F. L.; Pinion, J. P.; Filipescu, N.J. Phys. Chem.1971, 75,1794.

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