Site-Specific Interaction between 2-Dibenzofuran Carboxylate and

14154

J. Phys. Chem. B 2004, 108, 14154-14162

Site-Specific Interaction between 2-Dibenzofuran Carboxylate and β- and γ-Cyclodextrins Determined by Intermolecular NOE and Molecular Modeling Gustavo Gonza´ lez-Gaitano,*,† Pablo R. Sainz-Rozas,† Jose´ Ramo´ n Isasi,† Andre´ s Guerrero-Martıńez,‡ and Gloria Tardajos‡ Departamento de Quı´mica y Edafologıá, UniVersidad de NaVarra, 31080 Pamplona, NaVarra, Spain, and Departamento de Quı´mica-Fı´sica 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) and β- 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 stoichiometry with β-CD. The stability constants have been calculated by multivariable nonlinear least-squares regression from the changes in the chemical shifts of the protons of both host and guest molecules. For the β-CD complex, the interproton distances between the host and guest have been deduced from the NOE enhancements. Rigid docking calculations using the geometrical restraints given by the NMR experiments, together with molecular dynamics simulations assuming a continuum solvent model, indicate that DBFC is oriented with the carboxylate group at the narrow rim of the CD. The radial distribution functions obtained by considering explicit water molecules with periodic boundary conditions indicate that the solvation degree of the charged group of DBFC in its free or bound form is the same. In the case of γ-CD, the NMR data indicate the presence of 1:1 and 2:1 complexes [(DBFC)2/γ-CD], with a constant for the second binding step higher than that of the first. The stoichiometry and binding constants, apparently in disagreement with previously reported fluorescence experiments, are satisfactorily explained by considering the range of working concentrations.

Introduction

CHART 1

Cyclodextrins (CDs) are cyclic oligosaccharides built up from R-D-glucopyranose residues linked by glycosidic bonds, with the most common being those formed by six, seven, or eight glucose units (R-, β-, and γ-CD, respectively). Because of the lack of free rotation about the glycosidic bonds, CDs display a torus-like or hollow truncated cone shape, with a hydrophobic cavity and two hydrophilic rims in which the primary and secondary OH groups are inserted (Chart 1). The main feature that makes CDs of interest is their ability to form inclusion complexes with a variety of guest molecules, in solution or in the solid phase. This quality offers many interesting applications, which have been described extensively in the literature.1 The first condition required for a molecule to form an inclusion complex with CD is that it fits in the cavity, either completely or partially. In addition, a favorable energetic balance is required, which depends on the nature of the guest, the inner diameter of the CD, and the CD’s substitution degree.2 In a previous work,3 we investigated the photophysics (mainly by absorption and steady-state fluorescence) of a dibenzofuran (DBF) derivative, 2-dibenzofuran carboxylic acid (DBFCA), in several solvents and in the presence of CDs. DBFCA forms inclusion complexes with R-, β-, and γ-cyclodextrins, with the spectral behavior being highly dependent on the type of CD and pH. Yet, the information that such techniques can provide * Corresponding author. Address: Departamento de Quı´mica y Edafologıá, Universidad de Navarra, 31080 Pamplona, Navarra, Spain. E-mail: [email protected]. † Universidad de Navarra. ‡ Universidad Complutense.

about the complexes in solution is usually limited to the stoichiometry and the evaluation of the association constants and thermodynamic parameters that can be extracted from this (i.e., enthalpy and entropy, from the temperature dependence of K). From the structural point of view, nuclear Overhauser spectroscopy is considered one of the most definitive methods for the study of complexes with cyclodextrins,4 because the dipolar interactions that are detected as NOE enhancements reflect the spatial proximity between protons. For medium-sized systems, such as those studied here, the appropriate technique is rotating frame Overhauser effect spectroscopy (ROESY), because the NOESY signals are too weak for a reliable evaluation of distances.5 This technique, used jointly with molecular modeling calculations, can provide detailed information on the structure of the complexes, always keeping in mind the dynamic character of these systems, in which a fast equilibrium between complex and free molecules is taking place. It is precisely due to this dynamic nature, and to the high symmetry of CDs, that the information about interproton distances is usually considered only from the qualitative point of view, thus losing the most important potentiality of ROESY.

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

Site-Specific Interaction between DBFC and β- and γ-CDs In this framework, we have investigated the topology of the inclusion complexes formed between 2-dibenzofuran carboxylate (DBFC) and β-CD and γ-CD. An exhaustive analysis of the NOE volumes, together with different strategies of molecular modeling (mainly rigid docking and molecular dynamics), has been performed to achieve a full concordance between all sets of experimental data. The results complete the previous ones obtained by fluorescence measurements and shed light on aspects that emission spectroscopy cannot ascertain. Materials and Methods NMR Experiments. β-CD was obtained from Roquette and γ-CD from Wacker, having water contents of 10.6% and 7.91%, respectively, as determined by thermal analysis. 2-Dibenzofuran carboxylic acid (DBFCA) was manufactured by Aldrich (Rare Chemicals Library). The solutions were prepared in D2O (Aldrich Chemical Co., 99.9% minimum in D), with the necessary amount of NaOD (Merck, 40% solution of NaOD in D2O, 99.5% in D) to reach pH 10. All reactants were used without further purification. For the 1H NMR experiments, a stock solution of 2-dibenzofuran carboxylate (DBFC) was added to vials containing weighed amounts of CD, and the mixtures were sonicated and transferred to NMR tubes (final volumes of ca. 0.5 mL). The spectra were recorded at 300 K in a Bruker Avance 400 Ultrashield spectrometer (9.36 T) by averaging 600 scans, with a digital resolution of 0.15 Hz. The HDO signal was used as the reference. The resonances of DBFC were assigned with the aid of the 1D and COSY spectra. No dependence of the chemical shifts of DBFC on the concentration was detected. For the calculation of the binding constants from the chemical shifts, the actual concentration of DBFC was obtained by the ratio between the area of the H1 signal of the CD (integrating for seven or eight protons for β-CD or γ-CD, respectively) and that of proton a (Chart 1), after a fine baseline correction of the spectrum. The H1 signal is the narrowest of all of the CD resonances and is free of overlapping. The concentration of the CD, well-known by weighing, is taken as the reference. The concentrations thus calculated were 7.5 × 10-4 and 1.05 × 10-3 M for the studies with β-CD and γ-CD, respectively. For the 2D ROESY experiments, the sample concentrations were 9.98 × 10-3 M β-CD + 4.11 × 10-3 M DBFC and 9.82 × 10-3 M γ-CD + 6.10 × 10-3 M DBFC prepared by adding alkaline solutions of β- and γ-CD to weighed amounts of DBFCA. The concentration of DBFC was calculated as mentioned above, and the temperature was kept constant in these experiments at 298 K. A Bruker Avance DPX-300 spectrometer (7.05 T) was used, by applying the pulse sequence defined in the literature.6 The power level for the spin-lock pulse was γB1/ 2π ) 2500 Hz. Different spin-lock mixing times (ranging between 400 and 800 ms) were applied to ensure the validity of the linear approximation for the NOE peak intensities and to obtain the best signal-to-noise ratio, which was achieved with 600 ms for both CD/DBFC systems. Thirty-two scans were collected in each spectrum, which consisted of a matrix with 512 × 1024 data points covering a spectral width of 3307 Hz. The treatment of the free induction decays (FIDs) was carried out with MestRe-C software.7 Before the Fourier transformation and the subsequent 2D phase tuning were executed, linear prediction in F1 and cosine square apodization in both dimensions were applied to the FIDs. The resulting spectra were baseline corrected in each dimension with third-order polynomials prior to the integration of the NOEs. The interproton distances have been calculated from the NOE peaks by the equation5,8

J. Phys. Chem. B, Vol. 108, No. 37, 2004 14155

( ) crefaref cijaij

rij ) rref

1/6

(1)

where aij is the NOE cross-peak volume and rref is a reference distance between two protons yielding an NOE volume, aref. The coefficients cij are introduced to account for the offset dependence of the cross-peak intensities relative to the transmitter center, according to the equations described by A ¨ mma¨lahti et al., i.e.

cij )

1 sin θi sin2 θj 2

and

tan θR )

γB1 , ω R - ω0

R ) i or j

In these expressions, ωR - ω0 is the difference between the chemical shift of the peak and the center of the spectral window (1426 Hz in our experiments), and γB1 is the spin-lock power, expressed in Hz. Computational Studies and Methodology. Computations were performed with Insight II software,9 on an SGI-Cray Origin 2000 computer at the CSC (Centro de Supercomputacioń Complutense, Madrid, Spain), employing the AMBER10,11 force field, which is included in the software. Energy minimization of the isolated host and guest molecules was performed with the Discover module, employing different algorithms (beginning with steepest descents and finishing with a modified Newton-Raphson to refine the structures) until the root-mean squares of the derivatives were less than 0.0001 kcal Å-1. Afterward, short molecular dynamics (MD) simulations were run at 298 K, and the process of minimization was repeated to reach a stable conformation. For the rigid docking experiments, an xy plane was defined by the glycosidic oxygen atoms of the CD, and the coordinate origin as the center of mass of these seven O4s. The z axis is perpendicular to this plane, with positive orientation toward the wider rim. The coordinate origin of DBFC is its center of mass, and the axes are defined by the principal axes of inertia of the molecule. The centers of the host and guest are separated by 2.5 Å, and the DBFC approaches the CD along the z direction. DBFC is allowed to rotate freely around its three axes at each z value, in steps of 20°. For each point, defined by (z, R, β, γ), the distances between the H atoms that give rise to significant NOE intensities are measured to obtain the effective interproton distances (see the Results and Discussion section). To avoid atomic overlap, only those computed geometries that yield reasonable values of the intermolecular van der Waals energy of interaction (as calculated with the Docking module of the software) are recorded. These values are compared with the experimental distances obtained by eq 1, and the root-mean-square (rms) values calculated. All of these tasks are executed with a program written in the Biosym Command Language. For the MD calculations, we accounted for the solvent both explicitly and implicitly. In the first case, a periodic cubic box of 26-Å length, containing 514 water molecules was defined, whereas in the second, the solvent was a continuous medium with bulk ) 80 and distance-dependent. All of the simulations were carried out at 300 K, in the NVT ensemble.

14156 J. Phys. Chem. B, Vol. 108, No. 37, 2004

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

In the former case, the starting points of the MD were the four 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 was previously minimized by the conjugate gradients method until a derivative of 2 kcal Å-1 was reached. Afterward, a 10-ps equilibration run was performed, followed by the collection of the trajectory for 1.2 ns. No significant variation of the energy was observed during the last 700 ps. Geometrical restraints are imposed between the a and a′ protons of DBFC (Chart 1) and H3 and H5 of CD, which are within 4 Å of each other, according to the NOE data. In the case of the continuum solvent model, the preceding minimization proceeded until a gradient of 0.1 kcal Å-1 was reached. Ten structures were used for each relative orientation of β-CD to DBFC, with a simulation time of 800 ps each. The additional energy contribution due to the geometrical constraints was included in the energy terms. The trajectories were analyzed with the Analysis module of the program.

Gonza´lez-Gaitano et al.

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

Results and Discussion 1D NMR Spectroscopy. Estimation of the Binding Constants. Upon addition of an alkaline solution of 7.5 × 10-4 M DBFC to variable amounts of β-CD, the resonances of all protons of the guest (see Chart 1 for notation) undergo shifting with the exception of d and d′. However, b′, c, and c′ move downfield, whereas a and a′ shift upfield. At the same time, all protons of β-CD, and especially H3 and H5, located in the inner part of the CD, move upfield (Figure 1). H6, at the rim made up of the primary hydroxyls, also shift to high fields, to an extent similar to that of H3. The maximum changes in some of these resonances reach -0.215 ppm in the case of H5 and -0.123 ppm for a′. The external protons H1, H2, and H4 are the least altered (-0.042, -0.045, and -0.032 ppm, respectively). The chemical shifts for the protons of both β-CD and DFBC are plotted versus the molar ratio in Figure 2.

Figure 3. Expansion of the 1H NMR spectra for DBFC + γ-CD mixtures at different molar ratios [DBFC]/[γ-CD], with [DBFC] ) 1.05 × 10-3 M (left, DBFC protons; right, γ-CD protons).

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

Site-Specific Interaction between DBFC and β- and γ-CDs

J. Phys. Chem. B, Vol. 108, No. 37, 2004 14157 In the case of a 2:1 stoichiometry (S2/CD complex) the equation that must be fulfilled is

δ ) Xiδi + Xi1 δi1 + nXi2 δi2

(4)

where δi2 and Xi2 stand for the chemical shift and mole fraction of the 2:1 complex, respectively, and n is a stoichiometric factor equal to 1 for the CD and 2 otherwise. In this case, a cubic polynomial in |S| is obtained

(

|S|3 + 2CD0 - S0 +

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.

H2, and H4, change almost twice as much as those in β-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 per γ-CD, as deduced from the intersections between the extrapolations from high and low molar ratios. This result is, apparently, different from that obtained by us by steady-state fluorescence, in which a 1:1 complex was determined.3 The binding constants can be obtained from the molar ratio plots, provided that the exchange between the free and bound forms of the molecule (host or guest) is fast in the NMR time scale.12 If such is the case, the chemical shifts are the weighted averages of all of the species present. In the case of a 1:1 complex, the measured chemical shift, δ, is

δ ) Xiδi + Xi1 δi1

(2)

that is, the sum of the contributions of the chemical shifts due to the free host (i ) CD) or substrate (i ) S), δi, and the complex, δi1, each weighted by its mole fraction. In this equation, X is calculated with respect to the molecule whose chemical shifts are being observed. The concentrations of all of the components in solution are connected by the corresponding mass balance and mass action law. The development in terms of the concentration of free substrate, |S|, leads to a quadratic equation in the form

(

)

S0 1 |S| )0 |S|2 + CD0 - S0 + K1 K1

)

(

)

1 1 1 |S|2 + CD0 - S0 + |S| K2 K2 K1 S0 ) 0 (5) K1K2

where K2 is the association constant for the second binding step. Note that any of the above equations can also be expressed as a function of |CD|. From the numerical point of view, the problem reduces to finding a vector (K1, K2, δi, δi1, δi2) that minimizes the sum of the squares of the residuals at each point. In the case of 1:1 binding, eq 2 can be linearized if one component is in large excess with respect to the other, which is the basis of graphical methods such as the Benesi-Hildebrand or Scatchard, among others. However, this experimental condition is not always attainable in NMR titrations with cyclodextrins, for example, because of limitations on the solubility of the components or on the sensitivity of the spectrometers, so the amounts of CD and host are nearly comparable. Moreover, the linearization is not applicable to more complex binding models.13 The common procedure for obtaining the association constants by NMR spectroscopy is the nonlinear least-squares fitting (NLSF) of the chemical shifts versus the concentration of the host, the guest, or their molar ratio, given by equations such as 2 and 4, provided that the stoichiometry is known.13 Any of the above equations must be fulfilled for all of the protons in the system that shift with the concentration. At this point, a possible strategy is to deal only with the protons, either of the host or the guest, that undergo the greatest changes and determine K from the average of values obtained independently from each proton.14 Another procedure is to use multivariable analysis by fitting the whole set of protons under study, imposing the condition that the binding constant or constants must be the same for each proton. The main advantage of the multivariable analysis versus the individual one arises from the increase in the number of data accompanied by the reduction of the number of parameters to be estimated, and it has been used frequently in the literature.15 In this case, an extension of eq 4 can be written as i i + nXi2 δ2,j δj ) Xiδji + Xi1δ1,j

(6)

where the j subindex refers to proton j of the ith molecule (CD or S). Now χ2 becomes m

χ2 )

n

(δj,kexp - δj,k)2 ∑ ∑ j)1 k)1

(7)

(3)

where S0 is the fixed DBFC concentration and CD0 is the concentration of the cyclodextrin added. The positive root of this polynomial is introduced into eq 2 and δ is expressed as a function of the parameters δi, δi1, and K1.

where m is the number of protons, n is the number of points per isotherm, and δexp j,k is the measured chemical shift. Given that the protons of both the CD and DBFC change in the system under study, we have treated our experimental data according to eq 6 by using multivariable analysis. To this end, we have written a MATLAB16 function that performs this analysis, based



TABLE 1: Parameters Fitted by Multivariable Analysis for the Complexes of DBFC with β-CD and γ-CD β-CD H1 H3 H6 H5 H2 H4 a a′ c b′ c′ d d′

γ-CD

δi

δi1

δi

δi1

δi2

4.970 ( 0.004 3.890 ( 0.002 3.777 ( 0.002 3.761 ( 0.002 3.561 ( 0.004 3.459 ( 0.005 8.468 ( 0.002 8.081 ( 0.002 7.937 ( 0.002 7.366 ( 0.003

4.877 ( 0.008 3.655 ( 0.006 3.534 ( 0.006 3.299 ( 0.011 3.460 ( 0.007 3.388 ( 0.010 8.372 ( 0.002 7.946 ( 0.002 8.033 ( 0.002 7.426 ( 0.003

5.00 ( 0.02 3.846 ( 0.012 3.755 ( 0.0012 3.729 ( 0.008 3.56 ( 0.023 3.46 ( 0.02 8.464 ( 0.004 8.080 ( 0.004 7.931 ( 0.008 7.358 ( 0.005 7.469 ( 0.004 7.566 ( 0.005 7.605 ( 0.004

5.0 ( 0.2 3.85 ( 0.14 3.75 ( 0.13 3.89 ( 0.12 3.5 ( 0.3 3.5 ( 0.3 7.94 ( 0.05 7.53 ( 0.05 7.73 ( 0.04 7.05 ( 0.04 7.04 ( 0.03 7.25 ( 0.04 7.06 ( 0.05

4.84 ( 0.02 3.57 ( 0.02 3.47 ( 0.02 3.283 ( 0.018 3.42 ( 0.04 3.31( 0.04 7.741 ( 0.017 7.313 ( 0.018 7.644 ( 0.016 6.918( 0.014 6.936 ( 0.014 7.134 ( 0.014 6.840 ( 0.018

K1 ) (1.84 ( 0.09) × 103 L mol-1

on the Newton-Raphson algorithm, although it automatically changes to the Levenberg-Marquardt method in the case of poor convergence. The input parameter is a vector that contains the initial guess for the binding constants and chemical shifts of each proton in its free and complexed states. The output is the estimation of the parameters together with their error bounds, defined as the confidence intervals corresponding to one standard deviation (significance level, R ) 0.16). As an addition to the described procedure, we have introduced a weight factor for each proton, wj, that is included in eq 7, defined as the absolute value of the difference between the chemical shift in the free form and the maximum value reached in the binding isotherm. In this way, the protons that are more affected by the inclusion make a more significant contribution to the calculated binding constant. The molar ratio plot in Figure 2 for β-CD + DBFC points to a 1:1 stoichiometry, in accordance to the Benesi-Hildebrand plots reported for this same system by steady-state fluorescence experiments.3 For the regression analysis, we have excluded the protons d and d′ of DBFC, whose chemical shifts do not change along the binding isotherm, and c′, which is poorly resolved because of overlap at high molar ratios. The fitted parameters are compiled in Table 1. The binding constant, measured at 300 K, is (1.84 ( 0.09) × 103 M-1. This value is in very good agreement with (2.12 ( 0.05) × 103 M-1 at 298 K obtained by fluorescence, considering that they were measured through very different spectroscopic techniques. For the γ-CD + DBFC system, the data in Figure 3 indicate that more than one molecule of DBFC per γ-CD form the complex. The chemical shifts were thus fitted to eq 4. In this case, we have used the whole proton set of both molecules because they all change substantially and their resonances are well-resolved. The results are collected in Table 1, yielding association constants K1 ) (6 ( 2) × 102 M-1 and K2 ) (7 ( 2) × 103 M-1. As always happens when dealing with multiple equilibria, the standard deviations of the parameters are higher when compared to a 1:1 binding, because of the increased number of variables. The explanation of the fact that the fluorescence experiments yield a 1:1 stoichiometry instead of the 2:1 deduced by NMR experiments lies in the different ranges of concentration used in the two experiments. In fluorescence spectroscopy, it is compulsory to work at low concentrations of fluorophore to keep the conditions within the interval of linearity and to avoid complications due to self-absorption or quenching. The experiments for this system were carried out at

K1 ) (6 ( 2) × 102 L mol-1 K2 ) (7 ( 2) × 103 L mol-1

|DBFC|0 ) 4.6 × 10-6 M. Under these conditions, the participation of a 2:1 complex is negligible, specially at high γ-CD concentration, so only the presence of the 1:1 complex can be perceived, which was the reported stoichiometry. In NMR experiments, on the other hand, the working concentrations are necessarily higher to detect the signals of the protons of either the host or the guest that shift upon inclusion. The aforementioned fluorescence study yielded a 1:1 stoichiometry with a binding constant at pH 10 and 298 K of 450 M-1, not very different from the K1 value obtained by the NMR experiments, within the experimental error. The relatively low value for this constant, compared to that of β-CD, is reasonable according to the wider cavity size of γ-CD, in which the first DBFC molecule that enters must fit loosely. The higher value of K2 reveals that the inclusion of a second guest molecule is more favorable than the inclusion of the first one. In this way, the cavity of γ-CD is wide enough to lodge two molecules of DBFC. This also happens with the guest in its acid form, DBFCA, which gives excimer emission in fluorescence, although at concentrations that are 3 orders of magnitude lower than for the guest in its ionized form.3 Structure of the Complexes (2D ROESY and Molecular Modeling). β-CD/DBFC. Figure 5 shows an expanded region of the 2D ROESY spectrum of a mixture 9.98 × 10-3 M β-CD and 4.11 × 10-3 M DBFC obtained according to the procedure described in the the NMR Experiments section. The inspection of this bidimensional spectrum reveals intense cross-peaks between the inner protons of β-CD and some of the DBFC moiety, namely, between H5 and a and H3 and a′. These findings are consistent with the changes in the 1D spectra and confirm the intracavity binding. Following in intensity are the cross-peaks between H5 and a′ and H3 and b′. The resonances corresponding to d, d′, and c′ correlate also with H5 and H3, although it is not possible to resolve each contribution because of signal overlap. H2 and H4 give weaker and overlapping crosspeaks with a and a′. Finally, H6 displays a small but significant correlation with a and c, and also with the band composed of c′, d, and d′. All of the NOE intensities are gathered in Table 2. The fact that the most intense NOE signals are paired as H5-a and H3-a′ suggests a preferred orientation of the DBFC inside the cavity, with the part that contains the carboxylate group pointing toward the narrower rim of β-CD. This is consistent with the smaller dipolar correlations for the pairs H3-a and H5-a′ and also with the weaker ones between H3 and b′ and between H6 and a and c.


J. Phys. Chem. B, Vol. 108, No. 37, 2004 14159

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

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

Figure 6. Root-mean-square deviations as a function of the distance between the centers of DBFC and β-CD.

β-CD + DBFC H3 H4, H2c H5 H6

a

a′

c

b′

c′, d′,dc

23 23 78 13

100 22 37 -

-d 23 8

33 -

38 17 50 17

γ-CD + DBFC H3 H5 H6

a

a′

c

d

b′, c′,d′c

63 46 32

73 63 21

-

100 31 34

96 15 48

a

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

At this point, molecular modeling experiments can provide a more tangible idea about the structure of the complexes, taking into account the quantitative information about the interproton distances obtained from ROESY experiments. To this end, we simulated different orientations of the guest within the cavity by rigid docking and measured, for each conformation, the distances between the proton pairs H3-a, H3-a′, H5-a, H5a′, H3-b′, and H5-c, the most intense and well-resolved crosspeaks. Because of the 7-fold symmetry of β-CD there are seven equivalent protons, and each NOE peak reflects the dipolar interactions due to all of them. It is possible to define an “effective distance”17 as an average that considers all of the equivalent protons giving rise to one NOE signal. This effective distance, reff, is calculated from the relationship

1 reff6

)

1

n

∑ n i)1

1

ri6

(8)

where n is the number of equivalent protons. The experimental distances can be extracted from the NOEs, provided a reference is 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 symmetry such as this, is instead to compare the ratios between distances, thus avoiding the use of a reference.18-20 This procedure has the advantage that it does not produce biased results in the geometry if the reference is not well assigned. We have used this latter method, by comparing the experimental ratios with the quotients of the NOEs to obtain the corresponding rootmean-square deviation for the distance

rms )

1 x3

x[ ( ) ] [ ( ) ] [ ( ) ] r5a eff

r3a eff

-

a3a a5a

1/6 2

+

r5a′ eff

a3a′ 3a′ a5a′ reff

1/6 2

+

r5c eff

3b′

reff

a3b′ a5c

1/6 2

(9)

Figure 6 shows the rms value obtained with eq 9 as a function of the distance between the center of β-CD and the center of mass of the DBFC. For a certain z value, there is a set of structures given by the combination of three angles that vary in 20° steps, so each point in Figure 6 represents the coordinates (z, R, β, γ). In this calculation, the angle R corresponds to the gyration around the main inertia axis, whereas β and γ, the rotations around the other inertia axes, are related to the extent of tilting within the CD. The absolute minimum is obtained at z ) 0.6 Å, and the rms value at this point is plotted as a cluster graph in Figure 7 for these two angles (R essentially does not affect the rms values, because of symmetry of the system and the choice of the coordinates). The 3D plot shows that the combination of angles that represents the structures with the lowest deviations are clustered around β ) γ ) 0° (note that β ) γ ) 180° represents the same family of structures by symmetry). This combination implies that DBFC has its charged group at the narrow border of the cavity (orientation A, hereafter). The other family of


Figure 7. Cluster plot for the rms deviations as a function of the extent of tilting of DBFC within β-CD cavity (given as angles β and γ).

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

structures, with higher rms values, is clustered around β ) 0°, γ ) 180° (or β ) 180°, γ ) 0°), i.e., with the COO- pointing toward the wider rim (orientation B). This second arrangement corresponds to the band of points that appear at higher rms values in Figure 6, whereas orientation A produces the lower band. The docked geometry giving the minimum rms value according 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 starting points of the dynamics, the docked structures with the lowest rms values for orientations A and B, according to the methodology described in the Computational Studies and Methodology section. With the continuum solvent model, by averaging the energies during the last 500 ps, the potential energy of the type A complex is found to be 186.9 kcal, whereas that of B is 188.2 kcal, signifying a more stable situation for the former. The difference between the two energy values is not large, a common situation in complexes in which the guest can enter both sides of the CD without steric hindrance, but the results are reproducible and in accordance with the experimental evidence. Such small differences in energy, and even lower, are responsible for effects such as enantiomeric separations in chromatography using chiral stationary phases with CDs, for example.21,22


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

When the MD calculations are carried out with explicit water molecules in a periodic box, it is not possible to distinguish between the potential energies of the two orientations. Although the model is formally more rigorous (and the computational time is demanding), the resulting potential energies are virtually the same. In this case, the system is composed of the complex plus an ensemble of 514 water molecules. The fluctuations of the potential energy due to the solvent mask the small differences between the two orientations, making the resulting energies indistinguishable. Either more trajectories or longer simulation times might be necessary to discern which is the most stable geometry. Yet, the calculation under periodic boundary conditions with the solvent treated explicitly allows other interesting structural information to be obtained via the radial distribution function, g(r), which gives the probability of finding a pair of atoms a distance r apart relative to the probability expected for a completely random distribution at the same density. This function is calculated for each frame of the trajectory and averaged along the productive time of the simulation. The radial distribution function between the carbon atom of the COO- group and the water oxygen atoms is plotted in Figure 9 for both geometries, together with the dynamics of a DBFC molecule in a periodic box with the same number of water molecules. The g(r) functions have one maximum in local density that corresponds to the first hydration shell, followed by a depression and a second maximum having a density almost equal to that of the bulk. The interesting point of these results is that the functions for orientations A and B are practically the same, with the maximum at r ) 3.5 Å. In addition, the two functions match that of the DBFC in the absence of β-CD, i.e., the hydration state of the charged group is the same whether the guest is forming the complex or is free. This undoubtedly indicates that the carboxylate group must remain outside the cavity and hydrated by the solvent and that it does not interact, or barely does so, with the OHs of β-CD. This conclusion had been suggested in the aforementioned fluorescence study by thermodynamic arguments. In that work, the enthalpy and entropy of the binding process were calculated from the temperature dependence of the binding constants through the


J. Phys. Chem. B, Vol. 108, No. 37, 2004 14161 aligned along the main axis of γ-CD but with their respective charged groups at the two borders of the cavity. The fact that all of the chemical shifts of the guest move to high field indicates a sort of homogeneous magnetic environment, which is not observed for the complex with β-CD, and which seems more consistent with a more symmetrical arrangement, such as the one suggested. In addition, all of the NOE cross-peaks are similar in value (Table 2), showing no special preference for the orientation inside the cavity, which seems to confirm the hypothesis about the structure. Conclusions

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).

van’t Hoff equation. The binding enthalpy for this system is -19.1 ( 0.4 kJ mol-1, the same as that for dibenzofuran with β-CD within the experimental uncertainty (-22 ( 3 kJ mol-1, ref. 23). Considering that the only difference between the two is the extra COO- group, the results suggest that the carboxylate would be preferentially hydrated by the solvent, having only a small effect on the binding. The present MD results seem to reinforce these experimental findings.24 γ-CD/DBFC. An enlarged view of the ROESY spectrum is shown in Figure 10. As a difference from the case of the β-CD/ DBFC complex, the cross-peaks of protons a, a′, and d with H3 are higher than those with H5. The NOEs of b′, c′, and d′ appear overlapped, whereas c does not correlate with any of the γ-CD protons. The structural interpretation of these facts is complicated, because of the coexistence of two stoichiometries with this CD. According to the calculated binding constants, K1 and K2, and the experimental conditions (6.10 × 10-3 M DBFC and 9.82 × 10-3 M γ-CD), the concentrations of the two complexes in solution are |DBFC/γ-CD| ) 1.1 × 10-3 M and |(DBFC)2/γ-CD| ) 2.4 × 10-3 M, i.e, the concentration of the 2:1 complex is twice that of the 1:1 complex, and they both contribute to the measured NOE intensity. To separate the two contributions, it would be necessary to work at concentrations where either the 1:1 or 2:1 stoichiometry is dominant. At a low DBFC concentration, the prevailing stoichiometry would be 1:1, but under these conditions, the sensitivity of the spectrometer is poor. The other case, i.e., production of the 2:1 complex, would imply an excess of γ-CD, but in this case, the contribution of the free CD makes H5 overlap H6, and the signals appear indistinguishable. Little can be said, then, about the structure from the NMR data, except that both molecules must be included in the cavity. If we are to consider the negative charge of the carboxylate group, it does not seem feasible to have the two molecules packed face-to-face. In fact, it has been shown by theoretical studies25 that DBF dimers are arranged with the molecules packed oppositely, keeping an interplanar distance of ca. 3.5 Å. This range of distances can be attained with two DBFC molecules within the γ-CD cavity. The most reasonable structure of the complex would have the two guest molecules

The structure and binding of the inclusion complexes between 2-dibenzofuran carboxylate anion (DBFC) and β- and γ-cyclodextrins (CDs) have been studied by 1D proton NMR and 2D ROESY spectroscopies together with molecular modeling. The stoichiometry for the complex with β-CD is 1:1, with an association constant, obtained by multivariable nonlinear regression analysis, that matches that obtained by steady-state fluorescence methods. For the β-CD complex, the DBFC molecule is oriented inside the CD cavity with the carboxylate group at the narrow rim of the cavity, as deduced from the interpretation, with the aid of rigid docking strategies, of the NOE enhancements. Molecular dynamics simulations assuming a continuum solvent model confirm these findings. The consideration of more accurate models for the solvent (formal water molecules under periodic boundary conditions) does not help in the discernment of the most stable conformation, but allows for the calculation of the radial distribution function that, for the complex with β-CD, indicates that the hydration state of the charged group is the same upon complexation and that this group does not take part in the formation of the complex, confirming the thermodynamic data previously reported. For the case of the association with γ-CD, the stoichiometry is 2:1 [(DBFC)2/γ-CD], with a constant for the second binding step higher than that for the first. The 1:1 stoichiometry reported by steady-state fluorescence is adequately explained in terms of the range of concentration used in each case. The current NMR results suggest an axial inclusion of two DBFC molecules within the cavity, with the carboxylate groups pointing to the two sides of the CD. Acknowledgment. This work has been carried out with the financial support from the Ministerio de Ciencia y Tecnologıá (Project BQU2001-1426-C02-02) and from the Gobierno de Navarra. The authors acknowledge the services of the “Centro de Supercomputacioń Complutense (CSC)” and the “Centro de Resonancia Magne´tica Nuclear” of the UCM. They also acknowledge Prof. M. Font and M. Romero for their valuable help with the computational calculations. References and Notes (1) Szejtli, J. Cyclodextrins and Their Inclusion Complexes; Kluwer Academic 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; Editions de 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.; Sańchez, M.; Tardajos, G.; Gonza´lez-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 Effect in Structural and Conformational Analysis; VCH: New York, 1989. (6) Bax, A.; Davis, D. G. J. Magn. Reson. 1985, 63, 207.

14162 J. Phys. Chem. B, Vol. 108, No. 37, 2004 (7) MestRe-C, version 3.5.1; Departamento de Quı´mica Orgańica, Universidad de Santiago de Compostela: Santiago de Compostela, Spain, 2003. (8) A ¨ mma¨lahti, 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. Biochemistry 1990, 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. Tetrahedron 2000, 56, 6151 and references therein. (14) Gonza´lez-Gaitano, G.; Guerrero-Martıńez, A.; Nuń˜ez-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.; Dıéz, C.; Jaime, C. J. Inclusion Phenom. Macrocyclic Chem. 1997, 27, 215. Al-Soufi, W.; Ramos Cabrer, P.; Jover, A.; Budal, R. M.; Va´zquez Tato, J. Steroids 2003, 68, 43.

Gonza´lez-Gaitano et al. (16) MATLAB, version 5.2, The MathWorks, Inc.: Natick, MA, 1998. (17) Funasaki, N.; Ishikawa, S.; Neya, S. J. Phys. Chem. B 2002, 106, 6431. (18) Salvatierra, D.; Jaime, C.; Virgili, A.; Sańchez-Ferrando, F. J. Org. Chem. 1996, 61, 9578. (19) Salvatierra, D.; Sańchez-Ruiz, X.; Gardunõ, R.; Cervello´, E.; Jaime, C.; Virgili, A.; Sańchez-Ferrando, F. Tetrahedron 2000, 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.; Sańchez, M.; Isasi, J. R.; Gonza´lez-Gaitano, G. Appl. Spectrosc. 2002, 56, 1490. (24) FTIR measurements of DBFC and β-CD in D2O at basic pH (not shown) point to the same conclusion: the stretching of the COO- group is not affected by the complexation. (25) Minn, F. L.; Pinion, J. P.; Filipescu, N. J. Phys. Chem. 1971, 75, 1794.

Site-Specific Interaction between 2-Dibenzofuran Carboxylate and

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