Complex formation of fenchone with α-cyclodextrin: NMR titrations

13C NMR titration studies of inclusion complexes of bicyclic terpenoid, fenchone enantiomers with α-cyclodextrin revealed their 1:2 guest–host stoichiometry. Sequential binding constants were determined indicating a strong binding cooperativity of two α-cyclodextrin to fenchone. The overall association constants were used to calculate the Gibbs free energies of diastereomeric complex formation, which might be used as a measure of chiral recognition of fenchone by α-cyclodextrin. These results were compared with corresponding data derived for camphor, which is an isomeric bicyclic terpenoid. Electronic supplementary material The online version of this article (doi:10.1007/s10847-013-0356-4) contains supplementary material, which is available to authorized users.


Introduction
Cyclodextrins (CDs) are macrocyclic oligosaccharides composed of a number of glucopyranoside units bound together by a-1,4 bonds. The naturally occurring a-, band c-cyclodextrins (aCD, bCD, and cCD) consist of six, seven, and eight glucopyranose units, respectively [1]. They are obtained by enzymatic starch degradation [1,2]. CDs, whose shape remains a truncated cone, contain a lipophilic central cavity and a hydrophilic outer surface. The size of aCD cavity: bottom diameter 0.53 nm, top diameter 0.47 nm, and cone height 0.79 nm [1,2] allows for accommodating many low molecular weight compounds. In aqueous solutions, CDs can form host-guest inclusion complexes with many partially or fully lipophilic molecules often increasing the guest solubility. Hence their wide application in chemistry, pharmacy, or food industry [1][2][3]. A number of non-covalent forces is responsible for the stabilization of inclusion complexes [4]. The stoichiometry and stability of such complexes strongly depend on the physicochemical properties of guest molecules [5].
NMR spectroscopy is very well suited to study weak and moderate strength molecular complexes and their properties. It is accepted that taking into account typical NMR sample concentrations, the best accuracy can be obtained for association constants within the range 10-10 6 M -1 [24,25]. Therefore, NMR has been widely used for studying inclusion complexes formed by CDs. The success of NMR spectroscopy in this field is due to its ability to study complex chemical systems, to determine complex stoichiometry, association constants, and conformations and to obtain information on their symmetry and dynamics [5,26,27]. Compared to other techniques, NMR spectroscopy provides a superior method to study complexation phenomena as guest and host molecules can be simultaneously observed at the atomic level. Since the rates of complex formation and decomposition are usually faster than the chemical shift time scale (often misleadingly named NMR time scale), the observed chemical shifts are the mole fraction weighted averages of the chemical shifts existing in the free and complexed molecules [5,24]. If the assumption of rapid equilibrium is not valid, an analysis of the total lineshape is required [16,28]. CDs are chiral and, therefore, can form diastereomeric complexes, usually of different stability, with enantiomeric species [29].

NMR measurements
aCD (Sigma, 99 % purity) and both enantiomers of fenchone (the gift from prof. H. Dodziuk) were used without further purification. The 2 H 2 O (Armar Chemicals, 99.8 at.% D) solutions of fenchone enantiomers contained small amount of acetone (Chempur, pure p.a.) whose NMR signal was used as the indicator of external magnetic field inhomogeneity and internal secondary reference: d H = 2.22 and d C = 30.89 [30]. All measurements were performed at magnetic field of 9.4 T, using a Varian Unity Inova 400 MHz, spectrometer. NMR measurements were performed at a temperature carefully adjusted to 300.6 K with an accuracy of 0.1 K and was checked by an ethylene glycol reference sample (composition: 80 % ethylene glycol, Aldrich/20 % dimethyl sulfoxide-D 6 , Armar Chemicals).

Determination of association constants
The changes in 1 H and 13 C chemical shifts of three methyl signals as a function of aCD concentration were analyzed assuming either simple 1:1 or complex 1:1 and 1:2 guesthost stoichiometry. In the latter case stepwise (sequential) binding [26] was assumed. Sequential macroscopic association constants were defined by the following eqns.: where d f is chemical shift in uncomplexed fenchone, whereas x i and d i are mole fractions and chemical shifts of i-th complex species. Association constants K i,c and complexation-induced shifts Dd i were determined by fitting the experimental dependence of d exp in fenchone molecules versus M various concentrations of aCD. The least-squares procedure used a Fortran routine written inhouse optimizing the model parameters that consisted of minimization through a grid search of the target function v 2 given by: Confidence limits of fitted parameters were estimated by use of constant v 2 boundaries [31]. Fisher-Snedecor statistics (F test) was used for the stoichiometry selection at the probability 0.01.

Results and discussion
The fenchone signal assignments had to be done de novo on the basis of COSY, NOESY and 1 H/ 13 C HSQC spectra since the literature values [32,33] corresponded to a different solvent. 1 H and 13 C chemical shifts of free fenchone are collected in Table 1. 1D 1 H-NMR and 2D 1 H/ 13 C HSQC spectra for (-)-fenchone in D 2 O are shown in Figs SF3 and SF4, respectively (Supplementary Materials). Three methyl signals exhibit by far the largest and easiest to detect 1 H and 13 C chemical shift changes on complexation. Their 13 C resonances with complexation shifts, exceeding those of 1 H signals, are especially convenient for quantitative analysis of NMR titration data. In order to provide satisfactory signal dispersion and signal-to-noise ratios of fenchone methyls at the concentration of 1 mM and the natural abundance of 13 C isotope, the 2D 1 H/ 13 C correlation spectra with 1 H detection are the method of choice. Superposition of a series of HSQC spectra showing C10 correlations in (-)fenchone-aCD complex is shown in Fig. 2. So derived 13 C methyl chemical shift changes upon variable ratios of aCD to fenchone enantiomers were used in a numerical procedure yielding best estimates of the association constants.
The sigmoidal shape of all titration curves (Figs. 3, 4) strongly suggests a composite stoichiometry of the studied complexes and a possibility of cooperative binding [34,35]. In fact, the best reproduction of experimental chemical shifts has been obtained assuming a sequential binding model, whereas a simple 1:1 stoichiometry was precluded on the basis of Fisher-Snedecor statistics. The best fit estimates of the association constants are collected in Table 2. Their K 1,c values are smaller than those averaged for a variety of many 1:1 inclusion complexes built up of aCD host molecules [36]. Nevertheless, an association of second aCD molecule to 1:1 fenchone-aCD complexes significantly increases their stability.
Association constants expressed on the molar concentration scale, K i,c , are not suitable for determining thermodynamic quantities. Therefore, recalculation of association constants K i,c on molar fraction scale, K i,a , has to be done [16,26]. The K i,a values and estimates of the corresponding Gibbs free energies DG 0 for complex formation of both fenchone enantiomers with aCD are given in Table 3. A comparison of these data with earlier results obtained for camphor complexes with aCD [8,16] reveals that the overall association constants, b 12,a = K 1,a ÁK 2,a , for camphor complexes are three orders of magnitude higher than the corresponding values for fenchone complexes. On the other hand, chiral recognition, (i.e., differentiation of enantiomeric species, forming diastereomeric complexes which are, quantitatively expressed as DDG 0 = DG 0(-) -DG 0(?) ) for camphor complexes is lower than that observed for fenchone complexes.
The systems with at least two binding sites can exhibit a complex behavior that depends not only on the affinities for each site but also on the interaction between the sites. For instance, the facing rims of two cyclodextrin molecules may interact forming dimers via hydrogen bonds linking their hydroxyls at C2 and C3 glucopyranose units and promoting additional 1:2 complex stabilization. If the binding to one site enhances the affinity for a second site, the so called positive cooperativity takes place. Since cooperativity factors are specific for microscopic description of multisite association processes, it is not always possible to extract them from macroscopic association constants which are usually obtained experimentally [26,35,37]. A qualitative analysis, however, can be performed easily once the macroscopic association constants have been determined. For a system with two binding sites, the cooperativity factor a can be estimated from [37]:   Table 2 The association constants for (?)-fenchone-aCD and (-)fenchone-aCD complexes expressed on the molar (K c ) scale (-)-fenchone (a C 9.9 ± 0.7) F tabl (2,5; The complexation 13 C chemical shift displacements Dd 1 and Dd 2 for the 1:1 and 1:2 species, respectively, are given along with association constants. \C[ denotes the weighted mean calculated from C8-C10 data. The column with the heading F calc indicates the Fisher-Snedecor statistics calculated for a comparison of 1:1 with the sequential 1:1 and 1:2 model. F calc values greater than the corresponding F tabl estimates confirm a meaningful improvement due to an increase in the binding complexity. The cooperativity factor, a, has been evaluated from the macroscopic association constants K 1,c and K 2,c (e.g., a = 4 K 2,c /K 1,c ) [37] a ¼ 4K 2;c =K 1;c If a [ 1, the binding sites exhibit positive cooperativity reflecting the favorable energy loss due to a simultaneous host binding to both sites of the guest molecule [26,37]. One has to bear in mind that this equation is strictly valid only if the two lower order microscopic association constants, j 1i , are identical. It is a consequence of the relation between microscopic and macroscopic association constants: [26]. Fortunately, the cooperativity factor reaches a minimum at j 1A = j 1B = K 1,c /2, where the conclusion about positive cooperativity based on the inequality a [ 1 remains valid. Therefore, formation of the two chiral (?)-and (-)-fenchone-aCD complexes is characterized by strong cooperativity since their lower limit cooperativity factors are equal to 42.6 and 9.9 for (?) -fenchone and (-)-fenchone complexes, respectively (cf. Table 2). Moreover, it might seem intuitively obvious that a stronger complex is characterized by a larger cooperativity.
The stepwise association constants K i,c in complexes of fenchone with a-cyclodextrin differ by one order of magnitude. This result is in contrast with the data obtained for corresponding complexes of camphor studied by similar approach [8]. It has been estimated that their stepwise association constants differ by four orders of magnitude, thus, precluding their separation but supporting conclusion about strong cooperative binding in camphor-aCD complexes.
For a qualitative interpretation of complexation 13 C chemical shifts displacements Dd 1 and Dd 2 , corresponding to the 1:1 and 1:2 complexes, respectively, one should take into account the differential contribution of conformational freedom of guest molecules within the cavity built up of two CD molecules. This may be anticipated from the results obtained for camphor-aCD complexes using NMR relaxation and X-ray studies [10,17]. Crystallographic studies revealed three distinct guest orientations within host dimer capsule, whereas accompanying MD simulations pointed out to additional camphor fluctuations about its equilibrium orientations within the cavity [17]. Nuclear magnetic relaxation studies confirm fast reorientation of the guest molecules within the aCD capsule in addition to differential intramolecular rotations of the methyl groups [10].
All three methyl carbons in either (?)-or (-)-fenchone-aCD complexes exhibit complexation 13 C chemical shift displacement for the 1:2 complex (Dd 2 ) that is larger than that of the 1:1 complex (Dd 1 ). One can argue that two aCD molecules surrounding a fenchone molecule may exert stronger perturbation to the environment of a guest molecule than a single aCD molecule, thus resulting in a relatively larger complexation 13 C chemical shift displacements. In the absence of detailed information on the geometries of fenchone-aCD complexes, however, a detailed interpretation of Dd i values seems problematic. Nevertheless, all but one Dd i values are larger for the more stable (?)-fenchone-aCD complex than for the (-)-fenchone-aCD complex, thus the tighter the complex, the larger is the perturbation and hence the chemical shift displacement.

Conclusions
Stoichiometry and sequential association constants have been determined for diastereomeric complexes of fenchone enantiomers with a-cyclodextrin by means of NMR titrations. Estimation of stepwise association constants makes it possible to evaluate and confirm the presence of positive cooperativity for 1:2 complex formation, if any.
For both terpenoids, fenchone and camphor, the (?)enantiomers form more stable complexes with aCD than the corresponding (-)-isomers. Both fenchone complexes, however, are comparatively much less stable than those of camphor. In contrast, chiral recognition by aCD for fenchone is larger in comparison with camphor. It can be expected that the two geminal methyl groups attached to the C3 carbon atom in fenchone impose more steric hindrance to complex formation with aCD than their counterparts in camphor located at the C7 carbon. Table 3 Values of the association constants, (K i,a i = 1,2), in mole fraction scale, Gibbs free energies, DG 0 , for complex formation of both fenchone enantiomers with aCD and chiral recognition, DDG 0 , compared with corresponding data for camphor complexes taken from Ref. [16] Enantiomer K 1,a K 2,a b 12,a DG 0 (kJ/mol) DDG 0 (kJ/mol)