NMR Studies of Molecular Conformations in r-Cyclodextrin

Johan Thaning,† Baltzar Stevensson,† Jennie Ostervall,†,‡ Kevin J. Naidoo,§,⊥

Goran Widmalm,‡ and Arnold Maliniak*,†

DiVision of Physical Chemistry Arrhenius Laboratory, Stockholm UniVersity, S-106 91 Stockholm, Sweden,Department of Organic Chemistry, Arrhenius Laboratory, Stockholm UniVersity, S-106 91 Stockholm, Sweden,Department of Chemistry, UniVersity of Cape Town, Rondebosch, 7701, South Africa, and Centre for HighPerformance Computing, CSIR Campus Rosebank, 7701 South Africa

ReceiVed: March 28, 2008

A new approach for analysis of NMR parameters is proposed. The experimental data set includes scalarcouplings, NOEs, and residual dipolar couplings. The method, which aims at construction of the conformationaldistribution function, is applied to R-cyclodextrin in isotropic solution and dissolved in a dilute liquid crystal.An attempt to analyze the experimental data using an average molecular conformation resulted in unacceptableerrors. Our approach rests on the maximum entropy method (ME), which gives the flattest possible distribution,consistent with the experimental data. Very good agreement between experimental and calculated NMRparameters was observed. In fact, two conformational states were required in order to obtain a satisfactoryagreement between calculated and experimental data. In addition, good agreement with Langevin dynamicscomputer simulations was obtained.

Cyclodextrins (CDs) are cyclic R-(1f4)-linked carbohydrateoligomers constructed from glucose units.1 The smallest ho-mologue is R-CD, Figure 1, followed by �- and γ-CDs, whichcomprise 6, 7, and 8 units of a glucopyranose monomer,respectively. Due to their unique structural features, thesemolecules are invaluable in a variety of industrial applications.Almost all applications involve the ability of the CDs to alterthe physical, chemical, and biological properties of guestmolecules through the formation of inclusion complexes.1 It istherefore of utmost importance to determine details of themolecular structure of cyclodextrins in general and conforma-tional transitions in particular. The new method, described here,aims at construction of conformational distribution functionsfor complex molecules in isotropic solution and in a dilute liquidcrystal.

In the present letter, we investigate the conformationalproperties of R-CD using NMR spectroscopy and computersimulations. The ultimate goal in the description of the molecularstructure is the determination of conformational probabilitydistributions, P(φ,ψ), where the two torsion angles, φ and ψ,are related to the glycosidic linkage, Figure 1. Using experi-mental NMR parameters such as J couplings, NOEs, andresidual dipolar couplings (RDCs), we determine the torsionangle distribution function for R-CD. However, defining thestructure of carbohydrates still poses problems since usually onlya limited number of NMR observables are possible to obtain.

It is so because severe spectral overlap, even at high magneticfields, prevents sufficient resolution of many individual reso-nances. The second limitation is the fact that carbohydrates,rather than exhibiting a single well-defined structure, must becharacterized by a distribution of conformations,2 which in turnrequires an increased number of experimental data.3,4 In additionto the experimental investigations, we have carried out Langevindynamics (LD) computer simulations of R-CD. Several com-putational investigations of the hydration effects and confor-mational properties of CDs have been previously reported.5–8

In oligosaccharides, the major degrees of freedom are relatedto bond rotations at the glycosidic torsion angles φ and ψ. Theserotations are however significantly restricted in macrocycliccompounds such as the cyclodextrins. In initial tests, we assumedthat the CD can be described as a uniaxial molecule exhibitinga single conformational structure. It turned out, however, thatthis analysis produced unacceptable errors in comparison withthe experimental data for all three types of parameters.Therefore, we increased the sophistication level of the model

* To whom correspondence should be addressed. E-mail: arnold.maliniak@physc.su.se.

† Division of Physical Chemistry Arrhenius Laboratory, StockholmUniversity.

‡ Department of Organic Chemistry, Arrhenius Laboratory, StockholmUniversity.

§ University of Cape Town.⊥ CSIR Campus Rosebank.

Figure 1. Schematic of R-cyclodextrin.

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Published on Web 06/25/2008

2008, 112, 8434–8436

and considered the maximum entropy (ME) method,9,10 whichallows for continuous bond rotations. This approach is physicallymore sound than the average molecular conformation ap-proximation. The ME analysis introduced here is carried out intwo consecutive steps: First, we use the NMR parametersdetermined in the isotropic phase, that is, the scalar (3Jφ and3Jψ) couplings and the NOEs (σ, related to r-6), for determi-nation of Piso(φ,ψ)

Piso(φ, ψ)) Z iso-1Prep(φ, ψ)exp{-∑

ij

λij3Jij(φ, ψ)-

∑kl

λklrkl-6(φ, ψ)} (1)

where the adjustable parameters λij and λkl are determined bybringing calculated scalar couplings and NOEs into agreementwith experimental observables, and Prep(φ,ψ) accounts forpossible steric repulsions in the molecule. Second, the liquidcrystal distribution function is constructed by using RDCs withconformation independent distance10

PLC(�, γ, φ, ψ)) ZLC-1Piso(φ, ψ) ·

exp{-∑mn

λmndmn(�, γ, φ, ψ)} (2)

where dmn(�,γ,φ,ψ) is the orientation- and conformation-dependent dipolar coupling and � and γ are Euler anglesspecifying relative orientations of molecular and liquid crystaldirector frames. Ziso and ZLC are normalization factors.

The conformational dependence of the dipolar couplings witha constant spin-spin distance originates from the fact that theorientational order is always conformation-dependent. UsingPLC(�,γ,φ,ψ), we can calculate the averages of the RDCs

⟨d⟩ )∫ d(�, γ, φ, ψ)PLC(�, γ, φ, ψ)sin � d�dγdφdψ (3)

The isotropic parameters, 3Jij(φ,ψ) and rkl-6(φ,ψ), are averaged

in an analogous way using Piso(φ,ψ). The strategy used in theanalysis is to fit the experimental NMR parameters shown inTable S1 of the Supporting Information to eq 3. The distributionfunction PLC(�,γ,φ,ψ) is constructed using the λij, λkl, and λmn

parameters. The fitting was performed by employing a computercode written in-house based on the MATLAB subroutinefminu.11 The λ parameters derived from the numerical fittingare collected in Table S2 of the Supporting Information. InFigure 2a, the distribution function PLC(φ,ψ) is displayed (notethat the orientational variables � and γ have been integrated

out). Three peaks are observed in the distribution, with the globalmaximum located at {φ,ψ} ) {0°,0°}. The PLC(φ,ψ) distributionis essentially identical to the Piso(φ,ψ) probability (not shown).In principle, the analysis of experimental NMR parameters, thatis, J couplings and NOEs, determined for the glycosidic anglesφ and ψ will always result in a symmetric distribution functionPLC(φ,ψ).

In an attempt to eliminate possible sterical clashes, theavailable conformational space with atomic distances larger than1.5 Å was determined. In practice, the steric interactions weredescribed by short-range repulsion (including the Boltzmannfactor), Prep(φ,ψ) ) exp{-Urep(φ,ψ)/kBT}, where Urep(φ,ψ) )∑pq εpq(rpq

min /rpq)12, and the parameters were taken from theCHARMM22 force field.13 The permitted region Prep(φ,ψ) isindicated in Figure 2a and b as the shaded areas. Clearly, inFigure 2a, the conformation corresponding to {φ,ψ} ){70°,-80°} is located outside of the allowed region, and thesymmetry-related state {φ,ψ} ) {-70°,80°} is located at theborder of that region. We have therefore included Prep(φ,ψ) asa penalty term in eq 1. The distribution obtained by includingthis repulsion is shown in Figure 2b. Indeed, the conformationcorresponding to {φ,ψ} ) {70°,-80°} is absent, and the {φ,ψ}) {-70°,80°} state is slightly shifted. The global maxima inFigure 2a and b constitute 75% of each (total) population. Thecalculated values of the experimental parameters displayed inFigure 3 were obtained using eq 3 and PLC(φ,ψ) or Piso(φ,ψ).

The agreement is good; in particular, the conformation-dependent dH1′-H4 coupling not used in the analysis is accuratelyreproduced using PLC(φ,ψ). The conformational dependence ofthis coupling is shown in Figure 4; the calculated average is2.66 compared to the experimental value of (2.60(50) Hz.

Finally, in Figure 2c, we show the torsion angle distributioncalculated from the trajectory generated in the LD computersimulation, Ptraj(φ,ψ). This distribution is indeed similar to thatshown in Figure 2b derived from the experimental NMRparameters; in addition to the global maximum at {φ,ψ} ){0°,0°}, a broad peak is observed. In contrast to the distributionderived from the experimental parameters, Ptraj(φ,ψ) does notexhibit a local minimum between the maxima. It can also bepointed out that while the analysis of the experimental data doesnot include the explicit ring structure of the CD molecule, thecomputer simulation contains this restriction.

In conclusion, we have shown that it is possible to obtainthe conformational distribution function, PLC(φ,ψ), for R-CDusing NMR parameters, which included residual dipolar cou-plings (RDCs), cross-relaxation rates, and scalar J couplings.

Figure 2. Contour map derived for R-CD, where φ ) H1′-C1′-O4-C4 and ψ ) C1′-O4-C4-H4. The shaded areas in (a) and (b) representPrep(φ,ψ), which corresponds to the sterically allowed region. The distribution functions, PLC(φ,ψ), were determined using (a) the ME procedure(eq 2) with Prep(φ,ψ) ) 1, (b) as in (a) but with Prep(φ,ψ) ) exp{-Urep(φ,ψ)/kBT} (see text), and (c) the distribution function calculated from theLD trajectory, Ptraj(φ,ψ) (collision frequency12 γ ) 50 ps-1). The simulation was carried out for 5 ns at 300 K using CHARMM (parallel version,C27b4)13 employing a CHARMM22 type of force field, modified for carbohydrates and referred to as PARM22/SU01.14

Letters J. Phys. Chem. B, Vol. 112, No. 29, 2008 8435

The analysis rests on the maximum entropy (ME) approachapplied in two steps. Our results are of special interest due tothe well-known difficulty in describing conformational prefer-

ences of oligo- and polysaccharides. The fact that the confor-mational distribution for R-CD exhibits two conformationalstates may have important consequences for cyclodextrinsforming inclusion complexes.

Acknowledgment. Drs J.-C. P. Gabriel and H. Desvaux aregratefully thanked for a sample of V2O5 in D2O. We thank PatricSchyman for DFT-optimized coordinates of R-CD. This workwas supported by grants from the Swedish Research Counciland SIDA/SAREC.

Supporting Information Available: Experimental proce-dure, experimental values (Table S1), and parameters derivedfrom the ME analysis (Table S2). This material is available freeof charge via the Internet at http://pubs.acs.org.

References and Notes

(1) Dodziuk H. Cyclodextrins and Their Complexes: Chemistry,Analytical Methods, Applications; Wiley: London, 2006.

(2) Yi, X. B.; Venot, A.; Glushka, J.; Prestegard, J. H. J. Am. Chem.Soc. 2004, 126, 13636–13638.

(3) Stevensson, B.; Landersjo, C.; Widmalm, G.; Maliniak, A. J. Am.Chem. Soc. 2002, 124, 5946–5947.

(4) Landersjo, C.; Stevensson, B.; Eklund, R.; Ostervall, J.; Soderman,P.; Widmalm, G.; Maliniak, A. J. Biomol. NMR 2006, 35, 89–101.

(5) Koehler, J. E. H.; Saenger, W.; van Gunsteren, W. F. J. Mol. Biol.1988, 203, 241–250.

(6) Lipkowitz, K. B. Chem. ReV. 1998, 98, 1829–1873.(7) Naidoo, K. J.; Chen, J. Y. J.; Jansson, J. L. M.; Widmalm, G.;

Maliniak, A. J. Phys. Chem. B 2004, 108, 4236–4238.(8) French, A. D.; Johnson, G. P. Carbohydr. Res. 2007, 342, 1223–

1237.(9) Catalano, D.; Di Bari, L.; Veracini, C. A.; Shilstone, G. N.; Zannoni,

C. J. Chem. Phys. 1991, 94, 3928–3935.(10) Berardi, R.; Spinozzi, F.; Zannoni, C. J. Chem. Phys. 1998, 109,

3742–3759.(11) MATLAB; The MathWorks Natick: MA, 1999.(12) Widmalm, G.; Pastor, R. W. J. Chem. Soc., Faraday Trans. 1992,

88, 1747–1754.(13) Brooks, B. R.; Bruccoleri, R. E.; Olafson, B. D.; States, D. J.;

Swaminathan, S.; Karplus, M. J. Comput. Chem. 1983, 4, 187–217.(14) Eklund, R.; Widmalm, G. Carbohydr. Res. 2003, 338, 393–398.(15) Desvaux, H.; Gabriel, J. C. P.; Berthault, P.; Camerel, F. Angew.

Chem., Int. Ed. 2001, 40, 373–376.(16) Tjandra, N.; Bax, A. J. Magn. Reson. 1997, 124, 512–515.(17) Delaglio, F.; Wu, Z. R.; Bax, A. J. Magn. Reson. 2001, 149, 276–

281.(18) Lycknert, K.; Maliniak, A.; Widmalm, G. J. Phys. Chem. A 2001,

105, 5119–5122.(19) Kjellberg, A.; Widmalm, G. Biopolymers 1999, 50, 391–399.

JP802681Z

Figure 3. Comparison of observed and calculated NMR parametersfor R-CD (RDCs: 1H-13C (squares), 1H-1H (crosses), J couplings(circles) in Hz; proton-proton distances rNOE (triangles) in Å). Theliquid crystalline phase: V2O5 in D2O suspension.15 NMR experimentsperformed at 14.1 and 18.8 T: 2D 1JC,H-modulated 13C,1H CT-HSQC,16

2D 1H,1H COSY,17,18 1D DPFGSE 1H,1H T-ROESY.19 The experimentaldetails are collected in the Supporting Information.

Figure 4. The conformational dependence of the residual dipolarcoupling, dH1′-H4(φ,ψ). The maximum corresponds to the conformationwith a short distance between H1′ and H4, and the negative valuesoriginate from the ordering tensor. The calculated average of thisinteraction is 2.66 Hz, which is well within the experimental uncertaintyof (2.60(50) Hz.

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