Article

Molecular conformations of a disaccharide investigated using NMRspectroscopy

Clas Landersjoa, Baltzar Stevenssonb, Robert Eklunda, Jennie Ostervalla,b,Peter Sodermana, Goran Widmalma & Arnold Maliniakb,*aArrhenius Laboratory, Department of Organic Chemistry, Stockholm University, S-106 91, Stockholm,Sweden; bArrhenius Laboratory, Division of Physical Chemistry, Stockholm University, S-106 91, Stockholm,Sweden

Received 19 December 2005; Accepted 10 March 2006

Key words: carbohydrates, conformation, NMR spectroscopy, residual dipolar couplings, oligosaccharides

Abstract

The molecular structure of a-L-Rhap-(1 fi 2)-a-L-Rhap-OMe has been investigated using conformationsensitive NMR parameters: cross-relaxation rates, scalar 3JCH couplings and residual dipolar couplingsobtained in a dilute liquid crystalline phase. The order matrices of the two sugar residues are different,which indicates that the molecule cannot exist in a single conformation. The conformational distributionfunction, Pð/;wÞ, related to the two glycosidic linkage torsion angles / and w was constructed using theAPME method, valid in the low orientational order limit. The APME approach is based on the additivepotential (AP) and maximum entropy (ME) models. The analyses of the trajectories generated in moleculardynamics and Langevin dynamics (LD) computer simulations gave support to the distribution functionsconstructed from the experimental NMR parameters. It is shown that at least two conformational regionsare populated on the Ramachandran map and that these regions exhibit very different molecular order.

Abbreviations: R2R – a-L-Rhap-(1 fi 2)-a-L-Rhap-OMe; RDC – residual dipolar couplings

Introduction

Determination of biomolecular structure andproperties poses daunting challenges. Whereas thegoal is an understanding of the biomolecularinteractions and the processes that regulate dif-ferent functions, one should still try to elucidateconformation and dynamics of each constituent inthe system. The natural extension of these studies,namely a characterization of the interactions atatomic resolution, is presently being pursued inmany laboratories. These biomolecular entities arehighly complex systems in which nucleic acid–

protein, protein–protein and glycoconjugates–protein interactions play major roles.

Studies of these systems in both the solid andliquid states complement each other and lead to adeepened understanding. Besides X-ray crystal-lography, solid-state NMR spectroscopy is a rap-idly progressing technique (Castellani et al., 2002)that thereby can be used for comparison to pro-cesses taking place in solution. High resolutionNMR is probably the most powerful and versatilemethod to gain insight into biomolecular processesranging over many different time scales (Wang andPalmer, 2003). Information gained from NMR isof course further strengthened if additional, inde-pendent biophysical studies, such as time fluores-cence depolarization, surface plasmon resonance

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

Journal of Biomolecular NMR (2006) 35: 89–101 Springer 2006DOI 10.1007/s10858-006-9006-0

or isothermal titration calorimetry, can be per-formed on the same system.

In the field of biomolecular NMR studying nu-cleic acids, proteins and carbohydrates the nuclearOverhauser effect (NOE) and spin–spin couplingsare well-established methods to elucidatetheir three-dimensional structure. The moleculardynamics (MD), on the other hand, is often char-acterized by employing different types of relaxationexperiments. In several respects, a good descriptioncan now be obtained for a globular protein having afew hundred amino acids. However, defining thestructure of carbohydrates still poses problems sinceusually only a limited number of NMR observablesare possible to obtain between consecutive sugarresidues. It is so, because severe spectral overlap,even at high magnetic fields, prevents sufficientresolution of many individual resonances. The sec-ond limitation is the fact that carbohydrates, ratherthan exhibiting a single well define structure, mustbe characterized by a distribution of conformations,which in turn requires an increased number ofexperimental data. During the last few years the useof dilute liquid crystalline solvents in solution-stateNMRhas attracted significant attention, since thesesystems, in addition to the classical parameters,enable determination of residual dipolar couplings(RDCs) (Tjandra and Bax, 1997a; Prestegard et al.,2000; Fung, 2002; van Buuren et al., 2004). Incontrast to isotropic liquids, where the dipolarinteractions are averaged to zero, the RDCs deter-mined in liquid crystalline phases contain informa-tion on both inter-nuclear distances andorientations.

The ultimate goal in the description of themolecular structure is the determination of confor-mational probability distributions, which areessential for additional studies related to biomo-lecular interactions. In the present investigation, weanalyze the conformational flexibility of the disac-charide a-L-Rhap-(1 fi 2)-a-L-Rhap-OMe (R2R),shown in Figure 1, having a structural elementwhich is found in the lipopolysaccharides anchoredin the outer membrane of several pathogenic bac-teria of the species Shigella flexneri. The confor-mations of the R2Rmolecule are determined by thetwo torsion angles, / and w related to the glycosidiclinkage. Using experimental NMR parameters,NOEs, J-couplings and RDCs, we determine thetorsion angle distribution function, Pð/;wÞ forR2R. In particular we employ the APME model

(Stevensson et al., 2002, 2003, Thaning et al., 2005)for construction of Pð/;wÞ. The APME method,valid in the low orientational order limit, is based onthe additive potential (AP) model (Emsley et al.,1982) andmaximumentropy (ME)approach (Catalanoet al., 1991). The APME procedure was originallydemonstrated on R2R (Stevensson et al., 2002)using essentially the same experimental data set as inthe present article. Here, however the analysis issubstantially extended.

In addition to the experimental investigations,computer simulations of R2R in water have beencarried out. In systems where hydrogen bondingoccurs, it is of utmost importance that the simula-tions are carried out with explicit solvent molecules.Unlike a-D-Manp-(1 fi 2)-a-D-Manp-(1 fi O)-L-Ser (Lycknert et al., 2004) or cellobiose (Kroon-Batenburg et al., 1993) inter-residue hydrogenbonding is not readily accessible in R2R. Therefore,in addition to molecular dynamics (MD), we per-formed Langevin dynamics (LD) simulations of anisolated R2R molecule. Using LD we were able toextend the simulation length to 50 ns, which is oneorder of magnitude longer compared to the MDsimulation. From the trajectories generated in theMD and LD simulations the torsion angle distri-bution functions, Pð/;wÞ, were calculated andcompared with experimental counterparts.

Analysis of the dipolar couplings

The through-space magnetic dipolar couplingbetween spins i and j, with magnetogyric ratios ciand cj, is (in Hz) given by

dij ¼ l0

8p2

cicjh

2ð3 cos2 hij 1Þr3ij

D Eð1Þ

C1'

O5'

C2

O5

O

H1' H2

Me

OH

OMe

OH

HO

HO

HOMe

φ ψ

H4'H5'

H1

H5

H3

zR'

xR'zR

xR

Figure 1. Schematic of the disaccharide a-L-Rhap-(1 fi 2)-a-L-Rhap-OMe (R2R) in which the torsion angles at the glycosidiclinkage are denoted by / and w. Atoms in the terminal group aredenoted by a prime. The local reference frames are indicated.

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where hij is the angle between the spin–spin vectorand the external magnetic field, and rij is the spin–spin distance. The angular bracket denotes that theRDCs are averaged over both molecular tumblingand internal bond rotations.

For a flexible carbohydrate molecule, theobserved RDCs may be expressed as

dij ¼Z

dijðUÞPðUÞdU ð2Þ

where U ¼ /;wf g denotes a conformational statedefined by the two torsion angles related to theglycosidic linkage of the disaccharide. The torsionangle probability, P(F), is obtained from theensemble average over the singlet orientationaldistribution function (ODF) Pðb; c;UÞ

PðUÞ ¼ Z1ZZ

Pðb; c;UÞ sinb db dc ð3Þ

where b and c are Euler angles specifying relativeorientations of molecular and director frames, andZ is a normalization factor.

In Equation 2, dij (F) is the RDC for a confor-mation with probability P(F). The central task inthe interpretation of the RDCs is therefore todetermine the torsion angle distribution function.The expression for the ODF and thus P(F) isderived by combining the AP model (Emsley et al.,1982) and the ME approach (Catalano et al., 1991)resulting in PAPME (F). The details of the APMEprocedure are outlined in the Appendix A, and thefinal distribution function which includes contri-butions from the NOEs, and J-couplings is given by

PAPMEð/;wÞ ¼ Z001 exp

Xij

kijdijð/;wÞ(

Xkl

kkl1

r6klð/;wÞ

Xmn

kmn3Jmnð/;wÞ

)ð4Þ

where the conformational parameter F wasreplaced by the explicit torsion angles / and w, Z¢¢is a normalization constant, and the conforma-tion-dependent but orientationally averageddipolar coupling dijð/;wÞ is defined in EquationA.9 and Figure 2.

Using PAPMEð/;wÞ, we can calculate the aver-ages of all the conformation dependent NMRparameters, Xð/;wÞ

Xh i ¼ZZ

X /;wð ÞP /;wð Þd/ dw ð5Þ

where Xð/;wÞ corresponds to dijð/;wÞ, r6kl ð/;wÞ,and 3Jmnð/;wÞ. The strategy used in the analysis isto fit the NMR parameters collected in Tables 1, 2,and 3 to Equation 5. The APME distributionfunction PAPMEð/;wÞ is constructed using el and kparameters, which describe the orientational orderand molecular conformations, respectively. Notethat the numerical analysis must be carried outsimultaneously for all adjustable parameters. This

n

R| R

LD

RPΩΩ

Ω

MP

. j

i

dij .

zR|

yR|

xR|

yR

xR

zR

BO

εε

Figure 2. Required transformations in the analysis of residualdipolar couplings. The local coordinate systems are labeled xl,yl, zl with l=R,R¢ and n represents the director. The molecularcoordinate frame (M) was arbitrarily fixed in the subunit R¢.

Table 1. Averages related to the glycosidic torsion angles in

R2R

MD LD NMR

\/[ðÞ 38 40

\w[ðÞ )39 )33J/ (Hz) 3.3 3.7 4.2

Jw (Hz) 3.9 3.6 4.8

A-state (%) 90 83

B-state (%) 10 17

A and B refer to the relative populations of the two majorconformational states in the computer simulations.

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is because of the conformational dependence ofthe e tensor, indicated in Equation A.5. The fittingwas performed using a computer code written in-house, based on the MATLAB subroutine fminu(MATLAB v.5.0, MathWorks,1999). The fittingprogram minimizes the error function

Q ¼XNi¼1

Xexpi Xcalc

i

sexpi

2

ð6Þ

where Xexpi and Xi

calc are the experimental andcalculated parameters, respectively, si

exp is theexperimental standard deviation, and N is thenumber of measured parameters.

Materials and methods

Material

The synthesis of a-L-Rhap-(1 fi 2)-a-L-Rhap-OMe (R2R) has been described previously (Nor-berg et al., 1986) and the 1H and 13C NMRassignments in D2O have been reported (Janssonet al., 1991). For cross-relaxation NMR experi-ments, R2R was treated with CHELEX 100 inorder to remove any paramagnetic ions. Thesample was freeze-dried twice, dissolved in 0.7 mlD2O to give a sugar concentration of 100 mM,transferred to a 5 mm NMR tube, and flame-sealed under reduced pressure after degassing bythree freeze-pump-thaw cycles.

The phospholipids, 1,2-dimyristoyl-sn-glycero-3-phosphocholine (DMPC) and 1,2-hexanoyl-sn-glycero-3-phosphocholine (DHPC) were bothpurchased from Sigma (St. Louis, MO) and theamphiphile N-cetyl-N,N,N-trimethylammoniumbromide (CTAB) was obtained from Merck(Darmstadt, Germany), all with a purity >99%.The chemicals were used without further purifica-tion.

The liquid crystalline phase was prepared fromtwo stock solutions containing DMPC:CTAB(30:1) and DHPC in D2O containing 20 mMphosphate buffer (pDc = 7.1), both with a lipidconcentration of 5% w/v. After sonication, thesolutions were mixed to give a DMPC:DHPCmolar ratio of 30:10, determined by integration ofthe peaks in the 31P NMR spectrum at 37 C. Thesample homogeneity was ensured by several cyclesof cooling (0 C), sonication and heating (40 C)and checked by 2H NMR spectroscopy. Subse-quently, 7 mg of R2R was dissolved in 0.7 ml ofthe liquid crystalline solvent to give a sugar con-centration of 30 mM.

NMR spectroscopy

NMR experiments were performed on VarianInova spectrometers at 14.1 and 18.8 T corre-sponding to 1H frequencies of 600 and 800 MHz,respectively, and equipped with 5 mm PFG tripleresonance probes.

Proton–proton cross-relaxation rates (r) wereobtained at 37 C using 1D DPFGSE T-ROESYexperiments (Kjellberg and Widmalm, 1999).Selective excitations of H1, H2, H1¢ and H2¢ in

Table 2. Proton–proton cross-relaxation rates and distances

for R2R from 1D 1H, 1H T-ROESY NMR experiments and

from the computer simulationsa

Proton pair r (s)1) rexp (A) rMD (A) rLD (A)

H1¢–H2 0.128 2.24 2.31 2.31

H1–H5¢ 0.053 2.59 2.86 2.80

H1–H1¢ 0.018 3.10 2.92 3.07

H2–H2¢ 0.004 3.99 3.86 3.96

H1¢–H2¢ 0.060 2.54b 2.54 2.55

H1–H2 0.058 2.55 2.52 2.53

ar = hr6i1=6 from simulation.b Reference distance from MDsimulation.

Table 3. Residual dipolar couplings in R2R: experimental

errors in parentheses; calculated values in square parentheses

dCH (Hz) dHH (Hz)a

C1–H1 )17.5(0.06)b [)17.53]c H1–H3 ±2.3 [+2.33]

C2–H2 )20.3(0.04) [)20.29] H1–H5 ±4.4 [)5.8]C3–H3 +7.0(0.04) [+7.03] H1–H6 ±3.0 [)2.97]C4–H4 +6.6(0.06) [+6.44] H1¢–H2¢ +5.5/)7.4 [+7.98]

C5–H5 +4.9(0.06) [+5.09] H1¢–H3¢ ±1.0 [)2.04]C1¢–H1¢ )15.5(0.04) [)15.51] H1–H2¢ ±2.4 [+1.75]d

C2¢–H2¢ )0.8(0.02) [)0.79] H1–H3¢ ±1.6 [+0.07]

C3¢–H3¢ )13.9(0.06) [)14.44] H2–H1¢ ±4.2 [)6.07]C4¢–H4¢ )19.8(0.18) [)20.80] H2–H2¢ ±2.2 [+1.91]

C5¢–H5¢ )15.6(0.06) [)14.83] H3–H1¢ ±1.7 [)2.12]

aEstimated error for all dHH is ±0.2 Hz.bStandard deviation based on the jack-knife analysis procedure.cIntra-residue RDCs: calculated using the order matrices.dInter-residue RDCs: calculated using the AP approach.

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R2R were enabled in the DPFGSE part of thepulse sequence using two 30 Hz broad i-Snob-2shaped pulses of 57 ms duration, flanked by pulsedfield gradients with durations of 1 ms andstrengths of 0.8 and 2.3 G cm)1, respectively. TheRF field strength of the following T-ROESY spinlock was cB1=2p = 3.0 kHz.

Spectra were recorded with ten different mixingtimes between 30 and 800 ms, using a spectralwidth of 2800 Hz and 16384 complex data points.The number of transients acquired were 400–1280with a total relaxation delay between the transientsof 14.9 s, which corresponds to >5T1. Prior toFourier transformation, the FIDs were zero-filledtwice and multiplied with a 2 Hz exponential linebroadening factor. Spectra were phased, drift andbaseline corrected using a first-order correctionand integrated using the same integration limits atall mixing times. Peak integrals of resonances dueto cross-relaxation were normalized by division ofthe measured integrals with the extrapolated auto-peak value at zero mixing time, which wasobtained after fitting the auto-peak decay to anexponential function. Proton–proton cross-relaxationbuild-up curves were derived from the normalizedintegrals at different mixing times and the rateswere calculated as the initial slope by fitting thesecurves to a second-order polynomial. The qualityof the least-square fits, expressed as the regressioncoefficient, was R>0.994 in all cases. In addition,1H,1H cross-relaxation rates were obtained forthe deuterated analogue (Soderman, et al., 1998)a-L-Rhap-(1 fi 2)-[2-2H]-a-L-Rhap-OMe-2H3 un-der the same experimental conditions as describedabove, which showed excellent agreement with thosein R2R, in particular for H1¢–H1 revealing con-sistency in the subsequently derived inter-protondistances (data not shown). The errors in the cross-relaxation rates and the 3JCH values are estimatedto be less than 10% and less than 0.2 Hz, respec-tively.

The carbon–proton residual dipolar couplingswere calculated as the difference between the one-bond 13C,1H splitting measured at 37 C in iso-tropic phase (100 mM in D2O) and ordered phaseusing a slightly modified J-modulated HSQCexperiment (Tjandra and Bax, 1997b). The cou-plings were obtained by fitting the cross-peakintensities from a series of experiments with dif-ferent 2(T)D) values to C cos[2p 1JCH(T)D)]. Intotal, 7–10 spectra with 2(T)D) values between

23.5 and 28 ms were recorded with spectral widthsof 3000 and 10,600 Hz in F2 and F1, respectively.Each spectrum consisted of 4096 128 complexdata points with 64–112 transients/t1-increment,leading to an experimental time of 8 h/experi-ment (isotropic phase) and 13 h/experiment(ordered phase). Zero-filling to 16,384 2048complex points, was followed by multiplicationwith a Gaussian weighting function prior to theFourier transformation. Integration of the cross-peaks was performed using the same integrationlimits in all experiments. The quadrupolar splittingof the D2O resonance was 10.2 Hz.

Proton–proton scalar (3JHH) and residual dipolarcouplings (dHH) were extracted from phase-sensi-tive COSY spectra using the NMRPipe (Delaglioet al., 1995) based fitting program Amplitude-Constrained Multiple Evaluation (ACME) (Dela-glio et al., 2001). From the splittings in the spectrarecorded at 37 C, J and J+2d were obtained inthe isotropic (100 mM in D2O) and ordered phase,respectively. In all experiments a spectral width of3000 Hz was used with 16,384 128 complex datapoints. The 160 transients/t1-increment wereacquired with a relaxation delay between the scansof >5T1, since for a quantitative analysis of theCOSY cross-peaks it is important that the spinsystem is fully relaxed at the beginning of the pulsesequence. At the higher magnetic field strengthSigned COSY experiments (Otting et al., 2000)with a 1H,1H TOCSY mixing time of 40 ms and a1H,1H NOESY mixing time of 500 ms were per-formed in the ordered phase with 512 and 360transients/t1-increment, respectively.

Molecular simulation

Molecular dynamics and Langevin dynamics sim-ulations used CHARMM (Brooks et al., 1983)(parallel version, C27b4) employing a CHARMM22type of force field (MacKerell Jr. et al., 1998)modified for carbohydrates and referred to asPARM22/SU01 (Eklund and Widmalm, 2003).Initial conditions for the MD simulation wereprepared by placing one R2R molecule in a previ-ously equilibrated cubic water box of length29.972 A containing 900 TIP3P water molecules,and removing the solvent molecules that were clo-ser than 2.5 A to any solute atom. This procedureresulted in a system with R2R and 868 watermolecules. Energy minimization was performed

93

with Steepest Descent, 1000 steps, followed byAdopted Basis Newton–Raphson until the root-mean-square gradient was less than 0.001 kcal -mol)1 A)1. The simulation was carried out with theleap-frog algorithm (Hockney, 1970), a dielectricconstant of unity, a time step of 1 fs, and data weresaved every 0.1 ps for analysis. TheMD simulationwas performed by heating at 5 K increments dur-ing 6 ps to 300 K, where the system was equili-brated for 100 ps, followed by the production runwhich lasted for 4.86 ns. The temperature wasscaled by the algorithm based on a weak couplingto a thermal bath (Berendsen et al., 1984). Periodicboundary conditions and the minimum imageconvention were used with a non-bond frequencyupdate every 5th step and a force shift cutoff(Steinbach and Brooks, 1994) acting to 13 A.

In LD simulations mimicking of solute mole-cules in water, a collision frequency of c = 50 ps)1

is often used. However, significantly increasedsampling of the conformational space is possiblefor c = 2 ps)1 (Loncharich et al., 1992) whichtherefore was used herein at 300 K.

Simulations were performed on an IBM SP2computer at the Center for Parallel Computers,KTH, Stockholm, using 32 nodes, which in theMD case resulted in a CPU time of approximately25 h per ns.

Results and discussion

In a disaccharide such as R2R, the major degreesof freedom are related to bond-rotations at theglycosidic torsion angles / and w. The conforma-tional distribution function for R2R was derivedfrom the experimentally determined NMRparameters, namely: heteronuclear transglycosidiccoupling constants, proton–proton cross-relaxa-tion rates, and proton–carbon/proton–protonRDCs. In principle, these parameters can beused in the APME-analysis, Equation 4, to pro-duce the conformational distribution function,PAPME /;wð Þ. There is however a potential prob-lem in the data set: we were not able, using thepresent experimental methods, to determine thesigns of the five 1H,1H inter-residue RDCs. Thus,the solution is not unique, but consists of 32 (25)different distribution functions. We adopt, there-fore, the following strategy for the analysis of theexperimental data: (i) the conformational distri-

bution function PNOEJ /;wð Þ is determined usingthe cross-relaxation rates (NOEs) and scalar(3JCH) couplings, but excluding the RDCs, (ii) theconformational potential function, Uintð/;wÞ isderived from PNOEJ /;wð Þ and used together withthe intra-residue dipolar couplings in the AP pro-cedure to determine the signs of the inter-residueRDCs, and (iii) finally the entire data set is used inthe APME procedure to derive the conformationaldistribution function, PAPME /;wð Þ.

Cross-relaxation rates and scalar 3JCH couplings

The experimental values of the scalar couplings,3JCH, (Hardy et al., 1997) and the cross-relaxationrates from 1H,1H T-ROESY experiments are col-lected in Tables 1 and 2, respectively. Using thestandard reference distance, H1¢–H2¢, from themolecular mechanics calculations, the other cross-relaxation rates were interpreted as effective pro-ton–proton distances. In this interpretation, theisolated spin pair approximation (ISPA) (Keepersand James, 1984; Thomas et al., 1991) and theassumption about a single correlation time wereemployed. The analysis of experimental NOEs (theinternuclear distances) provides important infor-mation about the molecular structure in general(Berardi et al., 1998), and in R2R in particular(Widmalm et al., 1992). The conformational dis-tribution function, PNOEJ /;wð Þ, is now determinedfrom the combination of Equations 4 and 5. Sinceno RDCs were employed in the analysis, only thelast two terms of Equation 4 were included. Thus,the PNOEJ /;wð Þ distribution function, displayed inFigure 3a, was constructed using six k-parameters(two 3JCH, and four r). In general, as a result of theexo-anomeric effect (Lemieux and Koto, 1974), it isanticipated that conformations with / 50 arepopulated. In the PNOEJ /;wð Þ distribution a singlemaximum is located at / 15 and at w 0.

Residual dipolar couplings

We now turn to the analyses of the RDCsobtained in a lyotropic liquid medium. The het-eronuclear dCH couplings were obtained from aseries of J-modulated constant time HSQCexperiments and homonuclear dHH were derivedfrom phase-sensitive COSY spectra. The signs ofthe heteronuclear RDCs were readily determinedwhereas for the homonuclear RDCs severe

94

difficulties were experienced, because the J-con-tribution to the splitting is absent or very small.Employing a signed-COSY experiment withTOCSY transfer we could show that the same signwas exhibited by the H4–H5, H1¢–H2¢, and H3¢–H5¢ interactions. The signed-COSY experimentwith NOESY transfer revealed opposite signs be-tween H2–H3 and H3¢–H5¢.

In principle, five RDCs in each residue of R2Rare required for determination of the orientationalorder. The coordinates for all atoms in the R2Rmolecule, necessary for the analysis of the dipolarcouplings, are collected in Table S1 (Supplemen-tary Material). The first step in the analysis is to fixthe two local frames in the rigid residues R and R¢.The location of these frames is arbitrary, but wehave chosen the z axes, zR and zR¢, to coincide withthe bonds C2–O and C1¢–O in the glycosidiclinkage (Figures 1 and 2). The x axes were locatedin the O–C–H planes (O–C2–H2 and O–C1¢–H1¢),and the y axes are normal to these planes. Theorientations of the two local frames are providedin Table S2. The 15 intra-residual RDCs (10 heteronu-clear and five homonuclear, Table 3) are then usedto determine the order matrices of the rigid frag-ments. Diagonalisation of these matrices gives thefollowing principal values of the order parameters:Szz = 0.006251(92), Sxx)Syy = 0.003888(32) andSzz¢ = 0.00711(19), Sxx

¢ )Syy¢ = 0.008785(98)

where Szz>Sxx>Syy for R and R¢, respectively.The principal axes of the order tensors are given inTable S3, whereas the relative orientations of theprincipal axes and local reference axes are includedin Table S4. The order parameters Szz, Sxx)Syy

correspond to ÆD0,02 æ and ReÆD0,2

2 æ (Merlet et al.,1999) in the notation used in the Appendix A.Thus, the order matrices for the two residues aredifferent and we conclude that the structure of themolecule can not be described by a single confor-mation. Note, that the uncertainties of the orderparameters are based exclusively on the errors inthe measured dipolar couplings. A distribution ofthe RDCs was generated from the experimentaldata and 10,000 randomly chosen RDC sets wereused to calculate the average order tensor. We didnot, however, consider the effect of the vibrationalmotions i.e. the uncertainty in the structure is ne-glected in the analysis. Furthermore, we performeda systematic rotation of the two frames related tothe ordering matrix, but they were not superim-posable for any single /;w-combination. The cal-culated intra-residue RDCs agree well with thoseobserved (Table 3) indicating a reasonable choiceof the molecular geometry.

In the next step of the analysis we use the APmodel for determination of the signs of thehomonuclear inter-residue RDCs. The generaldrawback of the AP approach is that the func-tional form of the intra-molecular potential,

–180 –120

– 600

60120

180

–180 –120

– 600

60120

1800.0

0.2

0.4

0.6

0.8

1.0

φ /°ψ /°

° °

0.0

0.5

1.0

1.5

2.0

2.5

3.0

–180 –120

– 600

60120

180

–180 –120

– 600

60120

180

φ /ψ /

–180 –120

– 600

60120

180

–180 –120

– 600

60120

1800.0

0.2

0.4

0.6

0.8

1.0

φ /°ψ /°

PN

OE

J(φ,

ψ)

PA

PM

E(φ

,ψ)

PLD

(φ,ψ

)

(a)

(b)

(c)

Figure 3. The conformational probability distribution forR2R: (a) derived from the analysis of the cross-relaxation andscalar 3JCH couplings, PNOEJ /;wð Þ, (b) derived from theanalysis of all experimental NMR parameters using the APMEapproach, PAPME /;wð Þ, and (c) calculated from the trajectorygenerated in the LD simulation, PLD /;wð Þ.

95

Uintð/;wÞ, must a priori be known. Here however,we have access to the conformational distributionfunction, PNOEJ /;wð Þ, which, assuming theBoltzmann distribution of conformational states,gives the intra-molecular potential. Using the in-tra-residue RDCs and by combining Equations A3and A4 we can determine the AP orientationaldistribution function PAP b; c;/;wð Þ, as given inEquation A.2. The homonuclear, inter-residueRDCs were calculated using Equation 2 and areincluded in Table 3. The differences between theexperimental and calculated RDCs are most likelydue to non-optimized intra-molecular potentialfunction, Uintð/;wÞ. We have also made anattempt to analyze the RDCs using the MEapproach. This analysis produced, however, anessentially flat distribution function (not shown),which is in accordance with the ME-principle(Catalano et al., 1991, Thaning et al., 2005).

The final numerical analysis was performedusing the APME approach, in which 26 experi-mental points were used to determine 21 parame-ters (11 k and 10 e values). The values of theseparameters are collected in Table 4. In theanalysis, 15 intra-residue RDCs were used fordetermination of the el parameters while the con-formational parameters kij in Equation 4 wereassociated with the five available trans-glycosidicRDCs. In addition, four inter-residue cross-relaxationrates related to kkl and two conformation-dependentJ-couplings (kmn) were employed in the construc-tion of the distribution function PAPME /;wð Þ dis-played in Figure 3b. This distribution function isindeed similar to PNOEJð/;wÞ constructed from the

cross-relaxation rates and scalar couplings, butexcluding the RDCs. Three differences can, how-ever, be observed: (i) The maximum of thePAPME /;wð Þ distribution is shifted to higher/-values, ( Pmax

NOEJð/;wÞ 14 and PmaxAPME /;wð Þ

22) which is in accordance with the exo-anomericeffect, (ii) PAPME /;wð Þ predicts a distribution ofstates with positive and negative w-values, and (iii)in addition to the global maximum atw 0;PAPME /;wð Þ exhibits a weak local maxi-mum at w 160. In fact, the latter is identified asan anti-w conformer, which was previously ob-served in the Ramachandran map of the R2Rmolecule (Widmalm et al., 1992). Thus, we claimthat including of the RDCs to the experimentaldata set improves the quality of the conforma-tional distribution function.

Using this distribution and Equation 5 we cal-culated the averages of all the conformationdependent NMR parameters. The correlationbetween the calculated averages and the corre-sponding experimental values is displayed in Fig-ure 4. The agreement is indeed very good whichindicates reliability of the method for determina-tion of the conformational distribution function.

Before closing this section we comment on thefrequently encountered problem related to theconformational dependence of the ordering

Table 4. Parameters derived from the APME analysis of the

experimental residual dipolar couplings (d), cross-relaxation

rates (r), and transglycosidic coupling constants (3J)

elab kp with p=d, r, and 3J

eRzz 0.00255 k

3JC2H10 0.515

eRxxyy )0.00738 k

3JH2C10 )0.162

eRxy )0.00282 kr

H1H10 )6.30eR

xz )0.00173 krH1H50 )3.76

eRyz )0.00148 kr

H1H10 51.4

eR0zz 0.000778 kr

H2H20 )267eR0

xxyy 0.0108 kdH1H20 0.000421

eR0xy )0.000394 kd

H1H30 0.0000163

eR0xz )0.00505 kd

H2H10 0.163

eR0yz 0.00221 kd

H2H20 )0.200kdH3H10 0.426

–20 –15 –10 –5 0 5

–20

–15

–10

–5

0

5

Experimental

Cal

cula

ted

Figure 4. The correlation between observed and calculatedNMR parameters from the probability distribution function forR2R: dCH (squares), dHH (circles), 3JCH (diamonds), and rHH

(triangles), (dij and3Jmn couplings in Hz; rkl in A).

96

(alignment) tensor. A convenient scalar parameterthat characterizes the molecular ordering is thegeneralized degree of order (GDO), #ð/;wÞ (Pre-stegard et al., 2000; Tolman et al., 2001)

#ð/;wÞ ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiX2m¼2

D20;m XDMð Þ

D ED2

0;m XDMð ÞD E

vuut ð7Þ

where D20;m XDMð Þ

D Eis the orientational averaged

but conformation-dependent order parameter de-fined in Equation A7. The advantage of the GDOconcept is that it reflects both internal and orien-tational averaging and it can be expressed in anyframe fixed in the molecule. In Figure 5 the strongconformational dependence of the GDO is dem-onstrated. This is further clarified in Figure 6 in

which the conformational dependence of the wtorsion angle is depicted for / ¼ 38 in R2R.Thus, for the conformational regions populated byR2R (cf. Figure 3) the GDO differs by up to afactor of two. Note that the averaging of #ð/;wÞaccording to Equations 5 and 7 provides a singlevalue related to the orientational order for themolecule. Using the distribution function displayed inFigure 3b the averaged GDO # = 0.01008 0.00202was obtained.

Computer simulations

The analyses of the trajectories generated in theMD and LD computer simulations of R2R arefocused on the conformational states related to theglycosidic linkage. The scatter plot of / and wcalculated from the MD trajectory is shown inFigure 7. In the plot three different conforma-tional states can be observed: (i) the conformationreferred to as A with w\0, (ii) a state denoted Bwith w[0, and (iii) a non-exo-anomeric confor-mation with /\0 denoted C. The latter state,however, was only visited once during the MDsimulation and although not completely negligibleits presence is of minor importance in the presentanalysis. The state denoted D, ( w 160) referredto as an anti-w conformer and observed in theanalysis of the experimental data, is not present in

–180 –120 –60 0 60 120 180

0.006

0.008

0.010

0.012

0.014

ψ /°

ϑ

Figure 6. The conformational dependence of # as a function ofw; the slice corresponds to / = 38.

-120 -60 0 60 120

-120

-60

0

60

120

φ /o

ψ /

o

Figure 7. Scatter plot of / (H1¢–C1¢–O2–C2) vs. w (C1¢–O2–C2–H2) for R2R from the MD simulation.

Figure 5. The conformational dependence of the generalizeddegree of order (GDO), #ð/;wÞ.

97

the trajectory. Based on the LD and MD computersimulations we identify two conformational statesA and B with the relative populations 8:2 and9:1, respectively (Table 1). Thus, also in the LDsimulation the minor state is B.

The 3JCH values calculated from the trajectoryusing a Karplus-type relationship (Cloran et al.,1999) are given in Table 1. The experimentalcouplings are somewhat larger compared to thosepredicted by the computer simulations, indicatingsmall discrepancies in the conformational sam-pling. Another possible source of error may be adeficient parameterization of the Karplus-typerelationship for the 3JCH couplings. The averagedistances (Table 2), calculated from the trajectorywere compared to the effective distances derivedfrom the cross-relaxation rates measured employ-ing 1H,1H T-ROESY experiments. In fact, thedistances calculated from the LD simulation agreeslightly better, thus indicating that the populationof state A should be decreased compared to theMD simulation. Consequently, a significant pop-ulation of the B state or other states is required. InFigure 3c, the conformational distribution func-tion calculated from the LD trajectory, PLD /;wð Þis displayed. Considering the approximationsintroduced in the computer simulations and in theinterpretation of the experimental results, theagreement between PLD /;wð Þ and PAPME /;wð Þ isindeed reasonable.

In conclusion, we have shown that it is possibleto obtain the conformational distribution function,Pð/;wÞ, for a small biomolecule represented hereby a disaccharide. The distribution function wasderived from the analysis of the conformation-dependent NMR parameters, which includedresidual dipolar couplings (RDCs), cross-relaxa-tion rates and scalar J-couplings. The analysis in-volved three consecutive steps where MEapproach was followed by the mean field, APmethod, subsequently employing our own APMEprocedure. This elaborate route was chosen be-cause at the present stage we were not able toexperimentally determine the signs of the mostconformation-sensitive RDCs. In the analysis wehave shown that the experimental RDCs contrib-ute to an improved conformational characteriza-tion of the molecule. Our results are of specialinterest due to the well known difficulty indescribing conformational preferences of oligo-and polysaccharides. Furthermore, the analysis

indicates a possible route for conformationalinvestigations of more complex systems. Sincethere is rapid progress in the development ofsuitable NMR pulse sequences to allow for thedetermination of a large number of observables(O’Neil-Cabello et al., 2004) the methodology de-scribed here has large future potential.

Electronic supplementary material

The coordinates for all atoms in the a-L-Rhap(1 fi 2)-a-L-Rhap-OMe (R2R) molecule, togetherwith the orientations of various coordinate framesnecessary for the analysis of the RDCs are given inthe Supplementary Material. This material isavailable at http://dx.doi.org/10.1007/s10858-006-9006

Acknowledgements

This work was supported by grants from the CarlTrygger Foundation, the Swedish ResearchCouncil, the Magnus Bergvall Foundation, andSIDA/SAREC. We thank the Center for ParallelComputers, KTH, Stockholm, for putting com-puter facilities at our disposal and Dr. JohanWeigelt for helpful discussions. Finally, we thank areviewer for useful comments on the analysis ofthe experimental data.

Appendix

APME procedure: a hybrid model

based on maximum entropy and

molecular field theory

The crucial step in the analysis of residual dipolarcouplings (RDCs) in flexible molecules involvesconstruction of the torsion angle distributionfunction for the molecular fragment under con-sideration. The RDC for a fixed conformationalstate F is given by

dijðUÞ ¼ bijðUÞ D20;0ðXLPðUÞÞ

D E

¼ bijðUÞD20;0 XLDð Þ

X2m¼2

D20;mðXDMÞ

D ED2

m;0ðXMPÞ

ðA:1Þ

98

where the dipole–dipole coupling constant isdefined as bijðUÞ ¼ l0cicjh=8p

2r3ijðUÞ and Dn,m2 (W)

is the second rank Wigner function (Brink andSatchler, 1993). Note that the averaging in Equ-ation A.1 refers only to molecular orientations. Thus,the order parameters ÆD0,m

2 (WDM)æ become confor-mation dependent via the probability distributionfunction Pðb; c;UÞ. The transformation between theprincipal axis system (P) of the dipolar interactionand the laboratory frame (L) is performed explicitlyusing three successive rotations. Transformation be-tween frame P and the molecular frame is charac-terized by WMP, whereas the Euler angles b; c thatspecify relative orientations of molecular and direc-tor frames are denotedWDM. Finally, the orientationof the director in the magnetic field is given by WLD.The bicelles, in the present study, orient with thenormal orthogonal to the field, which results inD0,0

2 (WLD)=)1/2. Thus in the following we willconsider this rotation as a constant factor and omit itin the equations.

The additive potential (AP) model. The APmodel rests on equilibrium statistical mechanicsand the mean potential Uðb; c;UÞ is related to thesinglet ODF by (Emsley et al., 1982)

PAPðb; c;UÞ ¼ Z1 exp Uðb; c;UÞf g ðA:2Þ

whereUðb; c;UÞ, in units ofRT, is written as the sum

Uðb; c;UÞ ¼ UintðUÞ þUextðb; c;UÞ: ðA:3Þ

The conformational potential Uint (F) is inde-pendent of molecular orientation and it is usuallyexpressed as a cosine series. The potential of meantorque, Uextðb; c;UÞ, is written as

Uextðb; c;UÞ ¼ X2n¼2

e2;nðUÞD20;nð0; b; cÞ

ðA:4Þ

where the interaction parameters e2;nðUÞ dependon the segmental, anisotropic interactions. Theconformation dependence of these parametersis achieved by expressing them in terms of F-independent coefficients, el2;p, which represent theinteractions of the lth rigid subunit with the liquidcrystalline field. Thus

e2;nðUÞ ¼Xl

X2p¼2

el2;pD2p;nðXlMÞ ðA:5Þ

where WlM is the orientation of the lth subunit inthe molecular frame.

We will now consider a situation where theorientational order is low, which in turn impliesthat the potential of mean torque, Uextðb; c;UÞ, issmall. In this case, the ODF can be Taylor ex-panded and truncated after the second term. Theanalytical averaging over the molecular orienta-tions, gives the distribution function correspond-ing to the low order limit of the AP model, P ¢AP(F)(Stevensson et al., 2002, 2003; Thaning et al., 2005)

P0APðUÞ¼Z01Z Z

exp UintðUÞf g

1Uextðb;c;UÞ½ sinbdbdc

¼Z01Z Z

exp UintðUÞf g

1þX2n¼2

e2;nðUÞD20;nð0;b;cÞ

" #sinbdbdc

¼Z014pexp UintðUÞf g¼PisoðUÞðA:6Þ

where Piso (F) is related to the internal potentialUint(F), and Z¢, Z¢/4p are the normalization con-stants for PAP

¢ (F) and Piso(F), respectively. Thus,for a weakly ordered system, PAP

¢ (F)=Piso(F).The integral over the second term in Equation A.6vanishes for all n due to properties of the Wignerfunctions (Brink and Satchler, 1993). Using the loworder approximation and Equation A.4, we canexpress the conformation-dependent order parameters

D20;mðXDMÞ

D E QðUÞ1

Z Zexp UintðUÞf g

1Uextðb; c;UÞ½ D20;mð0;b; cÞ sinbdbdc

¼ 1

4p

Z Z "D2

0;mð0;b; cÞ þX2n¼2

e2;nðUÞ

D20;nð0;b; cÞD2

0;mð0;b; cÞ#sinbdbdc

¼ 1

4p0þ

X2n¼2

e2;nðUÞ4pdn;m

5

" #¼ e2;mðUÞ

5:

ðA:7Þ

The Kronecker delta dn,m is a consequence ofthe orthogonality of the Wigner functions (Brinkand Satchler, 1993), and Q(F)=4pexp)Uint(F)is the conformation dependent partition function.

99

The R2R disaccharide consists of two rigidsubunits R and R¢, in which the coordinate framesare fixed with a relative orientation given by XRR0 .The molecular coordinate frame (M) can be arbi-trarily chosen to coincide with one of these rigidsubunits. Using Equations A1, A5, and A7, we candefine a conformation-dependent but orientation-ally averaged RDC

dijðUÞ ¼bijðUÞ5

X2m¼2

eM2;mþX2n¼2

eR2;nD2n;mðXRMÞ

" #

D2m;0ðXMPÞ

ðA:8Þ

where the molecular frame was arbitrarily fixed inthe subunit R¢. Using the closure properties of theWigner functions (Brink and Satchler, 1993),Equation A.8 can be simplified to

dijðUÞ ¼bijðUÞ5

X2m¼2

eM2;mD2m;0ðXMPÞ

þ eR2;mD2m;0ðXRPÞ:

ðA:9Þ

In Figure 2 we show the location of the variousframes relevant for the analyses of the RDCs.

Combination of the AP and ME approaches: theAPME model. Assuming low orientational order,the conformational distribution function P ¢AP(F)was related, in Equation A.6, to the internalpotential Uint(F). The conformational distributionfunction for the glycosidic linkage in R2R dependson the torsion angles / and w. The choice of thefunctional form for the potential functions forthese angles is not obvious. The least biased ap-proach that requires minimum a priori informa-tion is the ME method (Catalano et al., 1991). Wetherefore use the ME approach to describe theconformational dependence of the RDCs. Inaddition, the functional form of the ME methodfacilitates inclusion of the conventional NMRparameters (NOEs and J-couplings) used in pres-ent study for structure determination. Combina-tion of the low orientational order approximationof the AP model with the ME distribution functionyields the APME distribution function (Stevenssonet al., 2003) given in Equation 4.

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101