Global Folds of Proteins with Low Densities of NOEs Using …brd/Teaching/Bio/asmb/current/4paper/16-1.pdf · Global Folds of Proteins with Low Densities of NOEs Using Residual Dipolar

doi:10.1006/jmbi.2000.3842 available online at http://www.idealibrary.com on J. Mol. Biol. (2000) 300, 197±212

Global Folds of Proteins with Low Densities of NOEsUsing Residual Dipolar Couplings: Application to the370-Residue Maltodextrin-binding Protein

Geoffrey A. Mueller1,2, W.Y. Choy1,2, Daiwen Yang1, Julie D. Forman-Kay2, Ronald A. Venters3 and Lewis E. Kay1*

1Protein Engineering NetworkCenters of Excellence andDepartments of MedicalGenetics and MicrobiologyBiochemistry, and ChemistryUniversity of Toronto, TorontoOntario, Canada M5S 1A82Structural Biology andBiochemistry, The Hospital forSick Children, 555 UniversityAvenue, Toronto, OntarioCanada M5G 1X83Duke University MedicalCenter, Box 3711, DukeUniversity, DurhamNC 27710, USA

E-mail address of the [email protected]

Abbreviations used: MBP, maltosCT, constant time; TAD, torsion anNOESY, nuclear Overhauser enhanC0, carbonyl carbon.

0022-2836/00/010197±16 $35.00/0

The global fold of maltose-binding protein in complex with the substrateb-cyclodextrin was determined by solution NMR methods. The two-domain protein is comprised of a single polypeptide chain of 370 resi-dues, with a molecular mass of 42 kDa. Distance information in the formof HN-HN, HN-CH3 and CH3-CH3 NOEs was recorded on 15N, 2H and15N, 13C, 2H-labeled proteins with methyl protonation in Val, Leu, and Ile(Cd1 only) residues. Distances to methyl protons, critical for the structuredetermination, comprised 77 % of the long-range restraints. Initial struc-tures were calculated on the basis of 1943 NOEs, 48 hydrogen bond and555 dihedral angle restraints. A global pair-wise backbone rmsd of 5.5 AÊ

was obtained for these initial structures with rmsd values for the N andC domains of 2.4 and 3.8 AÊ , respectively. Direct re®nement against one-bond 1HN-15N, 13Ca-13CO, 15N-13CO, two-bond 1HN-13CO and three-bond1HN-13Ca dipolar couplings resulted in structures with large numbers ofdipolar restraint violations. As an alternative to direct re®nement againstmeasured dipolar couplings we have developed an approach where dis-crete orientations are calculated for each peptide plane on the basis of thedipolar couplings described above. The orientation which best matchesthat in initial NMR structures calculated from NOE and dihedral anglerestraints exclusively is used to re®ne further the structures using a newmodule written for CNS. Modeling studies from four different proteinswith diverse structural motifs establishes the utility of the methodology.When applied to experimental data recorded on MBP the precision of thefamily of structures generated improves from 5.5 to 2.2 AÊ , while thermsd with respect to the X-ray structure (1dmb) is reduced from 5.1 to3.3 AÊ .

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Keywords: dipolar couplings; protein structure; labeling; maltodextrinbinding protein; protein domains
*Corresponding author
Introduction

Recent methodological developments in solutionstate NMR spectroscopy of proteins have dramati-cally reduced the size limitations that havetraditionally prohibited detailed NMR studies ofmany biologically important molecules (Bax, 1994;

ing author:

e-binding protein;gle dynamics;cement spectroscopy;

Wider & WuÈ thrich, 1999). Advances such as tripleresonance NMR (Bax, 1994), multidimensionalspectroscopy (Bax, 1994), deuteration (Farmer &Venters, 1998; Gardner & Kay, 1998) and morerecently TROSY (Pervushin et al., 1997, 1998) haveled to signi®cant gains in spectral sensitivity andresolution. These advances have, in turn, facilitatedstructural studies of proteins in the 20-30 kDamolecular mass range.

Despite these important advances, the number ofstructures determined by NMR techniques of pro-teins with molecular mass in excess of approxi-mately 30 kDa is small. While chemical shiftassignment of backbone resonances is now possible

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198 Global Folds of Large Proteins

for many high molecular mass proteins using 2H,15N, 13C spectroscopy (Farmer & Venters, 1998;Gardner & Kay, 1998), subsequent steps in thestructure determination process continue to be ratelimiting. For example, overlap in 1H-13C correlationspectra of large proteins complicates the assign-ment of NOEs to unique sites in the molecule.Moreover, correct assignment of NOEs presup-poses that chemical shifts are available for all ormost of the side-chain positions in the ®rst place,which is often dif®cult in the case of large proteins.With these limitations in mind, our laboratory hasdeveloped a labeling strategy where 15N, 13C,highly deuterated proteins are produced with pro-tonation at methyl groups of Val, Leu and Ile (Cd1

only) residues (Goto et al., 1999). This approachfacilitates chemical shift assignment of backbone aswell as methyl side-chain positions and allows dis-tance restraints in the form of HN-HN, HN-CH3 andCH3-CH3 NOEs to be recorded. Because methylgroups are typically located in the core of the pro-tein, these NOEs link residues that are often distalin primary sequence, providing key constraints forstructure determination (Gardner et al., 1997; Rosenet al., 1996).

An additional important advance has been theemergence of the use of dipolar couplings asprobes of molecular structure (Tjandra et al., 1997;Tolman et al., 1995). These couplings are measuredon molecules with a small amount of residualalignment provided by oriented particles such asphage (Clore et al., 1998c; Hansen et al., 1998) orbicelles (Tjandra & Bax, 1997). Studies by Bax andco-workers (Tjandra & Bax, 1997) and Tolman et al.(1995) have demonstrated the utility of dipolarcouplings for structure determination and, when adensity of NOEs of the order of ten per residue orgreater is available, direct re®nement againstmeasured dipolar couplings has resulted inimproved structures (Bewley et al., 1998; Cai et al.,1998). Very recently, Delaglio et al. (2000) usedmolecular fragment replacement in concert withdipolar couplings to fold ubiquitin without usingany NOE restraints. In cases where dipolar coup-lings are available for all or most residues, thisapproach appears very promising.

Maltose-binding protein, MBP, is a 370-residuemolecule comprised of a single polypeptide chainwhich binds a variety of sugars. Detailed X-ray dif-fraction studies of the protein have established thatthe two domains of the molecule, connected bytwo b-strands and an a-helix, change in relativeorientation in a manner dependent on the boundsugar (Sharff et al., 1993, 1992). The existence of anopen conformation (ligand free) and a closed con-former (maltose bound) is crucial for MBP's role inthe signal transduction cascade that regulates bothmaltodextrin uptake and chemotaxis (Sharff et al.,1993; Spurlino et al., 1991). For example, only theclosed form of the protein is able to bind to thechemoreceptor Tar protein, necessary for maltosetaxis (Zhang et al., 1999). MBP has been the focusof interest in our laboratory for a number of

reasons. First, the protein is relatively large byNMR standards and thus serves as a test case forthe development and application of new structuralmethodology. Second, the large numbers of crystalcontacts in the b-cyclodextrin form of the molecule(Sharff et al., 1993; Spurlino et al., 1991) suggestthat important differences in domain orientationmay exist between solution and crystal environ-ments, warranting further studies of this molecule.In this regard we have recently determinedsolution conformations of MBP in complex withb-cyclodextrin by using dipolar coupling data toadjust the relative orientation of domains in X-raystructures of MBP. The solution state conformationof the MBP/b-cyclodextrin complex obtained usingthis hybrid approach is signi®cantly different thanits X-ray-derived counterpart with the solutionstructure related to the crystal form (1 dmb) via an11 � domain closure (Skrynnikov et al., 2000).

Here, we describe the global fold of MBP incomplex with the cyclic heptasacharride, b-cyclo-dextrin (42 kDa). Solution structures were obtainedon the basis of 1943 NOEs, 48 hydrogen bonding,555 dihedral angle and 940 dipolar coupling basedrestraints derived from an 15N, 13C, 2H, Val, Leu,Ile (d1 only) methyl protonated sample. A newprotocol for the inclusion of dipolar couplingrestraints is described which, for large moleculeswith limited numbers of NOEs per residue, hassigni®cantly better convergence properties thanprevious methods based on direct re®nement strat-egies. All of the software discussed below is avail-able from the authors upon request.

NOE analysis of MBP

Preliminary solution structures of the MBP/b-cyclodextrin complex were calculated on thebasis of (f,c) dihedral retraints provided by chemi-cal shifts using the program TALOS (Cornilescuet al., 1999) and distance restraints measured fromNOESY spectra recorded on 15N,2H or 15N, 13C, 2H,Val, Leu, Ile (d1 only) methyl protonated samplesof the protein. Two 4D NOE experiments, the 4D15N, 15N-edited NOESY (Grzesiek et al., 1995;Venters et al., 1995) and the 4D 13C, 15N-editedNOESY (Muhandiram et al., 1993), were recordedwith mixing times of 175 ms. Figure 1(a) and (b)show planes from each of the two 4D data setsselected at the 15N, HN chemical shifts of Ile266,located in the middle strand of a three-strandedb-sheet. Correlations to residues on adjacentstrands of the sheet, Ile60, Phe61 and Tyr106 areillustrated in Figure 1(a), along with an NOE toAla264. Proximal methyl groups (Figure 1(b))include Leu76, in a loop extending from Leu75 toAsp82, as well as Leu280 at the C-terminal end ofan a-helix. As described, NOEs involving methylgroups are particularly signi®cant for structuredetermination by NMR in that they very oftenbridge elements of diverse secondary structure.This example, involving methyl-HN NOEs whichserve to orient a b-sheet, an a-helix and a loop

Figure 1. Planes from (a) 4D15N, 15N-edited NOESY (Grzesieket al., 1995; Venters et al., 1995),(b) 4D 13C, 15N-edited NOESY(Muhandiram et al., 1993) and(c) 3D CT-13C-edited NOESY(Zwahlen et al., 1998a) data setsrecorded on the MBP/b-cyclodex-trin complex. Cross-peaks corre-sponding to NOEs between Ile266HN (a) and (b) or Ile368 Hd1 (c) andproximal protons are labeled ineach slice. Diagonal peaks are indi-cated by d, with cross-peaks thatare more intense in different slicesindicated by *. (a) and (b) areextracted from 4D data sets at(9.41 ppm, 110.68 ppm) and (c) isextracted from the 3D 13C-editedNOESY at 15.28 ppm.

Global Folds of Large Proteins 199

serves as a good illustration of the importance ofthis class of restraints.

In addition to the 4D data sets described above,two 13C-edited 3D NOESY spectra (175 ms mixingtimes) were recorded that exploit the narrowmethyl group carbon linewidths in proteins. TheCT-13C-edited NOESY (Zwahlen et al., 1998a) pro-vides correlations of the form (oCm

i ,oCmj ,oHm

j ),where methyls i and j are proximal. High resol-ution is provided in this experiment by recordingthe frequency oCm

i in constant-time mode (Santoro& King, 1992; Vuister & Bax, 1992). In addition, asdescribed by Zwahlen et al. (1998), correlationslinking Cmi with neighboring 15N, HN spin-pairscan also be observed in this experiment. Figure 1(c)shows NOE correlations from Val343 and Val181to the d-methyl group of Ile368, located near theend of the last helix in the C-terminal domain.These NOE correlations are particularly importantin de®ning the orientation of this helix with respectto the rest of the molecule, since very fewadditional long range restraints have beenobserved. Because ``symmetry-related corre-lations'', (oCm

i ,oCmj ,oHm

j ) and (oCmj ,oCm

i ,oHmi ) are

obtained in this experiment, the assignment ofcross-peaks to speci®c methyl pairs in the proteinis often straight-forward.

A second 3D experiment, (HM)CMCB(CMHM)-NOESY (Zwahlen et al., 1998b) was also recorded,providing NOE correlations of the form(oCm

i ,oCBi ,oHm

j ), where CB is the carbon atom adja-cent to methyl group carbon Cmi. Because only asingle chemical shift is obtained which identi®esthe destination site of magnetization, oHm

j , thisexperiment is best used in combination with theCT-13C edited NOESY described above. In a sig-ni®cant number of cases correlations from the(HM)CMCB(CMHM)-NOESY allowed unambigu-ous assignment of NOEs from the 13C-editedNOESY that otherwise could not be uniquelyresolved.

Initially, NOESY spectra were analyzed in a veryconservative manner by assigning only symmetry-related pairs of NOEs from the 4D 15N, 15N-editedNOESY and the 3D CT-13C edited NOESY datasets. In the case of the 4D 13C, 15N-edited NOESYwhere symmetry related correlations are notobtained, weak cross-peaks were only included in

Figure 2. (a) Distribution of NOEs measured in MBPclassi®ed according to location in the protein and NOEtype. The ®ve categories corresponding to the locationof NOEs include: N domain (residues 1 to 109 and 264to 309), C domain (residues 114 to 258 and 316 to 370),linker (residues 110 to 113, 258 to 263, and 310 to 315),N to C (from the N domain to the C domain), linker toN or C (from the linker to the N or C domain). NOEsare divided according to HN-HN (826), HN-CH3 (769)and CH3-CH3 (348) and are classi®ed as either longrange (&, >i,i � 3) or short range (&). (b) Fraction ofpossible NOEs (HN-HN, HN-CH3 and CH3-CH3) thatwere observed in MBP NOESY data sets versus distancein the X-ray structure, 1dmb (Sharff et al., 1993).


preliminary structure calculations if they couldalso be found in the CT-13C-edited NOESY. Afterthe ®rst round of structure calculations, the initialset of structures were used to help resolve ambigu-ities in NOE assignment. Despite the fact that thestructures were of low quality at this stage (>8 AÊ

pair-wise rmsd) they were nevertheless helpful infurther assignment, since NOE ambiguities were inmany cases limited to no more than four possibili-ties. Typically only one of the possibilities involvedpairs of protons located within 7-8 AÊ in the pre-liminary set of structures, with the other distancesusually 30 AÊ or more. Note that the small numberof possibilities results directly from the labelingscheme employed where only methyl and amidegroups are protonated; in fully protonated mol-ecules the list of potential NOE partners in cases ofambiguous correlations would be more numerous.A second round of structure calculations was sub-sequently performed and many ambiguous NOEsthat could not be assigned on the basis of the pre-liminary structures could now be assigned. At thisstage 555 (f,c) dihedral angle and 1943 distanceretraints (826 HN-HN, 769 CH3-H

N, 348 CH3-CH3)were available. In addition, 48 hydrogen bondingrestraints were obtained from a comparison ofHN-15N correlation spectra recorded on a sample ofdeuterated MBP prior to and after back exchangeof protected amide protons, as described byGardner et al. (1998).

Figure 2 provides a summary of the types ofNOEs that were assigned from the spectradescribed above, with the NOEs subdivided intoshort range (4three residues apart in primarystructure) and long range (>three residues) cat-egories. Although signi®cant numbers of long-range NOEs are observed between residues ineither the N or C-domains and between the linkerregions and one of the two domains, very few (ten)long-range NOEs were assigned between the twodomains. The lack of NOEs between domains inmulti-domain proteins where each domain is onlyloosely connected to the other is a signi®cantlimitation of structure-based studies involvingonly short range distance restraints and scalarcouplings.

The importance of methyl NOEs is well illus-trated in Figure 2(a), showing that 77 % of all long-range restraints derive from methyl correlations. Itis interesting that a larger number of long rangeNOEs were obtained from the N-domain thanfrom the C domain (410 versus 382), despite thefact that the C domain has 40 more residues.Figure 2(b) illustrates the fraction of possible NOEswhich were actually observed, with the total poss-ible estimated from those expected on the basis ofthe X-ray structure of MBP loaded with b-cyclo-dextrin, 1dmb (Sharff et al., 1993). The number ofHN-HN NOEs decreases steeply with distance,while a considerable fraction of the expectedmethyl-methyl correlations out to 8 AÊ areobserved. In this regard it is noteworthy thatunder the conditions used to record the NOE data,

pH 7.2, 37 �C, there is signi®cant exchange withwater, leading to attenuation of HN-HN NOEs.

It is of interest to compare the observed fractionof possible NOEs in deuterated MBP with methylprotonation via a-ketobutyrate and a-ketoisovale-rate (Goto et al., 1999) with the fraction of corre-lations obtained for the methyl protonated,2H-labeled C-terminal SH2 domain from phospho-lipase Cg1, PLCC SH2 (Gardner et al., 1997). In thecase of the SH2 domain, methyl protonation wasachieved using 13C protonated pyruvate as the solecarbon source (Rosen et al., 1996). As described,this procedure produces signi®cant levels of CH2D,CHD2 and CD3 methyl isotopomers, whichseriously degrade both spectral resolution and sen-sitivity. For example, in methyl correlation spectraof the PLCC SH2 domain, only 10 % of theexpected methyl-methyl correlations between6-7 AÊ were observed (Gardner et al., 1997), com-pared to approximately 50 % for MBP.

Figure 3 presents the ten lowest energy solutionstructures of MBP calculated on the basis of thedihedral angle, hydrogen bonding and NOErestraints and results from the structure calcu-lations are summarized in Table 1. The N and

Table 1. Statistics for the ten ®nal structures of theMBP/b-cyclodextrin complex

No dipolarcouplingsa

With dipolarcouplingsb

Average pairwise rmsd (AÊ )c

Global 5.5 � 1.4 2.2 � 0.3N domain 2.4 � 0.3 1.7 � 0.2C domain 3.8 � 1.1 1.8 � 0.2

Average rmsd to 1dmbd

Global 5.1 � 0.7 3.3 � 0.1N domain 3.1 � 0.2 2.7 � 0.2C domain 3.8 � 0.7 2.8 � 0.1

f/c space: residuese

Most favored region (%) 71.2 � 2.0 74.7 � 1.9Additionally allowed region

(%)23.0 � 1.8 21.3 � 1.9

Generously allowed region(%)

3.7 � 1.0 3.0 � 0.7

Disallowed region (%) 1.4 � 0.4 1.1 � 0.4rmsd from covalent geometry

Bonds (AÊ )f 0.0001 � 0.0000 0.0030 � 0.0001Angles (deg.) 0.2746 � 0.0041 0.4514 � 0.0101Impropers 0.1255 � 0.0064 0.4668 � 0.0191

rmsd from experimentalrestraintsNOEs (AÊ ) 0.0044 � 0.0032 0.0117 � 0.0025(f,c) Dihedral angles (deg.) 0.3167 � 0.0409 1.1126 � 0.0716Dipolar couplings (deg.) 1.7471 � 2.1100

a Structures calculated on the basis of 1943 NOE, 555dihedral angle and 48 hydrogen bond restraints.

b Structures calculated using the restraints ina, above, anddipolar coupling-based restraints for 188 residues.

c Calculated with MOLMOL (Konradi et al., 1996). In thermsd calculations the following residues were used: Global:Lys6-Ile235, Asn241-Lys370 (Note that most of the assignmentsfor residues 229 to 239 are not available); N-domain: Lys6-Ala109, Ala264-Glu309; C-domain: Ser114-Ile235, Asn241-Phe258, Arg316-Lys370.

d 1dmb, Sharff et al. (1993).e Calculated with PROCHECK-NMR (Laskowski et al., 1998).f Evaluated by CNS (BruÈ nger et al., 1998).

Figure 3. Solution structures of MBP/b-cyclodextrincalculated on the basis of 1943 NOE, 555 dihedral angleand 48 hydrogen bond restraints. Backbone traces of theten lowest energy structures are displayed and superim-posed by ®tting to either (a) the N domain, alignmentover residues 6 to 109 and 264 to 309 or (b) theC domain, alignment over residues 114 to 258 and 316to 370. The domains are colored red (N domain, resi-dues 1 to 109 and 264 to 309) and blue (C domain,residues 114 to 258 and 316 to 370) with the linkerregion in green (residues 110 to 113, 258 to 263, and 310to 315).


C domains are aligned in Figure 3(a) and (b),respectively, with pair-wise rmsd values of 2.4 AÊ

(N-domain) and 3.8 AÊ (C domain). It is clear thatwhile the de®nition of the individual domains isreasonable, their relative orientation is somewhatill de®ned, and a global pairwise rmsd value of5.5 AÊ is thus obtained. Nevertheless, even at thislevel of precision it is possible to establish the over-all topology of the protein as well as its compo-sition of two domains connected via helical andb-sheet linkers. In addition, the relative orientationof individual elements of secondary structurewithin each domain can be ascertained. Althoughof a preliminary nature, these structures can sub-sequently be used in conjunction with dipolarcouplings to generate signi®cantly better struc-tures, as described below.

Incorporating dipolar couplings intostructure calculations

In addition to the restraints described above,supplementary restraints derived from residualdipolar coupling data can be included in structurecalculation protocols. Direct re®nement of theorientation of bond vectors using residual dipolarcouplings has been shown to improve the accuracyand precision of structures when used in conjunc-tion with nearly complete sets of NOE, couplingconstant and chemical shift data (Clore et al.,1998b). Furthermore, the use of dipolar couplingshas led to improvements in the accuracy and pre-cision of the structures of several small proteinswith well-de®ned topologies determined from alimited set of NOEs (Clore et al., 1999).

In the case of MBP we have used TROSY-basedHNCO experiments to measure 280 15N-1HN, 26215N-13C0 (carbonyl) and 276 13Ca-13C0 one-bond, 262two-bond 13C0-1HN and 276 three-bond 13Ca-1HN

dipolar couplings (Yang et al., 1999). A CNS(BruÈ nger et al., 1998) protocol which utilized thelimited NOE, dihedral angle and hydrogen bondrestraints described above in conjunction with


direct re®nement against the dipolar couplingslisted above produced structures with large num-bers of violations speci®cally in the dipolarrestraints (although the same protocol was muchmore successful in the case of ubiquitin). This islikely due to the fact that for each individual dipo-lar coupling there is an in®nite number of orien-tations consistent with the data, leading to anextremely complex energy surface over whichre®nement occurs. In this sense it is far easier toalter the orientation of individual dipole vectors inan attempt to satisfy restraints than it is to con-verge to a global minimum in the energy land-scape by changing the overall protein fold.Prestegard and co-workers have also observedrelated convergence problems in their study of atwo-domain lectin molecule using dipolar coup-lings and a limited set of NOE restraints (Fischeret al., 1999). In this case they were unable to deter-mine the relative orientation of the domains unlessa large number of distance restraints from theX-ray structure of the protein was included. Basedon these observations, it is clear that a newapproach is needed if dipolar couplings are to beused as restraints in the calculation of solutionstructures of large proteins where there is a limitedquantity of other structural data. The approachpresented here involves the use of dipolar coup-lings to orient peptide planes as discrete structuralunits.

The dipolar coupling, dAB, between two spin 1/2nuclei A and B is given by:

dAB � doABAa �3 cos2 yAB ÿ 1� � 3

2R sin2 yAB cos 2fAB

� ��1�

where yAB and fAB are the polar angles thatdescribe the orientation of the vector connecting Aand B with respect to the principal alignmentframe, Aa and R are the axial and the rhombiccomponents of the molecular alignment tensor,respectively, and

doAB � ÿ

1

2p

� �mo hÿ4p

� �hgAgBhrÿ3

ABi

is the dipolar interaction constant (Tjandra & Bax,1997). In principle, there are ®ve degrees of freedomassociated with the choice of an alignment frameincluding Aa, R and three Euler angles (a,b,g)describing the transformation from the coordinateframe of the molecule to the alignment frame. Thevalues of Aa and R can, however, be estimated fromthe distribution of measured dipolar couplings forthe entire protein (Clore et al., 1998a) leaving (a,b,g)to be determined. Accordingly, at least three dipolarcoupling measurements are required within a rigidsystem, such as the peptide plane, in order to solvefor the transformation. In general, however, we pre-fer to consider residues only if ®ve dipolar coup-lings are available in order to minimize the effectsof experimental error.

In MBP the ®ve dipolar couplings listed abovehave been measured for 240 of the 370 peptideplanes in the molecule (Yang et al., 1999). Thesedipolar couplings are illustrated using red arrowssuperimposed on the peptide plane drawn inFigure 4(a). The transformation from an initial setof molecular coordinates into the fragment (pep-tide plane) alignment frame is determined by agrid search in the space of (a,b,g) which minimizesthe difference between the measured couplingsand those predicted from a trial alignment framevia:

w2 �X5

j�1

�djPredicted ÿ dj

Measured�2 �2�

where the sum is over the ®ve measured dipolarcouplings at a particular site.

Unfortunately, dipolar coupling data alone doesnot de®ne a unique orientation of the peptidewithin its alignment frame. In fact, there areat least eight possible orientations that are con-sistent with the dipolar data. Rotation of theplane by 180 � about any of the three alignmentaxes gives four possible structures. Further rotationof each of these structures by an additional 180 �about the plane normal leads to four more struc-tures that satisfy the dipolar coupling data. Start-ing from a peptide plane lying in the X-Y plane ofa coordinate axis system it can be shown that if(a,b,g) are Euler angles that transform the peptideinto its alignment frame then equally validtransformations are given by (a,b,180 � � g),(180 � � a,180 � ÿ b,180 � ÿ g), (180 � � a,180 � ÿb,360 � ÿ g), (180 � � a,b,g), (180 � � a,b,180 � � g),(a,180 � ÿ b,180 � ÿ g) and (a,180 � ÿ b,360 � ÿ g).Illustrated in Figure 4(c) are the eight differentorientations of the peptide plane spanning residuesPhe149 and Asn150 in MBP consistent with themeasured dipolar coupling data. In order to choosethe proper orientation we use the preliminaryNMR structures calculated exclusively from theNOE, dihedral angle and hydrogen bondingrestraints described above. This is accomplished bycalculating an average structure from the lowestenergy preliminary structures and determining themolecular alignment frame using all of themeasured dipolar coupling values in concert withthis structure. Subsequently, the average structureis rotated into its alignment frame and the orien-tation of a given peptide plane extracted from theaverage structure is compared with the eight poss-ible peptide orientations obtained by consideringonly dipolar coupling data. Assuming that thestructure is static the orientation of the peptide inthe peptide alignment frame (Figure 4(c)) and inthe molecular alignment frame (Figure 4(b)) is thesame and the correct orientation in Figure 4 cantherefore be obtained.

The method of incorporating dipolar couplingsinto structure calculations described above is illus-trated using a ¯ow chart in Figure 5. In steps 1 and

Figure 4. Summary of the protocol used to choose between the eight possible orientations of peptide planes estab-lished on the basis of dipolar coupling data. Dipolar couplings are measured from the ®ve dipole vectors illustratedin (a), resulting in eight possible peptide plane orientations (example shown for the plane bridging residues Phe149and Asn150 of MBP). The eight orientations (c) are compared with the corresponding plane from the average struc-ture (in the alignment frame) derived on the basis of NOE, dihedral and hydrogen bonding data (b) in order to selecta set of restraints. The sum of the dot products of the ®ve dipole vectors from each plane with the corresponding vec-tors from the average structure are shown in (d), illustrating that structure 7 is the best match.


2 NOE and dihedral angle restraints along withdipolar couplings are collected. Subsequently,structures based solely on the NOE, hydrogenbonding and dihedral angle data are calculated asdescribed above (step 3) and an average structureobtained from a set of lowest energy structureswith no restraint violations (step 4). A molecularalignment frame (magnitude and orientation) iscalculated using all of the dipolar coupling dataand the average structure obtained in step 4 byminimizing the difference between the dipolarcouplings predicted from the structure and thosemeasured (step 5). The average structure is sub-sequently rotated into the alignment frame (step 6).Note that although there are four copies of thestructure in this alignment frame which satisfy thedipolar couplings (Skrynnikov et al., 2000) any onecan be chosen since the choice does not affect therelative orientation of planes selected using theprocedure shown in Figure 4.

Figure 4(b) illustrates the ensemble of the tenlowest energy structures of MBP calculated on thebasis of NOE, dihedral angle and hydrogen bondrestraints only. All of the structures are oriented inthe molecular alignment frame of the average struc-ture with the peptide plane spanning residuesPhe149-Asn150 illustrated. Independently, in steps

7 and 8, the dipolar coupling data are used to pre-dict the eight orientations for each peptide planethat satisfy the dipolar coupling data, illustrated forthe Phe149-Asn150 plane in Figure 4(c). At thisstage, the eight predicted peptide plane orientationsare compared with the orientation determined fromthe average structure (step 9). From a simple visualinspection of Figure 4(b) and (c) it is apparent thatthe seventh orientation is the best match in this par-ticular case. More generally, the level of agreementbetween the orientation of a given peptide plane inthe average structure and the eight orientationsgenerated from dipolar couplings exclusively canbe obtained by taking the sum of the dot products,Sk, of the normalized vectors spanning the one-bond N-HN, N-C0, C0-Ca, the two-bond C0-HN andthe three-bond Ca-HN coupled atoms in the averagestructure (vectors A

*

AÿB� with the corres-ponding vectors in each of the k (1 4 k 4 8)predicted orientations (vectors P

*kAÿB). The

score, Sk,

Sk �XA;B

A*

AÿB � P*

kAÿB �3�

for a given peptide plane k ranges from ÿ5 to 5.Values of Sk are displayed below the corresponding

Figure 5. Flow chart illustrating how dipolar coupling-based restraints are incorporated into the structure re®ne-ment scheme. The numbers next to the boxes refer tospeci®c steps which are described in the text.


peptide orientations in Figure 4(d), with the bestmatch, Sk,max � S7 � 4.8. This procedure is repeatedfor each peptide plane for which ®ve dipolar coup-lings are available and in each case the plane corre-sponding to Sk,max is used to obtain orientationalrestraints. It is noteworthy that restraints are notemployed in cases where Sk,max < 3.5 (step 9 inFigure 5). The cut-off value of 3.5 was chosen as agood compromise between minimizing the numberof incorrect restraints and ensuring that a highnumber of restraints are available for structurere®nement. Poor agreement between a peptideplane orientation predicted from NOE/dihedraldata and an orientation obtained on the basis ofdipolar couplings may be the result of a number offactors. These include errors in measured dipolarcouplings, errors in the values of Aa and R esti-mated on the basis of the distribution of couplings,poorly de®ned regions in NOE generated struc-tures, deviations from assumed ideal peptide planegeometry and internal dynamics at a peptide site.There is an additional source of error. In the abovediscussion we noted that in the general case thereare eight possible copies of a peptide plane that areconsistent with the ®ve dipolar couplings that aremeasured. However, if the z-axis of the peptidealignment frame lies in the peptide plane (with theplane making an angle of fa with respect to thex-axis of the alignment frame, for example) there isan additional twofold degeneracy. In this case allthe dipolar vectors are oriented with f � fa orf � fa � p in the alignment frame. From equation(1) it is clear that if the plane were rotated so that

the angle with respect to the x-axis of the alignmentframe becomes 2p ÿ fa the dipolar couplingswould still be satis®ed. In principle, this extra two-fold degeneracy can be taken into account, althoughin the present implementation we have not done so.

After establishing the best peptide plane orien-tation, restraints are written for subsequent struc-ture re®nement utilizing a new CNS module(BruÈ nger et al., 1998) that has been coded for thispurpose. In this case, a restraint is comprised ofthe polar angles (y,f) de®ning the orientation of avector connecting pairs of atoms listed above (redlines in Figure 4(a)) with respect to the peptidealignment frame. For each peptide plane whererestraints are to be written, ®ve statements orienteach of the ®ve atom pairs whose connecting vec-tors are de®ned by the dipolar coupling data (step10 of Figure 5). The new module for CNS is astraightforward modi®cation of the susceptibilityanisotropy module (SANI) described by Clore andco-workers (1998b) and details are given inMaterials and Methods. Finally, the new dipolarrestraints are added to the NOE and dihedralrestraints to build new structures, indicated by theloop from step 10 to 3 in Figure 5. This procedurecan be iterated to further re®ne the structures,although we have not done so here.

It is important to emphasize the differencesbetween direct re®nement against dipolar coup-lings and the procedure developed here. In thecase of direct re®nement, the orientations of indi-vidual bond vectors are changed to satisfy dipolarcouplings; in principle, for any given dipolar coup-ling value there are sets of solutions, which in thecase of an axially symmetric alignment frame aredescribed by a pair of cones. In our approach theorientation of each of the dipolar vectors in a pep-tide plane is determined from ®ve dipolar coup-lings and the preliminary NOE-based structure.The orientations of these planar vectors are self-consistent and are restrained (directly) to wellde®ned values, as described above.

Simulations using model protein systems

In order to test the general applicability of theapproach outlined above, structure calculationswere performed using simulated data derivedfrom the X-ray crystal structures of four large pro-tein domains (256 to 347 residues). The proteinsused for this study were chosen in order to includea variety of structural motifs as de®ned by thestructural classi®cation of proteins database, SCOP(Murzin et al., 1995). The following proteindomains belonging to each of the four structuralclassi®cations were used: all b (1bgl (Jacobson et al.,1994), residues 731 to 1023 from chain F of Escheri-chia coli b-galactosidase), all a (1fps (Tarshis et al.,1994), residues 20-367 of avian farnesyl dipho-sphate synthase), separated a � b (1mua (Tweedyet al., 1993), residues 4 to 260 of human carbonicanhydrase II), and intermixed a/b (1rla (Kanyoet al., 1996), residues 6 to 319 of rat arginase). For


the purpose of calculating rmsd values betweenstructures, the less well de®ned ``tails'' of 1mua(residues 4 to 25) and 1rla (residues 304 to 319)were not considered. Note that MBP belongs to themixed a/b category of structural motifs.

NOE and dihedral angle data for preliminarystructure calculations were predicted from thecrystal structures of each of these proteins. Sincethese simulations are intended to re¯ect the situ-ation typically encountered in the NMR study oflarge proteins, only NOEs that are available from2H, 15N, 13C methyl-protonated samples wereemployed. More speci®cally, these included HN-HN, CH3-CH3, and HN-CH3 NOEs where onlybackbone amides and methyls of Val, Leu, and Ile(Cd1 only) residues were included. Lower andupper bounds for the restraints were set as speci-®ed for MBP (see Materials and Methods). Typi-cally, not all of the possible NOEs are observableand/or assignable in experimental NMR data.Therefore, restraints from the list of possible NOEswere discarded at random in a type and distance-dependent manner consistent with our experiencein the examination of the experimental MBP data(Figure 2); for each protein ®ve different NOE datasets were generated by randomly eliminatingpotential NOEs in this manner. Dihedral angleswere restrained to the crystal structure values�40 � only for those residues found in regular sec-ondary structural elements. Preliminary NMRstructures were obtained using exactly the samesimulated annealing protocol and parameters usedin the calculation of initial MBP structures,described in Materials and Methods. A summaryof the restraints used in each of the calculations isprovided in Table 2A.

Table 2B presents, for each of the four proteinsconsidered, the resulting average pair-wise RMSDvalues for the ten lowest energy structures basedsolely on NOE and dihedral angle restraints. Thebackbone atom precision and accuracy of the pre-liminary structures are given in the ®rst andsecond columns, respectively. A range of rmsdvalues is found, extending from approximately 2.5to 6 AÊ , correlating roughly with the type of fold.

Dipolar coupling data were also simulated fromthe X-ray crystal structures. In all simulations thecalculated dipolar couplings were obtained assum-ing Aa and R values of 0.0017 and 0.26, respect-ively, very similar to the values calculated from thedistribution of dipolar couplings in MBP, and thealignment frame for each molecule was taken (arbi-trarily) to coincide with the x,y,z coordinate frameof the X-ray structure (referred to as AFPDB). Ran-dom errors, within the precision of the measuredvalues for MBP (Yang et al., 1999), were addedto the simulated dipolar couplings accordingto: dNi ÿ HN

i (�0.69) Hz, dNi ÿ C0i ÿ 1(�0.18) Hz,dCa

i ÿ 1 ÿ C0i ÿ 1(�0.75) Hz, dHNi ÿ C0i ÿ 1(�0.64) Hz,

and dHNi ÿ Ca

i ÿ 1(�0.78) Hz. In the case of MBP,69 % of the expected dipolar coupling data for non-Pro residues was obtained, corresponding to 240 of348 non-Pro residues. With this in mind, 31 % of

the calculated dipolar couplings for each of the testproteins were randomly removed from the calcu-lations. It is interesting to note that alignmentframes calculated from the X-ray structures of eachof the proteins using these simulated dipolar coup-lings with random errors (referred to as AFXTAL)were in all cases within 1.4 � of the correspondingAFPDB (no errors). These errors introduce, there-fore, only a very small uncertainty in the calcu-lation of the overall alignment.

Central to our approach for integrating dipolarcouplings into the structure calculation process isthe establishment of the molecular alignmentframe using the preliminary NOE/dihedral anglederived average structures and the dipolar coup-lings, referred to as AFAVG (Figure 5, step 5). Themain source of error in this step derives from theuncertainty in these preliminary structures. For allstructural classes listed in Table 2 the z-axes ofAFXTAL and AFAVG were within a few degrees (onaverage less than 5 �; worst case of 11 �), while theangle between the corresponding x and y-axes was11 � on average, with a worst case of 27 �. The poorde®nition of the x,y-axes relative to z is due to thefact that their position is determined by the magni-tude of R, which in the present calculations was setto 0.26; if R is set to 0.5, the largest deviationbetween the x and y-axis of AFAVG and the corre-sponding axes in AFXTAL is 17 �. Conversely ifR � 0.1 a maximum difference of 84 � is observedfor one of the ®ve NOE/dihedral-based structuresof 1fps (the least well de®ned of the four structuralclasses considered), although the other four align-ment frames were within 20 � of the crystal-de®nedx-y positions. Thus, despite the relatively pooraccuracy of the starting structures, it is neverthelesspossible to establish the orientation of the align-ment frame (AFAVG) reasonably well (except forone or two cases for R � 0.1). It is not surprisingthat the accuracy of AFAVG is signi®cantlyimproved when the average structure from thefamily of preliminary structures is used rather thanany one of the individual structures.

Once the molecular alignment frame has beenobtained (Figure 5, step 5), the correct orientationfor individual peptide planes aligned on the basisof dipolar data exclusively must be establishedusing the average preliminary structure as a guide(Figure 4(c); Figure 5, step 9). In contrast to deter-mining the molecular alignment frame where all ofthe dipolar coupling data is employed, the positionof individual peptide plane alignment frames (andhence the orientation of each peptide plane) isbased on a maximum of ®ve measurements. There-fore, errors in measurement become more criticalat this stage. In order to assess the effects of exper-imental error on the position of the peptide planes,all orientations which predict couplings that arewithin the error of measurement have been visual-ized using a program which places the dipole vec-tors on a sphere. For each peptide eight ``patches''corresponding to the eight predicted orientationsare generally observed, with the spread of vectors

Table 2.A. Model protein systems

Protein class PDB codea Residues NOEs restraints Dihedral restraintsResidue with

dipolar restraints

all b 1bgl 293 1162 315 146all a 1fps 348 1902 471 180a � b 1mua 256 1290 225 128a/b 1rla 323 1811 349 164

B. In¯uence of dipolar coupling based restraints on precision and accuracy

No dipolar couplings With dipolar couplings Control 1f Control 2g

Protein Simulation Precisionb Accuracyc Precisiond Accuracye Precision Accuracy Precision Accuracy

all b 1 3.7 4.1 2.6 3.5 2.6 3.4 1.7 2.32 3.1 3.7 2.3 3.0 2.3 2.7 1.5 2.13 3.6 3.8 2.3 2.9 2.5 2.8 1.5 2.14 3.3 3.5 2.5 3.1 2.6 3.0 1.5 2.35 3.2 3.7 2.4 3.3 2.4 2.9 1.5 2.1

all a 1 6.7 6.2 3.1 3.9 2.8 3.1 2.2 2.52 5.0 5.2 2.7 3.5 2.8 3.4 2.1 2.43 6.1 5.2 2.9 3.8 3.1 3.2 2.1 2.34 4.6 4.5 2.7 3.1 2.6 2.8 2.0 2.35 6.0 5.5 2.6 3.3 2.9 3.0 2.2 2.4

a � b 1 2.5 3.0 1.9 2.5 1.9 2.4 1.3 2.02 2.9 3.1 2.0 2.4 2.0 2.4 1.3 1.93 2.8 3.1 1.8 2.3 1.9 2.2 1.3 1.84 2.8 3.0 1.9 2.5 2.1 2.4 1.3 1.95 2.9 3.2 2.0 2.5 2.1 2.4 1.2 1.9

a/b 1 2.3 2.5 2.0 2.3 1.9 2.2 1.2 1.82 2.6 2.7 1.9 2.3 2.0 2.2 1.3 1.83 2.7 2.8 1.9 2.4 1.9 2.3 1.4 1.84 2.5 2.8 1.9 2.3 1.8 2.2 1.3 1.95 2.3 2.5 1.8 2.3 1.9 2.1 1.3 1.9

a 1bgl, Jacobson et al. (1994); 1fps, Tarshis et al. (1994); 1mua, Tweedy et al. (1993); 1rla, Kanyo et al. (1996).b Average pair-wise rmsd between the ten lowest energy structures calculated without the addition of dipolar coupling based

restraints.c Average rmsd between the X-ray structure and the ten lowest energy structures calculated without the addition of dipolar

coupling-based restraints.d Average pair-wise rmsd between the ten lowest energy structures calculated using dipolar coupling based restraints.e Average rmsd between the X-ray structure and the ten lowest energy structures calculated using dipolar coupling based

restraints.f Orientational restraints calculated from the X-ray structure substituted for dipolar coupling based restraints.g Orientational restraints calculated from the X-ray structure included for all residues in the protein.


as large as 30 � from the mean position in somecases. Therefore, the structures re®ned herein(described below) were all calculated using errorsof 30 � in the orientation of each dipole vector.

The experimental errors discussed above affectthe position of the peptide planes (Figure 4(c)) andhence can in¯uence which of the eight possibleorientations is ultimately selected (see Figures 4and 5). As described above, selection is achievedby comparing the planes with the correspondingplane from the average preliminary structure. Thelow resolution of the preliminary structure there-fore ultimately affects this choice. A comparisonhas been made between orientations of peptideplanes chosen using the preliminary structure(oriented in AFAVG) with those planes selected onthe basis of the crystal structure (oriented inAFXTAL) (step 9 of Figure 5). The orientationsselected by the two approaches were compared bysumming the dot products of the corresponding®ve dipolar vectors (Figure 4(a)) in each of the

selected planes. If the average angle betweendipole vectors based on this sum is within 30 �, cor-responding to the error bounds used in structurecalculations (see below), then the peptide planeorientations selected by the preliminary averagestructure and the X-ray are scored as similar. Thiswas the case for 80.1(�3.7) % of the peptide planesin the four model proteins considered. In order toestablish what level of improvement might beexpected if the molecular alignment frame wereknown exactly we have repeated the calculationsdescribed above using a single alignment frame,AFXTAL, for both the preliminary and X-ray struc-tures. In this case, 82 % of the orientations selectedare similar, suggesting that the majority of thedifferences, at least in the case of R � 0.26, resultfrom errors in the average structure. In order tominimize errors in peptide plane orientations pre-liminary structures are, of course, rejected fromconsideration if they contain any violations of theNOE or dihedral angle restraints.


As described above, for each protein consideredin Table 2 ®ve sets of NOE restraints were gener-ated, along with dihedral restraints and dipolarcouplings. Starting from dipolar couplings for 69 %of the residues and following the protocol outlinedin Figure 5, orientational restraints were obtainedfor approximately 50 % of the residues (i.e.Sk,max 5 3.5 for �50 % of the residues in each pro-tein or �75 % of the residues for which dipolarcouplings were available). Structures were calcu-lated as described in the previous section and inMaterials and Methods. A comparison of the pre-cision (average pair-wise rmsd between structures)and accuracy (average pair-wise rmsd betweenstructures and the X-ray) of the structures withoutand with the inclusion of dipolar coupling-basedrestraints is provided in Table 2, along with thenumber and type of restraints used for eachprotein. In all cases the results reported areaverages based on the ten lowest energy structuresfor which no NOE or dihedral angle violationswere obtained. A dramatic improvement in thequality of structures is noted in the case of 1fps,where initial structures were poor, with smallerbut signi®cant gains observed for the other motifsas well. Moreover, in every case the percentage ofresidues in the most favored region of Ramachan-dran space increased, on average by 4.2(�2.2) %, ascalculated by PROCHECK-NMR (Laskowski et al.,1998). Finally, the procedures described abovewere repeated with the same families of structuresusing Aa � 0.0017, R � 0.1 and R � 0.5 and verysimilar levels of precision and accuracy to thosereported in Table 2 for R � 0.26 were obtained.

The effect of incorporating incorrect peptideplane orientations on the precision and accuracy ofthe resultant structures was evaluated by replacingall of the dipolar based restraints obtained usingthe protocol outlined in Figure 5 with restraintsdetermined directly from the crystal structureoriented in AFXTAL. In columns ®ve and six ofTable 2, only the peptide planes that wererestrained by the preliminary NMR structureswere used (control 1), providing a picture of thequality of structures that could be expected if all ofthe available dipolar data were used correctly. Theaccuracy of the structures improve, on average,from 3.2 to 3.0 AÊ (1bgl), 3.5 to 3.1 AÊ (1fps), 2.4 to2.4 AÊ (1mua) and 2.3 to 2.2 AÊ (1rla), with some-what smaller gains in precision. Thus, an upperbound in accuracy that can be expected in caseswhere approximately 50 % of the peptide planesare restrained varies from 2 to 3 AÊ , depending onthe quality of the initial structures. In order todetermine the limit of the approach used here, allof the peptide planes of the protein were restrainedto the orientation found in the crystal structure(columns seven and eight of Table 2) and struc-tures calculated (control 2). Again, the structuresall improve in accuracy (accuracy between 2.4 AÊ

for 1fps and 1.8 AÊ for 1rla) and, in this case, in pre-cision as well. There are very few violations inthese structures (<0.5 % of the dipolar based

restraints are violated, on average); therefore, theprecision and accuracy in this case result from theerror limits (30 �) placed on the dipolar generatedrestraints.

MBP structures calculated with residualdipolar couplings

The goal of the present work has been to devel-op a simple and ef®cient approach for incorpor-ation of dipolar coupling-based restraints into astructural re®nement scheme for large proteinswhere only a limited number of NOEs and anincomplete dipolar coupling set are available.Although high-resolution structures cannot be gen-erated using the methodology described, theresults illustrated in Table 2 suggest that, in manycases, signi®cant improvements relative to struc-tures calculated from NOEs and dihedral anglesexclusively can be obtained, with an average coor-dinate accuracy on the order of �3 AÊ . We haveapplied this methodology to re®ne the NOE-basedsolution structures of MBP, shown in Figure 3.

Figure 6 illustrates the improvements in MBPstructures resulting from inclusion of dipolar coup-ling based restraints for 188 residues using the pro-tocol outlined in Figure 5 and described above. InFigure 6(a) a superposition of the ten lowestenergy structures generated from 1943 NOE, 555(f,c) dihedral angle and 48 hydrogen bondingrestraints is shown for reference, while in (b) theten lowest energy structures obtained by includingdipolar coupling derived restraints are illustrated.The X-ray structure of MBP with b-cyclodextrin,1dmb (Sharff et al., 1993), is superimposed on theten lowest energy NMR structures in Figure 6(c). Itis clear that including dipolar restraints has signi®-cantly improved the precision of the structures.The largest difference between the NMR and X-rayderived structures lies in a region extending fromPro229 to Lys239 (indicated by * in Figure 6).These residues are part of a helix which lies in thecleft between the two domains that interacts withbound sugar (Sharff et al., 1993) and because ofconformational heterogeneity, many of theexpected cross-peaks were not observed in anyspectra (Gardner et al., 1998).

Although high-resolution X-ray structures existfor MBP both in the absence of sugar and in thepresence of a number of different carbohydrateligands (Sharff et al., 1992), the relative orientationof domains in the molecule can be in¯uenced bycrystal packing interactions which are quite exten-sive in the b-cyclodextrin bound form (Sharff et al.,1993; Spurlino et al., 1991). It is of signi®cant inter-est, therefore, to compare the position of domainsas established by X-ray (1dmb) and NMR methods.In order to quantify differences between 1dmb andthe average, energy minimized NMR structure, theC domains of both molecules have been superim-posed and the transformation resulting in thesuperposition of the N domains of 1dmb and theNMR structure calculated. The Euler angles

Figure 6. Comparison of solutionstructures of the MBP/b-cyclodex-trin complex obtained with andwithout dipolar coupling-basedrestraints. Best-®t (residues 6 to370) superposition of the ten lowestenergy structures generated from(a) NOE, dihedral angle and hydro-gen bond restraints and (b) NOE,dihedral angle, hydrogen bond anddipolar restraints. The domains arecolored red (N domain), blue(C domain), and green (Linker). In(c) the structures from (b) arealigned with the crystal structure ofthe MBP/b-cyclodextrin complex,1dmb (black heavy line). The clo-sure, twist, bend (c,t,b) coordinateframe is illustrated, with the bendaxis extending out of the plane ofthe paper.


required for this transformation, in turn, de®ne ahinge axis about which rotation from one Ndomain to the other occurs, as well as the ampli-tude of this rotation. It is convenient, however, torecast this transformation in terms of another set of

angles which correspond to rotations about ade®ned molecular frame, providing more insightinto the changes. Speci®cally, we de®ne a closure,bend, twist axis frame where the twist axis is co-linear with a vector connecting the centers of mass


of the two domains, the closure axis lies in a planecomprising the twist and hinge axes and the bendaxis is perpendicular to the ®rst two (Skrynnikovet al., 2000). This frame is illustrated in Figure 6. Inthe absence of dipolar-based restraints, the extentof domain closure is ill de®ned, although it is clearthat the domains are more closed in solution thanin the corresponding crystal form. In contrast, theaddition of the dipolar restraints results in an aver-age closure angle of 12(�3) � relative to the X-raystructure. It is noteworthy that the values for clo-sure (12(�3) �), bend (ÿ2(�2) �) and twist(ÿ3(�4) �) obtained from the solution structure arevery similar to values calculated from a combinedNMR/X-ray study where the dipolar couplingswere used to ``guide'' the relative orientation of thedomains in a number of different X-ray structuresto their solution positions (Skrynnikov et al., 2000).However, we feel that this level of agreement issomewhat serendipitous, given the accuracy of theNMR structures (3 AÊ ). For example, if the dipolarcoupling data are reinterpreted using Aa andR-values obtained from a ®t of the measured dipo-lar couplings with those predicted from equation(1) using the crystal structure of the molecule(Aa � 0.00155, R � 0.18), an average closure angleof 4(�3) � is obtained. In this case structures withprecision and accuracy levels similar to what wascalculated with R � 0.26 have been generated.

Consistent with the results of the simulations,the accuracy of both of the domains haveimproved, illustrated in Table 1. In addition, thepercentage of residues in the most favored regionof Ramachandran space has also increased. It isalso noteworthy that although the ten lowestenergy structures calculated with dipolar restraintsdid not show NOE violations, on average six of the555 dihedral angle and 51 of the 940 dipolarrestraints from 41 peptide planes were violated(recall that each of the ®ve dipole vectors inFigure 4(a) is restrained/peptide plane). Table 1summarizes the violations; the average violation ofdipolar restraints is 1.7 � and a maximum violationof 10 � was obtained over all ten lowest energystructures. The level of convergence obtained withthe present approach is to be contrasted with thesituation when direct re®nement against dipolarcouplings was employed when roughly the samenumber of dihedral angles were violated, but thegreat majority of dipolar restraints could not besatis®ed to within the measured errors in dipolarcouplings. In the latter case structures were gener-ated with average rmsd values to 1dmb of 3.4 , 4.8and 6.2 AÊ for the N domain, C domain and theoverall molecule. These values are signi®cantly lar-ger than those reported in Table 1 using the meth-odology described in the text.

Summary

The global fold of MBP has been derived using aset of distance and dipolar coupling restraints

measured on an 15N, 13C, 2H, Val, Leu, Ile (d1)methyl-protonated sample. A new protocol forincorporation of orientational restraints has beenpresented which has better convergence propertiesthan previous methods in cases where structuresare de®ned by only a limited number of NOErestraints. Although the methodology offers ben-e®ts relative to previous approaches, signi®cantimprovements can, nevertheless, be envisioned.Speci®cally, protocols which are less sensitive tothe precise value of rhombicity, R, and are lessdependant on initial structures would representan important advance and are currently underdevelopment.

Materials and Methods

Sample preparation

Two MBP samples were prepared for data collection,including 15N,2H and 15N,13C,2H-Val, Leu, Ile (d1 only)methyl protonated molecules. 15N-labeled MBP was gen-erated with 2H,12C-glycerol as the sole carbon source(Mok et al., 1999), while the 13C-labeled sample was pre-pared using 13C, 2H-glucose as the carbon source, sup-plemented by the precursors [3,3 2H2]

13C a-ketobutyrateand [3-2H] 13C a-ketoisovalerate (Goto et al., 1999). Thesamples were puri®ed as described (Gardner et al., 1998).To fully protonate slowly exchanging backbone amidesites, the protein was partially unfolded for three hoursat room temperature using a guanidinium hydrochloridebuffer, as described (Gardner et al., 1998). Samples con-sisted of 1.0-1.4 mM protein, 2 mM b-cyclodextrin,20 mM phosphate buffer (pH 7.2), 3 mM NaN3, 100 mMEDTA and 5-10 % 2H2O. Dipolar coupling measurementswere made with Pf1 phage liquid-crystalline solvent at aconcentration of 19 mg/ml (2H splitting of 19 Hz), asdescribed by Yang et al. (1999).

Data collection and analysis

All spectra were recorded on a Varian Inova 600 MHzspectrometer at 37 �C. 4D 15N, 15N-edited NOESY(Grzesiek et al., 1995; Venters et al., 1995), 4D 13C,15N-edited NOESY (Muhandiram et al., 1993) and the 3DCT-13C-edited NOESY (Zwahlen et al., 1998a) data setswere recorded using mixing times of 175 ms with pulseschemes and parameters that have been described. Notethat the latter experiment was obtained with constant-time (CT) acquisition only in the t1 dimension and NOEsto both 15N and 13C-coupled protons were recordedduring acquisition. The (HM)CMCB(CMHM)-NOESYscheme used in the present study was modi®ed slightlyfrom the sequence reported (Zwahlen et al., 1998b), inthat the second CT period (t2 acquisition) was set to aduration of 1/JCC, the RE-BURP pulses at positions band e in Figure 1 by Zwahen et al. (1998b) were omittedand the RE-BURP pulse (Geen & Freeman, 1991) ofphase f5 covered the whole aliphatic bandwidth. In thisway NOEs originating on Leu residues can be observedwith a high level of intensity. Data sets were processedusing NMRPipe software (Delaglio et al., 1995) and ana-lyzed with NMRView version 3 (Johnson & Blevins,1994).

Distances between amide protons were estimatedfrom peak intensities in the 4D 15N, 15N-edited NOESYby calibrating assigned NOEs from elements of regular


secondary structure with distances measured in high res-olution X-ray structures of proteins. Speci®cally, sequen-tial amide protons in a-helices are less than 3 AÊ , i,i � 2NOEs in a-helices and sequential NOEs in b-sheets corre-spond to distances ranging from 3.5-4.5 AÊ , while i,i � 2distances in b-sheets and i,i � 4 distances in a-helices are6.4(�0.8) AÊ and 6.2 AÊ (�0.3) AÊ , respectively (WuÈ thrich,1986). The intensities of NOE correlations were classi®edas strong, medium and weak, corresponding to distancelimits of 1.8-3.5 AÊ , 1.8-5.0 AÊ , and 1.8-7.0 AÊ , respectively.NOEs measured in methyl-based experiments were notquantitated since intensities of correlations in theseexperiments can be in¯uenced signi®cantly by relaxationduring the CT intervals, as well as by strong couplingeffects in the case of some Leu residues. Thus, distancebounds of 1.8 to 8.0 AÊ for the amide-methyl NOEs and1.8 to 8.5 AÊ for the methyl-methyl NOEs wereemployed.

Dihedral angle predictions for backbone angles f andc were made from the backbone chemical shifts of MBPafter correction for the 2H (1H-methyl Val, Leu, Ile Cd1)labeling scheme employed, as described by Venters et al.(1996). Restraints were generated for the most part usingthe program TALOS (Cornilescu et al., 1999), after thechemical shifts for MBP had been removed from theTALOS database. Restraints consisting of the averagef,c values �2 standard deviations or at least �15 � fromthe average predicted value were employed for 219residues. In cases where angles found by TALOSdid not satisfy acceptance criteria, chemical shift index(Wishart & Sykes, 1994) predictions were used, resultingin constraints for an additional 59 residues. Valuesof f � ÿ 70(�50) � and c � ÿ 50(�50) � and f � ÿ 140(�60) � and c � 130(�90) � were employed for residuesin a-helices and b-sheets, respectively, when the chemicalshift index was used (LuginbuÈ hl et al., 1995).

In addition to the 1943 NOE and the 555 dihedralangle restraints employed in structure calculations, 48hydrogen bond restraints were also used for residues inregular elements of secondary structure. Residues withhydrogen bonding were identi®ed by comparing HN-15Ncorrelation spectra of samples of MBP prepared prior toback-exchange of slowly exchanging amide protons (seeabove) with spectra recorded after the exchange processwas allowed to occur. Note that hydrogen bondingrestraints were included only for residues in regularelements of secondary structure where a clear donor andacceptor could be identi®ed.

Dipolar couplings (dNi ÿ HNi , dNi ÿ C0i ÿ 1,

dCai ÿ 1 ÿ C0i ÿ 1, dHN

i ÿ C0i ÿ 1, and dHNi ÿ Ca

i ÿ 1) weremeasured using the methyl-protonated, 15N, 13C,2H-labeled MBP sample with TROSY-based HNCO pulsesequences described by Yang et al. (1999).

Structure calculations

Dipolar coupling based restraints have been incorpor-ated into a new module based on the original SANImodule (Clore et al., 1998b) for performing direct re®ne-ment against measured dipolar couplings and writtenfor CNS version 0.5 (BruÈ nger et al., 1998). Here, theorientation of a peptide plane is restrained by de®ningthe polar angles describing the orientation of the ®venormalized planar dipolar vectors (~Pk;best

AÿB ) illustrated inFigure 4(a). These polar angles de®ne the orientation ofdipolar vectors with respect to an alignment frame,described by a pseudo-residue, arbitrarily numbered

500, with the atoms OO, X, Y, and Z corresponding tothe origin and the x, y, and z-axes respectively.

The new restraints are of the form:assign (residue 500 and name OO)(residue 500 and name Z)(residue 500 and name X)(residue 500 and name Y)(residue iA and name A)(residue iB and name B) yAÿB fAÿB cerror,

where yAÿB and fAÿB are the polar angles that P*

k;bestAÿB

makes with the de®ned-axis system, P*

k;bestAÿB is a normal-

ized dipole vector from the peptide plane which givesSk,max (see above) and cerror is the allowed error in theangle between the target vector and the actual vector inthe calculated structures. Note that a separate restraint isneeded for each of the 5 A-B dipole vectors (P

*k;bestAÿB ) per

peptide plane. The square-well potential function:

EDIP �kDIP�1ÿ P*

k;bestAÿB � C

*

AÿB�2 if P*

k;bestAÿB � C

*

AÿB < coscerror

� 0 if P*

k;bestAÿB � C

*

AÿB > coscerror �4�is used to restrain each of the A-B dipolar vectors duringsimulated annealing, where EDIP is the energy, kDIP is theforce constant, and C

*

AÿB is the normalized vector con-necting atoms A and B in the structure.

Structure calculations were performed starting fromextended structures (Nilges et al., 1988) and using a com-bination of torsion angle dynamics, TAD (Stein et al.,1997), and Cartesian dynamics. In most cases defaultCNS parameters were employed; therefore only a briefdescription is provided which emphasizes the modi®-cations. An initial TAD (hot) phase was performed at atemperature of 50,000 K consisting of 6000 moleculardynamics steps each of 15 fs. During this stage all of theforce constants (set to standard values, kDIP � 50) werekept constant. Subsequently, a TAD cooling phase com-prised of 30,000 steps each of 2 fs was employed withthe temperature decreasing from 50,000 K to 0 K duringthis interval. All parameters are scaled using defaultvalues and kDIP increases from 50 to 10,000 over thecourse of this period. Finally, a second cooling phaseusing Cartesian dynamics (5000 steps with a 1fs timestep, starting from a temperature of 300 K) wasemployed with parameters starting from their valuesduring the hot TAD phase and increasing to their ®nalvalues over the duration of this interval, as in the secondTAD period. All structures were calculated using thesame basic protocol, whether or not dipolar couplingbased restraints were incorporated.

Protein Data Bank accession codes

Structures have been deposited in the RCSB ProteinData Bank, accession codes lezo and lezp.

Acknowledgments

G.A.M. would like to dedicate this paper to a friendand fellow scientist who passed away, Dr Jill Hunger-ford. The authors also wish to thank Drs Kevin Gardner,Catherine Zwahlen, Natalie Goto and especially NikolaiSkrynnikov for many helpful discussions. G.A.M. is a


recipient of a Human Frontiers Science Program Post-doctoral fellowship and L.E.K. is an InternationalHoward Hughes Scholar. This work was supported by agrant from the Medical Research Council of Canada toL.E.K. All software developed and all of the data used inthe structure calculations will be made available fromthe authors upon request.

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Edited by P. E. Wright

(Received 29 March 2000; received in revised form 4 April 2000; accepted 9 April 2000)

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