Journal of Biomolecular NMR, 10 (1997) 351–362 351

*To whom correspondence should be addressed.Abbreviations: 2D, 3D, two-, three-dimensional; TOCSY, total correlation spectroscopy; NOE, nuclear Overhauser enhancement; NOESY, nuclearOverhauser enhancement spectroscopy; REDAC, use of redundant dihedral angle constraints; rmsd, root-mean-square distance; RD, reliabilitydistance.

KLUWER/ESCOM© 1997 Kluwer Academic Publishers. Printed in The Netherlands.

J-Bio NMR 470

Automated combined assignment of NOESY spectra andthree-dimensional protein structure determination

Christian Mumenthalera, Peter Günterta, Werner Braunb and Kurt Wüthricha,*aInstitut für Molekularbiologie und Biophysik, Eidgenössische Technische Hochschule-Hönggerberg, CH-8093 Zürich, Switzerland

bDepartment of Human Biological Chemistry and Genetics, NMR Center, University of Texas Medical Branch, Galveston, TX 77555, U.S.A.

Received 24 April 1997Accepted 24 June 1997

Keywords: Protein structure determination; NOESY assignment; Error-tolerant target function

Summary

A procedure for automated protein structure determination is presented that is based on an iterativeprocedure during which the NOESY peak list assignment and the structure calculation are performedsimultaneously. The input consists of a list of NOESY peak positions and a list of chemical shifts asobtained from sequence-specific resonance assignment. For the present applications of this approachthe previously introduced NOAH routine was implemented in the distance geometry program DIANA.As an illustration, experimental 2D and 3D NOESY cross-peak lists of six proteins have been analyzed,for which complete sequence-specific 1H assignments are available for the polypeptide backbone and theamino acid side chains. The automated method assigned 70–90% of all NOESY cross peaks, which ison average 10% less than with the interactive approach, and only between 0.8% and 2.4% of the auto-matically assigned peaks had a different assignment than in the corresponding manually assigned peaklists. The structures obtained with NOAH/DIANA are in close agreement with those from manuallyassigned peak lists, and with both approaches the residual constraint violations correspond to high-quality NMR structure determinations. Systematic comparisons of the bundles of conformers thatrepresent corresponding automatically and interactively determined structures document the absence ofsignificant bias in either approach, indicating that an important step has been made towards automationof structure determination from NMR spectra.

Introduction

Protein structure determinations by NMR spectroscopyconsist of two main phases (Wüthrich, 1986): (i) sequence-specific resonance assignment; and (ii) collection of dis-tance constraints from the assignment of 2D homonuclearor 3D and 4D heteronuclear-resolved [1H,1H]-NOESYspectra, which is based primarily on the chemical shiftsobtained through the sequence-specific assignments. Inprinciple, the steps needed to obtain resonance assign-ments and conformational constraints are well understood.In practice, however, considerable difficulties in theirexecution may arise from spectral artifacts and noisebands, absence of expected signals because of fast relax-ation and, most of all, peak overlap with concomitant

limitations in the determination of accurate peak posi-tions and peak volumes. These inevitable shortcomings ofNMR data collection are the main reason that manualprocedures, usually now supported by interactive com-puter programs, have so far been used almost exclusivelyin 3D protein structure determinations.

Although many attempts have been made to automatethe sequential resonance assignment (Hare and Preste-gard, 1994; Olson and Markley, 1994; Zimmermann etal., 1994; Morelle et al., 1995; Bartels et al., 1996,1997),only few attempts of automatic assignment of NOESYspectra have so far been described, including combinedautomatic sequential resonance assignment and NOESYassignment (Oshiro and Kuntz, 1993; Kraulis, 1994) aswell as semiautomatic procedures (Güntert et al., 1993;

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Meadows et al., 1994). Assignment ambiguities caused by

Fig. 1. Flow diagram for combined NOESY cross-peak assignmentand 3D structure determination using NOAH/DIANA. Three mainsteps of each assignment cycle are indicated in the circle. In all calcu-lations described in this paper, the procedure of NOE assignment andstructure calculation, followed by analysis of the intermediary resultsobtained, was repeated 25 times.

limited accuracy of peak positions and proton chemicalshifts were usually not explicitly treated in these studies,except for Nilges (1993,1995) who accounted for thisproblem with an approach based on simulated annealingmolecular dynamics, where peak volumes are interpretedas an r−6-weighted sum of all possible peak assignments inthe NOE target function. This procedure was applied tocalculations of the structure of the basic pancreatic tryp-sin inhibitor (BPTI) from simulated NOESY spectra(Nilges, 1995), and has also been used for the calculationof symmetric oligomeric structures from NMR data,where all peaks are a superposition of at least two NOEsignals (Donoghue et al., 1996).

Recently, the NOAH routine was proposed as an alter-native approach for automatic NOESY assignment (Mu-menthaler and Braun, 1995). NOAH uses as input onlythe chemical shift lists obtained from the sequence-specificresonance assignment and a list of NOESY cross-peakpositions. Ambiguous peak assignments are treated asseparate distance constraints in the distance geometrycalculations, and erroneous assignments are eliminated initerative cycles using the principle of ‘self-correcting dis-tance geometry’ as employed by NOAH, where an error-tolerant target function reduces the impact of erroneous

constraints on the calculated structures. In contrast to theNilges approach, noise and artifactual peaks can be auto-matically removed during the procedure, and peaks areultimately assigned to single proton pairs. This allows acritical comparison of NOAH results with those frommanual procedures not only on the level of the finalstructures but also on the level of individual NOE assign-ments.

The present paper describes an implementation ofNOAH in the distance geometry program DIANA (Gün-tert et al., 1991), and the use of the method with 2D and3D experimental NOESY data sets. For proteins wherecomplete, or very nearly complete, sequence-specific 1Hassignments are available for the polypeptide backboneand the amino acid side chains, excellent agreement isachieved between the results obtained with the automaticand manual approaches, indicating that the NOAH/DIANA method is on the way to routine applications inprotein structure determination.

Methods

The NOAH/DIANA routine for NOE assignment and 3Dstructure determination

Figure 1 illustrates the main steps of the procedure. Theinput required for NOAH/DIANA includes the aminoacid sequence, a list of the chemical shifts obtained fromthe sequence-specific resonance assignment, and one orseveral NOESY peak lists containing the peak positionsand peak volumes. Optionally, predefined distance ordihedral angle constraints may be added. NOAH/DIANAperforms a user-defined number of cycles of automaticassignment (typically, 25 cycles yield satisfactory results),each with the following three main steps (Fig. 1, Mumen-thaler and Braun, 1995): (1) identification of those NOESYcross peaks for which the chemical shift list and the resultof the structure determination from the previous cycleenable either a unique assignment or a small number ofpossible assignments; (2) structure calculation using thepeak assignments from (1); and (3) evaluation of theresult obtained, whereby NOAH tries to identify thecorrect assignment for peaks with multiple possible as-signments at the start of the cycle. In the following, thesethree steps are explained in more detail.

In step (1) a listing is prepared for each so far unas-signed NOESY cross peak, which contains all possiblecombinations of spins with shifts that lie within a toler-ance range, ±∆tol, of the peak position. For protons weused ∆tol = 0.01 ppm in 2D NOESY spectra and ∆tol = 0.02ppm in 3D heteronuclear-resolved NOESY spectra. Inpeak lists from 15N- or 13C-resolved 3D [1H,1H]-NOESYspectra, the tolerance range for 15N or 13C was set to ∆tol

= 0.3 ppm. The fundamental considerations leading tothese tolerance ranges are given in the Discussion andConclusions section.

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After the first NOAH/DIANA cycle, a low-resolution3D structure is available, and following Güntert et al.(1993) this preliminary structure is used to eliminate alltentative NOE assignments to proton pairs that are fur-ther apart than 5.0 Å + dtol + dpseud. A ‘tolerance distance’dtol is added to allow for the large deviations within thebundles of conformers that represent the NMR structurein the early NOAH/DIANA cycles. Here, dtol was linearlydecreased from 5.8 Å in the first cycle to 0.4 Å in cycle25. dpseud, where applicable, is the standard pseudo-atomcorrection (Wüthrich et al., 1983) used by DIANA (Gün-tert et al., 1991). In peak lists from 3D heteronuclear-resolved [1H,1H]-NOESY spectra, a check for expectedtransposed peaks can be used to discriminate betweencorrect and erroneous assignments. The expected positionof the transposed peak is determined from the knownchemical shifts, and the peak list is screened for peakssituated within ±0.03 ppm of this position in the protondimensions, and ±0.6 ppm in the 15N or 13C dimension. Ifno transposed peak is found, the assignment is discarded.The check for transposed peaks can only be performedfor pairs of protons that are attached to heavy atoms ofthe same type with known chemical shifts. At the outsetof each new cycle, all peaks with less than a user-definednumber of possible assignments, Npa, are included into a‘test assignment list’. Here, Npa was 2 for cycles 2 to 15, 3for cycles 16 to 19, and 4 for cycles 20 to 25. Until cycle 10the unambiguously assigned peaks are translated intodistance constraints of fixed length (5.0 Å, plus pseudo-atom correction where applicable). Afterwards, they arecalibrated using an automatic calibration procedure in-cluded in DIANA (see below). If several NOESY peak listsare assigned simultaneously, the automatic calibration isapplied to each peak list separately. The test assignmentsare always added with fixed distances of 5.0 Å plus pseu-do-atom correction, except in cycles 4, 8, 12, 16, 20 and 24when they are not used for the structure calculation.

In step (2) an ensemble of N+20 conformers is calcu-lated in cycle N, using the variable target function methodwith an error-tolerant target function (Mumenthaler andBraun, 1995). During the initial cycles the input constraintsinclude large errors, and a smaller number of conformersis sufficient to detect them. In cycles 16, 20 and 24 theREDAC strategy (Güntert and Wüthrich, 1991) is usedto obtain better structures. One to four REDAC cycleswere necessary, depending on the size and the fold of theprotein. The dihedral angle constraints produced by theREDAC procedure are used in cycles 17, 18, 19, 21, 22and 23 to calculate conformers which are subsequentlyminimized on the highest target level with the experimen-tal angle constraints.

In step (3) the 10 conformers with the lowest targetfunction values obtained after each cycle are analyzed.For each assignment the percentage of conformers inwhich the residual constraint violation exceeds a given

user-defined value is evaluated and the correspondingNOESY cross peaks are classified as follows (Mumen-thaler and Braun, 1995). Peaks with a single test assign-ment possibility are unambiguously assigned if the corre-sponding constraint is fulfilled in more than L1 percent ofthe conformers. Peaks with multiple assignment possibil-ities are assigned only if one assignment is satisfied in allconformers and the second-best assignment is violated inL2 or more percent of the conformers. Peaks that havebeen assigned in previous cycles can be reclassified if thecorresponding distance constraint is violated in L3 ormore percent of the conformers. Values of 50%, 50% and80% were used for the parameters L1, L2 and L3, and L3

was decreased to 60% in the last cycle.To provide the user with an indication of the reliability

of each individual peak assignment, NOAH calculates the‘reliability distance’ (RD) (Mumenthaler and Braun,1995), which measures the superiority of the actual as-signment over all alternative assignments. For this pur-pose, a virtual distance constraint of 5.0 Å (plus pseudo-atom correction where applicable) is given to each alter-native assignment, and the RD is determined as the mini-mal violation any of these constraints have in the ensem-ble of 10 conformers. Thus, a high RD value indicatesthat no other assignment is compatible with the currentstructure bundle, while RD values close to 0 Å indicatethat an alternative assignment could in principle be ful-filled.

Structure refinementThe final structure was obtained by a calculation using

up to five REDAC cycles with the standard DIANAtarget function. Subsequent restrained energy minimiza-tion using the AMBER all-atom force field (Cornell etal., 1995) was performed with the program OPAL (Lugin-bühl et al., 1996) on the 10 NOAH/DIANA conformerswith lowest target function values. The minimization wascarried out after surrounding the DIANA conformerswith a 6 Å thick shell of water molecules, and using thedielectric constant ε = 1 for the electrostatic interactions.The potential for violated distance constraints was pro-portional to the sixth power of the violation and scaledsuch that a violation of 0.1 Å corresponded to an energyof kT/2 at room temperature. For each conformer 2000steps of conjugate gradient minimization were performed.

Automatic NOE-distance calibrationThe present automatic calibration makes use of the

fact that the spatial distribution of hydrogen atoms indifferent globular proteins is closely similar, and of theassumption that the range of NOE-observable 1H–1Hdistances is comparable in the different NOESY spectraused. On this basis, it predicts that the average of the dis-tance constraints calculated from a fully assigned NOESYspectrum should be similar for all globular proteins.

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The NOE cross peaks are divided into three distinct

TABLE 1EXPERIMENTAL PEAK LISTS USED AS INPUT FOR NOAH/DIANA; THESE ARE FINAL PEAK LISTS OBTAINED AF-TER MULTIPLE CYCLES OF NOESY CROSS-PEAK ASSIGN-MENT AND STRUCTURE CALCULATION

Protein Residues Spectra useda Peakspicked

Er-2b 040 2D, H2O2D, D2O

09861221

Hirudin (1–51)c 051 2D, H2O2D, D2O

05510722

434(R10M) (1–63)d 063 2D, H2O 1282WmKTe 088 2D, H2O 1998DnaJ (2–108)f 107 3D, 15N, H2O

3D, 13C, H2O07612080

P14ag 135 3D, 15N, H2O3D, 13C, H2O2D, H2O2D, D2O

1457305519252001

a 2D stands for 2D [1H,1H]-NOESY; H2O and D2O indicate the sol-vent used; 3D stands for heteronuclear-resolved 3D [1H,1H]-NOESY,where 13C and 15N specify the heterospin used.

b Pheromone Er-2 from Euplotes raikovi (Ottiger et al., 1994).c N-terminal 51-residue fragment of hirudin from the leach Hirudo

medicinalis (Szyperski et al., 1992).d N-terminal 63-residue domain of the phage 434 repressor carrying

the mutation R10M (Pervushin et al., 1996).e Killer toxin from Williopsis mrakii (WmKT) (Antuch et al., 1996).f Fragment of residues 2–108 of the E. coli molecular chaperone DnaJ

(Pellecchia et al., 1996).g Pathogenesis-related protein P14a from tomato leaves (Fernández et

al., 1997).

TABLE 2EXTENT OF THE NOESY ASSIGNMENTS OF SIX PROTEINS ACHIEVED BY THE AUTOMATIC NOAH/DIANA PROCEDUREAND BY THE INTERACTIVE APPROACH USED IN THE ORIGINAL STRUCTURE DETERMINATION

Protein Assignments (%)a

Manualb NOAH/DIANAc Identicald Differente Inconsistentf

Er-2 72 74 66 0.8 5.3Hirudin (1–51) 99 93 91 1.1 0.5434(R10M) (1–63) 99 80 78 2.4 1.1WmKT 85 83 75 1.0 3.3DnaJ (2–108) 96 82 80 1.4 2.0P14a 90 78 74 1.0 5.1

a All data are given as the percentage of the total number of identified NOESY cross peaks.b Peaks assigned by the original interactive approach.c Peaks assigned by NOAH/DIANA.d Peaks with identical assignments by the interactive and automatic procedures.e Peaks assigned differently in the interactively and automatically assigned peak lists.f Peaks that are inconsistent with the final structure obtained by NOAH/DIANA, i.e., for which all possible assignments within the given chemical

shift tolerance range are violated by more than 1.0 Å in all conformers.

calibration classes. Backbone–backbone NOEs betweenall Hα and HN are in class (i), which also includes intra-residual, sequential and medium-range NOEs (Wüthrich,1986) where one of the protons is Hβ. Class (ii) includesall the remaining NOEs except those with methyl groups.Class (iii) are all NOEs involving methyl groups. Thecorresponding peak volumes, V, are calibrated into dis-

tance constraints, d, with the functions (i) d = (A/V)1/6, (ii)d = (B/V)1/4, and (iii) d = (C/V)1/4 (Güntert et al., 1991).The parameter A is estimated automatically by assumingthat the average distance limit from the calibration class(i) is 3.4 Å. B is then determined from the condition thatthe calibration curves (i) and (ii) must intersect at dmin =2.4 Å, i.e., B = A/d2

min. C is set to B/2.All distance constraints are confined to the range 2.4–

5.5 Å by setting outliers to the closest boundary of thisdistance interval.

Results

Comparison of protein structure determinations using auto-matically or interactively assigned NOESY peak lists

The NOAH/DIANA procedure was applied to theexperimental data that were previously used for NMRstructure determinations of the six proteins listed in Table1. For all these proteins very nearly complete sequence-specific 1H assignments for the backbone and the sidechains are available. The NOESY peak lists used here are‘final’ lists that had been obtained by multiple cycles ofinteractive peak assignment and 3D structure calculation(Güntert et al., 1993). For the tests of the NOAH/DIANAprocedure all assignments in these NOESY peak lists weredeleted, and the resulting unassigned peak lists were usedas input for the automated structure determination. Thelists with the 1H, 15N and 13C chemical shifts were used aspublished, or as deposited in a data bank. Since corre-sponding chemical shifts may vary in different NOESYspectra of the same protein due to isotope shifts or slightdifferences in the experimental conditions, an ‘adapted’chemical shift list was prepared for each different NOESYspectrum, which specifies the actual shift value within anallowance range of, usually, ±0.01–0.02 ppm. For Er-2,DnaJ (2–108) and P14a, such adapted chemical shift listswere derived from the peak lists by averaging the posi-

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tions of all peaks assigned to the same proton. For the

a

b

c

Fig. 2. Stereoviews of NMR conformers obtained using either interactive NOESY cross-peak assignments (yellow) or automatic assignments withNOAH/DIANA (cyan): (a) Er-2; (b) hirudin (1–51); (c) 434(R10M) (1–63). The figure was prepared with the program MOLMOL (Koradi et al., 1996).

other three proteins, adapted chemical shift lists for allspectra used (Table 1) were available from the previous

structure determinations. Stereospecific assignments anddihedral angle constraints obtained in the earlier structuredeterminations were included in the NOAH/DIANA

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calculation. Additionally, distance constraints for disulfide

TABLE 3CONFORMATIONAL CONSTRAINTS USED IN THE FINAL STRUCTURE CALCULATION BASED EITHER ON INTERACTIVENOESY ASSIGNMENTS OR ON NOAH/DIANA

Protein Interactive assignment NOAH/DIANA

ir/seq/mr/lra Nconb ir/seq/mr/lra Ncon

b

Er-2 141/157/169/145 0612 114/157/174/133 0578Hirudin (1–51) 158/159/56/216 0589 127/166/59/192 0544434(R10M) (1–63) 203/183/213/147 0746 206/182/204/124 0716WmKT 317/285/99/352 1053 322/306/122/388 1138DnaJ (2–76) 310/158/121/93 0682 229/169/107/72 0577P14a 414/332/292/672 1710 308/337/282/524 1451

a Number of intraresidual (ir), sequential (seq), medium-range (mr) and long-range (lr) constraints.b Total number of conformational constraints used in the structure determination.

TABLE 4PARAMETERS CHARACTERIZING THE QUALITY OF CORRESPONDING STRUCTURE DETERMINATIONS BASED EITHERON INTERACTIVE NOESY ASSIGNMENTS OR ON NOAH/DIANA

Protein Interactive assignment NOAH/DIANA Diff.<rmsd>a

Rmsd (Å)b TF (Å2)c Rmsd (Å)d TF (Å2)e

Er-2 0.3 0.4–0.8 0.4 0.2–0.3 0.6Hirudin (1–51) 0.4 0.1–0.2 0.5 0.1–0.2 0.8434(R10M) (1–63) 0.6 0.3–0.7 0.6 0.7–0.8 0.9WmKT 0.7 1.9–4.3 0.6 1.0–1.5 0.5DnaJ (2–108) 1.0 0.5–1.3 1.7 0.1–0.5 1.0P14a 0.8 1.4–4.0 1.2 5.1–6.8 1.5

a Rmsd between mean structures obtained with the interactive and automatic assignments, <rmsd>int − <rmsd>NOAH/DIANA.b Average rmsd values relative to the mean for the backbone heavy atoms in groups of 20 conformers used to describe the NMR structure. The

following residues were used to calculate the rmsd values: 3–37 for Er-2, 3–30 and 37–48 for hirudin (1–51), 1–63 for 434(R10M) (1–63), 3–39and 47–87 for WmKT, 6–57 for DnaJ, and 1–135 for P14a.

c Final DIANA target function values for the 20 best conformers from the references given in Table 1.d Rmsd values for the 10 best energy-minimized conformers obtained with NOAH/DIANA calculated as described in footnote b.e Final DIANA target function values of the 10 best conformers from NOAH/DIANA.

bonds (Williamson et al., 1985) were used in all structurecalculations. For the 3D peak lists of P14a the high qual-ity of the spectra and the resulting good match betweenpeak positions and chemical shifts allowed one to lowerthe tolerance range, ∆tol, from ±0.02 ppm to ±0.015 ppmin the proton dimensions.

All DIANA computations were performed on Cray J-90 computers using six processors simultaneously for thestructure calculations. The total CPU time needed for afull NOAH/DIANA calculation ranged from 3 h for Er-2to about 60 h for P14a.

Table 2 contains the results of the automatic assign-ment procedure for the experimental peak lists of the sixproteins. On average, NOAH/DIANA assigned about82% of all peaks, which is lower than the average ofabout 90% assigned peaks by the interactive approach,with the most significant differences in cases where themanually established peak lists were nearly completelyassigned. The percentage of peaks that were assigned tothe same proton pair by the interactive and the automaticprocedure was on average 77%. About 5% of the peakspicked in the NOESY spectra were only assigned by

NOAH/DIANA, and 13% only by the interactive ap-proach. On average, different assignments by the twoapproaches were obtained for less than 2% of the peaks.

Table 3 provides an analysis of the meaningful confor-mational constraints used in the final structure calculationof both approaches. As expected from the lower percen-tage of assigned peaks, NOAH/DIANA usually produceda smaller total number of distance constraints, but thedistribution among intraresidual, short-range, medium-range and long-range constraints does not differ signifi-cantly between the two approaches.

The final structures obtained by NOAH/DIANA areanalyzed and compared with those obtained from interac-tive assignment in Table 4. Residual constraint violationsin the automatically determined structures were small, asevidenced by the fact that the DIANA target functionvalues are comparable and sometimes even lower thanthose from the interactive procedure. The higher value forP14a is largely due to the fact that, compared to theinteractive approach, the calculation schedule had to beshortened by a factor of 2 in the NOAH/DIANA calcula-tion to avoid excessive computation times. Restrainedenergy minimization with OPAL (Luginbühl et al., 1996)

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removed nearly all the remaining constraint violations.

Fig. 3. Ramachandran plot of the 10 energy-minimized NOAH/DIANAstructures of 434(R10M) (1–63). (φ,ψ)-conformations of all residuesare marked with white symbols (triangles are glycines, squares areother residue types). The figure was prepared with the programPROCHECK-NMR (Laskowski et al., 1996).

a

b

Fig. 4. Spectral region (ω1 = 2.4–3.1 ppm, ω2 = 7.6–8.3 ppm) from the2D [1H,1H]-NOESY spectrum of WmKT, with black dots identifyingpicked peaks. (a) Final peak list from the previous interactive struc-ture determination (Antuch et al., 1996). (b) New peak list pickedmanually without reference to the 3D WmKT structure.

No distance constraint violation larger than 0.12 Å andno angle constraint violation larger than 0.31° was de-tected in any of the energy-minimized conformers of allsix proteins.

The average backbone rmsd values of the energy-mini-mized NOAH/DIANA structures to their mean structureare 0.4–1.7 Å (Table 4). In four of the proteins studied,this is higher than the corresponding rmsd values for thefinal conformers from the interactive assignment. Super-positions of the conformers obtained from NOAH/DIANAwith those from interactive NOESY assignments (Fig. 2)visualize the good match between the two results.

The program PROCHECK-NMR v. 3.4 (Laskowski etal., 1996) was used to analyze the groups of energy-mini-mized NOAH/DIANA conformers. The average of the‘equivalent resolution’ parameters for main-chain hydro-gen bond energies, percentage of residues in the mostfavored regions of the (φ,ψ)-space, pooled standard devi-ations of χ1 from the three staggered rotamer positionsand standard deviations of χ2 angles that are in transposition ranged from 1.7 to 2.3 Å for the six proteins. Asan example, Fig. 3 shows the Ramachandran plot of the434(R10M) conformer group.

Calculation of the structure of WmKT from a de novopicked NOESY peak list

The peak lists in Table 1 are those used for the finalcalculation of the NMR structures. They are refineddescendants of initial lists, which were altered by refer-

ence to the results of early structure calculations (Güntertet al., 1993).

To investigate possible bias that might be introducedthrough the use of these refined peak lists, and to test theperformance of NOAH/DIANA when using an initial,possibly automatically picked peak list, we repicked theNOESY spectrum of WmKT. Neither the previous peaklists nor the proton chemical shift tables were used toguide this peak picking, and peaks were interactivelypicked at intensity maxima in the 2D NOESY spectrumrecorded in H2O. Especially in regions of strong peakoverlap, major differences to the refined peak list wereapparent. For example, we found only 15 peak positionsin the spectral region of the lower part of Fig. 4b, where-as the refined peak list contained 24 peak positions (Fig.

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4a). (In the refined peak list some of these peak identifi-

Fig. 5. Stereoview of a superposition for minimal rmsd of 10 conformers obtained with manual NOESY assignment (yellow) with 10 conformerscalculated by NOAH/DIANA (cyan) using a peak list that was manually picked without consideration of other peak lists or the known protonchemical shifts (see text).

cations were based on a TOCSY peak list that was usedas a starting point for the picking of the NOESY spec-trum; here, only NOESY data were considered.)

The 1746 peaks contained in the newly picked peak listwere integrated automatically by the in-house softwareSPSCAN (unpublished). The resulting list was comparedwith the previous final list, and 1424 peaks were found tobe common to both lists within a distance of ±0.01 ppm.Five hundred and seventy-four peaks, mainly located inoverlap regions, were present only in the refined list, and322 peaks turned out to be mostly noise peaks or veryweak NOEs. In spite of these differences, NOAH/DIANAyielded similar structures as the calculation based on therefined peak list (Fig. 5). Overall, 1328 peaks (76% of allentries in the peak list) were assigned. With an averagebackbone rmsd of 0.6 Å to the mean structure for resi-dues 4–39 and 47–87, the structures obtained from thisinput with NOAH/DIANA were nearly as well defined asthose calculated from the refined peak list. The rmsdbetween the mean structures obtained with the de novopicked NOESY peak list as input for NOAH/DIANAand with the interactive assignment approach was 1.0 Å.

Discussion and Conclusions

A rationale for the functioning of NOAH/DIANAIn the initial assignment cycle (Fig. 1) all peaks with

two assignment possibilities are included in the structurecalculation. In view of the large number of erroneousconformational constraints that are likely to be includedat this stage, it seems nontrivial that the NOAH/DIANAapproach ultimately converges to the correct structure.The explanation is related to the fact that while minimiz-ing its target function, DIANA attempts to satisfy amaximum number of conformational constraints simulta-

neously. The correctly assigned constraints form a largesubset of self-consistent constraints, whereas, in contrast,the erroneously assigned constraints are randomly distrib-uted in space, generally contradicting each other. As aconsequence, erroneously assigned constraints may distortthe structure but will not lead to a distinctly differentprotein fold. Thereby, one must keep in mind that theelimination of erroneously assigned constraints throughcontradiction with correct constraints will in general beless efficient in regions of low NOE density, such as chainends, surface loops or the periphery of long side chains,than in the well-defined protein core.

Another peculiarity of the randomly distributed erron-eously assigned constraints is that they are more likely tobe long-range than short-range or intraresidual. Thiscontrasts with the overall constraint distribution of acorrectly assigned NOESY spectrum, where more than50% of all NOESY cross peaks manifest intraresidual orshort-range NOEs (Wüthrich, 1986). Short-range con-straints are generally more uniformly satisfied in all con-formers because of their inclusion at an early stage of thevariable target function method (Braun and Go, 1985;Güntert et al., 1991).

Impact of the choice of tolerance ranges allowing for vari-able peak positions and chemical shifts

Probably the most important parameter to be definedin applications of NOAH/DIANA is the tolerance range,∆tol, that enables one to obtain assignments in spite of thefact that there are inevitably small errors in the determi-nation of chemical shifts and peak positions within aspectrum. Here, we use a simple mathematical model forthe treatment of 2D [1H,1H]-NOESY spectra to gaindeeper insight into the consequences of different choicesof ∆tol. N is the total number of hydrogen atoms in theprotein, Npeaks is the total number of peaks picked in the

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spectrum, and ∆ω is the chemical shift range within which

a

b

Fig. 6. The bars represent histograms of N(1) and N(2) versus theselected chemical shift tolerance range, ∆tol, allowed between peakposition and chemical shift of the peaks in a simulated NOESY peaklist for the protein WmKT. (a) Peaks that have one possible assign-ment, N(1). (b) Peaks with two possible assignments, N(2). The NOESYpeak list for WmKT was simulated by postulating that there is a crosspeak between any pair of protons that are closer than 4.0 Å in thebest NMR conformer. To avoid artifacts when using very small valuesfor ∆tol, the peak list had to be simulated so as to provide peak posi-tions that perfectly match the proton shifts. No structural informationhas been used to resolve ambiguities. In both (a) and (b) the curvedlines represent the corresponding values predicted by Eqs. 1–3 withthe parameters Npeaks = 1986, N = 457 and ∆ω = 9.0 ppm.

the vast majority of proton chemical shifts are located.Assuming that the proton shifts are distributed evenlyover the region ∆ω, the probability p of finding a protonshift in an interval [ω−∆tol,ω+∆tol] about any selectedposition ω is

p tol= 21

∆∆ω ( )

The number of peaks with only one possible assignment,N(1), i.e., peaks where for each dimension all N protonshifts except one are outside the tolerance range from thepeak position, is then

N(1) = Npeaks (1 − p)2N−2 ≈ Npeaks e−2Np (2)

Equation 2 predicts that the percentage of a priori unam-biguous peaks decreases exponentially with both increas-ing size of the protein and increasing value of the toler-ance range.

Peaks with two assignment possibilities are also includedin the NOAH/DIANA calculations from the beginning.Their number, N(2), is

N(2) = Npeaks 2p(N − 1)(1 − p)2N−3 ≈ 2Np N(1) (3)

N(2) vanishes for very small ∆tol values, but increases lin-early as a function of N(1) with a coefficient that is pro-portional to the protein size and the ∆tol value. In ourcalculations, with ∆tol = 0.01 ppm, N(2) was usually 2–3times larger than N(1) (Fig. 6). Figure 6 further shows thatEqs. 1–3 provide a good description of the situation inthe protein WmKT.

In order to assign the majority of the NOESY crosspeaks, the initial ambiguity of peak assignments based onchemical shifts must be resolved by reference to the pre-liminary protein structure, and the ambiguity is complete-ly resolved if all but one of the potential assignmentscorrespond to pairs of hydrogen atoms that are spatiallyseparated by more than a maximal distance, dmax, forwhich a NOE may be observed. Assuming that the hydro-gen atoms are evenly distributed within a sphere of radiusR that represents the protein, the probability that tworandomly selected hydrogen atoms are closer to eachother than dmax, q, is approximately given by the ratiobetween the volumes of two spheres with radii dmax andR, respectively:

qd=

max

R

3

4( )

WmKT is a nearly spherical protein with a radius ofabout 15 Å. Using dmax = 5.0 Å, q becomes approximately4%, indicating that only 96% of the peaks with two as-signment possibilities can be uniquely assigned by refer-

ence to the protein structure. The total number of unique-ly assigned peaks, Nunique, can optimally be increased to

Nunique = N(1) + (1 − q)N(2) + (1 − q)2N(3) + ... (5)

Even by reference to a perfectly refined structure, it istherefore impossible, on fundamental grounds, to resolveall assignment ambiguities, since q will always be largerthan 0. In particular for small structures, where R ap-proaches dmax, the decrease in ambiguity achieved byreference to the molecular structure becomes less import-ant. Here, separate treatment of peaks with differentintensities is helpful, since peaks with larger volumes willhave smaller corresponding dmax values.

For peak lists obtained from 13C- or 15N-resolved 3D[1H,1H]-NOESY spectra, two additional elements play animportant role. First, ambiguity in the proton dimensioncorrelated to the heterospin is usually resolved, so thatEq. 2 adopts the form

360

a

b

c

Fig. 7. Three spectral regions from the 2D NOESY spectrum ofWmKT. Lines represent the proton shifts to which a peak was as-signed interactively (dashed lines), or automatically with NOAH/DIANA (solid lines). (a) Both assignments are fully compatible withthe final conformer calculated with NOAH/DIANA and lie within thetolerance range of ±0.01 ppm from the peak position. (b) Both assign-ments are compatible with the final conformers from NOAH/DIANA,but along one dimension (ω2) the assignment from the interactiveapproach lies outside the tolerance range of ±0.01 ppm about thepicked peak position. (c) The interactive assignment is violated in theconformers from NOAH/DIANA, and along one dimension (ω1) theassignment from the interactive approach lies outside the tolerancerange of ±0.01 ppm about the picked peak position. The coincidingsolid and broken lines in the ω1 dimension of (a) and in the ω2 dimen-sion of (c) indicate the same proton shift.

N(1) ≈ Npeaks e−Np (6)

This effect is equivalent to reducing the influence of thesize (and therefore N) of the protein by a factor of 2.Second, supplementary analysis of transposed peaks, asdescribed in the Methods section, can significantly reducethe number of possible peak assignments. However, thisadvantage of the heteronuclear experiments cannot befully exploited in practice, since the tolerance ranges mustbe increased due to the lower digital resolution in 3DNMR experiments.

Analysis of the differences between the assignments ob-tained interactively and with NOAH/DIANA

For peaks that were assigned differently by the interac-tive approach and the automatic NOAH/DIANA pro-cedure, two parameters have been introduced that can beevaluated from the final conformers determined withNOAH/DIANA: Vmin, the minimal violation of the inter-active assignment in any of the conformers; and the RDof the NOAH/DIANA assignment (Mumenthaler andBraun, 1995). Peaks with different assignments can thusbe grouped into three categories. (a) Both assignments aresatisfied in the conformers from NOAH/DIANA (RD =0.0 Å; Vmin = 0.0 Å). Assuming that the conformers arecorrect solutions, such peaks must be superpositions oftwo NOE signals, so that both assignments are correct.(b) The assignment from NOAH/DIANA is supported byRD > 0.0 Å, but the interactive assignment is also satisfied(Vmin = 0.0 Å). Here, the interactive assignment was neverconsidered by NOAH, because one of its proton shifts istoo far away from the cross-peak position. Unless eitherthe proton shifts were not properly determined or thetolerance range ∆tol was too small, the NOAH assignmentseems more appropriate in such cases. (c) The assignmentfrom the interactive approach is violated in the conformerscalculated with NOAH/DIANA (RD ≥ 0.0 Å; Vmin > 0.0Å). These are the interesting cases, since they reflect asignificant discrepancy between the two assigned peaklists and the groups of conformers calculated from them.Figure 7 gives one example for each of these three possi-bilities from the 2D NOESY spectrum of WmKT. In Fig.7a, the shoulder on the right indicates that the peak isprobably a superposition of two NOE signals, whichcorrespond to the two different assignments and are bothsatisfied in the structure calculated using NOAH/DIANA.Figure 7b is a similar case, although the peak centerclearly corresponds to the assignment given by NOAH/DIANA. The apparent small error in the interactive ω2

chemical shift determination has no obvious consequencessince both NOEs are compatible with the calculated struc-ture. Finally, Fig. 7c shows a peak that was assignedwrongly in the manual peak list, since the peak is not lo-cated at the intersection of the chemical shifts of the as-signed protons. This case illustrates the use of NOAH/

361

DIANA to check and correct manually derived assign-ments.

Among the 168 differently assigned peaks of all spectrafrom Table 1 situation (a) is by far the most commonone, with 68% of all differently assigned peaks after as-signment by NOAH/DIANA or by the interactive pro-cedure, respectively, being characterized by RD = 0.0 Åand Vmin = 0.0 Å. Only 18% of the distance constraintsderived from the differently assigned peaks are violated inthe structures calculated by NOAH/DIANA. This indi-cates that the generally observed differences in the extentof 1–2% of the total number of assignments between theinteractively and automatically assigned peak lists are forthe most part insignificant because they have no bearing onthe 3D protein structure. Overall, the RD performs ratherwell in identifying ‘problematic’ assignments: 76% of thedifferently assigned peaks have an RD value of 0.0 Å.

Influence of incomplete sequence-specific assignmentAn important parameter for assessing proper function-

ing of NOAH/DIANA is the number of NOESY crosspeaks that are inconsistent with the final protein struc-ture, i.e., peaks for which no possible assignment withinthe given chemical shift tolerance range is compatiblewith the group of conformers used to represent the NMRstructure (Table 2). In practice, the sequence-specificassignments and hence the chemical shift lists tend to beincomplete, and peaks originating from the unassignednuclei cannot be explained correctly by NOAH/DIANA.Similarly, noise peaks included after de novo peak pickingcannot be assigned, so that a large number of inconsistentpeaks is not necessarily a reliable criterion for evaluationof a structure obtained from NOAH/DIANA.

To test the impact of incomplete or partly erroneousinput, we repeated the calculation for WmKT using dif-ferent chemical shift lists. First, we randomly deleted 10%of the proton shifts, which implies that about 20% of thecross peaks cannot be assigned. As a consequence, only66% of the peaks were assigned by NOAH/DIANA,which is 17% less than with the complete list of chemicalshifts. When compared with the NOAH/DIANA calcula-tion using the complete input for WmKT (Table 2), thepercentage of different assignments relative to the interac-tive approach stayed at 1.0%, and the percentage of in-consistent peaks increased from 3.3% to 12.1%. The num-ber of correct assignments was insufficient for obtainingconformers of good quality, since the target functionvalues of the final conformers were around 17 Å2. In asecond test, we displaced the same 10% of the protonchemical shifts by 0.015 ppm. In principle, this shouldhave the same consequences as removal to these shifts, ex-cept that the displaced chemical shifts lead to additionalassignment possibilities for neighboring peaks. Again,around 66% of the peaks were assigned by NOAH/DIANA, but the percentage of different assignments

relative to the interactive approach was 4.5% and thus 4times higher than after elimination of the peaks from thelist. When the tolerance range was increased from thestandard ±0.01 ppm to ±0.02 ppm, 73% of the peaks wereassigned by NOAH/DIANA, with 2.9% of the assign-ments being different from those of the interactive ap-proach.

In practice, missing chemical shifts are often fromperipheral side-chain protons, which are typically involvedin only few NOEs. Therefore, the problems caused byrandom deletion of 1/10th of the chemical shifts from anearly complete list may be more severe than those in atypical experiment where the same fraction of protons hasremained unassigned. Nonetheless, on the basis of theabove tests, in particular the observation that incompletechemical shift lists tend to lead to unacceptable structures,the use of NOAH/DIANA for proteins with incomplete1H chemical shift lists cannot presently be recommended.The rationale for the observation that absence of chemi-cal shifts for significant fractions of all protons degradesthe performance of the NOAH/DIANA procedure is thatincomplete shift lists exclude the correct assignments formany NOESY peaks. NOAH/DIANA then tends toincorrectly assign such peaks to other protons with chemi-cal shifts in the same range as the unassigned protons,which can lead to distorted structures.

Stereospecific assignmentIn the NOAH/DIANA calculations presented in this

paper, we included the stereospecific assignments and thedihedral angle constraints from the earlier interactive struc-ture determinations, which used the programs HABAS(Güntert et al., 1989) and GLOMSA (Güntert et al.,1991). This enabled a direct comparison of the resultingconformers with the interactively obtained ones withoutbias from other factors than the NOESY assignments,although stereospecific assignment by the NOAH/DIANAprocedure has not yet been implemented.

OutlookThe impressive performance, when using an input of

high-quality experimental data, of the combination ofself-correcting distance geometry and structure-basedspectral filters (Güntert et al., 1993; Mumenthaler andBraun, 1995) implemented in NOAH/DIANA provides aplatform for both continued methods development andpractical applications. (i) The tests conducted in thispaper show that NOAH/DIANA is remarkably robustwith respect to imperfect NOE peak lists and can yieldacceptable structure calculations for incomplete NOEinput. This is encouraging for future work where struc-ture calculations might start with automatically picked,incomplete NOESY peak lists, which would then be im-proved by reference to the preliminary structures (Güntertet al., 1993). In contrast, for the reasons outlined above,

362

NOAH/DIANA performs rather poorly with incomplete1H chemical shift lists, such as lists with missing assign-ments for the aromatic rings or other amino acid sidechains for which complete assignments are difficult toobtain. (ii) For proteins where the sequence-specific as-signment is nearly complete and peak lists with few arti-facts are available, the method is ready for practical usein the determination of the 3D structure; a structuredetermination of a mutant form of crambin has beenreported (Xu et al., 1997) and additional automated struc-ture determinations are in progress in our laboratories.

In spite of the progress made with the automaticNOAH/DIANA method, spectroscopists working inter-actively with original NOESY spectra still have severaladvantages, since they can exclude assignment possibilitiesby line-shape considerations and (in good-quality spectraand for well-separated peaks) intuitively use smaller toler-ance ranges between peak positions and chemical shifts.This will in general contribute to a more complete NOESYassignment by the interactive method than by the auto-mated approach. However, as long as the sequence-speci-fic assignment is nearly complete and artifacts are scarcein the NOESY peak list, it appears that this does notcause major differences between the structures basedeither on interactive or on NOAH/DIANA assignment ofthe NOESY spectra. Nonetheless, further progress withautomated procedures will foreseeably depend on tighterinteraction with the original spectral data. Note also thatNOAH/DIANA cannot replace the manual analysis ofNOESY spectra for obtaining sequence-specific resonanceassignments, for example, for the assignment of aromaticrings (Wüthrich, 1986).

For larger proteins the computing power is also acritical factor. The REDAC strategy employed here forthe structure calculation is time-consuming for large andcomplicated folds such as the one of P14a, since goodconvergence is only achieved with multiple REDAC cycles.New structure calculation methods, such as moleculardynamics in torsion angle space (Güntert et al., 1996;Stein et al., 1997), will be needed to enable practicalapplications of the presently outlined principles for auto-mated NMR structure determination to larger proteins.

Acknowledgements

The use of the computing facilities of the ETHZ-CrayJ-90 SuperCluster Cooperation and of the NEC SX-4supercomputer of the Centro Svizzero di Calcolo Scien-tifico is gratefully acknowledged. Financial support wasobtained from the ETH Zürich, the Schweizerischer Na-tionalfonds (Project 31.32033.91, K.W.) and the U.S.National Science Foundation (Project BIR-9632326, W.B.).We thank M. Salzmann for reports on the use of NOAH/DIANA with his protein structure determinations, andMrs. E. Ulrich for the careful processing of the manuscript.

References

Antuch, W., Güntert, P. and Wüthrich, K. (1996) Nat. Struct. Biol.,3, 662–665.

Bartels, Ch., Billeter, M., Güntert, P. and Wüthrich, K. (1996) J.Biomol. NMR, 7, 207–213.

Bartels, Ch., Güntert, P., Billeter, M. and Wüthrich, K. (1997) J.Comput. Chem., 18, 139–149.

Braun, W. and Go, N. (1985) J. Mol. Biol., 186, 611–626.Cornell, W.D., Cieplak, P., Bayly, C.I., Gould, I.R., Merz Jr., K.M.,

Ferguson, D.M., Spellmeyer, D.C., Fox, T., Caldwell, J.W. andKollman, P.A. (1995) J. Am. Chem. Soc., 117, 5179–5197.

Donoghue, S.I., King, G.F. and Nilges, M. (1996) J. Biomol. NMR,8, 193–206.

Fernández, C., Szyperski, T., Bruyère, T., Ramage, P., Mössinger, E.and Wüthrich, K. (1997) J. Mol. Biol., 266, 576–593.

Güntert, P., Braun, W., Billeter, M. and Wüthrich, K. (1989) J. Am.Chem. Soc., 111, 3997–4004.

Güntert, P., Braun, W. and Wüthrich, K. (1991) J. Mol. Biol., 217,517–530.

Güntert, P. and Wüthrich, K. (1991) J. Biomol. NMR, 1, 447–456.Güntert, P., Berndt, K.D. and Wüthrich, K. (1993) J. Biomol. NMR,

3, 601–606.Güntert, P., Mumenthaler, Ch. and Wüthrich, K. (1996) Abstracts

XVIIth International Conference on Magnetic Resonance in Biologi-cal Systems, Keystone, CO, U.S.A., August 18–23, p. 175.

Hare, B.J. and Prestegard, J.H. (1994) J. Biomol. NMR, 4, 35–46.Koradi, R., Billeter, M. and Wüthrich, K. (1996) J. Mol. Graph., 14,

51–55.Kraulis, P.J. (1994) J. Mol. Biol., 243, 696–718.Laskowski, R.A., Rullmann, J.A.C., MacArthur, M.W., Kaptein, R.

and Thornton, J.M. (1996) J. Biomol. NMR, 8, 477–486.Luginbühl, P., Güntert, G., Billeter, M. and Wüthrich, K. (1996) J.

Biomol. NMR, 8, 136–146.Meadows, R.P., Olejniczak, E.T. and Fesik, S.W. (1994) J. Biomol.

NMR, 4, 79–96.Morelle, N., Brutscher, B., Simorre, J.-P. and Marion, D. (1995) J.

Biomol. NMR, 5, 154–160.Mumenthaler, Ch. and Braun, W. (1995) J. Mol. Biol., 254, 465–480.Nilges, M. (1993) Proteins, 17, 297–309.Nilges, M. (1995) J. Mol. Biol., 245, 645–660.Olson Jr., J.B. and Markley, J.L. (1994) J. Biomol. NMR, 4, 385–410.Oshiro, C.M. and Kuntz, I.D. (1993) Biopolymers, 33, 107–115.Ottiger, M., Szyperski, T., Luginbühl, P., Ortenzi, C., Luporini, P.,

Bradshaw, R.A. and Wüthrich, K. (1994) Protein Sci., 3, 1515–1526.Pellecchia, M., Szyperski, T., Wall, D., Georgopoulos, C. and Wüth-

rich, K. (1996) J. Mol. Biol., 260, 236–250.Pervushin, K., Billeter, M., Siegal, G. and Wüthrich, K. (1996) J.

Mol. Biol., 264, 1002–1012.Stein, E.G., Rice, L.M. and Brünger, A.T. (1997) J. Magn. Reson.,

124, 154–164.Szyperski, T., Güntert, P., Stone, S.R. and Wüthrich, K. (1992) J.

Mol. Biol., 228, 1193–1205.Williamson, M.P., Havel, T.F. and Wüthrich, K. (1985) J. Mol. Biol.,

182, 295–315.Wüthrich, K., Billeter, M. and Braun, W. (1983) J. Mol. Biol., 169,

949–961.Wüthrich, K. (1986) NMR of Proteins and Nucleic Acids, Wiley, New

York, NY, U.S.A.Xu, Y., Wu, J., Gorenstein, D. and Braun, W. (1997) Abstracts 38th

Experimental Nuclear Magnetic Resonance Conference, Orlando,FL, U.S.A., March 23–27.

Zimmermann, D., Kulikowski, C., Wang, L., Lyons, B. and Monte-lione, G.T. (1994) J. Biomol. NMR, 4, 241–256.