Structure Determination

Speeding Up Biomolecular NMR Spectroscopy**Bernd Simon and Michael Sattler*

Keywords:GFT NMR spectroscopy · multidimensional NMRspectroscopy · proteins · structure determination

NMR spectroscopy is a well establish-ed method for the characterization ofthree-dimensional structures, dynamics,and molecular interactions of biomacro-molecules. Today about 20% of thestructures deposited in the Protein DataBank (http://www.rcsb.org/pdb) are de-termined by NMR spectroscopy, andinternational structural genomics initia-tives rely on both X-ray crystallographyand NMR spectroscopy for large-scaleprotein structure determination.[1] Alimitation for high-throughput NMRspectroscopy is the long time needed torecord a set of multidimensional NMRexperiments for the structure determi-nation. In the past, long measurementtimes were required to improve thesignal-to-noise ratio in NMR spectra,and to obtain sufficient spectral resolu-tion in indirectly detected dimensions ofmultidimensional NMR data.

Continuous improvements in NMRhardware, for example, the introductionof highest magnetic-field strengths andcryogenic probes, have dramatically in-creased the sensitivity of NMR spectro-scopy. Therefore, experimental timescould be significantly shortened if sam-pling of indirect dimensions in multi-dimensional NMR experiments was op-timized. Now, Kim and Szyperski reporta general scheme for the acquisition ofNMR spectra which involves reducingthe dimensionality of multidimensionalNMR experiments.[2] The method,

called GFTNMR, greatly reduces meas-urement time without compromisingspectral resolution and will be applica-ble where data acquisition is not limitedby sensitivity but rather resolution.

Multidimensional NMRSpectroscopy

NMR structure determination in-volves two main parts: The first stepcomprises sequential assignment of allchemical shifts, while for the second stepNMR spectra are recorded to derivestructural information from nuclearOverhauser effects (NOEs), scalar cou-plings, and residual dipolar couplings.[3,4]

Chemical shift and NOE assignmentsare hampered by spectral overlap owingto the growing number of NMR reso-nance signals associated with increasingmolecular weight. About 15 years ago,the introduction of efficient isotopelabeling schemes for the preparation ofuniformly 13C and 15N labeled proteinsallowed the use of heteronuclear corre-lation spectroscopy to resolve signaloverlap in the 1H NMR spectra.[5] Typ-ically, magnetization of a proton spin I istransferred to a directly bound hetero-nucleus S (13C or 15N) through large one-bond J couplings. In the simplest case,this yields a two-dimensional (2D)NMR spectrum[6] which correlates pro-ton (1H) and heteronuclear (13C, 15N)chemical shifts. Since the introduction ofmultidimensional, that is, three-[7–9] orfour-dimensional[10] experiments, a greatvariety of NMR pulse sequences hasbeen developed.[11] These are used toobtain correlations between all 1H, 13C,and 15N signals of a protein, based onone-bond J couplings.[12]

A 2D I,S correlation experimentuses a sequence of radio-frequency

pulses and delays to transfer magnet-ization between spins S and I. Chemicalshifts of the S spins are recorded in anindirect (digitized) time domain t1 bystepwise incrementing a delay duringwhich the chemical shift evolution of theS spins occurs. This approach leads to amodulation of the NMR signal with theS spin frequencies during t1. After mag-netization transfer, the chemical shifts ofthe I spins are directly observed duringt2. Fourier transformation of both timedimensions yields the chemical shifts ofthe S and I spins in a 2DNMR spectrum.

This concept is easily extended tomore than two dimensions, by introduc-ing additional indirect time domains.[7–9]

For example, a three-dimensional (3D)I,S,T correlation experiment may in-volve magnetization transfer and chem-ical shift evolution for three spins I, S,and T (Figure 1a). For sensitivity rea-sons, excitation and detection is usuallyperformed on proton spins.[6] With theintroduction of additional indirect timedomains, the total duration of an NMRexperiment increases dramatically, sincefor the m time points in the indirectdimension of an N-dimensional (ND)experiment m(N�1)D spectra have tobe acquired. The total experimentaltime is determined by the number oftime points (m) sampled in the indirectdimensions, the number of scans (NS)averaged in the directly detected dimen-sion, and the duration of each scan,typically about one second. Thus, as-suming NS= 1 and 60 time points perindirect dimension the minimum exper-imental time is 1 min (60 A 1 s) for a 2D,1 h (60 A 60A 1 s) for a 3D, 2.5 days for a4D, and almost 0.5 year for a 5Dspectrum. Even with these estimateswhich reflect the absolute lower limitwith respect to resolution, 5D experi-ments are not practical, and only spectra

[*] Dr. B. Simon, Dr. M. SattlerEuropean Molecular Biology LaboratoryMeyerhofstrasse 1, 69117 Heidelberg(Germany)Fax: (+49)6221-387-306E-mail: sattler@embl.de

[**] We thank Christian Griesinger for stimu-lating discussions and critical reading ofthe manuscript.

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782 � 2004 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim DOI: 10.1002/anie.200301680 Angew. Chem. Int. Ed. 2004, 43, 782 –786

with up to four dimensions are routinelyused.

Apart from the resolution require-ments, sensitivity considerations alsodetermine the minimum experimentaltime. Usually, a given NMR pulse se-quence is averaged over NS scans. Thesignals appear in allNS repetitions at thesame position, thus yieldingNS times thepeak intensity of each scan, whereas therandom noise only averages with squareroot of the number of scans. Therefore,the signal-to-noise ratio increases withffiffiffiffiffiffiNS

p.

Reduced Dimensionality NMRSpectroscopy

Until recently, poor signal-to-noisemade it necessary to record a typical 3Dexperiment for 2–3 days. Therefore, ex-perimental times were determined bythe required signal-to-noise (sensitivitylimited), which at the same time pro-vided sufficient sampling of indirecttime dimensions. Owing to dramaticimprovements in NMR hardware inrecent years, the intrinsic signal-to-noiseratio has increased by a factor 3–5, so

that experimental times can be reduced9–25-fold to achieve the same signal-to-noise ratio. Based on signal-to-noiseconsiderations, 3D experiments couldthus be recorded in less than a day, butthe requirement to obtain sufficientresolution in indirect dimensions stillnecessitates longer measurement times,that is, these experiments are samplinglimited. Amongst various strategies tooptimize sampling of indirect time do-mains, such as nonlinear time domainsampling[13,14] or simultaneous acquisi-tion,[15–17] reduced dimensionality NMRhad already been proposed 10 yearsago.[18,19]

Following the principle of accordionspectroscopy,[6] in reduced dimensional-ity (RD) experiments the evolutiontimes of two or more[2,20,21] indirectdimensions are jointly sampled, in thatthe corresponding delays are increasedsimultaneously (Figure 1b). As a result,the dimensionality of the experiment isreduced, since K indirect dimensions ofthe ND experiment are projected ontoN�K dimensions in the RD experiment.Using quadrature detection (see nextSection) by recording experiments I andII (Figure 1c), the frequency sign in theindirect time domain is determined onlyfor one of the chemical shift modula-tions (WT in Figure 1). The K projecteddimensions lead to additional cosinemodulations of the time-domain signalwhich give rise to cross peaks at W1�W2�W3…�WK+1. Therefore, spectra areobtained with duplicated peaks at thesum and difference frequencies of thesimultaneously incremented indirect di-mensions. For example, a 3D experi-ment with a peak coordinate at(WS,WT,WI) in the three frequency di-mensions (w1, w2, w3; Figure 2a) reducesto a 2D experiment with two peaks at(WT+WS,WI) and (WT�WS,WI) in (w1, w2)of the RD experiment (Figure 2c). Forthe equivalent of a 5D experiment eightpeaks corresponding to 2 A 2A 2 sum/difference frequencies are obtained inthe indirect dimension of a related 2DRD experiment, where three indirectdimensions are jointly sampled. In gen-eral, 2K signals are obtained in theindirect dimension of a (N,N�K)D RDexperiment with K+ 1 simultaneouslysampled (K projected) dimensions, com-pared to one signal in the correspondingND experiment.

Figure 1. Schematic representation of a) a 3D NMR experiment and b) a corresponding (3,2)Dreduced dimensionality (RD) experiment correlating three spins, I, S and T. During the prepara-tion period, equilibrium magnetization is (re)established. Chemical shifts of S and T spins arerecorded during indirect evolution periods, I spins are directly detected during acquisition. Inthe (3,2)D RD experiment, the chemical shift evolution period of the S spins is projected(K=1), and the chemical shifts of the T and S spins are recorded simultaneously during t1.Quadrature detection for S and T spins is achieved by applying the mixing sequences with phas-es (qS, qT) 08 and 908. This approach yields two pairs of signals with cosine and sine modula-tion, respectively (Figure 1c). For the (3,2)D GFT experiment, central-peak detection is achievedby performing an additional experiment with no chemical shift evolution of the S spins duringt1. This approach gives rise to a central-peak resonating at WT during w1. c) Quadrature detec-tion in the (3,2)D GFT experiment requires linear combinations of four different t1 time-domainsignals; R and I denote real and imaginary parts. Note, that there is a 908 phase shift betweensignals I,IV compared to II,III. In the first step, the cosine and sine modulated signals of the Tspins are combined for quadrature detection of the T spin frequencies. Next, the two signals ob-tained are multiplied in the time domain with a G matrix (for K=1) to yield two phase-sensitivesignals at frequencies WT�WS. d) Alternatively, the linear combinations required for quadraturedetection of the T and S spin frequencies can also be performed in the frequency domain.

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Reduced Dimensionality with FullQuadrature Detection: GFT NMRSpectroscopy

Serious drawbacks of this implemen-tation of RD experiments are a reduc-tion of signal-to-noise ratio by v

ffiffiffiffiffiffi2K

pin

the (N,N�K)D RD experiment com-pared to the corresponding ND experi-ment, and increased spectral overlap.This results from the cosine modulationobtained for each of the projected timedomains which yields a duplication ofpeaks in the indirect frequency domain,thereby also reducing the signal inten-sity for each of the two peaks by or 1/(2K) in a (N,N�K)D experiment (Fig-ure 2c). However, if a second spectrumwith sine modulation is recorded, one ofthe doublet components is inverted, andaddition and subtraction of the twodatasets yields two spectra with only asingle peak (Figure 1c). Since the orig-inal doublet signals are added, thesignal-to-noise ratio is improved by

ffiffiffi2

p

compared to the RD experiment. Thistechnique, called quadrature detection,is routinely used for frequency signdetermination in all dimensions of aconventional multidimensional NMRexperiment.[6] An improved implemen-tation of RD experiments thereforeemploys quadrature detection for alljointly sampled time domains.[2,21–23] Co-sine and sine modulation of the time-domain signals is achieved by independ-ently shifting the phase of radio-fre-quency pulses preceding each indirectevolution time by 908 (Experiments I toIV in Figure 1c). In a (3,2)D RD experi-ment (Figure 1b, 2c), conventionalquadrature detection is employed forthe T spins. For full quadrature detec-tion, two additional data sets with sinemodulation for the chemical shift evo-lution of the S spins are recorded. AfterFourier transformation the cosine- andsine-modulated S spin signals yield anin-phase and an anti-phase doublet atWT�WS, respectively. By linear combi-

nation, that is, addition and subtractionof these two datasets, two spectra areobtained with only one signal resonatingat eitherWT+WS orWT�WS (Figure 1c,dand Figure 2d). For an (N,N�K)D RDexperiment 2K linear combinations haveto be performed. The correspondingtransformations can be summarized ina transformation matrix, which consti-tutes part of the “G matrix” as definedby Kim and Szyperski. This part of a 2 A2 G matrix which achieves the appro-priate linear combination of the time-domain signals in a (3,2)D RD experi-ment is shown in Figure 1c. Fouriertransformation of the edited time-do-main signals yields a set of basic spectrawith a single peak at positions corre-sponding to all combinations of sum anddifference frequencies in the indirecttime domain (Figure 2d, left and mid-dle). If full quadrature detection isapplied, the signal-to-noise ratio of an(N,N�K)D RD experiment is equal tothe corresponding ND experiment,since in an ND experiment quadraturedetection is also employed for each timedomain.

However, some information is lost inan RD experiment if resonance frequen-cies are degenerate in all of the conven-tionally sampled (N�K�1) time do-mains, since only the sums and differ-ence frequencies are measured—ratherthan the individual frequencies in sepa-rate time domains as in an ND experi-ment.While the RD experiment will stillreveal that two signals with partialchemical shift degeneracy are present,the absolute resonance frequencies cannot be retrieved from the sum anddifference terms unless it is knownwhich peaks in the basic spectra arecorrelated, that is, are derived from thesame doublet. To overcome this prob-lem, additional experiments have to beperformed where for each projecteddimension a peak centered betweenthe cosine/sine modulated peak doubletis recorded (“central peak detection”,for example, at WT in Figure 2c,d right).If more than one dimension is projected,additional frequencies centered be-tween the “first-order” central peaksneed to be determined, and so on(Figure 2, 3 in ref. [2]). In a (N,N�K)RD experiment 2K basic and 2K�1 “cen-tral-peak” spectra have to be recorded.For example, a (3,2)D RD experiment

Figure 2. Schematic NMR spectra comparing conventional and RD implementations of a 3D ex-periment for two three-spin systems (blue and red) with degenerate chemical shifts of the Ispin, which resonate at WT,WT’,WS, WS’ and WI. a) Peak position in a conventional 3D FT NMR ex-periment. b) The chemical shift frequencies of the 3D experiment can be uniquely extractedfrom two 2D projections, if no signal overlap is present. Otherwise, the frequencies are notuniquely correlated and the partially overlapping spin systems cannot be assigned unambigu-ously. c) In a reduced dimensionality experiment, the frequencies of the T and S spins are meas-ured as sum and difference chemical shifts (left). To unambiguously derive the underlying fre-quencies, also in the case of chemical shift degeneracy, a “central-peak” spectrum (right) is re-corded, where no chemical shift modulation of the S spins has occurred during t1. d) Spectraobtained in a (3,2)D GFT NMR spectrum. After linear combination (multiplication with a G ma-trix in the time domain, see Figure 1c), two signals are obtained at the sum or the differencefrequencies of the T and S spins. To retrieve chemical shifts in case of degeneracies, the corre-sponding central-peak spectrum is required (right panel).

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requires only one additional central-peak spectrum, while a (5,2)D experi-ment (K= 3) requires four first-order,two second-order, and one third-ordercentral-peak spectra. By addition andsubtraction of all 2K+1�1 time-domainsignals (e.g. 15 signals for a (5,2)D RDexperiment), 2K+1�1 spectra with a sin-gle peak at all combinations of theK+ 1involved indirect frequencies(W1,W2,W3,W4) are obtained. The linearcombination of these 2 K+1�1 time-do-main signals (2K basic and 2K�1 central-peak spectra) can be combined anddescribed by the complete G matrix.Since the data processing involves multi-plication with the G matrix, followed byFourier transformation, Kim and Szy-perski propose the name GFT NMR forthis implementation of RD experiments.

Assuming equivalent total measure-ment time, the signal-to-noise ratio inthe basic spectra of GFT NMR isreduced by up to 1/

ffiffiffi2

pcompared to the

equivalent ND experiment. This results,since 2K+1�1 rather than 2K experimentshave to be recorded for the indirect timedomain, where signal contributions addup only in the 2K basic spectra. Depend-ing on K, up to almost half of themeasurement time has to be used forcentral-peak acquisition which does notimprove the signal-to-noise ratio in thebasic peak spectra.

The measurement times of GFTNMR compared to ND FT can beestimated from Equation (1). This re-

Minimal measurement time FT=GFT

¼ 2KYK

j¼0ðmjÞ=ð2Kþ1-1Þ

XK

j¼0ðmjÞ

ð1Þ

flects the dramatic reduction in meas-urement time, especially for higher di-mensionality experiments, that is, 1/20for (3,2)D GFT compared to 3D and1/30000 for (5,2)D GFT compared to5D assuming that 60 points are recordedfor each time domain (m= 60).

Another benefit of the GFT NMRapproach results because individualchemical shifts are extracted from thevarious GFT spectra by a least-squaresfitting routine. The accuracy for deter-mination of the chemical shifts is im-proved and error analysis can be per-formed, since each frequency contrib-utes to all 2K+1�1 spectra. This situation

is in contrast to an ND experiment,where each frequency is measured onlyonce, and with lower spectral resolution.However, the resolution in indirectdimensions of any multidimensional ex-periment can usually be improved bypost-acquisition techniques, such as lin-ear prediction or maximum entropymethods.[14]

Discussion and Perspectives

The generalized GFT NMR methodintroduced by Kim and Szyperski is aninteresting approach to overcome thesampling problem in multidimensionalNMR experiments—given that the sam-pling limit is fulfilled, that is, the totalexperimental time is not determined bysensitivity requirements. In that case,equivalents of 3D, 4D, and even 5DNMR experiments can be recorded inreasonable experimental time, and thechemical shifts can be determined withhigher accuracy than those extractedfrom conventional experiments. Analy-sis of GFT NMR data is not as straight-forward as that of ND experiments,since the chemical shifts are only re-corded as sum and difference frequen-cies. Therefore, specialized software isrequired for data analysis, which hasalready been incorporated into auto-mated assignment programs.[24]

An interesting simple alternative toGFT NMR is the acquisition of lower-dimensionality projections of an NDexperiment. For example, chemicalshifts recorded in a 3D experiment(W1,W2,W3) can also be extracted fromtwo 2D spectra where only one of theindirect dimensions is recorded withpeak positions at (W2,W3) and (W1,W3),respectively (Figure 2b). The signal-to-noise ratio of these experiments is equalto the corresponding 3D experiment,and high resolution can be achieved inthe indirect time domain. The informa-tion obtainable corresponds to that inthe basic spectra of GFT NMR. For a(5,2)D experiment, four 2D projectionshave to be recorded. Signal overlap canthen be detected if chemical shifts arenot degenerate in at least one dimen-sion. An advantage of this alternative isthat the chemical shifts can be directlyextracted from the spectra. However,since the indirect dimensions are re-

corded separately in the projections, thefrequencies are in fact uncorrelated. Inunfavorable cases, chemical shift degen-eracies between different spin systemscan thus not be resolved. This situationis in contrast to the GFT NMR method,where all indirect dimensions contributeto the peak positions, and degeneraciescan be resolved by central-peak detec-tion (Figure 2).

GFT NMR still employs Fouriertransformation to extract the frequen-cies from the time-domain signal. Thereare also interesting new alternatives forthe fast recording of NMR spectra in thesampling limit, which include filter di-agonalization[25] and maximum entropymethods[14] for which only a few (and notnecessarily linearly sampled) timepoints are sufficient. Another excitingperspective is the combination of spa-tially and time encoded NMR detectionwithin a single scan, as recently pro-posed by Frydman et al.[26]

A general problem when using FTorGFT NMR experiments with lowerdimensionality is signal overlap, whichis far better resolved in higher dimen-sionality experiments. Useful applica-tions of reduced-dimensionality experi-ments will therefore be limited to rela-tively small protein domains, that is, of10–15 kDa molecular weight.

It should also be noted, that thesensitivity of multidimensional NMRexperiments still needs to be consideredfor both RD and ND implementations.Typically, these experiments involve atleast N�1 magnetization transfer stepswhich involve numerous radio-frequen-cy pulses and delays for magnetizationtransfers during which relaxation of theNMR resonance signal occurs. Thiseffect reduces the overall sensitivitycompared to, for example, a 2D experi-ment with just a single magnetization-transfer step.

In summary, GFT and other newstrategies for optimized sampling ofmultidimensional spectra will signifi-cantly reduce measurement times forsampling-limited NMR experiments.Together with improved methods forautomated chemical shift assignmentsand structure calculation this promisesto reduce time requirements for NMR-based protein structure determinationfrom months to few weeks in the future,which is likely to have a great impact

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and strengthen the application of NMRspectroscopy in structural biology andstructural genomics.

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