Solid-State Dipolar INADEQUATE NMR Spectroscopy

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Journal of Magnetic Resonance136,86–91 (1999)Article ID jmre.1998.1631, available online at http://www.idealibrary.com on

1CA

with a Large Double-Quantum Spectral Width

Mei Hong

Department of Chemistry, University of Massachusetts, Amherst, Massachusetts 01003

E-mail: mhong@chem.umass.edu

Received July 6, 1998; revised September 22, 1998

A technique for obtaining dipolar-mediated INADEQUATE experiment is potentially useful for structure de

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MR spectra with a large spectral window in the double-quantumimension is presented. Using the dipolar recoupling sequence C7o excite the double-quantum coherence under magic-angle spin-ing, the technique involves incrementing the evolution period inynchrony with the phase of the radiofrequency pulses in the C7equence. The technique is demonstrated on a uniformly 13C-abeled amino acid and an extensively 13C-labeled protein todentify 13C connectivity patterns for spectral assignment. © 1999

cademic Press

Key Words: solid-state NMR; INADEQUATE; double-quan-um; C7; dipolar recoupling.

Recently, solid-state homonuclear double-quantum NMR sroscopy has been increasingly employed to obtain spectrignment, torsion angles, and distances in biological solids (1–7),ynthetic polymers (8), inorganic glasses (9, 10), and zeolite11, 12). The utilization of double-quantum (DQ) coherence sresses signals from isolated spins so that the spectrum is sed to contain only signals from spin pairs (13). The DQ cohernce can be exploited in various ways in the experimental d14, 15). In two-dimensional INADEQUATE spectroscopy (16),omonuclear DQ coherence is excited before the evolution pt1) and is then reconverted to observable, single-quantum, cnce for detection (t2). This gives rise to 2D spectra in which t

ndirect dimension (v1) exhibits the sum chemical shift of toupled spins that survive the double-quantum filter and iselated with the isotropic chemical shifts of the individual spinhe direct dimension (v2). Compared to single-quantum correion spectroscopy, which gives rise to spectra with both diagnd off-diagonal peaks, the double-quantum spectra havistinct advantage that coupled spins with small chemicalifferences can be observed clearly without interferenceiagonal peaks.The double-quantum coherence can be excited by eithe

ipolar coupling or the scalar coupling between the two sphe scalar-coupling-mediated INADEQUATE experimentemonstrated originally in solutions (16) and more recentllso in solids (1, 17). Since the dipolar coupling permits sparoximity to be probed, a dipolar-mediated INADEQUA

86090-7807/99 $30.00opyright © 1999 by Academic Pressll rights of reproduction in any form reserved.

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ination. Furthermore, it can be used in place of the scoupling-mediated version for resonance assignments in sue to its strong distance dependence, the dipolar couetween directly bonded13C spins is more than five timtronger than the two-bond couplings and other long-rouplings. Therefore, at short mixing times the dipolar INADUATE experiment is as valid as the scalar version for rance assignment. In addition, the dipolar interaction al

aster excitation of the DQ coherence, thereby reducingT2-nduced signal losses. Such a dipolar-mediated solid-staignment approach has been shown recently in a15N–13Ceteronuclear correlation experiment (18). When applying diolar INADEQUATE spectroscopy to unoriented solihemical site resolution must be achieved by magic-apinning (MAS). However, since MAS also averages outipolar interaction, which drives the DQ excitation and recersion, special radiofrequency (RF) pulse sequences mupplied to reintroduce the dipolar coupling. Many such houclear dipolar recoupling sequences are now available19–4).One feature of the INADEQUATE experiment is that thev1

imension intrinsically has a large spectral range sinceects the sum chemical shifts of pairs of coupled spins.olypeptides, the13C DQ spectral range is at least 250 pponsidering that DQ coherence between aromatic carhich resonate at about 110 ppm downfield from the cent

he aliphatic region, can occur easily (while carbonyl–carbouplings are weak enough to be ignored). Although thev1

pectral width may be reduced by a factor of two using delcquisition or foldover correction (14, 25, 26), folding crowds

he spectrum and complicates the interpretation of the conivity patterns for complex biological macromolecules. Toain an INADEQUATE spectrum with a large, unfoldedv1

idth on a static solid or a solution sample, one can simake thet1 dwell time small. However, to carry out a MA

NADEQUATE experiment involving dipolar recoupling suences, an additional requirement often arises: the recouulses must be synchronized with the sample rotation. Thieverely restrict the choice of thet1 dwell times. For example

when using the C7 sequence (23) to excite and reconvert theD arti itat has( rc ins wts ioud in-c u-i er-s

tho fd ralw larr De bel nc( ses thc tot niaC -c nt C7r relt DQc chf anif ncw ais sr nie

T dR eteat

T orien-t isi e allt fE ipal-a e.

isd ationob riods,w basicC endo sionp rm n fort ock.T t thefi C7s ,s rp lastCt oner uet geHt

utedv arged ATEe AS.A at beingr . Thee evenbc ed ifteda

87SOLID-STATE INADEQUATE NMR WITH A LARGE v1 SPECTRAL WIDTH

Q coherence, the reconversion pulses normally must stnteger multiples of the rotor cycle after the end of the excion period to maintain correspondence with the rotor p27). This would require a minimumt1 dwell time of one rotoycle. At currently feasible RF field strengths and spinnpeeds, one rotor cycle is usually much larger than the dimes required for a sufficiently wide13C double-quantumpectrum, as we discuss in more detail below. In a prevemonstration of the dipolar INADEQUATE experimentorporating C7 (15), this problem was circumvented fort

tously because31P signals with a small chemical shift dispion were detected.In this article, we show a phase-permuted version of

riginal C7 sequence which permits the measurement o13Cipolar INADEQUATE spectra with a large DQ spectidth in the v1 dimension. We chose C7 as our dipo

ecoupling sequence since it offers one of the highestxcitation efficiencies available so far. Our discussion

ow uses much of the original formalism of the C7 seque23). Briefly, C7 is a train of continuous sevenfold phawitched RF pulse cycles whose field strength fulfillsondition v1 5 7vr to achieve dipolar recoupling. Duehe weak orientation dependence of its average Hamilto7 and its variants (28, 29) have high recoupling efficienies and are thus ideal for DQ excitation and reconversiohe INADEQUATE experiment. In a DQ experiment, theeconversion block not only changes its overall phaseive to that of the excitation block in order to select theoherence, but also continues the sevenfold phase switrom the end of the excitation period. The latter is a mestation of the central requirement of the C7 sequehich is that the sevenfold RF phase shifts must remynchronous with the sample rotation.This requirement ieflected in the average Hamiltonian of a basic C7 uxpressed in the interaction frame of the RF field,

H# p~0! 5 O

Q

Olmlm

v# lmlmQ ~VPR, t0! 3 exp~ifp~2m2 m!!Tlm

Q . [1]

he symbols have the same meanings as defineef. (23). For the present discussion, the relevant paramre the pulse phase of thepth C7 unit,fp 5 2pp/7, and the

ime-averaged anisotropic frequencyv# lmlmQ (VPR, t0),

v# lmlmQ ~VPR, t0! 5

1

tcE

0

tc

vlmlmQ ~VPR, t0, t!dt

5 A~VPR! E0

tc

dm0l ~2bRF~t!!

3 exp~imvr~t 1 t0!!dt. [2]

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he dependence of the averaged frequency on the rotoration is reflected in the timet0 when the C7 sequencenitiated. To emphasize this time dependence, we includime-independent terms inA(VPR), whereVPR is the set ouler angles describing the relative orientation of the princxis frame of the interaction tensor and a rotor-fixed framA largev1 width in the dipolar INADEQUATE experiment

erived by inserting an evolution period that matches the durf one (or integer multiples of one) C7 unit,t1 5 tc 5 2tr /7,etween the double-quantum excitation and reconversion pehich are chosen to comprise an integer multiple of seven7 units,Cfp

. If, instead of continuing the RF phase from thef the excitation period to the beginning of the reconvereriod, we shift the phase of the latter byDf 5 2p/7 (or integeultiples of this value) (Fig. 1a), then the average Hamiltonia

he reconversion block is identical to that of the excitation blhis can be proved as follows. It is obvious from Fig. 1a tharst six C7 units in the phase-permuted and time-shiftedequence have the same average HamiltoniansH# p

(0) as beforeince neither the timing of the pulses (t0) relative to the rotoeriod nor the phases (fp) of the pulses have changed. For the7 unit, the pulse phase has returned to the initial valuef0 5 0 of

he original sequence, while the pulse cycle occurs exactlyotor period after the first C7 unitCf0

of the original sequence, do t0 5 t1 1 6tc 5 7tc 5 tr. Thus the amplitude of the averaamiltonian during this last C7 unit is identical to that ofCf0

inhe original sequence,

FIG. 1. (a) The original C7 sequence and its equivalent, phase-permersion used to acquire a dipolar INADEQUATE spectrum with a louble-quantum width. (b) Pulse sequence for the dipolar INADEQUxperiment incorporating C7 for homonuclear dipolar recoupling under Mfter cross-polarization, double-quantum13C–13C coherence is excited by

rain of C7 pulses. It evolves under the sum chemical shifts beforeeconverted into observable single-quantum magnetization for detectionxcitation and reconversion periods consist of an integer multiple of sasic C7 units,texc 5 trec 5 ntc (n 5 7, 14, . . .). The evolution timet1 ishosen to bemtc (m 5 0, 1, . . .); thus thet1 dwell time is equal to thuration of one C7 unit,tc. The phases of the reconversion pulses are shs described in the text to maintain synchrony with the rotor phase.

C pem en

wes tts rec otop enb st

hs DE-Q

ona m-b entw ng at ningmmi es by4w Hz.A con-s toa thep fg fD hes ar-a ing

Greekl ottedp time ofm of thep pulses int rum indict ed rumo

88 MEI HONG

v# lmlmQ ~VPR, t0 5 tr! 5 A~VPR! E

0

tc

dm0l ~2bRF~t!!

3 exp~imvr~t 1 tr!!dt

5 v# lmlmQ ~VPR, t0 5 0!. [3]

ombined, the zeroth-order average Hamiltonian of theuted C7 sequence is identical to that of the original sequ

H# 0~0!~0! 1 H# 1

~0!~tc! 1 · · ·1 H# 6~0!~6tc!

5 H# 1~0!~t1 5 tc! 1 · · ·H# 6

~0!~6tc! 1 H# 0~0!~tr). [4]

Therefore, to carry out a 2D INADEQUATE experiment,imply need to incrementt1 with a step oftc 5 2tr /7, and shifhe overall phase of the reconversion pulses byDf 5 2p/7 foruccessivet1 values. The durations of the excitation andonversion periods must be integer multiples of the reriod. In this way, we maintain the phase correspondetween the DQ excitation and reconversion blocks while

FIG. 2. (a) Two-dimensional13C dipolar INADEQUATE spectra of unetters represent the spectral assignment. The expected tilted diagonalrojections of positive and negative signals along each dimension are as (52tr) and at1 dwell time of 40.8ms. A total of 160 complext1 points whase cycle (32 steps), was 8.5 h. (b)13C INADEQUATE spectrum of the s

he DQ reconversion block. Otherwise, the conditions were the same ahe negative peaks observed. Note the inequality between the DQ freqimension. The chemical shift scale along thev1 axis was made arbitrarilyf (a).

r-ce

-rceill

aving a t1 dwell time small enough to ensure a largev1

pectral width. The pulse sequence of this dipolar INAUATE experiment is shown in Fig. 1b.This dipolar INADEQUATE experiment is demonstrateduniformly 13C- and15N-labeled sample of glutamine (Ca

ridge Isotope Laboratories, Andover, MA). The experimas carried out on a Bruker DSX-300 spectrometer usi

riple-resonance MAS probe equipped with a 4-mm spinodule. Phase-sensitive chemical shift spectra in thev1 di-ension were acquired in the hypercomplex manner (30). This

nvolves changing the phases of the DQ reconversion puls5° between the cosine and the sine data sets (31). The sampleas spun at 7 kHz, requiring a C7 RF field strength of 49 kccording to the above discussions, these conditionstrained thet1 dwell time totc 5 40.8ms. This corresponds

DQ spectral width of 325 ppm. Figure 2a displaysroperly acquired13C dipolar INADEQUATE spectrum olutamine. Only 90% of thev1 window is shown. Four pairs oQ cross peaks in thev1 dimension are observed for tix-carbon molecule. The tilted “diagonal” with slope 2, chcteristic of INADEQUATE spectra, is found by connect

ly13C-labeled glutamine. Dashed lines indicate the connectivities, andoss the center of each pair of double-quantum signals is shown as a dline. Theshown. The spectrum was acquired with a double-quantum excitation285.6

e acquired. The total acquisition time, which was limited by the lengthe sample acquired without the synchronous phase switching of the C7ose in (a). The dashed rectangle in the upper right corner of the spectatescies in thev1 dimension and the sum of the single-quantum frequencies in thv2

epresent the same (Cb, Cg) sum chemical shift as that in the correct spect

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89SOLID-STATE INADEQUATE NMR WITH A LARGE v1 SPECTRAL WIDTH

the midpoint of the two signals in each cross section. The twoc tiviw d tt thec thd ccc ex-h enn shm Qc ae

onv oftr riod¥

i g ai DEQ enw ths tchi tru( asc pes ectf ap r-bd glqm , thc nom trub ecl rint uenc ese thi

idthd 6-r x-t -p ot nc ngp ctr httsp mb1

This large-spectral-width dipolar INADEQUATE experi-m bout4 itiona e spin-n .7m 28k ns elL eds( lds( ssdfi

p the1 edp se-q as al tors mak-i nita pond-i ipo-l r-s allyp sucha

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90 MEI HONG

arbonyl resonances are assigned based on their connecith the aliphatic carbons. The upfield carbonyl is couple

he well-resolved Ca signal (which is assigned based onhemical shift alone); thus it results from C1. This makesownfield carbonyl carbon the sidechain Cd, whose aliphatioupling partner must then be assigned to Cg. Cg is in turnoupled to Cb, the most upfield resonance of all, whichibits a coupling to Ca. In the spectrum, couplings betweondirectly bonded carbons are suppressed due to theixing time (texc 5 trec 5 285.6ms) used to excite the D

oherence. In addition to the isotropic peaks, the spectrumxhibits weak spinning sidebands in both dimensions.It is clear from the above discussion that if the C7 rec

ersion pulses always start with the same phase at the endt1,hen the average Hamiltonian¥p H# p

(0)(t0 5 t1 1 ptc) of theeconversion period differs from that of the excitation pe

p H# p(0)(t0 5 ptc). To show that the pulse-synchronizedt1

ncrementation and the rotor-synchronized phase switchinndeed both necessary for the success of this dipolar INAUATE experiment, we performed an alternative experimithout these features for comparison. It was acquired withamet1 dwell time but without the synchronous phase-swi

ng scheme in the reconversion block. The resulting specFig. 2b) exhibits several remarkable features. First, the boupling pattern is correctly manifested. There are no disive intensities or spurious sidebands, which might be expor such a time-sensitive pulse sequence. However, thehatic DQ signals exhibitnegativeintensities while the caonyl-aliphatic cross peaks remainpositive. In addition, theouble-quantum frequency is no longer the sum of the sinuantum chemical shifts, i.e., (v1, v2) Þ (Vi 1 Vj, Vi,j). Thiseans no tilted diagonal exists for the spectrum. In fact

hemical shift scale of thev1 dimension seems to haveeaning, and it is not possible to derive the altered specy folding the correct double-quantum spectrum. These p

iar artifacts may be qualitatively understood by considehat the insertion of the evolution period without subseqompensation by the phase of the DQ reconversion pulsquivalent to imparting an additional modulation factor to

ndirectly detected signals.To further demonstrate the utility of this large-spectral-w

ipolar INADEQUATE experiment, we applied it to a 7esidue protein, ubiquitin (Mr 5 8565). The sample was eensively enriched with13C (32, 33). Over 50 peaks are comletely or partially resolved in the spectrum. About half

hem can be assigned to the amino acid types based oonnectivity patterns, the13C chemical shifts, and the labeliattern resulting from the biosynthetic expression. The speesolution is quite high for a protein of this molecular weighe peak widths (full width at half maximum) in thev2 dimen-ion are,1 ppm for methyl and carbonyl carbons and;1.5pm for methylene carbons. More complete assignmente obtained by combining other techniques such as 2D15N–3C correlation.

tieso

e

ort

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-

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fthe

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ay

ent is practically limited to spinning speeds between a000 and 8000 Hz. According to the C7 resonance condnd the phase permutation scheme discussed here, thesing speeds would yieldt1 dwell times between 71.4 and 35s, which correspond to DQ spectral widths from 14 toHz. The upper limit is sufficient for13C spectroscopy opectrometers up to 100 MHz13C Larmor frequency, while thower limit is insufficient for a DQ spectrum except for13Carmor frequencies below 50 MHz. Higher spinning spe.8 kHz) would require correspondingly higher RF fie.56 kHz) on the13C channel, which would induce signal loue to CP leakage to protons under the typical1H decouplingelds accessible today (;100 kHz).In conclusion, we have shown that high-resolution13C di-

olar INADEQUATE spectroscopy can be used to assign3C spectra of unoriented13C-labeled solids. The dipolar-basolarization transfer can be achieved with the recouplinguence C7 or its variants. The INADEQUATE spectrum h

arge unfolded DQ spectral width while maintaining roynchronization of the C7 sequence. This is achieved byng thet1 dwell time equal to the duration of one basic C7 und shifting the phase of the reconversion pulses corres

ngly forward. This large-double-quantum spectral-width dar INADEQUATE experiment, with the principal of rotoynchronizedt1- and RF-phase incrementation, can be equerformed using other DQ dipolar recoupling sequencess MELODRAMA (22).

ACKNOWLEDGMENTS

This work was partially supported by the NSF Materials Research Scnd Engineering Center. The author thanks K. Schmidt-Rohr for heiscussions.

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