ω1,-Scaling pulse sequences for two-dimensional homonuclear multiple-quantum spectroscopy

Volume

138. number

CHEMICAL

5

PHYSICS

o ,-SCALING PULSE SEQUENCES FOR TWO-DIMENSIONAL HOMONUCLEAR A. MAJUMDAR

31 July 1987

LETTERS

MULTIPLE-QUANTUM

SPECTROSCOPY

and R.V. HOSUR

Chemrcal Physrcs Group, Tata Institute of Fundamental Research, Homi Bhabha Road, Bombay 400005, Indra Received

4 May 1987; in final form 8 June I987

New pulse schemes have been proposed for different quantum spectroscopy. The advantages of the methods demonstrated

w ,-scaling [ 1- 10 ] has proved to be a very useful technique in two-dimensional correlated spectroscopy for purposes of sensitivity enhancement [ 21, resolution enhancement [ 3-5 1, observations of longrange coupling correlations [ 6,7], co,-decoupling [ 1,8], reduction of diagonal peaks [ 51, and has been used in studies of long oligonucleotides [ 9, lo]. It can also be used for accurate measurements of coupling constants which can then be used for structure determination in aqueous solutions. Sensitivity enhancement in correlated spectra is achieved by J-scaling which reduces the cancellation of the antiphase components of the cross peaks. Chemical shift scaling, on the other hand, allows increase of separation between the cross peaks and thus produces better resolutiop in the spectra. Two-dimensional multiple-quantum (MQ) spectroscopy [ 11,121 is another technique which is increasingly being used for resonance assignments in large biological molecules [ 13- 15 1. Multiple-quantum spectra are free of diagonals, which are excessively large in correlated spectra and often mask cross peaks lying very close to the diagonal. Zero-quantum spectra are also not affected by field inhomogeneities. Both double-quantum and zero-quantum spectra display peaks between directly coupled protons as well as remote protons having a common coupling partner. The latter type of peaks provide relay type of information and hence can be helpful in unambiguous resonance assignments. Multiplicity of peaks 0 009-2614/87/$ (North-Holland

03.50 0 Elsevier Science Publishers Physics Publishing Division)

posstbilities of w ,-scaling in two-dtmensional for resolution enhancement and sensitivity

homonuclear enhancement

multiplehave been

in multiple-quantum spectra is smaller than that of peaks in correlated spectra and thus multiple-quantum spectra have inherently higher resolution. Mulspectra suffer from certain tiple-quantum disadvantages as well. First of all, uniform excitation of multiple-quantum coherences is a serious problem. Several attempts have been made to overcome these difficulties [ 16,171. The preparation period which is used for exciting multiple-quantum coherences consists of certain delays and these lead to loss of signal due to transverse relaxation. Due to enhanced spectral widths along the o, axis, digital resolution is often poorer. Moreover, both direct as well as remote peaks contain mixed line shapes. Consequently, spectra have to be represented in the absolute value mode, which leads to further loss of resolution. The interpretation and analysis of multiple-quantum spectra is also more complex than the simple correlated spectra. Thus, in practice, both correlated spectroscopy and multiple-quantum spectroscopy should be used in conjunction for unambiguous spin system identification and resonance assignments. In this communication we propose some pulse schemes incorporating the ideas of or-scaling in multiple-quantum spectroscopy, which lead to several improvements in MQ spectra. Uniform excitation can be achieved, resolution can be improved, spectrometer time can be saved without any loss of resolution, o ,-decoupling can be achieved, etc. The B.V.

431

CHEMICAL PHYSICS LETTERS

Volume 138, number 5

SCALING

IN

MULTIPLE

QUANTUM

SPECTRXOX’Y

Fig. I. (A) Pulse scheme for two-dimensional MQ spectroscopy. Phase @is cycled through X, y, --x, -y and the data are alternately added and subtracted for DQ spectroscopy. T is a fixed delay for MQ excitation. (B) Pulse sequences for w ,-scaling in MQ-spectroscopy. (Yis a shift scaling factor and y a J-scaling factor. d is a constant delay. In schemes Bl and B4 y = 0 produces w ,-decoupling. r,, is a tixed delay and k is a constant factor < 1 useful for uniform excitation of MQ coherences. Phase I//is cycled through x, -x to eliminate artifacts due to imperfect 180” pulses.

method of uniform excitation is indeed identical to the “accordion” type of experiment reported earlier

1131. Fig. 1A shows the usual scheme of multiple-quantum spectroscopy. The phase 9 of the excitation pulses is cycled through x, y, - x and - y and the data co-added for zero-quantum spectroscopy and alternately added and subtracted for double-quantum spectroscopy. r is a fixed delay which has to be optimised for proper double-quantum excitation. Fig. 1B shows four pulse schemes Bl, B2, B3 and B4 which demonstrate different scaling possibilities in multiple-quantum spectroscopy. The phase w of the 180” pulse is alternately changed between x and -x, and the data are co-added. This eliminates some of the artifacts due to the imperfection in the 180” pulse. 7. is a fixed delay similar to 7 in fig. 1A. The behaviour of the nuclear spin system during the course of the above pulse sequences can be best understood by density operator calculations, and considering the observable part of the density oper432

3 I July 1987

ator at the beginning of the detection period. Following the product operator formalism involving I +, I- and ZZoperators [ 181, the calculations have been performed for different spin systems, and the elements of the density operator in each spin system are listed in table 1. The raising and lowering operators are very useful for calculation of multiple-quantum spectra of three or more spins. The calculations shown are for pulse scheme B2, but similar expressions for others can easily be derived by making suitable substitutions. For example, for B 1, t, should be replaced by d- yt,; for B3, 7 should be replaced by z. + kt,, etc. It is seen from the table that, in general, double-quantum spectra get contributions from absorptive (C(klm) terms) as well as dispersive (S(klm) terms) line shapes. The two contributions have the same sign for direct peaks but opposite signs for dispersive peaks. Linear systems such as klm, klm2, kzm, k,m (coupling between magnetically equivalent spins is effectively zero), however, show pure absorptive phases. A majority of the real spin systems fall into one of the categories of linear systems, and for all these systems it is seen that both direct peaks as well as remote peaks have in-phase character along the w,-axis. Along the oz-axis, all the peaks have anti-phase character. The separation between the components is larger for remote peaks than for direct peaks along the o,-direction. All the four-pulse schemes in fig. 1A achieve shift scaling of double- and zero-quantum coherence by a factor LYand the J are scaled by a factor y. Schemes B3 and B4 are similar to B2 and Bl, respectively, except for the fact that they incorporate the “accordion” type of variation in the preparation period for purposes of uniform excitation. This type of excitation increases the multiplicity of peaks and therefore the constant k has to be chosen small enough so as not to significantly lose resolution in the spectrum. Schemes Bl and B4 are useful for w,-decoupling ( y = 0) which can be used to selectively enhance particular peaks in the double-quantum spectrum. In all the schemes in fig. 2A, the scaling factors cx and y can be chosen independently. Scaling down of the shifts ((Y< 1) allows reduction of the spectral widths along the o ,-axis and thus ty will be higher compared to the normal double-quantum spectrum for the same number oft, increments. The J-scaling factor y can also be chosen smaller than 1 so that the

31 July 1987

CHEMICAL PHYSICS LETTERS

Volume 138, number 5

Table 1 Results of the density operator calculations for different spin systems for scheme B2 of fig. 1a) Spin system

Expressions for the observable part of the density operator at the beginning of the detection period

k /\ l-m

I,+I,~[C(kml)s’(c”+c”‘)+S(kml)s”s”’] cos[a(w~+o~)t,] +I~I,,,~[C(klm)s”(c’+c”‘)+S(klm)s”’s’] cos[a(w~+w,,)t,] -2il:I,,I,,,,[C(mkl)s”s’-S(mkl)s”’(c’+c”)] cos[a(~,+w,,)r,] +similar terms for spins 1and m

1

/\ k

m

I:I,r[C(/m)s’(l+c’v)] cos[a(oA +w,)f,] +I,:,I,~[C(kr)s~‘(l+c’)] cos[a(o,+w,,)t,] +I,+I,,[C(lm)s’(l+c’“)] cos[a(w~+w,)] +I,+I,,,,[C(kl)s”‘(l+c’)] cos[a(~,,,+~/)t,] -2il,?I,,I,,,,[C(mNc)s”‘s’] COS[~(W,:+W,,)~I]

kzm

211+I,,,,[Cs(l+c)l cos[a(ol +w,,,)t, 1 +21;IJcs(l+c)] COS[(Y(W~ +o,,)t,l -jiIz,[C(2)s2] cos[a(2o~)l,]

klm,

r~r,,[C2(rm)s’(r+c2-)]

cos[a(wk+wl)t,]

+~,+I,,{[C2(lm)s’(l+c2’“)]-2s’sZ”}cos[a(w~+w~)t,] +2I,+I,,,[C(k/)C(lm)s”‘(/+c’c”‘)] cos[a(w,+o,,,)t,] -jiI,+[C(2/m)s*“c’] cos[a2w,nt,] -4il,tI,,I,,=[C(klm)s’s”‘(2)] cos[a(wt+w,)t,] -r,+I*.S’S*‘“{cos[cr(o~-w,+2w,.)t,]+cos[ar(-w~+w,+2~,)1,])

abbreviations:

S(klm)=sin[xl,y(J~,+J,,,,)I C(klm)=cos[~~,~(J~,+J~,,,)l S(kl)=sin[nt,yJ,,] C(kl)=cos[rrf,yJ,,] S(2kl) =sin[xr, y2Jl,] C(2k/)=cos[xt,y2.J,,] c=cos[~f,YJI,,,1 S=sin[xt,yJk,,,] C(2) =cos[xr, Y2Jhl S(2)=s~n[~r~y2J~,,,l

s’=sin(nJk,Zs) =sk, I r =.%,, S”’= S,,” c’=cos(x~~,27) =c~, CO= q,, c”’= c,,m s’(2) =sm(x2.J1,27) ~‘(2)=cos(77~~,27) c=cos(nJ1,,,27) s=sin(xJ1,,27) c(2)=cos(rrU~,,,27) s(2)=sin(x2J~,,27)

” The phase Q has been assumed to be zero. Quadrature detection has been assumed along wz but not along w r.

width of the peak along the or-axis will get reduced. Both these factors lead to increased resolution along the w ,-axis as compared to normal double-quantum experiment. Fig. 2 shows a double-quantum spectrum of a threespin system, vinyl acetate, recorded with the conventional double-quantum pulse scheme. Fig. 3A shows the comparison of a particular portion (A in

fig. 2) with an w ,-scaled double-quantum spectrum of the same sample, recorded under identical conditions. The multiplicity of the peak at the doublequantum frequency of wA+mX, which is a doublet with a separation of 15.4 Hz, can be seen easily in the CO,-scaled spectrum. The lower peak at the frequency w~+w~ has a smaller separation of the components (7.4 Hz) and hence is not resolved in 433

Volume 138, number

CHEMICAL

5

PHYSICS

31 July 1987

LETTERS b

a

/

&A /

I

/’ /

W#+wX

I *I

Q WI

/

m/ . /

Wh +

wx

Wh+WU

/

A

/

Fig. 2. 500 MHz DQ spectrum of vinyl acetate recorded on a Bruker AM-500 FI NMR spectrometer. r =0.025 s. 256 t, experiments were performed with 2048 data points along the tz axis. The dtrect peaks areJoined by horizontal lines. The skew diagonal IS shown by the dashed line. Digital resolution is 3.5 Hz/point.

both the spectra. Fig. 3B shows the comparison of intensities of direct (D) and remote (R) peaks in the normal double-quantum and o ,-scaled ( cx= 0.5; y = 0.6) double-quantum spectra. A horizontal cross section is taken at the frequency of w,+ We. It is clearly seen that the direct peaks are stronger in the w ,-scaled spectrum (bottom trace) than in the normal double-quantum spectrum (top trace). This can be attributed to larger contribution of in-phase components to the direct peaks in the 2D spectrum. Fig. 4 shows an application of the technique to a biological molecule, an oligonucleotide having the sequence GGTACGCGTACC-d in DzO solution. Portions of the w i-scaled and normal double-quantum spectra are shown for comparison. Here again, it is clear that in the w,-scaled spectrum, the peaks are compressed along the w ,-axis and the resolution is superior. The spectra show direct (at H; + H; and Hi + H; ) as well as remote connectivities (at 434

Fig. 3. (A) (a) Blow up of a particular region corresponding to box A in fig. 2 from the o i-scaled spectrum. Scheme B2, y= 1, (r~O.5. 256 t, experiments with 2048 t2 prints were performed. (b) Blow up of box A m fig. 2 for comparison. (B) Comparison of horizontal cross sections through normal (top trace) and w Iscaled (bottom trace) DQ spectrum at o,=w,+o~. (u=O.5, y=O.6.

H; +H; ) at the chemical shift position of H; protons of the deoxy-ribose rings of the oligonucleotide. The w ,-scaled spectrum in other regions also shows great promise and a complete analysis will be published elsewhere. The facilities provided by 500 MHz FT-NMR National Facility supported by the Department of

CHEMICAL PHYSICS LETTERS

Volume 138, number 5

References

)

-4

HZ’+HZ

31 July 1987

I

f’

Bv vooP 41

-6

Fig. 4. Comparison of normal DQ (b) and o ,-scaled DQ (scheme B2) spectrum (a) of an oligonucleotide GGTACGCGTACC-d in DzO at 25°C. 400 t, experiments were performed with 2048 r2 points. (r=O.5 and y =0.6 in w,-scaled spectrum. The improved resolution due to or-scaling is clearly seen. The spectral regions show direct (H;+H;, H; +H;) peaks as well as remote (H;+H;) peaks.

Science and Technology, Government of India, are gratefully acknowledged. The authors also thank Professor G. Govil and Dr. H.T. Miles for the oligonucleotide sample used for the spectrum in fig. 4.

[ 1] L.R. Brown, J. Magn. Reson. 57 (1984) 513. [2] R.V. Hosur, K.V.R. Chary and M. Ravikumar, Chem. Phys. Letters 116 (1985) 105. [ 31 R.V. Hosur, M. Ravikumar and A. Sheth, J. Magn. Reson. 65 (1985) 375. [4] R.V. Hosur, A. Sheth and A. Mazumdar, to be published. [ 51 M. Ravikumar, A. Sheth and R.V. Hosur, J. Magn. Reson. 69 (1986) 418. [ 61 P. Gundhi, K.V.R. Chary and R.V. Hosur, FEBS Letters I9 1 (1985) 92. [7] A. Sheth, M. Ravikumar and R.V. Hosur, J. Magn. Reson. 70 (1986) 213. [8] R.V. Hosur, M. Ravikumar and A. Sheth, 23rd Congress Ampere, Rome (Sept. 15-19, 1986) p. 572. [9] R.V. Hosur, A. Sheth, K.V.R. Chary, M. Ravikumar, G. Govil, Tan Zu-Kun and H.T. Miles, Biochem. Biophys. Res. Commun. 139 (1986) 1224. [IO] W.J. Chazin, K. Wuthrich, S. Hyberts, M. Rance, W.A. Denny and W. Leupin, J. Mol. Biol. 190 (1986) 439. [ 11 ] A. Wokaun and R.R. Ernst, Chem. Phys. Letters 52 (1977) 407. [ 121 L. Muller, J. Am. Chem. Sot. 101 (1979) 4481. [ 131 L. Braunschweiler, G. Bodenhausen and R.R. Ernst, Mol. Phys. 48 (1983) 535. [ 141 G. Ottingand K. Wuthrich, J. Magn. Reson. 66 (1986) 359. [IS] P.E. Wright, R.M. Cooke, K.J. Cross, B.C. Mabbutt, B.A. Messevic and J.E. Wellington, in: Magnetic resonance in biology and medicine, ed. G. Govil (Tata McGraw-Hill, New Delhi, 1985) p. 13 1. [ 1610. W. Sorenson, M.H. Levitt and R.R. Ernst, J. Magn. Reson. 55 (1983) 104. [ 171 M. Rance, O.W. Sorensen, W. Leupin, H. Koggler, K. Wuthrich and R.R. Ernst, J. Magn. Reson. 61 (1985) 67. [ 181 L.R. Brown and J. Bremer, J. Magn. Reson. 68 (1986) 2 I?.

435