Resolution enhancement by ω1 chemical-shift scaling in two-dimensional homonuclear correlated spectroscopy

JOURNAL

OF MAGNETIC

RESONANCE

65,375-38

1 (1985)

Resolution Enhancementby w1Chemical-Shift Scalingin Two-Dimensional Homonuclear Correlated Spectroscopy R.V.HOSUR,M.RAVIKUMAR,ANDANUSHETH Tata

Institute

of Fundamental

Received

Research,

April

Homi

Bhabha

29, 1985; revised

Road,

August

Bombay

400 005, India

13, 1985

Two-dimensional J-correlated (1-3) (COSY and SECSY) and NOE-correlated (4, 5) (NOESY) spectroscopic techniques have been successfully applied to obtain detailed structural information on several proteins and nucleic acids (6) having molecular weights in the range of 6000-7000. The same techniques can possibly prove successful for slightly larger systems (MW - 8000-9000) as well. Beyond these sizes serious problems of spectral overlap and sensitivity arise and impose severe limitations on such systems. The question of sensitivity in two-dimensional correlated spectra has been discussed recently in a series of papers (7-10). Among the several reasons which cause loss of sensitivity, two are of special importance, namely, (i) sensitivity loss due to transverse relaxation (Tf) before the start of data acquisition and (ii) loss of intensity in the cross peaks in J-con-elated spectra due to cancellation of anti-phase components under conditions of poor resolution. The loss due to TT relaxation can be minimized by restricting to least possible resolution along wr axis. But then the poor resolution results in partial cancellation of intensities of the anti-phase components in the cross peaks. Recently pulse schemes have been proposed (9-12) to overcome this problem. The cancellation of intensities in the cross peaks can be avoided either by refocusing the anti-phase components (9) or by scaling up the J value along the w1axis (10). For an increase in resolution in two-dimensional NMR spectroscopy, the obvious way is to use higher fields. The highest field now available on commercial spectrometers corresponds to 500 MHz for ‘H and it is at this frequency that the detailed investigations on proteins and nucleic acids have been carried out. Thus achievable resolution by this method is dependent on technological advances. Another technique to overcome problems of overlap is to use double-quantum spectroscopy (II), which shows J correlations in a different kind of presentation. However, for biological systems, this technique is not suitable because of serious sensitivity problems and difficulties associated with uniform excitation of double-quantum coherences. In this communication we describe new pulse sequences to enhance resolution by frequency scaling along the or axis in the COSY, SECSY, and NOESY spectra. Arbitrary scaling factors can be chosen depending upon the extent of overlap of peaks in the conventional COSY, SECSY, and NOESY spectra. In this connection, we define resolution R as 375

0022-2364185

$3.00

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R = $6 -L) and resolution enhancement parameter E as

E=I _-(6-L) as--m LL

1

a

for uncoupled spins and for coupled spins 01’ - PL - rJ

E =i

L

a

1

- (6 -L-J)

where 6 = Iwk - ~11, the separation between chemical shifts of the spins k and 1. L = half of the sum of the linewidths at half heights, and cy, p, and y are the scaling factors for shifts, linewidths, and coupling constants, respectively. For no scaling a=p=r=landE=O. Figure 1 shows the various experimental schemes. Pulse scheme A depicts the basic idea of frequency scaling, while schemes B, C, and D incorporate this scaling idea in COSY, SECSY, and NOESY experiments. Schemes B, C, and D are thus abbreviated as COSS (correlation with shift scaling), SECOSS (spin echo correlation with shift scaling), and NOECOSS (NOE correlation with shift scaling), respectively. 90”

9 0”

A

r

180"

90” B

I

96

90" t2

Xtl

tl

time

I

p

I

1800 90" 180° Xf1/2

90”

180" 90"

90"

FIG. 1. Pulse schemes for wi scaling in (i) COSY (schemes A and B), (ii) SECSY (scheme C), (iii) NOESY (scheme D) experiments. In schemesB-D, A is a constant time delay. 7 is a delay which changes synchronously with the evolution period t, . Scheme A shows the basic principles of scaling and the schemes B-D achieve exclusively shift scaling along the wr axis. The constancy of A helps in suppressing Jscaling. rm is the mixing time.

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For scheme A, the observable part of the density operator (TAfor two spins k and 1, at the beginning of the detection period (calculated using the product operator formalism (12)) is given by

-I (21k,l,,sin (L’&r + 2Z,,lhsin o@,)sin rJtiqtl

[3]

where 77= 1 + x. The first two terms represent diagonal peaks with in phase components, while the last two terms represent cross peaks with anti-phase components. It is clear from Eq. [3] that both shifts and J values are scaled by the same factor 17 (LY= y = 7). Now considering also the transverse relaxation before the detection pulse the observable density operator may be written as CT;, =

t41

aA\eXp(-&l/T%).

This results in Lorentzian lineshapes along the w1 axis with linewidths scaled by the same factor (Y.The scaling achieved in this experiment is a mere consequence of the artificial contraction of the evolution time. Every frequency is scaled and thus the J values and linewidths also appear scaled by the same factor. Consequently, E = 0 and no net resolution enhancement is achieved. It is therefore necessary that the basic scaling scheme be modified to exclusively obtain shift scaling without scaling J values and the linewidths at the same time. Pulse schemes B-D are aimed at achieving this goal in the J-correlated and NOE-correlated experiments. For scheme B, the observable part of density operator at the beginning of the detection period is given by CB = (&sin

‘dkd,

+ &sin

rJkl(t, + A)

C0@!t&OS

+ (2&&sin

tikatk

+ 2Ir&.sin

wrolt,)sin 71;Jkl(tl+ A).

[5]

Here (Y = 1 + x. The first two terms represent diagonal peaks and the last two terms give rise to cross peaks. Now it is seen that, in both the cross peaks and the diagonal peaks, the shift is scaled by the factor (Y,while the J value remains unaffected (y = 1). The parameter A appears only as a phase factor. The scaling of linewidths can be calculated by including the transverse relaxation in the expression for the observable part of the density operator, u;B = oBexp(-A/T2)exp(-tr/T;)[(

1 + x) - xTf/T2].

161

The factor exp(- A/T& simply contributes to the reduction in intensity. The second factor contributes to modifications of the linewidths due to scaling. Here two cases can be distinguished: (i) If TT = T2, a case of perfect field homogenity, there is no scaling of linewidths and p = 1. Hence, E = (L + J)(l - l/or)/L. (ii) If TT < T2, the linewidths will be scaled and the scaling factor fi is given p = a - xTgjT2.

t71 by

PI

It is seen that linewidths are scaled by a smaller factor than the shift scaling factor a, unlike in scheme A.

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Thus the resolution enhancement, E, in this scheme is given as -@-L-J)

1 .

In the worst case when (Y= p, which implies xTf/T2 - 0 E = (1 - l/a)J/L. [lOI Thus, even under conditions of very poor homogeneity there will be a net resolution enhancement for coupled spin multiplets. The delay A also helps to change the phase characteristics of the diagonal and cross peaks and enables partial elimination of anti-phase characteristics of the cross-peak components. This results in a better intensity ratio of cross peaks to respective diagonal peaks. A projection of an absolute-value COSS spectrum along the w1 axis, in the case T.$ = T2, gives a one-dimensional spectrum which, as far as dispersion of the signals is concerned, corresponds to a spectrum at higher magnetic fields. For instance, on a 500 MHz spectrometer, a scaling factor of two would produce a 1000 MHz spectrum along the w1 axis. The choice of the scaling factor will be determined by (i) spectral overlap; (ii) size of data storage space available, since frequency scaling would necessitate larger data matrices to obtain reasonable digital resolution in the spectrum; (iii) the value of A one can afford without losing too much signal due to Tf relaxation; A should be at least equal to x - ty”, where tl”” is the maximum value of tr ; and finally (iv) the instrument time available, since frequency scaling reduces the increment in tr between two successive experiments and hence to achieve a particular maximum value of tr , a larger number of experiments will have to be performed. Pulse scheme C incorporates the scaling ideas into the SECSY pulse sequence, and produces shift scaling along the w1 axis. This can easily be seen by calculating the density operator using the product operator formalism, as was done for COSS spectra. We do not show these calculations here. Such calculations on the SECSY experiment have been recently described (9). The results for scheme C are identical except that in the shift terms, t, will be multiplied by the scaling factor cy. Considering that the SECSY spectrum depicts differences of shifts between coupled spins along the w1 axis, the digital resolution in the SECOSS spectra can be better than in the COSS spectra without having to increase the size of the data matrix. This results in a saving of disk storage space and data processing time on the spectrometer. Finally pulse scheme D indicates how shift scaling can be achieved in a NOESY spectrum. Figure 2 shows portions of 500 MHz COSS and COSY spectra of sucrose in D20 solution recorded on Bruker AM 500 spectrometer at 25°C. The shift scaling factor is two in the COSS spectrum and thus the scale along the w1 axis is twice that along the w2 axis. The spectrum has been plotted so as to be able to compare with the COSY spectrum which has identical scales along both w1 and w2 axes. It is clearly seen that the peaks in the COSS spectrum are compressed along the w1 axis as compared with the peaks in the COSY spectrum. This must indeed be expected since the J values are not scaled in the COSS spectrum. In the event of close proximity of cross peaks in the COSY spectrum, such a compression leads to better separation of the cross peaks and hence to better resolution along the w1 axis as discussed above. In Fig. 2 the fine structure also appears to be slightly different in the diagonal peaks of the COSS spectrum and this is due to the introduction of some antiphase character into the diagonal peaks caused by the parameter A. The cross-peak components acquire an equivalent in-

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Hz

(JJ2

HZ

FIG. 2. Portions of absolute-value 500 MHz COSS (A) and COSY (B) spectra of sucrose in DrO solution recorded on a Bruker AM 500 NMR spectrometer. Both spectra are a result of 256 tr experiments with 1024 data points along the tr axis. The time-domain data have been processed identically in both cases.The scaling factor is two in COSS spectrum and thus the scale along the w, axis is twice that along the w2 axis. Digital resolution is 3.3 Hz along both axes in both spectra.

phase character. Figure 3 shows vertical cross sections through an isolated cross peak of the COSS and COSY spectra of sucrose, and the widths of the lines at half heights are also indicated in the figure. It is seen that the linewidth in the COSS spectrum is less than twice the width in the COSY spectrum although the scaling factor is 2. By considering these linewidths and Eq. [6], it can easily be estimated that the inhomogeneity contribution is only 30%. Since in larger systems, Tf relaxation during the period A will be an important deciding factor, the COSS scheme has also been tried on the protein molecule lysozyme

cosy1”: 19.8 Hz_ FIG. 3. Vertical cross sections through a cross peak in the COSS and COSY spectra of sucrose. The timedomain data are the same as used in Fig. 2. The linewidths are also indicated in the figure to show that the linewidths in COSS spectrum are scaled by a factor less than the shift scaling factor which is 2. The peaks marked * are due to experimental imperfections.

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which has a molecular weight of 14,000. The resultant spectrum with a scaling factor of 1.2 is shown in Fig. 4. It is seen that the spectrum shows a large number of cross peaks indicating the usefulness of the technique even in large systems. Figure 5 shows blowups of cross peaks from COSS and COSY spectra of a deoxytetradecanucleotide, Q’GAATTCCCGAATTC, plotted at identical contour levels. The improvement in the resolution in the COSS spectrum is clearly seen. Pulse scheme C is expected to yield similar resolution improvements over the SECSY experiment although not as pronounced as the COSS experiment, since the SECSY inherently has better resolution than the COSY spectrum. In the case of NOECOSS, sensitivity becomes a more serious problem and the scaling factor has to be very carefully chosen. Very recently Brown (13) has also described the idea of scaling using a pulse sequence 90”-(T-t,)-180”-(1 - k)t,-90”+ where 7 is a constant and k is a variable which determines the magnitude of shift scaling and J scaling. The shifts are scaled by a factor (k - 2), while the J values are scaled by a factor k. Such a pulse sequence does not allow arbitrary scaling of shifts without affecting the J values. For example, if k < 1, the shifts will be scaled up while the J values will be scaled down resulting in poor cross-peak intensities. Thus we feel that the pulse sequences described in this communication provide much more flexibility in scaling and are very suitable for work with large biological molecules.

0

I a

I 6

I

I

I

2

0

FIG. 4. Symmetrized absolute-value 500 MHz COSS spectrum (pulse scheme B) of lysozyme in 40 solution. The scaling factor was 1.2 resulting in a 600 Hz/ppm scale along the wr axis. The maximum value oft, was 43.5 ms. The time-domain data consisting of 5 12 t, and 2048 rZpoints were multiplied by unshifted sine functions prior to Fourier transformation. Digital resolution in the spectrum is 9.6 Hz along wz and 11.5 Hz along O, axis and experimental time was 9 h.

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l-4

8. -

1.8

7

P CB

2.2

5%

6-

2.6

3(

I: N I-&I I

IA I 6-4

1

6 I 6-O w2(w

I 56 m)

Hl'

I

I

I

64

60

5-6

w L,(ppm)

FIG. 5. Portions of COSS and COSY splectraof d-GAATTCCCGAATTC at 25°C. 5 12 tt values and 2048 values were used in each case. The scaling factor pi in the COSS spectrum is 1.5. Digital resolution in the COSY spectrum is 7.9 Hz and that in the COSS spectrum is 7.9 Hz along the w2 axis and 11.8 Hz along the wr axis. The numbering of the nucleotides increases from left to right. The assignment of the peaks given in the figure will be published separately. t2

ACKNOWLEDGMENTS The facilities provided by 500 MHz FT NMR National Facility at the Tata Institute of Fundamental Research are gratefully acknowledged. Anu Sheth is grateful to Professor G. Govil for being permitted to work at the Tata Institute of Fundamental Research. The authors are also grateful to Professor G. Govil and Dr. H. T. Miles (National Institutes of Health, Bethesda, Md.) for providing the tetradecanucleotide, d-GAATTCCCGAATTC. REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. II. 12. IS.

W. P. AUE, E. BARTHOLDI, AND R. R. ERNST, J. Chem. Phys. 64,2229 (1976). K. NAGAYAMA, ANIL KUMAR, K. W~~THRICH,AND R. R. ERNST, J. Mugn. Reson. 40,321 (1980). A. BAX AND R. FREEMAN, J. Magn. Reson. 44,542 (198 1). A. KUMAR, R. R. ERNST, AND K. W~THRICH, Biochem. Biophys. Res. Commun. 95, 1 (1980). S. MACURA, Y. HUANG, D. SUTEN, AND R. R. ERNST, J. Magn. Reson. 43,259 (198 1). R. V. HOSUR, M. R. KUMAR, K. B. ROY, T. Z. KUN, H. T. MILES, AND G. GOVIL, in “Magnetic Resonance in Biology and Medicine” (G. Govil, C. L. Khetrapal, and A. Saran, Eds.), p. 243, Tata McGraw-Hill, New York, 1985. M. H. LEVITT, G. BODENHAUSEN,AND R. R. ERNST, J. Magn. Reson. 58,462 (1984). A. KUMAR, R. V. HOSUR, AND K. CHANDRASEKHAR,J. Mugn. Resort. 60, 143 (1984). A. KUMAR, R. V. HOSUR, K. CHA~IDRASEKHAR,AND N. MURALI, J. Magn. Reson. 63,7 (1985). R. V. HOSUR, K. V. R. CHARY, AND M. RAVI KUMAR, Chem. Phys. Lett, 116, 105 (1985). A. WOKAUN AND R. R. ERNST, Chem. Phys. Lett. 52,407 (1977). 0. W. SORENSEN,G. W. EICH, M. H. LEVITT, G. BODENHAUSEN, AND R. R. ERNST, Progr. N&. Magn. Reson. Spectrosc. 16, 163 (1983). L. R. BROWN, J. Magn. Reson. 57, 513 (1984).