Selective manipulation of locked spins

JOURNAL

OF MAGNETIC

RESONANCE

96,363-369 ( 1992)

SelectiveManipulation of Locked Spins A. A.BOTHNER-BY,J.JIMENEZ-BARBERO, Department

of Chemistry,

Carnegie

Mellon

University,

AND J. A.CUSHMAN Pittsburgh,

Pennsylvania

1.5213

ReceivedJune 13, 1991 Spins,lockedalongan effectivefield, Cr,,, can be causedto nutate in this field and to achievethe statein whichthey are lockedantiparallelto HO0 by a smallphasemodulation of HI, at frequencyo, = rH,, . This phenomenonis analogousto the conventionalexperiment in the laboratoryframe in which spinsare invertedby applyinga RF field perpendicularto HO at the resonantfrequencyW, = y H, . Variationsof the experimentin which the direction of HOP is reversedelicit interestingspin behavior.This providesan interestingalternativemethodof performingCAMELSPINexperimentsand maybe useful in solventsuppression. 0 1992 Academic Press. Inc.

The applications of spin locking in NMR spectroscopy have burgeoned in the past decade, with vigorous development having occurr~ in the techniques and applications of the transverse Overhauser effect ( I ) and in variations of the homonuclear HartmannHahn experiment (2). The manipulation of the spins, preparation of prerequisite spin states, and readout of the resultant spin states have been performed primarily by using pulse sequences designed for the particular need. It is interesting, however, especially in the light of the increasing use of selective excitation in multidimensional spectroscopies ( 3- 7)) to explore how the spins in a spin-locked ensemble might be selectively manipulated. A method for doing this has been developed which bears a strikingly simple analogy to the basic NMR method of selectively exciting spins in the static field & . The basic NMR method involves applying a weak amplitude-modulated field Hi at right angles to h&. The modulation frequency of H, is oi = YHi, where Hi = Ho( I- bi), accounting for the shielding of the particular set of spins. Application of H1 causes the nuclei to tip away from Ho and to reach an antiparallel orientation after time t = T/YH,, provided that yH, 9 1 / T, , 1/ T2. The analogous experiment may be performed on locked spins in the frame rotating at u. = yHO. Under these conditions each set of spins is locked along an effective field Ho,, given by I&, = H,i + QiHok,

111

where ci is zero if the spin is exactly resonant at wo, and i , j , and k are the unit vectors along the X, y, and z axis of the rotating frame. The strength of Hop is given by [H! + ufH$p2, and the spins may be tipped away from this axis by applying an amplitudemodulated field, H,, , at right angles to Hop, with modulation frequency w, = -r&P. The field HI, will be at right angles to H,,, if it is applied along j. The spins will tip 363

0022-2364192$3.00 Copyright 0 1992 by Academic Ress, Inc. AU rights of reproduction in any form I-WI-~.

364

BOTHNER-BY,

JIMENEZ-BARBERO,

AND

CUSHMAN

away from Hop and achieve an antiparallel orientation to it at t = ?r/ yH,,, provided that yH,, P 1/TIP, 1 / Tzp. Whether in the HO or HOPframes, the application of an off-resonant exciting field will result in nutation of the spin relative to the quantization axis, with a lesser effect as the resonant offset is increased. Selectivity in each case increases as the strength of the exciting field is reduced. For locked spins, the spread in resonance frequencies is also reduced by a factor ajHo/ [ H: + a f Hi] “*. Thus, the weaker the locking field, the more selective the process. Various methods might be considered to generate the required exciting field HI, j( cos wi,,t). It could be produced from a second RF transmitter with phase in quadrature to the first by amplitude modulation at wip. A simpler method is to phase modulate the primary transmitter, using a small phase angle 4 and a modulation frequency tiip. This will cause the field in the rotating frame to be given by H,( 1 - i4’cos2Wit)i

+ H,(c#J cos wit)j + aHok.

[21

The small term in ti* may be dropped, and the result is the sum of the original Hi and the desired HI,. In our experiments, we have used square-wave phase modulation rather than sinusoidal modulation. EXPERIMENTAL

DEMONSTRATION

The sequence employed is Preparation-SL,(

71) -[ Px++, &I,-SL,(

T*) -( focusing) -Acquisition.

[3]

For the sake of producing the parallel locked state, the preparation may be a simple 90; pulse, or the 90,“-225,” -71270 sequence (8), which aligns each spin along its effective field. The focusing sequence (7 9,.-270,” ), if used, will give higher signal intensities by rotating the locked spins into the xy plane (8) before acquisition. The initial spin-locking period is a trim pulse, which allows any imperfectly aligned magnetization to dephase and disappear. The modulation [ ,&+4, ,&IN is for the purpose of inverting the spin with respect to HO,. On resonance, B will be 180°, since one complete cycle of phase modulation produces a 360” rotation about HI, and this corresponds to phase modulation with frequency yHO,,. An alternative way to regard the inversion process is to follow the behavior for the individual phase pulses. Assuming the spin to be on resonance, it is aligned along the x axis (0”) at the beginning of the sequence. The first phase-shifted pulse will rotate it to the xy plane +24 from X. The succeeding x pulse will rotate it to -24. The second phase-shifted pulse will rotate it etc. The total number of phase-shifted pulses required, N, is thus 7r/24. to +4f#J, . . ...) This is also the ratio of yH,/yH,,. Off-resonance, /I is given by 180” HI /HOP. The second trim pulse is for the same purpose as the first. However, it may also be lengthened and the resulting spectrum examined for evidence of transverse NOE effects ( I ) . The result of applying sequence [ 31 to a sample of mesitylene in C6D12 at 296 K is shown in Fig. 1. The carrier was centered on the methyl peak and selective inversion was produced by application of phase-shift pulses with length equal to that of 180” pulses. An HI field strength of 2500 Hz was used. The phase shift employed was 10”. Spectra resulting from different H,, pulse lengths (or number of phase-shift pulses) are shown. The reason for the rapid decrease in intensity is a short T2p, or transverse

SELECTIVE

MANIPULATION

OF LOCKED

SPINS

365

4Isi4

4

FIG. 1. The result of applying sequence [ 31 to a sample of mesitylene in CsD,2 at 296 K. The carrier was centered on the methyl peak and selective inversion was produced by application of phase-shift pulses with length equal to that of 180” pulses. An HI field strength of 2500 Hz was used. The phase shift employed was 10”. N varies between 0 and 34 in steps of 2 units. The central peak is from residual water in the D20gelatin matrix.

relaxation in the rotating frame. The dominant cause for this is inhomogeneity in the RF field, which causes I&, to be inhomogeneous and creates a large 1 / T$ contribution. This fact prevents achievement of complete inversion with very small 4 or HI,. The homogeneity can be improved by using a microsample positioned in the centre of the RF probe, and this did improve the experiment, but only by a factor of two ( 4 smaller by a factor of two could be used). The microsamples were prepared by introducing a droplet of sample ( 10% of mesitylene in C6D12) by means of a Pasteur pipette into a warm 1% solution of gelatin in D20 contained in a standard 5 mm NMR sample tube. The droplet assumed a nicely spherical shape as a result of surface tension, while the gelatin solution set and immobilized the droplet. By applying the phase-shift pulses with the frequency yI&, corresponding to an offset of 1000 Hz, i.e., /3 = 167”, we could demonstrate selective inversion of the methyl group when the carrier was positioned 1000 Hz to higher field of this signal, as shown in Fig. 2, which also presents the result of applying this scheme to on-resonance magnetization. REFOCUSING

The effects of the inhomogeneity in I& in conventional experiments may be in part overcome by using echo techniques. Similarly, the effects of 1/ TT, may be combatted using rotary echoes ( 9). We have explored a number of avenues for this. We consider first the modified phase-pulse sequence [ P-X+ti, &IN with small 4 angle. For spins

366

BOTHNER-BY.

JIMENEZBARBERO,

AND CUSHMAN

A

B

t4 E Ppm N FIG. 2. (A) The result of applying the phase-shift pulses with the frequency yH,,, corresponding to an offset of 1000 Hz, i.e., /3 = 167”, when the carrier was positioned 1000 Hz to higher field of the methyl group signal. (B) The result of applying the same scheme to on-resonance magnetization.

exactly on resonance, this will also result in inversion after 7r/24 cycles, but the effects of T$ are suppressed, as in the CPMG experiment ( ZU, II). Figure 3 shows a set of spectra with increasing N and using a phase shift of 2“. A phase shift as small as 0.5 o can be used in our spectrometer. However, off-resonant spins are strongly affected by the phase modulation, even with 4 = 0”. This is most easily explained by considering

FIG. 3. The result of applying the refocusing sequence in the same conditions of Figure I. N varies between 0 and 32 in steps of 1 unit.

SELECTIVE

MANIPULATION

OF LOCKED

SPINS

367

the behavior of the magnetization components in the xz plane as a function of time. The trajectory is shown in Fig. 4. The magnetization is locked initially along H&, as represented by the vector marked 1. Switching to Hi& will cause the magnetization to precess around H;,, to the position marked 2. Returning to H&, will cause precession to the position marked 3. The continuation of these phase shifts will result in a motion in which the magnetization oscillates rapidly between positions approximately parallel to H& and H, . The inhomogeneity in Hop will cause the rapid disappearance of this cohe:rence. Numerical simulations show that even a 5% inhomogeneity in Hop is enough to cancel off-resonance magnetization which is 500 Hz away from the carrier in less time than that necessary for inversion of the on-resonance magnetization. This behavior creates an interesting way to observe ID CAMELSPIN spectra. Two sets of spectra are obtained with phase-shift pulses [ 180 DX++,180,“]Nand[180?,, 180,“lN.Nand$ are chosen to cause inversion in the resonant line in the first case and none in the second. The second trim pulse in [ 31 is lengthened to permit transverse relaxation. Subtraction of the second spectrum or FID from the first one will give a CAMELSPIN spectrum. Two favorable results are achieved: (A) The subtraction eliminates the steady-state contribution to the spectra, giving only the time-dependent cross-relaxation signals. Nevertheless, Hartmann-Hahn coherence can also be transferred as observed in the regular experiment (8). (B) Interfering peaks, such as solvent, are suppressed. Figure 5 shows a series of 1D spectra taken in this way. The residual water is almost completely suppressed, although the experiment is extremely dependent on spectrometer stability. A phase shift of 2” was used with an RF field of 2500 or 3200 Hz. Other modifications of the modulation sequence can be used in order to reduce the effects of the inhomogeneity. The sequence [ fl...i+g, p--, or+@, &IN produces results

FIG. 4. The trajectory of off-resonant spins as a function of time when the refocusing sequence is used (see text for discussion).

36%

BOTHNER-BY,

JIMENEZ-BARBERO,

AND CUSHMAN

H-l ,

+4 I n

’ L-

1--4

FIG. 5. One-dimensional CAMELSPIN spectra taken using the phase-modulation sequence. In each case the normal 1D spectrum is displayed above and the CAMELSPIN difference spectrum is shown below. (A) The anomeric B-H-1 proton of glucose in a 75:25 mixture of H,O:DzO is inverted. Enhancements are observed for the nearby H-2, H-3, and H-5 @protons. Hartmann-Hahn transfer is also observed for the (YH-l and a-H-2 protons for the particular mixing time used (300 ms). (B) The anomeric P-H-1 ’ proton of the galactose moiety of the disaccharide Gal+I, 4-Xyl-&OMe in DMSO-d, with some residual water was inverted. Nuclear Overhauser effects are observed for protons H-3’ and H-5’ of the galactose residue and H4 and H-5 of the xylose moiety. (C) The anomeric B-H- 1’ proton of thymidine is inverted. Nuclear Overhauser enhancements are observed for the base H-6 proton and H-2’ and H-4’ on the sugar ring. In all three cases the water is almost completely suppressed. A phase shift of 2’ was used with an RF field of 2500 Hz for (A) and 3200 Hz for ( B ) and (C) . A second trim pulse of 300 ms was used in every case.

identical to those of the sequence described previously, obviously with half the number of cycles. On the other hand, the sequence [ pWx+@,p-,]N[ &.+e, &.Jv does not eliminate completely the effects of the inhomogeneity, while maintaining the strong influence on the precession of the off-resonant spins. ACKNOWLEDGMENTS The spectra were obtained in the 620 MHz spectrometer at the NMR Facility for Biomedical Studies at CMU, supported by NIH Grant RRO0292. This work was also supported by NIH Grant DK 16532. J.J.-B. thanks the Ministerio de Education y Ciencia of Spain (D.G.I.C.Y.T.) for a fellowship.

SELECTIVE

MANIPULATION

OF LOCKED

SPINS

369

REFERENCES 1. A.. A. B~THNER-BY,

R. L. STEPHENS, J. LEE, C. D. WARREN, AND R. W. JEANLOZ, J. Am. Chem. Sot. 106,811(1984). 2. A. BAX AND D. G. DAVIS, J. Magn. Reson. 63,207 ( 1985). 3. W. S. WARREN AND M. S. SILVER, in “Advances in Magnetic Resonance” (J. S. Waugh, Ed.), Vol. 12, p. 248, Academic Press, New York, 1988. 4. R. BRUSCHWEILER, J. C. MADSEN, C. GRIESINGER, 0. W. SORENSEN, AND R. R. ERNST, J. Mugn.

Reson. 73,380 (1987). 5. 6. 7. 8. 9. 10.

Il.

GRIESINGER, 0. W. SORENSEN, AND R. R. ERNST, J. Mugn. Reson. 73,574 ( 1987). CAVANAGH, J. P. WALTHO, AND J. REELER, J. Mugn. Resort. 74, 386 (1987). EMSLEY AND G. BODENHAUSEN, J. Am. Chem. Sot. 113,3309 ( 1991). A. B~THNER-BY AND R. SHLIKLA, J. Magn. Reson. 77, 524 ( 1988). I. SOLOMON, Phys. Rev. Left. 2, 301 ( 1959). 1-I. Y. CARR AND E. M. PURCELL, Phys. Rev. 94,630 ( 1954). !j. MEIBOOM AKD D. GILL, Rev. Sci. Instrum. 29, 688 ( 1958). C. J. L. A.