Time dependence of 13C-13C magnetization transfer in isotropic mixing experiments involving amino acid spin systems

Time dependence of 13C-13C magnetization transfer in isotropic mixing experiments involving amino acid spin systems

JOURNAL OF MAGNETIC RESONANCE 90,452-463 ( 1990) Time Dependence of 13C-13C Magnetization Transfer in Isotropic Mixing Experiments Involving Amin...

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JOURNAL

OF MAGNETIC

RESONANCE

90,452-463

( 1990)

Time Dependence of 13C-13C Magnetization Transfer in Isotropic Mixing Experiments Involving Amino Acid Spin Systems HUGHL.EATON

AND STEPHENW.FESIK

Pharmaceutical Discovery Division, Abbott Laboratories, D-47G, AP9. Abbott Park, Illinois 60064 AND

STEFFENJ.GLASERANDGARYP.DROBNY Department of Chemistry, University of Washington, Seattle, Washington 98195 Received March 12, 1990 The time dependence of oC- “C coherence transfer for the aliphatic portions of amino acid side chains has been examined by calculating ideal coherence-transfer functions. These results were compared to experimentally determined cross- and diagonal-peak intensities obtained from a series of 2D 13CTOCSY experiments acquired with 12 mixing times ranging from 0.0 to 34.2 ms on a mixture of uniformly ‘%-labeled amino acids. In general, the calculated coherence-transfer functions agreed. Unlike ‘H- ‘H TOCSY experiments, the time dependence of 13C- “C coherence transfer for these spin systems is simple and well characterized due to the large and conformationally independent ‘%- 13Cspin-spin couplings. Spectra obtained at mixing times of 8, 14, 20, and 28 ms cover most features ofthe coherence-transfer functions such as vanishingly small cross peaks and local maxima and minima. These features, along with the fact that W-“C coherence transfer takes place in times which are short compared to relaxation times typical for small proteins, make this experiment ideal for the assignment of protein “C spectra, which in turn aids in the ‘H NMR assignment, 0 1990 Academic press, tnc. An important step in assigning NMR signals is the identification of nuclei that are scalar coupled ( I). For assigning proton resonances in small proteins, this is typically accomplished through 2D coherence-transfer experiments such as COSY (2), RELAY ( 3, 4)) or TOCSY ( 5- 7). For larger proteins ( > 10 kDa) , however, the broad linewidths of the NMR signals limit the number of proton-proton coherence-transfer steps that can be obtained due to the rapid decay of proton magnetization during the relatively long time required for coherence transfer involving small proton-proton J couplings. In contrast to the small, conformationally dependent proton coupling constants, one-bond 13C- 13CJcouplings are large (235 Hz) and uniform (8), resulting in efficient coherence transfer between 13C nuclei in a relatively short period of time. Thus, as demonstrated by Markley and co-workers ( 9-Z I ), 13C- 13Ccorrelations can be obtained in larger ( 13C-labeled) proteins (> 10 kDa), using a 2D double-quantum experiment, and can be used to assign 13C resonances of the amino acid spin systems. From the 13CNMR assignments, the proton resonances can be assigned using ‘H- 13Ccorrelations 0022-2364190 $3.00 Copyright 0 I990 by Academic Press. Inc. All rights of reproduction in any form reserved.

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obtained in separate 2D experiments. More recently, 2D and 3D NMR experiments which rely on 13C- 13C and 13C- ‘H chemical-shift correlations in a single experiment have been described ( 12, 13). In one approach ( 13) magnetization transfer between 13Cnuclei occurs in a 13CTOCSY experiment by isotropic mixing followed by transfer of this information to the protons. Because of the large magnitude of 13C- 13C and 13C- ‘H couplings ( ’ Jcc > 35 Hz, ’ JCH > 125 Hz) coherence transfer can be effected in a short period of time, and these methods are therefore useful in assigning the “C and ‘H signals of amino acid spin systems in high molecular weight biopolymers. In addition, since isotropic mixing (5-7) is used for the 13C- 13C coherence-transfer step (Z3), net 13Cmagnetization transfer occurs and absorption peak lineshapes are possible, resulting in high sensitivity and enhanced resolution. In order to optimize the 13C isotropic mixing experiments, it is important to determine the mixing time dependence of the carbon-carbon correlations for the spin systems of interest. Since one-bond ‘3C-13C coupling constants are regular and conformationally independent, this information may suggest assignment strategies based on the mixing time dependencies. In this paper, we have examined the time dependence of 13C-13C coherence transfer in 13C isotropic mixing experiments of the amino acid spin systems by calculating the ideal coherence transfer functions of the cross-peak and diagonal-peak intensities as functions of mixing time. We have also compared the results from these calculations to experimentally determined cross and diagonalpeak intensities measured from a series of 13CTOCSY experiments acquired at different mixing times on a mixture of 13C-labeled amino acids. METHODS

The integrated intensity of a cross peak between two spins k and 1 as a function of mixing time T,ix is proportional to the coherence-transfer function Tk,‘( T,ix), where (Yis x or y if transverse coherence is transferred, or z for longitudinal coherence transfer. The coherence-transfer function is defined as

the expectation value of Zlaas a function of the mixing time r,‘x if the density operator p( 0 ) at the beginning of the mixing time is prepared to be Zka. Under the ideal isotropic mixing Hamiltonian the x, y, and z coherence-transfer functions are identical and abbreviated Tk’. However, they can differ if real pulse sequences are used ( 14, 15). The intensity of a diagonal peak corresponding to spin 1 is proportional to T”( 7,ix). We have used the simulation program SIMONE ( 14, 1.5) to calculate the 13C coherence-transfer functions for all amino acid spin systems. The program allows us to simulate coherence transfer under the ideal isotropic mixing Hamiltonian X; = c Jk,ZkZl. Alternatively, coherence-transfer functions can be calculated under the effective Hamiltonian ti& created by practical pulse sequences. Relaxation effects during the mixing time were neglected in the computer simulations and all 13C- 13C coupling constants between aliphatic 13C spins were assumed to be 35 Hz. A mixture of amino acids uniformly labeled (99%) with 13C was kindly provided by Cambridge Isotope Laboratories (Cambridge, Massachusetts). The NMR sample was prepared by dissolving 10 mg of the amino acid mixture in D20/DMSO-d6 (2/

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1, v/v). This solvent was used to increase the viscosity of the solution and shorten the relaxation times ( 16). All NMR spectra were acquired on a Bruker AM500 NMR spectrometer at 30°C using a 5 mm dual 13C/‘H probe. The pulse sequence used to acquire the 2D 13C TOCSY spectra was 90,” --t,-(MLEV-17)--90: -77,-908”-(acquire)B in which 6 = x, y, -x, -y. Quadrature detection was obtained in tr by shifting the phase of the first pulse by 90” ( 17) and processing the data by the method of States et al. ( 18). A BSV3 (Bruker Instruments) CW amplifer connected to the observe channel was used for the “C pulses and the MLEV- 17 mixing scheme (6), which produced an RF field strength VRF = yB,/2a of 11 kHz, corresponding to a 90” pulse duration of 23 ps. Proton decoupling was applied throughout the experiment using a WALTZ-16 sequence ( 19). In order to allow for the recovery of the preamp, a z filter (90”- 7,90”) was added to the end of the pulse sequence (7, = 7 ms). Several 2D 13C TOCSY data sets were collected as a function of the MLEV-17 mixing time (0, 1.5, 4.5, 5.9, 7.4, 10.4, 13.3, 16.3, 19.2, 23.7, 28.1, and 34.2 ms) using a relaxation delay of 1.8 ms. The data were collected as 128 complex tl values of 2048 points over a spectral width of 7575 Hz (aliphatic region) using 32 acquisitions and four dummy scans. All spectra were processed in the format of the RNMR program of Dr. D. R. Hare with in-house software utilizing a CSPI minimap array processor interfaced to a VAX 8350 computer. A shifted (60” ) sine-bell window function was applied in tl and t2. RESULTS

In contrast to ‘H spectra, in which the chemical shifts of proteins typically range between 0 and 10 ppm, the resonances in 13C spectra are dispersed over a range of more than 150 ppm. This has important consequences because practical multiplepulse sequences like MLEV- 16 (20), MLEV-17 (6), WALTZ-16 ( 19), or DIPSI(21) effect coherence transfer through isotropic mixing or spin locking only within a limited frequency range. This active range is typically on the order of or smaller than the RF frequency VRF = yBI/2?r (14). If, in a spin system consisting of n spins, the chemical shifts of m spins fall well outside of this active range, then the coherencetransfer functions can be approximated by calculating coherence transfer within the reduced spin system of the n - m remaining spins. If, in addition, the error terms in the effective Hamiltonian created by the multiple-pulse sequence are small within the active frequency range, the effective Hamiltonian tice approaches the ideal isotropic mixing Hamiltonian %$ of the reduced spin system. Calculating coherence-transfer functions under the ideal isotropic mixing Hamiltonian ti; has the advantage of being completely independent of experimental parameters, but the accuracy of this approximation depends on the actual chemical shifts, the RF power, and the pulse sequence used. With a field strength of 11.7 T and the irradiation frequency in the center of the 13C aliphatic regio n, the aliphatic resonances fall within a range of 54 kHz, whereas the aromatic 13C spins are more than 10 kHz and the carbonyl spins more than 16 kHz off resonance. The MLEV- 17 mixing sequence effects coherence transfer only within a relatively limited frequency range of +0.3vRF (22), and thus, with an RF power of 11 kHz, coherence is transfered between aliphatic 13Cspins but not between

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aliphatic and carbonyl, carboxyl, or aromatic spins. This is illustrated in Fig. 1 for the T"@coherence-transfer function of a fictitious Ala-type spin system under the effective Hamiltonian &r created by an MLEV- 17 sequence for increasing offset of the carbonyl resonance. Here, for offsets larger than 12 kHz the resulting coherence-transfer functions are virtually identical to the ideal isotropic mixing case for the reduced spin system. The reduced spin systems of amino acids, which are obtained by excluding the carbonyl, carboxyl, and aromatic 13C spins, can be condensed into six distinct coupling topologies, which are depicted in Fig. 2. The reduced ’ 3C spin system of glycine consists only of the uncoupled C, spin which does not give rise to any cross peaks. We have calculated ideal coherence-transfer functions corresponding to the intensities of the cross and diagonal peaks as a function of mixing time for the reduced spin systems of Fig. 2. In the simulations the mixing time was varied between 0 and 60 ms. Experimental coherence-transfer functions were obtained by integrating the intensities of all cross and diagonal peaks in experimental 2D 13C TOCSY spectra sampled at 12 different mixing times between 0 and 34.5 ms. A representative 2D TOCSY spectrum of the amino acid mixture with a mixing time of 16.3 ms is shown in Fig. 3. There are a number of overlapping diagonal peaks, but most cross peaks are well resolved because of their dispersion in two frequency dimensions. As the concentrations of each amino acid in the solution differ, we normalized the experimental cross- and diagonal-peak intensities for each amino acid spin system relative to the average intensity of its diagonal peaks at r = 0 ms. Only well-resolved diagonal peaks were taken into account in the normalization process to avoid biasing due to overlapping peaks. The theoretical and experimental coherence-transfer functions are summarized in Fig. 4. Only one simulated coherence-transfer function is shown for each pair of spins,

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FIG. 1. Simulated coherence-transfer functions T”” of a fictitious Ala-type spin system consisting of three spins C’, C,, and CB with J(C’C,) = 55 Hz and J( C&J = 35 Hz. The heavy and fine solid curves represent coherence-transfer functions under the ideal isotropic mixing Hamiltonian for the full and reduced Alatype spin systems, respectively. Also shown are simulated coherence-transfer functions under an MLEV- I7 sequence with vrr = 11 kHz and increasing offsets of the C’ resonance of 1 kHz (open circles), 4 kHz (filled circles), 5 kHz (crosses), 6 kHz (filled squares), and 12 kHz (open squares). The resonances of C, and C,, are assumed to be on resonance.

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FIG. 2. The coupling topologies for the reduced “C amino acid spin systems. (A) Two-spin system corresponding to the coupled C, and C, spins of Ser, Cys, Asn, Asp, Phe, Tyr, His, Trp, and Ala. (B) Linear three-spin coupling topology corresponding to the C,, C,, and C, spins of Glu, Gln, Met and Thr. (C) The star-like four-spin coupling topology of the Val C,, C,, C,, and C,, spins. (D) Linear four-spin topology corresponding to the C, , CB, C, , and C, spins of Pro and Arg. ( E ) Linear five-spin coupling topology of the C, to C. spins of Lys. (F) The forked five-spin coupling topology of Leu and Be. Note that the base of the fork corresponds to the C,, C,, and C, spins of Leu, but to the C,, C,, , and C, spins of Be. The fork tines are formed by C,, and C+ in the Leu spin system but by C, and C,? in the Ile spin system.

kl. The symmetry of the mixing process results in the coherence-transfer functions Tk’( Tmix) and tIk( 7,ix) being identical. This is reflected in the global symmetry of the 2D TOCSY spectra with respect to the main diagonal (23). The intensities of symmetryrelated cross peaks at positions (&, 61) and (&, I&) were averaged for the experimental coherence-transfer functions in Fig. 4. In Fig. 4 we included experimental coherencetransfer functions only if the corresponding cross or diagonal peaks are well resolved in the 2D TOCSY spectra to avoid distortions as a result of overlapping peaks. In Fig. 4A experimental and ideal coherence-transfer functions are shown for systems consisting of two coupled spins (see Fig. 2A). The ideal coherence-transfer functions for two spin systems are well known (5). The simulated coherence-transfer function T’* reaches its first maximum at a mixing time of 1/ (2Jkl). Experimental cross-peak intensities are shown for a serine and an alanine spin system. The diagonal (Co/C& peak of Ser overlaps with the (WC,) diagonal peak of Thr, and thus its experimental coherence-transfer function was not included in Fig. 4A. Due to the symmetry of the coupling topologies of Fig. 2 and the uniform coupling constants, several ideal coherence-transfer functions are identical for each reduced amino acid spin system. In the case of the two-spin coupling topology, the calculated coherence-transfer functions corresponding to the two diagonal peaks are identical ( T” = T22). However, as discussed below, the symmetry may be broken as a result of varying experimental coupling constants and error terms in the effective Hamiltonian M&t created by the multiple-pulse sequence. Therefore, in Fig. 4 we display all these identical ideal coherence-transfer functions seperately to allow comparison of the potentially differing experimental coherence-transfer functions. Figure 4B summarizes the theoretical and experimental results for a linear threespin system (see Fig. 2B) with T l1 = T33 and T’* = T23. Experimental cross- and diagonal-peak intensities as a function of mixing time are presented for glutamic acid and threonine. Due to the symmetry of the star-like four-spin coupling topology of

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Fig. 2C, we have T 11 = p = 7744, 7712 = l-23 = l-24, and T13 = T14 = ~24. Ideal coherence-transfer functions for this coupling topology are shown in Fig. 4C together with the experimental coherence-transfer functions of valine. For the linear four-spin topology of Fig. 2D, T” = T44, T12 = T34, T13 = T24, and T22 = T33. Experimental peak intensities as a function of mixing time are shown for proline and arginine together with the calculated coherence-transfer functions in Fig. 4D. Figure 4E shows the results for the linear five-spin coupling topology shown in Fig. 2E, whose symmetry results in T 11 = i-55 T12 = T45 7-13 = 7-35 T'4 = 7-25, 7-22 = T44, and T23 = T34 and which is realized’by lysine. Finally, for the forked five-spin coupling topology of Fig. 2F, we have T’4 = T15 T24 = T25, T34 = T3’, and T44 = Ts5. Even though the side chains of leucine and isoleucine are very distinct, their

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Leu but to the C, and Cy2 spins for Ile. Experimental and theoretical coherencetransfer functions are shown in Fig. 4F. The simulated and experimental coherence-transfer functions match reasonably well. One obvious source of the small differences between the two functions is variation of the true values of J, which can range from 32 to 35 Hz (8), from the 35 Hz used in the calculations. Another possible source of discrepancy, relaxation during the mixing period, is not expected to play a dominant role because of the relatively short mixing

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times that were utilized in these experiments. Experimental artifacts and noise could also complicate comparisons between experimental and calculated coherence-transfer functions. In the TOCSY spectrum for T = 1.5 ms the intensities of the diagonal peaks are between 30 and 60% larger than those of the diagonal peaks at 7 = 0 ms. The reason for this artifact is unclear. No attempt was made to rescale these intensities; however, for this mixing time several normalized diagonal-peak intensities fell outside of the plot range in Fig. 4. For the relatively short mixing time of r = 1.5 ms most cross-peak intensities are still very small and a similar increase in their intensities had little effect on the experimental coherence-transfer functions. A similar but smaller spike common to all experimental coherence-transfer functions occurred for the data points at T = 7.4 ms. However, these relatively minor artifacts cannot fully explain the observed deviations between the experimental and theoretical coherence-transfer functions. A likely cause of the remaining deviations is the use in the calculations of the ideal isotropic mixing Hamiltonian X; rather than the effective Hamiltonian && created by the MLEV17 sequence. The effective Hamiltonian created by a multiple-pulse sequence depends on the actual pulse sequence, the chemical shifts bk, the irradiation frequency, the coupling constants Jkj, the RF field strength YRF = yB, / 27~, and the pulse and flip angle imperfections like phase and flip angle errors (2.5, 24, 25). Typical error terms in the case of two coupled spins are linear and bilinear in spin operators, corresponding to incompletely suppressed chemical shifts or reduced effective coupling constants. In general, error terms in the effective Hamiltonian influence the coherence-transfer amplitudes and frequencies (14). The experimental coherence-transfer frequency between

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the C, and CBspins of Ala in Fig. 4A is reduced by about 20% relative to the coherencetransfer frequency under the ideal isotropic mixing Hamiltonian. Simulated coherencetransfer functions under the effective Hamiltonian of the reduced spin system &?& created by MLEV- 17 with the given RF power and the relatively large chemical shift difference between the Ala C, and CB spins show a similar reduction in the coherencetransfer frequency. Another example in which the effective MLEV-17 Hamiltonian results in a better match between experimental and simulated curves is found in the coherence-transfer functions of valine shown in Fig. 4C. Under the ideal isotropic mixing Hamiltonian X; for the reduced spin system of valine (Fig. 2C), the coherencetransfer functions Tay, Tay', and TTY’ are identical. However, the symmetry of the ideal J-coupling topologies of Fig. 2 can be broken because of the dependence of the error terms in the effective Hamiltonian on the chemical shifts 8k. Under the effective Hamiltonian .# & created by MLEV- 17 the simulated coherence-transfer functions TaYand TaY'are less intense than TTY',which is a much better match to the experimental data (Fig. 5). These two examples indicate that most deviations between the calculated and experimental coherence-transfer functions in Fig. 4 are due to error terms in the effective Hamiltonian. The failure of MLEV- 17 to yield completely ideal coherence-transfer functions could be alleviated by using a more stable mixing sequence such as DIPSI- (21). SUMMARY

We have determined the time dependence of 13C-13C coherence transfer in isotropic mixing experiments for the spin systems which represent the aliphatic portions of

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7-7,i z becl FIG. 5. Coherence-transfer functions Ta7, TRY’, and Y’ for a reduced VaI spin system. The solid line represents coherence-transfer functions under the ideal isotropic mixing Hamiltonian W, of the reduced spin system with J(C&.) = J(C&,) = J(C&!,) = 35 Hz. The three coherence-transfer functions are identical due to the symmetry of the coupling network. The dashed lines show simulated coherence-transfer functions under the effective Hamiltonian .W& created by the MLEV-17 sequence with an RF power of 11 kHz and the chemical shifts 6, = 2835 Hz, & = -1039 Hz, 6, = -2337 Hz, and ?+ = 25 19 Hz. Error terms in the effective Hamiltonian *& of the reduced vahne spin system lift the symmetry of the coupling network and the coherence-transfer functions are dissimilar. The circles represent experimental cross-peak intensities (see Fig. 4C).

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amino acid side chains. The calculated coherence-transfer functions match well with those determined experimentally using the MLEV- 17 mixing sequence, with deviations between experimental and calculated functions attributed to error terms in the effective Hamiltonian produced by the MLEV-17 sequence. Compared to ‘H- ‘H TOCSY, 13C- 13CTOCSY offers two main advantages. First, typical 13C- 13Ccoupling constants of 35 Hz are significantly larger than ‘H- ‘H J couplings, which allows multiple-step coherence transfers throughout the complete reduced spin system within a time which is small relative to typical relaxation times of small proteins. Second, 13C- 13C couplings are conformationally independent which, along with the simple and symmetric reduced 13Ccoupling topologi es, y’relds a relatively small and well-characterized set of coherencetransfer functions. (This is in sharp contrast to the plethora of possible coherencetransfer functions for ‘H- ‘H TOCSY experiments (15). The 13C- 13C coherencetransfer functions are so characteristic and well defined that they may be used in the assignment of resonances. A relatively small number of TOCSY spectra at different mixing times seems to be sufficient to discriminate between most coupling topologies. A strategy for the assignment of protein side chains would include, at a minimum, one spectrum with 8 ms mixing time (to show most one-step 13C- r3C coherence transfers) and one spectrum with 20 ms mixing time (to show most of the remaining cross peaks in the reduced spin systems). The addition of spectra with mixing times of 14 and 28 ms would cover most of the characteristic features of the 13C- 13C coherence-transfer functions such as vanishingly small cross-peak intensities and local maxima and minima in the coherence-transfer functions. The information gained in a 13C- 13C TOCSY can then be used to assign proton resonances indirectly by the use of a separate heteronuclear correlation experiment, or in more direct fashion by including the 13C- 13C TOCSY as a component of a longer pulse sequence which transfers information directly to protons (13). Difficulties which remain in the application of r3C- 13CTOCSY to protein resonance assignment are caused by the limited chemical-shift range covered by current mixing schemes if the RF power is limited. In order to discriminate between amino acids that share the same reduced coupling topology, it is necessary to correlate aliphatic 13C spins to aromatic carbonyl and carboxyl 13C spins. One approach to this problem is to design new multiple-pulse sequences that transfer coherence over a larger range of chemical shifts for a given RF power. ACKNOWLEDGMENTS Support for this work comes in part from NIH under Grant RO 1 CA 45643-O 1A 1 and from NSF under Grant DMR-8700081 (G.P.D.). H.L.E. is a postdoctoral associate supported by NIH under Grant UOl AI 27220-o 1. REFERENCES 1. K. WOTHRICH, “NMR of Proteins and Nucleic Acids,” Wiley, New York, 1986. 2. W. P. AUE, E. BARTHOLDI, AND R. R. ERNST, .I. Chem. Phys. 64,2229 ( 1976). 3. G. EICH, G. BODENHAUSE, AND R. R. ERNST, J. Am. Chem. Sot. 104,373l (1982). 4. A. BAX AND G. DROBNY, J. Magn. Reson. 61,306 ( 1985 ). 5. 6. 7. 8.

L. A. R. V.

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9. W. M. WESTLER, M. KAINOSHO, H. NAGAO, N. TOMONAGA, AND J. L. MARKLEY, J. Am Chem. Sot. 110,4093 (1988). 10. B. J. STOCKMAN, W. M. WESTLER, P. DARBA, AND J. L. MARKLEY, J. Am. Chem. Sot. 110, 4095 (1988). Il. B. J. STOCKMAN, M. D. REILY, W. M. WESTLER, E. L. ULRICH, AND J. L. MARKLEY, Biochemistry 28,230 (1989). 12. L. E. KAY, M. IKURA, AND A. BAX, J. Am. Chem. Sot. 112,888 (1990). 13. S. W. FESIK, H. L. EATON, E. T. OLWNICZAK, E. R. P. ZUIDERWEG, L. P. MCINTOSH, AND F. W. DAHLQUIST, J. Am. Chem. Sot. 112, 886 (1990). 14. S. J. GLASER AND G. P. DROBNY, in “Advances in Magnetic Resonance” (W. S. Warren, Ed.). Vol. 14, p. 35, Academic Press, San Diego, 1990. IS. M. L. REMEROWSKI, S. J. GLASER, AND G. P. DROBNY, Mol. Phys. 68, 1191 ( 1989). 16. S. W. FESIK AND E. T. OLEJNICZAK, Magn. Resort. Chem. 25, 1046 ( 1987). 17. L. MOLLER AND R. R. ERNST, Mol. Phys. 38,963 ( 1979). 18. D. J. STATES, R. A. HABERKORN, AND D. J. RUBEN, J. Magn. Reson. 48,286 ( 1982). 19. A. J. SHAKA, J. REELER, T. FRENKIEL, AND R. FREEMAN, J. Magn. Reson. 52, 335 (1983). 20. M. LEVITT, R. FREEMAN, AND T. FRENKIEL, J. Magn. Reson. 47, 328 ( 1982). 21. A. J. SHAKA, C. J. LEE, AND A. PINES, J. Magn. Reson. 77,274 ( 1988). 22. S. SUBRAMANIAN AND A. BAX, J. Magn. Reson. 71,325 ( 1987). 23. C. GRIESINGER, C. GEMPERLE, 0. W. SORENSEN AND R. R. ERNST, Mol. Phys. 62,295 ( 1987). 24. J. S. WAUGH, J. Magn. Reson. 68, 189 (1986). 25. J. LISTERUD AND G. DROBNY, Mol. Phys. 67,97 (1989).