A General Approach for Determining Scalar Coupling Constants in Polypeptides and Proteins GAETANO T. MONTELIONE, S. DONALD EMERSON, and BARBARA A. LYONS Center for Advanced Biotechnology and Medicine, and Department of Chemistry, Rutgers University, Piscataway, New Jersey 08854-5638
SYNOPSIS
A general approach is described for measuring homo- and heteronuclear spin coupling constants in polypeptides and small proteins. This method uses selective magnetization transfer to generate cross peaks similar to exclusive correlated spectroscopy (E.COSY) and a large direct spin coupling ( ‘ J ) in one dimension to “pull apart” cross-peak components by frequencies much larger than the resonance line width. A general description of this method is presented, along with a brief discussion of spin topology and relaxation effects that must be considered in designing multidimensional nmr pulse sequences for measuring vicinal coupling constants. The principles are demonstrated in designs of several twodimensional nmr experiments for determining coupling constants in polypeptides and proteins. These include experiments for measuring 3 J (HN-Ha),3 J (Hr-1-15N,), 3 J (15N-H4), and 3 J ( H “ - H Bcoupling ) constants, which depend on the polypeptide dihedral angles 4, and xl.Multidimensional nmr experiments developed with this approach will allow measurements of many vicinal coupling constants in peptides, proteins, and other molecules. Coupling constants measured in these spectra can be used to determine backbone and sidechain conformations, to obtain stereospecific resonance assignments of prochiral atoms, and to characterize conformational distributions of dihedral angles. Combined with information obtained from nuclear Overhauser effect measurements, these data will provide more precise determinations of protein solution structures by nmr spectroscopy.
+,
INTRODUCTION Polypeptide and protein structure determination by nmr spectroscopy relies primarily on internuclear distance constraints derived from nuclear Overhauser effect measurements (NOEs). These data are supplemented by limited numbers of constraints from measurements of vicinal spin coupling constants and identification of sequence-specific hydrogen bonds, disulfide bonds, and electrostatic interactions. Although NOEs provide sufficient data for determining the overall chain fold of small proteins, they are difficult to interpret quantitatively and generally provide relatively imprecise determinations of local backbone and side-chain conformations. Vicinal spin coupling constants, on the Biopolymers, Vol. 32, 327-334 (1992) 0 1992 John Wiley & Sons, Inc.
CCC 0006-3525/92/040327-08$04.00
other hand, provide local conformational information and can potentially be measured precisely. Using isotope-enriched samples, it is feasible to determine constrained ranges for many dihedral angles in a polypeptide or small protein structure from combined measurements of homo- and heteronuclear coupling constants. This information is complementary to that available from NOE measurements. Thus, the quality of nmr structures can probably be improved significantly by developing nmr experiments for determining vicinal coupling constants and by developing computational methods for using these, together with NOE data, for protein structure determination. Recent work in our laboratory has focused on development of improved nmr methods for obtaining these data in polypeptides and proteins, and on incorporation of these data into protein structure generation calculations. In this paper, we will summarize some of our ideas and re327
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cent progress in developing new nmr experiments for accurately measuring homo- and heteronuclear vicinal coupling constants.
THEORETICAL BACKGROUND Consider the vicinal spin coupling 3J(A-D ) between two nuclei A and D. The magnitude of this spin coupling is related to the conformation of the intervening dihedral angle 0 by the Karplus relationship.',' If these nuclei are weakly coupled, the conformationdependent vicinal coupling constant can in principle be determined by the frequency separation between components within two-dimensional (2D ) nmr cross peaks of nuclei A and D.3 In large peptides and proteins, however, significant line broadening due to short transverse relaxation times (7'2) results in heavily overlapped cross-peak components and precludes reliable estimates of the associated coupling constant^.^ This problem can sometimes be addressed by curve-fitting procedures and cross-peak ~imulations.6~~ Unfortunately, these deconvolution methods are of limited utility when many splittings are present in the cross peak or when the cross-peak intensities are weak. An alternative approach that has been used primarily for measuring homonuclear vicinal coupling constants is the exclusive correlated spectroscopy (E.COSY) experiment'-'' in which linear combinations of multiple-quantum filtered spectra are used to simplify the cross-peak fine structure. These spectra have cross-peak components only for connected transitions that have significantly less overlap within the cross peak. Because of this simplification, errors from the line-broadening effects are less severe and passive coupling constants within these cross peaks can sometimes be determined reliably. Similar simplified COSY cross peaks can also be obtained using pulse sequences in which the mixing pulse has an amplitude much smaller than 900 3,ll-13 or is a frequency selective shaped pulse that excites only one of the two (or more) coupled spins contributing to the COSY cross Homonuclear E.COSY spectras-'0p'2 of polypeptides and proteins are now being used routinely in many laboratories for measuring 3 J (H a - H P )coupling constants. However, these pulse sequences cannot be used to measure many important homonuclear coupling constants [e.g., 3 J ( H N - H a ) ] ,and have not been useful for measurements of heteronuclear coupling constants. In addition, the resonance line widths in large polypeptides and small proteins (typically 5-15 Hz) are often so broad that even in
the simplified cross-peak fine structures of E.COSY spectra there are still significant perturbations of the component frequencies due to overlapping line shapes. A related approach'&20 uses a large direct coupling ( ' J ) in one dimension to "pull apart" components of the E.COSY-like cross peak by frequencies (e.g., 40-150 Hz) much larger than the resonance line widths. These experiments overcome some of the other shortcomings of homonuclear E.COSY by exploiting heteronuclear spin systemse.g., 'H- l3C,'H- 15N,or 'H-I3C-l5N.A simplified explanation of this general approach is presented in Figure 1. For the simple system of spin 1 / 2 nuclei shown in Figure la, a cross peak useful for measuring the conformation-dependent J (A-D ) coupling constant may be obtained by choosing a third nucleus that has a large direct coupling to either A or D. A triad of nuclei A, B, and D that satisfy these criteria and their essential scalar coupling information is shown in Figure Ib. Given these interactions, there are three key parts of the pulse sequence design. First, spin B is frequency labeled during an evolution period (e.g., t l ) with scalar coupling to spin A. Next, magnetization is transferred from spin B to spin D without putting a significant fraction of the spin A coherence into the transverse plane. The reason for this selectivity requirement will be explained below. Finally, spin D is detected (e.g., during t 2 )with multiple-bond scalar coupling to spin A. If it is convenient, spins B, C, and D can usually be decoupled from one another during the evolution and/or detection periods. The resulting cross peak will have two principal frequency components at:
and
9
-
when the product [ ' J (A-B) 3 J (A-D)] > 0, or
when the product [ ' J ( A - B ) e 3 J ( A - D ) ] < 0. The relative orientation of these two components provides information about the product of the signs of
DETERMINING COUPLING CONSTANTS
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a 01
b
\ /J
'J
1
0:
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Figure 1. ( a ) Diagram showing direct ( ' J ) and vicinal ( 3 J )scalar couplings and magnetization transfer used in developing E.COSY-like fine structure in the w l = COB, w2 = wD cross peak of a 2D-nmr experiment. ( b ) Schematic representation of the key elements involved in measuring the 3 J (A-D) vicinal coupling constant. In these experiments, spin B is first frequency labeled with direct scalar coupling to spin A, and then magnetization is transferred from B to D without putting the A spin into the transverse plane. Spin D is then detected under the influence of vicinal coupling to spin A. ( c ) Diagram of the crosspeak fine structure, which develops under the influence of direct 'J(A-B) and vicinal 3 J (AD) scalar couplings. For weak coupling between spins A, B, C, and D, the frequency difference along w 2 provides an accurate measure of 3 J (A-D) by separating the relevant overlapping components of the cross peak in the w l dimension by the large (40-150 Hz) ' J ( A - B ) coupling constant.
the ' J (A-B) and 3 J (A-D) coupling constants. The frequency difference between the centers of mass of these components can typically be measured with a precision of k0.5 Hz when the data in w2 are recorded with sufficient digital resolution. Additional splittings will also be present, but these will generally not prevent a reliable determination of 3 J (A-D) . A simplified explanation for the physical basis of these cross-peak patterns" is shown schematically in Figure lc. Consider a 2D-nmr cross peak between nuclei B (in w l ) and D (in w2 ) , both of which are spin coupled to the same third nucleus A. During the evolution period t l , nuclear spin B is split into two spin ensembles; half of the B nuclei are coupled to A nuclei with magnetic moments aligned with the applied magnetic field (+ ) and the other half are coupled to A nuclei aligned against this applied field (4;Figure l c ) . At the same time, the D nucleus is also split into two components, half with the spincoupled A nucleus aligned with the applied field (+ ) and half with A aligned against this field (4) . Hence, in the absence of relaxation effects, magnetization from the half of B nuclei coupled to an A spin-up is transferred to and detected on the half of the D nuclei that also have the A spin-up, resulting in the upper right component of the cross peak in Figure
lc. Similarly, magnetization from the half of the B nuclei coupled to an A spin-down is transferred to and detected on the half of the D nuclei that also have the A spin-down, resulting in the lower left component of the cross peak in Figure lc. From this description of the process, one can see that if the A spin is put into the transverse plane for a significant time during the magnetization transfer from B to D, the spin-up and spin-down states will no longer be distinct and the E.COSY-like pattern will be corrupted. Odd numbers of inversion pulses on the A spin will reverse the sign of the cross peak, but will not destroy the E.COSY -like pattern. An alternative description of the development of this cross peak using product operator formalism has been presented e1~ewhere.l~ Relaxation processes during the mixing time can also corrupt the E.COSY-like pattern. For example, if some A nuclear spins flip from spin-up to spindown states by longitudinal relaxation during the mixing time, they will give rise to additional components within the cross peak that are otherwise suppressed. However, these effects will be partially compensated by simultaneous relaxation-induced spin flips of the B and/or D spins. Accordingly, relaxation processes during the mixing time can result
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in inaccurate measurements of vicinal coupling constants if the relevant relaxation times of the A, B, and D spins are very different from one another, especially if long mixing times are used to transfer the magnetization from nucleus B to D.
EXPERIMENTAL RESULTS Based on the theoretical considerations discussed above, there are some important points to consider in designing pulse sequences for measurement of spin coupling constants. The target spin system must consist of a triad of nuclei (e.g., A, B, D ) involving a common coupling partner ( A nucleus), one large direct coupling [ 'J(A-B) 1 , and one conformation-dependent coupling [ 3 J (A-D ) ]. Next, a method is developed that transfers magnetization from nucleus B to D without putting a significant fraction of nucleus A magnetization into the transverse plane. For cases where A is heteronuclear with respect to B and D, this selectivity of the mixing pulses is readily achieved by conventional homonuclear experiments that correlate spins B and D without perturbing A." When A is the same nuclear type as B or D, small amplitude pulses ( 1Oo-45O), frequency selective shaped pulses, 2 1 ~ 2 4 or bilinear rotation decoupling (BIRD ) can usually provide sufficient selectivity in magnetization transfer between B and D. Finally, one must consider the effects of relaxation during the mixing time of magnetization transfer from B to D. This mixing time should be as short as possible and use pathways that provide "matched' relaxation of the A, B, and D spins. A family of 2D-nmr experiments utilizing this strategy to provide measurements of 3 J (HN-H") coupling constants, l8 which depend on the backbone dihedral angle 4, is described in Figures 2-4. In these experiments the A, B, D triad consists of the H", 13Ca,and H Nnuclei shown in Figure 2. Polarization is first transferred from the H a nucleus to the l3C" nucleus to enhance sensitivity. The 13Cais frequency labeled during the tl period while maintaining the large 140-Hz 'J(H"-C") spin coupling. Next, the magnetization is transferred from the 13Cato the H Nusing a heteronuclear relay through the 15Nnucleus. This is done with minimal mixing of the upand down-spin states of the H" by using a small amplitude (i.e., 10") proton pulse (Figure 3a), a BIRD ~ e q u e n c ecalled ~ ~ , ~"N-TANGO, ~ which is a 90" pulse for protons bound to 15Nand a 360" pulse for all other protons (Figure 3b), or a frequency selective shaped p ~ l s e , ~which l - ~ ~ provides a 90"
pulse on the amide protons only (Figure 3c). The proton magnetization is then detected with 3 J (HNH") coupling and broad-band 15N decoupling. The result of one of these experiments using a frequencyselective Gaussian pulsez1 on the amide protons is shown in Figure 4. In this spectrum, the partially overlapping 3 J (HN-Ha)splittings in the w2 dimension are resolved by the 140-Hz 1J(13Ca-Ha)spin coupling in the w l dimension. An analogous strategy has been used to measure 3 J ("Ni-Hf ) and 3 J (Hy-l- 15Ni) vicinal coupling constants in uniformly 15N-enriched protein^.'^^^^ In these experiments we consider the 15N,H N ,H p or 15Ni,Hy , Hr-l triads. The H y nucleus is first frequency labeled while spin coupled to 15Ni. This magnetization is then transferred to the Hf or H d l nuclei, which are coupled to the same 15Ni by homonuclear NOE spectroscopy (NOESY) ,rotating frame NOE spectroscopy (ROESY), total correlation spectroscopy (TOCSY) , or relayed COSY pulse sequences. Since the 15N spin is not put into the transverse plane by these homonuclear pulse sequences, the wl = HY and w2 = H f or w2 = HP-, cross peaks have E-COSY-like patterns with a large ' J ( HN-15N) splitting in w l and conformationdependent 35(HN-H8)or 3 J (H y - H t l ) splittings, respectively, in 02. These data can thus provide conformational constraints on side-chain ( xl) and backbone ( $) dihedral angles. Similar experiments can be used to measure 'H- 13Cvicinal coupling cons t a n k z 8 Furthermore, measurements can also be made at natural isotope abundance if one selects for
N-
Ca
Hetero Relay 13Ca
HN
\ JJ
'J
Figure 2. Diagrams showing direct ('J)and vicinal ( 3 J ) scalar couplings and magnetization transfer used in developing E.COSY-like fine structure in the wl = C", w2 = H Ncross peak. These experiments can be used to measure 3 J (HN-H")coupling constants, which provide information about the backbone dihedral angle 4.
DETERMINING COUPLING CONSTANTS
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a
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N
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R "
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I I ! I l l t
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Figure 3. Some triple-resonance pulse sequences useful for measuring homonuclear ' J ( HN-H")coupling constants in isotope-enriched polypeptides. These pulse sequences use either a ( a ) small 'H-pulse flip angle, ( b ) TANGO pulse sequence,26or (c) frequency selective shaped pulse'' to provide selective 90" pulses on the H Nnucleus without putting the H" nucleus in the transverse plane. The delays are tuned as a = 1/[4*'J( Hm-13C0)], 6 = 1/[4*'J('5N-13C")],and c = 1 / [ 4 * l J ( 15N-HN)],while phases were cycled as A = x , - x ; B = x , x , - x , - x ; and C = x , - x , - x , Time-proportional 90" incrementation of phase A provides quadrature detection in w l .
protons bound to 15N or I3C prior to beginning the homonuclear NOESY, ROESY, TOCSY, or relayed COSY experiment. We prefer to use ROESY or TOCSY for magnetization transfer in order t o best
match the relaxation of 15Nand 'H. In these rotating frame experiments, 'H relaxation is determined by TIp,which is usually a better match to the 13C and 15N TIrelaxation times in proteins.
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MONTELIONE, EMERSON, AND LYONS
- 150.0 -100.0
- 50.0 13Ca 0.0
50.0
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20.0
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homonuclear carbon COSY 32,33 or TOCSY 34335pulse sequences, and then onto the H Bby reverse-refocused insensitive nucleus enhancement by polarization transfer (INEPT),36where it is detected with 3 J (HaH@)coupling. I n order to produce a n E.COSY-like cross peak, the transfer from 13Ca to H' must be done without putting a significant fraction of the H a spins in the transverse plane. This can be accomplished either by frequency-selective excitation of the H Por by using a small proton pulse flip angle in the reversed INEPT, as shown in the pulse sequences of Figure 7. An example of a 3 J ( H e - H 0 ) coupling constant measurement made with the CA(CB)HB-COSY sequence (Figure 7b) is shown in Figure 8. These CA(CB)HB-COSY and -TOCSY pulse sequences (Figure 7 ) are being developed fur-
0 2 (Hz)
Figure 4. The w l = C", w 2 = H N2D-nmr cross peak of the peptide Ac-Asn-Pro-"N-Tyr-NHMe obtained using the pulse sequence in Figure 3c. The cross peak shows an E.COSY-like pattern with a 1J(13Ca-H'7 splitting of ca. 140 Hz in the w l dimension and a homonuclear 3 J (HNH") splitting of 8.5 k 0.5 Hz in the w2 dimension. This spectrum was obtained on a Varian Unity 500 spectrometer in ca. 2 h using a 20 mM peptide sample in uniformly
deuterated dimethysulfoxide solvent.
r
'.'l
a
3J(Hz) 12.0
11.0
10.0
9.0
Although 3 J (l5N-Ho) heteronuclear coupling constants provide useful information on side-chain dihedral angle conformations, 29 they are most valuable when used in combination with J ( Ha-H@)homonuclear coupling constants. Combinations of these coupling constants, which both depend on the side-chain dihedral angle XI, can be used t o overcome degeneracies in the Karplus curves and to determine stereospecific C@H2assignment^.^'-^' However, 3 J (He-H@)coupling constants generally provide tighter constraints on x1 than 3 J (15N-H@) coupling constants measured with the same degree of precision (Figure 5). While homonuclear E.COSY spectra can provide estimates of 3 J (H e - H @ )these , data are sometimes unreliable in protein nmr because the cross-peak components are separated in w l by only ca. 16 Hz. For this reason we are developing a family of experiments that use the heteronuclear 'J("C-'H) splitting in the wl dimension to provide better data from which to determine 3 J (HO-HO). Our general approach for measuring 3 J (H"-H@) spin couplings is summarized in Figure 6. Here we focus on the H a , I3C ,H triad. The I3C'' nucleus is frequency labeled during tl while coupled to the H". This magnetization is then transferred t o I3C0 by @
I
I
8.0 -90.0
I
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-w0
b
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-1.0
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I
I 8
333
DETERMINING COUPLING CONSTANTS
ther in our laboratory using an initial INEPT transfer from proton to enhance sensitivity and by exploring the effects of reverse INEPT proton pulses longer than 10" on the accuracy of 'J(H''-HO) measurements.
Ha
II
)lJ
N3-c' Hp-
Cp
DISCUSSION
\ /J
'J
Ha
Figure 6. Diagrams showing direct ( ' J )and vicinal ( 3 J ) spin couplings and magnetization transfers used in developing E.COSY-like fine structure in the wl = 13Cn,w 2 = H Bcross peak. These experiments can be used to measure 3 J (H"-H@)coupling constants, which provide information about the side-chain dihedral angle x ~ .
a 1 0 ;
The principles for designing pulse sequences outlined in this paper provide a general approach for measuring homonuclear and heteronuclear coupling constants in polypeptides and proteins. Of course, each particular experiment will have special additional features that must be considered in order to measure these nmr parameters reliably. These experiments provide E.COSY -like cross peaks with a large ' J splitting in one dimension (e.g., w l ) and long-range coupling constant information in the higher resolution dimension of detection (e.g., w2). Although the examples presented here have been restricted to ZD-nmr experiments, three-dimensional and four-dimensional versions can also be de~igned.~~ The , ~ 'same , ~ ~ principles can be applied to other chemical systems, including nucleic acids, carbohydrates, and natural products. These new ex-
HP H
250.0 1
1
C 125.0
b 10:
'J(c~-H~ 14OHZ
0.0
-
H C Figure 7. Double-resonance pulse sequences for measuring homonuclear 3 J (H"-HB) coupling constants in polypeptides. ( a ) CA(CB)HB-COSY,a 13C-'"C COSY experiment followed by reverse refocused INEPT transfer to protons for detection. ( b ) CA(CB)HB-TOCSY,a 13C'"C TOCSY experiment followed by transfer of magnetization to protons for detection. Both sequences used a 10" pulse in place of the 90" 'H pulse of the reverse refocused INEPT sequences in order to generate an E.COSY-like cross-peak fine structure. The delays are tuned as a = b = I/ [ 4 * ' J ( H4-13CB)]. The phase of the 90" y pulse on 13C is cycled + y , - y while the receiver is cycled -. Time-proportional 90" incrementation of the first I3C pulse in each sequence provides quadrature detection in wl.
+,
125.0
250.0
z 20.0
10.0
0.0
10.0
20.0
0 2 (Hz) Figure 8. Example of 2D CA(CB)HB-COSY cross peak for 20 m M uniformly I3C-enriched L-Ala in DzO showing an E.COSY-like pattern from which the homonuclear ' J ( Ha-H@) coupling constant has been determined. This spectrum was obtained without heteronuclear antiphase coherence refocusing. The cross peak shows a large ' J (HaC") splitting of ca. 140 Hz in w l and a 3J(H"-HP)splitting of ca. 7 Hz in w2. This experimental result agrees with the ensemble-averaged value of ca. 7 Hz calculated for three equally populated staggered rotamer states of XI.*'
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MONTELIONE, EMERSON, AND LYONS
periments will allow measurements of many vicinal coupling constants in proteins a n d other molecules of known structures t o be obtained. With these data it will be possible to calibrate the corresponding Karplus curves and t o characterize the effects of side-chain functionalities on these curves. Measurements of multiple homo- and heteronuclear coupling constants that depend on the same dihedral angle can be used t o obtain stereospecific assignments, and to characterize conformational distributions of backbone and side-chain dihedral angles. When applied to proteins of unknown structure, they will provide many additional local conformational constraints that can be combined with information obtained from NOE measurements to provide more precise determinations of protein solution structures by nmr spectroscopy. We thank Prof. Gerhard Wagner for helpful discussions and encouragement. This work was supported by The Searle Scholars Program/The Chicago Community Trust, The Johnson and Johnson Research Discovery Program, and The New Jersey Commission on Science and Technology.
REFERENCES 1. Karplus, M. (1959) J. Chem. Phys. 30, 11-15. 2. Karplus, M. (1963) J. Am. Chem. SOC.85,2870-2871. 3. Aue, W. P., Bartholdi, E. & Ernst, R. R. (1976) J . Chem. Phys. 64, 2229-2246. 4. Neuhaus, D., Wagner, G., Vashk, M., Kagi, J. H. R. & Wuthrich, K. (1985) Eur. J. Biochem. 151, 257273. 5. Smith, L. J., Sutcliffe, M. J., Redfield, C. & Dobson, C. M. (1991) Biochemistry 30,986-996. 6. Hyberts, S. G., Marki, W. & Wagner, G. (1987) Eur. J . Biochem. 164,625-635. 7. Widmer, H. & Wuthrich, K. (1987) J. Magn. Reson. 7 4 , 316-336. 8. Griesinger, C., Ssrensen, 0. W. & Ernst, R. R. (1985) J. Am. Chem. SOC.107,6394-6396. 9. Griesinger, C., Ssrensen, 0. W. & Ernst, R. R. (1986) J . Chem. Phys. 85,6837-6852. 10. Griesinger, C., Ssrensen, 0. W. & Ernst, R. R. (1987) J. Magn. Reson. 75, 474-492. 11. Bax, A. & Freeman, R. (1981) J. Magn. Reson. 44, 542-561. 12. Muller, L. ( 1987) J. Magn. Reson. 72, 191-196. 13. Oschkinat, H., Clore, G. M., Nilges, M. & Gronenborn, A. M. (1987) J . Magn. Reson. 75, 534-539.
14. Bruschweiler, R., Madsen, J. C., Griesinger, C., S0rensen, 0.W. & Ernst, R. R. (1987) J. Magn. Reson. 73, 380-385. 15. Kessler, H., Anders, U. & Gemmecker, G. (1988) J. Magn. Reson. 78,382-388. 16. Emsley, L., Huber, P. & Bodenhausen, G. (1990) Angew. Chem. Int. Ed. Engl. 29, 517-520. 17. Emsley, L. & Bodenhausen, G. (1991) J . Am. Chem. SOC.113, 3309-3316. 18. Montelione, G. T. &Wagner, G. ( 1989) J. Am. Chem. Soc. 111,5474-5475. 19. Montelione, G. T., Winkler, M. E., Rauenbuehler, P. & Wagner, G. (1989) J . Magn. Reson. 82, 198-204. 20. Wagner, G., Nirmala, N. R., Montelione, G. T. & Hyberts, S. (1990) Frontiers of N M R in Molecular Biology, R. Liss, New York, pp. 129-143. 21. Bauer, C., Freeman, R., Frenkiel, T., Keeler, J. & Shaka, A. J. (1984) J. Magn. Reson. 58,442-457. 22. Warren, W. S. (1988) Science 242, 878-884. 23. Emsley, L. & Bodenhausen, G. (1989) J. Magn. Reson. 82, 211-221. 24. Geen, H. & Freeman, R. (1990) J. Magn. Reson. 87, 415-421. 25. Garbow, J. R., Weitekamp, D. P. & Pines, A. (1982) Chem. Phys. Lett. 93, 504-509. 26. Wimperis, S. & Freeman, R. ( 1984) J . Magn. Reson. 58, 348-353. 27. Wider, G., Neri, D., Otting, G. & Wuthrich, K. (1989) J. Magn. Reson. 85, 426-431. 28. Edison, A. S., Westler, W. M. & Markley, J. L. (1991) J . Magn. Reson. 92, 434-438. 29. Bystrov, V. F. (1976) Progr. N M R Spectrosc. 10,4181. 30. Fischman, A. J., Live, D., Wyssbrod, H. R., Agosta, W. C. & Cowburn, D. (1980) J . Am. Chem. SOC.102, 2533. 31. Cowburn, D., Live, D., Fischman, A. J. & Agosta, W. C . (1983) J . Am. Chem. SOC.105, 7435. 32. Bax, A., Clore, G. M., Driscoll, P. C., Gronenborn, A. M., Ikura, M. & Kay, L. (1990) J . Magn. Reson. 87, 620-627, 33. Kay, L. E., Ikura, M. & Bax, A. (1990) J . Am. Chem. SOC.112, 888-889. 34. Bax, A., Clore, M. & Gronenborn, A. M. (1990) J. Magn. Reson. 88,425-431. 35. Fesik, S. W., Eaton, H. L., Olejniczak, E. T. & Zuiderweg, E. R. P. (1990) J . A m . Chem. SOC.112,886888. 36. Morris, G. A. (1980) J . Am. Chem. Soc. 102, 428429. 37. Montelione, G. T. & Wagner, G. (1990) J . Magn. Reson. 87, 183-188.
Received June 10, 1991 Accepted July 25, 1991
SYNOPSIS
A general approach is described for measuring homo- and heteronuclear spin coupling constants in polypeptides and small proteins. This method uses selective magnetization transfer to generate cross peaks similar to exclusive correlated spectroscopy (E.COSY) and a large direct spin coupling ( ‘ J ) in one dimension to “pull apart” cross-peak components by frequencies much larger than the resonance line width. A general description of this method is presented, along with a brief discussion of spin topology and relaxation effects that must be considered in designing multidimensional nmr pulse sequences for measuring vicinal coupling constants. The principles are demonstrated in designs of several twodimensional nmr experiments for determining coupling constants in polypeptides and proteins. These include experiments for measuring 3 J (HN-Ha),3 J (Hr-1-15N,), 3 J (15N-H4), and 3 J ( H “ - H Bcoupling ) constants, which depend on the polypeptide dihedral angles 4, and xl.Multidimensional nmr experiments developed with this approach will allow measurements of many vicinal coupling constants in peptides, proteins, and other molecules. Coupling constants measured in these spectra can be used to determine backbone and sidechain conformations, to obtain stereospecific resonance assignments of prochiral atoms, and to characterize conformational distributions of dihedral angles. Combined with information obtained from nuclear Overhauser effect measurements, these data will provide more precise determinations of protein solution structures by nmr spectroscopy.
+,
INTRODUCTION Polypeptide and protein structure determination by nmr spectroscopy relies primarily on internuclear distance constraints derived from nuclear Overhauser effect measurements (NOEs). These data are supplemented by limited numbers of constraints from measurements of vicinal spin coupling constants and identification of sequence-specific hydrogen bonds, disulfide bonds, and electrostatic interactions. Although NOEs provide sufficient data for determining the overall chain fold of small proteins, they are difficult to interpret quantitatively and generally provide relatively imprecise determinations of local backbone and side-chain conformations. Vicinal spin coupling constants, on the Biopolymers, Vol. 32, 327-334 (1992) 0 1992 John Wiley & Sons, Inc.
CCC 0006-3525/92/040327-08$04.00
other hand, provide local conformational information and can potentially be measured precisely. Using isotope-enriched samples, it is feasible to determine constrained ranges for many dihedral angles in a polypeptide or small protein structure from combined measurements of homo- and heteronuclear coupling constants. This information is complementary to that available from NOE measurements. Thus, the quality of nmr structures can probably be improved significantly by developing nmr experiments for determining vicinal coupling constants and by developing computational methods for using these, together with NOE data, for protein structure determination. Recent work in our laboratory has focused on development of improved nmr methods for obtaining these data in polypeptides and proteins, and on incorporation of these data into protein structure generation calculations. In this paper, we will summarize some of our ideas and re327
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MONTELIONE, EMERSON, AND LYONS
cent progress in developing new nmr experiments for accurately measuring homo- and heteronuclear vicinal coupling constants.
THEORETICAL BACKGROUND Consider the vicinal spin coupling 3J(A-D ) between two nuclei A and D. The magnitude of this spin coupling is related to the conformation of the intervening dihedral angle 0 by the Karplus relationship.',' If these nuclei are weakly coupled, the conformationdependent vicinal coupling constant can in principle be determined by the frequency separation between components within two-dimensional (2D ) nmr cross peaks of nuclei A and D.3 In large peptides and proteins, however, significant line broadening due to short transverse relaxation times (7'2) results in heavily overlapped cross-peak components and precludes reliable estimates of the associated coupling constant^.^ This problem can sometimes be addressed by curve-fitting procedures and cross-peak ~imulations.6~~ Unfortunately, these deconvolution methods are of limited utility when many splittings are present in the cross peak or when the cross-peak intensities are weak. An alternative approach that has been used primarily for measuring homonuclear vicinal coupling constants is the exclusive correlated spectroscopy (E.COSY) experiment'-'' in which linear combinations of multiple-quantum filtered spectra are used to simplify the cross-peak fine structure. These spectra have cross-peak components only for connected transitions that have significantly less overlap within the cross peak. Because of this simplification, errors from the line-broadening effects are less severe and passive coupling constants within these cross peaks can sometimes be determined reliably. Similar simplified COSY cross peaks can also be obtained using pulse sequences in which the mixing pulse has an amplitude much smaller than 900 3,ll-13 or is a frequency selective shaped pulse that excites only one of the two (or more) coupled spins contributing to the COSY cross Homonuclear E.COSY spectras-'0p'2 of polypeptides and proteins are now being used routinely in many laboratories for measuring 3 J (H a - H P )coupling constants. However, these pulse sequences cannot be used to measure many important homonuclear coupling constants [e.g., 3 J ( H N - H a ) ] ,and have not been useful for measurements of heteronuclear coupling constants. In addition, the resonance line widths in large polypeptides and small proteins (typically 5-15 Hz) are often so broad that even in
the simplified cross-peak fine structures of E.COSY spectra there are still significant perturbations of the component frequencies due to overlapping line shapes. A related approach'&20 uses a large direct coupling ( ' J ) in one dimension to "pull apart" components of the E.COSY-like cross peak by frequencies (e.g., 40-150 Hz) much larger than the resonance line widths. These experiments overcome some of the other shortcomings of homonuclear E.COSY by exploiting heteronuclear spin systemse.g., 'H- l3C,'H- 15N,or 'H-I3C-l5N.A simplified explanation of this general approach is presented in Figure 1. For the simple system of spin 1 / 2 nuclei shown in Figure la, a cross peak useful for measuring the conformation-dependent J (A-D ) coupling constant may be obtained by choosing a third nucleus that has a large direct coupling to either A or D. A triad of nuclei A, B, and D that satisfy these criteria and their essential scalar coupling information is shown in Figure Ib. Given these interactions, there are three key parts of the pulse sequence design. First, spin B is frequency labeled during an evolution period (e.g., t l ) with scalar coupling to spin A. Next, magnetization is transferred from spin B to spin D without putting a significant fraction of the spin A coherence into the transverse plane. The reason for this selectivity requirement will be explained below. Finally, spin D is detected (e.g., during t 2 )with multiple-bond scalar coupling to spin A. If it is convenient, spins B, C, and D can usually be decoupled from one another during the evolution and/or detection periods. The resulting cross peak will have two principal frequency components at:
and
9
-
when the product [ ' J (A-B) 3 J (A-D)] > 0, or
when the product [ ' J ( A - B ) e 3 J ( A - D ) ] < 0. The relative orientation of these two components provides information about the product of the signs of
DETERMINING COUPLING CONSTANTS
329
a 01
b
\ /J
'J
1
0:
A
Figure 1. ( a ) Diagram showing direct ( ' J ) and vicinal ( 3 J )scalar couplings and magnetization transfer used in developing E.COSY-like fine structure in the w l = COB, w2 = wD cross peak of a 2D-nmr experiment. ( b ) Schematic representation of the key elements involved in measuring the 3 J (A-D) vicinal coupling constant. In these experiments, spin B is first frequency labeled with direct scalar coupling to spin A, and then magnetization is transferred from B to D without putting the A spin into the transverse plane. Spin D is then detected under the influence of vicinal coupling to spin A. ( c ) Diagram of the crosspeak fine structure, which develops under the influence of direct 'J(A-B) and vicinal 3 J (AD) scalar couplings. For weak coupling between spins A, B, C, and D, the frequency difference along w 2 provides an accurate measure of 3 J (A-D) by separating the relevant overlapping components of the cross peak in the w l dimension by the large (40-150 Hz) ' J ( A - B ) coupling constant.
the ' J (A-B) and 3 J (A-D) coupling constants. The frequency difference between the centers of mass of these components can typically be measured with a precision of k0.5 Hz when the data in w2 are recorded with sufficient digital resolution. Additional splittings will also be present, but these will generally not prevent a reliable determination of 3 J (A-D) . A simplified explanation for the physical basis of these cross-peak patterns" is shown schematically in Figure lc. Consider a 2D-nmr cross peak between nuclei B (in w l ) and D (in w2 ) , both of which are spin coupled to the same third nucleus A. During the evolution period t l , nuclear spin B is split into two spin ensembles; half of the B nuclei are coupled to A nuclei with magnetic moments aligned with the applied magnetic field (+ ) and the other half are coupled to A nuclei aligned against this applied field (4;Figure l c ) . At the same time, the D nucleus is also split into two components, half with the spincoupled A nucleus aligned with the applied field (+ ) and half with A aligned against this field (4) . Hence, in the absence of relaxation effects, magnetization from the half of B nuclei coupled to an A spin-up is transferred to and detected on the half of the D nuclei that also have the A spin-up, resulting in the upper right component of the cross peak in Figure
lc. Similarly, magnetization from the half of the B nuclei coupled to an A spin-down is transferred to and detected on the half of the D nuclei that also have the A spin-down, resulting in the lower left component of the cross peak in Figure lc. From this description of the process, one can see that if the A spin is put into the transverse plane for a significant time during the magnetization transfer from B to D, the spin-up and spin-down states will no longer be distinct and the E.COSY-like pattern will be corrupted. Odd numbers of inversion pulses on the A spin will reverse the sign of the cross peak, but will not destroy the E.COSY -like pattern. An alternative description of the development of this cross peak using product operator formalism has been presented e1~ewhere.l~ Relaxation processes during the mixing time can also corrupt the E.COSY-like pattern. For example, if some A nuclear spins flip from spin-up to spindown states by longitudinal relaxation during the mixing time, they will give rise to additional components within the cross peak that are otherwise suppressed. However, these effects will be partially compensated by simultaneous relaxation-induced spin flips of the B and/or D spins. Accordingly, relaxation processes during the mixing time can result
330
MONTELIONE, EMERSON, AND LYONS
in inaccurate measurements of vicinal coupling constants if the relevant relaxation times of the A, B, and D spins are very different from one another, especially if long mixing times are used to transfer the magnetization from nucleus B to D.
EXPERIMENTAL RESULTS Based on the theoretical considerations discussed above, there are some important points to consider in designing pulse sequences for measurement of spin coupling constants. The target spin system must consist of a triad of nuclei (e.g., A, B, D ) involving a common coupling partner ( A nucleus), one large direct coupling [ 'J(A-B) 1 , and one conformation-dependent coupling [ 3 J (A-D ) ]. Next, a method is developed that transfers magnetization from nucleus B to D without putting a significant fraction of nucleus A magnetization into the transverse plane. For cases where A is heteronuclear with respect to B and D, this selectivity of the mixing pulses is readily achieved by conventional homonuclear experiments that correlate spins B and D without perturbing A." When A is the same nuclear type as B or D, small amplitude pulses ( 1Oo-45O), frequency selective shaped pulses, 2 1 ~ 2 4 or bilinear rotation decoupling (BIRD ) can usually provide sufficient selectivity in magnetization transfer between B and D. Finally, one must consider the effects of relaxation during the mixing time of magnetization transfer from B to D. This mixing time should be as short as possible and use pathways that provide "matched' relaxation of the A, B, and D spins. A family of 2D-nmr experiments utilizing this strategy to provide measurements of 3 J (HN-H") coupling constants, l8 which depend on the backbone dihedral angle 4, is described in Figures 2-4. In these experiments the A, B, D triad consists of the H", 13Ca,and H Nnuclei shown in Figure 2. Polarization is first transferred from the H a nucleus to the l3C" nucleus to enhance sensitivity. The 13Cais frequency labeled during the tl period while maintaining the large 140-Hz 'J(H"-C") spin coupling. Next, the magnetization is transferred from the 13Cato the H Nusing a heteronuclear relay through the 15Nnucleus. This is done with minimal mixing of the upand down-spin states of the H" by using a small amplitude (i.e., 10") proton pulse (Figure 3a), a BIRD ~ e q u e n c ecalled ~ ~ , ~"N-TANGO, ~ which is a 90" pulse for protons bound to 15Nand a 360" pulse for all other protons (Figure 3b), or a frequency selective shaped p ~ l s e , ~which l - ~ ~ provides a 90"
pulse on the amide protons only (Figure 3c). The proton magnetization is then detected with 3 J (HNH") coupling and broad-band 15N decoupling. The result of one of these experiments using a frequencyselective Gaussian pulsez1 on the amide protons is shown in Figure 4. In this spectrum, the partially overlapping 3 J (HN-Ha)splittings in the w2 dimension are resolved by the 140-Hz 1J(13Ca-Ha)spin coupling in the w l dimension. An analogous strategy has been used to measure 3 J ("Ni-Hf ) and 3 J (Hy-l- 15Ni) vicinal coupling constants in uniformly 15N-enriched protein^.'^^^^ In these experiments we consider the 15N,H N ,H p or 15Ni,Hy , Hr-l triads. The H y nucleus is first frequency labeled while spin coupled to 15Ni. This magnetization is then transferred to the Hf or H d l nuclei, which are coupled to the same 15Ni by homonuclear NOE spectroscopy (NOESY) ,rotating frame NOE spectroscopy (ROESY), total correlation spectroscopy (TOCSY) , or relayed COSY pulse sequences. Since the 15N spin is not put into the transverse plane by these homonuclear pulse sequences, the wl = HY and w2 = H f or w2 = HP-, cross peaks have E-COSY-like patterns with a large ' J ( HN-15N) splitting in w l and conformationdependent 35(HN-H8)or 3 J (H y - H t l ) splittings, respectively, in 02. These data can thus provide conformational constraints on side-chain ( xl) and backbone ( $) dihedral angles. Similar experiments can be used to measure 'H- 13Cvicinal coupling cons t a n k z 8 Furthermore, measurements can also be made at natural isotope abundance if one selects for
N-
Ca
Hetero Relay 13Ca
HN
\ JJ
'J
Figure 2. Diagrams showing direct ('J)and vicinal ( 3 J ) scalar couplings and magnetization transfer used in developing E.COSY-like fine structure in the wl = C", w2 = H Ncross peak. These experiments can be used to measure 3 J (HN-H")coupling constants, which provide information about the backbone dihedral angle 4.
DETERMINING COUPLING CONSTANTS
331
a
X
B
N
BB
I
I
I
I
b TANGO
B
X
I
N I
1
BE
I
I
C shaped Pulse
N
I
I
I
I
I
I
I
I
R "
I
X
X
I I ! I l l t
BB
1
I
Figure 3. Some triple-resonance pulse sequences useful for measuring homonuclear ' J ( HN-H")coupling constants in isotope-enriched polypeptides. These pulse sequences use either a ( a ) small 'H-pulse flip angle, ( b ) TANGO pulse sequence,26or (c) frequency selective shaped pulse'' to provide selective 90" pulses on the H Nnucleus without putting the H" nucleus in the transverse plane. The delays are tuned as a = 1/[4*'J( Hm-13C0)], 6 = 1/[4*'J('5N-13C")],and c = 1 / [ 4 * l J ( 15N-HN)],while phases were cycled as A = x , - x ; B = x , x , - x , - x ; and C = x , - x , - x , Time-proportional 90" incrementation of phase A provides quadrature detection in w l .
protons bound to 15N or I3C prior to beginning the homonuclear NOESY, ROESY, TOCSY, or relayed COSY experiment. We prefer to use ROESY or TOCSY for magnetization transfer in order t o best
match the relaxation of 15Nand 'H. In these rotating frame experiments, 'H relaxation is determined by TIp,which is usually a better match to the 13C and 15N TIrelaxation times in proteins.
332
MONTELIONE, EMERSON, AND LYONS
- 150.0 -100.0
- 50.0 13Ca 0.0
50.0
100.0
150.0
-
20.0
10.0
0.0
-10.0
-20.0
homonuclear carbon COSY 32,33 or TOCSY 34335pulse sequences, and then onto the H Bby reverse-refocused insensitive nucleus enhancement by polarization transfer (INEPT),36where it is detected with 3 J (HaH@)coupling. I n order to produce a n E.COSY-like cross peak, the transfer from 13Ca to H' must be done without putting a significant fraction of the H a spins in the transverse plane. This can be accomplished either by frequency-selective excitation of the H Por by using a small proton pulse flip angle in the reversed INEPT, as shown in the pulse sequences of Figure 7. An example of a 3 J ( H e - H 0 ) coupling constant measurement made with the CA(CB)HB-COSY sequence (Figure 7b) is shown in Figure 8. These CA(CB)HB-COSY and -TOCSY pulse sequences (Figure 7 ) are being developed fur-
0 2 (Hz)
Figure 4. The w l = C", w 2 = H N2D-nmr cross peak of the peptide Ac-Asn-Pro-"N-Tyr-NHMe obtained using the pulse sequence in Figure 3c. The cross peak shows an E.COSY-like pattern with a 1J(13Ca-H'7 splitting of ca. 140 Hz in the w l dimension and a homonuclear 3 J (HNH") splitting of 8.5 k 0.5 Hz in the w2 dimension. This spectrum was obtained on a Varian Unity 500 spectrometer in ca. 2 h using a 20 mM peptide sample in uniformly
deuterated dimethysulfoxide solvent.
r
'.'l
a
3J(Hz) 12.0
11.0
10.0
9.0
Although 3 J (l5N-Ho) heteronuclear coupling constants provide useful information on side-chain dihedral angle conformations, 29 they are most valuable when used in combination with J ( Ha-H@)homonuclear coupling constants. Combinations of these coupling constants, which both depend on the side-chain dihedral angle XI, can be used t o overcome degeneracies in the Karplus curves and to determine stereospecific C@H2assignment^.^'-^' However, 3 J (He-H@)coupling constants generally provide tighter constraints on x1 than 3 J (15N-H@) coupling constants measured with the same degree of precision (Figure 5). While homonuclear E.COSY spectra can provide estimates of 3 J (H e - H @ )these , data are sometimes unreliable in protein nmr because the cross-peak components are separated in w l by only ca. 16 Hz. For this reason we are developing a family of experiments that use the heteronuclear 'J("C-'H) splitting in the wl dimension to provide better data from which to determine 3 J (HO-HO). Our general approach for measuring 3 J (H"-H@) spin couplings is summarized in Figure 6. Here we focus on the H a , I3C ,H triad. The I3C'' nucleus is frequency labeled during tl while coupled to the H". This magnetization is then transferred t o I3C0 by @
I
I
8.0 -90.0
I
-75.0
-60.0
-45.0
-w0
b
3J(Hz) 0.0
-1.0
-2.0
-3.0 I
I
I 8
333
DETERMINING COUPLING CONSTANTS
ther in our laboratory using an initial INEPT transfer from proton to enhance sensitivity and by exploring the effects of reverse INEPT proton pulses longer than 10" on the accuracy of 'J(H''-HO) measurements.
Ha
II
)lJ
N3-c' Hp-
Cp
DISCUSSION
\ /J
'J
Ha
Figure 6. Diagrams showing direct ( ' J )and vicinal ( 3 J ) spin couplings and magnetization transfers used in developing E.COSY-like fine structure in the wl = 13Cn,w 2 = H Bcross peak. These experiments can be used to measure 3 J (H"-H@)coupling constants, which provide information about the side-chain dihedral angle x ~ .
a 1 0 ;
The principles for designing pulse sequences outlined in this paper provide a general approach for measuring homonuclear and heteronuclear coupling constants in polypeptides and proteins. Of course, each particular experiment will have special additional features that must be considered in order to measure these nmr parameters reliably. These experiments provide E.COSY -like cross peaks with a large ' J splitting in one dimension (e.g., w l ) and long-range coupling constant information in the higher resolution dimension of detection (e.g., w2). Although the examples presented here have been restricted to ZD-nmr experiments, three-dimensional and four-dimensional versions can also be de~igned.~~ The , ~ 'same , ~ ~ principles can be applied to other chemical systems, including nucleic acids, carbohydrates, and natural products. These new ex-
HP H
250.0 1
1
C 125.0
b 10:
'J(c~-H~ 14OHZ
0.0
-
H C Figure 7. Double-resonance pulse sequences for measuring homonuclear 3 J (H"-HB) coupling constants in polypeptides. ( a ) CA(CB)HB-COSY,a 13C-'"C COSY experiment followed by reverse refocused INEPT transfer to protons for detection. ( b ) CA(CB)HB-TOCSY,a 13C'"C TOCSY experiment followed by transfer of magnetization to protons for detection. Both sequences used a 10" pulse in place of the 90" 'H pulse of the reverse refocused INEPT sequences in order to generate an E.COSY-like cross-peak fine structure. The delays are tuned as a = b = I/ [ 4 * ' J ( H4-13CB)]. The phase of the 90" y pulse on 13C is cycled + y , - y while the receiver is cycled -. Time-proportional 90" incrementation of the first I3C pulse in each sequence provides quadrature detection in wl.
+,
125.0
250.0
z 20.0
10.0
0.0
10.0
20.0
0 2 (Hz) Figure 8. Example of 2D CA(CB)HB-COSY cross peak for 20 m M uniformly I3C-enriched L-Ala in DzO showing an E.COSY-like pattern from which the homonuclear ' J ( Ha-H@) coupling constant has been determined. This spectrum was obtained without heteronuclear antiphase coherence refocusing. The cross peak shows a large ' J (HaC") splitting of ca. 140 Hz in w l and a 3J(H"-HP)splitting of ca. 7 Hz in w2. This experimental result agrees with the ensemble-averaged value of ca. 7 Hz calculated for three equally populated staggered rotamer states of XI.*'
334
MONTELIONE, EMERSON, AND LYONS
periments will allow measurements of many vicinal coupling constants in proteins a n d other molecules of known structures t o be obtained. With these data it will be possible to calibrate the corresponding Karplus curves and t o characterize the effects of side-chain functionalities on these curves. Measurements of multiple homo- and heteronuclear coupling constants that depend on the same dihedral angle can be used t o obtain stereospecific assignments, and to characterize conformational distributions of backbone and side-chain dihedral angles. When applied to proteins of unknown structure, they will provide many additional local conformational constraints that can be combined with information obtained from NOE measurements to provide more precise determinations of protein solution structures by nmr spectroscopy. We thank Prof. Gerhard Wagner for helpful discussions and encouragement. This work was supported by The Searle Scholars Program/The Chicago Community Trust, The Johnson and Johnson Research Discovery Program, and The New Jersey Commission on Science and Technology.
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14. Bruschweiler, R., Madsen, J. C., Griesinger, C., S0rensen, 0.W. & Ernst, R. R. (1987) J. Magn. Reson. 73, 380-385. 15. Kessler, H., Anders, U. & Gemmecker, G. (1988) J. Magn. Reson. 78,382-388. 16. Emsley, L., Huber, P. & Bodenhausen, G. (1990) Angew. Chem. Int. Ed. Engl. 29, 517-520. 17. Emsley, L. & Bodenhausen, G. (1991) J . Am. Chem. SOC.113, 3309-3316. 18. Montelione, G. T. &Wagner, G. ( 1989) J. Am. Chem. Soc. 111,5474-5475. 19. Montelione, G. T., Winkler, M. E., Rauenbuehler, P. & Wagner, G. (1989) J . Magn. Reson. 82, 198-204. 20. Wagner, G., Nirmala, N. R., Montelione, G. T. & Hyberts, S. (1990) Frontiers of N M R in Molecular Biology, R. Liss, New York, pp. 129-143. 21. Bauer, C., Freeman, R., Frenkiel, T., Keeler, J. & Shaka, A. J. (1984) J. Magn. Reson. 58,442-457. 22. Warren, W. S. (1988) Science 242, 878-884. 23. Emsley, L. & Bodenhausen, G. (1989) J. Magn. Reson. 82, 211-221. 24. Geen, H. & Freeman, R. (1990) J. Magn. Reson. 87, 415-421. 25. Garbow, J. R., Weitekamp, D. P. & Pines, A. (1982) Chem. Phys. Lett. 93, 504-509. 26. Wimperis, S. & Freeman, R. ( 1984) J . Magn. Reson. 58, 348-353. 27. Wider, G., Neri, D., Otting, G. & Wuthrich, K. (1989) J. Magn. Reson. 85, 426-431. 28. Edison, A. S., Westler, W. M. & Markley, J. L. (1991) J . Magn. Reson. 92, 434-438. 29. Bystrov, V. F. (1976) Progr. N M R Spectrosc. 10,4181. 30. Fischman, A. J., Live, D., Wyssbrod, H. R., Agosta, W. C. & Cowburn, D. (1980) J . Am. Chem. SOC.102, 2533. 31. Cowburn, D., Live, D., Fischman, A. J. & Agosta, W. C . (1983) J . Am. Chem. SOC.105, 7435. 32. Bax, A., Clore, G. M., Driscoll, P. C., Gronenborn, A. M., Ikura, M. & Kay, L. (1990) J . Magn. Reson. 87, 620-627, 33. Kay, L. E., Ikura, M. & Bax, A. (1990) J . Am. Chem. SOC.112, 888-889. 34. Bax, A., Clore, M. & Gronenborn, A. M. (1990) J. Magn. Reson. 88,425-431. 35. Fesik, S. W., Eaton, H. L., Olejniczak, E. T. & Zuiderweg, E. R. P. (1990) J . A m . Chem. SOC.112,886888. 36. Morris, G. A. (1980) J . Am. Chem. Soc. 102, 428429. 37. Montelione, G. T. & Wagner, G. (1990) J . Magn. Reson. 87, 183-188.
Received June 10, 1991 Accepted July 25, 1991
