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Are true scalar proton—proton connectivities ever measured in COSY spectra of paramagnetic macromolecules?
Volume 203, number 5,6
CHEMICAL PHYSICS LETTERS
5 March 1993
Are true scalar proton-proton connectivities ever measured in COSY spectra of paramagnetic macromolecules? Ivano Bertini a, Claudio Luchinat b and Dario Tarchi a a Department of Chemistry, University of Florence, Via Gino Capponi 7, 50121 Florence, Italy b Institute ofAgricultural Chemistry, University ofBologna,
Kale Berti Pichat IO, 40127 Bologna, Italy
Received 5 January 1993
The problem of the detectability of ‘H COSY cross peaks between hypertine broadened signals in paramagnetic macromolecules in order to ascertain whether they are observable and, if so, to understand their nature, is addressed. It is shown that cross peaks often arise from relaxation-allowed coherence transfer rather than from true scalar couplings. The effect arises from cross correlation between interproton dipolar coupling and Curie relaxation. The latter, which is often the dominant source of ‘H line broadening in paramagnetic macromolecules, effectively acts as a chemical shift anisotropy relaxation mechamsm, which is known to cross correlate with proton-proton dipolar relaxation. Literature data are critically evaluated in the light of the above finding.
1. Introduction
Wimperis and Bodenhausen [ 1 ] have explicitly pointed out in 1989 the concept, developed earlier by them and others [ 2-8 1, that in a dipolar coupled AX system with JAx=O the two degenerate components of the Zeeman transitions for each spin may have different longitudinal and transverse relaxation times. Different transverse relaxation times result in different linewidths, detectable from the lineshape of the corresponding signals. If both A and X signals have different linewidths of the two components, cross peaks appear in COSY experiments [ 11. The presence of a scalar coupling and the consequent removal of component degeneracy are absolutely unnecessary for the phenomenon to be present and detected. Differences in linewidths typically arise from cross-correlation effects between the dipole-dipole (DD) relaxation between the A and X spins and chemical shift anisotropy (CSA) relaxation [ 1,7101. This phenomenon has never been of great concern for ‘H NMR spectroscopy because CSA for protons is always small [ 1l-141, although a few examples of non-negligible CSA for protons [ lo] and of relaxation-allowed cross peaks [ 1] have been looked for and emphasized. In paramagnetic compounds Elsevier Science Publishers B.V.
NMR
signals are
often broad, and J splittings are often unresolved. This is particularly true for protons in paramagnetic macromolecules [ 15,161. Despite this unfavorable situation, detection of COSY cross peaks has been reported [ 17-261, even for linewidths as large as 500- 1000 Hz [ 17,181. It is the purpose of this Letter to evaluate the possible contribution to the cross peak intensity from other mechanisms based on cross-correlation effects. Nuclear relaxation of an AX system in a paramagnetic compound is due to the coupling of each nucleus with the unpaired electron(s) through dipolar [ 271 or contact [ 28,291 contributions, to the DD AX interaction [ 11,271, and to the so-called Curie relaxation (CR ) mechanism [ 30,3 1 ] which is due to the dipolar coupling of each nucleus with the
time-averaged electron magnetic moment induced by the external magnetic field [ 15,161. It has never been noted, up to now, that the latter two mechanisms, i.e. CR and DD AX relaxation cross correlate exactly as CSA and DD AX relaxation do in diamagnetic systems. As does CSA, transverse CR relaxation increases with the square of the magnetic field. Since many experiments on paramagnetic metalloproteins are performed at high magnetic fields, CR relaxation is always sizeable. As a consequence 445
CHEMICALPHYSICS LETTERS
Volume 203, number 5,6
of this effect, it is shown that COSY cross peaks are generated #I,
2. Curie relaxation and dipolar interactions We have computer-simulated COSY spectra of an AX system, and calculated the intensity of the COSY cross peaks under a variety of conditions, using the density matrix description of the system [ 12,32-341, including relaxation effects [ I 1,35 1. Calculations have been performed for all interactions being in the slow motion limit, as is the case for macromolecules. All the results will be shown for magnitude-type [ 121 spectra obtained with P-type peak selection, but the same conclusions can be obtained from N-type peak selection or phase sensitive [ 121 phase cycles. In all cases the ty and ,pX time domains were chosen to be the same and adapted to twice the T2 (or average T,) of the signals, also taken to be equal to one another. A sine squared weighting function was always applied. Curve (A) in fig. 1 shows as a reference behavior the decrease in intensity of the cross peak for +J’Another underevaluated effect ofcross correlation is that, when the linewidths of the two components are different, the presence of the broader component may not be appreciated in a crowded spectral region and a seemingly fractional signal intensity may result.
5 March 1993
an AX system scalar-coupled with JAx= 10 Hz as a function of the increased linewidth of the signals. The horizontal dashed lines show the unit intensity and the detectability threshold when the S/N ratio in the experiment is as high as 1000. Even with such a high S/N ratio, not easily achievable on a paramagnetic metalloprotein solution, the cross peaks fall below detection already for linewidths of the order of 300 HZ. If, however, under these conditions signals A and X both have signal components with different linewidths, the cross peak intensity is dramatically enhanced. The different linewidths result from cross correlation between DD AX relaxation and CR relaxation of both A and X spins, according to the following equations (for protons in the slow motion limit ) :
R
4 h CR(A)=
5
z 0
R CR(X)=
2 y~B&+‘BS2(S+ ( 3kr)2r&,
4 PLgI2y:B&$&?(S+ J
G
(3kT)2r$x
0
&A, x
1)2 7r ’
(2)
1)2 ‘I’’
(3)
=2 J~&Dwx&R(A) (3Cos2e~*X-1)
)
(4)
R cccx,=2JfR~~(A~)R~~(~) Proton Lormor Frequency (MHz) MI00 zm m4w5006m
‘“6
x(3cos2e~x~-l),
is the dipolar relaxation contribution to both A and X protons, RCRcAj and RCRcXj are the Curie relaxation contributions on the A and X protons, and Rcct,, and RCCcXj are the cross-correlation terms for the A and X protons; in the five equations YAand yx are the gyromagnetic ratios ofthe two protons, rAx is their internuclear distance, rMA and rMx are the metal-nucleus A and metal-nucleus X distances, 75, is the rotational correlation time of the molecule, BrYiAX and 0,,, are the angles metal-A-X and metal-X-A, respectively, B, is the external magnetic field, g, is the electronic g factor, S is the electron spin multiplicity and all the other symbols have their usual meaning. It clearly appears that CR behaves identically with CSA [ 1,7-IO] in giving cross correlation with DD. whereh~(AX,
100 Linewidth
(Hz)
Fig. I. Fractional COSY cross peak intensities for an AX system as a function of signal linewidth in the presence of scalar coupling (J= 10 Hz) (A) or in absence of scalar coupling and in presence ofCurie relaxation anddifferent AX coupling (rAx= 1.6 (B), 2.2 (C), 2.9 (D), 3.7 A (E)).
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CHEMICAL PHYSICS LETTERS
Under slow motion conditions, the rate C in eq. ( 10) of ref. [ I] vanishes, and in the absence of scalar coupling between A and X the evolution of the four single quantum coherences in the density matrix, aif, oaf, a:+ and c$+ is thus given by at*(t)=
exp(D$+t) exp( -iw,t)
a;+(O),
(6)
c++(t)=
exp(D$+l) exp(-iw,t)
a;+(O),
(7)
c:+(t)=
exp(D,X+t) exp(-iw,t)
a:+(O),
(8)
a;+(O),
(9)
a,X+(t)= exp(@+ t) exp( -iw,t)
where DA+ ct Z-R
DD(AX)-&R(A)
f&c(A)
3
D+-R
DD(AX)-&R(A)
-&c(A)
,
x+ D,
=-RDD(Ax)-RcR(X)+RCC(X,,
I$+=-R
DD(AX)-&R(X)-
R CC(X)*
COSY cross peak intensities were calculated using eqs. ( 1)-(9) for rAx= 1.6 A, rM,=5.2 8, r,,=5.2 A, 3 co&% 1 = -0.928 for both protons, a r, value of 10y8 s and S = 5/2 over a range of B0 values from 1.4 to 14 T, corresponding to values of the proton Larmor frequency from 60 to 600 MHz, to produce an increase of Curie relaxation. These values for the above parameters are common values easily encountered in many experimental cases. With increasing field, CR relaxation increases from about half the value of the DD relaxation contribution to about two orders of magnitude higher. Curve (B) in fig. 1 shows the calculated cross peak intensities plotted as a function of the average linewidth of the two signals, in such a way as to make the comparison easy with the calculated intensity of the “true” scalar cross peak (curve (A ) ). As stated above the linewidth increase is generated here by an increase of CR with magnetic field, at constant DD. The results are self-explanatory. Not only is the intensity of the relaxation-allowed cross peak much stronger at all values of linewidth, but it decreases more slowly when the total linewidth increases as a result of in&eased CR relaxation. Data at larger rAx values (2.2, 2.9, 3.7 8) are shown in curves (C), (D) and (E) in fig. 1. Only for relatively long internuclear distances the DD relaxation becomes so small that relaxation-allowed cross peak intensities become smaller than true sca-
5 March 1993
lar cross peaks, at least above the detectability threshold. Although cross-correlation effects are maximal when the CR and DD interactions are equal, they remain significant up to CR/DD relaxation ratios as large as 100; in other words, in large paramagnetic metalloproteins, detection of relaxation-allowed COSY cross peaks should be considered a rule rather than an exception. The data in fig, 1 have been calculated in the presence of either scalar or dipolar interactions between the nuclei. Of course, when both are present, the two effects add up. In practice, every time cross correlation is present, the major contribution to the COSY cross peak intensity arises from the latter effect. A comment is due on the dependence of the effect on the two 0 angles characterizing the system. Relaxation-allowed cross peak intensity drops to zero if one (or, more unlikely, both) angle equals 54.7”, i.e. the magic angle. Except for this singularity, an effect is always present, the largest effect being expected when both angles are zero (e.g. for a linear M-A-X arrangement). The sign of either or both the 3 cos2B- 1 functions can also be negative. A change in sign simply means interchange of the corresponding doublet component linewidths (even if they are degenerate), which is irrelevant as far as the magnitude of the cross peak is concerned. The calculations can be easily extended to the fast or intermediate motion regimes, as well as to three or four spins cases, in exactly the same way as developed by Wimperis and Bodenhausen [ 11. Detailed descriptions of the relative magnitudes of the effects under these conditions are outside the scope of this Letter.
3. A critical evaluation of literature data Many COSY cross peaks have been reported in paramagnetic metalloproteins under a variety of conditions [ 17-261. Among those involving the broadest signals are the cross peaks observed between the geminal P-CH2 protons of the iron-bound axial histidine in cytochrome c’ from C. vinosum (with about 1000 Hz linewidths) [ 171 and that between the geminal protons of a-methylene groups of a propionate of the heme in the resting-state horse447
Volume 203,number5,6
CHEMICAL PHYSICS LETTERS
radish peroxidase (with about 400 Hz linewidths) [ 18 1. In both cases the observation of a COSY cross peak was used for the assignment but the correctness of the assignment was also based on other considerations and indirect evidence. These are two typical cases where the relaxation-allowed cross peaks should be dominant over the scalar peaks, if any. Calculations using eqs. ( I)-( 9) show that the ratio between relaxation-allowed and scalar effects is about 700 in the former case and about 400 in the latter. These considerations may easily hold for a number of other cases. Genuine scalar (or predominantly scalar) cross peaks may still be expected for metalloproteins when (i) the protein is small, i.e. rr is relatively short; (ii) 5 is smaH (e.g. l/2, or small on the average as in reduced Fe& high potential iron sulfur proteins or oxidized Fe& ferredoxins having an S= 0 ground state and paramagnetic excited states close in energy [ 36 ] ); (iii) the scalar coupling constant is large even when the two protons are relatively far apart, as when the protons are in trans positions in a heme vinyl group, or in a Ha-HP moiety of, e.g., a cysteine ligand. As an example, we comment the COSY cross peak observed between the a and p protons of cysteine 63 in HiPIP from C. vinosum [ 191. The system has total spin S= l/2, obtained by antiferromagnetic coupling among four iron ions; the rotational correlation time can be estimated to be around 4 x 10e9 s; from the X-ray structure the relevant distances and angles are rAx= 3.1 A, r,,=4.0 A, rMx=4.4 A, BMAX=76”, BMXA= 62” [ 37,381; from the T, values of the signals the contribution of electron-nucleus dipolar coupling to the linewidth can be estimated to be around 150 s-r; the CR contribution is then estimated to be also around 150 s-t; given the relatively large AX distance the DD AX relaxation is small, around 0.8 s-l; a reasonable Jvalue is 10 Hz. With these estimates of the parameters the cross peak intensity should arise about 90% from the scalar effect and about 10% from the relaxation-allowed effect. The next obvious question would be whether there are experimental ways to discriminate between true scalar and relaxation-allowed cross peaks, or to factor one from the other in the presence of both. It should again be stressed that, once recognized, relaxation-allowed cross peaks also contain precious 448
5 MarchI993
structural and geometric information. A simple way of checking which is the predominant contributor could be to follow the temperature dependence of the cross peak intensity; a true scalar cross peak should increase in intensity when the lines sharpen up with temperature; on the contrary, a relaxation-allowed cross peak should have little temperature dependence because both DD AX and CR decrease with increasing temperature. In any case, the presence of a strong NOESY cross peak should always be taken as a caveat. As suggested by Wimperis and Bodenhausen [ 11, refocusing of chemical shifts could be an experimental scheme to achieve separation between the two effects. Pulse sequences for removing cross correlation effects in the measurement of heteronuclear T, and T2 have already appeared [ 391. Schemes of this kind are likely to become a must, once the risks of mistaking dipolar for scalar interactions onthe one hand, and the advantages of using relaxation-allowed cross peaks to obtain additional structural information on the other hand, are fully appreciated by researchers in the field.
Acknowledgement We wish to thank Ad Bax for warning us on the detectability of scalar COSY cross peaks between broad signals, and Hartmut Oschkinat for helpful discussion. We are particularly grateful to Geoffrey Bodenhausen for his prompt and careful reading of the manuscript and for his precious comments. We acknowledge IBM SEMEA for providing DT with a research fellowship to develop NMR-related software. The scientific collaboration with Bruker Analytische Messtechnik GMBH aimed at developing NMR applications on paramagnetic metalloproteins is likewise acknowledged.
References [ I ] S. WimperisandG. Bodenhausen, Mol.Phys.66 (I 989) 897. [ 21N. Miiller, G. Bodenhausen, IL Wiithrich and R.R.Ernst, J. Magn. Reson. 65 (1985) 53 I. [3] L.E.Kayand J.H.Prestegard, J. Am. Chem. Sot. 109 (1987) 3829.
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CHEMICAL PHYSICS LETTERS
[4] M. Rance and P.E. Wright, Chem. Phys. Letters 124 (1986) 512. [5] J. Pekarand J.S. Leigh, J. Magn. Reson. 69 (1986) 582. [6] G. Jaccard, S. Wimperis and G. Bodenhausen, J. Chem. Phys. 85 (1986) 6282. [ 71 S. Wimp& and G. Bodenhausen, Chem. Phys. Letters 140 (1987) 41. [8] M. Goldman, J. Magn. Reson. 60 (1984) 437. [ 91 M. Gutron, J.L. Leroy and R.H. Griffey, J. Am. Chem. Sot. 105 (1983) 7262. [lo] L. Di Bari, J. Kowalewksi and G. Bodenhausen, J. Chem. Phys. 93 (1990) 7698. [ 1I ] A. Abragam, The principles of nuclear magnetism (Oxford Univ. Press, Oxford, 1961) [ 121R.R. Ernst, G. Bodenhausen and A. Wokaun, Principles of nuclear magnetic resonance in one and two dinlcnsions (Oxford Univ. Press, Oxford, 1987). [ 131J. McConnell, The theory of nuclear relaxation in liquids (Cambridge Univ. Press, Cambridge, 1987). [ 141R.K. Harris, Nuclear magnetic resonance spectroscopy (Longman, London, 1986). [ 151L. Banci, I. Bertini and C. Luchinat, Nuclear and electron relaxation. The magnetic nucleus-unpaired electron coupling in solution (VCH, Weinheim, 1991) [ 161I. Bertini and C. Luchinat, NMR of paramagnetic molecules in biological systems (Benjamin/Cummings, Menlo Park, 1986). [ 171L. Banci, I. Bertini, P. Turano and M. Vicens Oliver, Eur. J. Biochem. 204 (1992) 107. [ 181J.S. de Ropp and G.N. La Mar, J. Am. Chem. Sot. 113 (1991) 4348. [ 191I. Bertini, F. Capozzi, S. Ciurli, C. Luchinat, L. Messori and M. Piccioli, J. Am. Chem. Sot. 114 (1992) 3332.
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[20] L.P. Yu, G.N. La Mar and K. Rajarathnam, J. Am. Chem. Sot. 112 (1990) 9527. [21] L. Banci, I. Bertini, P. Turano, J.C. Ferrer and A.G. Mauk, Inorg. Chem. 30 (1991) 4510. [22] J.D. Satterlee, D.J. Russell and J.E. Erman, Biochemistry 30 (1991) 9072. [23] J.S. de Ropp, L.P. Yu and G.N. La Mar, J. Biomol. NMR 1 (1991) 175. [24] Y. Yamamoto, K. Iwafune, N. Nanai, A. Osawa, R. Chujo and T. Suzuki, Eur. J. Biochem. 198 ( 1991) 299. [25] L. Banci, I. Bertini, E. Pease, M. Tien and P. Turano, Biochemistry 31 (1992) 10009. [261 L. Banci, I. Bertini, P. Turano, M. Tien and T.K. Kirk, Proc. Natl. Acad. Sci. US 88 ( 1991) 6956. [27] I. Solomon, Phys. Rev. 99 (1955) 559. [28] N. Bloembergen, J. Chem. Phys. 27 (1957) 575. [29] I. Solomon andN. Bloembergen, J. Chem. Phys. 25 (1956) 261. [30] M. Gueron, J. Magn. Reson. 19 (1975) 58. [31] A.J. VegaandD. Fiat, Mol. Phys. 31 (1976) 347. [ 321 C.P. Slichter, Principles of magnetic resonance (Springer, Berlin, 1989). [33] S. Schaublin, A. Hohener and R.R. Ernst, J. Magn. Reson. 13 (1974) 196. [34] A. Bax, Two dimensional nuclear magnetic resonance in liquids (Reidel, Dordrecht, 1982). [35] A.G. Redfield, Advan. Magn. Reson. 1 (1965) I. [ 361 C. Luchinat and S. Ciurli, in: Biol. Ma.gn.Reson., Vol. 12, eds. L.J. Berliner and J. Reuben, in press. [37] C.W. Carter, J. Kraut, ST. Freer, NgH. Xuong, R.A.Alden and R.G. Bartsch, J. Biol. Chem. 249 (1974) 4212. [38] C.W. Carter, J. Kraut, S.T. Freer and R.A. Alden, J. Biol. Chem. 249 (1974) 6339. [39] L.E. Kay, L.K. Nicholson, F. Delaglio, A. Bax and D.A. Torchia, J. Magn. Reson. 97 ( 1992) 359.
449
CHEMICAL PHYSICS LETTERS
5 March 1993
Are true scalar proton-proton connectivities ever measured in COSY spectra of paramagnetic macromolecules? Ivano Bertini a, Claudio Luchinat b and Dario Tarchi a a Department of Chemistry, University of Florence, Via Gino Capponi 7, 50121 Florence, Italy b Institute ofAgricultural Chemistry, University ofBologna,
Kale Berti Pichat IO, 40127 Bologna, Italy
Received 5 January 1993
The problem of the detectability of ‘H COSY cross peaks between hypertine broadened signals in paramagnetic macromolecules in order to ascertain whether they are observable and, if so, to understand their nature, is addressed. It is shown that cross peaks often arise from relaxation-allowed coherence transfer rather than from true scalar couplings. The effect arises from cross correlation between interproton dipolar coupling and Curie relaxation. The latter, which is often the dominant source of ‘H line broadening in paramagnetic macromolecules, effectively acts as a chemical shift anisotropy relaxation mechamsm, which is known to cross correlate with proton-proton dipolar relaxation. Literature data are critically evaluated in the light of the above finding.
1. Introduction
Wimperis and Bodenhausen [ 1 ] have explicitly pointed out in 1989 the concept, developed earlier by them and others [ 2-8 1, that in a dipolar coupled AX system with JAx=O the two degenerate components of the Zeeman transitions for each spin may have different longitudinal and transverse relaxation times. Different transverse relaxation times result in different linewidths, detectable from the lineshape of the corresponding signals. If both A and X signals have different linewidths of the two components, cross peaks appear in COSY experiments [ 11. The presence of a scalar coupling and the consequent removal of component degeneracy are absolutely unnecessary for the phenomenon to be present and detected. Differences in linewidths typically arise from cross-correlation effects between the dipole-dipole (DD) relaxation between the A and X spins and chemical shift anisotropy (CSA) relaxation [ 1,7101. This phenomenon has never been of great concern for ‘H NMR spectroscopy because CSA for protons is always small [ 1l-141, although a few examples of non-negligible CSA for protons [ lo] and of relaxation-allowed cross peaks [ 1] have been looked for and emphasized. In paramagnetic compounds Elsevier Science Publishers B.V.
NMR
signals are
often broad, and J splittings are often unresolved. This is particularly true for protons in paramagnetic macromolecules [ 15,161. Despite this unfavorable situation, detection of COSY cross peaks has been reported [ 17-261, even for linewidths as large as 500- 1000 Hz [ 17,181. It is the purpose of this Letter to evaluate the possible contribution to the cross peak intensity from other mechanisms based on cross-correlation effects. Nuclear relaxation of an AX system in a paramagnetic compound is due to the coupling of each nucleus with the unpaired electron(s) through dipolar [ 271 or contact [ 28,291 contributions, to the DD AX interaction [ 11,271, and to the so-called Curie relaxation (CR ) mechanism [ 30,3 1 ] which is due to the dipolar coupling of each nucleus with the
time-averaged electron magnetic moment induced by the external magnetic field [ 15,161. It has never been noted, up to now, that the latter two mechanisms, i.e. CR and DD AX relaxation cross correlate exactly as CSA and DD AX relaxation do in diamagnetic systems. As does CSA, transverse CR relaxation increases with the square of the magnetic field. Since many experiments on paramagnetic metalloproteins are performed at high magnetic fields, CR relaxation is always sizeable. As a consequence 445
CHEMICALPHYSICS LETTERS
Volume 203, number 5,6
of this effect, it is shown that COSY cross peaks are generated #I,
2. Curie relaxation and dipolar interactions We have computer-simulated COSY spectra of an AX system, and calculated the intensity of the COSY cross peaks under a variety of conditions, using the density matrix description of the system [ 12,32-341, including relaxation effects [ I 1,35 1. Calculations have been performed for all interactions being in the slow motion limit, as is the case for macromolecules. All the results will be shown for magnitude-type [ 121 spectra obtained with P-type peak selection, but the same conclusions can be obtained from N-type peak selection or phase sensitive [ 121 phase cycles. In all cases the ty and ,pX time domains were chosen to be the same and adapted to twice the T2 (or average T,) of the signals, also taken to be equal to one another. A sine squared weighting function was always applied. Curve (A) in fig. 1 shows as a reference behavior the decrease in intensity of the cross peak for +J’Another underevaluated effect ofcross correlation is that, when the linewidths of the two components are different, the presence of the broader component may not be appreciated in a crowded spectral region and a seemingly fractional signal intensity may result.
5 March 1993
an AX system scalar-coupled with JAx= 10 Hz as a function of the increased linewidth of the signals. The horizontal dashed lines show the unit intensity and the detectability threshold when the S/N ratio in the experiment is as high as 1000. Even with such a high S/N ratio, not easily achievable on a paramagnetic metalloprotein solution, the cross peaks fall below detection already for linewidths of the order of 300 HZ. If, however, under these conditions signals A and X both have signal components with different linewidths, the cross peak intensity is dramatically enhanced. The different linewidths result from cross correlation between DD AX relaxation and CR relaxation of both A and X spins, according to the following equations (for protons in the slow motion limit ) :
R
4 h CR(A)=
5
z 0
R CR(X)=
2 y~B&+‘BS2(S+ ( 3kr)2r&,
4 PLgI2y:B&$&?(S+ J
G
(3kT)2r$x
0
&A, x
1)2 7r ’
(2)
1)2 ‘I’’
(3)
=2 J~&Dwx&R(A) (3Cos2e~*X-1)
)
(4)
R cccx,=2JfR~~(A~)R~~(~) Proton Lormor Frequency (MHz) MI00 zm m4w5006m
‘“6
x(3cos2e~x~-l),
is the dipolar relaxation contribution to both A and X protons, RCRcAj and RCRcXj are the Curie relaxation contributions on the A and X protons, and Rcct,, and RCCcXj are the cross-correlation terms for the A and X protons; in the five equations YAand yx are the gyromagnetic ratios ofthe two protons, rAx is their internuclear distance, rMA and rMx are the metal-nucleus A and metal-nucleus X distances, 75, is the rotational correlation time of the molecule, BrYiAX and 0,,, are the angles metal-A-X and metal-X-A, respectively, B, is the external magnetic field, g, is the electronic g factor, S is the electron spin multiplicity and all the other symbols have their usual meaning. It clearly appears that CR behaves identically with CSA [ 1,7-IO] in giving cross correlation with DD. whereh~(AX,
100 Linewidth
(Hz)
Fig. I. Fractional COSY cross peak intensities for an AX system as a function of signal linewidth in the presence of scalar coupling (J= 10 Hz) (A) or in absence of scalar coupling and in presence ofCurie relaxation anddifferent AX coupling (rAx= 1.6 (B), 2.2 (C), 2.9 (D), 3.7 A (E)).
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Under slow motion conditions, the rate C in eq. ( 10) of ref. [ I] vanishes, and in the absence of scalar coupling between A and X the evolution of the four single quantum coherences in the density matrix, aif, oaf, a:+ and c$+ is thus given by at*(t)=
exp(D$+t) exp( -iw,t)
a;+(O),
(6)
c++(t)=
exp(D$+l) exp(-iw,t)
a;+(O),
(7)
c:+(t)=
exp(D,X+t) exp(-iw,t)
a:+(O),
(8)
a;+(O),
(9)
a,X+(t)= exp(@+ t) exp( -iw,t)
where DA+ ct Z-R
DD(AX)-&R(A)
f&c(A)
3
D+-R
DD(AX)-&R(A)
-&c(A)
,
x+ D,
=-RDD(Ax)-RcR(X)+RCC(X,,
I$+=-R
DD(AX)-&R(X)-
R CC(X)*
COSY cross peak intensities were calculated using eqs. ( 1)-(9) for rAx= 1.6 A, rM,=5.2 8, r,,=5.2 A, 3 co&% 1 = -0.928 for both protons, a r, value of 10y8 s and S = 5/2 over a range of B0 values from 1.4 to 14 T, corresponding to values of the proton Larmor frequency from 60 to 600 MHz, to produce an increase of Curie relaxation. These values for the above parameters are common values easily encountered in many experimental cases. With increasing field, CR relaxation increases from about half the value of the DD relaxation contribution to about two orders of magnitude higher. Curve (B) in fig. 1 shows the calculated cross peak intensities plotted as a function of the average linewidth of the two signals, in such a way as to make the comparison easy with the calculated intensity of the “true” scalar cross peak (curve (A ) ). As stated above the linewidth increase is generated here by an increase of CR with magnetic field, at constant DD. The results are self-explanatory. Not only is the intensity of the relaxation-allowed cross peak much stronger at all values of linewidth, but it decreases more slowly when the total linewidth increases as a result of in&eased CR relaxation. Data at larger rAx values (2.2, 2.9, 3.7 8) are shown in curves (C), (D) and (E) in fig. 1. Only for relatively long internuclear distances the DD relaxation becomes so small that relaxation-allowed cross peak intensities become smaller than true sca-
5 March 1993
lar cross peaks, at least above the detectability threshold. Although cross-correlation effects are maximal when the CR and DD interactions are equal, they remain significant up to CR/DD relaxation ratios as large as 100; in other words, in large paramagnetic metalloproteins, detection of relaxation-allowed COSY cross peaks should be considered a rule rather than an exception. The data in fig, 1 have been calculated in the presence of either scalar or dipolar interactions between the nuclei. Of course, when both are present, the two effects add up. In practice, every time cross correlation is present, the major contribution to the COSY cross peak intensity arises from the latter effect. A comment is due on the dependence of the effect on the two 0 angles characterizing the system. Relaxation-allowed cross peak intensity drops to zero if one (or, more unlikely, both) angle equals 54.7”, i.e. the magic angle. Except for this singularity, an effect is always present, the largest effect being expected when both angles are zero (e.g. for a linear M-A-X arrangement). The sign of either or both the 3 cos2B- 1 functions can also be negative. A change in sign simply means interchange of the corresponding doublet component linewidths (even if they are degenerate), which is irrelevant as far as the magnitude of the cross peak is concerned. The calculations can be easily extended to the fast or intermediate motion regimes, as well as to three or four spins cases, in exactly the same way as developed by Wimperis and Bodenhausen [ 11. Detailed descriptions of the relative magnitudes of the effects under these conditions are outside the scope of this Letter.
3. A critical evaluation of literature data Many COSY cross peaks have been reported in paramagnetic metalloproteins under a variety of conditions [ 17-261. Among those involving the broadest signals are the cross peaks observed between the geminal P-CH2 protons of the iron-bound axial histidine in cytochrome c’ from C. vinosum (with about 1000 Hz linewidths) [ 171 and that between the geminal protons of a-methylene groups of a propionate of the heme in the resting-state horse447
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radish peroxidase (with about 400 Hz linewidths) [ 18 1. In both cases the observation of a COSY cross peak was used for the assignment but the correctness of the assignment was also based on other considerations and indirect evidence. These are two typical cases where the relaxation-allowed cross peaks should be dominant over the scalar peaks, if any. Calculations using eqs. ( I)-( 9) show that the ratio between relaxation-allowed and scalar effects is about 700 in the former case and about 400 in the latter. These considerations may easily hold for a number of other cases. Genuine scalar (or predominantly scalar) cross peaks may still be expected for metalloproteins when (i) the protein is small, i.e. rr is relatively short; (ii) 5 is smaH (e.g. l/2, or small on the average as in reduced Fe& high potential iron sulfur proteins or oxidized Fe& ferredoxins having an S= 0 ground state and paramagnetic excited states close in energy [ 36 ] ); (iii) the scalar coupling constant is large even when the two protons are relatively far apart, as when the protons are in trans positions in a heme vinyl group, or in a Ha-HP moiety of, e.g., a cysteine ligand. As an example, we comment the COSY cross peak observed between the a and p protons of cysteine 63 in HiPIP from C. vinosum [ 191. The system has total spin S= l/2, obtained by antiferromagnetic coupling among four iron ions; the rotational correlation time can be estimated to be around 4 x 10e9 s; from the X-ray structure the relevant distances and angles are rAx= 3.1 A, r,,=4.0 A, rMx=4.4 A, BMAX=76”, BMXA= 62” [ 37,381; from the T, values of the signals the contribution of electron-nucleus dipolar coupling to the linewidth can be estimated to be around 150 s-r; the CR contribution is then estimated to be also around 150 s-t; given the relatively large AX distance the DD AX relaxation is small, around 0.8 s-l; a reasonable Jvalue is 10 Hz. With these estimates of the parameters the cross peak intensity should arise about 90% from the scalar effect and about 10% from the relaxation-allowed effect. The next obvious question would be whether there are experimental ways to discriminate between true scalar and relaxation-allowed cross peaks, or to factor one from the other in the presence of both. It should again be stressed that, once recognized, relaxation-allowed cross peaks also contain precious 448
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structural and geometric information. A simple way of checking which is the predominant contributor could be to follow the temperature dependence of the cross peak intensity; a true scalar cross peak should increase in intensity when the lines sharpen up with temperature; on the contrary, a relaxation-allowed cross peak should have little temperature dependence because both DD AX and CR decrease with increasing temperature. In any case, the presence of a strong NOESY cross peak should always be taken as a caveat. As suggested by Wimperis and Bodenhausen [ 11, refocusing of chemical shifts could be an experimental scheme to achieve separation between the two effects. Pulse sequences for removing cross correlation effects in the measurement of heteronuclear T, and T2 have already appeared [ 391. Schemes of this kind are likely to become a must, once the risks of mistaking dipolar for scalar interactions onthe one hand, and the advantages of using relaxation-allowed cross peaks to obtain additional structural information on the other hand, are fully appreciated by researchers in the field.
Acknowledgement We wish to thank Ad Bax for warning us on the detectability of scalar COSY cross peaks between broad signals, and Hartmut Oschkinat for helpful discussion. We are particularly grateful to Geoffrey Bodenhausen for his prompt and careful reading of the manuscript and for his precious comments. We acknowledge IBM SEMEA for providing DT with a research fellowship to develop NMR-related software. The scientific collaboration with Bruker Analytische Messtechnik GMBH aimed at developing NMR applications on paramagnetic metalloproteins is likewise acknowledged.
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[4] M. Rance and P.E. Wright, Chem. Phys. Letters 124 (1986) 512. [5] J. Pekarand J.S. Leigh, J. Magn. Reson. 69 (1986) 582. [6] G. Jaccard, S. Wimperis and G. Bodenhausen, J. Chem. Phys. 85 (1986) 6282. [ 71 S. Wimp& and G. Bodenhausen, Chem. Phys. Letters 140 (1987) 41. [8] M. Goldman, J. Magn. Reson. 60 (1984) 437. [ 91 M. Gutron, J.L. Leroy and R.H. Griffey, J. Am. Chem. Sot. 105 (1983) 7262. [lo] L. Di Bari, J. Kowalewksi and G. Bodenhausen, J. Chem. Phys. 93 (1990) 7698. [ 1I ] A. Abragam, The principles of nuclear magnetism (Oxford Univ. Press, Oxford, 1961) [ 121R.R. Ernst, G. Bodenhausen and A. Wokaun, Principles of nuclear magnetic resonance in one and two dinlcnsions (Oxford Univ. Press, Oxford, 1987). [ 131J. McConnell, The theory of nuclear relaxation in liquids (Cambridge Univ. Press, Cambridge, 1987). [ 141R.K. Harris, Nuclear magnetic resonance spectroscopy (Longman, London, 1986). [ 151L. Banci, I. Bertini and C. Luchinat, Nuclear and electron relaxation. The magnetic nucleus-unpaired electron coupling in solution (VCH, Weinheim, 1991) [ 161I. Bertini and C. Luchinat, NMR of paramagnetic molecules in biological systems (Benjamin/Cummings, Menlo Park, 1986). [ 171L. Banci, I. Bertini, P. Turano and M. Vicens Oliver, Eur. J. Biochem. 204 (1992) 107. [ 181J.S. de Ropp and G.N. La Mar, J. Am. Chem. Sot. 113 (1991) 4348. [ 191I. Bertini, F. Capozzi, S. Ciurli, C. Luchinat, L. Messori and M. Piccioli, J. Am. Chem. Sot. 114 (1992) 3332.
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