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Effects of cross relaxation on the analysis of T1 data in paramagnetic proteins
JOURNAL
OF MAGNETIC
RESONANCE
52,492-496
( 1983)
NOTES Effects of Cross Relaxation on the Analysis of T, Data in ParamagneticProteins EINAR SLETTEN,* J. TIMOTHY JACKSON, PHILLIP D. BURNS, AND GERD N. LA MAR? Department of Chemistry, University of California, Davis, Ca/$ornia 95616 Received August 2, 1982
It has long been known that cross relaxation (CR) can strongly influence and even dominate T, measurements in diamagnetic proteins (1-3). However, it was initially assumed that CR and NOES are negligible in paramagnetic systems where intrinsic relaxation rates are relatively fast (4). Andre (5) has pointed out that neglect of CR when using relaxing paramagnetic probes for distance determination in proteins may lead to erroneous results, and recently Granot (6) has presented a theory for the effect of CR on the longitudinal relaxation in a dipolar coupled homonuclear spin system that also interacts with a paramagnetic probe. However, little experimental evidence has been published for the importance of CR, and the degree to which it interferes with the interpretation of the paramagnetic relaxation in such systems. CR manifests itself by curved semilogarithmic T, plots or deviations from singleexponential decay of the z-component magnetization. The absence of curvature, however, does not always mean that CR is absent. The CR rate may be either very fast, giving initially a single exponential decay curve, or very slow so as to produce curvature outside the chosen observation range of T values. Several paramagnetic proteins with molecular weights in the range lO,OOO-20,000 are presently being studied by ‘H NMR in this laboratory. Semilogarithmic Ti plots for all these proteins exhibit pronounced curvature for at least several of the resonances. We have been studying the Gd3+-induced paramagnetic relaxation (7) of the low spin (S = l/2) horse heart ferricytochrome c (cyto. c). Specific Gd3+ binding to the protein results in differential broadening of various resonances as depicted in Fig. 1. These hyperfme shifted resonances arise from the assigned heme, axial methionine (4, 8), as well as some as yet unassigned probable amino acid protons. Analysis of this Gd3+-induced dipolar relaxation (9), which varies as the inverse sixth power of the distance to the Gd3+, using the assigned resonances is expected to define a binding site, which in turn can be used to assign new resonances. While the binding site is not yet defined, our studies have produced some interesting observations relevant to the interpretation of such data. The structural data are derived from the increase in relaxation due to the fractional increase in Gd3+ binding (9) and are more appro* On sabbatical leave. from the Department of Chemistry, University of Bergen, Bergen, Norway. t To whom correspondence should be addressed. 492 0022-2364183 $3.00 Copyright 0 1983 by Academic Pres, Inc. All ri@ts of rtprcduction in any form resewed.
493
NOTES
30
20
10
-10
-20
wm
F% 1. The hyperline shifted regions of the 360 MHz ‘H NMR spectra of 5 mM horse heart ferricytochrome c in *Hz0 at 25°C and pH 6.0: A, pure protein [cd”] = 0; B, [cd”] = 10 mM, C, [Gd’+] = 20 mM. Spectra were recorded on a Nicolet NT-360 instrument using the TlIRCA pulse sequence, and consist of 320 scans collected at 16K points over a 30 kHz bandwidth with a 12.5 psec 90’ pulse. Signal-to-noise was improved by apodization of the free-induction decay.
priately studied using the spin-lattice rather than the spin-spin relaxation (IO). This requires characterization of the spin-lattice relaxation behavior of the Cd-free protein. However, determination of the spin-lattice relaxation rate by the conventional nonselective “inversion recovery” method yields data which clearly do not fit single exponential decays, as demonstrated by the curved semilogarithmic Ti plots in Fig. 2. It has been suggested that such nonexponential spin-lattice relaxation plots can be ascribed to ill-determined 1, values arising from poor experimental procedures (II). That this explanation is unlikely in this case is indicated by the fact that deviations from singly exponential behavior produce curvatures in both positive and negative directions when examined in semilogarithmic plots (cf. Fig. 2, curves a and h). Furthermore the degree of curvature so observed is correlated with the initial slopes, viz, increasing the initial slope causes the deviation to become more effective in producing upward curvature (Fig. 2). The employment of repetition times and r values well in excess of 5 X T, aids in ruling out the possibility of inaccurate 1, determination. Hyperhne shifted heme resonances generally have relatively fast relaxation rates and since in most cases the nuclei producing CR are slowly relaxing protons of the peptide chain, the semilogarithmic plots will be concave, i.e., the slope U with increasing T values (2). In cyto. c most well resolved hype&e shifted resonances are found to exhibit the expected concave curvature. However, resonance h, which has
494
NOTES
\
\ \. \
\ \
.I
.2
.3
b-a
\
.4
iskec)
FIG. 2. Plots of In (I, - I,)/2I, vs T for selected hype&e shifted resonances of cyto. c in the absence of Gd3+. The nomenclature corresponds to the peak labels in Fig. 1. The lines reflect the initial linear portions for each peak: dashed curves indicate connectivity and have no theoretical significance. The curve labeled SL was obtained by a selective inversion-recovery experiment [5 msec 90’ pulse, carrier at 33 ppm]; the other curves repreSent nonselective inversion recovery. All curves are plotted to the same scale but are displaced vertically for clarity.
a relatively slow intrinsic relaxation rate, is shown to exhibit an initial convex curvature, indicating CR with an ensemble of nuclei with appreciably faster relaxation rates (2). Hence, in contrast to peaks a and b, whose cross relaxation is probably dominated by diamagnetic protein protons, peak h has its relaxation governed by a strongly paramagnetically a&cted nucleus or nuclei. The intrinsic relaxation rate for
495
NOTES
the pure protein required for an analysis of Gd3+-induced relaxation will presumably be derived from the initial slopes of the semilogarithmic plots in Fig. 2 (2). The addition of Gd3+ will increase the paramagnetic contribution to the relaxation rate (i.e., “leakage”) which should further suppress CR effects. The influence of adding Gd3+ upon the relaxation rate of peak a are illustrated in Fig. 3. The effects of increasing [Gd3’] are clearly discernible: the apparent initial slope increases and the curvature becomes less at the same fractional recovery of the z magnetization. Curve C in Fig. 3 is derived from the behavior of the sample characterized by trace C in Fig,. 1. It is to be anticipated that the addition of sufficient Gd3+ will lead to singleexponential behavior. However, considerable loss of resolution of peaks of interest (i.e., peaks i and j) has occurred under conditions depicted in C of Fig. 1 and, in fact less Gd3+ should be used for a quantitative analysis. Hence the data in Figs. 2 and 3 bear out the salient features of Granot’s work (6). These data also demonstrate It
-7
I <
I-
.l
.2
.3
.4
rkec
1
FIG. 3. The effect of Gd3+ upon the plot of In (f, - I,)/21, vs T for peak a in Fig. 1. The curves are designated by letters which correspond to the samples used to obtain the spectra in Fig. 1. The straight lines indicate the initial slopes; dashed curves indicate connectivity and have no theoretical significance. All curves are plotted to the same scale but are displaced vertically for clarity.
496
NOTES
that it is necessary to cope with CR in any attempted quantitative analysis of the Gd3+-induced relaxation in terms of metal-proton distances in this protein. In any study of lanthanide-induced relaxation in diamagnetic proteins it should be appreciated that CR will be more severe and the analysis consequently more involved (2, 3). in principle, additional structural information can be obtained from the CR rates by a more complete analysis of the magnetization decay (this is more conventionally and more conveniently achieved through analysis of the NOES (12)). However this information is contained at longer 7 values, precisely in that region where errors in the measurement of the decaying magnetization are largest. Morris and Freeman (13) have suggested the use of selective (SL) rather than nonselective (NS) inversionrecovery experiments to extract both the intrinsic relaxation rate and the cross-relaxation rate. In the SL experiment, in the slow motion limit, the CR rate is positive and at its maximum at 7 = 0. Thus the measured SL rate should be faster than the NS rate. This is shown for peaks a and b in the absence of Gd3+ in Fig. 2. The data in Fig. 2 show that the semilogarithmic plot for the SL experiment indicates behavior closer to a single exponential (i.e., less curvature) than for the NS experiment. Since the molecule is in the region where CR is expected to be slow compared to the intrinsic relaxation, the reduced curvature in the SL case with respect to the NS experiment is inconsistent with predictions. At this time we are unable to offer an explanation for this apparent discrepancy. ACKNOWLEDGMENTS We thank Joseph Granot for sending us a preprint of his manuscript. This work was supported by a grant from the National Science Foundation (CHE-8 I-08766) and by the University of California, Davis, Nuclear Magnetic Resonance Facility. ES. thanks the Norwegian Scientific Research Council for Science and the Humanities for financial support. REFERENCES
1. I. D. CAMPBELL 2. 3. 4. 5. 6. 7. 8. 9. IO. I I. 12. 13.
AND R. FREEMAN, J. Mum. Resort. 11, 143 (1973). KALK AND H. J. C. BERENDSEN, J. Mum. Resort. 24, 343 (1976). D. SYKES, W. E. HULL, AND G. H. SNYDER, Biophys. J. 21, 137 (1978). M. KELLER AND K. WUTHRICH, Biochim. Biophys. Acta 533, 195 (1978). J. ANDRE& J. Magn. Reson. 29, 419 (1978). GRANOT, J. Magn. Reson. 49, 257 (1982). D. BURNS AND G. N. LA MAR, .J. Biol. Chem. 256,4934 (1981). M. KELLER AND K. WUTHRICH, Biol. Magn. Reson. 3, 1 (198 1). JARDETZKY AND G. C. K. ROBERTS, “NMR in Molecular Biology,” Chap. 3, Academic Press, New York, 1981. P. D. BURNS AND G. N. LA MAR, J. Mugn. Reson. 46,61 (1982). M. SASS AND D. Zmssow, J. Magn. Reson. 25,263 ( 1977). J. H. NOGGLE AND R. E. SCHIRMER, “The Nuclear Overhauser Effect,” Academic Press, New York, 1971. G. A. MORRIS AND R. FREEMAN, J. Mugn. Reson. 29,433 (1978).
A. B. R. P. J. P. R. 0.
OF MAGNETIC
RESONANCE
52,492-496
( 1983)
NOTES Effects of Cross Relaxation on the Analysis of T, Data in ParamagneticProteins EINAR SLETTEN,* J. TIMOTHY JACKSON, PHILLIP D. BURNS, AND GERD N. LA MAR? Department of Chemistry, University of California, Davis, Ca/$ornia 95616 Received August 2, 1982
It has long been known that cross relaxation (CR) can strongly influence and even dominate T, measurements in diamagnetic proteins (1-3). However, it was initially assumed that CR and NOES are negligible in paramagnetic systems where intrinsic relaxation rates are relatively fast (4). Andre (5) has pointed out that neglect of CR when using relaxing paramagnetic probes for distance determination in proteins may lead to erroneous results, and recently Granot (6) has presented a theory for the effect of CR on the longitudinal relaxation in a dipolar coupled homonuclear spin system that also interacts with a paramagnetic probe. However, little experimental evidence has been published for the importance of CR, and the degree to which it interferes with the interpretation of the paramagnetic relaxation in such systems. CR manifests itself by curved semilogarithmic T, plots or deviations from singleexponential decay of the z-component magnetization. The absence of curvature, however, does not always mean that CR is absent. The CR rate may be either very fast, giving initially a single exponential decay curve, or very slow so as to produce curvature outside the chosen observation range of T values. Several paramagnetic proteins with molecular weights in the range lO,OOO-20,000 are presently being studied by ‘H NMR in this laboratory. Semilogarithmic Ti plots for all these proteins exhibit pronounced curvature for at least several of the resonances. We have been studying the Gd3+-induced paramagnetic relaxation (7) of the low spin (S = l/2) horse heart ferricytochrome c (cyto. c). Specific Gd3+ binding to the protein results in differential broadening of various resonances as depicted in Fig. 1. These hyperfme shifted resonances arise from the assigned heme, axial methionine (4, 8), as well as some as yet unassigned probable amino acid protons. Analysis of this Gd3+-induced dipolar relaxation (9), which varies as the inverse sixth power of the distance to the Gd3+, using the assigned resonances is expected to define a binding site, which in turn can be used to assign new resonances. While the binding site is not yet defined, our studies have produced some interesting observations relevant to the interpretation of such data. The structural data are derived from the increase in relaxation due to the fractional increase in Gd3+ binding (9) and are more appro* On sabbatical leave. from the Department of Chemistry, University of Bergen, Bergen, Norway. t To whom correspondence should be addressed. 492 0022-2364183 $3.00 Copyright 0 1983 by Academic Pres, Inc. All ri@ts of rtprcduction in any form resewed.
493
NOTES
30
20
10
-10
-20
wm
F% 1. The hyperline shifted regions of the 360 MHz ‘H NMR spectra of 5 mM horse heart ferricytochrome c in *Hz0 at 25°C and pH 6.0: A, pure protein [cd”] = 0; B, [cd”] = 10 mM, C, [Gd’+] = 20 mM. Spectra were recorded on a Nicolet NT-360 instrument using the TlIRCA pulse sequence, and consist of 320 scans collected at 16K points over a 30 kHz bandwidth with a 12.5 psec 90’ pulse. Signal-to-noise was improved by apodization of the free-induction decay.
priately studied using the spin-lattice rather than the spin-spin relaxation (IO). This requires characterization of the spin-lattice relaxation behavior of the Cd-free protein. However, determination of the spin-lattice relaxation rate by the conventional nonselective “inversion recovery” method yields data which clearly do not fit single exponential decays, as demonstrated by the curved semilogarithmic Ti plots in Fig. 2. It has been suggested that such nonexponential spin-lattice relaxation plots can be ascribed to ill-determined 1, values arising from poor experimental procedures (II). That this explanation is unlikely in this case is indicated by the fact that deviations from singly exponential behavior produce curvatures in both positive and negative directions when examined in semilogarithmic plots (cf. Fig. 2, curves a and h). Furthermore the degree of curvature so observed is correlated with the initial slopes, viz, increasing the initial slope causes the deviation to become more effective in producing upward curvature (Fig. 2). The employment of repetition times and r values well in excess of 5 X T, aids in ruling out the possibility of inaccurate 1, determination. Hyperhne shifted heme resonances generally have relatively fast relaxation rates and since in most cases the nuclei producing CR are slowly relaxing protons of the peptide chain, the semilogarithmic plots will be concave, i.e., the slope U with increasing T values (2). In cyto. c most well resolved hype&e shifted resonances are found to exhibit the expected concave curvature. However, resonance h, which has
494
NOTES
\
\ \. \
\ \
.I
.2
.3
b-a
\
.4
iskec)
FIG. 2. Plots of In (I, - I,)/2I, vs T for selected hype&e shifted resonances of cyto. c in the absence of Gd3+. The nomenclature corresponds to the peak labels in Fig. 1. The lines reflect the initial linear portions for each peak: dashed curves indicate connectivity and have no theoretical significance. The curve labeled SL was obtained by a selective inversion-recovery experiment [5 msec 90’ pulse, carrier at 33 ppm]; the other curves repreSent nonselective inversion recovery. All curves are plotted to the same scale but are displaced vertically for clarity.
a relatively slow intrinsic relaxation rate, is shown to exhibit an initial convex curvature, indicating CR with an ensemble of nuclei with appreciably faster relaxation rates (2). Hence, in contrast to peaks a and b, whose cross relaxation is probably dominated by diamagnetic protein protons, peak h has its relaxation governed by a strongly paramagnetically a&cted nucleus or nuclei. The intrinsic relaxation rate for
495
NOTES
the pure protein required for an analysis of Gd3+-induced relaxation will presumably be derived from the initial slopes of the semilogarithmic plots in Fig. 2 (2). The addition of Gd3+ will increase the paramagnetic contribution to the relaxation rate (i.e., “leakage”) which should further suppress CR effects. The influence of adding Gd3+ upon the relaxation rate of peak a are illustrated in Fig. 3. The effects of increasing [Gd3’] are clearly discernible: the apparent initial slope increases and the curvature becomes less at the same fractional recovery of the z magnetization. Curve C in Fig. 3 is derived from the behavior of the sample characterized by trace C in Fig,. 1. It is to be anticipated that the addition of sufficient Gd3+ will lead to singleexponential behavior. However, considerable loss of resolution of peaks of interest (i.e., peaks i and j) has occurred under conditions depicted in C of Fig. 1 and, in fact less Gd3+ should be used for a quantitative analysis. Hence the data in Figs. 2 and 3 bear out the salient features of Granot’s work (6). These data also demonstrate It
-7
I <
I-
.l
.2
.3
.4
rkec
1
FIG. 3. The effect of Gd3+ upon the plot of In (f, - I,)/21, vs T for peak a in Fig. 1. The curves are designated by letters which correspond to the samples used to obtain the spectra in Fig. 1. The straight lines indicate the initial slopes; dashed curves indicate connectivity and have no theoretical significance. All curves are plotted to the same scale but are displaced vertically for clarity.
496
NOTES
that it is necessary to cope with CR in any attempted quantitative analysis of the Gd3+-induced relaxation in terms of metal-proton distances in this protein. In any study of lanthanide-induced relaxation in diamagnetic proteins it should be appreciated that CR will be more severe and the analysis consequently more involved (2, 3). in principle, additional structural information can be obtained from the CR rates by a more complete analysis of the magnetization decay (this is more conventionally and more conveniently achieved through analysis of the NOES (12)). However this information is contained at longer 7 values, precisely in that region where errors in the measurement of the decaying magnetization are largest. Morris and Freeman (13) have suggested the use of selective (SL) rather than nonselective (NS) inversionrecovery experiments to extract both the intrinsic relaxation rate and the cross-relaxation rate. In the SL experiment, in the slow motion limit, the CR rate is positive and at its maximum at 7 = 0. Thus the measured SL rate should be faster than the NS rate. This is shown for peaks a and b in the absence of Gd3+ in Fig. 2. The data in Fig. 2 show that the semilogarithmic plot for the SL experiment indicates behavior closer to a single exponential (i.e., less curvature) than for the NS experiment. Since the molecule is in the region where CR is expected to be slow compared to the intrinsic relaxation, the reduced curvature in the SL case with respect to the NS experiment is inconsistent with predictions. At this time we are unable to offer an explanation for this apparent discrepancy. ACKNOWLEDGMENTS We thank Joseph Granot for sending us a preprint of his manuscript. This work was supported by a grant from the National Science Foundation (CHE-8 I-08766) and by the University of California, Davis, Nuclear Magnetic Resonance Facility. ES. thanks the Norwegian Scientific Research Council for Science and the Humanities for financial support. REFERENCES
1. I. D. CAMPBELL 2. 3. 4. 5. 6. 7. 8. 9. IO. I I. 12. 13.
AND R. FREEMAN, J. Mum. Resort. 11, 143 (1973). KALK AND H. J. C. BERENDSEN, J. Mum. Resort. 24, 343 (1976). D. SYKES, W. E. HULL, AND G. H. SNYDER, Biophys. J. 21, 137 (1978). M. KELLER AND K. WUTHRICH, Biochim. Biophys. Acta 533, 195 (1978). J. ANDRE& J. Magn. Reson. 29, 419 (1978). GRANOT, J. Magn. Reson. 49, 257 (1982). D. BURNS AND G. N. LA MAR, .J. Biol. Chem. 256,4934 (1981). M. KELLER AND K. WUTHRICH, Biol. Magn. Reson. 3, 1 (198 1). JARDETZKY AND G. C. K. ROBERTS, “NMR in Molecular Biology,” Chap. 3, Academic Press, New York, 1981. P. D. BURNS AND G. N. LA MAR, J. Mugn. Reson. 46,61 (1982). M. SASS AND D. Zmssow, J. Magn. Reson. 25,263 ( 1977). J. H. NOGGLE AND R. E. SCHIRMER, “The Nuclear Overhauser Effect,” Academic Press, New York, 1971. G. A. MORRIS AND R. FREEMAN, J. Mugn. Reson. 29,433 (1978).
A. B. R. P. J. P. R. 0.