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DOSY-NOESY: Diffusion-Ordered NOESY
JOURNAL OF MAGNETIC RESONANCE, ARTICLE NO.
Series B 111, 94–96 (1996)
0066
DOSY-NOESY: Diffusion-Ordered NOESY ELLIOTT K. GOZANSKY
AND
DAVID G. GORENSTEIN *
Sealy Center for Structural Biology and the Department of Human Biological Chemistry and Genetics, University of Texas Medical Branch, Galveston, Texas 77555-1157 Received January 25, 1996
With the advent of PFG NMR, a myriad of new and refined experiments have been created. One experiment gaining popularity is the 2D DOSY (diffusion-ordered spectroscopy) experiment (1–6). It yields two-dimensional data where chemical shift is along one axis and diffusion coefficient is along the other (1) —DOSY is the 2D extension of the LED sequence (7) shown in Fig. 1. The attraction to DOSY stems from its ability to provide accurate, noninvasive, diffusion measurements on multicomponent solutions. As anticipated by Barjat, Morris, Smart, Swanson, and Williams (4), an extension of the DOSY experiment is proposed named diffusion-ordered NOESY (DOSY-NOESY). Created by placing the NOESY sequence after the DOSY sequence, the DOSY-NOESY experiment is given in Fig. 2. It yields NOESY planes with diffusion-coefficient-labeled peaks (diagonal and cross peaks). We show that diffusion labeling provided by the DOSY portion of the experiment is retained in the NOE cross peaks of the NOESY planes. The purpose of DOSY-NOESY is not to measure diffusion coefficients, but rather to use the effects of diffusion to enhance the study of complex mixtures or molecules in dynamic equilibrium with bound and free states. Provided the components of the system have significantly different diffusion coefficients, the NOE data can be resolved based on the rate of diffusion. If the rate of exchange is slow on the NMR time scale, then the NOE cross peaks will be separated by the respective diffusion coefficients. However, if the exchange rate is moderate to fast on the NMR time scale, then the NOEs from the complex will have an apparent diffusion coefficient based on the rate of exchange. The fast-exchange regime and a large molecular weight difference are required for a transfer NOE experiment to yield NOE data on complexes. DOSY-NOESY, however, does not have the dramatic molecular size dependence of transfer NOE experiments. Theoretically, the only requirement is the ability to resolve the diffusion coefficients between the species of interest and the rest of the chemical system. Equation [1] describes how the magnitude of net magneti-
zation is affected by gradient strength in the DOSY experiment (8)
F S
An (K, i) Å An (K Å 0, i)exp 0 Dn D 0
[1] where K Å gg d, g is the gyromagnetic ratio, and g and d are experimental parameters described in Fig. 1. Dn is the diffusion coefficient for the nth diffusion species. An (K Å 0, i) is the signal amplitude for spin i in the absence of field gradients and An (K, i) is the resulting signal amplitude, for the same spin, under the influence of field gradients. (Equation [1] is often reported with relaxation terms. These terms arise from the signal decay caused by relaxation during the experiment. Provided the same sequence and delay parameters are used for all data collection, relaxation effects will cancel.) In the DOSY-NOESY experiment, signal intensity available for NOE transfer is determined by the DOSY portion of the sequence. The equation describing saturation NOE enhancement is him (s) Å [An (i) 0 An (K, i)]/An (K, i),
6o0b$$7373
03-25-96 13:24:27
94
maga
[2]
where him (s) is the NOE enhancement for spin i from saturation of spin s. The diffusion indices m and n will be equal so long as the lifetime of the diffusive species is long on the experimental time scale. Similar to 2D DOSY, the diagonal and NOE cross-peak intensities will have a Gaussian dependence on the gradient field strength as a function of diffusion. Equation [1] can be rewritten such that the slope of ln[An (K, i)] {cross-peak intensity} vs g 2 {gradient strength} is proportional to the nth diffusion coefficient [with An (K Å 0, i) arbitrarily set to unity]. To demonstrate the diffusion labeling of NOE cross peaks, a D2O sample (0.6 ml) of 1.6 mg d(pAG) dinucleotide and 5 mg 14-mer duplex d(ACAATATATATTGT)2 was used. The solvent conditions were 55 mM potassium phosphate
* To whom correspondence should be addressed. 1064-1866/96 $18.00 Copyright q 1996 by Academic Press, Inc. All rights of reproduction in any form reserved.
DG
d K2 , 3
AP: Mag Res
COMMUNICATIONS
FIG. 1. The LED pulse sequence is used in 2D DOSY. Wide rectangles are gradient pulses with strength g and duration d. The d1 delay is for magnetization recovery, D is the delay between the leading edges of gradient pulses, t is the delay for eddy current dissipation, T is the diffusion labeling delay, and Te is a delay to remove unwanted signal, by a homospoil pulse (not shown), and to allow for full eddy current dissipation before the observe pulse. Long, thin, rectangles are 907 RF pulses. Three gradient prepulses are used to establish an eddy current steady state. The diffusion dimension is generated by incrementing the gradient strength g. As the gradient strength is increased, the signal amplitudes will decay in a Gaussian fashion.
buffer, 150 mM potassium chloride, and 0.1 mM sodium azide at pH 7.4. Data were taken on a specially constructed (Houston Advanced Research Center), actively shielded, 89 mm bore, 400 MHz magnet operated by a Varian UNITYplus console. A standard Varian 5 mm triple-resonance probe, with an actively shielded z gradient, was used. The gradient coils were powered by a 20 A Highland Technology gradient driver. Nine NOESY planes were acquired with a gradient strength (g) step size of 2000 DAC units (approx. 4.22 G/cm). An initial gradient strength of 4.22 G/cm was used to provide residual HOD signal suppression. The delay times in the experiment were d1 Å 1.9 s, D Å T / t, d Å 6.0 ms, t Å 6.6 ms, T Å 20.0 ms, Te Å 5.0 ms, hs1 Å 3.0 ms, hs2 Å 97.0 ms, and tm Å 100 ms. All RF pulses were calibrated to be 907, and the homospoil gradients hs1 and hs2 were 6.33 and 3.17 G/cm, respectively. A spectral window of 4000 Hz was used in both NOESY dimensions with 8192 complex points taken in the t2 dimension and 1024 complex points taken in the t1 dimension. Sixteen transients were acquired for each increment, and a temperature of 28.07C was maintained. The data were collected in pure adsorption mode with States phase cycling for t1 quadrature detection. Data processing was performed—using VNMR—by weighted 2D Fourier transform of the NOESY planes at each increment in the DOSY dimension. The planes were processed with identical weighting and phase correction. Since every DOSY-NOESY plane had identical delays, the phase correction did not appreciably change. Cross peaks were manually integrated with VNMR, and diffusion-coefficient linear-regression analysis was performed using Cricket Graph. The dinucleotide was small enough to have cross peaks in the positive NOE regime, whereas the 14-mer DNA had exclusively negative NOE cross peaks. This simplified cross-peak identification served as a verification for difference in diffusion rate and indicated that interactions between the two molecules were not long lived on the NMR time scale. Chemical shifts of the assigned signals for
6o0b$$7373
03-25-96 13:24:27
maga
95
the pure 14-mer ( 9 ) were unchanged in the mixture. The dinucleotide did have some minor changes in chemical shift possibly due to change in solvent ionic strength ( unpublished data ) . Located in similar chemical-shift regions, four dinucleotide cross peaks and four 14-mer cross peaks were used in the study. Gaussian decay of the dinucleotide cross peaks yielded an average diffusion coefficient » D …pAG Å 3.74 1 10 06 cm2 / s with a standard deviation s Å 3.0 1 10 07 cm2 / s. 14-mer cross peaks yielded an average diffusion coefficient » D …14-mer Å 1.42 1 10 06 cm2 / s with a standard deviation of s Å 3.4 1 10 08 cm2 / s. Since absolute diffusion coefficients were not necessary, the calculations were simplified by using a scaling factor such that HOD had a diffusion coefficient of 2.0 1 10 05 cm2 / s. The Stokes – Einstein equation provided a ‘‘zero-order’’ calculation of the diffusion coefficients. This verified that the measured values were in the correct range ( D14-mer Å 1.45 1 10 06 cm2 / s and DpAG Å 5.89 1 10 06 cm2 / s ) . Figure 3 is a linear-regression plot of the cross-peak volumes used in the study. The slopes are proportional to the diffusion coefficients. Integration of cross-peak volumes established that NOESY cross peaks did retain the diffusion labeling introduced by the DOSY portion of the experiment. Peaks that were assigned to the dinucleotide yielded a diffusion coefficient that was over 2.5 times faster than that for the 14-mer DNA. We have observed that the diffusion coefficients have some dependence upon the delay T. A rough calibration set (T Å 20, 40, 60, and 100 ms) revealed that the difference in diffusion coefficient was maximal (4.73 1 10 06 cm2 /s) at a delay of 60 ms. Since we are in the diffusion-limited regime (10), the dependence is possibly due to the presence
FIG. 2. The DOSY-NOESY experiment is based on the LED and the NOESY sequences. h1 and h2 are homospoil type gradients and tm and t1 are the NOESY evolution and mixing times, respectively. All RF pulses are 907 and the rest of the gradients and delays are described in Fig. 1. Note the last pulse of the LED sequence is the first pulse of the NOESY sequence. The phases of the RF pulses are labeled in the order they appear in the sequence. u1 ( / x), u2,1 ( / x, 0 x, 0 x, / x, 0 x, / x, / x, 0 x), u2,2 ( / x, 0 x, 0 x, / x, 0 x, / x, / x, 0 x, 0 x, / x, / x, 0 x, / x, 0 x, 0 x, / x), u3 ( / x), u4 ( / x, / x, 0 x, 0 x), u5,1 ( / x, / x, / x, / x, 0 x, 0 x, 0 x, 0 x, / y, / y, / y, / y, 0 y, 0 y, 0 y, 0 y), u5,2 ( / y, / y, / y, / y, 0 y, 0 y, 0 y, 0 y, / x, / x, / x, / x, 0 x, 0 x, 0 x, 0 x), u6 ( / x, / x, / x, / x, / x, / x, / x, / x, / y, / y, / y, / y, / y, / y, / y, / y), u7 ( / x, / x, / y, / y, 0 x, 0 x, 0 y, 0 y, / y, / y, 0 x, 0 x, 0 y, 0 y, / x, / x), urcv ( / x, 0 x, / y, 0 y, 0 x, / x, 0 y, / y, / y, 0 y, 0 x, / x, 0 y, / y, / x, 0 x), where the first index is the pulse number and second (if needed) refers to the two sets for t1 quadrature detection.
AP: Mag Res
96
COMMUNICATIONS
FIG. 3. Plot of eight different DOSY-NOESY cross peaks—four from d(pAG) dinucleotide and four from d(ACAATATATATTGT)2 . The absolute value of the slope is the diffusion coefficient where the diffusion coefficient of HOD was set to 2.0 1 10 05 cm2 . Empty markings belong to the 14-mer DNA and filled markings belong to the deoxy-dinucleotide. In the cross-peak data, D is the diffusion coefficient and R 2 is the correlation coefficient: ( h ) T 12 H2 * –H2 9, D14-mer Å 1.39 1 10 06 cm2 /s, and R 2 Å 0.993; ( s ) A8 H1 * –H2 *,2 9, D14-mer Å 1.40 1 10 06 cm2 /s, and R 2 Å 0.998; ( L ) C2 H6–H2 *, D14-mer Å 1.40 1 10 06 cm2 /s, and R 2 Å 0.988; ( n ) T 5 H5 * –H5 9, D14-mer Å 1.47 1 10 06 cm2 /s, and R 2 Å 0.996; ( j ) G H5 * – H5 9, DpAG Å 3.57 1 10 06 cm2 /s, and R 2 Å 0.984; ( m ) G H2 * –H2 9, DpAG Å 3.59 1 10 06 cm2 /s, and R 2 Å 0.984; ( l ) G H1 * –H2 *, DpAG Å 3.53 1 10 06 cm2 /s, and R 2 Å 0.985; ( l ) A H1 * –H2 9, DpAG Å 4.25 1 10 06 cm2 / s and R 2 Å 0.945.
of eddy currents. We attempted to minimize all delays for the purpose of maximizing the signal-to-noise ratio. Analysis of diffusion-ordered data has been known to be an ill-posed problem—assuredly even before the NOE effect is introduced. As noted in some of Johnson’s 2D DOSY work (11, 12), polydispersity in a system can further complicate the analysis. Polydispersity can introduce systematic deviations from linearity in the linear regression. In addition, NOE-cross-peak integration is subject to significant error (approximately 20%). This integration error will lead to random deviations in the analysis; thus, great care must be taken to distinguish polydispersity from integration error. Our data do have greater nonlinearity for the dinucleotide than for the 14-mer, but it is not likely due to polydispersity. As noted earlier, the dinucleotide NOE cross peaks that were positive in the pure dinucleotide sample were also positive in the mixture. The dinucleotide cross peaks for the G H5 * – H5 9 were very close to the diagonal, creating significant overlap in the first few DOSY-NOESY planes, thus explaining the systematic error in the first few data points. The rest of the deviation is fairly random, which is expected from integration error, not polydispersity. Whereas polydispersity does not seem to be a problem in this example, it can be an important aspect of data analysis. It will be essential to utilize 2D DOSY data giving complete prior diffusion knowledge for DOSY-NOESY data analysis.
6o0b$$7373
03-25-96 13:24:27
maga
An experiment similar to ours has been proposed by Do¨tsch and Wider (13) in which their sequence was used to study the exchange rates of water bound internally in proteins. The sequence has an advantage of being a shorter experiment; however, our experiment minimizes the crosspeak distortion that was noted in Do¨tsch and Wider’s work. Since the spectrometer used in this study was not equipped with shaped PFG, we chose not to use bipolar paired pulses as it would reduce signal-to-noise by introducing significant delays for gradient settling. Similar to 2D DOSY, it should be possible to diffusively resolve chemical-shift-overlapped NOE cross peaks from different diffusion species. That being true, DOSY-NOESY can be used for structural determination in various multicomponent and associative complex systems. The most convenient method for data analysis would be a program that automatically fits the diffusion coefficients for each integrated cross peak in the Fouriertransformed data, yielding a 3D DOSY-NOESY data set ( work in progress ) . DOSY-NOESY makes available NOE data for complex systems that could not previously be studied by NMR. ACKNOWLEDGMENTS This work was supported by NIH (AI27744), the Welch Foundation (H1296), the Lucille P. Markey Charitable Trust, and the Sealy and Smith Foundation. We also thank Dr. A. G. Swanson for sharing the 2D DOSY sequence and E. Ezell, Dr. J. Post, Dr. P. Pellechia, and Dr. D. Carlson for their valuable assistance.
REFERENCES 1. K. F. Morris and C. S. Johnson, Jr., J. Am. Chem. Soc. 114, 3139 (1992). 2. D. P. Hinton and C. S. Johnson, Jr., Chem. Phys. Lipids 69, 175 (1994). 3. K. F. Morris and C. S. Johnson, Jr., J. Am. Chem. Soc. 115, 4291 (1993). 4. H. Barjat, G. A. Morris, S. Smart, A. G. Swanson, and S. C. R. Williams, J. Magn. Reson. B 108, 170 (1995). 5. D. Wu, A. Chen, and C. S. Johnson, Jr., J. Magn. Reson. A 115, 260 (1995). 6. A. S. Altieri, D. P. Hinton, and R. A. Byrd, J. Am. Chem. Soc. 117, 7566 (1995). 7. S. J. Gibbs and C. S. Johnson, Jr., J. Magn. Reson. 93, 395 ( 1991 ) . 8. E. O. Stejskal and J. E. Tanner, J. Chem. Phys. 42, 228 (1965). 9. M. V. Botuyan, Ph.D. thesis, Purdue University, 1994. 10. L. Z. Wang, A. Caprihan, and E. Fukushima, J. Magn. Reson. A 117, 209 (1995). 11. K. F. Morris, C. S. Johnson, Jr., and T. C. Wong, J. Phys. Chem. 98, 603 (1994). 12. A. Chen, D. Wu, and C. S. Johnson, Jr., J. Am. Chem. Soc. 117, 7965 (1995). 13. V. Do¨tsch and G. Wider, J. Am. Chem. Soc. 117, 6064 (1995).
AP: Mag Res
Series B 111, 94–96 (1996)
0066
DOSY-NOESY: Diffusion-Ordered NOESY ELLIOTT K. GOZANSKY
AND
DAVID G. GORENSTEIN *
Sealy Center for Structural Biology and the Department of Human Biological Chemistry and Genetics, University of Texas Medical Branch, Galveston, Texas 77555-1157 Received January 25, 1996
With the advent of PFG NMR, a myriad of new and refined experiments have been created. One experiment gaining popularity is the 2D DOSY (diffusion-ordered spectroscopy) experiment (1–6). It yields two-dimensional data where chemical shift is along one axis and diffusion coefficient is along the other (1) —DOSY is the 2D extension of the LED sequence (7) shown in Fig. 1. The attraction to DOSY stems from its ability to provide accurate, noninvasive, diffusion measurements on multicomponent solutions. As anticipated by Barjat, Morris, Smart, Swanson, and Williams (4), an extension of the DOSY experiment is proposed named diffusion-ordered NOESY (DOSY-NOESY). Created by placing the NOESY sequence after the DOSY sequence, the DOSY-NOESY experiment is given in Fig. 2. It yields NOESY planes with diffusion-coefficient-labeled peaks (diagonal and cross peaks). We show that diffusion labeling provided by the DOSY portion of the experiment is retained in the NOE cross peaks of the NOESY planes. The purpose of DOSY-NOESY is not to measure diffusion coefficients, but rather to use the effects of diffusion to enhance the study of complex mixtures or molecules in dynamic equilibrium with bound and free states. Provided the components of the system have significantly different diffusion coefficients, the NOE data can be resolved based on the rate of diffusion. If the rate of exchange is slow on the NMR time scale, then the NOE cross peaks will be separated by the respective diffusion coefficients. However, if the exchange rate is moderate to fast on the NMR time scale, then the NOEs from the complex will have an apparent diffusion coefficient based on the rate of exchange. The fast-exchange regime and a large molecular weight difference are required for a transfer NOE experiment to yield NOE data on complexes. DOSY-NOESY, however, does not have the dramatic molecular size dependence of transfer NOE experiments. Theoretically, the only requirement is the ability to resolve the diffusion coefficients between the species of interest and the rest of the chemical system. Equation [1] describes how the magnitude of net magneti-
zation is affected by gradient strength in the DOSY experiment (8)
F S
An (K, i) Å An (K Å 0, i)exp 0 Dn D 0
[1] where K Å gg d, g is the gyromagnetic ratio, and g and d are experimental parameters described in Fig. 1. Dn is the diffusion coefficient for the nth diffusion species. An (K Å 0, i) is the signal amplitude for spin i in the absence of field gradients and An (K, i) is the resulting signal amplitude, for the same spin, under the influence of field gradients. (Equation [1] is often reported with relaxation terms. These terms arise from the signal decay caused by relaxation during the experiment. Provided the same sequence and delay parameters are used for all data collection, relaxation effects will cancel.) In the DOSY-NOESY experiment, signal intensity available for NOE transfer is determined by the DOSY portion of the sequence. The equation describing saturation NOE enhancement is him (s) Å [An (i) 0 An (K, i)]/An (K, i),
6o0b$$7373
03-25-96 13:24:27
94
maga
[2]
where him (s) is the NOE enhancement for spin i from saturation of spin s. The diffusion indices m and n will be equal so long as the lifetime of the diffusive species is long on the experimental time scale. Similar to 2D DOSY, the diagonal and NOE cross-peak intensities will have a Gaussian dependence on the gradient field strength as a function of diffusion. Equation [1] can be rewritten such that the slope of ln[An (K, i)] {cross-peak intensity} vs g 2 {gradient strength} is proportional to the nth diffusion coefficient [with An (K Å 0, i) arbitrarily set to unity]. To demonstrate the diffusion labeling of NOE cross peaks, a D2O sample (0.6 ml) of 1.6 mg d(pAG) dinucleotide and 5 mg 14-mer duplex d(ACAATATATATTGT)2 was used. The solvent conditions were 55 mM potassium phosphate
* To whom correspondence should be addressed. 1064-1866/96 $18.00 Copyright q 1996 by Academic Press, Inc. All rights of reproduction in any form reserved.
DG
d K2 , 3
AP: Mag Res
COMMUNICATIONS
FIG. 1. The LED pulse sequence is used in 2D DOSY. Wide rectangles are gradient pulses with strength g and duration d. The d1 delay is for magnetization recovery, D is the delay between the leading edges of gradient pulses, t is the delay for eddy current dissipation, T is the diffusion labeling delay, and Te is a delay to remove unwanted signal, by a homospoil pulse (not shown), and to allow for full eddy current dissipation before the observe pulse. Long, thin, rectangles are 907 RF pulses. Three gradient prepulses are used to establish an eddy current steady state. The diffusion dimension is generated by incrementing the gradient strength g. As the gradient strength is increased, the signal amplitudes will decay in a Gaussian fashion.
buffer, 150 mM potassium chloride, and 0.1 mM sodium azide at pH 7.4. Data were taken on a specially constructed (Houston Advanced Research Center), actively shielded, 89 mm bore, 400 MHz magnet operated by a Varian UNITYplus console. A standard Varian 5 mm triple-resonance probe, with an actively shielded z gradient, was used. The gradient coils were powered by a 20 A Highland Technology gradient driver. Nine NOESY planes were acquired with a gradient strength (g) step size of 2000 DAC units (approx. 4.22 G/cm). An initial gradient strength of 4.22 G/cm was used to provide residual HOD signal suppression. The delay times in the experiment were d1 Å 1.9 s, D Å T / t, d Å 6.0 ms, t Å 6.6 ms, T Å 20.0 ms, Te Å 5.0 ms, hs1 Å 3.0 ms, hs2 Å 97.0 ms, and tm Å 100 ms. All RF pulses were calibrated to be 907, and the homospoil gradients hs1 and hs2 were 6.33 and 3.17 G/cm, respectively. A spectral window of 4000 Hz was used in both NOESY dimensions with 8192 complex points taken in the t2 dimension and 1024 complex points taken in the t1 dimension. Sixteen transients were acquired for each increment, and a temperature of 28.07C was maintained. The data were collected in pure adsorption mode with States phase cycling for t1 quadrature detection. Data processing was performed—using VNMR—by weighted 2D Fourier transform of the NOESY planes at each increment in the DOSY dimension. The planes were processed with identical weighting and phase correction. Since every DOSY-NOESY plane had identical delays, the phase correction did not appreciably change. Cross peaks were manually integrated with VNMR, and diffusion-coefficient linear-regression analysis was performed using Cricket Graph. The dinucleotide was small enough to have cross peaks in the positive NOE regime, whereas the 14-mer DNA had exclusively negative NOE cross peaks. This simplified cross-peak identification served as a verification for difference in diffusion rate and indicated that interactions between the two molecules were not long lived on the NMR time scale. Chemical shifts of the assigned signals for
6o0b$$7373
03-25-96 13:24:27
maga
95
the pure 14-mer ( 9 ) were unchanged in the mixture. The dinucleotide did have some minor changes in chemical shift possibly due to change in solvent ionic strength ( unpublished data ) . Located in similar chemical-shift regions, four dinucleotide cross peaks and four 14-mer cross peaks were used in the study. Gaussian decay of the dinucleotide cross peaks yielded an average diffusion coefficient » D …pAG Å 3.74 1 10 06 cm2 / s with a standard deviation s Å 3.0 1 10 07 cm2 / s. 14-mer cross peaks yielded an average diffusion coefficient » D …14-mer Å 1.42 1 10 06 cm2 / s with a standard deviation of s Å 3.4 1 10 08 cm2 / s. Since absolute diffusion coefficients were not necessary, the calculations were simplified by using a scaling factor such that HOD had a diffusion coefficient of 2.0 1 10 05 cm2 / s. The Stokes – Einstein equation provided a ‘‘zero-order’’ calculation of the diffusion coefficients. This verified that the measured values were in the correct range ( D14-mer Å 1.45 1 10 06 cm2 / s and DpAG Å 5.89 1 10 06 cm2 / s ) . Figure 3 is a linear-regression plot of the cross-peak volumes used in the study. The slopes are proportional to the diffusion coefficients. Integration of cross-peak volumes established that NOESY cross peaks did retain the diffusion labeling introduced by the DOSY portion of the experiment. Peaks that were assigned to the dinucleotide yielded a diffusion coefficient that was over 2.5 times faster than that for the 14-mer DNA. We have observed that the diffusion coefficients have some dependence upon the delay T. A rough calibration set (T Å 20, 40, 60, and 100 ms) revealed that the difference in diffusion coefficient was maximal (4.73 1 10 06 cm2 /s) at a delay of 60 ms. Since we are in the diffusion-limited regime (10), the dependence is possibly due to the presence
FIG. 2. The DOSY-NOESY experiment is based on the LED and the NOESY sequences. h1 and h2 are homospoil type gradients and tm and t1 are the NOESY evolution and mixing times, respectively. All RF pulses are 907 and the rest of the gradients and delays are described in Fig. 1. Note the last pulse of the LED sequence is the first pulse of the NOESY sequence. The phases of the RF pulses are labeled in the order they appear in the sequence. u1 ( / x), u2,1 ( / x, 0 x, 0 x, / x, 0 x, / x, / x, 0 x), u2,2 ( / x, 0 x, 0 x, / x, 0 x, / x, / x, 0 x, 0 x, / x, / x, 0 x, / x, 0 x, 0 x, / x), u3 ( / x), u4 ( / x, / x, 0 x, 0 x), u5,1 ( / x, / x, / x, / x, 0 x, 0 x, 0 x, 0 x, / y, / y, / y, / y, 0 y, 0 y, 0 y, 0 y), u5,2 ( / y, / y, / y, / y, 0 y, 0 y, 0 y, 0 y, / x, / x, / x, / x, 0 x, 0 x, 0 x, 0 x), u6 ( / x, / x, / x, / x, / x, / x, / x, / x, / y, / y, / y, / y, / y, / y, / y, / y), u7 ( / x, / x, / y, / y, 0 x, 0 x, 0 y, 0 y, / y, / y, 0 x, 0 x, 0 y, 0 y, / x, / x), urcv ( / x, 0 x, / y, 0 y, 0 x, / x, 0 y, / y, / y, 0 y, 0 x, / x, 0 y, / y, / x, 0 x), where the first index is the pulse number and second (if needed) refers to the two sets for t1 quadrature detection.
AP: Mag Res
96
COMMUNICATIONS
FIG. 3. Plot of eight different DOSY-NOESY cross peaks—four from d(pAG) dinucleotide and four from d(ACAATATATATTGT)2 . The absolute value of the slope is the diffusion coefficient where the diffusion coefficient of HOD was set to 2.0 1 10 05 cm2 . Empty markings belong to the 14-mer DNA and filled markings belong to the deoxy-dinucleotide. In the cross-peak data, D is the diffusion coefficient and R 2 is the correlation coefficient: ( h ) T 12 H2 * –H2 9, D14-mer Å 1.39 1 10 06 cm2 /s, and R 2 Å 0.993; ( s ) A8 H1 * –H2 *,2 9, D14-mer Å 1.40 1 10 06 cm2 /s, and R 2 Å 0.998; ( L ) C2 H6–H2 *, D14-mer Å 1.40 1 10 06 cm2 /s, and R 2 Å 0.988; ( n ) T 5 H5 * –H5 9, D14-mer Å 1.47 1 10 06 cm2 /s, and R 2 Å 0.996; ( j ) G H5 * – H5 9, DpAG Å 3.57 1 10 06 cm2 /s, and R 2 Å 0.984; ( m ) G H2 * –H2 9, DpAG Å 3.59 1 10 06 cm2 /s, and R 2 Å 0.984; ( l ) G H1 * –H2 *, DpAG Å 3.53 1 10 06 cm2 /s, and R 2 Å 0.985; ( l ) A H1 * –H2 9, DpAG Å 4.25 1 10 06 cm2 / s and R 2 Å 0.945.
of eddy currents. We attempted to minimize all delays for the purpose of maximizing the signal-to-noise ratio. Analysis of diffusion-ordered data has been known to be an ill-posed problem—assuredly even before the NOE effect is introduced. As noted in some of Johnson’s 2D DOSY work (11, 12), polydispersity in a system can further complicate the analysis. Polydispersity can introduce systematic deviations from linearity in the linear regression. In addition, NOE-cross-peak integration is subject to significant error (approximately 20%). This integration error will lead to random deviations in the analysis; thus, great care must be taken to distinguish polydispersity from integration error. Our data do have greater nonlinearity for the dinucleotide than for the 14-mer, but it is not likely due to polydispersity. As noted earlier, the dinucleotide NOE cross peaks that were positive in the pure dinucleotide sample were also positive in the mixture. The dinucleotide cross peaks for the G H5 * – H5 9 were very close to the diagonal, creating significant overlap in the first few DOSY-NOESY planes, thus explaining the systematic error in the first few data points. The rest of the deviation is fairly random, which is expected from integration error, not polydispersity. Whereas polydispersity does not seem to be a problem in this example, it can be an important aspect of data analysis. It will be essential to utilize 2D DOSY data giving complete prior diffusion knowledge for DOSY-NOESY data analysis.
6o0b$$7373
03-25-96 13:24:27
maga
An experiment similar to ours has been proposed by Do¨tsch and Wider (13) in which their sequence was used to study the exchange rates of water bound internally in proteins. The sequence has an advantage of being a shorter experiment; however, our experiment minimizes the crosspeak distortion that was noted in Do¨tsch and Wider’s work. Since the spectrometer used in this study was not equipped with shaped PFG, we chose not to use bipolar paired pulses as it would reduce signal-to-noise by introducing significant delays for gradient settling. Similar to 2D DOSY, it should be possible to diffusively resolve chemical-shift-overlapped NOE cross peaks from different diffusion species. That being true, DOSY-NOESY can be used for structural determination in various multicomponent and associative complex systems. The most convenient method for data analysis would be a program that automatically fits the diffusion coefficients for each integrated cross peak in the Fouriertransformed data, yielding a 3D DOSY-NOESY data set ( work in progress ) . DOSY-NOESY makes available NOE data for complex systems that could not previously be studied by NMR. ACKNOWLEDGMENTS This work was supported by NIH (AI27744), the Welch Foundation (H1296), the Lucille P. Markey Charitable Trust, and the Sealy and Smith Foundation. We also thank Dr. A. G. Swanson for sharing the 2D DOSY sequence and E. Ezell, Dr. J. Post, Dr. P. Pellechia, and Dr. D. Carlson for their valuable assistance.
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AP: Mag Res