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The application of multiple-quantum techniques for the suppression of water signals in 1H NMR spectra
JOURNAL
OF MAGNETIC
RESONANCE
64,
38-46 (1985)
The Application of Multiple-Quantum Techniques for the Suppression of W a ter Signals in ‘H NMR Spectra CHARLESL.DUMOULIN General Electric Corporate Research and Development Center, P.0. Box 8, Schenectady,New York 12301 Received November 20, 1984; revised February 15, 1985 Pulse sequenceswhich generate multiple- and zero-quantum coherence and suppress the detection of singlequantum coherence have been used to reduce greatly the intensity of the water peak in ‘H NMR spectra of biological interest. In addition to suppressing the strong water signal, other resonances having only singlequantum behavior are attenuated or eliminated, thus simplifying the spectrum. Unlike other suppression methods, the use of a multiple-quantum filter does not cause severe spectral distortions or loss in sensitivity near the HZ0 peak. In principle, total suppression of the water signal is possible. Suppression of the water resonance by a factor of more than 2500 was routinely observed experimentally. 0 1985 Academic press, hc. INTRODUCTION
The elimination of the water resonance in ‘H NMR spectra has been a goal of many workers, particularly those interested in biological systems, Elimination of the water peak is frequently performed by substituting deuterium for the protons in water. This procedure is often unacceptable, however, since HZ0 is frequently a vital or inseparable part of the chemical system. Suppression of the water signal during the pulsed NMR experiment is feasible and is frequently obtained by selectively saturating the water resonance before data acquisition (1-3). Alternative experimental schemes make use of selective excitation designed to avoid exciting the water resonance (4, 5). Inversion-recovery experiments have also been used to null the water resonance in spectra whose components have T, values which are substantially different from the T, of water (6). All of these techniques have disadvantagesand have been discussedin a recent review by P. J. Hore (7). No one method is universally applicable. All water suppression techniques exploit a difference in .one or more intrinsic parameters of the water resonance as compared to the other signals of interest. Selective saturation and selective detection schemes discriminate on the basis of chemical shift. T i-null techniques of course exploit r,. The experiment proposed and demonstrated here exploits the lack of m u ltiple-quantum behavior in the water m o lecule. It is widely recognized that only single-quantum transitions in an NMR spin system are directly observable. In the case of an isolated, noncoupled spin-4 nucleus in a magnetic field, there are only two energy states possible and consequently only 0022-2364185 $3.00 Copyright Q 1985 by Academic Pres. Inc. All rights of reproduction in any form reserved.
38
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single-quantum transitions exist (Fig. 1A). Coupled nuclei, on the other hand, possessa more complicated energy level arrangement which allows the establishment of zero-, multiple-, and single-quantum coherence (Fig. 1B). While zero- and multiple-quantum coherences cannot be directly detected, they can be established, allowed to evolve, and converted to single-quantum coherence which can then be detected. Multiple- and zero-quantum coherences manifest themselves as a modulation of the detected single-quantum signal. Spins which are coupled to other spins can have multiple-quantum coherence which can be detected by suitable experiments. For example, the double-quantum coherence permitted in coupled i3C-13C spin systems has been used in the INADEQUATE (8) and INADEQUATE-2D (9) experiments to map the carbon backbone of organic molecules. The detection of the isotopically dilute i3C spin pairs in the presence of uncoupled i3C nuclei is possible because the phase behavior of multiplequantum coherence is different than the phase behavior of single-quantum coherence. The phase of the pulses can be manipulated in such a way that the single-quantum component of the NMR signal cancels while the double-quantum component adds constructively. DISCUSSION
Multiple-photon transitions occur in pulse as well as continuous wave spectroscopy (10-12). In pulsed NMR spectroscopy, however, more than one pulse is required to excite a multiple-quantum transition. The simplest pulse sequence used to
FB)/2
-FA-
F,W
-
-
J/4
J/4
+-
++
A FIG. 1. (A) The energy level diagram for an isolated energy-level diagram for a coupled AB spin system is a (6M = +l) occur at FA + J/2, FA - J/2, Fe + J/2, Fs occurs at FA + F,, and one zeroquantum transition (6M
-(F,
- FBY2
+ J/4
B spin-i system in a magnetic field, H,,. (B) The magnetic field. Four singlequantum transitions J/2. One double-quantum transition (6M = k2) = 0) occurs at FA - Fs.
40
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generate multiple-quantum coherence is a pair of a/2 pulses separated by a time T which is equal to 1/4J (Fig. 2A). Multiple-quantum coherence is generated after the second r/2 pulse but is unobservable. After establishing multiple-quantum coherence, a detection 7r/2 pulse can be applied to convert the multiple-quantum coherence into transverse magnetization which can then be detected. Using density matrix calculations the amount of zero- and double-quantum coherence can be shown to be a function of the offset frequencies of the single-quantum transitions. Thus, the
A
.
e
T=lM.l
B
C
.
M
ACQ.
T = 112J
ACQ.
D
E H’.S.
n
F
n/2
n/4(Y)
ACQ
t
H.S.
G
r
fl”
ACQ
FIG. 2. (A) A simple pulse sequence which generates doublequantum coherence which is dependent on the chemical shift of the coupled resonances. (B) The addition of a ?r refocusing pulse removes the chemical-shift dependence. (C) The addition of a delay after the detection pulse allows the multiplet components time to attain the same phase. (D) The addition of a refocusing pulse during this delay allows broad signals to be retained while allowing the multiplet components time to attain the same phase. (E) A simple method to generate zeroquantum coherence. (E) The addition of a delay and (G) the addition of a refocusing pulse.
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amount of multiple-quantum coherence is a function of the coupling constant J and the difference (or sum) of the chemical shifts of the coupled spins as well as the chemical shifts of the individual spins. The chemical-shift dependence of multiplequantum coherence can be removed by inserting a 7~pulse between the two a/2 pulses (13) as shown in Figs. 2B-D. For an AB system, the resulting pulse sequence generatestotal doublequantum coherence and no zero- or single-quantum coherence. Using a density matrix calculation, the double- and single-quantum coherence created by the ax-T-r-T-& subsequence as a function of (Y and 0 was investigated. The results of this calculation (Figs. 3A, B) show that the establishment of double-quantum coherence is not particularly sensitive to misadjustments of the flip angle and is optimal when a! and /I equal r/2. Pulse sequences B, C, and D establish double-quantum coherence using the 7r/2T-r-T-m/2 scheme followed by a 7r/2 detection pulse. After the detection pulse the individual multiplet components are in antiphase. Thus, resulting multiplet components have alternating signs in their intensity, While this may not pose a problem for many spectra, it can create difficulty in some cases. For example, if the spectrum is broadened by field inhomogeneities which dominate the linewidth, the antiphase shape of the multiplets will cause partial cancellation of signal resulting in broad and possibly unrecognizable spectral lines. In pulse sequence B, data are acquired immediately after the detection pulse. After Fourier transformation the data can be phased so that the multiplets have the characteristic multiple-quantum appearance using the same phase parameters required in an ordinary experiment. A magnitude calculation can be performed to remove the phase information and give the spectrum an absorption-mode appearance which will compensate for the alternating multiplet components. The magnitude spectrum,
"-
90' P
180"
0'
90'
160"
P
FIG. 3. (A) Doublequantum coherence in a a,-T-rr-T-IB, experiment where T = 1/4J. Maximum doublequantum coherence occurs when (Y and /3 are equal to rr/2. The maximum has a normalized intensity of I. (B) The single-quantum coherence generated by the same sequence. The single-quantum coherence is zero when cy and fl are r/2 and has a maximum value of 0.5 when (Y and /3 differ by r/2 and are a multiple of rr/2. Note that no zeroquantum coherence is generated.
42
CHARLES L. DUMOULIN
however, may have unacceptably broadened lineshapes. Alternatively, a zero- and first-order phase correction can be calculated using the expression zero-order correction = 0” = 180”
if N is even if N is odd
first-order correction = 180” X N where N is equal to the number of data points collected in the time it took the multiplet components to attain the same phase (1/2J). For quadrature phase detection N = SWI2J where SW is the spectral width. A first-order phase correction in the frequency domain is equivalent to a shift in the time domain. Since the shift is circular (i.e., data shifted out of one end reappears at the other), the shape of the FID envelope should be modified by a suitable weighting function so that both ends of the FID return smoothly to zero. Otherwise, the discontinuity introduced by the start of the FID would cause severe baseline distortions. An alternative to applying large phase corrections is to begin data acquisition 1/2J after the detection pulse (sequence C). This allows the multiplet components time to attain the same phase. For narrow-line ‘H spectra with a relatively long Tf , this does not result in a substantial loss in signal. If T; - 1/2J however, the FID has died out or is greatly attenuated before 1/2J. In this case pulse sequence D can be used. The second ?r pulse refocuses the dephasing components of the multiplet caused by field inhomogeneities while allowing time for the multiplet components to attain the same phase. This pulse is analogous to the refocusing pulse in the refocused INEPT experiment. Using a preacquisition delay or a large phase correction can be successful in correcting all peak phases only if all the spins in the system have the same coupling constant. Often this is not the case and one must either accept the phase distortions or make use of the magnitude presentation of the data. Pulse sequences E, F, and G generate zero-quantum coherence using a 7r/2-T7r-T-7r/4 scheme. As in the double-quantum sequences, the center ?r pulse removes chemical-shift dependency. The establishment of zero-quantum coherence was shown to be relatively insensitive to mis-settings in the pulse width by evaluating the zero-, single-, and double-quantum coherence generated by a a,-T-VT-P,, subsequence as a function of cy and & The results of this calculation are shown in Figs. 4A, B. Notable differences exist between the schemes for the generation of multiple- and zero-quantum coherence. For example, no zero- or single-quantum coherence is generated in the 7r/2-T-7r-T-a/2 subsequence. Only double-quantum coherence is generated. The r/2-T-r-T-r/4 subsequence on the other hand, generates equal amounts of zero-quantum and doublequantum coherence and no single-quantum coherence. Thus, the signal-to-noise ratio of a zero-quantum experiment is half that of the corresponding double-quantum experiment. Another important difference between zero-quantum and other types of coherences (including single-quantum coherence) is that zero-quantum transitions are not broadened by inhomogeneous
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magnetic fields. Thus, homospoil pulses can be used to destroy undesired singleand multiple-quantum signals without affecting the zero-quantum coherence. Pulse sequences E, F, and G include a homospoil pulse to eliminate single- and multiplequantum signals. This homospoil is made strong enough to remove all higher order coherences. Thus, single-quantum signals arising from phase or amplitude errors in the zero-quantum subsequence are rigorously excluded from the acquired data thus simplifying the phase-cycling program. As in the case of the double-quantum-generating subsequence, the components of the multiplet are in antiphase after the detection pulse. Consequently, a delay (sequence F) and refocusing ?r pulse (sequence G) can be added to ensure that all multiplet components are in phase. Separation of the single-quantum signals arising from uncoupled nuclei and the multiple-quantum signals from coupled nuclei is accomplished by manipulating the phases of the receiver and radiofrequency pulses. The success of a particular phasealternation scheme is limited by imperfections in the radiofrequency and computer hardware of the spectrometer. The phase-cycling program can be complete so that all possible useful combinations of phases are generated. For a four-pulse sequence such as B, C, E, and F, such a phase program would have 128 steps (assuming that the spectrometer is capable of generating phases of 0, a/2, ?r, and 3~/2 for each pulse and for the receiver). Adding the refocusing pulse (sequences D and G) extends the complete cycle to 5 12 steps. Details of phase-cycling programs have been discussed for 13C INADEQUATE experiments (9) and zero-quantum experiments (14). These phase-cycling schemes are directly applicable to the ‘H water suppression experiment. The multiple-quantum (or alternatively zero-quantum) spectrum of the sample can be obtained using these pulse sequences in a two-dimensional experiment. The delay between the second and third 7r/2 pulse in sequences B, C, and D (or the B
FIG. 4. (A) Double- and zero-quantum coherence in a cr,-T-*-T-& experiment where T = maximum has an intensity of 0.5 for both orders of coherence and occurs at a = p/2 and 3x/4. (B) The singlequantum coherence generated by the same sequence. The singlequantum is zero when the double- and zero-quantum coherence is maximized. Maximum singlequantum occurs at a = 3%/4 and j3 = r/2 and has a value of 0.707.
1/4J. The /I = 7r/4, coherence coherence
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7r/4 and a/2 pulse in sequences E, F, and G) can be incremented to form the second dimension, Fourier transformation of both dimensions results in a data matrix in which each peak is correlated with other peaks by their multiple-quantum frequencies. Since only coupled spins can have multiple-quantum coherence, this experiment gives direct information about the coupling network of the molecule. The multiple-quantum spectrum is simply the projection of the data matrix in the second dimension. This two-dimensional experiment is analogous to the i3C INADEQUATE-2D (9) experiment. Addition of a presaturating radiofrequency pulse or a Ti-null subsequence does not have any affect on the two-dimensional experiment other than to further suppress the water signal. EXPERIMENTAL
Spectra were acquired on a Varian XL-200 spectrometer with a Sperry Univac data system V77-200 and 12 bit ADC. Ordinary homogenized and pasturized cow’s milk was diluted by 4 part D20 in 5 mm NMR tubes. Spectra were acquired at room temperature, with deuterium lock. All spectra were recorded in magnitude mode to circumvent phase problems. A 32-step phase-cycling program was used to cancel the singlequantum water signal. Time delays were chosen using the assumption of a 7 Hz coupling constant. In an ordinary single-pulse experiment, the HZ0 peak dominated the spectrum and was about 1300 times more intense than the doublet occurring at 4.4 ppm. Presaturation of the water peak using low-power, continuous-wave decoupling caused a 32-fold suppression of the water signal. Pulse sequence II, on the other hand, gave a suppression of about 110. The suppression was not perfect due to the physical limitations of the spectrometer. Perhaps the most significant limitation on the spectrometer for the multiplequantum water suppression experiment is the requirement of a large dynamic range. Since the suppression of the water signal is accomplished by cancellation, the spectrometer must be capable of linearly reproducing and digitizing the signal from both the water and the signals of interest. Any means available which will attenuate the water signal will lessen the dynamic range of the spectrum and thus will have a multiplicative effect in reducing the water signal when combined with a multiplequantum suppression scheme. The spectrum shown in Fig. 5 was acquired with pulse sequence C and presaturation of the water resonance. The doublet which is approximately 25 Hz downfield of the water peak is not noticeably attenuated. Lipid resonances at 0.9 and 1.3 ppm were attenuated because their broad lineshape was not detected during data acquisition due to the preacquisition delay. The suppression ratio of the water signal in Fig. 5 is in excess of 2500. Stability of the magnetic field and radiofrequency components is critical to the suppression of the water signal. Several spectra were acquired in which the water signal was entirely suppressed. These results were not reproducible, however, and the suppression shown in Fig. 5 is typical for this experiment and spectrometer. Addition of the refocusing pulse to obtain sequence D showed less suppression (Fig. 6). The lipid peaks at 0.9 and 1.3 ppm, however, refocused and appear with normal intensity. The loss in suppression observed with the addition of a refocusing
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I
I
I
I
I
5.0
4.0
3.0
2.0
1.0
45
twm FIG. 5. 200 MHz spectrum of milk in 40 (2:l) using the pulse sequence given in Fig. 2C. 32 scans were acquired using a 32-step phase-cycling program. The water peak was presaturated by low power cw decoupling prior to the radiofrequency pulses and data acquisition. The small highlighted peak is the residual water signal. The water signal is suppressed by a factor of more than 2500.
pulse is possibly due to lower stability of the broader components of the water signal caused by subtle changes in the magnetic field. These broader components are refocusable and thus appear during data acquisition. Unless the magnetic field is kept perfectly stable during the experiment the water signal cannot be totally canceled. While small changes in the magnetic field may be unobservable in a normal spectrum, the multiple-quantum water-suppressed spectrum is in effect a difference spectrum and consequently subtle differences can result in large perturbations of the spectrum. This was clearly demonstrated when the experiments were performed on spinning samples, Despite a very homogeneous magnetic field and the lack of any readily
I I
I
I
I
I
5.0
4.0
3.0
2.0
1.0
pm
FIG. 6. 200 MHz spectrum of milk in D20 (2:I) using the pulse sequence in Fig. 2D. 64 scans were acquired using a 32-step phase-cycling program. As in Fig. 5, the spectrum was acquired with presaturation of the water signal. Instabilities in the broad components of the water peak (presumably caused by small changes in the magnetic field) were refocused and incompletely canceled.
46
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discernable spinning sidebands in normal experiments, the water-suppressed spectra exhibited large (20%) spinning sidebands. This was caused by the incomplete cancellation of sidebands due to short-term spin-rate drift in the instrument. CONCLUSION
The use of multiple-quantum techniques has several advantages over other water suppression methods. For example, spectra are simplified since only resonances with multiple-quantum coherence are observed. In addition, the resonances are excited by a uniform excitation spectrum. Consequently, signals which are very close to the water peak can be observed. Furthermore, very good suppression can be achieved with low radiofrequency power levels. When multiple-quantum watersuppression techniques are combined with other water-suppression techniques such as presaturation (and presumably Tl null) the result is approximately a multiplicative increase in the suppression. In theory, no water signal should be obtained in a multiple-quantum experiment. In practice, however, minor imperfections in the instrument cause some signal to be observed. The most severe limitation is the dynamic range of the instrument. In addition to a large ADC, good linearity in the receiver is important. Furthermore, the phase of the radiofrequency pulses and the receiver should be accurately controlled by the hardware. All aspects of the instrument should be as stable as possible since small perturbations such as minor field or spin-rate drift are greatly amplified. Since the signals of interest which are observed in a multiple-quantum experiment have multiple-quantum coherence, their intensity is a function of the chemical shifts and coupling constant of the coupled nuclei in addition to the other intrinsic and extrinsic parameters of the experiment. Thus, quantitative measurements of a given peak in a series of spectra are possible as long as identical experimental conditions are used. Calibration is required, however, if resonances arising from different species within the same spectra are to be quantitatively compared. REFERENCES 1. A. G. REDFIELD AND R. K. GUPTA, “Advances in Magnetic Resonance” (J. S. Waugh, Ed.), Vol. 5, p. 8 1, Academic Press, New York, 197 1. 2. J. SCHAEFER, J. Magn. Reson. 6, 670 (1972). 3. J. P. JESSON, P. MEALSIN, AND G. KNIESSEL, J. Am. Chem. Sot. 95, 618 (1973). 4. A. G. REDFIELD, “NMR: Basic Principles and Progress” (M. M. Pintar, Ed.), Vol. 13, p. 137, Springer-Verlag, Berlin, 1976. 5. A. G. REDFIELD AND S. D. KINZ, “NMR and Biochemistry” (S. G. Opella and P. Lu, Eds.) p. 115, Dckker, New York, 1979. 6. S. L. PATTAND B. D. SYKES, J. Chem. Phys. 56, 3182 (1972). 7. P. J. HORE, J. Magn. Reson. 55, 283 (1983). 8. A. BAX, R. FREEMAN, AND S. P. KEMPSELL, J. Am. Chem. SK 102, 4851 (1980). 9. A. BAX, R. FREEMAN, T. A. FRENKIEL, AND M. H. LEVITT, J. Magn. Reson. 43, 478 (1981). 10. W. ANDERSON, Phys. Rev. 104, 850 (1956). II. J. 1. KAPLAN AND S. MEIBOOM, Phys. Rev. 106,499 (1957). 12. S. YATSIV, Phys. Rev. 113, 1522 (1959). 13. 0. W. WRENSEN, M. H. LEVIS, AND R. R. ERNST, J. Mugn. Reson. 55, 104 (1983). 14. L. MILLER, J. Magn. Reson. 59, 326 (1984).
OF MAGNETIC
RESONANCE
64,
38-46 (1985)
The Application of Multiple-Quantum Techniques for the Suppression of W a ter Signals in ‘H NMR Spectra CHARLESL.DUMOULIN General Electric Corporate Research and Development Center, P.0. Box 8, Schenectady,New York 12301 Received November 20, 1984; revised February 15, 1985 Pulse sequenceswhich generate multiple- and zero-quantum coherence and suppress the detection of singlequantum coherence have been used to reduce greatly the intensity of the water peak in ‘H NMR spectra of biological interest. In addition to suppressing the strong water signal, other resonances having only singlequantum behavior are attenuated or eliminated, thus simplifying the spectrum. Unlike other suppression methods, the use of a multiple-quantum filter does not cause severe spectral distortions or loss in sensitivity near the HZ0 peak. In principle, total suppression of the water signal is possible. Suppression of the water resonance by a factor of more than 2500 was routinely observed experimentally. 0 1985 Academic press, hc. INTRODUCTION
The elimination of the water resonance in ‘H NMR spectra has been a goal of many workers, particularly those interested in biological systems, Elimination of the water peak is frequently performed by substituting deuterium for the protons in water. This procedure is often unacceptable, however, since HZ0 is frequently a vital or inseparable part of the chemical system. Suppression of the water signal during the pulsed NMR experiment is feasible and is frequently obtained by selectively saturating the water resonance before data acquisition (1-3). Alternative experimental schemes make use of selective excitation designed to avoid exciting the water resonance (4, 5). Inversion-recovery experiments have also been used to null the water resonance in spectra whose components have T, values which are substantially different from the T, of water (6). All of these techniques have disadvantagesand have been discussedin a recent review by P. J. Hore (7). No one method is universally applicable. All water suppression techniques exploit a difference in .one or more intrinsic parameters of the water resonance as compared to the other signals of interest. Selective saturation and selective detection schemes discriminate on the basis of chemical shift. T i-null techniques of course exploit r,. The experiment proposed and demonstrated here exploits the lack of m u ltiple-quantum behavior in the water m o lecule. It is widely recognized that only single-quantum transitions in an NMR spin system are directly observable. In the case of an isolated, noncoupled spin-4 nucleus in a magnetic field, there are only two energy states possible and consequently only 0022-2364185 $3.00 Copyright Q 1985 by Academic Pres. Inc. All rights of reproduction in any form reserved.
38
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single-quantum transitions exist (Fig. 1A). Coupled nuclei, on the other hand, possessa more complicated energy level arrangement which allows the establishment of zero-, multiple-, and single-quantum coherence (Fig. 1B). While zero- and multiple-quantum coherences cannot be directly detected, they can be established, allowed to evolve, and converted to single-quantum coherence which can then be detected. Multiple- and zero-quantum coherences manifest themselves as a modulation of the detected single-quantum signal. Spins which are coupled to other spins can have multiple-quantum coherence which can be detected by suitable experiments. For example, the double-quantum coherence permitted in coupled i3C-13C spin systems has been used in the INADEQUATE (8) and INADEQUATE-2D (9) experiments to map the carbon backbone of organic molecules. The detection of the isotopically dilute i3C spin pairs in the presence of uncoupled i3C nuclei is possible because the phase behavior of multiplequantum coherence is different than the phase behavior of single-quantum coherence. The phase of the pulses can be manipulated in such a way that the single-quantum component of the NMR signal cancels while the double-quantum component adds constructively. DISCUSSION
Multiple-photon transitions occur in pulse as well as continuous wave spectroscopy (10-12). In pulsed NMR spectroscopy, however, more than one pulse is required to excite a multiple-quantum transition. The simplest pulse sequence used to
FB)/2
-FA-
F,W
-
-
J/4
J/4
+-
++
A FIG. 1. (A) The energy level diagram for an isolated energy-level diagram for a coupled AB spin system is a (6M = +l) occur at FA + J/2, FA - J/2, Fe + J/2, Fs occurs at FA + F,, and one zeroquantum transition (6M
-(F,
- FBY2
+ J/4
B spin-i system in a magnetic field, H,,. (B) The magnetic field. Four singlequantum transitions J/2. One double-quantum transition (6M = k2) = 0) occurs at FA - Fs.
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generate multiple-quantum coherence is a pair of a/2 pulses separated by a time T which is equal to 1/4J (Fig. 2A). Multiple-quantum coherence is generated after the second r/2 pulse but is unobservable. After establishing multiple-quantum coherence, a detection 7r/2 pulse can be applied to convert the multiple-quantum coherence into transverse magnetization which can then be detected. Using density matrix calculations the amount of zero- and double-quantum coherence can be shown to be a function of the offset frequencies of the single-quantum transitions. Thus, the
A
.
e
T=lM.l
B
C
.
M
ACQ.
T = 112J
ACQ.
D
E H’.S.
n
F
n/2
n/4(Y)
ACQ
t
H.S.
G
r
fl”
ACQ
FIG. 2. (A) A simple pulse sequence which generates doublequantum coherence which is dependent on the chemical shift of the coupled resonances. (B) The addition of a ?r refocusing pulse removes the chemical-shift dependence. (C) The addition of a delay after the detection pulse allows the multiplet components time to attain the same phase. (D) The addition of a refocusing pulse during this delay allows broad signals to be retained while allowing the multiplet components time to attain the same phase. (E) A simple method to generate zeroquantum coherence. (E) The addition of a delay and (G) the addition of a refocusing pulse.
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amount of multiple-quantum coherence is a function of the coupling constant J and the difference (or sum) of the chemical shifts of the coupled spins as well as the chemical shifts of the individual spins. The chemical-shift dependence of multiplequantum coherence can be removed by inserting a 7~pulse between the two a/2 pulses (13) as shown in Figs. 2B-D. For an AB system, the resulting pulse sequence generatestotal doublequantum coherence and no zero- or single-quantum coherence. Using a density matrix calculation, the double- and single-quantum coherence created by the ax-T-r-T-& subsequence as a function of (Y and 0 was investigated. The results of this calculation (Figs. 3A, B) show that the establishment of double-quantum coherence is not particularly sensitive to misadjustments of the flip angle and is optimal when a! and /I equal r/2. Pulse sequences B, C, and D establish double-quantum coherence using the 7r/2T-r-T-m/2 scheme followed by a 7r/2 detection pulse. After the detection pulse the individual multiplet components are in antiphase. Thus, resulting multiplet components have alternating signs in their intensity, While this may not pose a problem for many spectra, it can create difficulty in some cases. For example, if the spectrum is broadened by field inhomogeneities which dominate the linewidth, the antiphase shape of the multiplets will cause partial cancellation of signal resulting in broad and possibly unrecognizable spectral lines. In pulse sequence B, data are acquired immediately after the detection pulse. After Fourier transformation the data can be phased so that the multiplets have the characteristic multiple-quantum appearance using the same phase parameters required in an ordinary experiment. A magnitude calculation can be performed to remove the phase information and give the spectrum an absorption-mode appearance which will compensate for the alternating multiplet components. The magnitude spectrum,
"-
90' P
180"
0'
90'
160"
P
FIG. 3. (A) Doublequantum coherence in a a,-T-rr-T-IB, experiment where T = 1/4J. Maximum doublequantum coherence occurs when (Y and /3 are equal to rr/2. The maximum has a normalized intensity of I. (B) The single-quantum coherence generated by the same sequence. The single-quantum coherence is zero when cy and fl are r/2 and has a maximum value of 0.5 when (Y and /3 differ by r/2 and are a multiple of rr/2. Note that no zeroquantum coherence is generated.
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however, may have unacceptably broadened lineshapes. Alternatively, a zero- and first-order phase correction can be calculated using the expression zero-order correction = 0” = 180”
if N is even if N is odd
first-order correction = 180” X N where N is equal to the number of data points collected in the time it took the multiplet components to attain the same phase (1/2J). For quadrature phase detection N = SWI2J where SW is the spectral width. A first-order phase correction in the frequency domain is equivalent to a shift in the time domain. Since the shift is circular (i.e., data shifted out of one end reappears at the other), the shape of the FID envelope should be modified by a suitable weighting function so that both ends of the FID return smoothly to zero. Otherwise, the discontinuity introduced by the start of the FID would cause severe baseline distortions. An alternative to applying large phase corrections is to begin data acquisition 1/2J after the detection pulse (sequence C). This allows the multiplet components time to attain the same phase. For narrow-line ‘H spectra with a relatively long Tf , this does not result in a substantial loss in signal. If T; - 1/2J however, the FID has died out or is greatly attenuated before 1/2J. In this case pulse sequence D can be used. The second ?r pulse refocuses the dephasing components of the multiplet caused by field inhomogeneities while allowing time for the multiplet components to attain the same phase. This pulse is analogous to the refocusing pulse in the refocused INEPT experiment. Using a preacquisition delay or a large phase correction can be successful in correcting all peak phases only if all the spins in the system have the same coupling constant. Often this is not the case and one must either accept the phase distortions or make use of the magnitude presentation of the data. Pulse sequences E, F, and G generate zero-quantum coherence using a 7r/2-T7r-T-7r/4 scheme. As in the double-quantum sequences, the center ?r pulse removes chemical-shift dependency. The establishment of zero-quantum coherence was shown to be relatively insensitive to mis-settings in the pulse width by evaluating the zero-, single-, and double-quantum coherence generated by a a,-T-VT-P,, subsequence as a function of cy and & The results of this calculation are shown in Figs. 4A, B. Notable differences exist between the schemes for the generation of multiple- and zero-quantum coherence. For example, no zero- or single-quantum coherence is generated in the 7r/2-T-7r-T-a/2 subsequence. Only double-quantum coherence is generated. The r/2-T-r-T-r/4 subsequence on the other hand, generates equal amounts of zero-quantum and doublequantum coherence and no single-quantum coherence. Thus, the signal-to-noise ratio of a zero-quantum experiment is half that of the corresponding double-quantum experiment. Another important difference between zero-quantum and other types of coherences (including single-quantum coherence) is that zero-quantum transitions are not broadened by inhomogeneous
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magnetic fields. Thus, homospoil pulses can be used to destroy undesired singleand multiple-quantum signals without affecting the zero-quantum coherence. Pulse sequences E, F, and G include a homospoil pulse to eliminate single- and multiplequantum signals. This homospoil is made strong enough to remove all higher order coherences. Thus, single-quantum signals arising from phase or amplitude errors in the zero-quantum subsequence are rigorously excluded from the acquired data thus simplifying the phase-cycling program. As in the case of the double-quantum-generating subsequence, the components of the multiplet are in antiphase after the detection pulse. Consequently, a delay (sequence F) and refocusing ?r pulse (sequence G) can be added to ensure that all multiplet components are in phase. Separation of the single-quantum signals arising from uncoupled nuclei and the multiple-quantum signals from coupled nuclei is accomplished by manipulating the phases of the receiver and radiofrequency pulses. The success of a particular phasealternation scheme is limited by imperfections in the radiofrequency and computer hardware of the spectrometer. The phase-cycling program can be complete so that all possible useful combinations of phases are generated. For a four-pulse sequence such as B, C, E, and F, such a phase program would have 128 steps (assuming that the spectrometer is capable of generating phases of 0, a/2, ?r, and 3~/2 for each pulse and for the receiver). Adding the refocusing pulse (sequences D and G) extends the complete cycle to 5 12 steps. Details of phase-cycling programs have been discussed for 13C INADEQUATE experiments (9) and zero-quantum experiments (14). These phase-cycling schemes are directly applicable to the ‘H water suppression experiment. The multiple-quantum (or alternatively zero-quantum) spectrum of the sample can be obtained using these pulse sequences in a two-dimensional experiment. The delay between the second and third 7r/2 pulse in sequences B, C, and D (or the B
FIG. 4. (A) Double- and zero-quantum coherence in a cr,-T-*-T-& experiment where T = maximum has an intensity of 0.5 for both orders of coherence and occurs at a = p/2 and 3x/4. (B) The singlequantum coherence generated by the same sequence. The singlequantum is zero when the double- and zero-quantum coherence is maximized. Maximum singlequantum occurs at a = 3%/4 and j3 = r/2 and has a value of 0.707.
1/4J. The /I = 7r/4, coherence coherence
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7r/4 and a/2 pulse in sequences E, F, and G) can be incremented to form the second dimension, Fourier transformation of both dimensions results in a data matrix in which each peak is correlated with other peaks by their multiple-quantum frequencies. Since only coupled spins can have multiple-quantum coherence, this experiment gives direct information about the coupling network of the molecule. The multiple-quantum spectrum is simply the projection of the data matrix in the second dimension. This two-dimensional experiment is analogous to the i3C INADEQUATE-2D (9) experiment. Addition of a presaturating radiofrequency pulse or a Ti-null subsequence does not have any affect on the two-dimensional experiment other than to further suppress the water signal. EXPERIMENTAL
Spectra were acquired on a Varian XL-200 spectrometer with a Sperry Univac data system V77-200 and 12 bit ADC. Ordinary homogenized and pasturized cow’s milk was diluted by 4 part D20 in 5 mm NMR tubes. Spectra were acquired at room temperature, with deuterium lock. All spectra were recorded in magnitude mode to circumvent phase problems. A 32-step phase-cycling program was used to cancel the singlequantum water signal. Time delays were chosen using the assumption of a 7 Hz coupling constant. In an ordinary single-pulse experiment, the HZ0 peak dominated the spectrum and was about 1300 times more intense than the doublet occurring at 4.4 ppm. Presaturation of the water peak using low-power, continuous-wave decoupling caused a 32-fold suppression of the water signal. Pulse sequence II, on the other hand, gave a suppression of about 110. The suppression was not perfect due to the physical limitations of the spectrometer. Perhaps the most significant limitation on the spectrometer for the multiplequantum water suppression experiment is the requirement of a large dynamic range. Since the suppression of the water signal is accomplished by cancellation, the spectrometer must be capable of linearly reproducing and digitizing the signal from both the water and the signals of interest. Any means available which will attenuate the water signal will lessen the dynamic range of the spectrum and thus will have a multiplicative effect in reducing the water signal when combined with a multiplequantum suppression scheme. The spectrum shown in Fig. 5 was acquired with pulse sequence C and presaturation of the water resonance. The doublet which is approximately 25 Hz downfield of the water peak is not noticeably attenuated. Lipid resonances at 0.9 and 1.3 ppm were attenuated because their broad lineshape was not detected during data acquisition due to the preacquisition delay. The suppression ratio of the water signal in Fig. 5 is in excess of 2500. Stability of the magnetic field and radiofrequency components is critical to the suppression of the water signal. Several spectra were acquired in which the water signal was entirely suppressed. These results were not reproducible, however, and the suppression shown in Fig. 5 is typical for this experiment and spectrometer. Addition of the refocusing pulse to obtain sequence D showed less suppression (Fig. 6). The lipid peaks at 0.9 and 1.3 ppm, however, refocused and appear with normal intensity. The loss in suppression observed with the addition of a refocusing
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twm FIG. 5. 200 MHz spectrum of milk in 40 (2:l) using the pulse sequence given in Fig. 2C. 32 scans were acquired using a 32-step phase-cycling program. The water peak was presaturated by low power cw decoupling prior to the radiofrequency pulses and data acquisition. The small highlighted peak is the residual water signal. The water signal is suppressed by a factor of more than 2500.
pulse is possibly due to lower stability of the broader components of the water signal caused by subtle changes in the magnetic field. These broader components are refocusable and thus appear during data acquisition. Unless the magnetic field is kept perfectly stable during the experiment the water signal cannot be totally canceled. While small changes in the magnetic field may be unobservable in a normal spectrum, the multiple-quantum water-suppressed spectrum is in effect a difference spectrum and consequently subtle differences can result in large perturbations of the spectrum. This was clearly demonstrated when the experiments were performed on spinning samples, Despite a very homogeneous magnetic field and the lack of any readily
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FIG. 6. 200 MHz spectrum of milk in D20 (2:I) using the pulse sequence in Fig. 2D. 64 scans were acquired using a 32-step phase-cycling program. As in Fig. 5, the spectrum was acquired with presaturation of the water signal. Instabilities in the broad components of the water peak (presumably caused by small changes in the magnetic field) were refocused and incompletely canceled.
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discernable spinning sidebands in normal experiments, the water-suppressed spectra exhibited large (20%) spinning sidebands. This was caused by the incomplete cancellation of sidebands due to short-term spin-rate drift in the instrument. CONCLUSION
The use of multiple-quantum techniques has several advantages over other water suppression methods. For example, spectra are simplified since only resonances with multiple-quantum coherence are observed. In addition, the resonances are excited by a uniform excitation spectrum. Consequently, signals which are very close to the water peak can be observed. Furthermore, very good suppression can be achieved with low radiofrequency power levels. When multiple-quantum watersuppression techniques are combined with other water-suppression techniques such as presaturation (and presumably Tl null) the result is approximately a multiplicative increase in the suppression. In theory, no water signal should be obtained in a multiple-quantum experiment. In practice, however, minor imperfections in the instrument cause some signal to be observed. The most severe limitation is the dynamic range of the instrument. In addition to a large ADC, good linearity in the receiver is important. Furthermore, the phase of the radiofrequency pulses and the receiver should be accurately controlled by the hardware. All aspects of the instrument should be as stable as possible since small perturbations such as minor field or spin-rate drift are greatly amplified. Since the signals of interest which are observed in a multiple-quantum experiment have multiple-quantum coherence, their intensity is a function of the chemical shifts and coupling constant of the coupled nuclei in addition to the other intrinsic and extrinsic parameters of the experiment. Thus, quantitative measurements of a given peak in a series of spectra are possible as long as identical experimental conditions are used. Calibration is required, however, if resonances arising from different species within the same spectra are to be quantitatively compared. REFERENCES 1. A. G. REDFIELD AND R. K. GUPTA, “Advances in Magnetic Resonance” (J. S. Waugh, Ed.), Vol. 5, p. 8 1, Academic Press, New York, 197 1. 2. J. SCHAEFER, J. Magn. Reson. 6, 670 (1972). 3. J. P. JESSON, P. MEALSIN, AND G. KNIESSEL, J. Am. Chem. Sot. 95, 618 (1973). 4. A. G. REDFIELD, “NMR: Basic Principles and Progress” (M. M. Pintar, Ed.), Vol. 13, p. 137, Springer-Verlag, Berlin, 1976. 5. A. G. REDFIELD AND S. D. KINZ, “NMR and Biochemistry” (S. G. Opella and P. Lu, Eds.) p. 115, Dckker, New York, 1979. 6. S. L. PATTAND B. D. SYKES, J. Chem. Phys. 56, 3182 (1972). 7. P. J. HORE, J. Magn. Reson. 55, 283 (1983). 8. A. BAX, R. FREEMAN, AND S. P. KEMPSELL, J. Am. Chem. SK 102, 4851 (1980). 9. A. BAX, R. FREEMAN, T. A. FRENKIEL, AND M. H. LEVITT, J. Magn. Reson. 43, 478 (1981). 10. W. ANDERSON, Phys. Rev. 104, 850 (1956). II. J. 1. KAPLAN AND S. MEIBOOM, Phys. Rev. 106,499 (1957). 12. S. YATSIV, Phys. Rev. 113, 1522 (1959). 13. 0. W. WRENSEN, M. H. LEVIS, AND R. R. ERNST, J. Mugn. Reson. 55, 104 (1983). 14. L. MILLER, J. Magn. Reson. 59, 326 (1984).