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Logo of nihpaAbout Author manuscriptsSubmit a manuscriptNIH Public Access; Author Manuscript; Accepted for publication in peer reviewed journal;
 
J Biomol NMR. Author manuscript; available in PMC Apr 8, 2008.
Published in final edited form as:
PMCID: PMC2290856
NIHMSID: NIHMS18782
Joint Composite-Rotation Adiabatic-Sweep Isotope Filtration
Elizabeth R. Valentine,1 Fabien Ferrage,2,3 Francesca Massi,1 David Cowburn,2 and Arthur G. Palmer, III1
1 Department of Biochemistry and Molecular Biophysics, Columbia University, 630 West 168th Street, New York, NY 10032
2 New York Structural Biology Center, 89 Convent Avenue, New York, NY 10027-7556
Address correspondence to A. G. P. (voice 212 305-8675, fax 212 305-6949, email agp6/at/columbia.edu).
3Present address: CNRS UMR 8642, École normale supérieure, Département de Chimie, 24 rue Lhomond, 75231 Paris Cedex 5, France
Joint composite-rotation adiabatic-sweep isotope filter are derived by combining the composite-rotation [A. C. Stuart, K. A. Borzilleri, J. M. Withka, and A. G. Palmer, J. Am. Chem. Soc. 121, 5346–5347 (1999)] and adiabatic-sweep [C. Zwahlen, P. Legault, S. J. F. Vincent, J. Greenblatt, R. Konrat, and L. E. Kay, J. Am. Chem. Soc. 119, 6711–6721 (1997); Ē. Kupče and R. Freeman, J. Magn. Reson. 127, 36–48 (1997)] approaches. The joint isotope filters have improved broadband filtration performance, even for extreme values of the one-bond 1H-13C scalar coupling constants in proteins and RNA molecules. An average Hamiltonian analysis is used to describe evolution of the heteronuclear scalar coupling interaction during the adiabatic sweeps within the isotope filter sequences. The new isotope filter elements permit improved selective detection of NMR resonance signals originating from 1H spins attached to an unlabeled natural abundance component of a complex in which other components are labeled with 13C and 15N isotopes.
Keywords: composite pulse, J-filter, NOESY, structure determination, vts SAM domain
Isotope-filtered and isotope-edited techniques are essential to the investigation of biological complexes by NMR spectroscopy (Otting and Wüthrich, 1990). In these studies, one or a subset of the components of a complex are enriched in one or more NMR-active heteronuclei, for example 15N or 13C, and the other components are natural abundance or depleted in NMR-active isotopes. An isotope-filter selectively suppresses and an isotope-editor selectively detects resonance signals from 1H spins directly attached to the NMR-active heteronuclei. These techniques rely on the differential evolution of 1H spins subject to a large or small (near-zero) heteronuclear scalar coupling Hamiltonian. An alternative, more specific, nomenclature refers to an isotope-filter as a low-pass J-filter and an isotope-editor as a high-pass J-filter. Isotope filters are incorporated into NMR pulse sequences, such as COSY or TOCSY experiments, to permit resonance assignments of an unlabeled component of a complex and are incorporated into NOESY experiments to selectively detect NOE cross peaks between the 1H spins within the unlabeled species or between the unlabeled and labeled components (Breeze, 2000, Peterson, et al., 2004).
The efficiency of isotope filters is reduced by variations in the one-bond scalar coupling constant between the 1H spin and the heteronucleus. This difficulty is particularly severe for 1Hn13C (n = 1, 2, 3) moieties because JCH depends on the on the nature of the chemical group, varying from approximately ~120 Hz for CH3 groups to ~220 Hz for the 1Hε1-13Cε1 spin pair in histidine and the 1H8-13C8 spin pair in purine nucleotides. Two general approaches have emerged for improving the robustness of low-pass J-filters despite variation in JCH. The one approach relies on the isomorphism between pulse rotations and scalar coupling evolution (Levitt, 1986). Composite pulses compensated for B1 inhomogeneity are converted to sequence elements compensated for variation in JCH (Stuart, et al., 1999). The other approach uses the empirical relationship between the heteronuclear scalar coupling constant and isotropic 13C chemical shifts. Designed adiabatic broadband inversion pulses are used to effectively scale the coupling constants to a uniform value during an INEPT or other polarization transfer period (Kupče and Freeman, 1997, Zwahlen, et al., 1997).
In the present paper, the two approaches are combined to generate joint composite-rotation adiabatic-sweep isotope filter sequences, or low pass J-filters. The theoretical performance of the proposed sequences is evaluated using an average Hamiltonian description of the evolution of the heteronuclear scalar coupling interaction during an adiabatic sweep. The proposed sequences are validated using a 13C-labeled Ala, Tyr, and His amino acid mixture, representing the range of JCH encountered in proteins, and by recording a 1H-1H F1-filtered, F2-edited NOESY spectrum of the [U-13C, U-15N] vts SAM domain complexed with its unlabeled cognate RNA ligand (Edwards, et al., 2006).
Evolution of a spin system under the heteronuclear scalar coupling Hamiltonian during an adiabatic sweep has been treated theoretically by Kay and coworkers (Zwahlen, et al., 1997, Zwahlen, et al., 1998). The adiabatic sweep is divided into a series of equal time intervals short enough that the amplitude and resonance offset of the rf field can be treated as constant during each interval. The evolution of the density matrix during the ith interval is calculated using as initial conditions the state of the density operator after the (i − 1)th interval. Thus, evolution through the entire adiabatic sweep is calculated iteratively for the N intervals Δti for i = 1,…, N, beginning with the initial conditions at the start of the adiabatic sweep. To simplify these calculations, Kay and coworkers developed compact expressions for efficiently calculating the evolution of a reduced set of basis operators during each interval.
In most applications, and in particular for isotope filtration, the state of the density operator does not need to be known at any arbitrary point within an adiabatic sweep; rather the net evolution of the density operator at the end of the sweep is of primary concern. In these circumstances, an average Hamiltonian theoretical treatment of evolution under the heteronuclear scalar coupling Hamiltonian is sufficiently accurate and yields simple intuitive results. Average Hamiltonian theory has been applied to adiabatic pulses for isolated spin systems, i.e. in the absence of scalar couplings, by Mitschang and Rinneberg (Mitschang and Rinneberg, 2003) and to homonuclear scalar coupled systems by Bennett and coworkers (Bennett, et al., 2003).
The experimental situation of interest is illustrated in Figure 1. The initial state of the density operator for an I-S spin system (I = 1H and S = 13C) is described by an expansion in terms of in-phase (Ix and Iy) and antiphase transverse I spin product operators (2IxSz and 2IySz). An adiabatic sweep of duration τp is applied to the S spin and a refocusing 180° is optionally applied to the I spin at time τinv. The sequence element in Fig. 1a is formally equivalent to the sequence -τp-[180°(I)] in which the Hamiltonian in the rotating frames of reference of the I and S spins during the period τp is given by
Figure 1
Figure 1
Frequency-modulated interaction frame. (a) An adiabatic sweep is applied to the S spin while an 180° pulse is applied to the I spins at time tinv. (b) The functional form of a(t) is illustrated. (c) The tilted reference frame is shown schematically (more ...)
equation M1
[1]
and the bracketed 180°(I) pulse is included only if a refocusing pulse is applied. The refocusing pulse inverts the scalar coupling interaction at time τinv; the effect of this pulse is represented by the function a(t) with values
equation M2
[2]
Without loss of generality, the I spin is assumed to be on-resonance in the rotating frame. The rotating frame of the S spin is defined relative to the instantaneous radiofrequency field of the adiabatic sweep, ωrf(t); therefore, the frequency offset of the S spin is given by the time-dependent function Ω(t) = ωSωrf(t) and ωS is the resonance frequency of the S spin. The amplitude of the adiabatic sweep, assumed to be applied with x-phase is given by ω1(t). The amplitude and the tilt angle of the effective field in the rotating frame are given by ωe(t) = [Ω(t)2+ ω1(t)2]1/2 and tan[θ(t)] = ω1(t)/Ω(t), respectively. The time-variation of ωe(t) and θ(t) are assumed to satisfy the adiabatic condition, in which the adiabaticity factor Q = ωe/|(t)/dt|[dbl greater-than sign]1; typically, the adiabaticity factor at resonance, Ω(t) = 0, is chosen to satisfy Q0 > 5.
Evolution under this Hamiltonian is analyzed most conveniently in a tilted frame of reference whose z′-axis is oriented along the instantaneous direction of ωe(t). Transformation to the tilted frame is defined by equation M3 with U1 = exp[(t)Sy]:
equation M4
[3]
The propagator for evolution under this Hamiltonian can be written as (Haeberlen and Waugh, 1968)
equation M5
[4]
in which
equation M6
[5]
equation M7
[6]
T is the Dyson time-ordering operator (Evans and Powles, 1967), and equation M8 is the effective Hamiltonian in an interaction frame rotating around the z′-axis with frequency ωe(t). In this frame, illustrated in Fig. 1c, the Hamiltonian is given by:
equation M9
[7]
The average Hamiltonian is
equation M10
[8]
in which
equation M11
[9]
equation M12
[10]
In the applications envisioned, the transverse components of the interaction frame Hamiltonian given in Eq. [7], are negligible owing to rapid evolution of the sinusoidal terms that depend on ωe(t). Thus, the zero-order average Hamiltonian is given by
equation M13
[11]
in which the reduced scalar coupling constant is defined by
equation M14
[12]
In the absence of a refocusing pulse:
equation M15
[13]
in which angle brackets indicate the average value over the adiabatic sweep. The density operator in the laboratory frame at the end of the adiabatic sweep is given by:
equation M16
[14]
The second equality is obtained because the propagator U0(τp) commutes with equation M17 and the initial density operator and because the adiabatic sweep achieves a total rotation θ(τp) = π. Thus, evolution of the density operator during τp is obtained by the simple product operator rules for evolution under a reduced scalar coupling Hamiltonian equation M18 followed by an ideal πSy rotation; for example:
equation M19
[15]
If a 180°(I) refocusing pulse is applied during the adiabatic sweep, then these results are modified by applying the 180°(I) pulse to the operators present after τp.
For a chirp pulse, a linear frequency sweep with a constant value of ω1, Eq. [13] can be integrated to give
equation M20
[16]
in which ΔF is the sweep bandwidth and δ is the frequency offset between the S spin and the center of the frequency sweep. The second line is obtained assuming that equation M21. When this approximation is valid, evolution of the scalar coupling during an adiabatic sweep (in the absence of a refocusing 180° pulse applied to the I spins), can be represented as the sequence element τ′ − 180°(S) − (τpτ′), in which
equation M22
[17]
In Eq. [17], τ′ is equal to the time at which the adiabatic frequency sweep is resonant with the S spin (Zwahlen, et al., 1997). These results are approximately correct for the WURST family of adiabatic pulses (Kupče and Freeman, 1995) as well, provided that δ is restricted to the central constant-amplitude region of the pulse.
The accuracy of the average Hamiltonian result of Eq. [12] is illustrated in Figure 2 for the pulse sequence element of Fig. 1a using a series of WURST-20 adiabatic pulses (Kupče and Freeman, 1995) with increasing field strengths and shorter durations, typical of values used for these pulses in biological NMR spectroscopy. As shown in Fig. 2d, the accuracy of the average Hamiltonian result is weakly dependent on the adiabaticity of the sweep, provided that adiabaticity is maintained (Q0 ≥5). However, accuracy depends strongly on ω1maxτp, in which ω1max is the peak value of ω1(t), for two reasons. First, the accuracy of the approximation equation M23, that is, keeping only the zero-order Hamiltonian in Eq. [8], requires that ω1max [dbl greater-than sign]πJIS. Second, the cosine and sine terms that depend on ωe(t)t in Eq. [7] are averaged to zero only if ω1maxτp [dbl greater-than sign] 1. Thus, the accuracy of the above results is reduced for either weak rf fields or short pulse lengths.
Figure 2
Figure 2
Accuracy of average Hamiltonian theory. Results from average Hamiltonian theory calculated using Eq. [12] for the sequence element of Fig. 1a with τinv = τp/2 are compared to numerical calculations using the Liouville equation. The sweep (more ...)
Rotations under on-resonance radiofrequency pulses in the operator space {Ix, Iy, Iz} are isomorphous to rotations under the scalar coupling Hamiltonian in the operator space {2IzSz, 2IxSz, Iy} (Levitt, 1982). Thus, a composite 90° pulse that efficiently rotates Iz magnetization into the transverse plane independently of variation in the nominal rotational angle can be converted into a pulse-interrupted-free-precession period that transforms Iy magnetization efficiently into two-spin operators independently of variation in JIS. The composite 90° pulse sandwich β0(2β)2π/3, in which the bracketed term is the nominal rotation angle and the subscript is the phase of the pulse, has previously been used by Stuart and coworkers to develop a highly efficient composite-rotation isotope filter (Stuart, et al., 1999). Using the aforementioned isomorphism, the composite filter propagator is given by:
equation M24
[18]
The leftmost Iy rotation is not needed to implement an isotope filter and can be eliminated to simplify the propagator to
equation M25
[19]
in which β = πJτ and the filter is tuned to for a nominal scalar coupling constant J0 by setting the evolution delay τ = 1/(2J0). This propagator is realized by the ideal filter pulse sequence:
equation M26
[20]
A product operator analysis of the sequence shows that the evolution of I-spin coherence between points a and b of Fig. 3a is given by −Iy → −εIy in which:
Figure 3
Figure 3
Joint composite-rotation adiabatic-sweep isotope filters using (a) 120° I-spin rotation and (b) 60° S-spin rotation. Both filters are derived from the composite-rotation β0(2 β)2 π/3. Narrow and wide black bars (more ...)
equation M27
[21]
For a filter, the two-spin product operators created in this sequence, 2IzSz and 2IxSz, are purged by a 90° pulse applied to the S spins. In other applications, optimal transfer to 2IzSz longitudinal two-spin order can be obtained by appending a final 30°y rotation to the sequence. For 1H spins attached to 12C nuclei, JIS = 0 and ε = 1 under all conditions (ignoring relaxation).
As emphasized by Kay and coworkers (Zwahlen, et al., 1997) and by Kupče and Freeman (Kupče and Freeman, 1997), one-bond C-H scalar coupling constants and isotropic chemical shifts are linearly related for 1H spins attached to 13C nuclei in amino acid residues and RNA nucleotides:
equation M28
[22]
equation M29
[23]
in which JIS is measured in Hz and δC is the chemical shift measured in ppm (relative to DSS). As shown by Eq. [12], the reduced scalar coupling constant during an adiabatic sweep also depends on the S-spin resonance offset. Accordingly, the pulse element shown in Fig. 1a can be substituted for the central pair of 180° pulses in an INEPT element. The properties of the adiabatic sweep are chosen to obtain broadband polarization transfer from initial −Iy magnetization to 2IxSz for the desired range of JIS. This strategy has been elegantly incorporated into double-tuned isotope filters by Kay and coworkers (Zwahlen, et al., 1997).
Two implementations of a joint composite-rotation adiabatic-sweep filter element are shown in Figure 3. The two filter sequences have essentially the same theoretical performance. In the sequence of Fig. 3a, the two adiabatic pulses have the same frequency bandwidth and are swept in the same sense; therefore, the values of JIS calculated using Eq. [12] are identical for the two adiabatic sweeps. A product operator analysis of the sequence shows that the evolution of I-spin coherence between points a and b of Fig. 3a is given by −Iy → −εIy in which:
equation M30
[24]
In the sequence of Fig. 3b, the second adiabatic pulse, of length τp, has the same sweep bandwidth, but is swept in the opposite sense as the first adiabatic sweep. Therefore <cos[θ(t)]>sweep2 = −<cos[θ(t)]>sweep1 = <cosθ> using Eq. [13]. A product operator analysis of the sequence shows that the evolution of I-spin coherence between points a and b of Fig. 3b is given by −Iy → −εIy in which:
equation M31
[25]
The filters are implemented by numerically optimizing the adiabatic sweeps in order to minimize ε in Eqs. [24] and [25] over the desired range of JIS (while maintaining adiabaticity of the sweep as a constraint). For 1H spins attached to 12C nuclei, JIS = 0 and ε = 1 under all conditions (ignoring relaxation). Figure 4 compares the theoretical performance of the joint composite-rotation adiabatic-sweep isotope filter for scalar coupling constants in proteins with other approaches that have been described in the literature. The corresponding theoretical performance for scalar coupling constants in RNA is shown in Figure 5. The improvements obtained with the new sequences, particularly at the low and high extremes of the scalar coupling constants, are evident. The sequence of Fig. 3a is derived from the basic composite rotation β0(2β)2π/3 in a more straightforward fashion; however, as discussed below, the sequence of Fig. 3b has only 180° pulses on the I-spin when transverse coherences are present and allows convenient water suppression with the excitation sculpting (Hwang and Shaka, 1995) approach. In addition, resonance offset effects are smaller for a 60° pulse compared with a 120° pulse.
Figure 4
Figure 4
Net I-spin coherence, ε, for isotope filters applied to proteins. (a) Second-order isotope filter with ε = cos2[πJIS/(2J0)] and J0 = 144 Hz. The filter is realized by setting τd = τf = 1/(2J0) and eliminating the (more ...)
Figure 5
Figure 5
Net I-spin coherence, ε, for isotope filtration in RNA. Joint composite-rotation adiabatic-sweep isotope filter of Fig. 3b with ε given by Eq. [25]. Calculations used τa = 3.69 ms and the WURST-20 adiabatic sweep (Kupče (more ...)
The above theoretical analyses do not include the effects of relaxation. The joint composite-rotation adiabatic-sweep isotope filters are longer than the corresponding composite-rotation sequences of Stuart and coworkers (Stuart, et al., 1999), for example, the sequence of Fig. 3b is longer by 3τp/2, leading to reduced sensitivity, owing to relaxation losses. Thus, the lengths of the adiabatic sweeps also should be minimized while satisfying Eqs. [24] and [25]. Transverse relaxation for 1H spins attached to 13C nuclei is more efficient than for 1H spins attached to 12C nuclei, because the 1H-13C dipolar interaction constitutes an additional relaxation pathway. Consequently, the apparent filter efficiency, measured as the ratio of peak intensities for 1H spins attached to 12C nuclei and for 1H spins attached to 13C nuclei is increased in larger proteins with larger transverse relaxation rate constants.
The new isotope filter elements can be used as building blocks in a number of different pulse sequences as shown in Figures 6 and and7.7. Figure 6a shows an F1/F2-edited, F3-filtered HMQC-NOESY experiments based on a semi-constant-time HMQC pulse sequence. The excitation sculpting water suppression technique (Hwang and Shaka, 1995) has been built into the filter element, without increase in any delays, for water suppression. Figure 6b shows an F1-filtered, F2/F3-edited NOESY-HMQC pulse sequence. The excitation sculpting technique has been built into the HMQC pulse sequence for water suppression. Both of these sequences use phase cycling for 13C editing and subtraction artifacts may pose a significant problem if large excesses of unlabeled ligands (or buffer components) are present in the sample; however, the HMQC-NOESY sequence in particular has the advantage for use with cryogenic probes of not requiring decoupling during acquisition. Figure 7 shows a F1-filtered, F2/F3-edited NOESY-HSQC pulse sequence that uses the gradient-selected sensitivity-enhanced pulse sequence element (Kay, et al., 1992, Palmer, et al., 1991, Schleucher, et al., 1994) for improved 13C editing.
Figure 6
Figure 6
(a) F1/F2-edited, F3-filtered HMQC-NOESY and (b) F1-filtered, F2/F3-edited NOESY-HMQC pulse sequences. Narrow and wide black bars represent 90° and 180° pulses, respectively. The narrow open bar represents a 60° pulse. Wide open (more ...)
Figure 7
Figure 7
F1-filtered, F2/F3-edited NOESY-HSQC isotope filtered pulse sequence. Narrow and wide black bars represent 90° and 180° pulses, respectively. The narrow open bar is a 60° pulse. Wide open bars are the two adiabatic sweeps. All (more ...)
The accuracy of the average Hamiltonian treatment of adiabatic sweeps and the performance of the proposed composite-rotation adiabatic-sweep isotope filter elements were validated using a sample containing [99%-13C]-labeled Ala, His, and Tyr amino acids (~1 mM in 100% D2O) (Cambridge Isotopes). The reduced scalar coupling constant for the Ala 1Hα resonance was measured as a function of resonance offset using the pulse sequence in the inset to Figure 8b. The performance of the proposed filter was measured using the sequence in Figure 3b by recording a single-transient free-induction decay immediately following the filter sequence (i.e., no additional isotope-editing was performed after the filter). Weak presaturation was used prior to the first pulse for water suppression. A 1H-1H F1-filtered, F2-edited NOESY spectrum was recorded using a 0.5 mM sample of a 1:1 complex between [U-13C, U-15N] VTS SAM domain and natural abundance TCE 13mer RNA (10% D2O/90% H2O, pH = 6.25) described elsewhere (Edwards, et al., 2006). The spectrum was recorded using the pulse sequence of Figure 7 by setting t2 = 0. The spectrum was recorded in ~18 hours using (t1 × t2) spectral widths of (6250 Hz × 12500 Hz) as a (175 × 1024) complex matrix. A total of 128 scans were recorded per complex t1 point. The NOE mixing time was 250 ms. All experiments were recorded using a Bruker DRX600 NMR spectrometer equipped with a cryogenic triple resonance probe with a z-axis gradient.
Figure 8
Figure 8
J-scaling during adiabatic sweep. (a) Plots of cos[θ (t)] versus t during an adiabatic sweep. The sweep used the WURST-20 shape (Kupče and Freeman, 1995) with τp = 2.359 ms, a sweep bandwidth ΔF/2π = 60 kHz (swept (more ...)
Figure 8 illustrates the application of average Hamiltonian theory for treating scalar coupling interactions during adiabatic sweeps. Figure 8a shows the instantaneous values of cos[θ(t)] during an adiabatic sweep for three different values of the resonance offset. The value of cos[θ(t)] is null at the moment during the adiabatic sweep that the rf field is resonant with the nuclear spin. The value of <cosθ> is given by the integral of the curves and is equal to zero only for a spin resonant with the rf field at the center of the sweep. Figure 8b shows the reduced scalar coupling constant measured for the Ala 1Hα resonance as a function of resonance offset from the value of the rf field as the center of the sweep for the spin-echo pulse sequence shown in the inset. Measured values of the reduced coupling constant are shown as solid circles. The line is not a fit to the data; rather, the line is calculated using average Hamiltonian theory and independently determined parameters used for the adiabatic sweep in the pulse sequence element.
Figure 9 shows the degree of suppression achieved by the joint composite-rotation adiabatic-sweep filter in a single scan using the pulse sequence of Fig. 3b (nearly identical results are obtained using the pulse sequence of Fig. 3a). The residual filter breakthrough peaks, even for the His 1Hε1 resonances (8.28 and 8.66 ppm) and Ala 1Hβ resonances (1.26 and 1.50 ppm) are < 0.01 (smaller than the centerband resonance peaks for 1H spins attached to 12C nuclei, resulting from the ~1% of carbon sites that are not isotopically enriched in the 99% labeled amino acids). Improvements compared with the individual composite-rotation isotope filter and the adiabatic-sweep isotope filter are particularly evident for the His 1Hε1 resonances.
Figure 9
Figure 9
Isotope filtration efficiency. A sample containing [U-13C] Ala, [U-13C] Tyr, and [U-13C] His amino acids was used to test the isotope filtration performance in a single (one-scan) transient. (a) One-pulse 1H NMR spectrum; (b) isotope filtered 1H NMR spectrum (more ...)
Figure 10 displays the region of the 1H-1H F1-filtered, F2-edited NOESY spectrum corresponding to the F1 RNA sugar region and F2 protein methyl region. A number of RNA-protein crosspeaks are visible (along with a ridge of water-to-protein NOE crosspeaks). The residual diagonal resonances, resulting from filter breakthrough, are inverted and approximately are of the same intensity as the stronger NOE crosspeaks.
Figure 10
Figure 10
NOESY-HSQC spectra for VTS SAM domain/TCE RNA complex. The spectrum was acquired using the pulse sequence of Fig. 7 by setting t2 = 0. Filter parameters were identical as described for Fig. 9b. Other experimental details are given in the text.
Two distinct approaches for improving the performance of isotope filters, one based on composite-rotations (Stuart, et al., 1999) and the other based on designed adiabatic sweeps (Kupče and Freeman, 1997, Zwahlen, et al., 1997), have been reported previously. Combination of the two approaches yields superior filtration efficiency, compared with methods individually, particularly for 1H spins with coupling constants that are near the extrema of the range of values or that do not satisfy empirical relationships between isotropic chemical shifts and scalar coupling constants. The latter property makes the new filter sequences particularly useful for molecular complexes that are weakly aligned in anisotropic media (Tjandra and Bax, 1997). In such samples, the residual heteronuclear dipole coupling adds to the heteronuclear scalar coupling constant and renders the approximate relationships between scalar coupling constants and isotropic shifts in Eqs. [22] and [23] less accurate. The joint composite-rotation adiabatic-sweep isotope filter can be incorporated as a building block in a variety of NMR pulse sequences to obtain NMR spectra that are isotope-filtered in one or more frequency domains.
Theoretical optimization and analysis of the isotope filter pulse sequences are simplified by using average Hamiltonian theory to describe evolution of I-spin coherence under the heteronuclear scalar coupling Hamiltonian while an adiabatic sweep is applied to the S spin in an InS spin system. The compact results that emerge from average Hamiltonian theory in this context are likely to be applicable to other experimental NMR methods that utilize adiabatic sweeps in heteronuclear scalar-coupled spin systems.
The joint composite-rotation adiabatic-sweep isotope filter is extremely efficient in suppressing coherence from 1H spins directly attached to 13C nuclei. In all existing isotope filters, increased suppression efficiency inevitably is obtained at cost of increased filter length. Recently optimal control theory has been applied to the design of solution NMR pulse sequences for coherence transfer with optimal relaxation properties (Khaneja, et al., 2004); similar methods may prove fruitful for further developments in J-filtration.
Acknowledgments
This work was supported by NIH grants GM50291 (A.G. P.) and GM47021 (D. C.). Helpful discussions with Mark Rance (Univ. Cincinnati) are acknowledged gratefully.
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