4.5. Spin-state-selective filtering

The J-resolved, DQ/ZQ and E.COSY type experiments can be combined with a technique referred to as spin-state-selective filtering, first presented by Meissner (et al. 1997a-b). Spin-state-selective filtering separates the α- and β-states of the corresponding doublet into two subspectra, thus preventing the increase of the resonance overlap due to coupled evolution. Two separate experiments are recorded, one with the corresponding doublet in-phase and the other one with an antiphase splitting (Figure 4). When the two subspectra are added together, a single resonance line, corresponding to either the doublet’s α-state or β-state, is observed. On the other hand, when the in- and antiphase data sets are subtracted, a spectrum containing the other spin-state of the doublet is obtained.

Figure 5 represents different spin-state-selective filter elements. The function of the filter elements can be described using the product operator description. Initially in-phase magnetization I_y evolves under scalar (+dipolar) coupling J_IS to

2I_yS_z cos(πJ_ISτ) – I_x sin(πJ_ISτ)

during the S³E element (A) (Meissner et al. 1997a) and the antiphase filter elements (B-D) (Andersson et al. 1998; IV). The filter delay in the S³E element (A) is matched to 1/(4J_IS), and thus cosine and sine modulated terms are equal in their intensity. At this point, the S³E applies two 90°(I) pulses, either in the same or opposite phase, to invert or to preserve the sign of one of the magnetization terms. When these two experiments are stored separately, they can be added or subtracted to yield the up- and downfield components of the corresponding J_IS doublet.

The filter element in Figure 5B (Andersson et al. 1998) allows subspectral editing by recording two data sets with and without J_IS decoupling. This filter element is less sensitive to variation in coupling constants than the S³E element since the filter delay is matched to 1/(2J_IS). Thus, one data set is recorded without a 180° editing pulse on S spin (in-phase filter element), and another data set is recorded in the presence of the 180°(S) editing pulse (antiphase filter element). Additionally, a 90°(S) purge pulse is applied during the antiphase filter to remove any residual cosine-modulated magnetization, which would otherwise contribute to the line shape as a dispersive magnetization component. The filter element in Figure 5C (Andersson et al. 1998) achieves subspectral editing in a similar way, but two 180° pulses are applied during the in-phase filter element. The function of these pulses is to average the relaxation rates of the two doublet components in the presence of DD/CSA cross-correlated relaxation (vide infra). The filter element in Figure 5D (IV) is mostly similar to the element in 5C, but it can be used for in-phase I magnetization. It employs pulsed field gradient z-filtering (PFG-z) by preserving the desired magnetization component in a longitudinal zz-order during the pulsed field gradient. This purges any undesired magnetization components. It should be noted that a 90° pulse prior to the gradient pulse is applied both in the in- and antiphase (90° phase shift between the in- and antiphase elements) filter elements in order to select the desired magnetization component.

The S³CT filter element (Figure 5E) (Meissner et al. 1997b) was designed to obtain spin-state selection concomitantly with coherence transfer. It is thus obvious that S³CT element requires antiphase 2I_yS_z at the start. Its applicability to IS, I₂S, and I₃S editing is somewhat limited because S³CT necessitates different filter delays for CH, CH₂, and CH₃ moieties (Andersson et al. 1998).

An obvious advantage of subspectral editing with respect to spin-states is that each subspectrum consists of either the upfield or downfield components of a doublet, thus there is no increase in spectral crowding due to coupling evolution. A second aspect concerns the overlapping doublet components. If the in-phase doublet is not resolved to the baseline, the apparent splitting will underestimate the true coupling since the peaks shift towards each other due to partial overlap of line shapes. In spin-state-selective experiments, the peak placements are not affected by each other owing to the subspectral editing of upfield and downfield components. The practical advantage of this is that it is possible to measure couplings in the case of rapid transverse relaxation. Consider, for instance, the 3D-HNCO(α/β-NC’-J) experiment (II; Permi et al. 2000), where ¹J_NC’ is 15 Hz. In order to resolve a 15 Hz coupling adequately, at least a 60 millisecond collection period is needed. In a three-dimensional experiment, the experimental time would then increase considerably. However, by utilizing spin-state-selective filtering, the acquisition time in the carbonyl dimension can be shortened significantly because the partially resolved doublet components are separated in two subspectra. The sensitivity of the spin-state-selective experiment is inherently somewhat lower than the corresponding J-resolved experiment owing to the additional delays or radio-frequency pulses. However, other factors that can be achieved by the spin-state-selective filtering must also be considered. First, contrary to the usual ¹⁵N-¹³C’-coupled HNCO spectrum, it provides improved resolution since spectral overlap does not increase. Second, owing to the shorter acquisition time needed in the ¹³C’-dimension, the sensitivity of the experiment is improved with respect to ¹³C’ transverse relaxation. Third, the α/β-filtered HNCO spectrum can also be used for backbone assignment because it resembles the ordinary HNCO spectrum (Ikura & Bax 1990), thus reducing the total number of spectra needed for structure determination.

Numerous reasons lead to insufficient subspectral editing, such as J-mismatch, differential relaxation, cross-correlation, and pulse imperfections. Let us first focus on J-mismatch. If the filter is not exactly matched to the true coupling value, the observed signal has a dispersive contribution because the undesirable magnetization component leaks through the filter. The dispersive component can be efficiently removed, i.e. purged, using various techniques for the selection of the desired coherence pathway (vide supra). However, the amplitude of the desired signal also diminishes due to its sin(πJτ) dependence, where J is the true coupling and τ is the delay to which the filter is matched (τ = 1/nJ, where n is usually 1, 2, 4, or 8). The J-mismatch is problematic only in cases in which there is a large variation in couplings. For example, the ¹J_NH couplings in proteins, in the isotropic phase, are usually within the range of 91 to 95 Hz, and very good to excellent subspectral editing can be obtained with filters selective to the ¹J_NH coupling. The same also holds true for the ¹J_C’Cα and ¹J_NC’ couplings, which are in the range of 51 to 55 Hz, and 14 to 16 Hz for the majority of amino acid residues in isotropic phase, respectively. Figure 6 illustrates J-leaking profiles for the filters sensitive to ¹J_NH, ¹J_C’Cα, and ¹J_NC’ couplings in the isotropic phase. However, the situation can be somewhat different in the presence of a large residual dipolar contribution to the scalar coupling. Dipolar contributions to the ¹J_NH splitting as large as 30 Hz are usual and J-crosstalk due to J-mismatch is likely to occur, i.e. the subspectrum corresponding to the doublet in the α-state also receives a contribution from the undesired doublet component corresponding to the β-state, and vice versa. The corresponding maximal dipolar contribution to the ¹J_NC’ splitting can be as large as 3 Hz, and J-crosstalk appears when ¹J_NC’ differs from the canonical 14-16 Hz. Fortunately, J-crosstalk can be almost completely removed from the subspectra by taking appropriate linear combinations of the in- and antiphase spectra (Meissner et al. 1998b; Ottiger et al. 1998; Sørensen et al. 1999; II-IV).

The differential relaxation can also affect subspectral editing. If the relaxation rate of the in-phase coherence differs from that of antiphase coherence, this results in an amplitude imbalance between the in- and antiphase spectra and eventually leads to J-crosstalk. Thus, to prevent J-crosstalk due to differential relaxation, the time period during which differential relaxation is effective should be kept to a minimum. In practice, one should avoid using long coherence transfer delays or mixing periods between the spin-state-selective filter and the evolution period for the coupling constant of interest.

Cross-correlation between CSA and DD relaxation mechanisms may lead to amplitude imbalance between the in- and antiphase time domain spectra. A careful inspection of the in-phase filter elements shown in Figure 5B and 5C reveals that the only difference between them is the lack of a 180°(S) pulse in the former, and the use of a pair of 180°(S) pulses in the latter. At first glance, this may not seem to be a significant difference since the coupling between I and S is effectively decoupled in both schemes. However, relaxation interference between spin I CSA and I-S DD interactions is not averaged in the former scheme. Eventually, this results in an amplitude imbalance between the in-phase and the antiphase spectra. On the other hand, the scheme in Figure 5C interchanges α- and β-states of the spin S during the filter element, and averages the cross-correlated relaxation during the in-phase filter. This can be realized by considering the effect of the 180°(I) pulse alone on I_z (CSA) and I_zS_z (DD) operators, and the concomitant 180° pulses on I and S spins. Hence, in the middle of the filter element in Figure 5B, the 180°(I) inverts both the I_z and I_zS_z operators, and thus, the cross-correlated relaxation mechanism between CSA and DD interactions is not averaged. In the case of 180° pulses applied both to I and S spins in the filter element of the Figure 5C, the cross-correlated relaxation is averaged owing to inversion of I_z, whereas the I_zS_z operator is not inverted.