5.1.1. J-resolved experiments for measuring ³J_H^NH^α

A phase-sensitive COSY is suitable for small proteins, but the cancellation of antiphase cross-peaks is a problem for large proteins with broad lines. Therefore, it is helpful to measure the couplings from in-phase splittings. For smaller proteins with favorable relaxation rates, ³J_H^NH^α coupling constants can be determined most efficiently and conveniently from in-phase multiplets in a ¹⁵N-HSQC type spectrum, either from the directly detected dimension by a line-fitting technique (Szyperski et al. 1992), or directly from the ¹⁵N-dimension, when accordion style spectroscopy (Bodenhausen & Ernst 1981) is used (Heikkinen et al. 1999). A limiting factor in both of these cases is the rapid transverse relaxation of proton single-quantum coherence, and consequently the applicability of ¹⁵N-HSQC and MJ-HSQC experiments is somewhat limited.

The problems arising from rapid transverse relaxation can be alleviated if multiple-quantum coherence between the amide proton and nitrogen is formed. Due to the absence of dipolar interaction between ¹H^N and ¹⁵N spins in the ¹H^N-¹⁵N multiple-quantum spin-state, this coherence relaxes much more slowly than the corresponding amide proton single-quantum coherence. For example, the protein staphylococcal nuclease (SNase), with a correlation time of 9 ns at 37°C, has been shown to have a T_{2, (H^N)}/T_{2, (MQ)} ratio of 0.27 at a ¹H frequency of 500 MHz (Kay & Bax 1990). A very simple approach employs the familiar HMQC experiment for the determination of ³J_H^NH^α, which offers good sensitivity and robustness, due to a small number of RF pulses. In addition, it is applicable to ¹⁵N-enriched samples. Unfortunately, due to a mixture of absorptive and dispersive line shapes, it is necessary to correct the measured couplings to obtain accurate coupling constants (Kay & Bax 1990). A slight modification of the HMQC is the HMQC-J scheme (Kay et al. 1989; Kay & Bax 1990). The HMQC-J experiment differs from HMQC only by the implementation of an additional 90°(¹H) pulse immediately before the acquisition period. The pulse serves as a purge pulse for the dispersive antiphase magnetization that arises from the homonuclear coupling evolution during t₁. The pulse has no influence on the desired cosine-modulated magnetization, but it transfers dispersive sine-modulated magnetization to the α-proton frequency. It is then possible to measure the coupling in the ¹⁵N-dimension from the in-phase splitting of the ¹⁵N, ¹H^N cross-peak with an absorptive line shape.

Using a J-multiplied, pseudo-constant-time evolution period for the coupling and the ¹⁵N chemical shift evolution, the ³J_H^NH^α coupling can also be rapidly measured by the JM-HMQC experiment (Permi et al. 1999b) that is a modification of the CT-HMQC-J experiment (Kuboniva et al. 1994). The advantage over the conventional HMQC-J experiment is greater accuracy due to a multiplication of ³J_H^NH^α, because the error in the measured couplings is divided by 1+κ, where κ is the J-multiplication factor. The factor κ is incremented in concert with t₁ to downscale chemical shift evolution with respect to coupling evolution, i.e. κ is a multiple of t₁. In addition, fewer time increments are required to resolve the couplings adequately, allowing more transients per increment. However, this will not affect signal averaging, as fewer increments are used for the same experiment time. One should be aware that in neither the HMQC-J nor the JM-HMQC experiment is the signal purely absorptive, due to homonuclear J-modulation during the polarization transfer steps. Therefore, line width-dependent corrections should be applied for accurate determination of ³J_H^NH^α. On the other hand, selective decoupling of the alpha-proton can easily be employed during polarization transfer steps in order to prevent formation of spurious antiphase magnetization before the t₁ evolution period (Permi et al. 1999b).

5.1.2. DQ/ZQ experiments for measuring ³J_H^NH^α

It is also possible to determine ³J_H^NH^α by DQ/ZQ spectroscopy. If a mixed DQ/ZQ coherence is created between ¹H^N(i) and ¹³C^α(i) spins, and chemical shift evolution and coupling to the ¹H^α spin are allowed to take place simultaneously during t₁, the ³J_H^NH^α couplings can be measured from the HNCA-type correlation spectrum (Rexroth et al. 1995). Thus, ³J_H^NH^α can be extracted from DQ and ZQ multiplet patterns, which are split by ~145 + ³J_H^NH^α Hz and ~145 – ³J_H^NH^α Hz in the ¹³C^α-dimension, respectively. Although this approach is rather insensitive to the effects of differential relaxation, it is not very suitable for large proteins due to rapid relaxation of the ¹³C^α spin. On the other hand, by utilizing a semi-constant time TROSY evolution (Permi et al. 2000) during t₂, it is possible to decrease the time period during which ¹³C^α and ¹H^N are in transverse plane, while preserving high resolution in the ¹⁵N-dimension.

5.1.3. Methods utilizing the E.COSY principle

One of the first E.COSY-type experiments used for determination of coupling constants in ¹⁵N/¹³C-labeled proteins was the HNCA-J experiment (Wagner et al. 1991). The pulse sequence is based on HNCA (Kay et al. 1990). During the t₁ evolution period, the ¹³C^α spin is allowed to couple to its directly bound ¹H^α spin by a large ~145 Hz coupling. Subsequently, the magnetization is transferred back to the amide proton, without perturbing the ¹H^α spin-state. As ¹H^N couples to the passive ¹H^α spin during acquisition, ¹H^α acts as a passive spin during the evolution periods t₁ and t₃, resulting in the E.COSY pattern. As long as the large ¹J_Cα_Hα coupling is resolved in the F₁-dimension, the small ³J_H^NH^α coupling can be measured from the orthogonal F₃-dimension. As mentioned earlier, a partial collapse of the E.COSY pattern due to ¹H^α spin flips between the t₁ and t₃ periods will lead to too small values of the measured ³J_H^NH^α coupling constants. This effect can be reduced by shortening the time periods of the ¹³C’-¹⁵N and ¹⁵N-¹H back-INEPT steps.

5.1.4. Quantitative J-correlation

The very first method for determination of ³J_H^NH^α, which exploited quantitative J-correlation, was the HNHA experiment (Vuister & Bax 1993). It correlates the ¹H^N, ¹⁵N, and ¹H^α spins in a three-dimensional spectrum, permitting extraction of ³J_H^NH^α from the intensity ratio of diagonal peak and cross-peak. The essential idea behind the HNHA experiment is to use a constant time period (T) during which the ³J_H^NH^α coupling is allowed to evolve. While a part of the magnetization is subsequently transferred to the ¹H^α spin, another part remains on the ¹H^N. The transferred magnetization resonates at the ¹H^α frequency during the period t₂ and corresponds to the cross-peak. The other part of the magnetization resonates at the ¹H^N frequency, corresponding to the diagonal peak in the spectrum. At the end of the period t₂, the magnetization is transferred back to the ¹H^N spin and is refocused with respect to the ¹H^α and ¹⁵N spins prior to acquisition. Because ‘diagonal peak’ has cos²(π³J_H^NH^αT) dependence on signal intensity and the ‘cross-peak’ has sin²(π³J_H^NH^αT) dependence, ³J_H^NH^α can be extracted from the intensity ratio of the diagonal peak and the cross-peak based on the simple equation

I_c/I_d=tan²(π³J_H^NH^αT)

It should be noted that the determination of the ³J_H^NH^α couplings of the individual ¹H^α spin in glycines is also obtained if ¹H^α shifts are not degenerate. The HNHA scheme has proven to be a robust method, but a few limitations exist for large proteins. Although cross-peaks are virtually free from overlap, the dispersion of diagonal peaks is somewhat limited despite the three dimensions of the HNHA experiment. In fact, the dispersion of diagonal peaks relies entirely on the two-dimensional ¹⁵N-¹H^N correlation map. Sufficient resolution in the ¹⁵N-dimension in the HNHA experiment requires a rather long measurement time, even with minimal phase cycling.

Recently, Ponstingl and Otting (1998) introduced a rapid method for the measurement of ³J_H^NH^α in ¹⁵N-labeled protein samples. The basic idea in their CT-HMQC-HA experiment is rather simple (Figure 7A). Two constant-time HMQC experiments are recorded. A semi-selective ¹H^α decoupling is applied during the course of the pulse sequence in one experiment, whereas ³J_H^NH^α -modulation is allowed in the other experiment. This results in two ¹⁵N-¹H correlation spectra, in which the intensity ratio between cross-peaks is determined by cos(2πJ_H^NH^ατ), and 2τ (=4T+4Δ) is the length of the J-modulation period. As the period 2τ is known, ³J_H^NH^α can be determined by using a simple trigonometric relation

I_m/I_d = cos(2π³J_H^NH^ατ),

where I_d and I_m are the cross-peak intensities in the decoupled and J-modulated experiments, respectively. The experiment has high sensitivity and it allows a rapid measurement of the ³J_H^NH^α coupling constants. However, it is obvious that the resolution in the ¹⁵N-dimension is constrained by the delay 4T. To avoid ambiguities in cross-peak intensities, the delay 2τ should not be chosen in such a way that the period 2τ is > 1/(³J_H^NH^α). In practice, J-modulation periods exceeding 80-90 ms should be avoided. Thus, the available resolution in the F₁-dimension depends on the magnitude of the coupling constants as well. For example, choosing the 4(T+Δ) period equal to 50 ms would cause the disappearance of cross-peaks from residues having ³J_H^NH^α equal to 10 Hz. This allows an acquisition time of 40 ms in the F₁-dimension, which is insufficient for larger or helical proteins. Of course, it is possible to increase the length of the J-modulation period, but this is rather ‘costly’ from the relaxation point of view. Additionally, cross-peaks of certain residues will disappear from the J-modulated spectrum, owing to the cos(2πJ_H^NH^ατ) dependence.

If separate time periods for the J-modulation and ¹⁵N chemical shift evolution are used, the signal in the F₁-dimension can be acquired independently from the J-modulation period. Figure 7B illustrates the pulse sequence of the Intensity-Modulated HSQC (IM-HSQC) experiment for the measurement of ³J_H^NH^α in ¹⁵N-labeled protein samples (I). The basic idea is the very same as in the CT-HMQC-HA experiment. Thus, two separate experiments are recorded: ³J_H^NH^α is allowed to evolve in the J-modulated experiment, whereas it is effectively decoupled in the reference experiment during time period 2τ. The ¹H^N magnetization is subsequently transferred to its directly bound ¹⁵N, whose chemical shift is detected in a manner analogous to the ¹⁵N-HSQC experiment (Bodenhausen & Ruben 1980). Eventually the desired coherence is transferred back to the amide proton, whose chemical shift is detected during the acquisition. In summary, two ¹⁵N-HSQC-type spectra result, in which ³J_H^NH^α couplings can be extracted by comparison of cross-peak intensities between the J-modulated and the reference experiments. Figure 8 clearly emphasizes the gain in resolution obtained with the IM-HSQC over the CT-HMQC-HA experiment. For large proteins, with unfavorable relaxation properties, it is judicious to exploit the slower relaxation rate of ¹⁵N-¹H^N multiple-quantum coherence and concatenation of J-modulation and ¹⁵N chemical shift labeling periods then in the SCT-HMSQC-HA experiment (Aitio & Permi 2000).

The longitudinal relaxation rate of the ¹H^α spin (or passive spin in general) causes the phenomenon called differential relaxation, which may alter the multiplet pattern or distort the cross-peak intensities, leading to systematic errors in the measured coupling values (Abragam 1961; Harbison 1993; Rexroth et al. 1995). Due to the rapid spin flip of the ¹H^α spin, the ¹H^N in-phase and antiphase magnetizations relax at different rates in the HNHA and CT-HMQC-HA experiments, as well as in the IM-HSQC experiment. The difference in the relaxation rates of the in-phase and antiphase coherences is approximately proportional to the selective longitudinal relaxation rate of the ¹H^α spins (Vuister & Bax 1993). Analogously, the passive ¹H^α spin changes its spin-state between the t₁ and t₃ acquisition periods in the HNCA-J experiment, leading to partial collapse of the E.COSY pattern. Altogether, the differential relaxation results in a systematic decrease of the apparent ³J_H^NH^α coupling. If the period used for the J-modulation in the HNHA, CT-HMQC-HA, or IM-HSQC experiments constitutes a considerable fraction of T₁, _Hα, a systematic error in the measured coupling constant, develops. Furthermore, as the differential relaxation affects the magnitude of the measured couplings by an amount depending on the length of the J-modulation period used, it is advantageous to use the shortest possible delay for the coupling evolution. Thus, the shorter the delay used for the J-modulation, the smaller the correction factor needed. On the other hand, the larger the coupling, the smaller the effect of differential relaxation, and consequently, the smaller the correction factor required. The effects of differential relaxation can be corrected for the measured ³J_H^NH^α values in the HNHA, CT-HMQC-HA, and IM-HSQC experiments if T_{1, H}α is known (Vuister & Bax 1993; Kuboniwa et al. 1994; Ponstingl & Otting 1998). The correction provides coupling constants with higher accuracy for larger proteins. It should be noted that the DQ/ZQ-HNCA experiment is insensitive to the effects of differential relaxation. This can be understood by realizing that the absolute error in J, induced by the differential relaxation, is inversely proportional to the magnitude of J. As the effect of differential relaxation on ³J_H^NH^α is inversely proportional to the magnitude of the DQ and ZQ splittings, the DQ/ZQ-HNCA method compensates for the effects of differential relaxation.