Chapter 3. Problems associated with measurement of coupling constants in proteins

Traditional one-dimensional ¹H NMR spectroscopy is sufficient to provide information on chemical shifts and coupling constants in small organic molecules. Owing to the long transverse relaxation times, proton resonances have very narrow line widths in comparison with the inhomogeneity of the magnetic field. Hence, relatively small coupling constants can often be measured with high accuracy from a well-dispersed spectrum.

In the case of biological macromolecules, the situation is very different for two reasons: increased spectral overlap and faster transverse relaxation of protons. The number of proton resonances in the same rather limited chemical shift range increases rapidly as the protein size increases. For example, a 10-kDa protein has approximately 100 amide proton resonances in the chemical shift range of 3 to 4 ppm. In the case of a 30-kDa protein, the number of resonances is on the order of 300. In addition, as the isotropic molecular rotational correlation time, τ_c, increases with increasing molecular weight, the line width is dictated by the shorter transverse relaxation time of the corresponding spin instead of magnetic field inhomogeneity. Ultimately, the line width is larger than the coupling constant of interest. These two dilemmas make it impossible to obtain structurally important vicinal proton-proton coupling constants simply from a 1D proton spectrum.

An obvious solution to the overlap problem is to increase the dimensionality of the spectrum. For example, a two-dimensional phase-sensitive COSY experiment (Marion et al. 1983) has been successfully used with small proteins. The dispersion of the proton signals in the COSY spectrum is to the power of two better than in the 1D proton spectrum. However, applicability of the phase-sensitive COSY is limited to small proteins, because in the case of determination of ³J_H^NH^α, the cross-peak intensity between ¹H^N and ¹H^α is low due to self-cancellation of antiphase splitting in the presence of broad lines. Furthermore, the magnitude of the coupling constant is not accurate because the antiphase splitting greatly overestimates the true coupling constant (Neuhaus et al. 1985). For this reason, several line-fitting techniques have been developed for the extraction of the true coupling constant in the phase-sensitive COSY experiment (Neuhaus et al. 1985).

One major limitation of homonuclear experiments stems from the rapid transverse relaxation of protons. This reduces their usability for protein structure determination due to coherence transfer inefficiency in multi-dimensional experiments. Proton relaxation is dominated by the large dipole-dipole (DD) interaction between protons in the protein main-chain and side-chains. Consequently, the proton line width increases rapidly with increasing rotational correlation time. As can be seen from Figure 1a, the proton line width is close to 10 Hz when the correlation time is of the order 10 ns. In contrast, the line width of the backbone amide nitrogen is less than 5 Hz (Figure 1b). It is then obvious that the development of heteronuclear correlation experiments, which allow a greater dispersion of NMR signals with higher coherence transfer efficiency, is indispensable for larger proteins.

Introduction of isotopic labeling in protein NMR spectroscopy in the late 1980’s improved the sensitivity and resolution of protein NMR spectra. Thus, magnetically inactive ¹²C, and spin-1 ¹⁴N nuclei are replaced by active spin- nuclei ¹³C and ¹⁵N. In addition, the isotope enrichment facilitated the measurement of several, also heteronuclear, coupling constants in the protein main-chain. More importantly, new techniques were devised to determine coupling constants in general. It is now possible to measure finite couplings, without the need to resolve them directly, by utilizing for instance, E.COSY (Griesinger et al. 1986), multiple-quantum coherence principles (Braunschweiler et al. 1983) and quantitative J-correlation (Blake et al. 1992). The ¹⁵N, ¹³C double labeling of protein samples has increased the size limit of NMR-feasible proteins from 10 kDa to the 20-30 kDa limit. Table 1 represents typical transverse relaxation times found for ¹H, ¹⁵N, and ¹³C nuclei in a protein backbone at a 30-kDa size regime.

To increase the protein size further, rapid transverse relaxation of heteronuclei must be taken into account as well. Transverse relaxation times for aliphatic carbons with proteins at the 20-30 kDa regime have been shown to be as short as 10-20 ms (Gardner & Kay 1998) (Table 1). It is inevitable that this seriously limits sensitivity and resolution in the experiments that record chemical shift or relay magnetization via aliphatic carbons. A very efficient solution to this problem is perdeuteration, that is, replacement of non-exchangeable protons with deuterium. This decreases the carbon relaxation rate over 10-fold, since the dipole-dipole relaxation between ¹³C and its directly bound ²H is much smaller than that between ¹³C and ¹H, owing to the 6.5 times smaller magnetogyric ratio of ²H. Perdeuteration is beneficial for ¹⁵N, ¹H correlation experiments as well, since the relaxation rate of the amide proton decreases approximately twofold, due to the disappearance of homonuclear dipolar relaxation caused by aliphatic protons. It has been shown that 40% of the transverse relaxation rate of the amide proton arises from the dipolar contribution with the aliphatic protons (Markus et al. 1994). Amide nitrogens and carbonyl carbons are, however, much less affected by perdeuteration (Table 1).

Unfortunately, the improved sensitivity and resolution does not come without a cost. As mentioned earlier, NOE information available from non-exchangeable protons is reduced or completely lost (in the case of fully perdeuterated proteins), which results in low-resolution protein structures (Venters et al. 1995; Gardner & Kay 1998). Problems associated with a phenomenon referred to as spin diffusion are, however, less serious because of the decreased proton density (Gardner & Kay 1998; Farmer & Venters 1999). Thus, a separation between protons i and j can be determined more accurately thanks to the absence of magnetization relay via mutual spin k. Furthermore, it permits the use of longer NOE mixing times, allowing the measurement of larger distances than would be possible in protonated systems (Venters et al. 1995).

Chemical shift anisotropy (CSA) is a significant source of T₂ relaxation for ¹⁵N and ¹³C’ spins in proteins. As the CSA interaction increases with increasing magnetic field, it reduces the gain in sensitivity and resolution obtained by the use of the highest magnetic fields. The second important source of relaxation is dipole-dipole (DD) interaction between spins. It has been commonly known for several years that the interference between chemical shift anisotropy (CSA) and dipole-dipole (DD) relaxation mechanisms results in differently relaxing ¹⁵N-¹H multiplet components (Goldman 1984). Pervushin and co-workers recently showed that at proton frequencies near 1.1 GHz, almost complete cancellation of transverse relaxation effects within a ¹⁵N-¹H moiety is expected for one of the four multiplet components in fully ¹⁵N-¹H coupled 2D experiment. By using a certain spin-state edited experiment for the selection of the most slowly relaxing ¹⁵N-¹H multiplet component (TROSY, transverse relaxation optimized spectroscopy), significant improvement in sensitivity and resolution in ¹⁵N-¹H detected experiments, especially with larger perdeuterated protein samples, can be achieved (Pervushin et al. 1997). Interestingly, in addition to ¹H^N spin relaxation, use of perdeuterated samples with TROSY selection also dramatically decreases the relaxation rate of ¹⁵N spin. Remote protons have been shown to correspond with 75% of the residual T₂ of ¹⁵N relaxation (Pervushin et al. 1997). Therefore, TROSY selection concomitantly with perdeuteration is most effective for large β-sheet proteins, where there are only a few routes to amide nitrogen relaxation. For α-helical proteins, the TROSY effect is somewhat less dramatic because of the proximity of ¹H^N(i-1) and ¹H^N(i+1) spins to the ¹⁵N(i) spin. In highly perdeuterated β-sheet proteins, it may also be advantageous to prevent the formation of N_xC_z antiphase coherence by coherent carbon decoupling, since longitudinal ¹³C_z spin relaxation forms a significant source of residual relaxation for ¹⁵N T₂. Table 2 shows the average T₂ relaxation times of the TROSY peak for the backbone ¹⁵N spin in the uniformly ¹⁵N/¹³C-labeled protein EIN, and the corresponding T₂ (¹⁵N) for the ¹⁵N/¹³C/²H labeled sample (Kontaxis et al. 2000).

According to Table 2, it can be seen that the transverse relaxation time of the ¹⁵N spin shortens with respect to increasing magnetic field strength due to increasing cross-correlation between CSA and DD in the usual ¹⁵N-HSQC experiment, where slow and fast relaxing spin-states are interchanged by a 180°(1H) pulse applied during t₁. Consequently, the ¹⁵N line width increases with increasing magnetic field strength. On the other hand, line width of the TROSY component becomes narrower as a function of polarizing magnetic field strength. Interestingly, the transverse relaxation of ¹⁵N is largely affected by remote ¹H spins in the regular HSQC experiment, resulting in a broader line for the ¹⁵N spin than for that in the corresponding refocused INEPT experiment. In contrast, the transverse relaxation of the ¹⁵N spin in perdeuterated proteins does not receive any major contribution from the ¹H spin flips, yielding comparable line widths between the regular HSQC and the refocused INEPT experiments. It can also be seen that the ¹⁵N transverse relaxation time in perdeuterated proteins can be almost twice as long as that in protonated samples due to cancellation of remote, aliphatic proton interaction with the ¹⁵N nucleus. The so-called TROSY implementation (Pervushin et al. 1997; Andersson et al. 1998; Meissner et al. 1998; Salzmann et al. 1998; Yang & Kay 1999; Rance et al. 1999), together with deuterium labeling and utilization of directional information available through dipolar couplings, will increase the size limit of proteins applicable for structure determination much further than was predicted earlier.