Observing In-phase Single-Quantum ¹⁵N Multiplets for NH₂/NH₃⁺ Groups with Two-dimensional Heteronuclear Correlation Spectroscopy

Abstract

Two-dimensional (2D) F1-¹H-coupled HSQC experiments provide 3:1:1:3 and 1:0:1 multiplets for AX₃ and AX₂ spin systems, respectively. These multiplets occur because, in addition to the 2S⁺H_z^a → 2S⁺H_z^a process, the coherence transfers such as 2S⁺H_z^a → 2S⁺H_z^b occurring in t₁ period provide detectable magnetization during the t₂ period. Here we present a 2D F1-¹H-coupled ¹H-¹⁵N heteronuclear correlation experiment that provides a 1:3:3:1 quartet for AX₃ spin system and a 1:2:1 triplet for AX₂. The experiment is a derivative of 2D HISQC experiment (Iwahara et al. [2007] J. Am. Chem. Soc. 129, 2971–2980) and contains a scheme that kills anti-phase single-quantum terms generated in the t₁ period. The purge scheme is essential to observe in-phase single-quantum multiplets. Applications to the NH₂ and NH₃⁺ groups in proteins are demonstrated.

For heteronuclear AX₃ and AX₂ spin systems, one-dimensional NMR measurement on nucleus A that comprises a single excitation pulse immediately followed by detection without decoupling generally gives an in-phase 1:3:3:1 quartet and a 1:2:1 triplet, respectively, provided that relaxation rates for individual multiplet components are identical. It is because overall modulations of detected magnetizations due to J and chemical shift evolutions are

$$\begin{array}{c}\text{exp}(i\mathrm{\Omega }t){\text{cos}}^3\pi Jt\hfill \\ =\frac{1}{8}\text{exp}\{i(\mathrm{\Omega }-3\pi J)t\}+\frac{3}{8}\text{exp}\{i(\mathrm{\Omega }-\pi J)t\}+\frac{3}{8}\text{exp}\{i(\mathrm{\Omega }+\pi J)t\}+\frac{1}{8}\text{exp}\{i(\mathrm{\Omega }+3\pi J)t\}\hfill \end{array}$$ (1)

for an AX₃ spin system, and

$$\begin{array}{c}\text{exp}(i\mathrm{\Omega }t){\text{cos}}^2\pi Jt\hfill \\ =\frac{1}{4}\text{exp}\{i(\mathrm{\Omega }-2\pi J)t\}+\frac{1}{2}\text{exp}(i\mathrm{\Omega }t)+\frac{1}{4}\text{exp}\{i(\mathrm{\Omega }+2\pi J)t\}\hfill \end{array}$$ (2)

for AX₂. For simplicity sake, we use terms such as ‘1:3:3:1’ and ‘1:2:1’ hereafter, although actual intensity ratios of multiplet components can deviate due to cross-correlations [1].

In the case of a two-dimensional heteronuclear correlation experiment, it is not trivial to obtain the in-phase 1:3:3:1 quartet and 1:2:1 triplet. In an F1-¹H coupled HSQC experiment (such as one shown in Figure 1A), heteronuclear AX₃ and AX₂ spin systems exhibit 3:1:1:3 quartet and 1:0:1 triplet, respectively [2–4], because not only the $2S_y{H}_z^a\to 2S_y{H}_z^a$ process but also the coherence transfers such as $2S_y{H}_z^a\to 2S_y{H}_z^b$ occurring during the t₁-evolution period generate magnetizations detectable in the t₂-period. With the additional contributions, the real part of the overall modulation due to J and chemical shift evolutions in the t₁-period for AX₃ is given by:

$$\begin{array}{c}({\text{cos}}^3\pi J{t}_1-2{\text{sin}}^2\pi J{t}_1\text{cos}\pi J{t}_1)\text{cos}\mathrm{\Omega }{\text{t}}_1\hfill \\ =\frac{3}{8}\text{cos}(\mathrm{\Omega }-3\pi J)t_1+\frac{1}{8}\text{cos}(\mathrm{\Omega }-\pi J)t_1+\frac{1}{8}\text{cos}(\mathrm{\Omega }+\pi J)t_1+\frac{3}{8}\text{cos}(\mathrm{\Omega }+3\pi J)t_1,\hfill \end{array}$$ (3)

resulting a 3:1:1:3 quartet. Likewise, the corresponding modulation for AX₂ is:

$$\begin{array}{c}({\text{cos}}^2\pi J{t}_1-\text{sin}\pi J{t}_1\text{cos}\pi J{t}_1)\text{cos}\mathrm{\Omega }{t}_1\hfill \\ =\frac{1}{2}\text{cos}(\mathrm{\Omega }-2\pi J)t_1+\frac{1}{2}\text{cos}(\mathrm{\Omega }+2\pi J)t_1{}^{,}\hfill \end{array}$$ (4)

which gives a 1:0:1 triplet. Since it appears to be a doublet, the multiplet itself does not indicate whether the spin system is of AX₂ or AX unless the true J-coupling is known.

Figure 1.

Two-dimensional ¹H-¹⁵N correlation experiments to observe in-phase ¹⁵N multiplets. (A) F1-¹H-coupled ¹H-¹⁵N HSQC (B) F1-¹H-coupled ¹H-¹⁵N HISQC (C) F1-¹H-coupled HISQC without the AP purge scheme. Thin and thick bars represent 90° and 180° pulses, respectively. Unless indicated otherwise, pulse phases are along x. Water-selective half-Gaussian (2.0 ms) and soft-rectangular (1.2 ms) 90° pulses are represented by half-bell and short-bold shapes, respectively. A gray bell-shape represents a ¹⁵N 180° pulse (rectangular or shaped; See legends for Figure 2–4). The ¹H carrier position was set at the water resonance. The delay τ_a, for which the optimal value is considerably shorter than (4¹J_NH)⁻¹ because of fast ¹H relaxation caused by rapid water exchange for NH₃⁺/NH₂ groups, was set to 2.0–2.7 ms. The other delays: τ_b = 1.3 ms; τ_d = τ_a −1.2 ms. Phase cycles: ψ₁ = {x, −x}, ψ₂ = {2x, 2(−x)}, and rec. = {x, 2(−x), x} for A; ϕ₁ = {y, −y},ϕ₂ = {2y, 2(−y)}, ϕ₃ = {4y, 4(−y)}, ϕ₄ = {4x, 4(−x)}, and rec. = {x, 2(−x), x, −x, 2x, −x} for B and C. Quadrature detection in the t₁-domain was achieved using States-TPPI, incrementing the phase ψ₁ for A and ϕ₂ for B and C. Field-gradients were optimized to minimize the water signal. For higher sensitivity, water-flip-back principle [13] is implemented in each experiment. The pulse sequence in panel C, which does not include the AP purge scheme, is just for comparison purpose and of no practical use (see Figure 2C, Figure 3C and Figure 4C).

In the present study, we have developed a new 2D ¹H-¹⁵N correlation experiment to observe an in-phase 1:3:3:1 quartet for a NH₃⁺ group and a 1:2:1 triplet for a NH₂ group along F1 axis. Figure 1B shows the 2D ¹H-¹⁵N F1-coupled ¹H-¹⁵N heteronuclear correlation experiment to observe 1:3:3:1 and 1:2:1 multiplets for NH₃ ⁺ and NH₂, respectively. The experiment was derived from the water-flip-back 2D ¹H-¹⁵N HISQC (heteronuclear in-phase single quantum coherence; Figure 1C) experiment for NH₃⁺ groups [2], and therefore we refer to it as F1-¹H-coupled HISQC. This pulse sequence starts with the ¹H excitation, and the coherence transfer form H_y to N_x occurs before the t₁ period. The length of delay τ_b (= 1.3 ms) is a compromise to simultaneously observe NH₃⁺, NH₂, and NH, and overall J-modulations for these groups through four τ_b periods are given by 3cos⁴ 2πJτ_b sin² 2πJτ_b (=0.49 with J = 74 Hz), 2cos² 2πJτ_b sin² 2πJτ_b (=0.74 with J = 89 Hz), and sin² 2πJτ_b (=0.55 with J = 93 Hz), respectively. Due to these attenuations along with relaxation loss during the additional schemes, the sensitivity of the F1-¹H-coupled HISQC experiment is roughly a half of that of the F1-¹H-coupled HSQC. A similar experiment that starts with the ¹⁵N excitation instead of the ¹H excitation could be more sensitive if the magnetization loss during the coherence transfer from H_y to N_x in the scheme of Figure 1B is over 90% (≈1-γ_N/γ_H), which is not the case in the present study; however, such an experiment that starts on ¹³C with NOE enhancement via ¹H saturation should be with acceptable sensitivity for ¹H-¹³C systems [5]. At the beginning of the t₁ period, the observed magnetization is an in-phase single-quantum term N_y or N_x, depending on the phase ϕ₂. Since there is no ¹H- decoupling during the t₁ period, anti-phase single-quantum terms such as 2N⁺H_z, 4N⁺H_zH_z, and 8N⁺H_zH_zH_z are generated. The scheme right after the t₁-period (hereafter, referred to as the AP purge scheme; indicated with an arrow in Figure 1B) kills the 2N⁺H_z and 8N⁺H_zH_zH_z terms, so only N⁺ and 4N⁺H_zH_z terms can survive. The reason for the survival of 4N⁺H_zH_z is that 4N_zH_xH_x generated by ¹H 90° pulses in the AP purge scheme cannot be killed with the pulse field gradient because it is a homonuclear zero-quantum term [6–8]. However, the following scheme for coherence transfers does not allow such zero-quantum terms to become observable magnetizations in the t₂ acquisition period. Therefore, only the in-phase single quantum term N⁺ at the end of the t₁ period is detectable. Since the real part of the overall modulation for the N⁺ term in t₁ is given by cosⁿπJt₁cosΩt₁ (n, number of hydrogens), the spectra obtained with this pulse sequence should show 1:3:3:1, 1:2:1, and 1:1 multiplets for NH³⁺, NH₂, and NH, respectively.

Using the pulse sequences shown in Figure 1, we recorded 2D ¹H-¹⁵N heteronuclear correlation spectra on NH₃⁺/NH₂ groups in proteins (Figure 2 and Figure 3). Data were collected with Varian 800-MHz or 750-MHz NMR systems. Figure 2 displays spectra recorded on the Lys57 NH₃⁺ group of the HoxD9 homeodomain bound to 24-bp DNA complex. Owing to formation of an ion-pair with a DNA phosphate group, this NH₃⁺ group exhibits relatively slow hydrogen-exchange with water molecules and the ¹H-¹⁵N cross peak from this group can clearly be observed [2]. Just as expected from considerations above, F1-¹H-coupled HSQC (Figure 2A) and F1-¹H-coupled HISQC (Figure 2B) exhibits in-phase quartets of 3:1:1:3 and 1:3:3:1 types, respectively. Actual intensity ratios deviate from these numbers because the relaxation rates for inner and outer components of the quartet are different due to cross-correlations [2,5,9].

Figure 2.

¹⁵N multiplets observed for the Lys57 NH₃⁺ group of ²H/¹⁵N-labeled homeodomain bound to 24-bp DNA (Solid contours, positive; Dashed, negative). Spectra in panels A, B and C were recorded at 16 °C with the pulse sequences shown in Figures 1A, 1B, and 1C, respectively. The ¹⁵N carrier position was at 30 ppm and r-SNOB pulses[14] selective to lysine ¹⁵Nζ nuclei were employed for ¹⁵N 180° pulses. Acquisition times for ¹H and ¹⁵N dimensions were 54 ms and 79 ms, respectively. For data processing, 60°-shifted sine-bell window functions were applied prior to Fourier transformations. The protein-DNA complex was prepared as described previously [15–18] and dissolved with a buffer of 20 mM sodium phosphate and 20 mM NaCl (pH 5.8, 100% ¹H₂O). The solution was sealed into the inner compartment of the co-axial NMR tube, and D₂O for NMR lock was put in the outer compartment to avoid NH₂D and NHD₂ species[2]. Data were collected at ¹H-frequency of 800 MHz and analyzed with the NMRPipe[19] and NMRView[20] programs. The J-coupling was measured to be 74 Hz.

Figure 3.

¹⁵N multiplets observed for NH₂ groups. (A, B, C) Spectra recorded on Gln20 NH₂ group in ¹⁵N-labeled HMGB1 A-domain. Data were collected at 25 °C with a 750-MHz spectrometer. Acquisition times for ¹H and ¹⁵N dimensions were 60 ms and 66 ms, respectively. The protein was prepared according to previous literature [10,21] and dissolved with a buffer of 50 mM Tris•HCl and 100 mM KCl (pH 7.4, 100% ¹H₂O). The protein solution was sealed into the inner compartment of the co-axial tube, and D₂O for NMR lock was put in the outer compartment to avoid NHD species. (D, E, F) Spectra recorded on the Gln12 NH₂ group of ²H/¹⁵N-labeled HoxD9 homeodomain bound to 24-bp DNA. The sample is identical to that used for Figure 2. Spectra were recorded at 16 °C with a 800-MHz spectrometer. Acquisition times for ¹H and ¹⁵N dimensions were 54 ms and 72 ms, respectively. All ¹⁵N 90° and 180° pulses were rectangular with the rf strength of 6 kHz and the carrier position at 116 ppm. For data processing, 60°-shifted sine-bell window functions were applied prior to Fourier transformations.

Figure 3 shows spectra recorded on side-chain NH₂ groups of glutamine (Gln) residues in proteins. Panels A, B, and C display spectra recorded on Gln20 in the ¹⁵N-labeled HMGB1 A-domain. The rotational correlation time τ_r for this protein at 25 °C is 9 ns [10]. The NH₂ group exhibited 1:0:1 triplets in the F1-¹H-coupled HSQC spectrum (Figure 3A) and 1:2:1 triplets in the F1-¹H-coupled HISQC spectrum (Figure 3B). The J-coupling was measured to be 89 Hz. For a system with a long τ_r, the relaxation rates of individual triplet components for a AX₂ spin system can be quite different because of cross-correlations between distinct relaxation mechanisms [11]. Such a case is clearly seen in the spectra measured on the Gln12 NH₂ groups in the ²H/¹⁵N-lableled HoxD9 homeodomain bound to 24-bp DNA at 16 °C (Figure 3D, 3E, and 3F). The value of τ_r is 15 ns for this system. In this case, the downfield components are substantially shaper than the other components in triplets.

Although one may think that removal of ¹H-decoupling from the original HISQC experiment [2] would simply result in 1:3:3:1 and 1:2:1 multiplets, such a pulse sequence (Figure 1C) does not give the desired multiplets. This occurs because the anti-phase single-quantum terms generated in the t₁-period also become ¹H magnetizations detectable in the t₂ acquisition period. In fact, the spectra measured with the simplistic pulse sequence on the same NH₃⁺ and NH₂ groups (Figure 2C, Figure 3C, and 3F) are very different from those measured with the AP purge scheme (Figure 2B, Figure 3B, and 3E). Intensity ratios are far from 1:3:3:1 for NH₃⁺ and 1:2:1 for NH₂; indeed, the multiplets in Figures 3C and 3F are more similar to 1:0:1 triplets. In addition, some contributions from the anti-phase terms occur with 90°-shifted phases that cause dispersive distortion of the multiplets, which is evident especially in Figure 2C. Thus, the AP purge scheme is essential to obtain 1:3:3:1 and 1:2:1 multiplets.

In conclusion, we have demonstrated the 2D F1-¹H-coupled ¹H-¹⁵N correlation experiment that permits observation of in-phase 1:3:3:1 quartets for NH₃⁺ groups and 1:2:1 triplets for NH₂ groups along the F1 axis. This experiment provides a means to distinguish AX, AX₂, and AX₃ spin systems in a straightforward manner. It is particularly useful when ¹H chemical shifts are degenerated. For example, the deprotonated state of an alkyl amino group (NH₂) shows a single ¹H resonance because of rapid chiral inversion [12]. In such a case, it is hard to distinguish AX and AX₂ spin systems with F1-¹H-coupled HSQC unless J-coupling is already known, because a 1:0:1 triplet appears to be a doublet. A 1:2:1 triplet is easier to interpret. It should be noted that a rapid hydrogen exchange with a rate greater than 2πJ can cause the self-decoupling effect that results in a ¹⁵N singlet even in absence of ¹H-decoupling. Considering the range of ¹J_NH coupling constants, however, it is likely that such a rapid hydrogen exchange simply broadens the signal beyond the detection limit in the present case, because the hydrogen exchange also increases ¹H transverse relaxation rates. Finally, it should be pointed out that the principle presented here can readily be applied to ¹H-¹³C systems.