A Unique and Simple Approach to Improve Sensitivity in ¹⁵N-NMR Relaxation Measurements for NH₃⁺ Groups: Application to a Protein-DNA Complex

Abstract

NMR spectroscopy is a powerful tool for research on protein dynamics. In the past decade, there has been significant progress in the development of NMR methods for studying charged side chains. In particular, NMR methods for lysine side-chain NH₃⁺ groups have been proven to be powerful for investigating the dynamics of hydrogen bonds or ion pairs that play important roles in biological processes. However, relatively low sensitivity has been a major practical issue in NMR experiments on NH₃⁺ groups. In this paper, we present a unique and simple approach to improve sensitivity in ¹⁵N relaxation measurements for NH₃⁺ groups. In this approach, the efficiency of coherence transfers for the desired components are maximized, whereas undesired anti-phase or multi-spin order components are purged through pulse schemes and rapid relaxation. For lysine side-chain NH₃⁺ groups of a protein-DNA complex, we compared the data obtained with the previous and new pulse sequences under the same conditions and confirmed that the ¹⁵N relaxation parameters were consistent for these datasets. While retaining accuracy in measuring ¹⁵N relaxation, our new pulse sequences for NH₃⁺ groups allowed an 82% increase in detection sensitivity of ¹⁵N longitudinal and transverse relaxation measurements.

1. Introduction

NMR spectroscopy is one of the most powerful techniques for studying protein dynamics. NMR studies have revealed the functional importance of structural dynamics in many biological molecular processes of proteins (e.g., reviewed in Refs [1–8]). While the vast majority of NMR investigations of protein dynamics have probed motions of either backbone NH or side-chain CH₃ groups, NMR investigations on polar or charged side chains remain rare. Recently, there has been significant progress in NMR methods for investigating the dynamics of charged side chains of proteins [9–17]. In particular, NMR methods for Lys side-chain NH₃⁺ groups have proven to be extremely useful for investigating the dynamics of hydrogen bonding and/or ion pairing [14–25].

Lys side-chain NH₃⁺ groups of proteins undergo rapid hydrogen exchange with water [26–28]. As a result of this rapid hydrogen exchange, signals from NH₃⁺ groups in ¹H-¹⁵N heteronuclear single-quantum coherence (HSQC) and heteronuclear multiple-quantum coherence (HMQC) spectra are severely broadened [26]. Importantly, this broadening occurs not only in the ¹H dimension but also in the ¹⁵N dimension, because rapid hydrogen exchange greatly enhances scalar relaxation of ¹⁵N transverse coherence anti-phase with respect to ¹H (e.g., 2N_xH_z, 4N_yH_zH_z, and 8N_xH_zH_zH_z).

To avoid this problem, Iwahara et al. developed NH₃⁺-selective heteronuclear in-phase single-quantum coherence (HISQC) and its derivatives [26]. In the HISQC experiment, the in-phase single quantum term N_x or N_y is created at the beginning of the ¹⁵N evolution period, and in-phase single-quantum coherence N₊ (= N_x + iN_y) is maintained via the ¹H WALTZ decoupling scheme throughout the evolution period. Evolutions to the anti-phase terms such as 2N₊H_z, 4N₊H_zH_z, and 8N₊H_zH_zH_z are suppressed to remove the impact of scalar relaxation on line shape of ¹⁵N resonances. Scalar relaxation arises from auto-relaxation of the coupled ¹H nuclei [29,30], and substantially increases the relaxation rates of the 2N₊H_z, 4N₊H_zH_z, and 8N₊H_zH_zH_z terms, compared to the relaxation rates of N₊. The scalar relaxation rate R_sc for each ¹H nucleus is given by [26]:

$$R_{sc}={\rho }_{HH}+k_{ex}^{\mathit{water}}$$ (1)

where ρ_HH is the rate for dipole-dipole relaxation with external ¹H nuclei and $k_{ex}^{\mathit{water}}$ is the rate for hydrogen exchange with water. Scalar relaxation rates for the N₊, 2N₊H_z, 4N₊H_zH_z, and 8N₊H_zH_zH_z terms are 0, R_sc, 2R_sc, and 3R_sc, respectively [31]. Typically, hydrogen exchange is much faster than ρ_HH rates and intrinsic ¹⁵N relaxation rates for NH₃⁺ groups [14–16,26]. Therefore, rapid hydrogen exchange governs relaxation of the anti-phase terms through the scalar relaxation mechanism and severely broadens ¹⁵N line shapes of NH₃⁺ signals in typical 2D ¹H-¹⁵N correlation spectra. By maintaining in-phase single-quantum terms N_x and N_y, and thereby removing the scalar relaxation from the t₁ time domain for the ¹⁵N dimension, the HISQC experiment drastically improved observation of ¹H-¹⁵N cross peaks from NH₃⁺ groups in sensitivity and resolution [26]. Since then, many NMR pulse sequences for NH₃⁺ groups have implemented the principle of HISQC, and minimized the adverse impacts of scalar relaxation of anti-phase terms with respect to ¹H nuclei [14–17,26,32].

Nevertheless, relatively low sensitivity due to rapid hydrogen exchange has been a major practical problem in NMR experiments for Lys side-chain NH₃⁺ groups of proteins. While some side-chain NH₃⁺ groups exhibit relatively slow hydrogen-exchange rates due to hydrogen bonds or ion pairs [26,33], many other NH₃⁺ groups exhibit very rapid hydrogen-exchange rates that severely broaden ¹H resonances. Due to this problem, NMR experiments on protein side-chain NH₃⁺ groups are often conducted at relatively low pH (typically pH 4.5–6.0) and low temperature (typically, 2–25 °C) to observe a larger number of signals with stronger intensity [32,34]. In these NMR experiments, co-axial NMR tubes that separate lock solvent (usually, D₂O) from a sample solution are typically used to avoid isotopically different species (i.e., NDH₂⁺, and ND₂H⁺, and ND₃⁺) of NH₃⁺ groups. The use of co-axial tubes further decreases sensitivity due to a smaller sample volume and multilayer glass walls. Thus, sensitivity improvement would be desirable for NMR experiments on NH₃⁺ groups, especially for quantitative experiments such as ¹⁵N relaxation measurements.

To address these practical needs, we present a unique and simple approach to improve sensitivity in ¹⁵N relaxation measurements on protein side-chain NH₃⁺ groups. Our approach involves only minor modifications of the existing pulse sequences. Nevertheless, the pulse sequences implementing this approach significantly improve the detection sensitivity, while maintaining the accuracy in the ¹⁵N relaxation measurements on NH₃⁺ groups.

2. Results

Figure 1 shows the optimized NMR pulse sequences for measuring ¹⁵N R₁ and R₂ relaxation and heteronuclear NOE of NH₃⁺ groups. In the description below, using the product operator formalism [35] for AX₃ spin systems, we first explain the previous approach that resolves problems arising from undesired anti-phase or multi-spin-order components of ¹⁵N magnetizations of NH₃⁺ groups in ¹⁵N relaxation measurements. Then, we describe our new approach to improving sensitivity and eliminating undesired components in ¹⁵N relaxation measurements, showing data that demonstrate the effectiveness of this approach.

Figure 1.

Pulse sequences for the ¹⁵N relaxation measurement on lysine side-chain NH₃⁺ groups. The key elements in the current work are indicated in red. Thin and bold bars in black represent hard rectangular 90° and 180° pulses, respectively. Water-selective half-Gaussian (2.1 ms) and soft-rectangular (1.2 ms) 90° pulses are represented by half-bell and short-bold shapes, respectively. Unless indicated otherwise, pulse phases are along x, and the carrier position for ¹H was set to the position of the water resonance. The ¹⁵N carrier position was set to 33.1 ppm. A gray bell-shape for ¹⁵N represents an r-SNOB[36] 180° pulse (1.0 ms) selective to Lys side-chain ¹⁵N_ζ nuclei. The delays τ_a and τ_b were 2.7 ms and 1.3 ms, respectively. Quadrature detection in the t₁ domain was achieved using States-TPPI, incrementing the phase φ₁. Pulsed field gradients (PFGs) were optimized to minimize the water signal. (a) ¹⁵N R₁ measurement. Although it is not essential owing to negligible CSA-DD cross correlation for NH₃⁺, a ¹H 180° pulse, which does not affect H₂O resonance, was applied every 10 ms during the delay T_r for longitudinal relaxation. Phase cycles: φ₁ = (2y, 2(−y)), φ₂ = (y, −y), φ₃ = (4x, 4(−x)), φ₄ = (8y, 8(−y)), and receiver = (x, −x, −x, x, 2(−x, x, x, −x), x, −x, −x, x); (b) ¹⁵N R_2,ini measurement. The RF strength for ¹⁵N pulses for the CPMG scheme was 5.4 kHz. The ¹H carrier position was shifted to 7.8 ppm right after the PFG g₄ and set back to the position of water resonance right after the PFG g₅. The RF strength ω_CW/2π of ¹H CW during the CPMG was set to 4.3 kHz, which was adjusted to satisfy ω_CW/2π = 2kν_CPMG (k, integer) [37]. The delays ξ₁ and ξ₂ are for alignment of ¹H magnetization and given by ξ₁ = 1/ω_CW − (4/π)τ_90H and ξ₂ = τ_90N − (2/π)τ_90H [37,38], in which τ₉₀ represents a length of a relevant 90° pulse. Phase cycles: φ₁ = (4y, 4(−y)), φ₂ = (8y, 8(−y)), φ₃ = x, φ₄ = (x, −x), φ₅ = (2y, 2(−y)), φ₆ = (2x, 2(−x)), φ₇ = (2(−y), 2y), and receiver = (x, −x, x, −x, 2(−x, x, −x, x), x, −x, x, −x); (c) Heteronuclear ¹H-¹⁵N NOE measurement. Measurement with ¹H saturation (5 s) was performed with a train of 180°x and 180°(−x) pulses (RF strength, 11 kHz) at an interval of 10 ms. The ¹H carrier position was at 7.8 ppm during the ¹H saturation period. The reference spectrum was measured without the scheme in the bracket. The recycle delay (including the saturation period) was set to 18 s for a 750-MHz spectrometer. Phase cycles: φ₁ = (y, −y), φ₂ = (4x, 4y, 4(−x), 4(−y)), φ₃ = (2x, 2(−x)), and receiver = (x, −x, −x, x, −x, x, x, −x); (d) Efficiency in coherence transfers as a function of the delay τ_b calculated using Equations (2) and (3) with |¹J_NH| = 74 Hz and ¹H 180° pulse length of 20 μs. The results for the N_y and 4N_yH_zH_z terms are shown in solid and dotted lines, respectively. Red and green arrows indicate the values of the delay τ_b in the current and previous pulse sequences, respectively.

2.1. Previous and Current Approaches to Eliminating the Adverse Effects of Multi-Spin Order Terms

The first step for measuring ¹⁵N longitudinal (R₁) and transverse (R₂) relaxation rates is to create the ¹⁵N in-phase single-quantum term via coherence transfer from ¹H to ¹⁵N nuclei through a refocused INEPT scheme [39]. With regard to NH₃⁺ groups, the product operator terms N_x, 2N_yH_z, 4N_xH_zH_z, and 8N_yH_zH_zH_z are generated in the period of 2τ_b in the first refocused INEPT scheme of our pulse sequence for ¹⁵N R₁ and R₂ measurements (Figure 1a,b). Because the only term of interest among them is N_x, any effects of the other three terms should be eliminated in these relaxation measurements. The 2N_yH_z and 8N_yH_zH_zH_z terms are eliminated by the pulsed field gradient (PFG) g₄ after the ¹H 90°(−x) and ¹⁵N 90°(y) pulses at the end of the refocused INEPT scheme. These 90° pulses convert the N_x and 4N_xH_zH_z terms into N_z and 4N_zH_yH_y, both of which survive the PFG g₄. The 4N_zH_yH_y term survives because a PFG alone cannot destroy homonuclear zero-quantum coherence [40]. To avoid any adverse impact of the 4N_xH_zH_z term generated in the refocused INEPT scheme, the previous pulse sequences used a value of the time τ_b that erases the 4N_xH_zH_z term, but retains the N_x term. This is possible because coherence transfer to these terms depends differently on the time τ_b. The coefficients of these transfers are given by [39]:

$$f_{CT}(2N_y{H}_z\to N_x)={\text{cos}}^2\theta \text{sin}\theta$$ (2)

$$f_{CT}(2N_y{H}_z\to 4N_x{H}_z{H}_z)=(3{\text{cos}}^2\theta -1)\text{sin}\theta$$ (3)

where θ = 2πJ_NHτ_b and ¹J_NH represents the one-bond ¹H-¹⁵N scalar coupling constant. The use of the time τ_b satisfying 3cos²θ − 1 = 0 thus eliminates the 4N_xH_zH_z term, but retains the N_x term [15]. This approach was used for ¹³C R₁ and R₂ relaxation measurements for protein CH₃ groups as well [41,42]. Because ¹J_NH is typically ~74 Hz for lysine side-chain NH₃⁺ groups [26], the condition to suppress the 4N_xH_zH_z term was achieved using τ_b = 2.1 ms in the original pulse sequences [15]. This condition was also used in the second refocused INEPT scheme for backward coherence transfer, so that any coherence transfer from 4N_xH_zH_z to 2N_yH_z does not contribute to the observed signals. A practical problem in using the condition of f_CT(2N_yH_z → 4N_xH_zH_z) = 0 is that it also reduces f_CT(2N_yH_z → N_x) from its maximum level, and thereby weakens signals in the ¹⁵N relaxation measurements for NH₃⁺ groups (Figure 1d).

In the current work, we eliminate the adverse effects of the 4N_xH_zH_z term in a different manner, and maximize f_CT(2N_yH_z → N_x) to increase sensitivity in ¹⁵N relaxation measurements for NH₃⁺ groups. As shown in Figure 1d, the signal arising from the N_x term should be strongest when τ_b = 1.3 ms. Although this condition increases the 4N_xH_zH_z term generated through the refocused INEPT scheme, our pulse sequences shown in Figure 1 prevent the undesired 4N_xH_zH_z term from becoming observable in the ¹H detection period t₁. This allows us to use τ_b = 1.3 ms and improve sensitivity without compromising accuracy in ¹⁵N relaxation measurements.

2.2. Assessment of the Sensitivity-Improved ¹⁵N R₁ Experiment for NH₃⁺ Groups

Our pulse sequence for the ¹⁵N R₁ relaxation measurements on NH₃⁺ groups is shown in Figure 1a. This pulse sequence is the same as that in Esadze et al. [15], except that the time τ_b is set to 1.3 ms instead of 2.1 ms. The ¹H 90°(−x) and ¹⁵N 90°(y) at the end of the first refocused INEPT convert the N_x and 4N_xH_zH_z terms into the N_z and 4N_zH_yH_y terms. As mentioned above, both of these terms survive the PFG g₄, and are subjected to the period T_r for relaxation measurement. For measuring ¹⁵N R₁ relaxation rates, however, only the N_z term should be retained, and any contribution of the 4N_zH_yH_y term should be removed. During the period T_r, not only longitudinal relaxation, but also cross-correlation of three ¹H-¹⁵N dipole-dipole (DD) relaxation mechanisms occur for the N_z term. The DD-DD cross-correlation causes partial transitions from N_z to 4N_zH_zH_z [43]. The composite of water-selective ¹H 90°(−x) and hard ¹H 90°(x) pulses was originally introduced to prevent this term from becoming detectable while maintaining water ¹H magnetization along +z [15]. However, if a considerable amount of the 4N_zH_yH_y term is present at the beginning of the period T_r, the composite pulses at the end can partially convert this term into 4N_zH_zH_z, which can survive the rest of the pulse sequence and become observable through the second refocused INEPT with τ_b = 1.3 ms. This problem in the ¹⁵N R₁ measurement can readily be resolved by taking advantage of rapid relaxation of the 4N_zH_yH_y term. Due to rapid hydrogen exchange with water, scalar relaxation of anti-phase and multi-spin order terms of ¹⁵NH₃⁺ are far faster than the intrinsic ¹⁵N R₁ and R₂ relaxation of NH₃⁺ groups [15,26]. Even under the conditions of pH 5.0 and 2 °C, where hydrogen exchange is relatively slow, the relaxation rates of the 4N_zH_zH_z term were ~20–100-fold faster than the relaxation rates of the N_z term for the Lys side-chain NH₃⁺ groups of ubiquitin [15]. The relaxation of the 4N_zH_yH_y term should be even faster because of its transverse nature. Therefore, if the minimum duration of period T_r in the ¹⁵N R₁ relaxation experiment is sufficiently long to let the 4N_zH_yH_y term completely decay, the relaxation rates of the N_z term (i.e., ¹⁵N R₁) can be measured without any adverse contribution from the 4N_zH_yH_y term.

We applied this approach to the Lys side-chain NH₃⁺ groups of the Antp homeodomain-DNA complex at pH 5.8 and 15 °C. The interfacial Lys side chains K46, K55, K57, and K58 of this protein-DNA complex exhibit well-resolved ¹H-¹⁵N cross peaks in the NH₃⁺-selective ¹H-¹⁵N HISQC spectra (Figure 2). For these NH₃⁺ groups, we measured ¹⁵N R₁ relaxation rates with the previous and current pulse sequences using the same number of scans and data points. In these ¹⁵N R₁ measurements, we recorded 2D ¹H-¹⁵N spectra using T_r = 100, 200, 400, 600, 900, 1200, 1600, and 2100 ms in an interleaved manner. The minimum duration, T_r = 100 ms, is expected to be long enough to let the 4N_zH_yH_y term completely decay through its rapid relaxation. As predicted in Figure 1d, the signals from NH₃⁺ groups in the spectra recorded with τ_b = 1.3 ms showed significantly stronger intensities than in those recorded with τ_b = 2.1 ms. Figure 3a shows the signal intensity of the K46 NH₃⁺ group as a function of T_r. The sensitivity was found to improve by a factor of 1.82 on average, which was consistent with the ratio of |f_CT(2N_yH_z → N_x)|² at τ_b = 1.3 ms and 2.1 ms. The ¹⁵N relaxation rates R₁ were determined through nonlinear least-squares fitting with a single exponential function. Table 1 shows the ¹⁵N R₁ relaxation rates measured with the previous and current pulse sequences for the Lys NH₃⁺ groups in the Antp homeodomain-DNA complex. The ¹⁵N R₁ rates from the two experiments were virtually the same, within experimental uncertainties. Not surprisingly, improvement in sensitivity led to higher precision in measured ¹⁵N R₁ relaxation rates.

Figure 2.

The ¹H-¹⁵N HISQC spectrum recorded at 15 °C for the NH₃⁺ groups in the complex of ¹⁵N-labeled Antp homeodomain and unlabeled 15-bp DNA containing a phosphorodithioate at the K46 interaction site. The resonance assignment is based on that for the unmodified DNA complex and unique chemical shift perturbation upon site-specific dithioation (i.e., sulfur substitutions of two non-bridging oxygen atoms) of the DNA phosphate at the K46 interaction site [44].

Figure 3.

Comparison of the previous [15] and current pulse sequences for measuring ¹⁵N relaxation of NH₃⁺ groups. (a,b) ¹⁵N longitudinal (Panel a) and transverse (Panel b) relaxation of the K46 NH₃⁺ group. The vertical axis represents the signal intensity in the two-dimensional spectra measured as a function of the relaxation period T_r. Solid lines represent the best-fit curves obtained through nonlinear least-squares fitting with a mono-exponential function; (c) Slices of the K46 NH₃⁺ signals along the ¹H dimension from the two-dimensional spectra with and without ¹H saturation for the heteronuclear NOE measurements. In each panel, data obtained with the previous and current pulse sequences are shown in blue and red, respectively.

Table 1.

Comparison of ¹⁵N relaxation parameters measured with the previous and current pulse sequences ^a). Shown below are data for the Lys side-chain NH₃⁺ groups in the complex of ¹⁵N-labeled Antp homeodomain and unlabeled 15-bp DNA containing a phosphorodithioate at the K46 interaction site.

	K46	K55	K57	K58
15N R1 (s−1) b)	1.093 ± 0.013	0.637 ± 0.005	1.035 ± 0.004	0.363 ± 0.002
15N R1 (s−1) c)	1.081 ± 0.023	0.617 ± 0.008	1.037 ± 0.008	0.364 ± 0.003
15N R2,ini (s−1) b)	2.55 ± 0.10	1.76 ± 0.07	2.95 ± 0.04	1.20 ± 0.03
15N R2,ini (s−1) c)	2.74 ± 0.20	2.05 ± 0.12	2.76 ± 0.06	1.14 ± 0.06
Heteronuclear NOE b)	−2.44 ± 0.12	−2.83 ± 0.10	−2.54 ± 0.05	−2.71 ± 0.05
Heteronuclear NOE c)	−2.53 ± 0.18	−2.75 ± 0.13	−2.60 ± 0.08	−2.65 ± 0.07

^a)The experiments were conducted at 15 °C and the ¹H frequency of 750 MHz. Uncertainties were estimated using the Monte Carlo approach based on the noise standard deviation of the spectra.

^b)Measured with the current pulse sequences shown in Figure 1.

^c)Measured with the previous pulse sequences [15].

2.3. Assessment of the Sensitivity-Improved ¹⁵N R₂ Experiment for NH₃⁺ Groups

Our new pulse sequence for ¹⁵N R₂ measurements is shown in Figure 1b. This pulse sequence differs from our previous one in two ways. First, τ_b = 1.3 ms is used instead of τ_b = 2.1 ms. Second, a composite of water-selective ¹H 90°(−x) and hard ¹H 90°(x) pulses is implemented before the PFG g₅. This additional component is important for canceling the effects of the 4N_yH_zH_z term generated through the refocused INEPT scheme. The pulse sequence uses the CW-CPMG scheme together with H₂O alignment pulse trains [37]. During the ¹⁵N CPMG spin-echo periods for ¹⁵N transverse relaxation measurements, a ¹H continuous wave (CW) is applied at the ¹H resonances of NH₃⁺ groups to maintain the in-phase single-quantum term N_x and prevent the anti-phase terms from being produced. Through the ¹H pulse scheme developed by Hansen et al. [37], water ¹H magnetization is aligned to the axis of ¹H CW in the rotating frame to avoid saturation through ¹H RF inhomogeneity and then is brought back to +z. Because this scheme does not align the 4N_zH_yH_y term, the terms arising from it are largely purged due to the RF inhomogeneity of the ¹H CW. However, their component parallel to the CW axis can remain and become the 4N_zH_zH_z term through the back-alignment scheme after the period T_r. Unlike the period T_r in the ¹⁵N R₁ relaxation measurement, the period T_r in the ¹⁵N R₂ relaxation measurement should be relatively brief, because only a limited number of hard ¹⁵N 180° pulses can practically be used during the ¹⁵N CPMG scheme. Therefore, this remaining undesired term cannot be purged completely through relaxation. However, the composite of the water-selective ¹H 90°(−x) and hard ¹H 90°(x) pulses purges this 4N_zH_zH_z in the same manner as the 4N_zH_zH_z term arising from DD-DD cross-correlation during the period T_r is canceled in the ¹⁵N R₁ measurement.

For the Lys side-chain NH₃⁺ groups of the Antp homeodomain in complex with 15-bp DNA, we compared the ¹⁵N R₂ relaxation data obtained with the old and new pulse sequences under the same conditions. We recorded nine ¹H-¹⁵N spectra in an interleaved manner using T_r = 4.8, 14.4, 33.6, 48.0, 76.8, 91.2, and 105.6 ms. Strictly speaking, ¹⁵N transverse relaxation of NH₃⁺ groups should occur bi-exponentially due to DD-DD cross-correlation [15,41], but the first 30% decay from the maximum can be treated as a mono-exponential decay, as demonstrated by Esadze et al. [15]. Using mono-exponential fitting, the initial rate constants (R_2,ini) for this ¹⁵N transverse relaxation were determined from the signal intensity as a function of T_r. The results from the data obtained with the previous and current pulse sequences are shown in Figure 3b and Table 1. The R_2,ini rates from these two datasets are in good agreement. Due to the use of τ_b = 1.3 ms, the signal intensities in the spectra recorded with the current pulse sequence were significantly higher than those in the spectra recorded with the previous pulse sequence. As expected, the gain in intensity in the ¹⁵N R₂ experiment was the same as that in the ¹⁵N R₁ experiment (i.e., 82% increase on average). This improvement in sensitivity led to significantly higher precision in measured ¹⁵N R_2,ini rates.

2.4. Assessment of the Sensitivity-Improved Heteronuclear NOE Experiment for NH₃⁺ Groups

Figure 1c shows the pulse sequence for heteronuclear NOE measurements for NH₃⁺ groups that implements the abovementioned approach. As described by Esadze et al. [15], steady states of the N_z and 4N_zH_zH_z terms are created through saturation of ¹H nuclear magnetization via a train of 180° pulses for heteronuclear NOE measurements on NH₃⁺ groups. The 4N_zH_zH_z steady state occurs due to DD-DD cross-correlation that drives transitions between the N_z and 4N_zH_zH_z terms [15]. In the original pulse sequence, τ_b = 2.1 ms was used to avoid any contribution of the 4N_zH_zH_z term to the observed signals. However, in the current pulse sequence (Figure 3c), the composite of the water-selective ¹H 90°(−x) and hard ¹H 90°(x) pulses convert the 4N_zH_zH_z term into 4N_zH_yH_y immediately before the ¹⁵N 90° pulse leading to the evolution period t₁. As described for the ¹⁵N R₁ and R₂ experiment, the rest of the pulse sequence does not allow the 4N_zH_yH_y term to become observable in the ¹H detection period t₂. Therefore, the use of τ_b = 1.3 ms improves sensitivity without compromising the quality of heteronuclear NOE data, though the gain in sensitivity is relatively small because there is only a single refocused INEPT scheme in this pulse sequence.

We compared the heteronuclear NOE data obtained with the previous and current pulse sequences for the Lys NH₃⁺ groups of the Antp homeodomain-DNA complex. Figure 3c shows ¹H slices of the 2D ¹H-¹⁵N spectra recorded with and without ¹H saturation in the heteronuclear NOE experiments. The heteronuclear NOE values from the datasets obtained with the previous and current pulse sequences agreed well, as shown in Table 1. As expected, the spectra recorded with the new pulse sequence exhibited an increase in the intensity of each signal compared with those recorded with the previous pulse sequence under the same conditions. The improvement in the sensitivity was by a factor of 1.35 on average for the heteronuclear NOE measurements.

3. Discussion

As demonstrated above, our new pulse sequences improve sensitivity in ¹⁵N relaxation measurements on protein side-chain NH₃⁺ groups without compromising accuracy in measuring intrinsic ¹⁵N relaxation parameters. By eliminating contributions from the undesired terms and maintaining the maximum level of coherence transfers of the desired terms, this method increased sensitivity by a factor of 1.82 for the R₁ and R₂ experiments and by a factor of 1.35 for the heteronuclear NOE experiment. Although our current paper shows data for a protein-DNA complex only, a similar degree of improvement is expected for other systems of different sizes because Equations (2) and (3) are independent of the molecular rotational correlation time. The sensitivity gains for the ¹⁵N R₁ and R₂ experiments are larger because these experiments include two refocused INEPT schemes, whereas the heteronuclear NOE experiment has one. In fact, the relative magnitudes of the sensitivity gains (i.e., 1.82 ≈ 1.35²) support this explanation. With the current approach, the time for recording the same quality of data can be significantly reduced compared with the previous ¹⁵N relaxation experiments for NH₃⁺ groups. The total measurement times for ¹⁵N R₁ relaxation, R₂ relaxation, and heteronuclear NOE experiments on a 0.8 mM protein-DNA complex (17 kDa) were 18, 20, and 26 h, respectively. Note that signal to noise ratios are proportional to $\sqrt{N_s}$, where N_s is the number of accumulated scans per free induction decay (FID). To get the same data quality using the previous pulse sequences by increasing the number of scans, the total measurement times would approximately be tripled for ¹⁵N R₁ and R₂ measurements and doubled for the heteronuclear NOE measurement. Because rapid hydrogen exchange of NH₃⁺ groups weakens their ¹H signals, the improvement in sensitivity in these relaxation experiments is practically helpful. We hope that this approach will facilitate NMR studies of dynamic processes involving hydrogen bonds and ion pairs and help advance our understanding of protein dynamics and its functional roles.

4. Materials and Methods

The complex of the ¹⁵N-labeled Antp homeodomain and unlabeled 15-bp DNA was prepared as described in our previous papers [21,25,44]. The DNA phosphate group at the K46 interaction site was dithioated in the chemical synthesis, as previously described [14,25]. A 370-μL solution of 0.8 mM complex in a buffer of 20 mM sodium phosphate (pH 5.8) and 20 mM NaCl was sealed in a 5-mm outer tube of a co-axial NMR tube system. To avoid the deuterated species of NH₃⁺ groups (i.e., NDH₂⁺, ND₂H⁺, and ND₃⁺), D₂O for the NMR lock signal was sealed separately in an inter insert of the co-axial tube. The NMR experiments were performed at 15 °C with a Bruker Avance III spectrometer operated at the ¹H frequency of 750 MHz. A TCI cryogenic probe was used for NMR detection. The ¹H and ¹⁵N acquisition times were 54 ms and 222 ms, respectively. In each experiment, 16 scans were accumulated per FID, and sub-spectra were recorded in an interleaved manner. The NMR data were processed and analyzed using the NMR-Pipe [45] and NMR-View [46] programs. Other experimental details are given in figure captions.