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

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.

As a result of this rapid hydrogen exchange, signals from NH 3 + groups in 1 H- 15 N heteronuclear single-quantum coherence (HSQC) and heteronuclear multiple-quantum coherence (HMQC) spectra are severely broadened [26]. Importantly, this broadening occurs not only in the 1 H dimension but also in the 15 N dimension, because rapid hydrogen exchange greatly enhances scalar relaxation of 15  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 15 N evolution period, and in-phase single-quantum coherence N + (= N x + iN y ) is maintained via the 1 H WALTZ decoupling scheme throughout the evolution period. Evolutions to the anti-phase terms such as 2N + H z , 4N + H z H z , and 8N + H z H z H z are suppressed to remove the impact of scalar relaxation on line shape of 15 N resonances. Scalar relaxation arises from auto-relaxation of the coupled 1 H nuclei [29,30], and substantially increases the relaxation rates of the 2N + H z , 4N + H z H z , and 8N + H z H z H z terms, compared to the relaxation rates of N + . The scalar relaxation rate R sc for each 1 H nucleus is given by [26]: where ρ HH is the rate for dipole-dipole relaxation with external 1 H nuclei and k water ex is the rate for hydrogen exchange with water. Scalar relaxation rates for the N + , 2N + H z , 4N + H z H z , and 8N + H z H z H 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 15 N relaxation rates for NH 3 + groups [14][15][16]26]. Therefore, rapid hydrogen exchange governs relaxation of the anti-phase terms through the scalar relaxation mechanism and severely broadens 15 N line shapes of NH 3 + signals in typical 2D 1 H-15 N correlation spectra. By maintaining in-phase single-quantum terms N x and N y , and thereby removing the scalar relaxation from the t 1 time domain for the 15 N dimension, the HISQC experiment drastically improved observation of 1 H-15 N cross peaks from NH 3 + groups in sensitivity and resolution [26]. Since then, many NMR pulse sequences for NH 3 + groups have implemented the principle of HISQC, and minimized the adverse impacts of scalar relaxation of anti-phase terms with respect to 1 H nuclei [14][15][16][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 NH 3 + groups of proteins. While some side-chain NH 3 + groups exhibit relatively slow hydrogen-exchange rates due to hydrogen bonds or ion pairs [26,33], many other NH 3 + groups exhibit very rapid hydrogen-exchange rates that severely broaden 1 H resonances. Due to this problem, NMR experiments on protein side-chain NH 3 + 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, D 2 O) from a sample solution are typically used to avoid isotopically different species (i.e., NDH 2 + , and ND 2 H + , and ND 3 + ) of NH 3 + 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 NH 3 + groups, especially for quantitative experiments such as 15 N relaxation measurements.

Previous and Current Approaches to Eliminating the Adverse Effects of Multi-Spin Order Terms
The first step for measuring 15 N longitudinal (R1) and transverse (R2) relaxation rates is to create the 15 N in-phase single-quantum term via coherence transfer from 1 H to 15 N nuclei through a refocused INEPT scheme [39]. With regard to NH3 + groups, the product operator terms Nx, 2NyHz, 4NxHzHz, and 8NyHzHzHz are generated in the period of 2τb in the first refocused INEPT scheme of our pulse sequence for 15 N R1 and R2 measurements (Figure 1a,b). Because the only term of interest among them is Nx, any effects of the other three terms should be eliminated in these relaxation measurements. The 2NyHz and 8NyHzHzHz terms are eliminated by the pulsed field gradient (PFG) g4 after the 1 H 90°(−x) and 15 N 90°(y) pulses at the end of the refocused INEPT scheme. These 90° pulses 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 1 H was set to the position of the water resonance. The 15 N carrier position was set to 33.1 ppm. A gray bell-shape for 15 N represents an r-SNOB [36] 180 • pulse (1.0 ms) selective to Lys side-chain 15 N ζ nuclei. The delays τ a and τ b were 2.7 ms and 1.3 ms, respectively. Quadrature detection in the t 1 domain was achieved using States-TPPI, incrementing the phase ϕ 1 . Pulsed field gradients (PFGs) were optimized to minimize the water signal. (a) 15 N R 1 measurement. Although it is not essential owing to negligible CSA-DD cross correlation for NH 3 + , a 1 H 180 • pulse, which does not affect H 2 O resonance, was applied every 10 ms during the delay T r for longitudinal relaxation. Phase cycles: ϕ 1 = (2y, 2(−y)), ϕ 2 = (y, −y), ϕ 3 = (4x, 4(−x)), ϕ 4 = (8y, 8(−y)), and receiver = ( 15 N R 2,ini measurement. The RF strength for 15 N pulses for the CPMG scheme was 5.4 kHz. The 1 H carrier position was shifted to 7.8 ppm right after the PFG g 4 and set back to the position of water resonance right after the PFG g 5 . The RF strength ω CW /2π of 1 H 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 ξ 1 and ξ 2 are for alignment of 1 H magnetization and given by ξ 1 = 1/ω CW − (4/π)τ 90H and ξ 2 = τ 90N − (2/π)τ 90H [37,38], in which τ 90 represents a length of a relevant 90 • pulse. Phase cycles: ϕ 1 = (4y, 4(−y)), ϕ 2 = (8y, 8(−y)), ϕ 3 = x, ϕ 4 = (x, −x), ϕ 5 = (2y, 2(−y)), ϕ 6 = (2x, 2(−x)), ϕ 7 = (2(−y), 2y), and receiver = ( Efficiency in coherence transfers as a function of the delay τ b calculated using Equations (2) and (3)

Previous and Current Approaches to Eliminating the Adverse Effects of Multi-Spin Order Terms
The first step for measuring 15 N longitudinal (R 1 ) and transverse (R 2 ) relaxation rates is to create the 15 N in-phase single-quantum term via coherence transfer from 1 H to 15 N nuclei through a refocused INEPT scheme [39]. With regard to NH 3 + groups, the product operator terms N x , 2N y H z , 4N x H z H z , and 8N y H z H z H z are generated in the period of 2τ b in the first refocused INEPT scheme of our pulse sequence for 15 N R 1 and R 2 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.  [40]. To avoid any adverse impact of the 4N x H z H z term generated in the refocused INEPT scheme, the previous pulse sequences used a value of the time τ b that erases the 4N x H z H 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]: where θ = 2πJ NH τ b and 1 J NH represents the one-bond 1 H-15 N scalar coupling constant. The use of the time τ b satisfying 3 cos 2 θ − 1 = 0 thus eliminates the 4N x H z H z term, but retains the N x term [15]. This approach was used for 13 C R 1 and R 2 relaxation measurements for protein CH 3 groups as well [41,42]. Because 1 J NH is typically~74 Hz for lysine side-chain NH 3 + groups [26], the condition to suppress the 4N x H z H 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 x H z H z to 2N y H z does not contribute to the observed signals. A practical problem in using the condition of f CT 2N y H z → 4N x H z H z = 0 is that it also reduces f CT 2N y H z → N x from its maximum level, and thereby weakens signals in the 15 N relaxation measurements for NH 3 + groups (Figure 1d).
In the current work, we eliminate the adverse effects of the 4N x H z H z term in a different manner, and maximize f CT 2N y H z → N x to increase sensitivity in 15 N relaxation measurements for NH 3 + 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 x H z H z term generated through the refocused INEPT scheme, our pulse sequences shown in Figure 1 prevent the undesired 4N x H z H z term from becoming observable in the 1 H detection period t 1 . This allows us to use τ b = 1.3 ms and improve sensitivity without compromising accuracy in 15 N relaxation measurements.

Assessment of the Sensitivity-Improved 15 N R 1 Experiment for NH 3 + Groups
Our pulse sequence for the 15 N R 1 relaxation measurements on NH 3 + 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. were~20-100-fold faster than the relaxation rates of the N z term for the Lys side-chain NH 3 + groups of ubiquitin [15]. The relaxation of the 4N z H y H y term should be even faster because of its transverse nature. Therefore, if the minimum duration of period T r in the 15 N R 1 relaxation experiment is sufficiently long to let the 4N z H y H y term completely decay, the relaxation rates of the N z term (i.e., 15 Figure 2). For these NH 3 + groups, we measured 15 N R 1 relaxation rates with the previous and current pulse sequences using the same number of scans and data points. In these 15 N R 1 measurements, we recorded 2D 1 H-15 N 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 z H y H y term completely decay through its rapid relaxation. As predicted in Figure 1d, the signals from NH 3 + 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 NH 3 + 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 y H z → N x 2 at τ b = 1.3 ms and 2.1 ms. The 15 N relaxation rates R 1 were determined through nonlinear least-squares fitting with a single exponential function. 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 1 H-15 N cross peaks in the NH3 + -selective 1 H-15 N HISQC spectra ( Figure 2). For these NH3 + groups, we measured 15 N R1 relaxation rates with the previous and current pulse sequences using the same number of scans and data points. In these 15 N R1 measurements, we recorded 2D 1 H-15 N spectra using Tr = 100, 200, 400, 600, 900, 1200, 1600, and 2100 ms in an interleaved manner. The minimum duration, Tr = 100 ms, is expected to be long enough to let the 4NzHyHy term completely decay through its rapid relaxation. As predicted in Figure 1d, the signals from NH3 + groups in the spectra recorded with τb = 1.3 ms showed significantly stronger intensities than in those recorded with τb = 2.1 ms. Figure 3a shows the signal intensity of the K46 NH3 + group as a function of Tr. The sensitivity was found to improve by a factor of 1.82 on average, which was consistent with the ratio of | 2 → | at τb = 1.3 ms and 2.1 ms. The 15 N relaxation rates R1 were determined through nonlinear least-squares fitting with a single exponential function. Table 1 shows the 15 N R1 relaxation rates measured with the previous and current pulse sequences for the Lys NH3 + groups in the Antp homeodomain-DNA complex. The 15 N R1 rates from the two experiments were virtually the same, within experimental uncertainties. Not surprisingly, improvement in sensitivity led to higher precision in measured 15 N R1 relaxation rates.    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]. Figure 2. The 1 H-15 N HISQC spectrum recorded at 15 °C for the NH3 + groups in the complex of 15 N-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].  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 NH 3 + signals along the 1 H dimension from the two-dimensional spectra with and without 1 H 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.

Assessment of the Sensitivity-Improved 15 N R 2 Experiment for NH 3 + Groups
Our new pulse sequence for 15 N R 2 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 1 H 90 • (−x) and hard 1 H 90 • (x) pulses is implemented before the PFG g 5 . This additional component is important for canceling the effects of the 4N y H z H z term generated through the refocused INEPT scheme. The pulse sequence uses the CW-CPMG scheme together with H 2 O alignment pulse trains [37]. During the 15 N CPMG spin-echo periods for 15  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 15 N 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 15 N R 2 experiment was the same as that in the 15 N R 1 experiment (i.e., 82% increase on average). This improvement in sensitivity led to significantly higher precision in measured 15 N R 2,ini rates. Figure 1c shows the pulse sequence for heteronuclear NOE measurements for NH 3 + groups that implements the abovementioned approach. As described by Esadze et al. [15], steady states of the N z and 4N z H z H z terms are created through saturation of 1 H nuclear magnetization via a train of 180 • pulses for heteronuclear NOE measurements on NH 3 + groups. The 4N z H z H z steady state occurs due to DD-DD cross-correlation that drives transitions between the N z and 4N z H z H z terms [15]. In the original pulse sequence, τ b = 2.1 ms was used to avoid any contribution of the 4N z H z H z term to the observed signals. However, in the current pulse sequence (Figure 3c) 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.

Discussion
As demonstrated above, our new pulse sequences improve sensitivity in 15 N relaxation measurements on protein side-chain NH 3 + groups without compromising accuracy in measuring intrinsic 15 N 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 R 1 and R 2 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 15  Note that signal to noise ratios are proportional to √ 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 15 N R 1 and R 2 measurements and doubled for the heteronuclear NOE measurement. Because rapid hydrogen exchange of NH 3 + groups weakens their 1 H 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.

Materials and Methods
The complex of the 15 N-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 NH 3 + groups (i.e., NDH 2 + , ND 2 H + , and ND 3 + ), D 2 O 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 an Avance III spectrometer (Bruker BioSpin, Fällanden, Switzerland) operated at the 1 H frequency of 750 MHz. A TCI cryogenic probe was used for NMR detection. The 1 H and 15 N 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. The pulse programs and parameter sets for Bruker NMR spectrometers are available upon request via https://scsb.utmb.edu/labgroups/iwahara/software.