Introduction

Among a variety of multi-dimensional NMR experiments for studies of proteins, two-dimensional (2D) heteronuclear single-quantum correlation (HSQC) experiments (Bodenhausen and Ruben 1980; Bax et al. 1990) are commonly used on 13C- and 15N-enriched proteins. A 2D 15N−1H HSQC experiment is expected to provide one backbone amide resonance for each amino acid residue (except for proline) of the protein, where the signals in the spectrum are usually well-dispersed and well-resolved for small folded proteins. It is also possible to separate between backbone 15NH and side-chain 15NH2 signals of proteins (Kay and Bax 1989; Schmidt and Rueterjans 1990; Tate et al. 1991). The experiment is often performed in protein interaction studies as chemical shift changes in the protein can be readily observed (Zuiderweg 2002; Williamson 2013). In contrast, a 2D 13C−1H HSQC experiment detects all backbone and side-chain 13C−1H moieties, and the spectrum is usually less resolved in comparison with 2D 15N−1H HSQC. High resolution in the 13C dimension is therefore required to alleviate resonance overlap in the crowded spectrum, and for effective decoupling of homonuclear one-bond 13C−13C couplings that limit spectral resolution, a constant-time (CT) chemical shift evolution scheme (Santoro and King 1992, van de Ven and Philippens 1992, Vuister and Bax 1992) is extensively used. However, resonance overlap in the 2D CT 13C−1H HSQC spectrum that complicates spectral interpretation is still significant even for proteins as small as ubiquitin (76 amino acid residues) used in this study.

Several types of multiplicity-based editing of NMR signals have been proposed for spectral simplification. The one-bond 13C−1H couplings (1JCH) have been used to separate 13CH2 signals from 13CH and 13CH3 signals (Bendall et al. 1981). The 13C DEPT is routinely used in the field of organic chemistry for differentiation between 13CH, 13CH2, and 13CH3 groups (Doddrell et al. 1982). These techniques have been then applied to multi-dimensional experiments (Kessler et al. 1989; Davis 1990, 1991; Nagana Gowda 2002; Chen et al. 2015; Sakhaii and Bermel 2015). Moreover, selective observation of aliphatic 13C (13Cali) carbons adjacent to a carbonyl/carboxyl (13CO) and an aromatic (13Caro) carbon in 13C-enriched proteins can be achieved by spectral editing with the one-bond couplings between the 13Cali and 13CO carbons (1JCCO) and between the 13Cali and 13Caro carbons (1JCCaro), respectively (Grzesiek and Bax 1993). Furthermore, several sophisticated multiplicity-dependent coherence transfer schemes in triple (1H/13C/15N) resonance experiments are proposed for selecting amino acid types based on the particular chemical shifts and spin coupling topologies of the side-chains (Tashiro et al. 1995; Feng et al. 1996; Rios et al. 1996; Schubert et al. 1999, 2001a, b, 2005; Van Melckebeke et al. 2004; Lescop et al. 2008; Pantoja-Uceda and Santoro 2008; Feuerstein et al. 2012; Brenner and Frøystein 2014; Dubey et al. 2016).

While selection of desired coherence pathways can be useful for unambiguous resonance assignments in protein NMR spectroscopy, it often requires additional coherence transfer steps that cause a significant reduction in sensitivity, and besides, different spectra need to be obtained as such tailored experiments select only desired coherences for specific amino acid residues. On the other hand, experiments with sign encoding provides signals for all amino acid residues simultaneously, thereby increasing the sensitivity of the method. Brutscher and coworkers have proposed the use of a Hadamard-based sign encoding scheme to discriminate among amino acid types in a 2D 15N−1H correlation experiment (Lescop et al. 2008; Feuerstein et al. 2012) and in 2D and 3D methyl NOESY experiments (Van Melckebeke et al. 2004).

Separation of NMR signals based on multiplicity can be achieved by means of collecting sub-spectra; The experiment is recorded twice, once where a particular J-coupling evolution is active such that the signal is inverted, and once where it is not. Summation of the two sub-spectra will lead to cancellation of the particular signal, whereas subtraction will restore its full intrinsic intensity. Importantly, full signal intensity for all signals is registered every time, and the unscrambling for a given peak is obtained from a straight-forward linear combination (vide infra). For example, a 13CHn multiplicity-based experiment (n = 1, 2, and 3) can be recorded with or without 1JCH evolution active during the editing period of 1/1JCH. This will result in two spectra where the phases of the 13CH and 13CH3 signals are opposite for the two repetitions of the experiment, whereas the sign for the 13CH2 signals is unchanged. The addition and subtraction of the two sub-spectra then yields two complementary spectra with only 13CH2 or 13CH/13CH3 concurrently (Chen et al. 2015). In 2D CT 13C−1H HSQC experiments on 13C-enriched proteins, signals of 13Cali attached to 13CO and 13Caro carbon can be separated in a similar manner utilizing 1JCCO and 1JCCaro couplings (Grzesiek and Bax 1993). The editing period with the 1JCCO (or 1JCCaro) coupling renders opposite the signals for 13CO-coupled (or 13Caro-coupled) 13Cali carbons in the two sub-spectra, and the difference spectrum separates their signals from the others.

This study aims at separating NMR signals of 13C-enriched proteins in a 2D CT 13C−1H HSQC experiment by means of combinatorial sign-encoding of the following three couplings: 1JCH, 1JCCO, and 1JCCaro. Eight sub-spectra are collected with the binary editing (i.e. J-active or J-inactive) schemes for each of the three couplings. A linear combination of sums and differences of these eight sub-spectra using a Hadamard matrix generates a series of multiplicity-separated NMR spectra. Because all three editing periods, 1/1JCH, 1/1JCCO, and 1/1JCCaro, are incorporated into the CT 13Cali chemical shift evolution period without any additional delays, no additional relaxation loss is produced in comparison with the corresponding unedited 2D CT 13C−1H HSQC experiment. The strategy proposed in this article, hereinafter referred to as OROCHI (Orthogonal Registration Of Constant-time HSQC Intensities), allows selective observation of the following classes of complementary NMR signals:

  1. I.

    Aliphatic 13CH2 resonances whose 13C carbon is not coupled to a carbonyl, carboxyl, or aromatic 13C carbon

  2. II.

    Aliphatic 13CH/13CH3 resonances whose 13C carbon is not coupled to a carbonyl, carboxyl, or aromatic 13C carbon

  3. III.

    13Cβ−1Hβ correlations of asparagine and aspartic acid (Asx), 13Cγ−1Hγ correlations of glutamine and glutamic acid (Glx), and 13Cα−1Hα correlations of glycine

  4. IV.

    13Cα−1Hα correlations of all residues except for glycine

  5. V.

    13Cβ−1Hβ correlations of phenylalanine, tyrosine, histidine, and tryptophan (F/Y/H/W)

Materials and methods

NMR experiments were performed on uniformly 13C-labelled human ubiquitin. Ubiquitin (5 mg as lyophilized powder) was purchased from Taiyo Nippon Sanso (Tokyo, Japan) and was dissolved at a protein concentration of 1 mM into D2O (0.55 mL) containing 50 μM sodium 2,2-dimethylsilapentane-5-sulfonate (DSS) as chemical shift reference (Markley et al. 1998). Unless otherwise indicated, NMR data were acquired at 298 K with a Bruker spectrometer at the magnetic field of 11.7 T (i.e. 1H frequency of 500 MHz) equipped with a cryogenic BBO probe, and were processed with the Bruker Topspin 3.6.2 and NMRPipe (Delaglio et al. 1995). Spectral assignment of ubiquitin was taken from BMRB entries 5387 and 17769 (http://www.bmrb.wisc.edu/).

In the 2D CT 13C−1H HSQC experiments, the homonuclear one-bond 13C−13C couplings between 13Cali carbons (herein written 1JCC) are active during the entire CT period 2TC (between points b and c in Fig. 1a, b) whereas the 13Cali chemical shift evolves for t1/2 + TC−(TC−t1/2) = t1. The first INEPT step converts the initial magnetization to the longitudinal two-spin order term 2HzCz (point a in Fig. 1a,b) (Morris and Freeman 1979), and at time point b, the 13Cali anti-phase 2HzCy (or −2HzCy, depending on the phase of ϕ1) magnetization is generated. The evolution of the 13Cali magnetization during 2TC due to the 1JCC couplings (~ 35 Hz) for weakly coupled spin systems yields 2HzCycosm(2π1JCCTC), where m is the number of neighboring 13Cali carbons and anti-phase terms with respect to the adjacent 13Cali spins are ignored. When 2TC = 1/1JCC (~ 28 ms), the factor cosm(2π1JCCTC) can be simplified as (− 1)m, that is, opposite signs of 13Cali magnetization between an even and an odd number of neighboring 13Cali carbons are obtained (Santoro and King 1992; Vuister and Bax 1992). However, in common implementations of the CT 13C−1H HSQC experiment signals from 13Caro-coupled 13CH2 and from 13CO-coupled 13CH/13CH2 are strongly attenuated when a broadband pulse is used for inversion of longitudinal magnetization of the coupled 13C nuclei, as can be seen in Fig. 1c. This is so because the 1JCCO (~ 50–55 Hz) and 1JCCaro (~ 45–50 Hz) coupling values, listed in Supplementary Tables S1 and S2, are larger than 1JCC (Bystrov 1976). Given that the 13Cali magnetization evolution takes place under the 1JCCO or 1JCCaro coupling of 1.5 × 1JCC (~ 53 Hz) during the CT period 2TC = 1/1JCC, the transfer amplitude of the spin operator, cos(2π1JCCOTC) or cos(2π1JCCaroTC), will be close to zero. On the other hand, selective inversion of 13Cali, 13Caro, and 13CO carbon nuclei with band-selective pulses (see Supplementary Fig. S1) enables refocusing of evolution due to 1JCCO and 1JCCaro couplings, as shown in Fig. 1d, which ensures stronger full sensitivity for the signals of 13CO- and 13Caro-coupled 13CH2 and backbone 13Cα−1Hα correlations. A few example traces from Fig. 1c,d are given in Fig. 1e to demonstrate the extent of sensitivity improvement. Furthermore, spectral editing with 1JCCO and 1JCCaro couplings can be achieved with the band-selective pulses, as will be discussed in the following.

Fig. 1
figure 1

Broadband and band-selective 2D CT 13C−1H HSQC experiments. a Pulse sequence of the 2D CT 13C−1H HSQC with an adiabatic pulse. A 2-ms composite smoothed Chirp (Crp60comp.4) (Hwang et al. 1997) centered at 100 ppm was used for refocusing of 13Cali transverse magnetization and for broadband inversion of longitudinal magnetization of the neighboring 13C nuclei. b Pulse sequence of the 2D CT 13C−1H HSQC with band-selective 13C pulses. For 13C band-selective irradiations on the 13Cali, 13CO, and 13Caro regions with a flip angle of 180°, Q3 pulses (Emsley and Bodenhausen 1992) with durations of 375, 1020, and 510 μs, respectively, were used at the magnetic field of 11.7 T (i.e. 1H frequency of 500 MHz). In the pulse sequences (panels a and b), the narrow and wide filled bars correspond to hard pulses with flip angles of 90° and 180°, respectively. All pulses were applied with phase x unless otherwise indicated. The hatched bar represents a trim pulse along the x-axis for a duration of 1 ms to suppress unwanted magnetization (Otting and Wüthrich 1988). Composite pulses on 13C were used for the INEPT and reverse-INEPT steps (Levitt and Freeman 1979). For 13C,15N-labelled samples, a simultaneous inversion of the 15N magnetization for lysine 15Nζ and arginine 15Nε together with backbone 15N nuclei can be effectively achieved by a composite pulse, 90°(x)-240°(y)-90°(x) (Freeman et al. 1980), with the 15N frequency placed at 84 ppm. The pulsed field gradients along the z-axis, g0, g1, and g2, were 1 ms in length. The spectrum was collected with the following phase cycle: ϕ1 = (x, − x), ϕ2 = (x, x, − x, − x), ϕ3 = (x, x, x, x, − x, − x, − x, − x), and ϕrec = (x, − x, − x, x). The delays were: τ = 1.7 ms, TC = 14 or 28 ms, The GARP decoupling scheme (Shaka et al. 1985) was applied with a radiofrequency field of 3.6 kHz during acquisition (t2). Quadrature detection in the t1 dimension was achieved with States-TPPI (Marion et al. 1989), where the phase ϕ1 was increased by 90°. c 2D CT 13C − 1H HSQC spectrum of 13C-enriched ubiquitin collected using the pulse sequence shown in panel a. d 2D CT 13C−1H HSQC spectrum of 13C-enriched ubiquitin collected using the pulse sequence shown in panel b. e 1D slices of the 2D CT 13C−1H HSQC spectra of panels c (black) and d (blue). The side-chain 1JCCaro coupling of H68 and 1JCCO coupling of N25 are 54.7 and 49.3 Hz, respectively, and the backbone 1JCCO couplings of I23 and I61 are 54.2 Hz (Supplementary Tables S1 and S2)

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In the OROCHI experiment, a set of the 2D CT 13C−1H HSQC sub-spectra with multiplicity editing were recorded in an interleaved manner using the pulse sequence shown in Fig. 2. For each sub-spectrum, the number of scans was one per indirect (t1) increment. The corresponding 2D CT 13C−1H HSQC spectrum without multiplicity editing was collected with the pulse sequence shown in Fig. 1b. The 1H carrier frequency was placed at the water resonance (4.8 ppm), and the 13C pulses for 13Cali, 13CO, and 13Caro were centered at 42, 181, and 125 ppm, respectively. Spectral widths were 13 ppm (6.5 kHz) and 80 ppm (10 kHz) for 1H and 13C, respectively. When the CT period, 2TC, is set at 28 ms, the spectrum was collected with a matrix size of 512 (1H) × 240 (13C) complex points. When 2TC = 56 ms, the spectrum was collected with a matrix size of 512 (1H) × 512 (13C) complex points. For sign-encoding of NMR signals based on 13CHn multiplicity, where n is the number of protons attached to the 13Cali carbon, a set of 1JCH-inactive and 1JCH-active sub-spectra were recorded. In Fig. 2, the 1H 180° pulse applied during the CT period is indicated in blue and red for the 1JCH-inactive and 1JCH-active experiment, respectively. As the net 1JCH evolution time in the 1JCH-inactive experiment is t1/2−TC + (TC−t1/2) = 0, the phase of the magnetization is unaffected by the 1JCH coupling. In contrast, the net 1JCH evolution time in the 1JCH-active experiment is (t1/2 + ΔCH)−(TC−ΔCH) + (TC−t1/2) = 2ΔCH, yielding the magnetization 2HzCycosn(2π1JCHΔCH). When 2ΔCH = 1/1JCH, cosn(2π1JCHΔCH) is equal to (− 1)n, generating opposite signs for 13CH2 (n = 2) with respect to 13CH/13CH3 (n = 1 and 3) signals. Likewise, 13CO- and 13Caro-attached 13Cali carbons were selected utilizing the 1JCCO and 1JCCaro couplings, respectively. In the 1JCCO-active (or 1JCCaro-active) experiment, where the net 1JCCO (or 1JCCaro) evolution time 2ΔCCO = 1/1JCCO (or 2ΔCCaro = 1/1JCCaro), the phase of these signals are inverted in comparison with the corresponding 1JCCO-inactive (or 1JCCaro-inactive) experiment, whereas other 13Cali signals are identical. Hadamard matrices were utilized for separation of sign-encoded NMR signals with k binary parameters (Kupče et al. 2003; Brutscher 2004). Linear combinations of sums and differences of N sub-spectra (from s1 to sN), where N = 2k, generate a series of multiplicity-separated NMR spectra (from S1 to SN):

$$\left[ {\begin{array}{*{20}c} {S_{1} } \\ \vdots \\ {S_{N} } \\ \end{array} } \right] = H_{N} \left[ {\begin{array}{*{20}c} {s_{1} } \\ \vdots \\ {s_{N} } \\ \end{array} } \right]$$
(1a)
Fig. 2
figure 2

Pulse sequence of the OROCHI experiment for recording eight binary combinations of 2D CT 13C−1H HSQC sub-spectra. For each of the 1JCH, 1JCCO, and 1JCCaro couplings, the pulses shown in blue were applied for the J-inactive experiments, whereas the pulses in red were for the J-active experiments. Unless otherwise indicated, the phases of ϕC and ϕrec are x when both 1JCCO and 1JCCaro are either active or inactive and −x when only one of either 1JCCO or 1JCCaro is active (see Table 1). The delays were: τ = 1.7 ms, TC = 14 or 28 ms, ΔCH = 3.8 ms, ΔCCaro = 11 ms, and ΔCCO = 10 ms. Quadrature detection in the t1 dimension was achieved with States-TPPI (Marion et al. 1989), where the phase ϕC was increased by 90°. All other parameters are the same as in Fig. 1. The pulse sequence code for Bruker spectrometers is provided in the Supplementary Material. In the pulse sequence, the use of solvent presaturation during the recycle delay is optional

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where HN, a Hadamard matrix of order N, is given by the following recursive definition with H1 = 1:

$$H_{{2^{k} }} = \left[ {\begin{array}{*{20}c} {H_{{2^{k - 1} }} } & {H_{{2^{k - 1} }} } \\ {H_{{2^{k - 1} }} } & { - H_{{2^{k - 1} }} } \\ \end{array} } \right]$$
(1b)

where k is a positive integer. NMRPipe scripts are provided in the Supplementary Material for generating separate time-domain FID data according to Hadamard transform of the interleaved raw FID before processing so that mirror-image linear prediction (LP) in the 13C dimension can be separately applied to the spectra. This is advantageous as these are more sparse and the reduced number of signals improves the robustness of root finding by the LP algorithm. These separate FIDs are apodized with a squared cosine function before zero filling and Fourier transform in both 1H and 13C dimensions.

Results and discussion

Figure 3 shows separation of NMR signals of ubiquitin by means of individual sign-encoding with 1JCH, 1JCCO, and 1JCCaro couplings. The J-coupling evolution is inactive in one of the two sub-spectra (Fig. 3a) and is active in the other (Fig. 3b−d). The resulting sum (Ssum) and difference (Sdif) spectra were obtained by the following equation:

$$\left[ {\begin{array}{*{20}c} {S_{{{\text{sum}}}} } \\ {S_{{{\text{dif}}}} } \\ \end{array} } \right] = H_{2} \left[ {\begin{array}{*{20}c} {s_{{{\text{inactive}}}} } \\ {s_{{{\text{active}}}} } \\ \end{array} } \right]$$
(2a)
Fig. 3
figure 3

a−d 2D CT 13C−1H HSQC sub-spectra of 13C-enriched ubiquitin collected using the pulse sequence shown in Fig. 2, where the phases of ϕC and ϕrec were kept x. The CT period (2Tc) was set at 28 ms. The positive and negative peaks are shown in black and red, respectively. a Unedited (i.e. 1JCH-inactive, 1JCCO-inactive, and 1JCCaro-inactive) sub-spectrum. b 1JCH-active sub-spectrum. The 1JCCO- and 1JCCaro-editings were inactive. c 1JCCO-active sub-spectrum. The 1JCH- and 1JCCaro-editings were inactive. d 1JCCaro-active sub-spectrum. The 1JCH- and 1JCCO-editings were inactive. e−j Linear combination of the sum (e−g) and difference (h−j) of the 2D CT 13C−1H HSQC sub-spectra. In panels e and h, undesired artifacts due to 1JCH mismatch are indicated in blue dotted circles. In panel f, 1JCCO-mismatched artifact is indicated in an orange dotted circle

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where sinactive and sactive are the J-inactive and J-active sub-spectra, respectively. H2 is a Hadamard matrix of order 2 (H2):

$$H_{2} = \left[ {\begin{array}{*{20}c} 1 & 1 \\ 1 & { - 1} \\ \end{array} } \right]$$
(2b)

As shown in Fig. 3e,h, the sum and difference of the 1JCH-inactive and 1JCH-active sub-spectra at a ratio of one to one therefore yielded the 13CH2 and the 13CH/13CH3 spectra. In the same way, subtraction of the 1JCCO-inactive and 1JCCO-active sub-spectra separated the Asx 13Cβ−1Hβ and Glx 13Cγ−1Hγ correlations together with 13Cα−1Hα of all residues (Fig. 3f,i). Likewise, the difference spectrum calculated from the 1JCCaro-inactive and 1JCCaro-active sub-spectra selected the 13Cβ−1Hβ resonances of aromatic amino acid residues (Fig. 3g,j). As individual sub-spectra shown in Fig. 3a−d were obtained in a single scan per indirect increment, the undesired magnetization from residual water, which is not scalar-coupled to 13C, at the point of acquisition gave rise to spectral artifact in the sum spectra (Fig. 3e−g) whereas it was effectively suppressed in the difference spectra which were generated by subtraction between the two sub-spectra (Fig. 3h−j). While repetition of the experiment with a phase cycling scheme can eliminate the solvent artifact, we will, instead of increasing the number of scans, introduce a combinational sign-encoding strategy with 1JCH, 1JCCO, and 1JCCaro couplings, where eight sub-spectra are recorded in a single scan per indirect increment.

In the OROCHI experiment, eight combinations of multiplicity-edited 2D CT 13C−1H HSQC sub-spectra with three binary parameters (i.e., whether each of the 1JCH-, 1JCCO-, and 1JCCaro-coupling evolution periods was included or removed) were recorded. Linear combinations of sums and differences of these eight sub-spectra (s1 to s8) generated a series of multiplicity-separated NMR spectra (S1 to S8):

$$S = H_{8} S_{{{\text{sub}}}}$$
(3a)

where S and Ssub are the column vector represented respectively by S = [S1 S2 S3 … S8]T and Ssub = [s1 s2 s3 … s8]T. H8 is a Hadamard matrix of order 8, that is,

$$H_{8} = \left[ {\begin{array}{*{20}c} 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 \\ 1 & { - 1} & 1 & { - 1} & 1 & { - 1} & 1 & { - 1} \\ 1 & 1 & { - 1} & { - 1} & 1 & 1 & { - 1} & { - 1} \\ 1 & { - 1} & { - 1} & 1 & 1 & { - 1} & { - 1} & 1 \\ 1 & 1 & 1 & 1 & { - 1} & { - 1} & { - 1} & { - 1} \\ 1 & { - 1} & 1 & { - 1} & { - 1} & 1 & { - 1} & 1 \\ 1 & 1 & { - 1} & { - 1} & { - 1} & { - 1} & 1 & 1 \\ 1 & { - 1} & { - 1} & 1 & { - 1} & 1 & 1 & { - 1} \\ \end{array} } \right]$$
(3b)

Listed in Table 1 are the eight binary combinations of the 2D CT 13C−1H HSQC sub-spectra. As shown in Table 2, Hadamard transform of these sub-spectra generates five HSQC spectra (S1 to S5) with desired signals, while the last three (S6, S7, and S8) are empty. When the phases of the 13C excitation pulse (ϕC) and the receiver (ϕrec) were fixed for all sub-spectra in the OROCHI experiment, the solvent artifact appeared in the spectrum S1, which was generated by adding up the eight sub-spectra (Supplementary Fig. S2). To avoid the risk of peak burial in the solvent artifact, the solvent artifact can be moved to an empty spectrum. In Supplementary Fig. S3, the phases of ϕC and ϕrec were x when both 1JCCO and 1JCCaro were either active or inactive and −x when only one of either 1JCCO or 1JCCaro was active (see Table 1), so that the solvent artifact accumulated in the S7 spectrum. We note that the solvent resonance in each HSQC spectrum could further be suppressed by presaturation although irradiation of 1Hα resonances that are close to the solvent frequency would result in their absence from the spectrum.

Table 1 Eight combinations of 2D CT 13C−1H HSQC sub-spectra (s1 to s8)
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Table 2 All possible linear combinations of sums and differences of the J-active and J-inactive sub-spectra according to the Hadamard transform
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Figure 4 shows separation of NMR signals of ubiquitin by means of combinatorial sign-encoding with 1JCH, 1JCCO, and 1JCCaro couplings. The S5 spectrum selected 13Caro-coupled 13CH2 correlations, that is, F/Y/H/W 13Cβ−1Hβ correlations. The S4 spectrum was for 13CO-coupled 13CH/13CH3 groups; it selected 13Cα−1Hα correlations of all residues but glycine. In the S3 spectrum, the Asx 13Cβ−1Hβ and Glx 13Cγ−1Hγ correlations together with 13Cα−1Hα of glycine residues were obtained. Other aliphatic 13CH/13CH3 and 13CH2 groups were separated in the S2 and S1 spectra, respectively. It is possible to further enhance the resolution in the 13C dimension by extending the CT period, 2TC, from 1/1JCC (~ 28 ms) to 2/1JCC (~ 56 ms) unless the attenuation of the signals during the CT period due to 13C transverse relaxation is prohibitive (Supplementary Fig. S4). On the other hand, signals displayed with opposite sign can be distinguished when 2TC = 1/1JCC. For example, methionine γ-13CH2 and ε-13CH3 correlations can be distinguished in the S1 and S2 spectra, respectively. Figure 5 shows an expanded region of the 2D CT 13C−1H HSQC to display backbone 13Cα−1Hα correlations. In the unedited spectrum, serine β-13CH2 and proline δ-13CH2 correlations were indistinguishable (Fig. 5a). In contrast, these correlations were readily separated in the OROCHI experiment (Fig. 5b). Separation of aliphatic NMR signals in the OROCHI experiment is summarized in Table 3.

Fig. 4
figure 4

Selective observation of complementary NMR signals with an OROCHI experiment on 13C-enriched ubiquitin. In the 2D CT 13C−1H HSQC experiments, the CT period (2Tc) was set at 28 ms. The positive and negative peaks are shown in black and red, respectively. a Unedited 2D CT 13C−1H HSQC spectrum (same as Fig. 1d). b−f Multiplicity-separated 2D CT 13C−1H HSQC spectra generated by linear combinations of the sums and differences of the sub-spectra with the Hadamard matrix of order 8. A series of 2D CT 13C−1H HSQC sub-spectra, shown in Supplementary Fig. S3a, were collected using the pulse sequence shown in Fig. 2. Undesired artifacts due to 1JCH mismatch are indicated in blue dotted circles, and 1JCCO-mismatched artifact is indicated in an orange dotted circle. All the eight spectra (S1 to S8) are shown in Supplementary Fig. S3b

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Fig. 5
figure 5

Distinguishing side-chain 13CH2 groups from backbone 13Cα−1Hα correlations. In the 2D 13C−1H HSQC experiment, the CT period (2Tc) was set at 28 ms. a Unedited spectrum of 13C-enriched ubiquitin. The positive and negative peaks are shown in black and red, respectively. b Corresponding multiplicity-separated spectrum of 13C-enriched ubiquitin. The S1, S2, S3, and S4 spectra are color-coded in blue, gray, green, and red, respectively, and superimposed on the same spectrum

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Table 3 Separation of aliphatic NMR signals in the OROCHI experiment
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Figure 6 shows an expanded region of the 2D CT 13C−1H HSQC of ubiquitin. In the unedited spectrum, the left-side peak of the F45 13Cβ−1Hβ correlations was hidden under the intense peak due to R42 δ-13CH2. In addition, the right-side peak of the F4 13Cβ−1Hβ correlations overlapped with a β-13CH2 correlation due to D32. In the multiplicity-separated spectra, on the other hand, the F45 and F4 13Cβ−1Hβ correlations obtained by the OROCHI experiment were resolved unambiguously (see Fig. 6 and Supplementary Fig. S5). Although NMR experiments can allow elimination of resonance overlap by introducing additional spectral dimensions (Supplementary Fig. S5d), these experiments require longer measurement time. In addition, working with 2D data is more intuitive and data manipulations are easy (Walinda et al. 2017). Such simplified HSQC experiments can greatly facilitate NMR titration experiments with ligand or pH, where spectral crowding is often a limiting factor. The ability to generate 2D 13C−1H maps may be particularly fruitful for the characterization of protein–protein and protein–ligand interactions, as the 13C and 1H chemical shift changes of aliphatic groups due to binding may be understood in structural terms more readily than those of backbone amide 15N and 1H groups (Williamson 2013).

Fig. 6
figure 6

Resolving resonance overlap in the 2D 13C−1H HSQC spectrum of 13C-enriched ubiquitin. The CT period (2Tc) was set at 28 ms. a A close-up view of the unedited spectrum. b Corresponding multiplicity-separated spectrum. The S1, S3, and S5 spectra are color-coded in red, green, and purple, respectively, and superimposed on the same spectrum. Each of these spectra are shown in Supplementary Fig. S5

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As a drawback, we acknowledge that, while no additional relaxation loss was generated by the sign-encoding strategy achieved within the CT 13C chemical shift evolution period, deviation of the J coupling from the nominal value can lead to sensitivity losses and the appearance of spectral artifacts (Figs. 3 and 4 and Supplementary Figs. S2 and S3). Aliphatic 1JCH couplings range from 125 to 160 Hz (Zwahlen et al. 1997). For example, the 1JCH coupling for the M1 ε-13CH3 group of ubiquitin was 142 Hz, while the average 1JCH coupling for leucine δ-13CH3 groups was 125 Hz (Supplementary Fig. S6a, b). In the 1JCH-active experiment, the net 1JCH-evolution time (2ΔCH) was set so that a compromise of 1JCH = 130 Hz was used. As shown in Fig. 7, the ratio of the signal intensity in the S2 spectrum to that of the corresponding unedited spectrum was 91% for M1 ε-13CH3 and 94% for L50 δ2-13CH3. Imperfect cancellation for intense 13CH3 peaks resulted in detectable artifacts in the methyl region of the added spectrum that selected aliphatic 13CH2 groups (Supplementary Fig. S7). On the other hand, for intense signals of 13CH2 groups (e.g. arginine δ-13CH2, lysine ε-13CH2, and serine β-13CH2), imbalance due to 1JCH mismatch caused artifacts that appeared with attenuated intensity. The average 1JCH couplings are 146, 145, and 156 Hz for arginine δ-13CH2, lysine ε-13CH2, and serine β-13CH2 groups, respectively (Supplementary Fig. S6c, d). The average drop in the intensity was 10% for lysine ε-13CH2, 5% for arginine δ-13CH2 and 17% for serine β-13CH2 (Fig. 7 and Supplementary Fig. S8). The 1JCCO and 1JCCaro couplings were obtained from peak splitting along the 13C dimension of a 2D CT 13C−1H HSQC spectrum without pulses on 13CO and 13Caro carbons (Supplementary Fig. S9). For well-resolved resonances, the 1JCCO and 1JCCaro coupling values were obtained (Supplementary Tables S1 and S2). The average 1JCCO and 1JCCaro couplings are 52.2 and 46.1 Hz, respectively. In the OROCHI experiments, we used the 1JCCO and 1JCCaro values of 50 and 45 Hz, respectively. Mismatch of the 1JCCO and 1JCH couplings of intense glycine α-13CH2 correlations resulted in appearance of the mismatched artifact in the S1 and S4 spectra (Fig. 4 and Supplementary Fig. S10). Mismatch of the 1JCCaro coupling was seen for H68 β-13CH2 (Supplementary Fig. S11).

Fig. 7
figure 7

Imperfect cancellation due to mismatch of 1JCH couplings. Shown are 1D slices for the M1 ε-13CH3 (a), L50 δ2-13CH3 (b), R54 δ-13CH2 (c), and S20 β-13CH2 (d) correlations. The CT period (2Tc) was set at 28 ms. Unedited and multiplicity-separated spectra are indicated in black and blue, respectively. The corresponding spectra with J-mismatched artifacts are shown in magenta

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It has been pointed out that strong couplings that occur when the chemical shift difference between the two coupling 13C nuclei is not sufficiently larger than 1JCC could cause serious distortion of the spectrum (Vuister and Bax 1992). In the case of limited leucine side-chain mobility in proteins, one of the methyl groups may have the 13Cδ frequency close to the chemical shift of the neighboring 13Cγ nuclei (Mulder 2009; Hoffmann et al. 2018). There are a few more residues where the chemical shifts of the neighbors can be close to each other: serine 13Cα/13Cβ, arginine 13Cβ/13Cγ, and methionine 13Cβ/13Cγ. Nevertheless, the artifact caused by strong couplings is not usually a significant issue in the aliphatic 13C−1H HSQC experiments (Vuister and Bax 1992).

In conclusion, we have introduced OROCHI, a method for selective observation of complementary NMR signals by combinatorial editing of 2D CT 13C−1H HSQC spectroscopy using 1JCCaro, 1JCCO, and 1JCH couplings. 13CO-coupled side-chain 13CH2 correlations of Asx/Glx residues and 13Caro-coupled β-13CH2 correlations of aromatic amino acid residues are easily separated in the S3 and S5 spectra, respectively. Spectral simplification alleviates resonance overlap and can be useful for unambiguous resonance assignment. It may also be possible to separate tryptophan from the other three aromatic amino acid residues (i.e. phenylalanine, tyrosine, and histidine) if the selective pulses are finely tuned (Schubert et al. 2001b). In addition, OROCHI may benefit from methods for improved suppression of 1JCH-dependent artifacts (Zwahlen et al. 1997; Brutscher 2001; Boyer et al. 2003; Heikkinen et al. 2003), albeit at the expense of lengthening experimental time. The demonstrated method would provide a basis of multi-dimensional NMR experiments with 13Cali frequency encoding in a CT chemical shift evolution manner, so long as signal attenuation due to 13C transverse relaxation is acceptable.