# Sensitivity enhancement of homonuclear multidimensional NMR correlations for labile sites in proteins, polysaccharides, and nucleic acids

## Abstract

Multidimensional TOCSY and NOESY are central experiments in chemical and biophysical NMR. Limited efficiencies are an intrinsic downside of these methods, particularly when targeting labile sites. This study demonstrates that the decoherence imparted on these protons through solvent exchanges can, when suitably manipulated, lead to dramatic sensitivity gains per unit time in the acquisition of these experiments. To achieve this, a priori selected frequencies are encoded according to Hadamard recipes, while concurrently subject to looped selective inversion or selective saturation procedures. Suitable processing then leads to protein, oligosaccharide and nucleic acid cross-peak enhancements of ≈200–1000% per scan, in measurements that are ≈10-fold faster than conventional counterparts. The extent of these gains will depend on the solvent exchange and relaxation rates of the targeted sites; these gains also benefit considerably from the spectral resolution provided by ultrahigh fields, as corroborated by NMR experiments at 600 MHz and 1 GHz. The mechanisms underlying these experiments’ enhanced efficiencies are analyzed on the basis of three-way polarization transfer interplays between the water, labile and non-labile protons, and the experimental results are rationalized using both analytical and numerical derivations. Limitations as well as further extensions of the proposed methods, are also discussed.

## Introduction

Two-dimensional (2D) homonuclear NMR correlations1,2 are an integral part of the tools used to elucidate the structure and dynamics of organic, and biological molecules3,4. These correlations can be mediated by chemical exchange or nuclear overhauser effects (NOEs)5,6, and are probed by monitoring how polarization from one spin reservoir travels to another via dipolar interactions or chemical kinetics7,8,9,10,11,12. Magnetization transfer (MT) within a J-coupled spin network as achieved by TOtal Corelation SpectroscopY (TOCSY)13,14, leads to complementary information based on bond connectivities. Despite being routinely performed these 2D NMR experiments, and particularly NOESY, suffer from relatively low efficiencies, leading to cross-peaks with low signal-to-noise ratio (SNR), and to a need for extensive signal averaging times to improve this SNR. Detection of NOESY and TOCSY cross-peaks becomes even more difficult when involving labile protons (1Hs), as information is then “lost” through chemical exchange with the solvent. Hydroxyl 1Hs in saccharides, amino 1Hs in proteins and nucleic acids, amide 1Hs in disordered proteins, and imino 1Hs in RNA/DNA, are prototypical examples of such challenging systems: when placed in their natural aqueous environment all of these will undergo a rapid exchange with the solvent, which dramatically reduces the efficiency of their intramolecular polarization transfers.

We have recently introduced Looped PROjective SpectroscopY (L-PROSY)15, an approach that alleviates these problems by regarding these exchange processes as “resets” within the framework of Anti-Zeno Effects16,17,18. Instead of applying a single mixing period for homonuclear transfers that will then reach kinetically-compromised amplitudes, L-PROSY “freezes” these transfers after they begin to act with their (fastest) initial rate, resets the labile 1H states to their initial conditions by exploiting their exchange with an unperturbed solvent polarization reservoir, and repeats this process multiple times19,20. The ensuing “L-PROSY encoding” acts then as a sort of conveyor belt, causing the NOE/TOCSY cross-peaks to grow with the much more favorable rates characterizing their initial buildups, and lasting for as long as either thermodynamic considerations or the recipient’s T1 will accommodate them, before performing the latter’s signal detection. By selectively addressing only the targeted 1Hs and avoiding water perturbation L-PROSY exploits some elements of SOFAST NMR21,22; at the same time, by its repeated action, it is also reminiscent of CEST-based polarization transfer23,24,25,26. Despite their sensitivity gains, L-PROSY experiments are still long, requiring traditional t1 evolution periods to build-up multidimensional information. L-PROSY acquisitions can also lead to artifacts arising from an incomplete replenishment of the targeted sites’ polarization by the solvent, appearing as harmonics of genuine evolution frequencies and/or as anti-diagonal peaks. The present study demonstrates a new approach capable of alleviating both drawbacks while achieving even more complete MTs, which relies on Hadamard-encoded27,28,29 selective polarization transfers from the targeted labile 1Hs. It is shown that, whether involving multiple selective inversions or a continuous saturation procedure, this provides the highest per-scan enhancements we have seen on either conventionally- or L-PROSY-encoded NOESY and TOCSY experiments involving labile or fast-relaxing 1Hs. When combined with the compressed-sensing advantages and multiplexing provided by Hadamard encoding, gains of ca. two orders of magnitude in SNR/unit_time were observed over conventional counterparts. These gains were noted for a variety of biomolecular systems including sugars, nucleic acids, and proteins, illustrating their generality. The physical principles underlying these gains are described on the basis of a simple multi-site exchange model, leading to analytical descriptions that are generalized by numerical calculations, and which reproduce well the experimental observations.

## Results

### Principles of Hadamard-encoded 2D homonuclear correlations on labile sites

The mechanism underlying the resulting enhancements is reminiscent to that in in vivo CEST NMR24,33,34,35, and HMT enhancement factors ε vs NOESY/TOCSY can be computed using a similar theoretical framework. For concreteness, we consider here a NOESY spin dynamics as depicted by the Bloch-McConnell-Solomon equations, incorporating a continuous saturating field targeting a labile 1H; these are then used to evaluate the magnetization build-up arising from labile→non-labile 1H cross-relaxation-driven transfers in MT and conventional NOESY scenarios24,33,36,37. These calculations are detailed in the Supplementary Information; as shown in Supplementary Equations (15), the steady-state solutions describing the MT from the labile 1H’s equilibrium magnetization $$M_{z_l}^0$$ into the non-labile 1H state $$m_{z_{nl}}^{MT_{ss}}$$ can, for a cross-relaxation rate σ and saturating field ν1, be approximated as

$$m_{z_{nl}}^{MT_{ss}} = \frac{{\nu _1^2\sigma }}{{pq + \nu _1^2(R_{1_{nl}} + \sigma )}}M_{z_l}^0$$
(1)

where l and nl subscripts depict parameters for the labile and non-labile 1Hs, $$p = R_{2_l} + k_{ex}^l - \frac{{k_{ex}^l \ast k_{ex}^w}}{{R_{2_w} + k_{ex}^w}}$$ and $$q = \Big( {R_{1_l} + k_{ex}^l + \sigma - \frac{{k_{ex}^l \ast k_{ex}^w}}{{R_{1_w} + k_{ex}^w}}} \Big)(R_{1_{nl}} + \sigma ) - \sigma ^2$$ are quantities depending on the exchange rates $$k_{ex}^l$$ and $$k_{ex}^w$$ between the labile site and the water reservoir (scaled by their population ratio), as well as on the longitudinal and transverse relaxation rates $$R_{1(2)} = 1{\mathrm{/}}T_{1(2)}$$ of the labile, non-labile and water 1Hs. Similar differential Bloch-McConnell-Solomon equations have been solved analytically for the conventional NOESY experiment8; these solutions lead to symmetric $$M_{z_l} \to M_{z_{nl}}$$, $$M_{z_{nl}} \to M_{z_l}$$ cross-peaks, reaching maximal values given by:

$$m_{z_{nl}}^{NOESY_{max}} = m_{z_l}^{NOESY_{max}} = \frac{\sigma }{{\lambda _ + - \lambda _ - }}\left( {{\mathrm{e}}^{ - \lambda _ - \frac{{{\mathrm{ln}}\frac{{\lambda _ + }}{{\lambda _ - }}}}{{\lambda _ + - \lambda _ - }}} - {\mathrm{e}}^{ - \lambda _ + \frac{{{\mathrm{ln}}\frac{{\lambda _ + }}{{\lambda _ - }}}}{{\lambda _ + - \lambda _ - }}}} \right)M_{z_l}^0$$
(2)

where $$\lambda _ \pm = \frac{1}{2}\left\{ {(R_{1_l} + R_{1_{nl}} + 2\sigma + k_{ex}^l) \pm \sqrt {(R_{1_l} + k_{ex}^l - R_{1_{nl}})^2 + 4\sigma ^2} } \right\}$$, and other symbols are as introduced above (see Supplementary Equations (610), for a derivation of these maxima conditions). For the labile 1H scenario of interest here we can assume that $$k_{ex}^l \gg R_{1l},R_{1nl},\sigma$$; this greatly simplifies Eqs. (1) and (2), leading to MT vs conventional NOESY enhancement factors

$$\varepsilon = \frac{{m_{z_{nl}}^{MT_{ss}}}}{{m_{z_{nl}}^{NOESY_{max}}}} \approx \frac{{\nu _1^2k_{ex}^lT_{1_{nl}}}}{{(k_{ex}^{l2} + \nu _1^2)}}$$
(3)

Notice that according to this model, the enhancement of the labile 1H’s signature will, for an efficient $$\nu _1 \,> \,\,k_{ex}^l$$ saturation scenario, be given by $$k_{ex}^lT_{1_{nl}}$$. This represents the number of exchanges that labile 1Hs can imprint on their cross-relaxing non-labile neighbors given the latter’s “memory time”, and is reminiscent of similar behaviors derived for CEST24,35. More complete analyses of the predictions deriving from this Bloch-McConnell-Solomon model are presented in the Supplementary Information, including numerical solutions of the labile→non-labile transfer upon selectively perturbing the labile spins’ for a variety of solvent exchange rates, couplings and cross-relaxation rates. Supplementary Figures 14 confirm that substantial sensitivity improvements may arise from this approach, and examine their dependence on irradiation strength, solvent exchange rate and molecular correlation time. Additional insight is provided by Supplementary Fig. 5, which compares the conceptually similar but practically very different L-PROSY experiment to the current HMT proposal, highlighting the advantages of the latter experiment.

### HMT and the effects of increased magnetic field strengths

Like CEST34,38,39, HMT-based methods that target labile 1Hs could benefit significantly from operating at the highest possible magnetic fields. Under these conditions (i) more rapid exchange rates $$k_{ex}^l$$ can be accommodated, leading to higher enhancements ε without resolution penalties (in ppm); (ii) resolution between sites improves, leading to more facile conditions for implementing the 1D Hadamard encoding while relying on more intense ν1 saturating fields and/or shorter inversion pulses; (iii) $$T_{1_{nl}}$$ relaxation times tend to get longer, facilitating the extent of the intramolecular transfers40,41,42; and (iv) it becomes generally easier to study the exchanging 1Hs closer to physiologically-relevant temperatures. These advantages reinforce one another when targeting rapidly exchanging groups like the OHs of saccharides, something demonstrated in Fig. 2 for the α2,8-linked sialic acid tetramer (SiA)4. Higher fields improve the 1D spectrum for these sites leading, at 5 °C and 1 GHz, to a nearly full resolution of all hydroxyl 1Hs in the spectrum (Fig. 2b). Figure 2c compares conventional and HMT NOESY spectra acquired on (SiA)4 under such conditions; Supplementary Fig. 6a provides similar data but compared at a lower (600 MHz) field. Correlations involving the hydroxyl protons are hard to discern in the conventional experiments: even at 1 GHz, the fast chemical exchange reduces NOESY correlations between hydroxyl and aliphatic 1Hs to neighbors that are ≤2 Å away, like IVOH8-IV8 (at 1.7 Å) and IVOH8-IV6 (at 1.9 Å). By contrast, HMT NOESY at 1 GHz (and despite the challenges of selective saturation at lower fields, even at 600 MHz) provides a wealth of cross-peaks, in a fraction of the time needed by its conventional counterpart. The fact that in the conventional TOCSY and NOESY spectra many of the cross-peaks are invisible even after protracted acquisitions complicates the quantification of the experimental enhancements; still, Table 1 provides lower bounds for these values. The newly observed correlations involve hydroxyls with a wide rate of solvent exchange rates –ranging from ~10 s−1 for IVOH8, to ~40 s−1 for IIOH7 and even to ~100 s−1 for IIOH943. The reason for this efficiency is as explained earlier: faster exchanges hurt cross-relaxation, but at the same time, supply fresh polarization for the repeated transfer of magnetization (see for instance Supplementary Figs. 13). As for the lineshapes displayed by the 2D HMT plots: these are somewhat artificial, as in the Hadamard processing cross-peak traces were simply placed at the frequency positions used for implementing the selective RF irradiation/encoding. In principle, however, the information in the 2D HMT correlations has a well-defined point-spread function, given by 1D absorptive lineshapes along the direct domain, and by T1-, T2-, and ν1-dependent combinations along the indirect-domain axis. Once again, an analogy to what happens in CEST allows one to compute how these parameters influence the effective F1 spectral peak width24,35: this will be given by $$\nu _{1/2} \approx \sqrt {\nu _1^2\frac{p}{q} + p^2}$$, where the p and q symbols are as introduced in relation to Eq. (1). Notice that although line-broadening effects are introduced by the saturating RF into these spectral lineshapes, these are less critical than what they may appear at first sight—primarily owing to the labile nature of the 1Hs whose 2D correlations these new experiments target. This lability leads to exchange-broadened 1D linewidths, whose spectral resolution is not compromised much further by the RF used in their HMT encoding. In fact, one of the features of HMT is its ability to tailor the saturating field or the inversion bandwidth used in its implementation to each spectral peak individually, enabling an optimal compromise between resolution and the extraction of the information being sought.

Based on a previous (SiA)4 study performed at lower fields under super-cooled conditions44, the new data arising from HMT NOESY and TOCSY experiments can be used for both assignments and for structural refinements. The latter data are illustrated in Supplementary Fig. 6b, showing a number of sizable intra-residue J-driven correlations (Table 1); in fact, these TOCSY enhancements are often larger than their NOESY counterparts, reflecting perhaps the slightly higher temperatures at which they were measured. The HMT NOESY experiments also reveal correlations that had so far remained unseen, including inter-residue cross-peaks between IOH9-II5/II6, IIOH7-I6/I7/I8/I9, IIOH9-I8, IVOH7-III8, IVOH8-III8. When considering the structure proposed for the glycan under super-cooled conditions44 a number of conflicts arise, as, according to it, some of the cross-peaks observed by HMT NOESY would then correspond to internuclear distances between 1Hs positioned ≈7–9 Å apart (yellow dashes in Fig. 2d). As no strong additional cross-peaks that could justify such long-distance correlations on the basis of a relaying mechanism are visible, this called for a refinement of the glycan’s structure. Further investigations to be discussed in further detail separately evidence that, with temperature, (SiA)4 may undergo a rearrangement; this rearranges the oligosaccharide into the average structure shown in Fig. 2e, making it compatible with the observed HMT NOESY cross-peaks.

### Amide, amino, and imino proton correlations in proteins and nucleic acids

HMT at ultrahigh magnetic field turns out to be especially informative when implemented on the imino protons of nucleic acids. At 1 GHz these imino resonances, which can be broadened by chemical exchange with the solvent at lower fields, are sharper and better resolved. Figure 3 shows the superiority of the HMT experiment over conventional NOESY for detecting cross-peaks involving imino resonances, utilizing a 14mer hairpin RNA as prototypical example. This can be visualized by comparing 1D traces extracted from the conventional and HMT NOESY spectra (Fig. 3). Notice that several of the correlations are only detected in the HMT experiment, especially for iminos arising from bases that, like U7 and U8, are positioned in loop regions that undergo facile solvent exchanges. The wealth of peaks in the HMT experiment facilitates the elucidation of peaks in the amine, aromatic and sugar regions: with these, it is possible to obtain many more spectral assignments than what is possible with conventional experiments. Also illustrated in this Figure is HMT’s ability to fine-tune the extent of the saturation to the rate of solvent exchange for various labile 1Hs—a potentially important feature for heterogeneous structures, as the tailored excitation helps overcome the fast exchange arising in flexible regions without compromising the resolving power needed to address other, more rigid regions in the RNA. Even for more slowly exchanging iminos, like U11H3, enhancements are significant, both for correlations with aromatic protons that like A4H2 can be clearly detected in the conventional experiment, as well as with labile amino protons that like C10/C3H41, barely yield cross-peaks in the conventional NOESY. A summary of the resulting enhancements for representative peaks is presented in Table 1. Comparisons of conventional and HMT NOESY experiments for this 14mer were also performed at 600 MHz; although slices extracted from these data for various imino sites also lead to substantial enhancements, the relative enhancements provided by HMT over conventional experiments were larger at 1 GHz than at 600 MHz (Table 1). This reflects one of the aforementioned field-derived advantages: at 1 GHz, the inversion/saturation pulses addressing the labile 1Hs can be stronger, leading to a more efficient MT and to ~25–100% larger enhancements when assessed against their conventionally collected counterparts.

Another advantage of operating at ultrahigh fields is that most amide backbone signals in small and medium-sized proteins become well resolved in 1D experiments, enabling HMT experiments on these N-bound 1H resonances as well. Figure 4 illustrates the benefits resulting from this with comparisons between conventional and HMT NOESY acquisitions recorded on LA5, a 40-residue protein45, and on ubiquitin, a 76-residue protein. As in the case of the RNA, these HMT experiments utilized a polychromatic looped encoding instead of single long saturation pulses, as both of these proteins were 15N labeled and looping facilitated heteronuclear decoupling during the encoding (sequence in Fig. 1a). Extracted 1D projections show a 1:1 match between the HMT and conventional spectra, with sensitivity enhancements of ≈2x provided by the faster former scheme. These enhancements are smaller than those observed for saccharides and nucleic acids owing to the slower exchange rates that amide protons exhibit in the structured environments of these proteins; still when combined with fivefold shorter acquisitions, it is clear that HMT also brings substantial gains in SNR/unit_time to proteins (Table 1). Even larger enhancements could result in disordered proteins; in such cases, however, limited spectral dispersion would require the incorporation of a third, heteronuclear-encoding dimension in order to resolve the amide peaks. Such experiments will be considered in a separate study.

The strong correlations that HMT can deliver also open up the possibility of better exploiting amino groups, whose 1Hs are sometimes underutilized in NOESY and TOCSY experiments both in proteins and nucleic acids. Figure 5 shows how such 2D correlations can be put to good use, with HMT NOESY examples targeting amino groups in both ubiquitin and in the 14mer RNA sample. Strong correlations are observed in both spectra among the amino protons themselves, arising from combined chemical exchange and Overhauser effects among these moieties. Similar correlations are detected, much more weakly, in the conventional experiments depicted in Supplementary Fig. 7c for ubiquitin and in Supplementary Fig. 8b for the RNA. Moreover, HMT experiments reveal many additional long-range NOE-driven cross-peaks with the aliphatic protons for the protein case, and with the imino protons of nucleotides that are both in the same and in neighboring base pairs throughout the nucleic acid chain. When compared ith the amide protons, it is clear that the faster chemical exchange of these amine sites endows their HMT data with sizable gains when considering SNR/unit_time.

### HMT: exploiting hydroxyl correlations in proteins and nucleic acids

In addition to nitrogen-bound labile protons, hydroxyl 1Hs in sidechains and in sugars are notoriously challenging targets to work with in protein and nucleic acid NMR, respectively46,47,48. In both cases, these -OH peaks are often buried under other, sharper, and more intense amine and amide resonances. On the other hand, hydroxyl 1Hs usually undergo faster chemical exchange with water than the latter; as illustrated in Figs. 1 and 2, this qualifies them for potentially large cross-peak enhancements when targeted by the HMT scheme. Figure 6a shows a version of the HMT pulse sequence that could allow such usually “hidden” hydroxyl 1Hs be encoded, by incorporating additional 15N/13C-based filters49,50 aimed at suppressing the intense signals from 1Hs bound to 15N and 13C that would otherwise complicate the OH’s observation. To investigate if the OH 1Hs could be targeted in such experiments, a series of 1D variable-temperature (5–25 °C) 15N/13C-suppressed spectra were acquired; 1H resonances that survived the N-H and C-H suppression and became sharper at lower temperatures owing to slower chemical exchange with water, and were confirmed as likely candidates to arise from the labile hydroxyl 1Hs (Supplementary Fig. 7b). Figure 6b, c exemplify the cross-correlations arising from this experiment on a doubly 13C/15N-labeled ubiquitin and on a 14mer RNA sample, respectively. Highlighted in these spectra are the hydroxyl 1Hs addressed in the HMT NOESY; particularly interesting are OH-OH inter-residue correlations detected in ubiquitin, and the long-range correlations between the OHs of sugar and the base 1Hs resonating between 7 and 8 ppm in the 14mer RNA that are mostly missing in the conventional spectrum (Supplementary Fig. 8c). The latter include interesting correlations between the 2′-OH groups and aromatic nucleotide sites in the 5′-direction46,51. Whereas in the conventional NOESY only a single such interaction is observed (between the 2′-OH group of C13 and the aromatic proton of C14), in the HMT NOESY a total of 12 such correlations were detected. These give hitherto unavailable inter-residue correlations and distance information –including interactions between the 2′-OH of C10 and the H6 of U11, 2′OH of C3 and H8 of A4, and 2′-OH of G5 and H6 of C6. Additional cross-peaks are observed, but their unambiguous assignment is still challenging in this 2D NOESY spectrum due to resonance overlap persisting even at 1 GHz. The incorporation of the HMT NOESY segment into a 3D experiment incorporating further information regarding the ribose 1Hs, could potentially lift such ambiguities and contribute substantially to 3D structure determinations.

## Discussion

Hadamard MT was introduced here as an extension of projective-measurement experiments where, instead of a looped t1 time-domain encoding15, selective irradiations are used to impart significant SNR/unit_time gains in homonuclear correlation experiments involving fast-exchanging protons. To achieve these gains, HMT exploits the flow of water polarization to reset the states of the targeted sites, which are then perturbed away from equilibrium via selective saturation or inversions. Polarization transfer processes spreading throughout the molecules via dipole–dipole relaxation or J-couplings are thus magnified, in a manner that resembles CEST-derived enhancements52,53. Thus, although chemical exchange with the solvent deteriorates conventional homonuclear transfer experiments, the abundant, slowly relaxing water resonance improves these processes by several-fold when switching to this new encoding scheme. Relaxation properties of the non-labile 1Hs on the receiving end of these transfers will limit the extent of these gains, as the MT process will only be effective over their “memory times” T1. The efficiency of these experiments improves by operating at ultrahigh fields, where the labile 1Hs are better resolved, and the extent of the saturation-derived transfer can be increased. Possible drawbacks of relying on such high-field MT processes concern potential sample heating effects, but these were not found to be a problem even when operating at 1 GHz. Specificity in these MT experiments could be compromised by spin-diffusion among the non-labile 1Hs in the system; we investigated a similar possibility for the case of L-PROSY, where it was found that a 1:1 correlation with conventional NOESY cross-peak intensities was preserved even in the presence of a spin-diffusion sink pool15. This correspondence will persist over a wide range of solvent exchange rates and correlation times; it remains to be investigated whether the continuous-irradiation or the repeated inversion versions of HMT, might perform differently in terms of potential spin-diffusion effects. It is also interesting to note that while HMT and L-PROSY operate based on related principles, the per-scan enhancements in HMT will generally be equal to or higher than in L-PROSY. This is a consequence of: (i) the additional degree of freedom that tailoring the intensity of the saturating/inverting RF field provides to the MT experiments, and (ii) the higher per-scan efficiency enjoyed by frequency-based Hadamard methods over time-domain encoded counterparts, where signals decay owing to T2 and exchange-driven losses over the course of the t1 evolutions. On top of this there is Hadamard’s “compressed sensing” time savings, whereby in the absence of signal averaging needs, the overall duration of the experiment should not require more scans than the actual number of peaks; given sufficient SNR, suitably regularized non-uniform-sampling Fourier reconstruction schemes can also enjoy from such benefits.

Although this study focused on homonuclear transfers originating from labile 1Hs being replenished by the solvent, the HMT concept could be exploited in additional NMR settings where fast-relaxing sites can be individually addressed; in such instances, cross-peaks to slower-relaxing sites could be enhanced without a need for exchanges with the solvent. These cases may include methyl groups in otherwise deuterated proteins, small molecules interacting dynamically with bigger ones (e.g., drug–protein binding processes)54,55,56, as well as fast-relaxing sites in paramagnetic biomolecules. It is also worth exploring extension of the method to incorporate other mixing schemes, particularly those that could serve to distinguish spin-diffusion and relaxation-driven transfers from chemical exchange effects57,58,59. The high efficiency and short-acquisition of HMT experiments can be further utilized for fast multidimensional reaction monitoring, especially involving small reagents/products in the fast tumbling regime that are traditionally hard to correlate with NOESY. Last but not least, the 2D Hadamard concepts introduced here could also be included as part of correlations with heteronuclei in 3D spectral acquisitions27,60. Heteronuclear analogs of the homonuclear polarization transfer processes discussed here can also be envisaged. Examples of these developments will be discussed in upcoming studies.

## Methods

### Sample preparation

Myo-inositol was purchased from Sigma Aldrich (Israel) and prepared as 5 mM solution at pH 6.0. 5 mM sucrose was prepared using household sugar at pH 6.5. Natural abundance α2–8 (SiA)4 was purchased from EY Laboratories Inc (San Mateo, CA); 25 mg of this tetramer were dissolved in 400 μL of 20 mM phosphate buffer at pH 6.5 containing 0.05% NaN3, yielding a ~50 mM final solution at pH 7.35. The 13C/15N-labeled 14mer gCUUGc tetraloop (5′-pppGGCAGCUUGCUGCC-3′) was prepared from a linearized plasmid DNA by a run-off in vitro transcription using the T7 RNA polymerase61. In addition, the plasmid DNA contained a self-cleaving HDV ribozyme to ensure 3′ homogeneity. Labeled rNTPs were purchased from Silantes (Munich, Germany). The RNA was folded in NMR buffer (10 mM phosphate buffer + 1 mM EDTA pH: 6.4) in 90% H2O and 10% D2O by denaturing it for 5 min at 95 °C and subsequently slowly cooling down to room temperature. The final concentration of the RNA was 1 mM. Ubiquitin was purchased from Asla Biotech and was dissolved in PBS (Dulbecco’s Phosphate Buffer Saline at physiological pH, purchased from Biological Industries) at a concentration of 1 mM; LA5, the ligand binding domain 5 of the low-density lipoprotein receptor LDLR, was prepared as described by Szekely et al.45 at pH 7.4 and concentration 3 mM in 10 mM Tris buffer with 1 mM CaCl2. All protein samples were prepared in H2O/D2O (90%:10%) solutions containing NaN3. Although the use of 13C/15N spin labels in these protein and RNA samples was not needed within the context of this study, they were used as a result of their immediate availability. It is worth noting that, because of this labeling, efficient composite pulse or adiabatic decoupling could be implemented throughout the acquisition of all 2D NOESY/TOCSY data (rather than just during t2 and at t1/2).

### NMR experiments

NMR experiments were conducted using either a 14.1 T Bruker magnet equipped with an Avance III console and TCI Prodigy probe; or a 1 GHz, 23.5 T Bruker Avance Neo equipped with a TCI cryoprobe. Hadamard experiments were carried out using 8x8 through 64 × 64 Hadamard encoding matrices, depending on the number of peaks in the spectrum. In total, 10–40 Hz nutation fields were used for saturation, whereas 20–25 Hz bandwidth sinc1 pulses were used in looped inversion method. The number of loops and/or duration of the saturation, were determined according to T1 values of the receiving protons. Optimal values for NOESY and TOCSY mixing times were used in conventional experiments. Conventional TOCSY were acquired using dipsi2gpph19/dipsi2esgpph Bruker sequences employing DIPSI2 isotropic mixing13, whereas for NOESY experiments noesyfpgpph19/noesyesgpph was used employing Watergate 391962 with a flip-back pulse63, or excitation sculpting for water suppression. For most of the compounds, Watergate 3919 with water flip-back pulses showed excellent performance in keeping the water unperturbed31,64,65,66, and was preferred over jump-return techniques owing to the larger bandwidth of their binomial excitation. In all comparisons between HMT and conventional NOESY or TOCSY acquisitions, the experiments differed only in their encoding and mixing principles; water-suppression techniques, recovery delays d1 and receiver gains were otherwise set identical, in order to ensure faithful comparisons. Mixing times and Watergate delays for the binomial water suppression were optimized according to the magnetic field. All spectra were processed in Bruker® TopSpin® 4.0.6 and 4.0.9. All spectra were apodized with QSINE or SINE window functions and while conventional spectra were zero-filled once, all Hadamard spectra were zero-filled to 256 × 1024 points. Spectra were analyzed using NMRFAM-SPARKY67.

### Reporting summary

Further information on research design is available in the Nature Research Reporting Summary linked to this article.

## Data availability

The data sets generated and analysed during the current study are available from the corresponding author on reasonable request.

## Code availability

HMT sequences were deposited in an RNA-specialized Bruker NMR User Library, and its details/uses further explained in the Bruker-sponsored website https://www.bruker.com/service/information-communication/nmr-pulse-program-lib/bruker-user-library/liquids/avance-neo.html. Parameters there are given for the imino-based experiments; adjustments to target other kinds of 1Hs may require adjusting offsets and powers.

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## Acknowledgements

We are grateful to professor D. Fass (Weizmann Institute) for the LA5 sample and to Dr. Tali Scherf (Weizmann Institute) for the assistance in the GHz experiments. This work was supported by the Kimmel Institute for Magnetic Resonance (Weizmann Institute), the EU Horizon 2020 program (FET-OPEN Grant 828946, PATHOS), Israel Science Foundation Grant 965/18, and the Perlman Family Foundation. H.S. was supported by DFG-funded collaborative research center 902. Work at BMRZ is supported by the state of Hesse. Joint support to L.F., H.S. was given by the German-Israel Foundation (grant G-1501-302). We wish to thank Boris Fürtig, Robbin Schnieders, and Christian Richter for stimulating discussions.

## Author information

Authors

### Contributions

M.N., E.K., and L.F. conceived the project. M.N., E.K., and L.F. implemented the method. M.N. carried out the NMR measurements and the spin simulations. M.N. and E.K. processed the data. M.N., A.O., H.S., and L.F. conceived the nucleic acids applications and evaluated their NMR data. M.N., M.D.B., D.F., and L.F. conceived the oligosaccharide applications and evaluated their NMR data. M.N. and L.F. wrote the paper. All authors contributed to the discussions leading to the final manuscript.

### Corresponding author

Correspondence to Lucio Frydman.

## Ethics declarations

### Competing interests

Dr. Eriks Kupce is an employee of the Bruker Corporation. The remaining authors declare no competing interests.

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Novakovic, M., Kupče, Ē., Oxenfarth, A. et al. Sensitivity enhancement of homonuclear multidimensional NMR correlations for labile sites in proteins, polysaccharides, and nucleic acids. Nat Commun 11, 5317 (2020). https://doi.org/10.1038/s41467-020-19108-x

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