More than ADEQUATE: doubling the sensitivity of ¹³CH–¹³CH correlations in double-quantum NMR experiments

Abstract

We present modifications of the ADEQUATE experiment which more than double the sensitivity of carbon–carbon correlations of ¹³CH–¹³CH moieties. Additionally, these improvements can be applied without a sensitivity penalty to obtain spectra with a ¹³C chemical shift axis in the indirectly detected dimension, instead of a double-quantum frequency, allowing simpler interpretation of spectra. The modified experiments, which use refocussing of ¹J_CH couplings and ¹H decoupling during J_CC evolution intervals, were tested on several molecules, including a pentasaccharide (20 mg, 19 mM), where on average a 2.6-fold signal-to-noise improvement was achieved and the number of observable correlations increased. Doubling sensitivity results in a 4-fold reduction of the experimental time, allowing ADEQUATE spectra to be recorded overnight instead of over multiple days.

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The INADEQUATE (incredible natural abundance double-quantum transfer experiment) NMR experiment^1,2 is of substantial interest to chemists as it allows tracing out the carbon skeleton of a molecule.³ It relies on the detection of double-quantum (DQ) coherences between two coupled ¹³C spins and therefore has inherently inadequate sensitivity, as the probability of a molecule containing a pair of ¹³C atoms is approximately 1-in-8300. Historically, this has limited its use, as long experimental times and/or high sample concentrations were typically required. However, the development of cryogenically cooled NMR probes and the associated sensitivity gains enabled INADEQUATE and its variants to become routine experiments, which have been reviewed extensively.^4–9

For protonated ¹³C atoms, sensitivity of INADEQUATE can be increased by using ¹H detection as demonstrated by the INEPT-INADEQUATE experiment.¹⁰ The addition of the INEPT (insensitive nuclei enhancement by polarisation transfer) step offers increased sensitivity due to the higher gyromagnetic ratio (γ) of ¹H compared to ¹³C. Considering proton singlets and neglecting the sensitivity enhancement of ¹³C-detected INADEQUATE through heteronuclear NOE, the maximum theoretical signal-to-noise ratio (SNR) increase associated with ¹H detection is (γ_H/γ_C)^5/2 ≈ 32.¹¹ However, such a SNR increase is not achieved for various reasons.¹² A factor of √2 is lost due to pulsed-field gradient (PFG) selection,¹³ and a loss of a further factor of 2 occurs because in the ¹H-detected experiment the DQ coherences start and end on the same proton, whereas in ¹³C-detected INADEQUATE the coherences are generated from two nuclei. Additional sensitivity loses occur due to relaxation effects: the INEPT transfer of the ¹H-detected experiments generates mixed proton–carbon coherences that in medium size molecules relax faster than pure carbon coherences. While sharp ¹H-decoupled antiphase ¹³C–¹³C doublets are acquired in ¹³C-detected INADEQUATE, complex ¹H multiplets degrade sensitivity of ¹H-detected methods.

As a result, approaches have been developed to improve the sensitivity of ¹H detection. It has been demonstrated that removing the proton term from mixed CH coherences prolongs their relaxation times and increases the overall sensitivity of experiments.¹² This approach is especially beneficial for long-range (ⁿJ_CC, n ≥ 2) optimised ¹H-detected experiments containing longer ⁿJ_CC evolution delays. The sensitivity of ¹H-detected INADEQUATE was substantially increased by ¹H-detected ADEQUATE (adequate sensitivity double-quantum spectroscopy).^14,15 This method employs a 120° ¹³C pulse to optimise the ¹³C multiple-quantum to single-quantum coherence transfer and incorporates the preservation of equivalent pathways (PEP) element that offers sensitivity improvements of up to √2-fold.¹⁶ Sensitivity can be further improved by homonuclear decoupling that at least partially simplifies the structure of ¹H multiplets.^17,18

In order to avoid complications associated with the setup and interpretation of experiments that produce DQ frequencies in the indirectly detected dimension (F₁), a version of the ADEQUATE experiment was reported that samples ¹³C single-quantum (SQ) coherences in F₁.^14,15 This modification, originally termed ω₁-refocussed ADEQUATE, is referred to as SQ ADEQUATE herein. It works by incorporating an additional t₁ period into the pulse sequence, during which the ¹³C–¹³C DQ coherences are modulated by a single-quantum ¹³C frequency with an opposite sign to the DQ ¹³C–¹³C frequency. For an H_n-C_n-C_m-H_m spin system this amounts to H_n being modulated by the C_m frequency (and H_m by C_n), and thus the ¹J_CC-optimised SQ ADEQUATE experiment produces a spectrum containing pseudo-2-bond C–H correlations at the (F₂, F₁) chemical shifts of (H_n, C_m) and (H_m, C_n). A comparison of SQ ADEQUATE and 2D ¹H, ¹³C HSQC spectra (the latter acquired in a fraction of time) allows for a straightforward interpretation of ¹³C–¹³C correlations observed in SQ ADEQUATE experiments.

In this work, we present modifications of the ADEQUATE experiments that significantly increase the sensitivity of ¹³C–¹³C correlations for molecular moieties containing CH–CH fragments. These modifications can be applied to experiments that sample either DQ or SQ frequencies in F₁ and are herein referred to collectively as ¹J_CH-refocussed ADEQUATE (Fig. 1). The full pulse sequence parameters and experimental details are presented in Fig. S1 (ESI†).

Fig. 1 ¹ J _CH-refocussed ADEQUATE pulse sequence. If κ = 0, double-quantum chemical shift is obtained in F₁. If κ = 1, single-quantum ¹³C chemical shift is obtained in F₁. For full description of parameters, see ESI.†

The first minor modification of the original experiments is the addition of a 90° ¹³C pulse and a PFG purge element at the beginning of the pulse sequence, which defocusses any ¹³C magnetisation, thus eliminating polarisation transfer pathways starting on ¹³C. Although the ADEQUATE experiment employs phase cycling and PFG selection to remove the strong signals coming from ¹²C-bonded protons, isolated ¹³C-bonded protons or ¹³C atoms, imperfect defocussing of these signals can obscure correlations of interest. The addition of this purge element reduced cancellation artefacts and slightly increased the SNR as shown in Fig. S2 (ESI†).

A major sensitivity increase was achieved by refocussing the ¹J_CH coupling at the beginning of the 1/(2^1,nJ_CC) evolution interval following the initial ¹H → ¹³C INEPT transfer. This conversion of carbon-proton antiphase coherences into pure ¹³C coherences prior to excitation of DQ coherence removes the leakage of signal into undetectable zero-quantum coherences and generates a 2-fold sensitivity increase.¹⁹ Application of ¹H decoupling while SQ or DQ ¹³C coherences are present, reduces relaxation and further increases the sensitivity of experiments.¹² To regenerate the antiphase proton–carbon coherences required for the reverse ¹³C → ¹H INEPT step, the decoupling is turned off for a period of 1/(2¹J_CH) at the end of the 1/(2^1,nJ_CC) refocussing interval.

The increased SNR of the modified ADEQUATE experiments was evaluated using a concentrated sample of methyl β-D-xylopyranoside (I, 1.1 M, Scheme 1). This model compound was chosen because it contains CH, CH₂ and CH₃ carbons; its high concentration enabled fast and accurate comparison of related spectra. Relative SNR changes for CH groups are presented in Table 1 and Fig. 2; full spectra are shown in Fig. S3 (ESI†). SNR improvement for selected correlations is highlighted in Fig. S4 (ESI†). Not reported previously in the literature, these results indicated that the original ¹J_CC-optimised SQ (ω₁-refocussed) ADEQUATE experiment shows an up to 32% sensitivity loss compared to the DQ ADEQUATE experiment. This loss, which can be tolerated in exchange for a more straightforward analysis of spectra when sample concentration is not limiting, is associated with the appearance of HSQC-like artefacts at frequencies of (H_n, C_n) as shown in Fig. S3c (ESI†). These extra correlations, which can be much more efficiently obtained from ¹H, ¹³C HSQC spectra, can hinder analysis of complicated spectra by introducing peak overlap. The proposed ¹J_CH-refocussed SQ ADEQUATE eliminates this leakage (cf. Fig. S3c and d, ESI†), which explains larger SNR increases observed for the ¹J_CC-optimised SQ compared to the DQ experiment (2.1× vs 1.7×). Long-range SQ ADEQUATE spectra do not show significant HSQC-like artefacts, hence the increase in sensitivity is comparable for the DQ and SQ experiment (2.3× for both).

Scheme 1 Compounds used for ADEQUATE experiments: methyl β-D-xylopyranoside (I), strychnine (II) and fondaparinux (III).

Table 1 Average (mean ± SD) signal-to-noise ratio (SNR) gain obtained for CH–CH correlations of I in DQ and SQ ADEQUATE experiments^14,15 with and without refocussing of ¹J_CH couplings

Experiment	SNR fold change
	One-bond^a	Long-range^b
a n (number of correlations) = 6. b n = 4. c With respect to original DQ ADEQUATE. d With respect to original SQ ADEQUATE.
DQ ADEQUATE	1.0	1.0
SQ ADEQUATE^c	0.9 ± 0.1	0.9 ± 0.1
^1 J CH-refocussed DQ^c	1.7 ± 0.3	2.3 ± 0.3
^1 J CH-refocussed SQ^c	1.8 ± 0.3	2.0 ± 0.4
^1 J CH-refocussed SQ^d	2.1 ± 0.2	2.3 ± 0.4

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Fig. 2 Positive projections of ADEQUATE spectra of I optimised for one-bond (45 Hz) and long-range (6 Hz) J_CC couplings. The factors indicate the average SNR improvement for CH groups compared to DQ ADEQUATE. Full one-bond 2D spectra are shown in Fig. S3 (ESI†).

Overall, the data summarised in Table 1 indicate that ¹J_CH-refocussed SQ ADEQUATE experiment performs best for both one-bond and long-range ¹³CH–¹³CH correlations. Therefore, simpler spectra, displaying SQ ¹³C chemical shift along F₁ can now be obtained without a sensitivity penalty and with a 1.8–2.0-fold enhancement compared to original DQ ADEQUATE. As the ¹J_CH-refocussed ADEQUATE experiments are designed to refocus couplings of CH groups only, the sensitivity of CH₃-detected correlations is reduced and CH₂-detected correlations are absent. The CH-detected CH–CH_x (x = 0, 2, 3) connectivities are present with improved sensitivity (1.3–2.0×) compared to the original ADEQUATE spectra as evaluated on the spectra of L-isoleucine (Fig. S5, ESI†).

In order to investigate the SNR improvements on a compound with a more diverse structure, one-bond and long-range optimised SQ ADEQUATE spectra were acquired for strychnine (II, 32 mM). Despite the wide range of coupling constants reported for II (¹J_CH = 124–168 Hz, ¹J_CC = 32–71 Hz, ³J_CC = 3–7 Hz),^20,21 experiments optimised for ¹J_CH (150 Hz) and ^1,nJ_cc (50 Hz or 6 Hz) yielded sensitivity improvements similar to those observed for I. A SNR gain of (1.9 ± 0.4)× was observed for CH–CH correlations in ¹J_CC-optimised ADEQUATE (Fig. S6 and Table S1, ESI†). A more significant increase in sensitivity was observed in the long-range spectra (Fig. S7 and Table S2, ESI†), with an average SNR increase of 2.3× for CH–CH correlations (Fig. 3). The sensitivity is also improved for CH–CH_x (x = 0, 2) moieties, although by not as much, especially for quaternary carbons. The lower increase can be attributed to quaternary carbons of II having relaxation times of ≥20 s,²² therefore not benefiting much from reducing relaxation losses.

Fig. 3 Correlations observed and the SNR improvement achieved by ¹J_CH refocussing in ⁿJ_CC-optimised SQ ADEQUATE experiments for II. F₂ projection with and without ¹J_CH refocussing are shown. Full spectra are presented in Fig. S7 (ESI†). Note that correlations observed for the aromatic system have been omitted for clarity.

To illustrate the benefits of the improved ADEQUATE experiment on a weaker sample of a larger molecule, one-bond and long-range ¹³CH–¹³CH correlations of a sulfated pentasaccharide, fondaparinux Na (III, Scheme 1, M_w = 1728 g mol⁻¹, 19 mM), were obtained on an 800 MHz spectrometer equipped with a TCI cryoprobe in 7 and 21 hours, respectively (Fig. 4 and Fig. S8–S10, ESI†). SNR improvements in the range of 1.4- to 4.4-fold were obtained for the ¹J_CH-refocussed SQ ADEQUATE experiment optimised for ¹J_CC coupling constants (Table S3, ESI†). Low SNR of the spectra is responsible for such large variations, yielding an average (2.6 ± 0.7)-fold sensitivity increase. Increased SNRs were also seen in the ⁿJ_CC-optimised ¹J_CH-refocussed SQ ADEQUATE spectra (2.2 ± 0.5-fold, Table S4, ESI†). The increase in sensitivity is larger than for I or II, which illustrates that larger molecules benefit more from reduced relaxation losses due to their shorter ¹H relaxation times.

Fig. 4 ¹ J _CC-optimised SQ ADEQUATE spectra of III (a) without (black) and (b) with ¹J_CH refocussing (blue). The spectra were recorded for the same length of time and are plotted at the same intensity level. Comparison of marked traces (c) shows the sensitivity gains obtained by refocussing. Note that the 1B trace for spectrum (a) contains a weak HSQC-like artefact (*) which could be confused with a genuine correlation. For full peak assignment, see Fig. S8 (ESI†).

The sensitivity increase in both one-bond and long-range optimised ¹J_CH-refocussed experiments is significant, however the values only refer to SNR increases for signals present in both the original and improved spectra. In fact, ¹J_CH-refocussing revealed extra correlations not present in the spectra of the original experiments, therefore the sensitivity gains are even larger than the calculated factors. This is particularly true for the ⁿJ_CC-optimised experiments.

Correlations between adjacent monomer units in the pentasaccharide, providing valuable ring connectivity information, were observed. These experiments demonstrate that with <4 mg per monosaccharide residue, ¹J_CH-refocussed SQ ADEQUATE is an efficient experiment for structure determination of oligosaccharides.

It is worth noting that due to fast evolution of ¹J_CC compared to ⁿJ_CC coupling constants, one-bond correlations can appear in long-range optimised spectra. In this work, these correlations were identified by comparison to ¹J_CC-optimised spectra, however methods exist to allow discrimination between ¹J_CC and ⁿJ_CC correlations in ⁿJ_CC-optimised experiments.²³

In conclusion, the pulse sequences presented in this work provide significant improvements for the detection of ¹³CH–¹³CH correlation by double-quantum NMR experiments. Larger than 2-fold increases have been achieved, which translate to a 4-times reduction in spectrometer time. Double quantum ¹³C–¹³C experiments are regularly recorded over multiple days, yet the sensitivity-improved experiments will be able to provide the same information overnight. The new method is compatible with other schemes, such as homonuclear decoupling and non-uniform sampling, that have already been successfully applied to ADEQUATE experiments.^17,18,24,25 Additionally, the proposed modifications allow observation of SQ ¹³C frequency in the F₁ dimension without a sensitivity penalty. These sensitivity enhancements increase the potential of using ¹³C–¹³C correlations for structure elucidation and will benefit areas such as carbohydrates, natural products or mixture analysis, as well as general NMR applications when sample quantities are limited.

This research was supported by EPSRC grants EP/T517884/1 and EP/R030065/1. The authors thank Mr Juraj Bella and Dr Lorna Murray for the maintenance of the NMR spectrometer. Raw data for the spectra presented in this communication can be found at https://doi.org/10.7488/ds/3779.

Conflicts of interest

There are no conflicts to declare.

Notes and references

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Footnote

† Electronic supplementary information (ESI) available: Experimental details, additional results, NMR spectra and pulse programs. See DOI: https://doi.org/10.1039/d2cc05214h

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