Corentin Jacquemmoz

Jean-Nicolas Dumez

Acceleration of 3D DOSY NMR by spatial encoding of the chemical shift

Diffusion-ordered NMR spectroscopy (DOSY) is a powerful method for the analysis of solution mixtures. With 3D DOSY, the 2D NMR spectra of a mixture's components can be separated according to the translational diffusion coefficient of each component. The acquisition of 3D DOSY data is however very time consuming, because of the need to consecutively acquire scans for both the diffusion and the indirect spectral dimensions. We show that spatial encoding of the indirect spectral dimension, of the kind used in ultrafast 2D NMR, can accelerate 3D DOSY experiments by an order of magnitude or more. This is illustrated with homonuclear single-quantum (COSY) and double-quantum (DQS) correlation spectra. Implementations with concatenated and incorporated (iDOSY) diffusion blocks are compared and in both cases, 2D spectra are separated with less than 6 min of experiment time.

Introduction

Nuclear magnetic resonance (NMR) spectroscopy is an essential analytical technique for chemistry. NMR is used for a variety of purposes including identification and quantification, structure elucidation, kinetic measurement, titration, etc. In many cases, the sample of interest consists of a solution mixture. Within the suite of NMR experiments, one of the most relevant for mixture analysis is diffusion-ordered NMR spectroscopy (DOSY), [1], [2] which makes it possible to separate signals and entire spectra according to the translational diffusion coefficient of the corresponding molecule.

In DOSY experiments, the diffusion information is encoded by applying a pair of field gradient pulses separated by a fixed delay. A series of spectra are acquired for increasing values of the gradient amplitude, and the diffusion-attenuated signals are fitted with the Stejskal-Tanner equation:

𝐼(𝑔) = 𝐼 ! 𝑒 "#$ ! % ! & ! ' " [1]
where I(g) and I0 are the intensity of the signal with and without the diffusion-encoding gradients, D is the diffusion coefficient of the compound, γ the gyromagnetic ratio of nucleus used for diffusion encoding, ∆′ the delay between the encoding and decoding gradient (corrected for finite pulse width), δ and g the duration and intensity of the encoding gradient. The DOSY concept is applicable to the separation of near-arbitrary nD spectra and requires the acquisition of a (n+1)-dimensional data set.

DOSY is most frequently used to separate 1D spectra, with the diffusion gradient pulses included in a spin or stimulated echo. While this method is really efficient when signals are well resolved, for overlapped signals the modelling of the diffusion curve is more complex and loses in accuracy. Multivariate processing methods exist that can address the problem of overlapped spectra. [3] Another approach to deal with crowded spectra is to spread signals over two spectral dimensions to decrease the amount of signal overlap. This 3D DOSY approach has been demonstrated with a variety of 2D experiments; [4][5][6][7][8] a further advantage is that 3D DOSY spectra combine the separation power of DOSY with the information-content that 2D spectra provide, such as connectivity (COSY, HSQC…) or spatial organization (NOESY, HOESY…). The applicability of 3D DOSY is however limited by the long experiment duration required for the acquisition of multidimensional experiments with two incremented dimensions (the indirect spectral dimension and the diffusion dimension). This long duration (from 3 h to more than 14 h when phase cycling is needed) can be a problem. For samples that evolve over time (degradation, reaction monitoring…) more artefacts (such as t1-noise) are expected to appear for long experiments. Moreover the measured diffusion coefficient will be influenced by the appearance of disappearance speed of the compounds.

Multidimensional NMR experiments can be accelerated in a number of ways, and several of them have already been exploited for 3D DOSY. [9][10][11] For example, Hadamard encoding can be used when a small number of resonances is present in the 1D spectrum. [10] Sparse [9] and accordion [11] samplings of the incremented dimensions have also been considered. For 2D NMR, the fastest methods rely on spatial encoding of the indirect dimension, as proposed by Frydman and co-workers for indirect spectral dimensions [12][START_REF] Frydman | Proc. Natl. Acad. Sci[END_REF][START_REF] Pelupessy | [END_REF] and Keeler and co-workers for the diffusion dimension. [15], [16] This so-called ultrafast approach makes it possible to decrease the experimental time needed for a 2D acquisition from several minutes to less than one second. It has already been studied for 2D experiments such as COSY, [17] J-resolved, [18] DQS [19], [20] and also with pseudo 2D experiments such as DOSY [21], [22] or diffusion-relaxation correlation experiments. [23] For 3D DOSY, either the indirect spectral or the diffusion dimension could in principle be spatially encoded, and the latter option has been explored recently. [22] In this paper, we show that the acquisition of 3D DOSY spectra can be accelerated by one order or magnitude or more, with spatial encoding of the indirect spectral dimension. The virtual separation of homonuclear correlation spectra is demonstrated, with experiment durations of less than 6 minutes. Several implementations of the experiment are compared, and the relative merits of spatially encoding the indirect spectral and the diffusion dimension are discussed. The proposed 3D DOSY-UFNMR approach should be a practical and useful tool for the analysis of solution mixtures.

[a]

C Jacquemmoz, Dr J-N. Dumez Institut de Chimie des Substances Naturelles, CNRS UPR2301, Univ. Paris Sud, Université Paris Saclay, Avenue de la Terrasse, 91190 Gif-sur-Yvette, France E-mail: jeannicolas.dumez@cnrs.fr

Theory

In ultrafast 2D NMR, temporal encoding of the indirect dimension is replaced by spatial encoding. This is achieved with the joint application of a magnetic-field gradient and a chirp frequency-swept pulse, which results in a position-dependent evolution period. The detection scheme consists of a train of bipolar gradient pulses, to obtain at once the spatially encoded and the direct dimension.

In order to collect 3D DOSY data based on a given 2D pulse sequence, a pair of gradient pulses should be included to encode the diffusion dimension. For conventional experiments three approaches exist: DOSY-X, where a classic DOSY pulse sequence is followed by the chosen 2D pulse sequence (COSY, [4] DQS, HSQC…), X-DOSY, where the 2D pulse sequence is followed by the DOSY one, [8] and the iDOSY approach where the DOSY pulse sequence is integrated in the 2D pulse sequence. [5][6][7] Figure 1 shows two examples of COSY-DOSY pulse sequences. Any of these methods could in principle be implemented with spatial encoding of the indirect spectral dimension. In this implementation, diffusion and spatial encoding are fully separated. The use of a stimulated echo, however, results in a loss of half of the signal. Moreover STE pulse sequences usually need a long phase cycling, increasing the experimental time, although this may be circumvented with the Oneshot approach [24] or orthogonal coherence-selection gradients.

An alternative implementation of fast 3D DOSY is based on the iDOSY approach. The COSY-iDOSY sequence is appealing, as it is expected to be more sensitive and can help to observe signals for weakly coupled spins. [25] , The iDOSY method is however not suitable for every compound. Unlike in the stimulated echo approach, spins stay in the transverse plane during the entire diffusion delay; the method can thus be used as long as the T2 of the observed compounds stays small compared to the relaxation delay Δ. The pulse sequence for ufCOSY iDOSY is shown in Figure 2.b), based on the COSY-iDOSY pulse sequence of Ref. [7] . This pulse sequence will however face sensitivity problems, because of the long delay between the spatial-encoding step and acquisition. To avoid unnecessary signal losses during the diffusion delay, a better pulse sequence for ufCOSY-iDOSY is proposed (Figure 2

.c).

Placing the first diffusion gradient before the beginning of spatial encoding makes it possible to minimise the diffusion-losses due to spatial encoding.

The sequence of events found in the ufCOSY-iDOSY pulse sequences can potentially complicate the analysis of the diffusion decay of the peak volumes. The Stejskal-Tanner equation shown in Eq. [1] is only valid if the spin phase before the first diffusion-gradient pulse does not vary along the gradient axis, and if no further gradients are applied along that axis during the diffusion delay. In the two pulse sequences proposed for ufCOSY-iDOSY, if the axis for spatial encoding gradient is the same as that for diffusion-encoding, not only are these conditions not satisfied, but the modification to the Stejskal-Tanner equation is peak-dependent and difficult to calculate. The simplest way to circumvent this problem is to use orthogonal axes for spatial encoding and diffusion encoding, with the consequence that a triple-axis gradient probe is needed. To give meaningful results for iDOSY, the spatial encoding and the diffusion gradient pulses must be applied on orthogonal axes. For DOSY-ufCOSY, the diffusion gradients can be on any axis, giving similar results.

Note that the ufX-DOSY has not be studied here because of the signal losses that are expected if the diffusion delay happened after spatial encoding in the pulse sequence.

Results and Discussion

ufCOSY-DOSY

3D DOSY data were collected with the DOSY-ufCOSY and ufCOSY-iDOSY pulse sequences shown in Figure 2 on a test sample containing L-valine, propanol, ethanol and methanol at a concentration of 100 mM in D2O. Figure 3.a) shows the ufCOSY spectra of the DOSY-ufCOSY data set with the weakest diffusion gradient. A good-quality spectrum is obtained and regions can be delineated for DOSY processing. Not all peaks are detected and this is expected because of the constant-time nature of the experiments. [25] Similar results are obtained with the ufCOSY-iDOSY pulse sequence, with the notable difference that the signal-to-noise ratio is higher since the use of a stimulated echo is avoided. Differences also arise in the relative peak intensities, as in the conventional experiments, because of J-modulation during the added delay. Spatial encoding was performed here along the Zaxis. While good results are obtained for the DOSY-ufCOSY version with diffusion gradient along Z or X, diffusion-encoding along X was necessary to obtain meaningful results with COSY-iDOSY.

Figure 4 shows slices extracted from the reconstructed 3D spectrum for the DOSY-ufCOSY data set. The spectra for all the compounds are well separated, as in the conventional DOSY COSY experiments. A notable difference is that the data shown in Figure 4 was recorded in about 3 minutes, compared to 3 hours minimum for the conventional version.

The comparison between diffusion coefficients obtained with DOSY-ufCOSY and those obtained with the conventional sequence is shown in Figure 5 (blue crosses), for experiments carried out with a classic 5 mm NMR tube. The mixture's components are well separated and ordered in both cases. However, a clear systematic difference is observed between the measured diffusion coefficients obtained with the two experiments. This difference is largely due to the non-uniform gradient in our triple-axis-gradient probe -the field variation when a gradient pulse is applied is larger at the centre of the RF coil than at the edges. [26] Such gradient non-uniformity results in a subtle influence of the spatial apodisation process used in UF 2D NMR. Figure 6 shows the spatial profile obtained after 2D Fourier transformation of the rearranged UF data of the entire sample. Window multiplication by a Gaussian function is usually employed to increase signal to noise ratio and to decrease sinc wiggles in the spatially encoded spectral dimension. With nonluniform gradients, the estimated diffusion coefficient will depend on the wideness of the sample that is selected by spatial apodisation. This is illustrated in Figure 7, where the apparent diffusion coefficient is plotted as a function of the width of the window function. The measured values are found to converge for width of the window of 3 mm or less (the data shown in Figure 5 in blue correspond to a value of 3 mm for the width of the Gaussian window).

For the conventional DOSY-COSY experiment, the effect of non-uniform gradients can be reduced by using a susceptibilitymatched (Shigemi) tube with a restricted sample length. The experiment was thus repeated, with a sample length of 10 mm, selected because further reduction of the sample length did not change significantly the measured diffusion coefficient noticeably. An updated comparison of diffusion coefficients obtained with the conventional and UF COSY DOSY sequence is shown in Figure 5 (red crosses). The systematic deviation is largely reduced. Table 1 summarises the diffusion coefficient values obtained in conventional tube, Shigemi tube and with DOSY-ufCOSY with sigma = 3 mm). Overall, in this case the use of spatial encoding and spatial apodisation helps to reduce the systematic error due to gradient non uniformity.

uf DQS-DOSY

Another interesting 1 H homonuclear 2D experiment for mixture analysis is Double Quantum Spectroscopy (DQS). It has been shown to be useful for the analysis of complex samples such as biofluids [19,20] as it yields spectra that are less crowded than COSY ones. As in the case of COSY, two ways of writing the pulse sequence for 3D DQS-DOSY were used: DOSY-DQS and DQS-iDOSY (the pulse sequences are shown in Figure 8). In this case a triple-axis gradient probe is not mandatory since the spatial encoding and diffusion steps are separated (it would be needed in an alternative iDOSY approach with diffusion encoding of multiple-quantum coherences). However, it is still useful to avoid interferences between diffusion and coherenceselection gradients. For the DQS-iDOSY case, as in the conventional experiment, the choice of τ delay is more complicated than for the COSY. It has to be long enough to let signal decrease due to diffusion and be in the good range to build up anti-phase terms which will lead to double coherences. Unfortunately, because of the poor sensitivity of the method (due to decrease of the signal during diffusion delay and less efficient excitation of double quanta coherences), no spectra could be recorded on the 100 mM test sample. A more concentrated sample of ethanol and propanol was prepared (1 M). Figure 9a) shows the spectrum obtained with the weakest gradient for the ufDQS-iDOSY sequence on the new concentrated sample. On Figure 9b-c) are plotted the spectra of the two compounds separated thanks their diffusion coefficient. A similar separation is obtained with the DOSY-ufDQS approach, although again with reduced sensitivity due to the additional stimulated echo. Overall, while the principle of accelerating 3D DOSY with a spatial encoding of the chemical shift is also validated in the DQS case, sensitivity limitations turn out to be more significant in this case.

Spatial encoding of diffusion of chemical shifts?

3D DOSY can be accelerated by spatial encoding of either the diffusion or the indirect spectral dimension. While the latter is described here, the former was recently reported in Ref. [22] . (in particular, a figure analogous to Fig. 4, using SPEN COSY DOSY instead of ufCOSY-DOSY, may be found in Fig. 2 of Ref. 22). Both methods provide a decrease of the experiment duration by more than one order of magnitude. However, the duration and results for these two approaches are not identical. The first noticeable difference is the experiment duration. When the chemical-shift information is encoded spatially, the typical number of scans required for the complete experiment is of 16, corresponding to one scan per gradient value. When the diffusion information is encoded spatially, the typical number of scans is instead 64 or more. As a result, encoding chemical shifts spatially is 4 to 8 times shorter than encoding diffusion coefficients. Note however that this comparison assumes that magnetic-field gradients are use to perform CTP selection in a single scan. For the ufCOSY-iDOSY approach, this requires the use of triple-axis gradients. If phase cycling were used instead, the time advantage of spatially encoding chemical shifts would be lost.

One other difference between the two methods lies in the dimension (either the diffusion dimension or the indirect spectral dimension) for which resolution and accuracy are impacted by spatial encoding. With SPEN DOSY, both the trueness and precision of the diffusion information are impacted in the present implementation of the method. [22] For ufCOSY-iDOSY, the resolution and spectral width of the indirect spectral dimension are restricted, in a well-documented way. [27,28] The two experiments also have their spectral resolution in the direct dimension limited by the maximum acquisition time that can be achieved with classic high-resolution NMR hardware. In conventional experiment the only limit is the relaxation and the size of data, whereas in spatially encoded experiments the hardware is a limitation as the probe and the gradient amplifier cannot sustain the acquisition conditions for more than 100 ms usually, hence the loss in resolution in the temporal dimension compared to conventional experiments. Since the acquisition gradient intensity is lower in the SPEN DOSY COSY experiments than in the ufCOSY-iDOSY one, the former can include longer acquisition periods, leading to better resolution in the direct spectral dimension.

Spatial encoding of either the diffusion or the chemical-shift dimension also comes with a sensitivity penalty. In both cases, the signal-to-noise ratio per square root of total experiment time is predicted to decrease by a factor of √𝑀 , where M is the number of parallelised increment. Since M is larger for the ufCOSY-DOSY experiment than for the ufDOSY-COSY one, the sensitivity penalty is expected to be larger for the former. A more detailed comparison of the two approaches, included sensitivity aspects, is the topic of current investigations.

Conclusions

In summary, a fast method for 3D DOSY NMR analysis is reported here, combining the time-efficiency of ultrafast 2D NMR and the separation power of DOSY. For COSY DOSY, the concatenation and incorporation of diffusion-weighting gradients into a UF COSY experiments have been compared and the two approaches give a good separation of spectra. While the iDOSY implementation has a sensitivity advantage, it requires a tripleaxis gradient probe. The separation of UF DQS spectra has also been demonstrated but reaches the sensitivity limit of the method. Overall, 3D DOSY with a spatial encoding of the chemical shift will be useful for the time-limited analysis of mixtures.

Experimental Section

Samples

Two model mixtures of small molecules were prepared. The first mixture is composed of L-valine (7.2 mg), methanol (2.4 μL), ethanol (3.4 μL) and n-propanol (4.5 μL) solubilized in 590 μL of D2O. The solution was shaken until complete dissolution of valine and filtered to remove any solid particles. The concentration is near 100 mM for each compound. The second mixture is composed of ethanol (35 μL) and propanol (45 μL) solubilized in 520 μL of D2O. The concentration is near 1 M for each compound.

Spatially encoded experiments were carried out with standard 5 mm tube, while conventional DOSY experiments were carried out using a 5 mm Shigemi tube with a restricted sample length.

Experiments

All the experiments were carried out on a Bruker Avance III spectrometer operating at a 1 H Larmor frequency of 600.13 MHz and equipped with a room-temperature 5 mm TXI 1 H/ 13 C/ 15 N probe with triple-axis gradients. The intensity of gradients was calibrated along each axis using a Shigemi tube filled with doped water (1% H2O + 0.1 % CuSO4 in D2O) and a restricted sample length of 10 mm. The temperature inside the probe was calibrated with a standard methanol sample and then set to a value of 298 K with airflow of 535 L/h. All the experiments were done without sample rotation. Conventional 2D spectra were recorded using a stimulated echo sequence with bipolar gradient pulses (stebpgp1s Bruker sequence with additional lock stabilisation gradients).

For 3D SPEN experiments, conventional parameters for DOSY were used: a diffusion delay of 100 ms (Δ) and a duration of the encoding pulse (δ) of 1.5 ms on Z-axis and 2 ms on X-axis. For COSY-DOSY a the diffusion-encoding gradient values consisted of a linear ramp ranging from 0.1032 T/m to 0.5504 T/m with 16 increments when diffusion gradients were applied on Z-axis and from 0.0762 T/m to 0.4062 T/m when diffusion gradients were applied on X-axis. For DQS-DOSY the diffusion-encoding gradient values consisted of a linear ramp ranging from 0.0688 T/m to 0.5504 T/m with 8 increments when diffusion gradients were applied on Z-axis and from 0.0508 T/m to 0.4062 T/m when diffusion gradients were applied on X-axis For ufCOSY, an encoding gradient of 0.01121 T/m was used combined with a 15 ms chirp pulse with a 12 kHz bandwidth. Acquisition parameters were a 0.4816 T/m acquisition gradient strength with 128 gradient loops of 180 points each and a 0.767 μs dwell time. A recycle delay (D1) of 10 s, 2 dummy scans and 1 scans per gradient increment were used, resulting in an experimental time of 2 min 55s.

For ufDQS, an encoding gradient of 0.00516 T/m was used combined with a 15 ms chirp pulse with a 12 kHz bandwith. Acquisition parameters were a 0.4816 T/m acquisition gradient strength with 128 gradient loops of 180 points each and a 0.767 μs dwell time. A recycle delay (D1) of 10s, 2 dummy scans and 4 scans per gradient increment were used, resulting in an experimental time of 5min 49s.

Processing

All the data were processed using custom-written MATLAB processing programs, adapted in part from the DOSY ToolBox for the diffusion dimension. [29] Data processing is done in two steps. First, 2D spectra are reconstructed for each gradient increment. Second, 3D DOSY processing is applied to the list of 2D spectra.

The first step corresponds to the usual processing of UF 2D NMR data set. For each gradient increment, the data are rearranged into a 2D matrix and odd and even echoes are separated (only odd echoes were processed here for simplicity). Along the spatial dimension, the data is inverse Fourier transformed, apodised with a Gaussian window, zerofilled and Fourier transformed. Along the spectral dimension the data is apodised with a sine window, zero-filled and Fourier transformed. Magnitude spectra are used in all cases.

The second step corresponds to the usual processing of 3D DOSY data with magnitude spectra. Regions are defined on the spectrum obtained with the weakest diffusion gradient, and the diffusion-attenuated peak volumes are fitted with the Stejskal-Tanner equation to obtain a diffusion coefficient and a standard error for each peak. A 3D display is then constructed, with the diffusion dimension obtained by placing, for each selected spectral region, a Gaussian centred at the diffusion coefficient with a width determined by the statistics of the fit [29] . Figures show slices taken from such 3D displays.

Entry for the Table of Contents

Figure 1 :

 1 Figure 1: Pulse sequences for (a) DOSY-COSY and (b) COSY-iDOSY. For DOSY-X, the pulse sequence used for the DOSY part includes a longitudinal delay (LED) and bipolar gradient pulses. Black and white lines respectively represent 90° and 180° pulses. Diffusion gradients are represented in gray and coherence selection gradients in black.

Figure 2 .

 2 Figure 2.a) shows the proposed pulse sequence for DOSY-ufCOSY.In this implementation, diffusion and spatial encoding are fully separated. The use of a stimulated echo, however, results in a loss of half of the signal. Moreover STE pulse sequences usually need a long phase cycling, increasing the experimental time, although this may be circumvented with the Oneshot approach[24] or orthogonal coherence-selection gradients.

Figure 2 :

 2 Figure 2: Pulse sequences for (a) DOSY-ufCOSY, (b) ufCOSY-iDOSY (initially proposed) and (c) ufCOSY-iDOSY (final).To give meaningful results for iDOSY, the spatial encoding and the diffusion gradient pulses must be applied on orthogonal axes. For DOSY-ufCOSY, the diffusion gradients can be on any axis, giving similar results.

Figure 3 .

 3 b) shows the evolution of the peak volumes as a function of the gradient intensity. From this figure four distinct patterns can already be seen, allowing the separation of the four compounds. Note that the residual HOD is not seen on this figure as its signal is outside the detected spectral window.

Figure 3 :

 3 Figure 3: First slice of the DOSY-ufCOSY spectrum of a model mixture of short chain alcohols and an amino acid (corresponding to the first gradient increment) (a) and diffusion decay curves for all the peaks in the 2D COSY spectrum (b). Some peaks are missing in the spectra for valine because of J modulation. The signal at the low edge of the spectrum is an artefact. Diffusion gradient were along the Z-axis.

Figure 4 :

 4 Figure 4: 3D DOSY-ufCOSY of a model mixture of three short chain alcohols and an amino acid. (a)-(d) slices extracted from the 3D spectra. The name of the compound and the selected range of D in shown on each figure.

Table 1 :

 1 Comparison of diffusion coefficients obtained on the test sample with conventional DOSY in classic and Shigemi tube and with 3D DOSY-ufCOSY on a classic (unrestricted) tube. Each value here is calculated as the mean of the diffusion coefficient calculated for all signals of one compound. D.10 10 (m

Figure 5 :

 5 Figure 5: Comparison signal by signal between diffusion coefficients calculated from 3D DOSY-ufCOSY with 3D conventional DOSY-COSY in a classic NMR tube (blue) and in shigemi tube set with L = 10 mm (red). The diagonal line is shown as a guide to the eye..

Figure 6 :

 6 Figure 6: Spatial projection of the 2D spatial-spectral data set resulting from the first increment of the DOSY-ufCOSY experiment. The processing of UF NMR data involved multiplication by a window function in the spatial domain. Three Gaussian windows are shown here, for three values of the width: σ = 1 (red), 3 (yellow) and 7 (purple) mm.

Figure 7 :

 7 Figure 7: Estimated diffusion coefficients as a function of the spatial apodisation width (sigma) used for the processing of 3D DOSY-ufCOSY data, for a model mixture of short-chain alcohols and an amino acid.. The diffusion coefficients obtained from conventional DOSY with either a conventional tube (dashed lines) or a Shigemi tube set to 4 mm (dots) are displayed for comparison

Figure 8 :

 8 Figure 8: Pulse sequences for (a) DOSY-ufDQS and (b) ufDQS-iDOSY.

Figure 9 :

 9 Figure 9: 3D ufDQS-iDOSY on a concentrated mixture of alcohols sample. (a) ufDQS spectrum, (b)-(c) slice extracted from 3D spectra. The selected range of D in shown on each figure.

  (Please choose one layout) Layout 1: ARTICLE Spatial encoding of chemical shift has been used to accelerate 3D COSY-DOSY Corentin Jacquemmoz, Jean-Nicolas Dumez* Page No. -Page No. Title Layout 2: ARTICLE Author(s), Corresponding Author(s)* Page No. -Page No.

Acknowledgements

The authors thank Ludmilla Guduff for useful discussions. This research was supported by the Agence Nationale de la Recherche (ANR-16-CE29-0012).

Keywords: NMR • ultrafast • DOSY • 3D • spatial encoding


Jean-Nicolas Dumez

Perspective on long-lived nuclear spin states

Keywords: Relaxation, molecular dynamics, hyperpolarisation, diffusion, microstructure

This perspective article describes the concept of a long-lived nuclear spin state (LLS) and some of its applications. Classes of molecular environments for which nuclear spin order can be stored for extended periods of time are described, and applications to studies of molecular dynamics and interactions, diffusion NMR, and hyperpolarisation are presented. Some of the opportunities and challenges in the field are discussed.

Introduction

Nuclear spin relaxation is of prime importance in nuclear magnetic resonance (NMR) spectroscopy and imaging (MRI). The relaxation properties of nuclear spins, including longitudinal and transverse relaxation rate constants, cross-relaxation rate constants, etc, provide a rich source of information on molecular structure and dynamics, as well as on microscopic environments. Relaxation times are also a measure of the 'memory' of a nuclear spin system. In some contexts, short relaxation times are beneficial in order to, e.g. run closely spaced consecutive scans without inter-scan interferences.

In many cases, however, long relaxation times are desirable, to extend the timescales during which information may be stored with magnetic resonance. For an ensemble of uncoupled spins, the return to equilibrium of longitudinal magnetisation is the slowest relaxation process. As a result, the longitudinal relaxation time constant T 1 is often considered as the upper limit of the memory time of a spin system.

Long-lived nuclear spin order is a form of nuclear spin order that returns to equilibrium on a timescale that can be much longer that the longitudinal relaxation time constant T 1 . A 'long-lived state' (LLS) is the corresponding operator, of which the longlived spin order is the expectation value. LLSs were first described in 2004 by Levitt and co-workers for a pair of spins I = 1/2 [1,2]. LLSs have the potential to extend the timescales that can be accessed in a range of experiments such as diffusion-ordered or exchange NMR spectroscopy, microstructure analysis, or ex-situ hyperpolarisation.

Because their dependence on molecular dynamics and geometry is different from that of other relaxation parameters, LLS relaxation rate constants also provide a new class of NMR-based probes. All of these ideas have been explored over the past 15 years, and long-lived states have turned into an active area of research. The use of long-lived states in NMR spectroscopy and imaging presents many opportunities, such as novel approaches to ligand binding assays or hyperpolarised molecular imaging. Important challenges also remain for a move beyond proof-of-concept applications, such as the design or discovery of a molecule that simultaneously bears a LLS and is compatible with the process of interest.

In this perspective, the concept of long-lived states is first described, together with several generations of molecular structure that have been found or designed to bear long-lived states, and the corresponding NMR experiments. The use of LLS relaxation properties as a probe of structure and dynamics, and as a source of contrast is then described. Applications of LLS to store information on extended timescales are also detailed. Finally, some of the routes that are currently explored to expand the scope of LLS experiments are discussed.

2. What are long-lived states?

Definition and existence

Long-lived nuclear spin order may be defined as a distribution of spin populations that returns to its equilibrium value on a timescale that is longer than that for the relaxation of longitudinal magnetisation (quantified by the longitudinal relaxation time constant T 1 ) [3]. It typically corresponds to population differences between manifolds of spin energy levels with different symmetry properties. The prototypical long-lived spin order concerns pairs of nuclear spins of spin quantum number I = 1/2, and consists of the difference between the population of the singlet state

|S 0 = |αβ -|βα √ 2 , (1)
and the average population of the three triplet states:

|T +1 = |αα , (2)
|T 0 = |αβ +|βα √ 2 , |T -1 = |ββ .
While the singlet state is antisymmetric with respect to permutation of the two spins, the triplet states are symmetric. This population difference is also called 'singlet order' or 'triplet-singlet imbalance'. The corresponding energy level diagram is shown in Fig. 1a for a pair of magnetically equivalent spins.

[Figure 1 about here.]

As is generally the case in NMR relaxation theory, the relaxation behaviour of LLSs is more conveniently described by first distinguishing the coherent spin interactions, that are identical for all the members of the ensemble, from the fluctuating spin interactions [4,5,6]. In high-resolution solution-state NMR, the former comprise the isotropic chemical shift and J coupling interactions, while the latter include the dipole-dipole, chemical shift anisotropy (CSA), quadrupolar and spin-rotation inter-actions.

Long-lived states exist when transitions under the effect of the fluctuating Hamiltonian are forbidden between manifolds of spin energy levels, or occur at a reduced rate. For example, singlet order for two spins 1 and 2 is not affected by the fluctuating intra-pair dipole dipole coupling H DD 12 (t), because H DD 12 is itself symmetric with respect to permutation of the two spins [2,1,3]. Since H DD 12 (t) is the main relaxation mechanism for longitudinal magnetisation, the relaxation of singlet order can in comparison be greatly reduced. On the other hand, relaxation due to the dipole-dipole interaction with a third spin is attenuated for singlet order, not suppressed, to an extent that depends on geometry [4].

The relaxation properties of long-lived states have been thoroughly characterised [7,8,10,11,[START_REF] Levitt | Encycl. Magn. Reson[END_REF]4,[START_REF] Tayler | [END_REF]3,5,6,14,15,16], with two main objectives. First, the understanding of LLS relaxation makes it possible to design molecules that are expected to display states that are exceptionally long-lived. This has recently led to the synthesis of a molecular scaffold with a central pair or 13 C spins, for which the singlet lifetime is longer than one hour [6]. In some cases, such as methyl groups [5], internal motion was found to play an important role in the properties of the long-lived state, and the observed LLS lifetime sometimes cannot be explained by considering a rigid molecule [17].

Second, establishing quantitative relations between LLS relaxation rate constants, and structural and dynamical properties, makes it possible to use LLS relaxation rate constants as new ways to probe the structure and dynamics of molecules [8,[START_REF] Tayler | [END_REF].

Interestingly, because the relaxation mechanisms that are mainly responsible for T 1 are ineffective for long-lived states, the description of LLS relaxation requires accounting for interactions, such as the antisymmetric CSA or spin rotation [6], that are typically neglected in NMR relaxation studies.

Overall, the dependence of LLS relaxation properties on the geometry of spin interactions and molecular dynamics is complex, and in many cases population imbalances between spin-state manifolds of different symmetry return to their equilibrium value on a timescale that is shorter than that of longitudinal relaxation (i.e., T LLS < T 1 ).

Access and leakage

The possibility to manipulate long-lived states experimentally is determined by coherent spin interactions. There are, however, conflicting requirements for the possibility to 'access' long-lived states using pulse sequences, and the degree of 'isolation' of these states at high magnetic fields. These conflicting requirements have led to several generations of LLS-bearing molecules or molecular fragments. The mathematical aspects of coherent manipulations of LLS in several regimes (strong chemical inequivalence, weak chemical inequivalence, chemical equivalence and magnetic inequivalence) and of the associated pulse sequences have been described by Pileio [9] and Levitt [3] and only the results will be summarised here.

The first demonstration of the existence of long-lived states involved a pair of 1 H spins with a difference in chemical-shift frequency offsets much larger than their mutual J coupling in the field of a high-resolution NMR magnet [2,1]. The corresponding energy level diagram is shown in Fig. 1b. In this case of large chemical inequivalence, while singlet order is still immune to the relaxation caused by the intra-pair dipoledipole interaction, the singlet and triplet states are not eigenstates of the coherent Hamiltonian. This property has the important consequence that free evolution under the effect of the coherent Hamiltonian at high field interconverts singlet order and other multi-spin terms. On the one hand, this provides a convenient route to generate singlet order. On the other hand, it also means that additional measures are required to lock the system in its singlet state: while singlet order may be long-lived, the other multi-spin terms into which it coherently evolves are not, and spin order is overall lost through fast relaxation of the latter [4]. Two solutions were proposed by Levitt and co-workers to prevent coherent evolution of singlet order. The first solution consists of applying a continuous radio-frequency pulse of sufficient intensity to suppress the coherent evolution [2]. This scheme makes it possible to carry out experiments entirely at high field, but it is demanding on hardware as it requires unusually long spin-locking field, of up to several minutes. The second solution consists of shuttling the sample from the high magnetic field region, where a precursor state is prepared, to a low magnetic field region, where the difference in chemical-shift frequency offsets is much smaller than the J coupling [1]. This also suppresses the coherent evolution of singlet order. This approach however requires a setup that makes it possible to move the sample out of the high field region sufficiently fast.

A breakthrough in the development of LLS was the introduction of pulse sequences to convert magnetisation into singlet order for nuclear spin pairs with differences in chemical-shift frequency offsets that are much smaller, at high field, than their mutual J coupling (so-called 'nearly chemically equivalent' spin pairs) [START_REF] Pileio | Proc. Natl. Acad. Sci[END_REF]. The first, dubbed M2S (Magnetisation to Singlet), relies on trains of J-synchronised 180 • pulses to reintroduce singlet-triplet transitions [START_REF] Pileio | Proc. Natl. Acad. Sci[END_REF]. While the method was first developed for audio-frequency pulse sequence for low field conversion, it also made it possible to prepare singlet order at high field for spin pairs that then do not require a spin-lock field or sample shuttling to be long-lived [START_REF] Tayler | [END_REF]20]. Fig. 2 shows the corresponding pulse sequence diagram. Near-chemical-equivalence largely protects singlet order from coherent evolution into fast relaxing terms. While the application of a spin lock field can still extend the singlet lifetime, it does so only to a modest extent [START_REF] Tayler | [END_REF]. Other pulses sequences such as Spin-Lock Induced Crossing (SLIC) [21], based on a weak continuous irradiation, and frequency-swept versions [22,23] were also introduced to convert magnetisation to singlet order for these systems. The M2S and SLIC sequences can also be used to prepare long-lived multi-spin states for pairs of chemically equivalent but magnetically inequivalent spins [24,17,25,26] [Figure 2

about here.]

Long-lived states also exists for groups of nuclear spins that are both magnetically and chemically equivalent [27,28,29,5,30]. In this case, however, pulse sequences cannot be used to drive the conversion between magnetisation and LLS. A long-lived state may still be significantly populated with hyperpolarisation schemes such as dynamic nuclear polarisation [27,29,30,31], or quantum-rotor induced polarisation [32,28,5].

While the LLS is NMR silent, it can be turned into population differences across observable transitions by a chemical reaction [27,29], or by cross relaxation due to an external nuclear spins [28,5,30,31]. These preparation and conversion mechanisms have been demonstrated experimentally, but they provide less control than coherent manipulations and have been less exploited so far.

Probing molecular properties

The measurement of relaxation rate constants by NMR spectroscopy provides access to quantitative information on the structure and dynamics of molecules in solution.

For the analysis of complex solution mixtures and semi-solid samples, and for in vivo localised spectroscopy, relaxation mechanisms are used as a source of contrast to separate molecules of interest from background signals. Different relaxation rate constants encode different properties, and for this reason the relaxation properties of long-lived nuclear spin states can provide a new window on structure and dynamics, and provide new types of filters. Proof-of-principle experiments have been reported in all of these areas.

Singlet relaxation has been used as a probe of the interaction between smallmolecule ligands and proteins [33,34,35]. These studies used singlet states of the ligand, formed by pairs of chemically inequivalent spins, that require continuous RFbased spin locking to be long-lived at high field. Salvi et al. showed that the LLS relaxation time constant T LLS provides very good contrast between the free and bound form of the ligand, because small changes in chemical shifts, such as those induced by the ligand-protein interaction, have a significant effect on the efficiency with which spin locking prevents LLS leakage [33]. This contrast was used to detect weakly binding ligands in a fragment-based drug design approach. Since not all possible ligands have a suitable spin pair to form a long-lived state, ligand binding analyses were carried out using competition assay, or LLS-bearing molecular tags [34]. Fig. 3 shows the example identification of a weak binder in a mixture using a competition assay.

[Figure 3 about here.] Singlet states have also been used in methods to retrieve the signals of selected molecules from a complex background. DeVience et al. described a pulse sequence to select signals from a specific singlet-forming pair of coupled spins, such as geminal protons in N-aspartic acid (NAA) and suppress other proton signals. Singlet order is prepared with sequence of pulses, sustained with a continuous spin lock, and converted back to magnetisation [36]. Selectivity with respect to 1 H spins that do not form singlet states is obtained because terms other than singlet-order are saturated during the spin lock, and also filtered out by phase cycling. Selectivity among different singlet-forming spin pairs is achieved by choosing the parameters of the conversion pulse sequence to be more effective for the spin pair of interest. An improved implementation of this concept was described by Ivanov and co-workers, using a magnetisation to singlet conversion pulse sequence based on an adiabatic sweep, which led to an improved contrast between the selected singlet-forming 1 H pair and the suppressed background [37,38]. Singh et al. have proposed to use singlet relaxation as a tool for spectral editing in mixtures [39].

The dependence of singlet relaxation rate constants on geometry has been exploited to probe the relative orientation of CSA tensors as well as torsional angles in a small molecules [8,40]. The relaxation time constant T S of singlet order for a pair of spins 1 and 2 caused by an interaction H λ (t) depends on the degree of correlation between the fluctuations of H λ 1 and H λ 2 . For example, relaxation due to the CSA interaction depends on the angle between the two CSA tensors σ aniso 1 and σ aniso 2 . This property was used by Ahuja et al. to probe the relative orientation of 1 H CSA tensors in substituted benzene rings [8]. On the other hand, the contribution to T S caused by the dipole-dipole interaction with a third spin 3 depends on the angles between the internuclear vector r 13 and r 23 . By measuring T S for a spin pair whose singlet relaxation is dominated by a single neighbouring proton, and assuming fixed bond length and angles, Tayler et al. showed that torsional angle around the C β /C γ bond could be measured for a phenylalanine derivative [40].

Accessing longer timescales

For experiments that consist of multiple consecutive scans, be it for signal averaging, additional dimensions or monitoring, the relaxation rate constant of longitudinal magnetisation is often found to be longer than what the experimenter would wish. This results in inter-scan delays that account for most of the experiments' duration, and drives the design of an array of strategies to effectively increase relaxation rate constants. On the other hand, there exists a vast range of NMR experiments where longitudinal magnetisation is used for storage. This includes storage of the labelling of the spins' position or chemical-shift in the form of an amplitude modulation, and storage of enhanced spin order prepared by hyperpolarisation methods. In these cases, longitudinal relaxation sets the upper limit for the timescale over which information may be encoded. By using instead long-lived nuclear spin states for storage, longer timescales may in principle be accessed.

Storage of position and chemical-shift information

Using magnetic-field gradients, information about the spins' position in space can be encoded as a phase or amplitude modulation. In diffusion NMR experiments, position encoding and decoding steps are separated by a delay, and changes in the spins' position during the delay results in an attenuation that can be modelled to estimate translational diffusion coefficients. For free diffusion, the minimum spatial scale of translational diffusion that can be characterised is determined by the maximum gradient area that can be achieved, and by the duration of the diffusion delay. While the former is dictated by hardware limitations, the latter is, in classic diffusion experiments, limited by longitudinal relaxation. Using singlet order instead of longitudinal magnetisation for storage, Bodenhausen and co-workers have shown that longer diffusion delays could be used in diffusion NMR experiments [41]. As a result, diffusion coefficients were measured for a biomolecule, ubiquitin, using a reduced range of gradient areas [42].

Long-lived states have also been used in diffusion NMR experiments designed to characterise the microstructure of materials. Such experiments require storage delays that are sufficiently long for molecules to experience a restricted translational diffusion.

For example, for a molecule with a given diffusion coefficient, probing the size of larger pores requires longer diffusion delays. Price and co-workers have shown, using the singlet state formed by a proton pair in 2,3-dibromothiophene, that longer diffusion delays could be used, in order to probe the size of larger pores [43,44]. Pileio and coworkers further increased the accessible spatial scale by using singlet states for pairs of nearly-equivalent spins, with lifetimes of several minutes, to probe pores of up to 2 mm [45]. The diffusion-encoding gradients were embedded in the M2S pulse sequence.

They also showed that 'singlet-assisted diffusion' experiments also help to characterise higher-order microstructural features such as tortuosity [46].

An alternative approach to encode position information is to use spatially selective manipulations of the spins. With this objective, Pileio and co-workers have designed a spatially selective version of the M2S and S2M pulse sequences, in which hard pulses are replaced by combinations of soft pulses and magnetic-field gradient.

The selS2M sequence was used in phantom experiments to label a slice of a solutions of molecules with pairs of nearly equivalent 1 H or 13 C spins, and monitor either diffusion or flow in direct rather than reciprocal space, as illustrated in Fig. 4 [47].

[Figure 4 about here.]

In two-dimensional correlation experiments, it is the spins' chemical-shift in the indirect dimension that is encoded as a phase or amplitude modulation. In experiments for the characterisation of chemical exchange (EXSY) and cross relaxation (NOESY), this information is stored as longitudinal magnetisation, and this sets a limit to the duration of the relaxation or exchange delay. In EXSY, this in turns determines the range of exchange rate constants that can be measured accurately, with slower exchange processes requiring longer delays. Bodenhausen and co-workers have shown that the encoding of chemical sites could instead be stored with singlet order, using modified EXSY pulse sequences [48]. This required pulse sequence elements for the conversion from magnetisation to singlet order that are broadband with respect to sum and difference chemical-shift for the spin pairs and to their J coupling. The SS-EXSY was used to monitor slow conformational exchange in a partly deuterated saccharide.

Storage of hyperpolarised spin order

The maximum timescale during which spin order can be stored is a particularly important concern in the field of hyperpolarised magnetic resonance. Hyperpolarisation consists of increasing population differences between nuclear spin energy levels much beyond their thermal equilibrium values, in order to increase the sensitivity of NMR experiments. Currently, for solution-state and in vivo NMR, the most commonly used hyperpolarisation schemes involve an irreversible step: enhanced spin order is prepared only once and subsequently decays. When hyperpolarised spin order is kept in the form of longitudinal magnetisation, longitudinal relaxation again sets an upper limit on the time scale during which this order, and the corresponding signal, remains available. This limitation is particularly important for applications of hyperpolarisation to the monitoring of time-dependent processes. Long-lived states have the potential to increase significantly the timescales accessible in hyperpolarised magnetic resonance, and this was recognised already when their existence was first reported by Levitt and co-workers [1].

Dissolution dynamic nuclear polarisation

In dissolution dynamic nuclear polarisation (D-DNP), hyperpolarised substrates are first prepared by DNP in the solid state, then rapidly dissolved with a hot solvent and transferred to a solution-state NMR spectrometer or an MRI scanner for detection [START_REF] Ardenkjaer-Larsen | Proc. Natl. Acad. Sci[END_REF].

For the DNP step, the most common approach consists of: i/ mixing the substrates and radical-bearing molecules in a glass-forming solvent, ii/ placing the sample at a temperature of 1.1 to 4.2 K and a magnetic field of 3 to 10 T; iii/ irradiating the sample with microwave to build up nuclear polarisation [START_REF] Bornet | [END_REF]51]. While the combined effects of DNP and a temperature jump can result in signal enhancements of over 10 4 , the enhanced spin order decays irreversibly after dissolution and the timescales that can be probed with DNP-hyperpolarised substrates are limited by longitudinal relaxation .

The possibility to store DNP-enhanced spin order using long-lived nuclear spin states was first demonstrated by Bodenhausen and co-workers, who transferred DNPenhanced 13 C magnetisation to 1 H singlet order in the dipeptide Ala-Gly at high field, where the LLS was sustained with an RF spin lock [START_REF] Vasos | Proc. Natl. Acad. Sci[END_REF]. The experiment was later improved by directly preparing 1 H magnetisation with DNP, and shuttling the sample in a low field region during the storage delay, using the 1 H pair of 3-bromothiophene-2-carboxylic acid [START_REF] Bornet | [END_REF]54]. As explained in section 2.2, singlet order can be preserved for extended periods of time at high magnetic fields with no need for an RF spin lock in the case of pairs of nearly chemically equivalent spins. Pileio et al. have shown using the M2S/S2M pulse sequences for back-and-forth conversion between magnetisation and singlet order, that DNP-enhanced spin order could be stored for over 30 min using pairs of nearly equivalent 13 C spins [55]. They also demonstrated the acquisition of MR images on a pre-clinical scanner.

A possible route to prepare hyperpolarised singlet order, used in the examples described so far, consists of preparing enhanced magnetisation (single-spin longitudinal order) with D-DNP, then converting it to singlet order using a pulse sequence in the high-field NMR or MRI system. An alternative, more direct route consists of exploiting the fact that when very high polarisation levels are achieved by DNP, an appreciable level of singlet order is also generated (the level of singlet order is given by -p 2 /3, where p is the polarisation level). This was first shown by Tayler et al., with doubly 13 Clabelled pyruvic acid [56]. For this system there exists a large chemical-shift difference between the two 13 C spins, and the use of direct singlet preparation scheme makes it possible to avoid the need for pulse-sequence based conversion at high-field, where an RF irradiation would then be necessary to sustain the long-lived state.

The direct enhancement of singlet order is also possible for pairs of nearly chemically equivalent spins, as shown by Elliott et al. , who used D-DNP to prepare hyperpolarised singlet order in monodeuterated methyl groups, selected to have a chemicalshift difference between the two protons of the methyl group that is simultaneously much smaller than the intra-pair J coupling, and large enough to be able to drive the conversion between magnetisation and singlet order with an RF pulse sequence [57]. As already referred to in section 2.2, the direct hyperpolarisation of long-lived states is also particularly useful in the case of systems of equivalent spins, for which no pulse-sequence based conversion is possible [29,30,31]. This is illustrated in Fig. 5 with the DNP-based preparation of a long-lived state in methyl groups. In this case, A 1 H long-lived state is populated by DNP in the solid state, and yields population differences across observable transitions (for both 1 H and 13 C) by cross-relaxation in solution.

[Figure 5 about here.]

Parahydrogen-based hyperpolarisation

Hyperpolarised spin order can be prepared efficiently and with comparatively simple instrumentation for dihydrogen gas. Dihydrogen exists as two spin isomers, ortho and para, corresponding to the three symmetric (triplet) states and the antisymmetric (singlet) state of the spin pair. The existence of spin isomers is due to the Pauli principle and is only observed for small and highly symmetric molecules. For dihydrogen, the ortho and para forms interconvert efficiently when the gas is in contact with a paramagnetic solid, but an out-of-equilibrium ortho/para distribution can otherwise be retained for several days. At room temperature, the four energy levels are nearly equally populated, resulting in a 75:25 ortho:para distribution. 'Para-hydrogen gas' (dihydrogen gas with a non equilibrium ortho:para distribution) is prepared by flowing dihydrogen gas at temperatures of 20 to 80 K, in the presence of a paramagnetic solid particles. Parahydrogen may be seen as a reservoir of long-lived singlet order.

While parahydrogen is NMR silent and is unaffected by pulse sequences, its spin order can be released by a chemical addition. The addition is either directly onto a substrate of interest [58] (the PHIP mechanism, parahydrogen induced polarisation), in which case the enhanced spin order on the substrate is not renewable, or onto a metal centre on which a substrate is bound reversibly, in which case through-bond spin order transfer to the substrate spins can occur multiple times over several complex formations [59] (the SABRE mechanism, signal amplification by reversible exchange).

The connection between PHIP and long-lived states was illustrated experimentally in 2006 by Jonischkeit et al., who measured effective relaxation times at high and low field for the hydrogenation of symmetrically and asymmetrically substituted alkynes [60]. Several other asymmetrically substituted alkynes and alkenes have been hydrogenated with parahydrogen to prepare singlet states that are long-lived at low field. In particular, the hydrogenation of propene into hyperpolarised propane gas could potentially be used for low-field MRI of the lungs [61]. The hydrogenation of symmetric molecules, such that the two protons from parahydrogen remain chemically equivalent in the product molecule, has the advantage that singlet order for the 1 H pair remains long-lived at high magnetic field after the chemical addition, as illustrated by Franzoni et al. [62]. In that case, several strategies have been reported to generate observable signals from the parahydrogen-derived singlet order. These include, in the case of magnetically inequivalent spins, the conversion from singlet order to magnetisation for the 1 H pair, with pulse sequences that exploit difference in J coupling with other spins [63,64]. Jerschow and co-workers have also shown that a chemical reaction could be used to lift the chemical equivalence of the two protons [65]. Interestingly, pulse sequences for the conversion from singlet order to homonuclear magnetisation for pairs of nearly-chemically-equivalent spins can also be used, with little to no modification, to convert singlet order to heteronuclear magnetisation, in cases when the difference in J couplings with the heteronucleus is much smaller than the intra-pair coupling [66,67]. This was used to hyperpolarise 13 C spins at high field after addition of parahydrogen. While the release of singlet order by a chemical addition and its conversion to observable magnetisation predate the introduction of the concept of long-lived states, the LLS methodology has increased the range of chemical systems that can be addressed, with efficient conversion sequences for pairs near-equivalent spins, as well as sequences to prepare 13 C magnetisation from 1 H singlet order.

Long-lived states have also been used to store hyperpolarised spin order derived from parahydrogen with the SABRE approach. Also in this case, singlet order can be prepared from SABRE enhanced magnetisation with an RF pulse sequence at high field, as shown by Roy et al. [68,69]. They used pairs of chemically inequivalent spins in, e.g., nicotinamide [68], and pairs of chemically nearly equivalent spins, in pyridazine derivatives [69]. With partial deuteration of the substrate, the resulting hyperpolarised long-lived spin orders can be stored for several minutes at low field. The SABRE process can also be exploited to generate singlet order directly for pairs of heteronuclear spins. This was demonstrated by Theis et al., with molecules that bear doubly 15 Nlabelled diazirine tags [70]. They showed that in this case the polarisation transfer condition is field independent as long as the nitrogens are chemically equivalent, and that long-lived singlet order for the 15 N pair can have a lifetime of over 20 min at 3 G. Since the two nitrogen are chemically inequivalent at high field, an enhanced anti phase doublet is obtained upon 90 • excitation after transfer to the detection magnet. Fig. 6 shows the result of a SABRE experiment on a 15 N 2 -diazirine. Note that while the SABRE process, in contrast to PHIP and D-DNP, can be implemented as a multi-shot experiment, storage of SABRE-enhanced spin order is still relevant for a variety of proposed applications such as in vivo molecular imaging, which would require separating the hyperpolarised substrate from the SABRE catalyst.

[Figure 6 about here.]

Discussion

Long-lived nuclear spin states were first described in 2004 [1]. In the original publication of Levitt and co-workers, applications to the storage of spin order for flow, diffusion and hyperpolarisation experiments were already envisioned. Several proof-ofconcepts experiments have now been demonstrated in all of these areas. In parallel, the LLS theory and methodology have expanded and led to a much broader scope of chemical systems and experimental conditions for which timescales may be extended using long-lived states. The translation of these developments to the applications proposed so far in (bio)chemistry and biomedicine will depend on the possibility to find or design compounds that combine: i/ a chemical structure that is compatible with the chemical environment and/or reaction of interest, and, ii/ a long-lived state with a significantly enhanced lifetime in realistic experimental conditions.

Several routes are being explored, which may lead to molecules that would be used beyond proof-of-concept experiments. The longest LLS relaxation time constants so far have been measured for pairs of nearly chemically equivalent spins, in molecules designed such that known mechanisms for LLS relaxation would be minimised. These 'designer molecules', such as doubly 13 C-labelled oxalates with T S values of more than 1 hour [14], are in addition chosen to be easily functionalised, and may thus be further modified to be water-soluble, or to achieve molecular sensing. A remaining challenge for these molecules is to design molecular scaffolds that also minimise the contribution of paramagnetic dissolved dioxygen to LLS relaxation.

Conversely, a variety of chemical moieties or molecular fragments have been identified as potential molecular tags, that can be attached to a molecule of interest [35,71,70]. This approach has however so far involved pairs of spins with a difference in chemical shift that is too large for singlet order to be long-lived at high magnetic field in the absence of RF spin locking. While this was used as an advantage to probe protein ligand interactions [35], it is a limitation when LLS are used to store spin order, since long RF irradiation may not always be possible because of hardware-or sample-related limitations. For these systems, the possibility to prepare singlet order directly by hyperpolarisation methods, based on either DNP or parahydrogen [60,56], is particularly useful, as it circumvents the high-field RF-pulse-based conversion from magnetisation to singlet order. Molecular tags with pairs of near equivalent spins would be particularly useful to explore in vivo applications of long-lived states.

Hyperpolarised spin order in systems of magnetically equivalent spins, such as CH 2 groups or methyl groups [30,28], also has the advantage that it can be prepared in the vast number of molecules that include these chemical moieties. However, the cross-relaxation process that is needed to generate population differences across observable transitions from the silent LLS provides little control, and also limits the lifetime that may be achieved. In addition, fast internal motion or a highly anisotropic overall tumbling is then required for the LLS to relax significantly more slowly than longitudinal magnetisation [31].

A general challenge for the use of long-lived states to store hyperpolarise singlet order is the fact that the LLS concept intrinsically involves multiple spins. A pair of spins I = 1/2 is needed to form a singlet state, and, in the case of chemically equivalent spins, neighbouring spins are needed to lift the magnetic equivalence. For some compounds, while the singlet order of a 1 H or 13 C spin pair may be significantly longer lived than the longitudinal magnetisation of the same spin system, the increase in lifetime can be less dramatic when compared to the T 1 value of a singly-13 C-labelled compound [72]. Also, molecular platforms have been described in which nitrogen-15 spins have T 1 values of more than 10 min at high field [73].

Perhaps the most directly useful case concerns compounds that happen to have pairs of chemically equivalent and a small degree of magnetic inequivalence. For such systems singlet order can be efficiently converted to and from magnetisation -which can be heteronuclear magnetisation, and no RF spin lock is needed for singlet order to be long-lived at high field. Examples are [1-13 C]fumarate and dimethylmaleate, which can be hyperpolarised with the PHIP method [62,67].

For applications that use T S measurements as a probe of structure, dynamics and interactions, the challenge is also to find a suitable spin system to prepare singletorder. From that point of view, the use of competitive binding assays is an interesting opportunity, as it relaxes the requirement to finding just one ligand with a long-lived state.

In summary, the initial idea of "extending the memory of nuclear spins [. . . ] well beyond the T 1 limit" has led to a wealth of new concepts in nuclear spin relaxation, and applications in NMR spectroscopy and imaging. Recent development in the field show that there is steady progress towards the design of molecules that will unlock the potential of long-lived nuclear spin states.

Figure 1 .

 1 Figure 1. Energy level diagram for a a pair of magnetically equivalent spins I = 1/2 and a a pair of chemically inequivalent spins I = 1/2.

Figure 2 .

 2 Figure 2. The 'Magnetisation-to-Singlet' (M2S) RF pulse sequence. Reproduced with permission from Refs [19]

Figure 3 .

 3 Figure 3. Identification of a weak binder in a mixture. 1) Weak LLS signals of the spy ligand after sustaining the LLS for ∆ = 2.5 s in the absence of a competing binder in mixture 1 (spy ligand [II] = 500 µM with K D = 790 µM protein [Hsp90]=2.5 µM and three nonbinding ligands: 600 µM tyrosine, 600 µM 3,4difluorobenzylamine, and 600 µM 4-trifluoromethylbenzamidine). 2) Enhanced LLS signals in the presence of a weak binder (mixture 2 contains 600 µM of the weakly binding ligand [V] 3-bromo-5-methylpyridin-2-ylamine (K D = 2.2 mM), instead of 600 µM of the nonbinding ligand 3,4-difluorobenzylamine). 3) LLS signals observed in the presence of only the binding fragment (mixture 3 contains 500 µM spy ligand [II], 2.5 µM protein [Hsp90],and 600 µM of the weakly binding ligand [V] 3-bromo-5-methylpyridin-2-ylamine). 4) Conventional 1 H NMR spectrum of mixture 2. Reproduced with permission from Refs[34]

Figure 4 .Figure 5 .Figure 6 .

 456 Figure 4. (a0) axial RARE image of a 5 mm OD (4.2 mm ID) NMR tube containing a degassed 1 M solution of 1-(Ethyl-d 5 ) 4-(propyl-d 7 )(Z)-but-2-enedioate in CD 3 CN. (a1?a5) Real space imaging of macroscopic diffusion obtained by pulse sequence in Fig. 2 of Ref. [47]. The value of the diffusion interval τ is indicated. FOV = 20 × 20mm 2 , matrix size= 64 × 64, sagittal slice thickness = 0.9 mm, axial slice thickness = 15 mm, TE = 8.7 ms, acceleration factor 64.(b1?b5) Simulation of diffusion in a 5 mm OD NMR tube using a random walk model, a diffusion constant of 1.6×10 -9 m 2 s -1 and all other parameters as used in the experiment. Reproduced with permission from Ref.[47]

E-mail: jean-nicolas.dumez@univ-nantes.fr

Acknowledgement(s)

I am very grateful to many colleagues for discussions on long-lived nuclear spin states.

References References