On the potential of Fourier-encoded saturation transfers for sensitizing solid-state magic-angle spinning NMR experiments

Chemical exchange saturation transfer (CEST) is a widely used technique for enhancing the sensitivity of liquid-state nuclear magnetic resonance (NMR) spectra;^1–7 its main applications involve the magnified detection of metabolites and bio-macromolecules in vivo,^8–13 the detection of “invisible” states in high-resolution biomolecular NMR,^14–18 studies of exchange and enzymatic phenomena in vitro,^19–22 and NMR enhancements of hyperpolarized substrates.^23–25 CEST involves selectively saturating weak NMR resonances of labile or otherwise interconverting sites and then relying on chemical exchange processes to transfer this site-selective saturation onto a much stronger NMR resonance. By leveraging the fact that the rate k_exch of this exchange process can be much faster than the longitudinal relaxation rate 1/T₁ of the receiving pool, which is ultimately excited and detected, this saturation-transfer principle can lead to very large sensitivity enhancements on the order of k_exch^.T₁. Consequently, when discussing CEST experiments, it is useful to classify the chemical exchanging spin system into two distinct pools based on their relative populations and on their overall NMR receptivity. Spins giving NMR signals that are of interest, but are weak as a result from low natural abundance, small gyromagnetic ratios, low concentrations, and/or combinations of all these, constitute what we will call the magnetically dilute spin pool. This will, in turn, exchange information with the magnetically abundant spin pool, a highly populated and easier to detect reservoir (such as the protons in water). Given the ease and robustness with which CEST can be implemented, and the large gains in sensitivity that it can provide, CEST has since been exploited in the above-mentioned variety of liquid-state and in vivo NMR scenarios, providing a wealth of information pertaining to structure and dynamics.

As originally introduced, CEST is a continuous wave (cw), frequency-domain experiment targeting what is usually a peak of interest whose resonance frequency is a priori known. Frequency Labeled EXchange (FLEX)^26,27 endows CEST with the broadbandness associated with time-domain experiments. In FLEX, the resonances of the dilute pool are not saturated, but rather amplitude-modulated by a pair of selective excitation/storage pulses that avoid perturbing the abundant spin reservoir. These pulses are separated by a t₁ delay that is incremented in a normal 2D NMR fashion²⁸ but which, unlike conventional 2D NMR, is looped multiple times before the final observation. This allows the chemical exchange process to transfer the t₁ information onto the abundant reservoir as a magnified amplitude modulation that grows with the number of loops; applying an observation pulse on the abundant reservoir then enables, after Fourier transform (FT) vs t₁, the detection of the dilute pool NMR spectrum with an increased CEST-like sensitivity. By departing from the original cw saturation scheme, FLEX provides this experiment with additional flexibility. Recently, for example, sensitivity-enhanced solution-state NMR pulse sequences have been developed that exploit this approach for increasing not only the signal-to-noise ratio (SNR) of labile protons but also the SNR of non-labile (e.g., aliphatic) protons^29,30 and non-labile heteronuclei (¹³C, ¹⁵N)^26,27 for a variety of systems including carbohydrates, amino acids, and intrinsically disordered proteins. Some of these experiments also depart from traditional CW CEST approaches in that following the t₁ time-domain encoding, they rely not only on chemical exchange but also on coherent (e.g., TOCSY and INEPT) polarization transfer segments to achieve their substantial signal enhancements in either homonuclear or heteronuclear systems, starting from either labile or non-labile spins.³⁰ Inspired by these solution-state RElayed-FLEX (REFLEX) sequences,^27,29–31 we herein explore and test a protocol for implementing conceptually similar experiments, but aimed at acquiring NMR spectra from solid samples undergoing magic-angle spinning (MAS) and heteronuclear decoupling. As in the solution-state REFLEX counterparts, the aim of these methods will be to enhance 2D heteronuclear spin correlation (HETCOR) experiments involving dilute nuclei such as ¹³C; unlike the solution-state NMR cases, no chemical exchanges with a dominating solvent will be available for use, and acquisitions will have to be done under the stringent decoupling and spinning manipulations that are needed for collecting high-resolution NMR spectra from powdered solids.

A Fourier-encoded, solid-state NMR version of FLEX. To extend the solution-phase saturation-transfer principles described above to solids undergoing both heteronuclear ¹H decoupling and MAS, we put forward the Fourier-Encoded Saturation Transfer (FEST) experiment. FEST is, in principle, applicable to the observation of any X-nucleus surrounded by a ¹H reservoir; here, we target dilute ¹³C surrounded by an ensemble of abundant protons as a representative example. There are several conceptual elements of FEST experiments that have both similarities and differences to the elements involved in solution-state CEST/FLEX NMR; hence, they are introduced in this paragraph one by one. The enabling component of FEST are dipolar couplings, both those between the dilute ¹³C’s and its neighboring, strongly coupled ¹H’s and those between these ¹³C-coupled ¹H’s and the ¹H bulk ensemble at large. ¹³C–¹H dipolar couplings are normally used in 2D HETCOR solid state NMR for sensitizing experiments, for instance, upon pre-polarizing the ¹³C via cross polarization (CP) and/or when transferring back the ¹³C encoding to perform ¹H-detection with enhanced sensitivity.^32–36 However, by virtue of their separation and of the low ¹³C natural abundance, these dipolar-driven processes will involve only a small fraction of the total protons in the sample, as most ¹H’s are not coupled strongly enough to the carbon in order to participate in polarization transfers. Therefore, this abundant ¹H spin polarization goes largely unused. FEST seeks to exploit this large portion of the abundant ¹H spin system as part of the signal enhancement process, by making it the reporter of the ¹³C NMR time-domain free-induction decay (FID). To do so, the proposed experiment relies on the REFLEX-inspired approach introduced in Scheme 1. This depicts a typical organic solid in terms of three spin pools, each having varying populations and receptivities schematically illustrated by the size of their circles: the ¹³C, the ¹H(s) that is (are) strongly coupled to the ¹³C, and a more abundant, essentially ¹³C-decoupled ¹H reservoir that will make the bulk of the NMR signal in a ¹H-detected experiment. Furthermore, it is assumed that the distinct dipolar couplings that exist between these various spin pools allows each to be individually addressed with suitable radio-frequency (RF) manipulations; for instance, CP can be used to transfer polarization between ¹³C and its directly dipole-coupled ¹H’s, while spontaneous or RF-driven spin diffusion enables the communication between the latter ¹H’s and the much larger portion of the abundant ¹H spin pool (shown in blue).

With this as the background, the procedure by which we propose to use the latter for efficiently enhancing the dilute ¹³C NMR signature is described in Figs. 1(a)–1(d). According to this scheme, (1) the proximate ¹H pool is first used to polarize the ¹³C, (2) the latter’s time-domain evolution is triggered, encoded over a time t₁, and then passed back onto ¹H^(proximate) as an amplitude modulation, (3) a ¹H–¹H spin-diffusion interval is allowed to proceed, whereby this proximate ¹H pool depolarizes the distant ¹H^(abundant) to a degree that reflects the ¹³C t₁ evolution while getting repolarized in exchange, and (4) the whole process is repeated several times, so as to imprint the ¹³C evolution onto the bulk ¹H reservoir to the maximum possible extent. Step (2) acts here as the Fourier-encoding module in FLEX, while steps (3) and (4) would act as analogs of the chemical exchange saturation transfer process amplifying the signal. The ¹³C signal magnification that these processes bring about will depend on the number of times that the overall process is repeated, on the degree of ¹³C vs ¹H (bulk) dilution, on the strength of the couplings between the various pools, on the longitudinal ¹H and ¹³C T₁ and T_1ρ relaxation-time constants, and on the efficiency with which all these processes can be implemented while under the high-resolution requirements of solid-state ¹³C NMR.

Figure 1(e) introduces a time-domain pulse sequence that could be used for magnifying in this manner the chemical shift modulation of a dilute ¹³C spin pool on a more abundant bulk ¹H reservoir while remaining compatible with the decoupling and MAS demands imposed by high resolution ¹³C observations. The steps that are involved in the ensuing indirect-detection sequence and their approximate correlation with the processes introduced in Figs. 1(a)–1(d) include (1) An initial block where polarization is received by the ¹³C from its proximate, dipolar-coupled ¹H via an optimized CP process, which is long enough to be effective, but also short so as to not incur detrimental T_1ρ ¹H relaxation losses. Particularly important is the preservation of the spin polarization belonging to the abundant proton pool, which is, therefore, stored post-CP along the +z axis. (2) This is followed by a mixing interval τ_mix that is sufficiently long for enabling ¹H–¹H spin diffusion yet short vs the ¹³C T₁ so that the ¹³C remain fully polarized at the end of τ_mix, while spin polarization from ¹H^(abundant) spontaneously repolarizes the depleted ¹³C-coupled proton through spin diffusion.³⁷ (3) In a process that will be repeatedly executed, the ¹³C longitudinal spin polarization is excited and allowed to evolve for a short t₁ increment (≈μs-ms, best performed in a constant-time 2D fashion for t₁-noise reduction) under the effects of a heteronuclear decoupling sequence that removes the effects of ¹H^(proximate) while taking care to not significantly affect the bulk proton magnetization. At the end of the t₁ evolution time, the ¹³C magnetization is once again put into Hartmann–Hahn contact with its neighboring proton, which had in the preceding τ_mix and t₁ periods been repolarized. During this CP process, the ¹³C-coupled ¹H^(proximate) will be depolarized, by an amount that depends on the modulation imposed by the t₁ ¹³C chemical shift evolution (see the supplementary material, Figs. S1–S3). Once again, care is here taken to ensure that the protons of the abundant spin pool, which are not dipolar-coupled to ¹³C, remain as unaffected by this CP contact as possible. (4) Following this point, the spin polarization of the ¹³C-coupled ¹H^(proximate), which has now been depleted by an amount that depends on the ¹³C’s t₁ evolution, is repolarized via spin diffusion over a new mixing time τ_mix in a manner analogous to that described above in step 2. However, a key difference in this case is that it will now be the longitudinal spin polarization of the ¹H^(abundant) spin pool, which will be depleted by an amount depending on the ¹³C’s chemical shift t₁ evolution. Repeating steps 3–4 numerous (N) times per scan up to a point dictated by the T₁ and T_1ρ relaxation constraints of the ¹H and ¹³C spin systems should, thus, lead to an appreciable depletion of the ¹H polarization in a ¹³C chemical-shift-dependent fashion. A final excitation pulse measuring the ensuing abundant ¹H reservoir polarization then reveals the ¹³C t₁ modulation, which when incremented translates an entire ¹³C NMR time-domain (FID) signal as a modulation of the full proton reservoir response.

FEST NMR: Numerical Simulations. This approach to amplify and detect ¹³C chemical shifts in a natural abundance solid was numerically tested with idealized quantum-based density matrix simulations,³⁸ carried out using custom-written code. These simulations were performed for a polycrystalline powder assumed to be undergoing MAS at ν_rot = 40 kHz, and for simplicity, we assumed that the three spin pools schematically indicated by the three different colors in Figs. 1(a)–1(d) possessed a distinct, uniquely addressable chemical shift: the abundant and dilute proton pools were set to ν(¹H)^(abundant) = 0 kHz and ν(¹H)^(proximate) = 10 kHz. These pools were composed of 7 and 1 ¹H spins, respectively; a single ¹³C was dipole-coupled solely to the latter ¹H and given an offset ν(¹³C) = 2 kHz. The spin dynamics imposed by the FEST pulse sequence [Fig. 1(e)] were then simulated on this spin ensemble, and in lieu of the final ¹H excitation pulse, the expectation value of the abundant spin pool’s z-polarization $⟨Îz(abundant)⟩$ was monitored as a function of the number of FEST loops (N) and of the ¹³C t₁ evolution time. Figure 2(a) shows these expectation values, as calculated at the end of the last mixing interval in the sequence. The black curve in Fig. 2(a) shows the t₁-dependent trajectory of the x ¹³C spin polarization component, $⟨ŜxCt1⟩$⁠, which results immediately after a single CP contact. This would be the conventionally detected signal in an indirectly detected heteronuclear correlation experiment, and its clear 2 kHz frequency modulation serves as our reference. Calculated $⟨Îz(abundant)t1⟩$ expectation values normalized with respect to this $⟨ŜxCt1⟩$ modulation as a function of looping are shown in other colors in Fig. 2(a). Note that losses derived from pulse non-idealities and/or relaxation processes are here ignored, as are enhancements resulting from differences in the gyromagnetic ratios [i.e., γ(¹H)/γ(¹³C)]. In other words, any modulation larger than ±0.5 represents a net signal enhancement over an indirect ¹H-detected experiment. Figure 2(a) confirms that the ¹³C chemical shift modulation is ported with magnification onto the ¹³C-decoupled, abundant ¹H spin pool; this corroborates Sch. 1’s model, whereby a ¹H → ¹³C → ¹H CP transfer and subsequent ¹H–¹H spin diffusion processes allow one to impart the ¹³C-modulation even on distant, dipolar-decoupled spin pools under fast MAS rotation. Note that this ¹³C-derived, ¹H^(abundant)-detected modulation increases in amplitude as the number of loops N increases, as does the concomitant depletion of the abundant spin pool’s polarization. At some point, however, the FEST looping leads to deviations from the ideal sinusoidal t₁ modulation; this $⟨Îz(abundant)t1⟩$ distortion for large values of N reflects the small spin system here assumed and the lack of relaxation processes, which imposes non-linearities between the extent of the ¹³C-imposed modulation and the signal enhancement afforded by the ¹H’s. While we have observed this behavior in certain solution-state, J-based analogs of this experiment (data not shown), we have not seen such distortions in the solid-state NMR measurements described below, presumably due to the extended nature of the spin-coupled solid network and the effects of spin relaxation.

Figure 2(b) examines the maximum enhancement of the ¹³C-modulation, showing that in the absence of relaxation, it will ultimately depend on the number of spins in the abundant ¹H pool. In general, the maximum modulation depth will be given by half the number of ¹H spins in this pool [Fig. 2(c) and Fig. S1]; given the ¹³C dilution at its natural abundance, this means that the potential ¹³C signal magnification afforded by FEST in organic solids can be very large. The actual conditions at which the maximum ¹³C enhancement will be achieved and its signal magnification value will depend on additional factors, including the ¹H/¹³C T₁ relaxation times and the effective internuclear dipolar couplings. Ancillary sets of simulations conducted on a simplified model system and pulse sequences, which both recapitulate and further explain these behaviors, are described in the supplementary material (Figs. S1–S3).

Samples of ibuprofen and sucrose were purchased from Sigma-Aldrich. L-Histidine HCl was purchased from B.D.H laboratories. All were used as received without further purification. Samples were ground into fine powders and packed in 1.6 mm zirconium NMR rotors for measurement. NMR experiments were performed using a Varian VNMRS console interfaced to an Oxford 14.1 T [ν₀(¹H) = 600 MHz] wide-bore magnet. A Varian 1.6 mm triple-resonance HXY (e.g., H = ¹H, X = ¹³C, Y = ¹⁵N) MAS probe was used for all NMR experiments. All spectra were acquired at a spinning speed of ν_rot = 40 kHz with a stability of ±5 Hz, using active pulse triggering and temperature regulation at 20°C. The magic angle of the probe was calibrated to 54.74° by maximizing the number of rotational echoes observed in the ⁸¹Br FID of KBr. ¹H and ¹³C pulse width calibrations were performed using a sample of adamantane (40 kHz MAS), which was also used for chemical shift referencing. ¹H → ¹³C{¹H} transfers were first calibrated using conventional CPMAS pulse sequences (100 kHz on ¹H and ∼60 kHz on ¹³C for spin locking) on each individual sample; contact times and spin-locking radio frequency (RF) field strengths were then further refined in each 2D NMR experiment for the first t₁ = 0 increment. These conditions were chosen to avoid a strong rotational-driven recoupling of the ¹H–¹H homonuclear interactions that would lead to a dephasing of the ¹H magnetization (which is eventually FEST’s observable) while yielding sufficiently large fields to reduce T_1ρ(¹H)-driven decays during the CP. Rotary-resonance recoupling conditions were employed in the 2D indirectly detected heteronuclear correlation (idHETCOR) experiments to suppress unwanted background signals; these conditions were experimentally optimized by adjusting the length and power of the orthogonal recoupling pulses and then measuring the resulting ¹H NMR spectra.⁴¹ All 2D NMR experiments used the same heteronuclear π-based decoupling sequence, which gave optimized decoupling conditions, and had their t₁ evolution periods synchronized with the spinning frequency. Optimizing the FEST experiments required determining the combination of the mixing time (i.e., τ_mix) and number of loops (i.e., N) that resulted in the largest overall depletion of the ¹H spin polarization. This was done by repeatedly depolarizing proton magnetization via multiple-contact ¹H–¹³C CP for a fixed N/τ_mix combination, and then measuring the resulting ¹H signal; this gave the so-called S^(on) dataset. Repeating this under identical experimental conditions but in the absence of ¹³C spin-locking pulses gave the so-called S^(off) dataset. Plotting {S^(off)-S^(on)}/S^(off) as a function of both N and τ_mix revealed the percentage of protons that were depleted; the largest value of this parameter gives the largest overall enhancement in terms of ¹³C SNR. Additional details pertaining to experimental optimizations are provided in the main text as well as in the supplementary material.

FEST NMR Experiments. Having devised a way whereby ¹³C offsets can be imparted onto a distant abundant spin pool while under the effects of heteronuclear decoupling and MAS by exploiting the repeated depolarization/repolarization of a directly bonded, mutually coupled proton, a series of experimental tests were performed to corroborate these numerical predictions. These experiments were performed on the basis of auxiliary optimizations of the CP and mixing conditions, as provided in Fig. S2 of the supplementary material. Shown as an initial experimental test is a simpler version of the FEST sequence [Fig. 3(a)], where the ¹³C t₁ evolution is replaced by a variable-angle ¹³C nutation pulse θ (in red). This pulse modulates all ¹³C spins to the same extent (i.e., at a single frequency), which can then be easily seen in the bulk, single-scan ¹H NMR signal as the ¹³C nutation pulse is incremented in a pseudo-2D fashion [Fig. 3(b)]. As expected, the spin dynamics are such that when the ¹³C nutation angle is 0 or an integer multiple of 2π, the ¹³C polarization that is spin locked in the looped CP processes is maximal; consequently, these angles result in the least amount of bulk ¹H depolarization. By contrast, when θ(¹³C) is an integer multiple of π, the ¹³C spin polarization is stored along the –z-axis after the first CP and is, therefore, antiparallel with respect to its spin locking B₁ field during subsequent Hartmann–Hahn contacts; this results in the largest depolarization of the ¹H bulk signal (see Fig. S3 and the discussion therein for further details). Note that all other values of θ(¹³C) depolarize the bulk ¹H spins in the expected cos(θ)-dependent manner, with no evidence of the small-reservoir distortions noted in Fig. 2; this is a consequence of the small ratio in the ¹³C/¹H populations, for this polycrystalline natural-abundance sample. Note as well the strength of the FEST effect, which is sufficient to easily detect the ¹³C nutation frequency in these single-scan bulk proton signals and is akin to what we have observed in water-based ¹H CEST observations of non-labile ¹³C NMR spectra.²⁹ It is possible to approximately estimate the degree of the enhancement in the FEST MAS experiments, by comparing their modulation against that which can be indirectly detected in ¹³C-filtered polarization, by appropriate phase cycling of the ¹³C excitation pulse that precedes CP. The result of this is a modified idHETCOR pulse sequence,³⁴ whereby the t₁ evolution period has been replaced with a ¹³C nutation pulse [Fig. 3(c)]. Figure 3(d) shows ∼3× signal enhancement achieved with the nutation version of FEST over an idHETCOR-based counterpart, with both the datasets acquired under similarly optimized experimental conditions.

Experimental tests were also performed to explore FEST’s ability to read-out site-resolved ¹³C NMR spectra in this manner. Figure 4 compares the FEST NMR results obtained on a polycrystalline sample of naturally abundant sucrose, vs results from an optimized version of the idHETCOR sequence (Fig. S4). Additional comparisons collected on naturally abundant ibuprofen and L-histidine HCl samples are summarized in the supplementary material (Figs. S5 and S6). The resulting 2D FEST spectrum [Fig. 4(a)] consists of the single broad peak characteristic of the bulk ¹H’s observed under MAS conditions along the direct (F₂) dimension, showing strong correlations to seven ¹³C resonances observed in the indirect (F₁) dimension. A signal amplification of ∼7× is achieved against the optimized 2D idHETCOR counterpart [Fig. 4(b)], which is also visible by comparing the ¹H NMR spectra acquired for the first t₁ = 0 increment of FEST and idHETCOR [Fig. 4(c), top and bottom, respectively]. More modest (3–5×) FEST enhancements were observed on the ibuprofen and histidine HCl samples, probably because of the latter’s shorter T₁(¹H) values (Figs. S5 and S6). Note that in all the cases, the FEST experiment highlights both protonated and non-protonated ¹³C’s, owing to its reliance on relatively long CP times. Additional analyses on the SNR and t₁ noise of these data are presented in Table S1.

The present study puts forward a time-domain, saturation-driven experiment for increasing the sensitivity of solid-state HETCOR NMR experiments. Unlike liquid-state CEST, which relies on actual chemical exchanges to facilitate the transfer of chemical shift information between a magnetically dilute spin pool and an abundant water spin pool, the FEST experiments here presented rely on an abundant ¹H reservoir for achieving its sensitivity enhancement and on the discriminated use of heteronuclear and homonuclear dipolar couplings for driving the various transfers of polarization/saturation. The former is used, via CP contacts, to translate the heteronuclear chemical shift encoding into proton depolarization, while spin diffusion is used to extend this depletion throughout distant protons for the sake of achieving sensitivity enhancement. In this fashion, FEST experiments performed on naturally abundant organic compounds allow for the nutation or shift modulation of a magnetically dilute ¹³C spin pool to be encoded onto a magnetically abundant ¹H spin pool. In parallel to what was exploited in the solution-state REFLEX experiment,²⁹ a defining feature of FEST is the conceptual separation between magnetically dilute ¹H’s that are strongly dipolar-coupled with the heteronucleus, and the abundant essentially ¹³C-decoupled ¹H spin reservoir whose depletion will eventually lead to the signal enhancement. In the solution-state NMR case, the former were given by labile ¹H’s that are J-coupled to the heteronucleus, but also capable of exchanging with the water pool; in the latter, their definition is less clear, as the “dilute” ¹H’s are defined by the pool of spins that can cross-polarize to/from a given ¹³C site, while the “abundant” ¹H’s are those parts of the larger network that has so far remained mostly passive in heteronuclear NMR. In the case of naturally abundant organic solids, it is clear that the latter will entail a larger majority of protons, opening a new route to a more efficient use of these abundant species’ polarization for enhancing heteronuclear NMR. The present study relied on spontaneous spin diffusion for the relay of polarization between the dilute and abundant ¹H spin reservoirs; it is conceivable that, particularly at the faster MAS rates that should facilitate this experiment, RF-assisted approaches might enhance the effectiveness of this process (in fact, the train of π pulses inserted during the t₁ period for heteronuclear decoupling, facilitated this via an RFDR-like mechanism). It is also worth relating FEST’s reliance on ¹H–¹H spin diffusion to other sensitivity-enhancing modalities that also rely on a more efficient use of the ¹H bulk polarization, either by using short, flipped-back CP contact pulses^37,43,44 or frequency-selective ¹H excitation pulses,⁴⁵ to detect directly ¹H-bonded X nuclei. All these methods aim at reducing the effective recycle delays and, thus, accelerate the signal averaging of the dilute spins’ signals; FEST, by contrast, uses spin diffusion to repeatedly deplete the bulk ¹H’s over their time T₁. This allows FEST, in principle, to reach a much higher SNR per scan, even if at a loss of spectral resolution about the nature of the ¹H’s. It is interesting to note a certain parallelism between these ideas, and experiments that have been demonstrated in the past for sensitizing quadrupolar NMR in static solids.^46,47

The primary challenge facing the sensitivity enhancement achievable from these ¹³C-shift-encoded FEST experiments turned out to be choosing an optimized heteronuclear dipolar decoupling sequence during the t₁ evolution period. Such a sequence has to deliver a high-resolution ¹³C NMR spectrum without ¹H coupling artifacts or broadenings, while at the same time preserving and leaving the abundant ¹H spin polarization “untouched,” which will eventually be the source of any ¹³C FEST enhancement. Any scan-to-scan instability in the performance of this heteronuclear t₁-decoupling sequence led to unacceptable amplifications in the t₁ noise. Our final selection was a π-based, constant-time heteronuclear dipolar decoupling sequence, involving repeated units of eight short, high-power, rotor-synchronized ¹H π pulses applied at the end of a rotor period, with their phases XY8 phase-cycled.^37,42 The overall number of ¹H decoupling pulses was, thus, kept constant, and the effective ¹³C evolution time was defined by “walking” the ¹³C excitation pulse throughout this period, in increments matching the XY8 decoupling subunits. This procedure led to penalties both in terms of sensitivity losses associated with the constant-time operation, partial saturation of the ¹H reservoir, and the introduction of scan-to-scan instabilities leading to t₁ noise, but it was the best we managed to devise. Instabilities also decreased substantially upon rotor-synchronizing the whole sequence (Fig. S7), which included the synchronization of all events to the same initial sample rotor phase and by actively regulating the sample temperature (Fig. S8). Nevertheless, despite all these efforts, multiplicative t₁ noise artifacts were still observed in the final bulk ¹H signal. This can be clearly appreciated in the ¹³C F₁ trace taken from the 2D FEST spectrum [Fig. 4(d), top], which, unlike the idHETCOR counterpart [Fig. 4(d), bottom], features strong t₁ noise ridges. Furthermore, the application of common strategies such as rotary-resonance recoupling or phase cycling procedures to destroy ¹H spin polarization that has not been modulated over t₁ cannot be used in FEST, as this would eliminate any potential signal enhancement. Alternative methods to attenuate the F₁ artifacts are currently being developed and tested. These include saturation-transfer methods that progressively deplete the abundant proton reservoir while invoking dipolar-order-mediated CP, a strategy proven effective at reducing t₁ noise when targeting NMR spectra under static conditions.⁴⁸ Such dipolar-order states have also been reported for rotating solids,⁴⁹ opening an interesting alternative for FEST experiments. Using such protocols under conditions of fast (ν_rot > 60 kHz) MAS could also alleviate the need for heteronuclear decoupling during the t₁ evolution, thereby greatly reducing the t₁ noise distortions affecting the ¹H-decoupled CP FEST experiments here described. Alternative sequences performed at fast spinning rates but operating on the basis of J, instead of dipolar transfers, could further reduce t₁ noise artifacts. Efforts are under way to implement these, as well as customized denoising approaches based on data post-processing routines. Despite these current limitations and need for improvement, FEST seems to open hitherto untapped sensitivity enhancements in solid-state high-resolution NMR by the efficient use of abundant spin polarization that typically goes unused. Extensions of similar ideas to solution-phase experiments involving natural-abundance (non-exchanging) organic substrates are also being explored.

See the supplementary material for numerical simulations of FEST MAS NMR on a model solid-state homonuclear system, additional experimental details on setting up the FEST MAS NMR experiment, and additional experimental examples.

The authors are grateful to the late Koby Zibzener for technical assistance in the experiments described here. The authors also acknowledge fruitful discussions with Dr. Rob Tycko (NIDDK, NIH) regarding this work. This work was supported by the Israel Science Foundation (Grant No. 965/18), the EU Horizon 2020 program (Marie Skłodowska-Curie Grant No. 642773 and FET-OPEN Grant No. 828946, PATHOS), and the generosity of the Perlman Family Foundation. L.F. holds the Bertha and Isadore Gudelsky Professorial Chair and heads the Clore Institute for High-Field Magnetic Resonance Imaging and Spectroscopy, whose support is acknowledged.

The authors have no conflicts to disclose.

The data that support the findings of this study are available from the corresponding author upon reasonable request.