Artifact-free ultralow-temperature DNP-enhanced NMR of molecular assemblies at natural isotopic abundance

Abstract

Magic-angle spinning dynamic nuclear polarization (MAS-DNP) has greatly increased solid-state NMR sensitivity, enabling multidimensional correlation experiments (e.g., ¹³C–¹³C and ¹³C–¹⁵N) at natural isotopic abundance. Yet, these experiments often suffer from t₁-noise, an artifact that obscures weak cross-peaks, especially in natural abundance samples. Here, we present a method to suppress t₁-noise in ¹³C–¹³C double-quantum–single-quantum (DQ-SQ) spectra by converting DQ coherences into longitudinal two-spin order (zz-terms), enabling selective removal of uncoupled ¹³C magnetization. This zz-filter, compatible with both J- and dipolar-based sequences, markedly improves the spectral quality on both commercial (100 K) and custom-built helium-spinning (30 K) MAS-DNP setups. Up to a fivefold increase in signal-to-noise ratio in the indirect dimension allows detection of previously hidden long-range correlations, including intermolecular contacts. This method yields the first artifact-free ¹³C–¹³C DQ-SQ spectrum at 30 K, expanding the analytical reach of MAS-DNP NMR for characterizing molecular assemblies at natural abundance.

Artifact-free ultralow-temperature MAS-DNP NMR reveals hidden long-range ¹³C–¹³C correlations at natural abundance.

INTRODUCTION

Solid-state nuclear magnetic resonance under magic angle spinning (MAS ssNMR) (1, 2) has emerged as a versatile and powerful spectroscopy to study structure and dynamics at the atomic scale of a large variety of systems ranging from biomolecules to materials (3–6). This was enabled by many methodological and instrumental developments that include access to higher magnetic fields and faster MAS probes and also by the advent of high-power microwave sources (gyrotrons) (7, 8) for the development of high-frequency dynamic nuclear polarization under MAS (MAS-DNP) (3, 4, 7–18). These advancements have markedly broadened the scope of NMR, enabling increasingly challenging applications. Notably, it facilitated two-dimensional (2D) homonuclear and heteronuclear correlation experiments between low-γ/low natural isotopic abundance nuclei (19, 20). As demonstrated in 2012, MAS-DNP applied to systems at natural abundance enables the detection of one bond ¹³C–¹³C correlations (21, 22) and long-range ¹³C–¹³C polarization transfers within hours (21, 23). This strategy has proven key in various contexts, including the study of organic microcrystals (21, 22, 24), self-assembled peptides and proteins (20, 23, 25), and the identification of pharmaceutical polymorphs (26). In addition, this approach significantly advances the feasibility of biomolecular NMR at natural abundance. Remarkable applications include investigations of amyloid fibrils relevant to Huntington’s disease (27); bone-tissue materials, including GAG-collagen interactions in cartilage (28, 29); and ligno-cellulosic materials (30–35). These developments are particularly important as they overcome longstanding limitations that had severely constrained previous ssNMR studies (19). Beyond the primary advantage of eliminating the need of isotopic labeling, which is often costly and not applicable to all systems, working at natural isotopic abundance offers additional inherent benefits. These include simplified spin dynamics and the ability to probe long-range magnetization transfer (19–21, 23, 26, 36). In 2017, Märker et al. (37) demonstrated the feasibility of achieving strong agreement between experimental and simulated dipolar build-up curves, arising from the superposition of various distances up to 7 Å in organic solids at natural abundance. In the same year, Kobayashi et al. introduced CHHC correlation experiments under MAS-DNP to probe long-range intra- and intermolecular ¹³C–¹³C distances in the same range by exploiting proton-mediated polarization transfer (36). The steady increase in MAS-DNP sensitivity over the past decade, driven by advances in polarizing agents (24, 38–43) and innovations in hardware that enable experiments at ultralow temperatures with cryogenic helium sample spinning (12, 44–49), has significantly enhanced our ability to explore natural-abundance systems with up to two orders of magnitude of sensitivity improvement. However, this increased sensitivity also places greater demands on hardware stability. When experimental reproducibility is insufficient, multidimensional NMR experiments can be affected by a phenomenon known as t₁-noise, which results from fluctuations in the detected signal due to experimental instabilities. In multidimensional NMR experiments, these fluctuations introduce an additional incoherent modulation of the signal along the indirect evolution time (t₁). Because of its multiplicative nature, t₁-noise is proportional to the detected signal intensity (50). If t₁-noise exceeds thermal noise, it leads to signal-proportional ridges along the f₁ dimension in the Fourier-transformed spectrum, which can significantly degrade data quality. This issue becomes particularly problematic when cross-peaks of interest are of similar or lower intensity than the t₁-noise, as often encountered in DNP-enhanced correlation experiments involving low abundance nuclei (e.g., ¹³C natural abundance 1.1%). In these cases, t₁-noise can obscure meaningful spectral features, posing a major obstacle to the broader application and further development of multidimensional spectroscopy at natural abundance. Here, we present an original approach to suppress t₁-noise in the context of ¹³C–¹³C double-quantum–single-quantum (DQ-SQ) correlation spectroscopy at natural abundance. It consists in converting DQ coherences (DQCs) into longitudinal two-spin order $I_{\mathit{jz}}{I}_{\mathit{kz}}$ (zz-terms) to selectively eliminate, through a “zz-filter,” unwanted magnetization of abundant, uncoupled ¹³C nuclei, which constitute the main t₁-noise contribution. This methodology is explained theoretically and demonstrated for both isotropic J- (through-bond) and anisotropic dipolar- (through-space) based polarization transfers. Furthermore, we demonstrate that the application of a zz-filter together with a simple z-filter—referred to as z³-filter—further reduces the t₁-noise to near the thermal noise level and thereby significantly enhances the overall signal-to-noise ratio (SNR) despite an approximately twofold loss in signal intensity. Using a commercial MAS-DNP setup at 100 K, we first show that spectral clarity is significantly enhanced, enabling straightforward assignment of numerous previously obscured cross-peaks corresponding to long-range correlations (3 to 4 Å), including intermolecular contacts. We then apply the zz-filter at 30 K using a custom-built He-spinning MAS-DNP system (44), where ultrahigh sensitivity, about one order of magnitude larger than at 100 K due to both larger signal enhancement and reduced thermal noise, leads in more pronounced t₁-noise artifacts. With the approach introduced here, we achieve a remarkable ~5× improvement in SNR along the f₁ dimension, enabling the acquisition of 30 K ¹³C–¹³C DQ-SQ spectrum of small molecules at natural abundance. These results pave the way for more challenging applications at natural abundance with MAS-DNP, including precise measurements of build-up curves for the extraction of long-range interatomic distances in organic and biomolecular solids. Last, we extend the z³-filter to the heteronuclear context using the transferred echo double resonance (TEDOR) experiment (51). Notably, we show that the zz-filter, originally implemented by Jaroniec and coworkers to dephase multiple-quantum coherences (MQCs) in ¹³C, ¹⁵N -labeled system, is equally essential in experiments at natural abundance for the suppression of t₁-noise artifacts.

RESULTS

t₁-noise and multidimensional ¹³C–¹³C correlation experiments at natural isotopic abundance

t₁-noise artifacts are typically encountered in multidimensional correlation experiments involving nuclei with low natural isotopic abundance. In these cases, cross-peaks coexist with unwanted signals from uncoupled spins that can be orders of magnitude more intense. Although these stronger signals are typically canceled out using phase cycling, it is well known that minor experimental fluctuations can induce t₁-noise of comparable intensity to the cross-peaks, thereby contaminating the 2D spectrum (52). In ¹³C–¹³C correlation experiments at natural abundance, DQ filtration via phase cycling is typically used to remove the large contribution from uncoupled nuclei to detect weaker contributions from coupled spin pairs (Fig. 1, A and C) (53, 54). Even if the latter can largely be removed, its fluctuation from one scan to another can lead to substantial t₁-noise artifacts under DNP conditions. This is especially true when using the latest generation of polarizing agents (24, 40, 43, 55) and when experiments are conducted at ultralow temperatures (<100 K) because it increases the signal while decreasing the thermal noise (44). Despite excellent experimental stability, the sensitivity can be so high with MAS-DNP that t₁-noise can be present, degrading the spectral quality and preventing unambiguous assignment of weak cross-peaks (see Fig. 2A). While improving instrumental stability is the most direct way to mitigate t₁-noise, identifying the relative contribution of the various potential sources of instabilities (probe detuning, MAS fluctuations, gyrotron instabilities, etc.) and refining the instrumentation accordingly are complex and long-term undertaking, which cannot always be fully achieved. For this reason, additional strategies have been proposed, which generally fall into two main categories: postprocessing methods and improved data-acquisition strategies. Postprocessing methods typically aim to separate the signal from t₁-noise by using the specific characteristics of either the signal or the noise itself, such as the general assumption of t₁-noise homogeneity across the f₂ dimension (i.e., all peaks experience similar fluctuations) (56). Consequently, a range of postprocessing methods has been developed since the initial observation of t₁-noise artifacts (52, 57–65). While these approaches can be highly beneficial, their applicability can be limited in some contexts by important drawbacks, such as the unintended generation of artificial cross-peaks or the suppression of true ones. On the other hand, experimental approaches tend to provide clearer and more reliable data by minimizing t₁-noise at its source. When t₁-noise results from slow-fluctuating instabilities (such as temperature variations), randomizing the acquisition order of the indirect dimension (66) or simply reducing the number of scans for each t₁ increment (67) result in its reduction. However, these techniques are ineffective on t₁-noise originating from scan-to-scan instabilities, which disrupt the reproducibility required for effective signal cancellation via phase cycling. This situation is typically encountered in solid-state NMR, where MAS fluctuations are commonly presumed to be the primary source of t₁-noise. Several methods have recently been proposed. Some of these aim at increasing the sequence robustness against MAS fluctuations, e.g., by the design of “γ-free” sequences (68) or by refocusing the ¹H chemical shift anisotropy (CSA) in heteronuclear correlation (HETCOR) experiments (69, 70). Other approaches focus on minimizing the coherences that generate t₁-noise by using selective saturation pulses to suppress specific intense signals (71) or removing isolated nuclear spin magnetization in proton-detected HETCOR experiments involving low-isotopic abundance nuclei, either via a z-filter (72) or more elaborate purging schemes (69, 73). More recently, Perras and coworkers (74) proposed a simple approach to limit t₁-noise by shortening the experimental recovery delay. This easy-to-implement solution can in principle be applied to any experiment affected by t₁-noise. However, it comes with a significant loss of sensitivity, particularly when the t₁-noise is much larger than the thermal noise. In addition, the described approach does not account for the recycle-delay limitations of solid-state NMR probes in the presence of high-power decoupling. In liquid-state NMR, coherence selection using pulsed field gradients has proven highly effective for t₁-noise suppression compared to phase-cycled selection (75, 76), although their comparatively lower sensitivity makes them advantageous only when the t₁-noise significantly exceeds the thermal noise level (76). While the implementation of gradient coils has been widely adopted in the context of high-resolution magic angle spinning (77, 78), it remains underdeveloped in the context of solid-state NMR (79).

Fig. 1. Concept and experimental validation of the zz-filter.

(A) Schematic of a generic DQ/SQ pulse sequence with the zz-filter applied after the DQ-excitation block. The sequence starts with ¹³C I_z magnetization, which can be prepared by a CP transfer followed by a flip-back 90° pulse (not shown in the sequence). The first ${(\mathrm{\pi }/2)}_{\mathrm{\theta }}$ pulse of the zz-filter converts half of the DQC into a zz-term and uncoupled spin magnetization, I_z, into SQC. During ${\mathrm{\Delta }}_{\mathit{zz}}$, the SQC is dephased, while the zz-term is preserved. The second ${(\mathrm{\pi }/2)}_{\mathrm{\theta }}$ pulse then converts the zz-term into a mix of DQC and ZQC. The coherence transfer pathway (CTP) of the sequence is given below it. The thick blue lines indicate the CTP of uncoupled spins, while the thin blue-red shaded lines are for coupled spin pairs. (B) Polar plot of the DQ-filtered normalized signal intensity as a function of the pulse phase θ relative to the phase ϕ of the excited DQC. Blue dots are experimental points acquired with the J-INADEQUATE pulse sequences (see figs. S3 and S4A) on ampicillin microcrystal powder, with a zz-filter of $25{\mathrm{\tau }}_r\simeq$ 3 ms. Experimental error intervals are represented by the shaded regions. The theoretical efficiency (Eq. 11) is indicated by the dotted blue line. (C) Detected 1D signal in a J-based DQ/SQ experiment as a function of ${\mathrm{\Delta }}_{\mathit{zz}}$, with $t_1=0$: (i) single-scan signal showing the strong reduction of SQCs with ${\mathrm{\Delta }}_{\mathit{zz}}$ as a result of signal dephasing and (ii) DQ phase-cycled signal over 64 scans showing conserved DQ-filtered signal intensity during ${\mathrm{\Delta }}_{\mathit{zz}}$.

Fig. 2. Proof-of-concept demonstration of the zz-filter on isotropic J-based correlation experiments.

(A) Carbonyl region of refocused INADEQUATE DNP-enhanced spectra on natural abundance ampicillin microcrystals impregnated with cAsymPol-POK, without (on the left) and with (on the right) a zz-filter of 6.25 ms (standard z-filter set to 3 ms). Contour levels are normalized to the maximum intensity in each spectrum. (B) f₁-traces from (A) at 175.2 and 170.1 ppm [red and orange dotted lines in (A), left and right panels in (B), respectively] without (top panels) and with (bottom panels) zz-filter. Intensities are normalized according to the maximum intensity in the corresponding trace without zz-filter. The gray region corresponds to noise within three times the SD of the thermal noise $3{\mathrm{\sigma }}_{\text{th}}$. The t₁-noise SD ${\mathrm{\sigma }}_{\mathrm{t}1}$ was calculated from regions without any peaks of the f₁-traces (from 0 to 120 ppm and 320 to 400 ppm; see section S3 for more details). Sidebands are indicated by orange and red stars. The orange triangle indicates a real signal corresponding to the foot of a more intense peak. AU, arbitrary unit.

Principles and theory of the zz-filter

Here, we consider the introduction of the zz-filter pulse sequence element ${(\mathrm{\pi }/2)}_{\mathrm{\theta }}-{\mathrm{\Delta }}_{\mathit{zz}}-{(\mathrm{\pi }/2)}_{\mathrm{\theta }}$ at the end of the DQ excitation block (Fig. 1A), with θ the phase of the two $(\mathrm{\pi }/2)$-pulses and ${\mathrm{\Delta }}_{\mathit{zz}}$ the delay between them. Isolated ¹³C nuclear spins, which account for most of the detected signal in 1D cross-polarization (CPMAS) experiments, cannot build any DQCs during this time. Considering the ideal case of radio frequency (rf) field strength perfectly matching the recoupling condition, and the absence of other interactions and rf inhomogeneity, the ¹³C I_z magnetization of isolated spins stays along the z axis during the DQ excitation block. The first ${(\mathrm{\pi }/2)}_{\mathrm{\theta }}$ pulse of the zz-filter brings it in the transverse plane as follows

$$I_z\stackrel{{(\mathrm{\pi }/2)}_{\mathrm{\theta }}}{⟶}{I}_{\mathrm{\theta }-\mathrm{\pi }/2}$$ (1)

The subsequent delay period ${\mathrm{\Delta }}_{\mathit{zz}}$ leads to a strong reduction of this isolated spin coherence through its dephasing by chemical shift interactions and heteronuclear couplings to protons (if present). Let us now consider the impact of the zz-filter on DQC generated for coupled two-spin system. In the most general case, the DQC created during the DQ excitation block can be defined in the DQ subspace as

$${\text{DQ}}_{\mathrm{\varphi }}=R_z(\mathrm{\varphi }/2){\text{DQ}}_x{R}_z(-\mathrm{\varphi }/2)$$ (2)

where $R_z\left(\mathrm{\alpha }\right)=e^{-i2{\mathrm{\alpha DQ}}_z}$ is the rotation operator about the z axis in the DQ subspace, ϕ is the phase of DQC, and the DQ subspace for two coupled spins j and k is defined by the following operators

$${\text{DQ}}_x=\frac{1}{2}(2I_{jx}{I}_{kx}-2I_{jy}{I}_{ky})=\frac{1}{2}(I_j^{+}{I}_k^{+}+I_j^{-}{I}_k^{-})$$ (3)

$${\text{DQ}}_y=\frac{1}{2}(2I_{jx}{I}_{ky}+2I_{jy}{I}_{kx})=\frac{1}{2i}(I_j^{+}{I}_k^{+}-I_j^{-}{I}_k^{-})$$ (4)

$${\text{DQ}}_z=\frac{1}{2}(I_{jz}+I_{kz})$$ (5)

If we first consider the case ϕ = 0 for simplicity, the ${\text{DQ}}_x$ coherence evolves under the first ${(\mathrm{\pi }/2)}_{\mathrm{\theta }}$ pulse of the zz-filter as follows (full calculation detailed in the section S8)

$${\text{DQ}}_x\stackrel{{(\mathrm{\pi }/2)}_{\mathrm{\theta }}}{⟶}\frac{1}{2}c\left(2\mathrm{\theta }\right)[{\text{ZQ}}_x+{\text{DQ}}_{2\mathrm{\theta }}-2I_{jz}{I}_{kz}]-s\left(2\mathrm{\theta }\right)(I_{j\mathrm{\theta }}{I}_{kz}+I_{jz}{I}_{k\mathrm{\theta }})$$ (6)

with the notation $s{\mathrm{\alpha }}^n\equiv \text{sin}{\left(\mathrm{\alpha }\right)}^n$ and $c{\mathrm{\alpha }}^n\equiv \text{cos}{\left(\mathrm{\alpha }\right)}^n$ and the operators $I_{j\mathrm{\theta }}=c\mathrm{\theta }{I}_{\mathit{jx}}+s\mathrm{\theta }{I}_{\mathit{jy}}$ and ${\text{ZQ}}_x=\frac{1}{2}(2I_{\mathit{jx}}{I}_{\mathit{kx}}+2I_{\mathit{jy}}{I}_{\mathit{ky}})$. The subsequent delay ${\mathrm{\Delta }}_{\mathit{zz}}$ will lead to the dephasing of terms that do not commute with the chemical shift and heteronuclear dipolar interactions. After dephasing, we expect only the zz-term to be preserved

$$\stackrel{{\mathrm{\Delta }}_{\mathit{zz}}}{\to }-\frac{1}{2}\text{cos}\left(2\mathrm{\theta }\right)2I_{jz}{I}_{kz}$$ (7)

It is now relevant to generalize the result to any DQC with an arbitrary phase ϕ. This can be done using Eq. 2 which, after a variable change $\mathrm{\theta }=\mathrm{\theta }-\mathrm{\varphi }/2$, gives the following result

$${\text{DQ}}_{\mathrm{\varphi }}\stackrel{{(\mathrm{\pi }/2)}_{\mathrm{\theta }}}{⟶}\stackrel{{\mathrm{\Delta }}_{\mathit{zz}}}{\to }-\frac{1}{2}\text{cos}(2\mathrm{\theta }-\mathrm{\varphi })2I_{jz}{I}_{kz}$$ (8)

The second ${(\mathrm{\pi }/2)}_{\mathrm{\theta }}$ pulse then converts this zz-term into a sum of DQ and zero-quantum (ZQ) coherences

$$2I_{jz}{I}_{kz}\stackrel{{(\mathrm{\pi }/2)}_{\mathrm{\theta }}}{⟶}2I_{j(\mathrm{\theta }-\mathrm{\pi }/2)}{I}_{k(\mathrm{\theta }-\mathrm{\pi }/2)}={\text{ZQ}}_x-{\text{DQ}}_{2\mathrm{\theta }}$$ (9)

Therefore, the effect of the zz-filter can be summarized as follows

$${\text{DQ}}_{\mathrm{\varphi }}\stackrel{\mathit{\text{zz}}\text{-filter}}{⟶}\frac{1}{2}\text{cos}(2\mathrm{\theta }-\mathrm{\varphi })({\text{DQ}}_{2\mathrm{\theta }}-{\text{ZQ}}_x)$$ (10)

Projection of ${\text{DQ}}_{2\mathrm{\theta }}$ on the initial state before the zz-filter (i.e., ${\text{DQ}}_{\mathrm{\varphi }}$) gives the global efficiency of the zz-filter, ${\mathrm{\eta }}_{\mathit{zz}}$

$${\mathrm{\eta }}_{\mathit{zz}}=\frac{1}{2}\text{cos}{(2\mathrm{\theta }-\mathrm{\varphi })}^2$$ (11)

The zz-filter has, therefore, a maximum efficiency of ¹/₂, obtained when the phase of the zz-filter pulses satisfies the condition

$$\mathrm{\theta }\equiv \mathrm{\varphi }/2 \text{mod }\mathrm{\pi }/2$$ (12)

with ϕ the phase of the generated DQC. The corresponding coherence transfer pathway (CTP) is represented on Fig. 1A below the pulse sequence. Overall, in the ideal case where all generated DQCs share the same phase ϕ, the zz-filter is expected to substantially suppress signals from uncoupled spins while scaling the intensity of DQ-filtered signal by a factor of 2. This condition is met with J-based polarization transfer (e.g., with refocused INADEQUATE), which will serve as a proof of concept to assess the efficiency of the zz-filter. Later, we will address the case of dipolar-based transfer, where the anisotropic nature of the dipolar coupling introduces additional complexity. Note that we chose to use the terminology “zz-filter” to stress that that the method relies on a two-spin order filtration, although it is clear that the z-filter terminology introduced by Sørensen and coworkers in 1984 (80) also preserves longitudinal multiple-spin order terms ($2I_{\mathit{\text{jz}}}{I}_{\mathit{\text{kz}}},4I_{\mathit{\text{jz}}}{I}_{\mathit{\text{kz}}}{I}_{\mathit{\text{lz}}}\dots$). The terminology zz-filter has also been used by Pelton and Wemmer for a case specifically aiming at filtering zz-terms (81). In modern NMR applications, zz-filters, which refer to double-isotope filters, have been used in liquid-state NMR on natural abundance molecules, to specifically select ¹H signal from ¹H–¹³C spin pairs (82–84).

zz-filter in the case of isotropic J-based correlation experiments

INADEQUATE is a major NMR experiment that enables probing through-bond homonuclear correlations (54, 85–87). It is based on the use of the isotropic J-coupling to transfer magnetization between nuclei connected through one or more chemical bonds. Because of the isotropic nature of the J-coupling, the phase of the DQC is the same regardless of the crystallite orientation. Following the phases of the pulse sequence used by Cadars and coworkers (see fig. S4A) (87), DQCs are generated along ${\text{DQ}}_{\mathit{y}}$ ($\mathrm{\varphi }=\mathrm{\pi }/2$). According to Eq. 11, the maximum efficiency of the zz-filter is then expected for pulse phases $\mathrm{\theta }=\mathrm{\pi }/4$. This prediction was experimentally verified by measuring the DQ-filtered signal intensity obtained using the zz-filtered refocused INADEQUATE sequence, as a function of the zz-filter pulse phase θ. The data are plotted as a function of $2\mathrm{\theta }-\mathrm{\varphi }$ on the polar plot in Fig. 1B (blue dots), together with the analytical expression from Eq. 11 (blue dashed lines), showing excellent agreement within the experimental error bounds (shaded region). The complete pseudo-2D spectrum is provided in the fig. S3. The behavior of uncoupled spins magnetization and of the generated DQCs during the zz-filter can be studied by following the signal evolution as a function of the zz-filter length and is illustrated on Fig. 1C. Signal from uncoupled spins is strongly dominating when the experiment is acquired with a single-scan (Fig. 1C, i), as CTP selection via phase cycling is then avoided. This strong initial signal, 300-fold more intense than the DQ-filtered signal (with zz-filter) usually detected with phase cycling, is dephased during the zz-filter and its intensity drastically decreases after a few ms (Fig. 1C, i). On the contrary, the DQ-filtered signal intensity obtained with the complete phase cycling, which aims at removing the strong signal from isolated spins, remains stable throughout the zz-filter (Fig. 1C, ii) on the same timescale. It is worth noting that the isolated spin signal of the carbonyls has not fully vanished after 6 ms of zz-filter duration, unlike that of the other carbons, as a result of a weaker dipolar coupling to ¹H for these quaternary carbons. Therefore, we investigated the possibility of actively reintroducing ¹H–¹³C dipolar interactions during the zz-filter using a dipolar-assisted rotational resonance (DARR) recoupling field (88) on the ¹H channel (spin-lock at ${\mathrm{\omega }}_{1H}=n{\mathrm{\omega }}_r$ with n = 1 or 2). As can be seen in the section S5, it enables a significantly faster decay of the unwanted SQCs but does not improve t₁-noise suppression in this specific case. However, it might be very useful, or even necessary, when using the zz-filter under different conditions (sample with a lower ¹H content, higher MAS frequencies, etc). The efficiency of the zz-filter to reduce t₁-noise in DQ/SQ refocused INADEQUATE experiments is illustrated in Fig. 2 using a 6.25-ms zz-filter duration. Figure 2A compares spectra acquired without and with zz-filter, with contour levels normalized to the maximum intensity in each dataset. The displayed spectra focus on the carbonyl region (see fig. S4B for full spectra). Very clearly, the zz-filter leads to a strong reduction of the t₁-noise, resulting in an increased SNR along signal-containing f₁-traces. To evaluate the improvement in SNR, f₁-traces taken at 175.2 parts per million (ppm) (C7) and 170.1 ppm (C15) are compared in Fig. 2B. The gray-colored parts of the spectra correspond to intensities which are below three times the thermal noise standard deviation (SD) ${\mathrm{\sigma }}_{\text{th}}$ (i.e., corresponding to the 99.7% confidence interval of the thermal noise). Further details on this representation are provided in Materials and Methods and section S3. As shown in the top panels of Fig. 2B, for the INADEQUATE experiment without the zz-filter, the noise in the extracted f₁-traces significantly exceeds the $3{\mathrm{\sigma }}_{\text{th}}$ threshold due to the presence of t₁-noise. This elevated noise level can obscure genuine peaks and potentially introduce artifacts. In contrast, for the INADEQUATE with zz-filter (bottom panels in Fig. 2B), most of the noise falls below the $3{\mathrm{\sigma }}_{\text{th}}$ threshold, indicating that the noise level is now close to the thermal noise limit. This notable reduction in t₁-noise enables the clear identification of several real signals in both the 2D spectra (Fig. 2A) and f₁-traces (Fig. 2B). These signals, marked by stars, were previously hidden in the t₁-noise. The SD of the t₁-noise, ${\mathrm{\sigma }}_{\mathrm{t}1}$, was estimated by measuring the SD in a signal-free region of the most contaminated f₁-trace (C7) (see fig. S2A) and was compared to the thermal noise SD ${\mathrm{\sigma }}_{\text{th}}$. The application of the zz-filter reduces the ${\mathrm{\sigma }}_{\mathrm{t}1}$/${\mathrm{\sigma }}_{\text{th}}$ ratio from 7.1 to 1.4, bringing the t₁-noise level close to the thermal noise limit. The zz-filter efficiency is ~40%, approaching the theoretical maximum of 50%. Consequently, the SNR of the f₁-traces increased from 10.3 to 19.8—an almost twofold enhancement—confirming the effective suppression of t₁-noise. On the other hand, note that the signal loss associated with the zz-filter makes this approach advantageous only when the t₁-noise substantially exceeds the thermal noise. This is illustrated in panel (ii) of fig. S2A, where we show an f₁-trace of an aliphatic carbon exhibiting less t₁-noise and a ${\mathrm{\sigma }}_{\mathrm{t}1}$/${\mathrm{\sigma }}_{\text{th}}$ ratio of only 2.3. In this case, although the application of the zz-filter further decreases the ${\mathrm{\sigma }}_{\mathrm{t}1}$/${\mathrm{\sigma }}_{\text{th}}$ ratio to 1.1, it also reduces the SNR from 32 to 26.3. It is worth noting that the J-refocused INADEQUATE experiment is typically combined with a z-filter before detection, as originally proposed by Cadars and coworkers (87) to suppress MQCs that may cause lineshape distortions in ¹³C-labeled solids. In natural-abundance samples, however, the strong spin dilution notably limits the formation of these MQCs, and the need for a z-filter is, in principle, less critical. Nonetheless, as shown in the section S6), we investigated whether a simple z-filter could also contribute to t₁-noise suppression in our experimental conditions. Although some variability in the measured t₁-noise prevented a fully quantitative conclusion, the results suggest that inserting a z-filter can indeed help further reduce the t₁-noise level in J-refocused INADEQUATE experiments. Consequently, achieving optimal t₁-noise suppression appears to require the combined use of the zz- and z-filters before detection. In the following section, we show that this combination—referred to as the z³-filter—is even more crucial in experiments involving long pulse trains, such as those using dipolar recoupling sequences.

Extension of the zz-filter to the case of dipolar-based correlation experiments

Dipolar-based DQ spectroscopy is particularly interesting to probe spatial proximities and estimate internuclear distances thanks to the distance dependence of the dipolar interaction (89). These experiments are typically based on dipolar recoupling sequences that reintroduce the anisotropic dipolar coupling, which is else averaged out by magic angle spinning. In the case of the widely used symmetry-based sequences introduced by Levitt and coworkers (90–92), the first-order average Hamiltonian (93) can be expressed as

$$\begin{array}{c}{\overline{\mathcal{H}}}^{\left(1\right)}({\mathrm{\Omega }}_{\text{MR}},t^0)\hfill \\ =\mid {\mathrm{\omega }}_{\text{MR}}\left({\mathrm{\beta }}_{\text{MR}}\right)\mid \text{exp}[-i{\mathrm{\varphi }}_{\text{DQ}}({\mathrm{\gamma }}_{\text{MR}},t^0){\text{DQ}}_z\text{]}{\text{DQ}}_x\text{exp}[-i{\mathrm{\varphi }}_{\text{DQ}}({\mathrm{\gamma }}_{\text{MR}},t^0){\text{DQ}}_z\text{]}\hfill \end{array}$$ (13)

with ${\mathrm{\Omega }}_{\text{MR}}=({\mathrm{\alpha }}_{\text{MR}},{\mathrm{\beta }}_{\text{MR}},{\mathrm{\gamma }}_{\text{MR}})$ as the set of Euler angles defining the rotation of the molecular frame into the rotor frame and t⁰ as the common time origin for the entire pulse sequence. For these so-called γ-encoded sequences, the phase of the DQ Hamiltonian ${\mathrm{\varphi }}_{\text{DQ}}$ is directly proportional to the Euler angle ${\mathrm{\gamma }}_{\text{MR}}$ associated with each crystallite’s orientation (93). As a result, the phases of the generated DQCs are uniformly distributed over the DQ subspace. The overall efficiency of the zz-filter, denoted $\langle {\mathrm{\eta }}_{\mathit{zz}}\rangle$, is thus obtained by integrating the filter efficiency ${\mathrm{\eta }}_{\mathit{zz}}$ (Eq. 11) over all DQCs’ phases ϕ

$$\langle {\mathrm{\eta }}_{\mathit{zz}}\rangle =\frac{1}{2\mathrm{\pi }}{\displaystyle \underset{0}{\overset{2\mathrm{\pi }}{\int }}}\frac{\text{cos}{(2\mathrm{\theta }-\mathrm{\varphi })}^2}{2}d\mathrm{\varphi }=0.25$$ (14)

Consequently, the zz-filter efficiency is reduced to $\langle {\mathrm{\eta }}_{\mathit{zz}}\rangle =0.25$ for γ-encoded sequences, independently of the zz-filter pulses phase θ. On the other hand, the phase of the first-order average Hamiltonian is independent on the γ-angle in non–γ-encoded sequences, such as Baba-xy16 (94), $S_0{S}_0^{\prime }$ supercycled symmetry-based sequences (95) or phase-optimized recoupling with five pi pulses per rotor period (PR5) (96). In this case, the zz-filter’s efficiency follows the theoretical framework previously introduced and illustrated with the INADEQUATE example, with a theoretical zz-filter efficiency of 0.5. This notably applies to supercycled dipolar recoupling sequences such as supercycled R26 (SR26), which are particularly useful for long-distance magnetization transfer (20, 95, 97, 98) because of their increased robustness with respect to chemical shift anisotropies and other higher-order average Hamiltonian theory (AHT) contributions (95, 97). The zz-filter efficiency difference for γ- and non–γ-encoded sequences is verified experimentally and computationally [using SIMPSON (99, 100) simulations] in section S7. In Fig. 3, we compare the respective impact of the z- (just before direct acquisition) and zz-filter (after the SR26 DQ excitation block) in mitigating t₁-noise in DNP-enhanced DQ/SQ SR26 experiments on organic microcrystals at natural abundance. It is worth noting that although SR26 is non–γ-encoded, the sequence can still be implemented with arbitrary spectral width by using the supercycle-timing-compensation (StiC) phase shift, introduced by Märker and coworkers (98). Comparing panels (A) with (B) and (C) with D, it is very clear that the zz-filter leads to a strong attenuation of the t₁-noise. The t₁-noise is not completely removed with the zz-filter alone (see Fig. 3B), highlighting the necessity of combining it with a z-filter of sufficient length (3 ms) before detection. This is a noteworthy observation, as it demonstrates that t₁-noise in this experiment arises not only from fluctuations of the longitudinal I_z components of uncoupled nuclei but also from transverse terms. These transverse coherences are generated due to the nonideal behavior of the SR26 excitation block, influenced by the ¹³C CSA, residual proton couplings, and rf inhomogeneities. As a result, transverse coherences can be generated from the I_z magnetization of isolated ¹³C spins after the excitation block. Even if this signal can be removed by phase cycling and adequate selection of CTP (e.g., DQ filter), its fluctuations can still lead to t₁-noise. While these terms are not suppressed by the zz-filter, they can be efficiently attenuated by a sufficiently long z-filter that allows their complete dephasing. Therefore, the combined action of the z- and zz-filters, previously introduced as the z³-filter, proves highly effective in eliminating the t₁-noise present in this experiment. This is illustrated in Fig. 4B, which compares the f₁-traces extracted from the 2D DQ/SQ SR26 experiments of Fig. 3, taken at 175.5 ppm (C7), 170.3 ppm (C15), and 56.2 ppm (C6), with the corresponding ¹³C assignment shown in Fig. 4A. Noise in f₁-traces from the experiment using only a very short z-filter of 100 μs (top black frames of Fig. 4B) is much larger than the thermal noise, whose $3{\mathrm{\sigma }}_{\text{th}}$ interval is highlighted in gray. Only obvious cross-peaks (black dashed lines on Fig. 4B and black arrows in Fig. 4C), corresponding to one- and two-bond correlations (Fig. 4C), can be identified. Any further, less intense cross-peaks originating from longer distance correlation are completely hidden in the t₁-noise, preventing the extraction of any quantitative intensity. Extending the z-filter length from 100 μs to 3 ms (middle dark-gray frames) undeniably reduces the t₁-noise, which, however, remains significantly above the thermal noise. Even if additional peaks can be guessed, they are of the same intensity level as the noise, making their interpretation very inaccurate. It is only with the introduction of the z³-filter (5-ms zz-filter and 3-ms z-filter) (bottom light-gray frames in Fig. 4B) that the noise of the traces is reduced to the level of the thermal noise, enabling the clear distinction of the small genuine cross-peaks (highlighted with colored dashed lines) from longer distance correlations (colored arrows in Fig. 4C). Most of the unraveled small cross-peaks are assigned to three-bond correlations with corresponding distances of 3 to 4 Å (see Fig. 4C), as expected from the anhydrate ampicillin crystal structure (101). One of the peaks on the C7 f₁-trace arises from the overlap between the C7-C11 cross-peak and the C7 autocorrelation peak [see zoom (i) of Fig. 3D]. The latter can be attributed to an intermolecular C7-C7 contact, with a reported distance of 3.65 Å (101). As described previously, we quantified the ${\mathrm{\sigma }}_{\mathrm{t}1}$/${\mathrm{\sigma }}_{\text{th}}$ ratio together with the SNR on the f₁-trace of C7, which shows the highest t₁-noise (see fig. S2B for further details). The zz-filter efficiency lies in the 45 to 50% range, while the ${\mathrm{\sigma }}_{\mathrm{t}1}$/${\mathrm{\sigma }}_{\text{th}}$ ratio (see Fig. 4B) decreases progressively from 6.2 with a short z-filter to 4.4 with a long z-filter and down to 1.4 with a z³-filter. This reduction directly translates into an SNR increase from 6.1 (short z-filter) to 8.6 (long z-filter) and 11.8 (z³-filter). Therefore, our experiments demonstrate that combining the zz-filter with a sufficiently long z-filter—dubbed z³-filter—significantly reduces t₁-noise and thereby enhances the resulting SNR in dipolar-based DQ/SQ 2D experiments despite the crystallite-orientation dependence of the Hamiltonian.

Fig. 3. Impact of the z- and zz-filters on dipolar-based 2D DQ/SQ correlation experiments.

2D DNP-enhanced DQ/SQ SR26 spectra of ampicillin at natural abundance (A) without any zz-filter and only a short z-filter of 100 μs, (B) with a zz-filter of 5 ms in addition to the short z-filter (100 μs), (C) with a longer z-filter of 3 ms and without zz-filter, and (D) with both the long z-filter (3 ms) and the zz-filter of 5 ms. Contour levels are displayed using absolute intensity values and are not normalized to the maximum intensity in each spectrum to accurately reflect the absolute t₁-noise levels. Red lines connect straightforward correlation peaks. Red stars indicate correlations between overlapping or autocorrelation peaks [see zoom (i) on (D)].

Fig. 4. Detailed analysis of the z- and zz-filters impact in dipolar DQ/SQ correlation experiments.

(A) 1D ¹³C DNP-enhanced CPMAS spectrum of ampicillin at natural abundance. Assignment is shown in the figure. ¹³C chemical shift positions used in (B) and (C) are highlighted with red (175.2 ppm), orange (170.3 ppm), and yellow (56.2 ppm) dashed lines. (B) f₁-traces through dipolar-based DQ/SQ SR26 2D spectra of Fig. 3 at f₂ positions 175.2 ppm (C7, left), 170.3 ppm (C15, middle), and 56.2 ppm (C6, right), without zz-filter and with a short z-filter of 100 μs (top panels, black frames), with a longer z-filter of 3 ms (middle panels, dark gray), and with both 3-ms z-filter and 5-ms zz-filter (bottom panels, light gray). Each f₁-trace is normalized to the maximum of the z-filtered trace to allow intensity comparison. The gray region indicates the thermal noise threshold at $3{\mathrm{\sigma }}_{\text{th}}$. 1D CP spectra (black) shifted according to f₂ positions are overlaid on traces obtained with both filters. Matching cross-peaks are highlighted with dashed lines: dark gray for peaks visible with z-filter alone and colored (red, orange, and yellow) for peaks revealed by the zz-filter. Sidebands are indicated by black stars. (C) Ampicillin chemical structure with arrows illustrating correlations revealed in (B) using the same color code.

z³-filter DNP-enhanced ¹³C–¹³C natural abundance spectroscopy at ultralow temperature

In the sections above, we have shown that t₁-noise can be present in ¹³C–¹³C natural abundance DNP-enhanced correlation spectra recorded at 100 K using a commercial setup. We expect this issue to get even worse at lower temperature because the thermal noise becomes smaller while the signal can be further enhanced. This hypothesis was tested on an experimental setup developed in house composed of a closed-loop cryogen-free Helium cryostat and an ultralow temperature probe that enables conducting MAS-DNP experiments down to 20 to 30 K. The overall stability of this DNP system with respect to sample spinning and rf/microwave power was discussed previously and is expected to be similar than for the 100 K experiments reported above (44). Up to one order of magnitude improvement in sensitivity have been reported previously conducting DNP experiments at 20 to 30 K compared to 100 K (12, 44, 45, 47–49, 102). As shown in the 30 K DNP spectrum reported on the left-hand side of Fig. 5A, we observe a significant t₁-noise contribution when using only a z-filter of 3 ms. The t₁-noise in the spectrum of Fig. 5A on the left has a clear antiphase character along the f₂ direct detection dimension, significantly different from the shape of the t₁-noise previously observed at 100 K. This observation underlines the variability of t₁-noise depending on the various potential contributions. Impressively, the introduction of a zz-filter of 3 ms, in addition to the z-filter, markedly reduces the t₁-noise, leading to a spectrum of unprecedented quality obtained under ULT-MAS-DNP conditions (Fig. 5A, right). The comparison of the three f₁-traces in Fig. 5B—taken through both 2D spectra at 64.4 ppm (C5), 74.8 ppm (C3), and 170.1 ppm (C15)—shows that the introduction of the z³-filter markedly reduces the t₁-noise to the thermal noise level (gray region of the trace). On the f₁-trace of C5, the zz-filter efficiency is estimated to be ~50%, while the ${\mathrm{\sigma }}_{\mathrm{t}1}/{\mathrm{\sigma }}_{\text{th}}$ ratio decreases from 16.8 to 1.8. This reduction translates into an increase in the SNR from 5.6 to 26.1 when using the z³-filter, corresponding to an almost fivefold enhancement (Fig. S2C). Further details about the spectrum representation and the measurements of the ${\mathrm{\sigma }}_{\mathrm{t}1}/{\mathrm{\sigma }}_{\text{th}}$ and the SNR are provided in Materials and Methods and in section S3).

Fig. 5. Impact of the z³-filter on dipolar-based 2D DQ/SQ correlation experiments at 30 K using cryogenic He spinning.

(A) 2D DNP-enhanced DQ/SQ SR26 spectra of ampicillin at natural abundance with only a z-filter of 3 ms (left spectrum with dark-gray frame) and with an additional zz-filter of 3 ms as well (i.e., z³-filter; right spectrum with light-gray frame). Contour levels are normalized to the maximum intensity in each spectrum. (B) f₁-traces through the dipolar-based DQ/SQ SR26 2D of (A) at f₂ chemical shift positions of 64.4 ppm (C5), 74.8 ppm (C3), and 170.1 ppm (C15), with the z-filter only (top panels with dark gray frames) and with a z³-filter (bottom panels with light gray frames). To account for the antiphase character of the t₁-noise along the f₂ (direct) dimension under these conditions [see zooms in panels (i) and (ii) of (A)], we chose to display the modulus (absolute value) of the complex spectrum along f₂ while retaining the real part along the indirect dimension (f₁). Each pair of f₁-traces is normalized relative to the maximum intensity in the corresponding z-filtered trace (top panels with dark gray frames), such that peak intensities can be compared between both experiments. The gray area in each trace indicates the thermal noise threshold, set at $3{\mathrm{\sigma }}_{\text{th}}$, with ${\mathrm{\sigma }}_{\text{th}}$ estimated assuming a Rayleigh distribution. Further details regarding the representation of the f₁-traces and the determination of ${\mathrm{\sigma }}_{\text{th}}$ are provided in section S3. To help cross-peak identification, 1D CP spectra (in black) shifted according to the corresponding f₂ position are plotted on top of each f₁-trace obtained with the z³-filter. Cross-peaks revealed by the application of the zz-filter are highlighted using red dashed lines.

Similarly to the 100 K case, the elimination of t₁-noise enables the clear and unambiguous assignment of many correlations that were not distinguishable before (red dashed lines). The application of a z³-filter leads to the first artifact-free DQ/SQ 2D ¹³C–¹³C DNP spectrum recorded at 30 K on a sample at natural abundance.

Extension of the z³-filter to the heteronuclear case

Although we focus in this study essentially on homonuclear DQ/SQ correlation experiments, it is interesting to note that the zz-filter present in the heteronuclear z-filtered TEDOR experiment (51) can also be used to mitigate t₁-noise problems. The zz-filter was originally introduced together with a z-filter before detection to dephase undesired MQCs encountered in spin-labeled spin systems. The authors used a delay between the two 90° pulses that convert $I_y{S}_z$- into $I_z{S}_y$-terms to preserve zz-terms only (see fig. S1). For samples at natural abundance, the formation of these undesired MQCs is very unfavored, and this extra delay is theoretically unnecessary. However, we demonstrate in section S2 that it is still useful to effectively suppress t₁-noise, similarly to the homonuclear case presented above.

DISCUSSION

In this work, we introduced a method for t₁-noise suppression in MAS-DNP ssNMR experiments in the context of samples at natural abundance. This method, called here zz-filter, consists in the conversion of DQCs into longitudinal two-spin order $I_{\mathit{\text{jz}}}{I}_{\mathit{\text{kz}}}$ (zz-terms), while the strong magnetization of uncoupled spins is rotated to the transverse plane. The subsequent zz-filter delay leads to the dephasing of the unwanted signal from uncoupled spins by chemical shift and heteronuclear proton interaction terms. The preserved longitudinal two-spin order zz-terms are then converted into a mixture of ZQCs and DQCs. The latter follow then the DQ to SQ CTP before being detected. This zz-filter is simple to implement (see section S1 for full implementation) and is, in principle, effective regardless of the source of instability leading to t₁-noise. We show that this approach is compatible with both J- and dipolar-based DQ/SQ homonuclear correlation experiments, and despite the sole trade-off of an almost twofold loss in signal intensity, it enables a tremendous reduction of the t₁-noise level, leading to spectra of improved sensitivity in the regions of t₁-noise. Demonstrated on a commercial Bruker MAS-DNP system, the combination of the zz-filter with a z-filter applied before detection, termed z³-filter, reduces the t₁-noise to the thermal noise level, thereby revealing weak signals from longer-range correlations and even intermolecular contacts that were previously obscured. The performances of the z³-filter are even more impressive for DNP experiments at ultralow temperature (~30 K), performed on a home-built He-spinning MAS-DNP system, where the increased sensitivity leads to an even more pronounced t₁-noise. The latter is drastically reduced with the application of the z³-filter, leading to a ~fivefold SNR improvement along the t₁-noise polluted f₁-traces. This approach yields spectra of unprecedented quality under these conditions—at ultralow temperatures and on natural abundance samples—and enables a natural abundance 2D DQ/SQ spectrum recorded at 30 K. This development paves the way for a broad range of applications where t₁-noise has long been the limiting factor, notably the investigation of complex biomolecular and organic systems by ultralow-temperature MAS-DNP and the precise quantification of dipolar build-ups from 2D datasets.

MATERIALS AND METHODS

Sample preparation

Ampicillin [d-(-)-α-aminobenzylpenicillin] was purchased from Sigma-Aldrich. Before impregnation, the powder was ground by hand using a mortar to reduce the grain size, and ~45 mg of powder was impregnated with 12 μl of 40 mM cAsymPol-POK (24) in d₈-glycerol/D₂O/H₂O (60:30:10, v:v:v). Two samples were prepared from the same stock solution, one packed in a sapphire rotor for the 100 K experiments and another in a zirconia rotor for the 30 K experiments.

DNP experiments at 100 K

DNP experiments at 100 K were carried out on a Bruker Advance III spectrometer operating at 9.4 T, equipped with a Bruker low temperature 3.2 mm widebore MAS probe and a 263 GHz (9.4 T) gyrotron. With microwave irradiation, the sample temperature was estimated at 106 K. The probe mode was in double resonance mode ¹H/¹³C for INADEQUATE and SR26 experiments and in triple resonance mode ¹H/¹³C/¹⁵N for TEDOR experiments. The spinning speed was set to 8 KHz for most experiments, except for the zz-filter efficiency comparison for γ-encoded and non-γ-encoded sequences in Sec. S7, for which the spinning speed was 6.5 kHz.

z³f-refocused INADEQUATE experiments

the 2D ¹³C–¹³C DQ/SQ z-filtered refocused INADEQUATE (54, 85–87) spectra presented in Fig. 2 (fig. S4 for the entire spectra) were acquired with 240 increments of 64 scans each using States-time-proportional phase incrementation (TPPI) (103) for quadrature detection, a recycle delay of 3 s and 100-kHz swept-frequency two-pulse phase modulation (SWf-TPPM) (104–106) ¹H decoupling. Acquisition times were 20 ms for the direct (f₂) and 3 ms for the indirect (f₁) dimension, respectively, leading to an overall experimental time of 13.5 hours. The delay τ was set to 29 rotor periods, corresponding to 3.6 ms (note that the $T_2^{\prime }$ on the ampicillin samples was measured at 54.5 ms). As recommended in the zfr-refocused INADEQUATE (87), a 3-ms z-filter before the detection has been used. The CP contact time was set to 1 ms with a ramped (80 to 100%) CP spin-lock on the ¹H channel. For the zz-filtered experiment, dubbed DQ/SQ z³-filtered refocused INADEQUATE, the zz-filter length was set to 50 rotor periods, corresponding to 6.25 ms, without the application of DARR field on the ¹H channel. Data were zero-filled before Fourier transform, and a line broadening of 50 Hz was used on the direct dimension. For the results presented in Fig. 1, we used the same sequence with 64 scans [except for Fig. 1C (i) with one scan only], a recycling delay of 4.2 s, and 15 ms of acquisition time. The delay τ was set to 31 rotor periods, which corresponds to 3.9 ms. We also used a z-filter of 3 ms, and the zz-filter length was set to 25 rotor periods, corresponding to 3.1 ms. Data were zero-filled before Fourier transformed, and a line broadening of 150 Hz was used on the 1D spectra of Fig. 1C (i) for better visualization. For Fig. 1B, the phase ϕ of the generated DQCs was fixed to π/4 according to the phases used in (87), and we varied the phase of the zz-filter pulses, θ. The resulting pseudo-2D spectrum is represented in fig. S3, and the normalized signal intensity represented in Fig. 1B (blue dots) was obtained by taking the integral of the DQ-filtered signal for each angle increment on the region represented by red-shaded regions. The signal intensities were then normalized by the intensity obtained for $2\mathrm{\theta }-\mathrm{\varphi }=0$.

z³f-SR26 experiments

the 2D ¹³C–¹³C DQ/SQ dipolar correlation experiments of Figs. 3 and 4 were performed with the SR26 recoupling sequence (95, 97) combined with StiC phase shifts (98). They were acquired with 240 increments of 16 scans each using the States-TPPI for the quadrature detection, and a recycle delay of 4.5 s, leading to an overall experimental time of 4.5 hours. For both the DQ excitation and reconversion blocks, one cycle of SR26 was used, corresponding to an overall mixing time of 4 ms, with 100-kHz continuous wave–Lee Goldburg (CW-LG) (107) ¹H decoupling. A 100-kHz SWf-TPPM ¹H decoupling was applied during both the direct and indirect evolution time of 15 and 3 ms, respectively. The CP contact time was set to 2 ms with a ramped (80 to 100%) CP spin-lock on the ¹H channel. For the zz-filtered experiment, the zz-filter length was set 40 rotor periods, corresponding to 5 ms, under a DARR field of ~8 kHz on the ¹H channel (${\mathrm{\omega }}_{1\mathrm{H}}={\mathrm{\omega }}_r$). The phases of the zz-filter were incremented for the States-TPPI quadrature detection along with the SR26 reconversion block to filter the DQCs. The data were zero-filled before Fourier transform, without any apodization.

z³f-TEDOR experiments

the 2D zfr-TEDOR (51) spectra presented in fig. S1 were acquired with 64 increments of 128 scans each using Stats-TPPI for quadrature detection, a recycle delay of 4 s and 100-kHz SWf-TPPM ¹H decoupling. Acquisition times were 8 ms for the direct (f₂) and 4 ms for the indirect (f₁) dimension, respectively, leading to an overall experimental time of 9.5 hours. The mixing time was set to 4 ms, which corresponds to four TEDOR block, during which a 100-kHz CW-LG decoupling was applied on the ¹H channel. For both experiments, we used a z-filter of 3 ms before detection, and we added—for the zz-filtered TEDOR—a zz-filter of 24 rotor period, corresponding to ~3 ms. We did not use any DARR field on the ¹H channel during the zz-filter. The CP contact time was set to 2 ms with a ramped (80 to 100%) CP spin-lock on the ¹H channel. The data were zero-filled before Fourier transform, without any apodization.

DNP experiments at 30 K

DNP experiments at 30 K were carried out on a Bruker Advance III spectrometer operating at 9.4 T, equipped with a 263 GHz (9.4 T) gyrotron and a self-developed closed-loop cryogenic He-spinning system, made of a cryogenic ultralow-temperature 3.2-mm wide bore MAS probe in double resonance mode ¹H/¹³C and its associated cryostat (44). With microwave irradiation, the sample temperature was estimated at 30 K. The spinning speed was set to 6850 Hz. 2D ¹³C–¹³C DQ/SQ dipolar correlation experiments of Fig. 5 were performed with the SR26 recoupling sequence combined with StiC phase shifts. They were acquired with 256 increments of 16 scans, each using the States-TPPI for the quadrature detection, and a recycle delay of 4.5 s, leading to an overall experimental time of 5 hours. For both the DQ excitation and reconversion blocks, one cycle of SR26 was used, corresponding to an overall mixing time of 4.7 ms, with 100-kHz CW-LG ¹H decoupling. A 100-kHz SWf-TPPM ¹H decoupling was applied during both the direct and indirect evolution time of 20 and 3.2 ms, respectively. The CP contact time was set to 2 ms with a ramped (80 to 100%) CP spin-lock on the ¹H channel. For the zz-filtered experiment, the zz-filter length was set 30 rotor periods, corresponding to 4.3 ms, without any DARR field on the ¹H channel. The phases of the zz-filter were incremented for the States-TPPI quadrature detection along with the SR26 reconversion block to filter the DQCs. The data were zero-filled before Fourier transform, without any apodization.

Noise analysis

The noise analysis was performed assuming a normal distribution $\mathcal{N}(0,\mathrm{\sigma })$ centered at zero, where σ denotes the noise SD. The thermal noise SD, ${\mathrm{\sigma }}_{\text{th}}$, was measured directly from signal-free f₁-traces at several positions in the spectra (f₂ = −100, −50, 0, 225, 250, 275, and 300 ppm, for all experiments). When displaying f₁-traces from various spectra (Figs. 2 and 4), we used a gray to dark blue color gradient to represent the 99.7% confidence interval of thermal noise, corresponding to the $\pm 3{\mathrm{\sigma }}_{\text{th}}$ limit. The color scale used in Figs. 2 and 4 is illustrated in Fig. 6A. For the 30 K MAS-DNP measurements, a zoom in Fig. 5 shows that the t₁-noise in the 2D spectrum is predominantly antiphase along the f₂ dimension. Because the f₁-trace representation does not reflect this behavior, we instead displayed the data as the absolute value along f₂ and the real part along f₁. Assuming that the real and imaginary components of the signal are independent and follow $\mathcal{N}(0,{\mathrm{\sigma }}_{\text{th}})$, the corresponding magnitude spectrum follows a Rayleigh distribution $\mathrm{ℛ}\left({\mathrm{\sigma }}_{\text{th}}\right)$. In this case, the noise SD ${\mathrm{\sigma }}_{\text{th}}$ can be estimated from the measured mean noise amplitude μ using

$${\mathrm{\sigma }}_{\text{th}}=\mathrm{\mu }\sqrt{2/\mathrm{\pi }}$$ (15)

Fig. 6. Color gradient representation of f₁-traces based on ${\mathrm{\sigma }}_{\text{th}}$.

Schema of the color gradient used to represent f₁-traces based on the thermal noise standard deviation ${\mathrm{\sigma }}_{\text{th}}$ in the case of a normal distribution $\mathcal{N}(0,{\mathrm{\sigma }}_{\text{th}})$ (A) and a Rayleigh distribution $\mathcal{R}\left({\mathrm{\sigma }}_{\text{th}}\right)$ (B).

To quantitatively assess the t₁-noise reduction achieved by the z³-filter, we estimated the t₁-noise standard deviation ${\mathrm{\sigma }}_{\mathrm{t}1}$ from the most noise-polluted f₁-trace, using signal-free regions (highlighted in red in Figure S2). The ratio ${\mathrm{\sigma }}_{\mathrm{t}1}/{\mathrm{\sigma }}_{\text{th}}$ thus reflects the relative amplitude of t₁-noise with respect to thermal noise, together with the SNR along the f₁-traces and the zz-filter efficiency ${\mathrm{\eta }}_{\mathit{zz}}$. These values, along with the regions used for their measurement, are shown in fig. S2.

Practical aspects of the zz-filter implementation

In all experiments presented here, the zz-filter was applied immediately after the DQ-excitation block and consisted of two 90° pulses with the same phase, separated by a delay ${\mathrm{\Delta }}_{\mathit{zz}}$. The phases of these pulses were incremented together with the DQ-excitation block to achieve DQ selection via phase cycling or to enable States-TPPI quadrature detection. If phase cycling and/or States-TPPI quadrature detection is encoded on the reconversion block, the zz-filter pulse phases should not be incremented. The delay ${\mathrm{\Delta }}_{\mathit{zz}}$ was generally set to maintain rotor synchronization. While rotor synchronicity is not strictly required in every case, it simplifies implementation without affecting performance. Detailed discussions on zz-filter implementation, rotor synchronicity, and optimization can be found in section S1.

Supplementary Materials

This PDF file includes:

Sections S1 to S8

Figs. S1 to S7

References