A tunable homonuclear dipolar decoupling scheme for high-resolution proton NMR of solids from slow to fast magic-angle spinning

Pure Isotropic Proton NMR Spectra in Solids using Deep Learning

The resolution of proton solid-state NMR spectra is usually limited by broadening arising from dipolar interactions between spins. Magic-angle spinning alleviates this broadening by inducing coherent averaging. However, even the highest spinning rates experimentally accessible today are not able to completely remove dipolar interactions. Here, we introduce a deep learning approach to determine pure isotropic proton spectra from a two-dimensional set of magic-angle spinning spectra acquired at different spinning rates. Applying the model to 8 organic solids yields high-resolution ¹ H solid-state NMR spectra with isotropic linewidths in the 50-400 Hz range.

Solid-State NMR: Methods for Biological Solids

In the last two decades, solid-state nuclear magnetic resonance (ssNMR) spectroscopy has transformed from a spectroscopic technique investigating small molecules and industrial polymers to a potent tool decrypting structure and underlying dynamics of complex biological systems, such as membrane proteins, fibrils, and assemblies, in near-physiological environments and temperatures. This transformation can be ascribed to improvements in hardware design, sample preparation, pulsed methods, isotope labeling strategies, resolution, and sensitivity. The fundamental engagement between nuclear spins and radio-frequency pulses in the presence of a strong static magnetic field is identical between solution and ssNMR, but the experimental procedures vastly differ because of the absence of molecular tumbling in solids. This review discusses routinely employed state-of-the-art static and MAS pulsed NMR methods relevant for biological samples with rotational correlation times exceeding 100's of nanoseconds. Recent developments in signal filtering approaches, proton methodologies, and multiple acquisition techniques to boost sensitivity and speed up data acquisition at fast MAS are also discussed. Several examples of protein structures (globular, membrane, fibrils, and assemblies) solved with ssNMR spectroscopy have been considered. We also discuss integrated approaches to structurally characterize challenging biological systems and some newly emanating subdisciplines in ssNMR spectroscopy.

Optimisation of 1H PMLG homonuclear decoupling at 60 kHz MAS to enable 15N-1H through-bond heteronuclear correlation solid-state NMR spectroscopy

The Lee–Goldburg condition for homonuclear decoupling in ¹H magic-angle spinning (MAS) solid-state NMR sets the angle θ, corresponding to arctan of the ratio of the rf nutation frequency, ν₁, to the rf offset, to be the magic angle, θ_m, equal to tan⁻¹(√2) = 54.7°. At 60 kHz MAS, we report enhanced decoupling compared to MAS alone in a ¹H spectrum of ¹⁵N-glycine with at θ = 30° for a ν₁ of ∼100 kHz at a ¹H Larmor frequency, ν₀, of 500 MHz and 1 GHz, corresponding to a high chemical shift scaling factor (λ_CS) of 0.82. At 1 GHz, we also demonstrate enhanced decoupling compared to 60 kHz MAS alone for a lower ν₁ of 51 kHz, i.e., a case where the nutation frequency is less than the MAS frequency, with θ = 18°, λ_CS = 0.92. The ratio of the rotor period to the decoupling cycle time, Ψ = τ_r/τ_c, is in the range 0.53 to 0.61. Windowed decoupling using the optimised parameters for a ν₁ of ∼100 kHz also gives good performance in a ¹H spin-echo experiment, enabling implementation in a ¹H-detected ¹⁵N–¹H cross polarisation (CP)-refocused INEPT heteronuclear correlation NMR experiment. Specifically, initial ¹⁵N transverse magnetisation as generated by ¹H–¹⁵N CP is transferred back to ¹H using a refocused INEPT pulse sequence employing windowed ¹H decoupling. Such an approach ensures the observation of through-bond N–H connectivities. For ¹⁵N-glycine, while the CP-refocused INEPT experiment has a lower sensitivity (∼50%) as compared to a double CP experiment (with a 200 μs ¹⁵N to ¹H CP contact time), there is selectivity for the directly bonded NH₃⁺ moiety, while intensity is observed for the CH₂¹H resonances in the double CP experiment. Two-dimensional ¹⁵N–¹H correlation MAS NMR spectra are presented for the dipeptide β-AspAla and the pharmaceutical cimetidine at 60 kHz MAS, both at natural isotopic abundance. For the dipeptide β-AspAla, different build-up dependence on the first spin-echo duration is observed for the NH and NH₃⁺ moieties demonstrating that the experiment could be used to distinguish resonances for different NH_x groups.

¹⁵N–¹H heteronuclear NMR correlation at natural abundance in the solid state via J couplings is enabled by optimisation of phase-modulated Lee–Goldburg (PMLG) ¹H homonuclear decoupling during the spin echoes, far from the ideal magic-angle condition.

Fast remote correlation experiments for 1H homonuclear decoupling in solids

In ¹H MAS spectra, the residual homogeneous broadening under MAS is due to a combination of higher-order shifts and splittings. We have recently shown how the two-dimensional anti-z-COSY experiment can be used for the removal of the splittings. However, this requires spectra with high resolution in the indirect dimension (t₁), leading to experiment times of hours. Here, we show how anti-z-COSY can be adapted to be combined with the two-dimensional one pulse (TOP) transformation which leads to significantly reduced experimental time while retaining the line narrowing effect. The experiment is demonstrated on a powdered sample of L-histidine monohydrochloride monohydrate, where the new TAZ-COSY sequence at 100 kHz MAS, yields between a factor 1.6 and 2.3 increase in resolution compared with the equivalent one-pulse experiment, in just 20 min. The same methodology is also adapted for the acquisition of liquid state ¹H homodecoupled data, and an example is given for testosterone.

Homonuclear Decoupling in 1 H NMR of Solids by Remote Correlation

The typical linewidths of ¹H NMR spectra of powdered organic solids at 111 kHz magic‐angle spinning (MAS) are of the order of a few hundred Hz. While this is remarkable in comparison to the tens of kHz observed in spectra of static samples, it is still the key limit to the use of ¹H in solid‐state NMR, especially for complex systems. Here, we demonstrate a novel strategy to further improve the spectral resolution. We show that the anti‐z‐COSY experiment can be used to reduce the residual line broadening of ¹H NMR spectra of powdered organic solids. Results obtained with the anti‐z‐COSY sequence at 100 kHz MAS on thymol, β‐AspAla, and strychnine show an improvement in resolution of up to a factor of two compared to conventional spectra acquired at the same spinning rate.

Origin of the residual line width under frequency-switched Lee-Goldburg decoupling in MAS solid-state NMR

Homonuclear decoupling sequences in solid-state nuclear magnetic resonance (NMR) under magic-angle spinning (MAS) show experimentally significantly larger residual line width than expected from Floquet theory to second order. We present an in-depth theoretical and experimental analysis of the origin of the residual line width under decoupling based on frequency-switched Lee-Goldburg (FSLG) sequences. We analyze the effect of experimental pulse-shape errors (e.g., pulse transients and B 1 -field inhomogeneities) and use a Floquet-theory-based description of higher-order error terms that arise from the interference between the MAS rotation and the pulse sequence. It is shown that the magnitude of the third-order auto term of a single homo- or heteronuclear coupled spin pair is important and leads to significant line broadening under FSLG decoupling. Furthermore, we show the dependence of these third-order error terms on the angle of the effective field with the B 0 field. An analysis of second-order cross terms is presented that shows that the influence of three-spin terms is small since they are averaged by the pulse sequence. The importance of the inhomogeneity of the radio-frequency (rf) field is discussed and shown to be the main source of residual line broadening while pulse transients do not seem to play an important role. Experimentally, the influence of the combination of these error terms is shown by using restricted samples and pulse-transient compensation. The results show that all terms are additive but the major contribution to the residual line width comes from the rf-field inhomogeneity for the standard implementation of FSLG sequences, which is significant even for samples with a restricted volume.

High-resolution 1H NMR of powdered solids by homonuclear dipolar decoupling

The development of homonuclear dipolar decoupling sequences to obtain high-resolution ¹H NMR spectra from solids has recently celebrated its 50th birthday. Over the years, a series of different decoupling schemes have been developed, starting with the pioneering Lee-Goldburg and WAHUHA sequences up to the most recent generation of experimentally optimized phase-modulated schemes such as eDUMBO-1₂₂ and LG4. These schemes can all yield over an order of magnitude reduction in ¹H NMR linewidths in solids. Here we provide an overview and a broad experimental comparison of the performance of the main sequences, which has so far been absent in the literature, especially between the newest and the oldest decoupling schemes. We compare experimental results obtained using eight different decoupling schemes (LG, WHH-4, MREV-8, BR-24, FSLG/PMLG, DUMBO-1, eDUMBO-1₂₂ and LG4) on three different microcrystalline powdered samples (alanine, glycine and β-AspAla) and at three different MAS rates (3.0, 12.5 and 22.0 kHz). Finally, since these sequences can be technically demanding, we describe the experimental protocol we have used to optimize these schemes with the aim to provide simple guidelines for the optimization of CRAMPS experiments for all NMR users.

1H line width dependence on MAS speed in solid state NMR - Comparison of experiment and simulation

Recent developments in magic angle spinning (MAS) technology permit spinning frequencies of ≥100 kHz. We examine the effect of such fast MAS rates upon nuclear magnetic resonance proton line widths in the multi-spin system of β-Asp-Ala crystal. We perform powder pattern simulations employing Fokker-Plank approach with periodic boundary conditions and ¹H-chemical shift tensors calculated using the bond polarization theory. The theoretical predictions mirror well the experimental results. Both approaches demonstrate that homogeneous broadening has a linear-quadratic dependency on the inverse of the MAS spinning frequency and that, at the faster end of the spinning frequencies, the residual spectral line broadening becomes dominated by chemical shift distributions and susceptibility effects even for crystalline systems.

The role of water in the degradation process of paper using 1H HR-MAS NMR spectroscopy

The thermodynamic properties of water are essential for determining the corresponding properties of every biosystem it interacts with. Indeed, the comprehension of hydration mechanisms is fundamental for the understanding and the control of paper degradation pathways induced by natural or artificial aging. In fact, the interactions between water and cellulose at the accessible sites within the fibres' complex structure are responsible for the rupture of hydrogen bonds and the consequent swelling of the cellulose fibres and consumption of the amorphous regions. In this paper we study the hydration process of cellulose in naturally and artificially aged paper samples by measuring the proton spin-lattice (T₁) and spin-spin (T₂) relaxation times of the macroscopic magnetization through nuclear magnetic resonance (NMR) experiments. The observed behaviour of T₁ and T₂ is quite complex and strictly dependent on the water content of paper samples. This has been interpreted as due to the occurrence of different mechanisms regulating the water-cellulose interaction within the fibres. Furthermore, we have measured T₁ as a function of the artificial aging time comparing the results with those measured on three paper samples dated back to the 15th century. We found that the evolution of T₁ in model papers artificially aged is correlated with that of ancient paper, providing therefore a way for estimating the degradation of cellulosic materials in terms of an equivalent time of artificial aging. These results provide fundamental information for industrial applications and for the preservation and restoration of cultural heritage materials based on cellulose such as ancient paper or textiles.

Five decades of homonuclear dipolar decoupling in solid-state NMR: Status and outlook

It has been slightly more than fifty years since the first homonuclear spin decoupling scheme, Lee-Goldburg decoupling, was proposed for removing homonuclear dipolar interactions in solid-state nuclear magnetic resonance. A family of such schemes has made observation of high-resolution NMR spectra of abundant spins possible in various applications in solid state. This review outlines the strategies used in this field and the future prospects of homonuclear spin decoupling in solid-state NMR.

High resolution triple resonance micro magic angle spinning NMR spectroscopy of nanoliter sample volumes

To be able to study mass-limited samples and small single crystals, a triple resonance micro-magic angle spinning (μMAS) probehead for the application of high-resolution solid-state NMR of nanoliter samples was developed. Due to its excellent rf performance this allows us to explore the limits of proton NMR resolution in strongly coupled solids. Using homonuclear decoupling we obtain unprecedented (1)H linewidths for a single crystal of glycine (Δν(CH2) = 0.14 ppm) at high field (20 T) in a directly detected spectrum. The triple channel design allowed the recording of high-resolution μMAS (13)C-(15)N correlations of [U-(13)C-(15)N] arginine HCl and shows that the superior (1)H resolution opens the way for high-sensitivity inverse detection of heteronuclei even at moderate spinning speeds and rf-fields. Efficient decoupling leads to long coherence times which can be exploited in many correlation experiments.

Minimizing the effects of RF inhomogeneity and phase transients allows resolution of two peaks in the (1)H CRAMPS NMR spectrum of adamantane

One of the limiting factors to achieving highly resolved (1)H NMR spectra with (1)H homonuclear decoupling sequences is imperfections in the applied radiofrequency (RF) pulses, most notably phase transients and RF inhomogeneity. Through a series of simulations and solid-state NMR experiments, it is demonstrated that the combined effects of phase transients and RF inhomogeneity can be minimized by a combination of (i) restricting the sample to small volume of the rotor, (ii) by employing a super-cycled version of the DUMBO decoupling sequence, and (iii) by carefully adjusting the probe tuning such that the asymmetric component of phase transients is minimized. Under these optimal conditions, it was possible to clearly resolve two signals in the (1)H CRAMPS NMR spectrum of adamantane arising from the CH and CH2 protons in the molecule. It is proposed that adamantane could be a very useful setup sample for (1)H CRAMPS NMR as the two peaks are only resolved when the effects of RF inhomogeneity and phase transients are minimized.

Improving the resolution in proton-detected through-space heteronuclear multiple quantum correlation NMR spectroscopy

Connectivities and proximities between protons and low-gamma nuclei can be probed in solid-state NMR spectroscopy using two-dimensional (2D) proton-detected heteronuclear correlation, through Heteronuclear Multiple Quantum Correlation (HMQC) pulse sequence. The indirect detection via protons dramatically enhances the sensitivity. However, the spectra are often broadened along the indirect F1 dimension by the decay of heteronuclear multiple-quantum coherences under the strong (1)H-(1)H dipolar couplings. This work presents a systematic comparison of the performances of various decoupling schemes during the indirect t1 evolution period of dipolar-mediated HMQC (D-HMQC) experiment. We demonstrate that (1)H-(1)H dipolar decoupling sequences during t1, such as symmetry-based schemes, phase-modulated Lee-Goldburg (PMLG) and Decoupling Using Mind-Boggling Optimization (DUMBO), provide better resolution than continuous wave (1)H irradiation. We also report that high resolution requires the preservation of (1)H isotropic chemical shifts during the decoupling sequences. When observing indirectly broad spectra presenting numerous spinning sidebands, the D-HMQC sequence must be fully rotor-synchronized owing to the rotor-synchronized indirect sampling and dipolar recoupling sequence employed. In this case, we propose a solution to reduce artefact sidebands caused by the modulation of window delays before and after the decoupling application during the t1 period. Moreover, we show that (1)H-(1)H dipolar decoupling sequence using Smooth Amplitude Modulation (SAM) minimizes the t1-noise. The performances of the various decoupling schemes are assessed via numerical simulations and compared to 2D (1)H-{(13)C} D-HMQC experiments on [U-(13)C]-L-histidine⋅HCl⋅H2O at various magnetic fields and Magic Angle spinning (MAS) frequencies. Great resolution and sensitivity enhancements resulting from decoupling during t1 period enable the detection of heteronuclear correlation between aliphatic protons and ammonium (14)N sites in L-histidine⋅HCl⋅H2O.

High-resolution proton CRAMPS NMR using narrowband analog filters and postponed data acquisition

Proton linewidths decrease with increasing magic-angle spinning (MAS) rates. However, without spin dilution by deuteration, even with the fastest MAS rates available today, the narrowest proton linewidths are obtained by using the combined rotation and multiple pulse spectroscopy (CRAMPS) method. Direct observation under windowed CRAMPS typically introduces several tens of times more noise, partly because wideband analog filters (e.g. 5 MHz) must be used or sometimes even bypassed. Here we report that it is possible to keep using narrowband analog filters (about 50 kHz cutoff frequency) in CRAMPS by taking advantage of the time delay caused by the filters, which is inversely proportional to the cutoff frequency. This delay coincides with typical CRAMPS cycle times, enabling acquisition of the data point in the next detection window. The noise of such CRAMPS spectra is only about 5 times larger than MAS-only spectra. This new method allows CRAMPS to be performed on systems that lack wideline hardware (wideband filters and fast ADCs), for example, older spectrometers originally intended for solution NMR.

Detailed analysis of the TIMES and TIMES0 high-resolution MAS methods for high-resolution proton NMR

We analyze and compare the specifications of TIMES and TIMES(0) proton high-resolution NMR methods for solid-state samples. This comparison is performed in terms of resolution versus magic-angle spinning (MAS) spinning speed, ν(R), rf-field amplitude, ν(1), and tilt-angle for the effective rf-field, θ(p). The chemical-shift and homo-nuclear dipolar scaling factors are calculated for both methods. For all MAS speeds, the best resolution is always observed with rf-field of ν(1)≈120-130 kHz. At slow MAS speed (ν(R)≤10 kHz), the best resolution is observed for a tilt-angle of θ(P)≈90°. At moderate spinning speed (15≤ν(R)≤35 kHz), θ(P)≈55° gives the best resolution. At higher MAS speed (ν(R)≥60 kHz), with TIMES and TIMES(0) the best resolution is obtained for θ(P)≤40°; but we then recommend TIMES(0), owing to its simpler set-up. We also show that in addition to the usual high rf-field regime (ν(1)≈120-130 kHz), another low rf-regime (ν(1)≈40-50 kHz) exists at MAS speed higher than ν(R)≥60 kHz, which also gives a good (1)H resolution. This low rf-regime should be useful for multi-dimensional analyses of bio-molecules with (1)H detection under high-resolution, in order to limit the heating of the sample.

Practical choice of ¹H-¹H decoupling schemes in through-bond ¹H-{X} HMQC experiments at ultra-fast MAS

Three (1)H-(1)H homonuclear dipolar decoupling schemes for (1)H indirect detection measurements at very fast MAS are compared. The sequences require the following conditions: (i) being operable at very fast MAS, (ii) a long T(2)(') value, (iii) a large scaling factor, (iv) a small number of adjustable parameters, (v) an acquisition window, (vi) a low rf-power requirement, and (vii) a z-rotation feature. To satisfy these conditions a modified sequence named TIlted Magic-Echo Sandwich with zero degree sandwich pulse (TIMES(0)) is introduced. The basic elements of TIMES(0) consist of one sampling window and two phase-ramped irradiations, which realize alternating positive and negative 360° rotations of (1)H magnetization around an effective field tilted with an angle θ from the B(0) axis. The TIMES(0) sequence benefits from very large chemical shift scaling factors at ultra-fast MAS that reach κ(cs)=0.90 for θ=25° at ν(r)=80kHz MAS and only four adjustable parameters, resulting in easy setup. Long κ(cs)T(2)(') values, where T(2)(') is a irreversible proton transverse relaxation time, greatly enhance the sensitivity in (1)H-{(13)C} through-bond J-HMQC (Heteronuclear Multiple-Quantum Coherence) measurements with (1)H-(1)H decoupling during magnetization transfer periods. Although similar sensitivity can be obtained with through-space D-HMQC sequences, in which (13)C-(1)H dipolar interactions are recoupled, J-HMQC experiments incorporating (1)H-(1)H decoupling benefit from lower t(1)-noise, more uniform excitation of both CH, CH(2) and CH(3) moieties, and easier identification of through-bond connectivities.

Rotor-synchronized dipolar-filter sequence at fast MAS in solid-state NMR

Dipolar filters are of considerable importance for eliminating the (1)H NMR signal of the rigid components of heterogeneous compounds while selecting the signal of their mobile parts. On the basis of such filters, structural and dynamical information of these compounds can often be acquired through further manipulations (e.g. spin diffusion) on the spin systems. To overcome the destructive interferences between the magic angle spinning (MAS) speed and the cycle-time of the widely-used Rotor-Asynchronized Dipolar Filter (RADF) sequence, we introduce a new method called Rotor-Synchronized Dipolar Filter (RSDF). This communication shows that this sequence does not present any interference with the spinning speed and is more compatible than RADF with high MAS frequencies (ν(R)>12 kHz). This new pulse sequence will potentially contribute to future researches on heterogeneous materials, such as multiphase polymer and membrane systems.

Progress in correlation spectroscopy at ultra-fast magic-angle spinning: basic building blocks and complex experiments for the study of protein structure and dynamics

Recent progress in multi-dimensional solid-state NMR correlation spectroscopy at high static magnetic fields and ultra-fast magic-angle spinning is discussed. A focus of the review is on applications to protein resonance assignment and structure determination as well as on the characterization of protein dynamics in the solid state. First, the consequences of ultra-fast spinning on sensitivity and sample heating are considered. Recoupling and decoupling techniques at ultra-fast MAS are then presented, as well as more complex experiments assembled from these basic building blocks. Furthermore, we discuss new avenues in biomolecular solid-state NMR spectroscopy that become feasible in the ultra-fast spinning regime, such as sensitivity enhancement based on paramagnetic doping, and the prospect of direct proton detection.