Improving spectral resolution in biological solid-state NMR using phase-alternated rCW heteronuclear decoupling

Tailoring solid-state DNP methods to the study of α-synuclein LLPS

Dynamic Nuclear Polarization (DNP) is a technique that leverages the quantum sensing capability of electron spins to enhance the sensitivity of nuclear magnetic resonance (NMR) signals, especially for insensitive samples. Glassing agents play a crucial role in the DNP process by facilitating the transfer of polarization from the unpaired electron spins to the nuclear spins along with cryoprotection of biomolecules. DNPjuice comprising of glycerol-d8/D2O/H2O has been extensively used for this purpose over the past two decades. Polyethylene glycol (PEG), also used as a cryoprotectant, is often used as a crowding agent in experimental setups to mimic cellular conditions, particularly the invitro preparation of liquid-liquid phase separated (LLPS) condensates. In this study, we investigate the efficacy of PEG as an alternative to glycerol in the DNP juice, critical for signal enhancement. The modified DNP matrix leads to high DNP enhancement which enables direct study of LLPS condensates by solid-state DNP methods without adding any external constituents. An indirect advantage of employing PEG is that the PEG signals appear at ∼72.5 ppm and are relatively well-separated from the aliphatic region of the protein spectra. Large cross-effect DNP enhancement is attained for 13C-glycine by employing the PEG-water mixture as a glassing agent and ASYMPOL-POK as the state-of-art polarizing agent, without any deuteration. The DNP enhancement and the buildup rates are similar to results obtained with DNP juice, conforming to that PEG serves as a good candidate for both inducing crowding and glassing agent in the study of LLPS.

Optimal-Control-Based Cβ Chemical Shift Encoding for Efficient Signal Assignment of Solid Proteins

Fast magic-angle spinning (MAS) solid-state NMR spectroscopy is a powerful tool for gaining structural and dynamic information on solid proteins. To access such information site-specifically, the signal assignment process is unavoidable. In the assignment process, Cα and Cβ chemical shifts are of paramount importance in identifying the type of amino acid residues. Conventionally, however, recording the Cβ chemical shift of solid proteins with relatively short transverse relaxation time is often limited by the long delay required for the magnetization transfer to Cβ spins and its evolution, that is, by the sensitivity drop. In this article, we propose a new method that encodes the Cβ chemical shifts onto the intensities of the scalar-coupled Cα signals by combining an optimal control-based spin manipulation pulse and a spin-state filter. This reduces the total required transverse evolution to less than half of that for the previously proposed method, opening up the concept of the Cβ-encoding nearest-neighbor NMR, for the first time, to solid proteins. Also, the total measurement time was shorter than that required for the explicit Cβ shift evolution. We demonstrate the sequential signal assignment for microcrystalline protein GB1, and then discuss the prospects for more challenging proteins.

"Activated Borane": A Porous Borane Cluster Polymer as an Efficient Lewis Acid-Based Catalyst

Borane cluster-based porous covalent networks, named activated borane (ActB), were prepared by cothermolysis of decaborane(14) (nido-B10H14) and selected hydrocarbons (toluene, ActB-Tol; cyclohexane, ActB-cyHx; and n-hexane, ActB-nHx) under anaerobic conditions. These amorphous solid powders exhibit different textural and Lewis acid (LA) properties that vary depending on the nature of the constituent organic linker. For ActB-Tol, its LA strength even approaches that of the commonly used molecular LA, B(C6F5)3. Most notably, ActBs can act as heterogeneous LA catalysts in hydrosilylation/deoxygenation reactions with various carbonyl substrates as well as in the gas-phase dehydration of ethanol. These studies reveal the potential of ActBs in catalytic applications, showing (a) the possibility for tuning catalytic reaction outcomes (selectivity) in hydrosilylation/deoxygenation reactions by changing the material's composition and (b) the very high activity toward ethanol dehydration that exceeds the commonly used γ-Al2O3 by achieving a stable conversion of ∼93% with a selectivity for ethylene production of ∼78% during a 17 h continuous period on stream at 240 °C.

Asynchronising five-fold symmetry sequence for better homonuclear polarisation transfer in magic-angle-spinning solid-state NMR

Recoupling, decoupling, and multidimensional correlation experiments in magic-angle-spinning (MAS) solid-state NMR can be designed by exploiting the symmetry of internal spin interactions. One such scheme, namely, C5₂¹, and its supercycled version SPC5₂¹, notated as a five-fold symmetry sequence, is widely used for double-quantum dipole-dipole recoupling. Such schemes are generally rotor synchronised by design. We demonstrate an asynchronous implementation of the SPC5₂¹ sequence leading to higher double-quantum homonuclear polarisation transfer efficiency compared to the normal synchronous implementation. Rotor-synchronisation is broken in two different ways: lengthening the duration of one of the pulses, denoted as pulse-width variation (PWV), and mismatching the MAS frequency denoted as MAS variation (MASV). The application of this asynchronous sequence is shown on three different samples, namely, U-¹³C-alanine and 1,4-¹³C-labelled ammonium phthalate which include ¹³C_α-¹³C_β, ¹³C_α-¹³C_o, and ¹³C_o-¹³C_o spin systems, and adenosine 5'- triphosphate disodium salt trihydrate (ATP⋅3H₂O). We show that the asynchronous version performs better for spin pairs with small dipole-dipole couplings and large chemical-shift anisotropies, for example, ¹³C_o-¹³C_o. Simulations and experiments are shown to corroborate the results.

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.

Maximizing efficiency of dipolar recoupling in solid-state NMR using optimal control sequences

Dipolar recoupling is a central concept in the nuclear magnetic resonance spectroscopy of powdered solids and is used to establish correlations between different nuclei by magnetization transfer. The efficiency of conventional cross-polarization methods is low because of the inherent radio frequency (rf) field inhomogeneity present in the magic angle spinning (MAS) experiments and the large chemical shift anisotropies at high magnetic fields. Very high transfer efficiencies can be obtained using optimal control–derived experiments. These sequences had to be optimized individually for a particular MAS frequency. We show that by adjusting the length and the rf field amplitude of the shaped pulse synchronously with sample rotation, optimal control sequences can be successfully applied over a range of MAS frequencies without the need of reoptimization. This feature greatly enhances their applicability on spectrometers operating at differing external fields where the MAS frequency needs to be adjusted to avoid detrimental resonance effects.

Floquet theory in magnetic resonance: Formalism and applications

Floquet theory is an elegant mathematical formalism originally developed to solve time-dependent differential equations. Besides other fields, it has found applications in optical spectroscopy and nuclear magnetic resonance (NMR). This review attempts to give a perspective of the Floquet formalism as applied in NMR and shows how it allows one to solve various problems with a focus on solid-state NMR. We include both matrix- and operator-based approaches. We discuss different problems where the Hamiltonian changes with time in a periodic way. Such situations occur, for example, in solid-state NMR experiments where the time dependence of the Hamiltonian originates either from magic-angle spinning or from the application of amplitude- or phase-modulated radiofrequency fields, or from both. Specific cases include multiple-quantum and multiple-frequency excitation schemes. In all these cases, Floquet analysis allows one to define an effective Hamiltonian and, moreover, to treat cases that cannot be described by the more popularly used and simpler-looking average Hamiltonian theory based on the Magnus expansion. An important example is given by spin dynamics originating from multiple-quantum phenomena (level crossings). We show that the Floquet formalism is a very general approach for solving diverse problems in spectroscopy.

On the direct relation between REDOR and DIPSHIFT experiments in solid-state NMR

Rotational-echo double resonance (REDOR) and Dipolar-coupling chemical-shift correlation (DIPSHIFT) are commonly used experiments to probe heteronuclear dipole-dipole couplings between isolated pairs of spin-12 nuclei in magic-angle-spinning (MAS) solid-state NMR. Their widespread use is due to their robustness to experimental imperfections and a straightforward interpretation of data. Both of these experiments use rotor-synchronised π pulses to recouple the heteronuclear dipole-dipole couplings, and the observed intensity of resonances is modulated by a recoupled phase factor depending on the position or duration of the recoupling pulses. Several modifications to both of these experiments have been proposed, for example, the development of DIPSHIFT which employs strategies that mimic the multi-rotor-period nature of REDOR. We show here that REDOR and DIPSHIFT are in fact alternate implementations of the same experiment. The overt similarity in the design of REDOR and DIPSHIFT is also reflected in their theoretical description. Dipolar dephasing curves in REDOR are obtained by increasing the recoupling duration whilst keeping the position of the pulses constant, which results in a dephasing factor that is a function of only the dephasing time. DIPSHIFT, on the other hand, is a constant-time version of REDOR; the dipolar dephasing is a function of the position of the pulses with respect to the rotor period. We discuss the advantages and disadvantages of each implementation and suggest domains of applicability for these sequences.

Novel Cerium Bisphosphinate Coordination Polymer and Unconventional Metal–Organic Framework

The first Ce(III)-based coordination polymer ICR-9 (ICR stands for Inorganic Chemistry Řež), with the formula Ce2(C8H10P2O4)3, containing ditopic phenylene-1,4-bis(methylphosphinic acid) linker, was synthetized under solvothermal conditions. The crystal structure, solved using electron diffraction tomography (EDT), revealed 2D layers of octahedrally coordinated cerium atoms attached together through O-P-O bridges. The structure is nonporous, however, the modification of synthetic conditions led to unconventional metal–organic framework (or defective amorphous phase) with a specific surface area up to approximately 400 m2 g-1.

A unified heteronuclear decoupling picture in solid-state NMR under low radio-frequency amplitude and fast magic-angle-spinning frequency regime

Heteronuclear spin decoupling is a highly important component of solid-state NMR experiments to remove undesired coupling interactions between unlike spins for spectral resolution. Recently, experiments using a unification strategy of standard decoupling schemes were presented for high radio-frequency (RF) amplitudes and slow-intermediate magic-angle-spinning (MAS) frequencies, in the pursuit of deeper understanding of spin decoupling under phase-modulated RF irradiation [A. Equbal et al., J. Chem. Phys. 142, 184201 (2015)]. The approach, unified two-pulse heteronuclear decoupling (UTPD), incorporates the simultaneous time- and phase-modulation strategies, commonly used in solid-state NMR. Here, the UTPD based decoupling scheme is extended to the experimentally increasingly important regime of low RF amplitudes and fast MAS frequencies. The unified decoupling approach becomes increasingly effective in identifying the deleterious dipole-dipole and, in particular, J recoupling conditions which become critical for the low-amplitude RF regime. This is because J coupling is isotropic and therefore not averaged out by sample spinning unlike the anisotropic dipole-dipole coupling. Numerical simulations and analytic theory are used to understand the effects of various nuclear spin interactions on the decoupling performance of UTPD, in particular, the crucial difference between the low-phase and high-phase UTPD conditions with respect to J coupling. In the UTPD scheme, when the cycle-frequency of the pulse-sequence is comparable to the RF nutation frequency, the existence of a non-zero effective rotation in the basic two-pulse scheme becomes an essential feature for the efficient and robust averaging out of the scalar J coupling. This broad viewpoint is expected to bring different optimum low-power decoupling pulse schemes under a common footing.

Simultaneous homonuclear and heteronuclear spin decoupling in magic-angle spinning solid-state NMR

We show here an effective way of implementing simultaneously homonuclear and heteronuclear dipolar decoupling in magic-angle spinning (MAS) solid-state NMR. Whilst the homonuclear spin decoupling is applied on the ¹H channel, heteronuclear spin decoupling is applied on the ¹³C channel. The ¹H spins are observed in a windowed fashion in this case. The resultant ¹H spectrum has higher resolution due to the attenuation of broadening arising from both homonuclear ¹H-¹H and heteronuclear ¹H-¹³C interactions, with the latter normally leading to additional line broadening in ¹³C labelled samples. The experiments are performed at MAS frequencies of ca. 60 kHz.

Refocusing pulses: A strategy to improve efficiency of phase-modulated heteronuclear decoupling schemes in MAS solid-state NMR

The strategy of using π pulses in conjunction with continuous-wave radio-frequency fields to refocus spin interactions has lead to robust and efficient family of heteronuclear decoupling schemes in magic-angle spinning solid-state NMR, denoted as, rCW schemes. Here, we investigate the generality of the application of such refocussing pulses in other phase-modulated decoupling schemes, notably the super-cycled XiX decoupling. XiX is a commonly used heteronuclear decoupling scheme under conditions of fast MAS and low-amplitude radio-frequency irradiation. The refocussing of interactions is achieved by inserting π pulses with a phase of 135° in the supercycled XiX scheme. The refocussed XiX, rXiX, scheme has improved decoupling efficiency, better offset tolerance, and easier experimental setup compared to the XiX scheme.

Significance of symmetry in the nuclear spin Hamiltonian for efficient heteronuclear dipolar decoupling in solid-state NMR: A Floquet description of supercycled rCW schemes

Symmetry plays an important role in the retention or annihilation of a desired interaction Hamiltonian in NMR experiments. Here, we explore the role of symmetry in the radio-frequency interaction frame Hamiltonian of the refocused-continuous-wave (rCW) pulse scheme that leads to efficient ¹H heteronuclear decoupling in solid-state NMR. It is demonstrated that anti-periodic symmetry of single-spin operators (I_x, I_y, I_z) in the interaction frame can lead to complete annihilation of the ¹H-¹H homonuclear dipolar coupling effects that induce line broadening in solid-state NMR experiments. This symmetry also plays a critical role in cancelling or minimizing the effect of ¹H chemical-shift anisotropy in the effective Hamiltonian. An analytical description based on Floquet theory is presented here along with experimental evidences to understand the decoupling efficiency of supercycled (concatenated) rCW scheme.

Rationalising Heteronuclear Decoupling in Refocussing Applications of Solid-State NMR Spectroscopy

Factors affecting the performance of 1 H heteronuclear decoupling sequences for magic-angle spinning (MAS) NMR spectroscopy of organic solids are explored, as observed by time constants for the decay of nuclear magnetisation under a spin-echo (T2' ). By using a common protocol over a wide range of experimental conditions, including very high magnetic fields and very high radio-frequency (RF) nutation rates, decoupling performance is observed to degrade consistently with increasing magnetic field. Inhomogeneity of the RF field is found to have a significant impact on T2' values, with differences of about 20 % observed between probes with different coil geometries. Increasing RF nutation rates dramatically improve robustness with respect to RF offset, but the performance of phase-modulated sequences degrades at the very high nutation rates achievable in microcoils as a result of RF transients. The insights gained provide better understanding of the factors limiting decoupling performance under different conditions, and the high values of T2' observed (which generally exceed previous literature values) provide reference points for experiments involving spin magnetisation refocussing, such as 2D correlation spectra and measuring small spin couplings.

A suite of pulse sequences based on multiple sequential acquisitions at one and two radiofrequency channels for solid-state magic-angle spinning NMR studies of proteins

One of the fundamental challenges in the application of solid-state NMR is its limited sensitivity, yet a majority of experiments do not make efficient use of the limited polarization available. The loss in polarization in a single acquisition experiment is mandated by the need to select out a single coherence pathway. In contrast, sequential acquisition strategies can encode more than one pathway in the same experiment or recover unused polarization to supplement a standard experiment. In this article, we present pulse sequences that implement sequential acquisition strategies on one and two radiofrequency channels with a combination of proton and carbon detection to record multiple experiments under magic-angle spinning. We show that complementary 2D experiments such as [Formula: see text] and [Formula: see text] or DARR and [Formula: see text], and 3D experiments such as [Formula: see text] and [Formula: see text], or [Formula: see text] and [Formula: see text]  can be combined in a single experiment to ensure time savings of at least 40 %. These experiments can be done under fast or slow-moderate magic-angle spinning frequencies aided by windowed [Formula: see text] acquisition and homonulcear decoupling. The pulse sequence suite is further expanded by including pathways that allow the recovery of residual polarization, the so-called 'afterglow' pathways, to encode a number of pulse sequences to aid in assignments and chemical-shift mapping.

Relative merits of rCW(A) and XiX heteronuclear spin decoupling in solid-state magic-angle-spinning NMR spectroscopy: A bimodal Floquet analysis

We present a bimodal Floquet analysis of the recently introduced refocused continuous wave (rCW) solid-state NMR heteronuclear dipolar decoupling method and compare it with the similar looking X-inverse X (XiX) scheme. The description is formulated in the rf interaction frame and is valid for both finite and ideal π pulse rCW irradiation that forms the refocusing element in the rCW scheme. The effective heteronuclear dipolar coupling Hamiltonian up to first order is described. The analysis delineates the difference between the two sequences to different orders of their Hamiltonians for both diagonal and off-diagonal parts. All the resonance conditions observed in experiments and simulations have been characterised and their influence on residual line broadening is highlighted. The theoretical comparison substantiates the numerical simulations and experimental results to a large extent.

Highly efficient19F heteronuclear decoupling in solid-state NMR spectroscopy using supercycled refocused-CW irradiation

We present heteronuclear¹⁹F refocused CW (rCW) decoupling pulse sequences for solid-state magic-angle-spinning NMR applications.

Proton-detected solid-state NMR spectroscopy of fully protonated proteins at slow to moderate magic-angle spinning frequencies

(1)H-detection offers a substitute to the sensitivity-starved experiments often used to characterize biomolecular samples using magic-angle spinning solid-state NMR spectroscopy (MAS-ssNMR). To mitigate the effects of the strong (1)H-(1)H dipolar coupled network that would otherwise severely broaden resonances, high MAS frequencies (>40kHz) are often employed. Here, we have explored the alternative of stroboscopic (1)H-detection at moderate MAS frequencies of 5-30kHz using windowed version of supercycled-phase-modulated Lee-Goldburg homonuclear decoupling. We show that improved resolution in the (1)H dimension, comparable to that obtainable at high spinning frequencies of 40-60kHz without homonuclear decoupling, can be obtained in these experiments for fully protonated proteins. Along with detailed analysis of the performance of the method on the standard tri-peptide f-MLF, experiments on micro-crystalline GB1 and amyloid-β aggregates are used to demonstrate the applicability of these pulse-sequences to challenging biomolecular systems. With only two parameters to optimize, broadbanded performance of the homonuclear decoupling sequence, linear dependence of the chemical-shift scaling factor on resonance offset and a straightforward implementation under experimental conditions currently used for many biomolecular studies (viz. spinning frequencies and radio-frequency amplitudes), we expect these experiments to complement the current (13)C-detection based methods in assignments and characterization through chemical-shift mapping.