Heteronuclear spin decoupling in solid-state NMR under magic-angle sample spinning

Low power supercycled TPPM decoupling

Improving the spectral sensitivity and resolution of biological solids is one of the long-standing problems in nuclear magnetic resonance (NMR) spectroscopy. In this report, we introduce low-power supercycled variants of two-pulse phase-modulated (TPPM) sequence for heteronuclear decoupling. The utility of the sequence is shown by improvements in the transverse relaxation time of observed nuclei (with 1H decoupling) with its application to different samples (uniformly 13C, 15N, 2H-labeled GB1 back-exchanged with 25% H2O and 75% D2O, uniformly 13C, 15N, 2H-labeled human derived Asyn fibril back-exchanged with 100% H2O and uniformly 13C, 15N -labeled human derived Asyn fibril) at fast MAS using low radiofrequency (RF) fields. To understand the effect of spinning speed, the transverse relaxation time is monitored under different spinning frequencies. In comparison to existing heteronuclear decoupling sequences, the supercycled TPPM (sTPPM) sequence significantly improves the spectral sensitivity and resolution and is robust towards B1 inhomogeneity and decoupler offset.

Probing Molecular Packing of Lipid Nanoparticles from 31P Solution and Solid-State NMR

Lipid nanoparticles (LNPs) are intricate multicomponent systems widely recognized for their efficient delivery of oligonucleotide cargo to host cells. Gaining insights into the molecular properties of LNPs is crucial for their effective design and characterization. However, analysis of their internal structure at the molecular level presents a significant challenge. This study introduces 31P nuclear magnetic resonance (NMR) methods to acquire structural and dynamic information about the phospholipid envelope of LNPs. Specifically, we demonstrate that the 31P chemical shift anisotropy (CSA) parameters serve as a sensitive indicator of the molecular assembly of distearoylphosphatidylcholine (DSPC) lipids within the particles. An analytical protocol for measuring 31P CSA is developed, which can be implemented using either solution NMR or solid-state NMR, offering wide accessibility and adaptability. The capability of this method is demonstrated using both model DSPC liposomes and real-world pharmaceutical LNP formulations. Furthermore, our method can be employed to investigate the impact of formulation processes and composition on the assembly of specifically LNP particles or, more generally, phospholipid-based delivery systems. This makes it an indispensable tool for evaluating critical pharmaceutical properties such as structural homogeneity, batch-to-batch reproducibility, and the stability of the particles.

A perspective on the relative merits/demerits of time-propagators based on Floquet theorem

The present report examines the nuances of analytic methods employed in the derivation of evolution operators in periodically driven quantum systems based on Floquet theorem. Specifically, time-propagators of the form, U(t) = P(t)e-iH̄t defined in the Hilbert space (of finite dimension), are derived through generalized multimodal expansion of the operators involved. While Floquet methods defined in the extended Hilbert space (of infinite dimension) have remained the method of choice for the description of time-evolution at non-stroboscopic time-intervals, the expansion schemes discussed do present an attractive option for similar studies in the standard Hilbert space. Nevertheless, the convergence criteria and suitability of such methods deserve formal validation in problems of experimental relevance. Employing examples comprising periodic Hamiltonians from magnetic resonance spectroscopy, the exactness of Floquet based time-propagators in the Schrödinger and interaction representation is discussed. Through rigorous comparisons between simulations emerging from analytic and exact numerical methods, the relative merits and demerits of different formulations of Floquet based methods are also discussed.

A continuous approach to Floquet theory for pulse-sequence optimization in solid-state NMR

We present a framework that uses a continuous frequency space to describe and design solid-state nuclear magnetic resonance (NMR) experiments. The approach is similar to the well-established Floquet treatment for NMR, but it is not restricted to periodic Hamiltonians and allows the design of experiments in a reverse fashion. The framework is based on perturbation theory on a continuous Fourier space, which leads to effective, i.e., time-independent, Hamiltonians. It allows the back-calculation of the pulse scheme from the desired effective Hamiltonian as a function of spin-system parameters. We show as an example how to back-calculate the rf irradiation in the MIRROR experiment from the desired chemical-shift offset behavior of the sequence.

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.

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.

Bimodal Floquet theory of phase-modulated heteronuclear decoupling experiments in solid-state NMR spectroscopy

A prescription based on bimodal Floquet theory is proposed to describe the nuances of phase-modulated supercycled decoupling experiments in solids. The frequency dependent interaction frames relevant to a particular supercycle are identified to facilitate faster convergence of perturbation corrections to the derived effective Hamiltonians. In contrast to silico-based methods, the proposed analytic method offers an attractive platform for faster optimization of experiments in solids. Additionally, the relevance of supercycling at ultrafast spinning conditions is also discussed.

The structure of a minimum amyloid fibril core formed by necroptosis-mediating RHIM of human RIPK3

Receptor-interacting protein kinases 3 (RIPK3), a central node in necroptosis, polymerizes in response to the upstream signals and then activates its downstream mediator to induce cell death. The active polymeric form of RIPK3 has been indicated as the form of amyloid fibrils assembled via its RIP homotypic interaction motif (RHIM). In this study, we combine cryogenic electron microscopy and solid-state NMR to determine the amyloid fibril structure of RIPK3 RHIM-containing C-terminal domain (CTD). The structure reveals a single protofilament composed of the RHIM domain. RHIM forms three β-strands (referred to as strands 1 through 3) folding into an S shape, a distinct fold from that in complex with RIPK1. The consensus tetrapeptide VQVG of RHIM forms strand 2, which zips up strands 1 and 3 via heterozipper-like interfaces. Notably, the RIPK3-CTD fibril, as a physiological fibril, exhibits distinctive assembly compared with pathological fibrils. It has an exceptionally small fibril core and twists in both handedness with the smallest pitch known so far. These traits may contribute to a favorable spatial arrangement of RIPK3 kinase domain for efficient phosphorylation.

The amyloid structure of mouse RIPK3 (receptor interacting protein kinase 3) in cell necroptosis

RIPK3 amyloid complex plays crucial roles during TNF-induced necroptosis and in response to immune defense in both human and mouse. Here, we have structurally characterized mouse RIPK3 homogeneous self-assembly using solid-state NMR, revealing a well-ordered N-shaped amyloid core structure featured with 3 parallel in-register β-sheets. This structure differs from previously published human RIPK1/RIPK3 hetero-amyloid complex structure, which adopted a serpentine fold. Functional studies indicate both RIPK1-RIPK3 binding and RIPK3 amyloid formation are essential but not sufficient for TNF-induced necroptosis. The structural integrity of RIPK3 fibril with three β-strands is necessary for signaling. Molecular dynamics simulations with a mouse RIPK1/RIPK3 model indicate that the hetero-amyloid is less stable when adopting the RIPK3 fibril conformation, suggesting a structural transformation of RIPK3 from RIPK1-RIPK3 binding to RIPK3 amyloid formation. This structural transformation would provide the missing link connecting RIPK1-RIPK3 binding to RIPK3 homo-oligomer formation in the signal transduction.

Receptor Interacting Protein Kinase 3 (RIPK3) has a key role in TNF-induced necroptosis. Here, the authors combine solid state NMR measurements, MD simulations and cell based assays to characterize mouse RIPK3 and they present the structure of the RIPK3 amyloid core.

Decoherence optimized tilted-angle cross polarization: A novel concept for sensitivity-enhanced solid-state NMR using ultra-fast magic angle spinning

Ultra-fast magic-angle spinning (UFMAS) at a MAS rate (ω_R/2π) of 60 kHz or higher has dramatically improved the resolution and sensitivity of solid-state NMR (SSNMR). However, limited polarization transfer efficiency using cross-polarization (CP) between ¹H and rare spins such as ¹³C still restricts the sensitivity and multi-dimensional applications of SSNMR using UFMAS. We propose a novel approach, which we call decoherence-optimized tilted-angle CP (DOTA CP), to improve CP efficiency with prolonged lifetime of ¹H coherence in the spin-locked condition and efficient band-selective polarization transfer by incorporating off-resonance irradiation to ¹H spins. ¹³C CP-MAS at ω_R/2π of 70-90 kHz suggested that DOTA CP notably outperformed traditional adiabatic CP, a de-facto-standard CP scheme over the past decade, in sensitivity for the aliphatic-region spectra of ¹³C-labeled GB1 protein and N-formyl-Met-Leu-Phe samples by up to 1.4- and 1.2-fold, respectively. ¹H-detected 2D ¹H/¹³C SSNMR for the GB1 sample indicated the effectiveness of this approach in various multidimensional applications.

On the equivalence between different averaging schemes in magnetic resonance

Evolution of quantum mechanical systems under time-dependent Hamiltonians has remained a challenging problem of interest across all disciplines. Through suitable approximations, different averaging methods have emerged in the past for modeling the time-evolution under time-dependent Hamiltonians. To this end, the development of analytic methods in the form of time-averaged effective Hamiltonians has gained prominence over other methods. In particular, the advancement of spectroscopic methods for probing molecular structures has benefited enormously from such theoretical pursuits. Nonetheless, the validity of the approximations and the exactness of the proposed effective Hamiltonians have always remained a contentious issue. Here, in this report, we reexamine the equivalence between the effective Hamiltonians derived from the Magnus formula and Floquet theory through suitable examples in magnetic resonance.

Distance measurement between trityl radicals by pulse dressed electron paramagnetic resonance with phase modulation

Distance measurement in the nanometre range is among the most important applications of pulse electron paramagnetic resonance today, especially in biological applications. The longest distance that can be measured by all presently used pulse sequences is determined by the phase memory time T m of the observed spins. Here we show that one can measure the dipolar coupling during strong microwave irradiation by using an appropriate frequency- or phase-modulation scheme, i.e. by applying pulse sequences in the nutating frame. This decouples the electron spins from the surrounding nuclear spins and thus leads to significantly longer relaxation times of the microwave-dressed spins (i.e. the rotating frame relaxation times T 1 ρ and T 2 ρ ) compared to T m . The electron-electron dipolar coupling is not decoupled as long as both spins are excited, which can be implemented for trityl radicals at Q-band frequencies (35 GHz, 1.2 T). We show results for two bis-trityl rulers with inter-electron distances of about 4.1 and 5.3 nm and discuss technical challenges and possible next steps.

Conformational Flexibility of p150Glued(1-191) Subunit of Dynactin Assembled with Microtubules

Microtubule (MT)-associated proteins perform diverse functions in cells. These functions are dependent on their interactions with MTs. Dynactin, a cofactor of dynein motor, assists the binding of dynein to various organelles and is crucial to the long-distance processivity of dynein-based complexes. The largest subunit of dynactin, the p150^Glued, contains an N-terminus segment that is responsible for the MT-binding interactions and long-range processivity of dynactin. We employed solution and magic angle spinning NMR spectroscopy to characterize the structure and dynamics of the p150^Glued N-terminal region, both free and in complex with polymerized MTs. This 191-residue region encompasses the cytoskeleton-associated protein glycine-rich domain, the basic domain, and serine/proline-rich (SP-rich) domain. We demonstrate that the basic and SP-rich domains are intrinsically disordered in solution and significantly enhance the binding affinity to MTs as these regions contain the second MT-binding site on the p150^Glued subunit. The majority of the basic and SP-rich domains are predicted to be random coil, whereas the segments S111-I116, A124-R132, and K144-T146 in the basic domain contain short α-helical or β-sheet structures. These three segments possibly encompass the MT-binding site. Surprisingly, the protein retains a high degree of flexibility upon binding to MTs except for the regions that are directly involved in the binding interactions with MTs. This conformational flexibility may be essential for the biological functions of the p150^Glued subunit.

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.

Refocusing CSA during magic angle spinning rotating-frame relaxation experiments

We examine coherent evolution of spin-locked magnetization during magic-angle spinning (MAS), in the context of relaxation experiments designed to probe chemical exchange (rotating-frame relaxation (R_1ρ)). Coherent evolution is expected in MAS based rotating-frame relaxation decay experiments if matching conditions are met (such as, ω₁ = nω_r) and if the chemical shielding anisotropy (CSA) is substantial. We show here using numerical simulations and experiments that even when such matching requirements are avoided (e.g., ω₁ < 0.5ω_r, ∼1.5ω_r, >2.5ω_r), coherent evolution of spin-locked magnetization with large CSA is still considerable. The coherent evolution has important consequences on the analysis of relaxation decay and the ability to extract accurate information of interest about dynamics. We present a pulse sequence that employs rotary echoes and refocuses CSA contributions, allowing for more sensitive measurement of rotating-frame relaxation with less interference from coherent evolution. In practice, the proposed pulse sequence, REfocused CSA Rotating-frame Relaxation (RECRR) is robust to carrier frequency offset, B₁-field inhomogeneity, and slight miscalibrations of the refocusing pulses.

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.

Peptide and Protein Dynamics and Low-Temperature/DNP Magic Angle Spinning NMR

In DNP MAS NMR experiments at ∼80-110 K, the structurally important -¹³CH₃ and -¹⁵NH₃⁺ signals in MAS spectra of biological samples disappear due to the interference of the molecular motions with the ¹H decoupling. Here we investigate the effect of these dynamic processes on the NMR line shapes and signal intensities in several typical systems: (1) microcrystalline APG, (2) membrane protein bR, (3) amyloid fibrils PI3-SH3, (4) monomeric alanine-CD₃, and (5) the protonated and deuterated dipeptide N-Ac-VL over 78-300 K. In APG, the three-site hopping of the Ala-C_β peak disappears completely at 112 K, concomitant with the attenuation of CP signals from other ¹³C's and ¹⁵N's. Similarly, the ¹⁵N signal from Ala-NH₃⁺ disappears at ∼173 K, concurrent with the attenuation in CP experiments of other ¹⁵N's as well as ¹³C's. In bR and PI3-SH3, the methyl groups are attenuated at ∼95 K, while all other ¹³C's remain unaffected. However, both systems exhibit substantial losses of intensity at ∼243 K. Finally, with spectra of Ala and N-Ac-VL, we show that it is possible to extract site specific dynamic data from the temperature dependence of the intensity losses. Furthermore, ²H labeling can assist with recovering the spectral intensity. Thus, our study provides insight into the dynamic behavior of biological systems over a wide range of temperatures, and serves as a guide to optimizing the sensitivity and resolution of structural data in low temperature DNP MAS NMR spectra.

Advanced solid-state NMR spectroscopy of natural organic matter

Solid-state NMR is essential for the characterization of natural organic matter (NOM) and is gaining importance in geosciences and environmental sciences. This review is intended to highlight advanced solid-state NMR techniques, especially a systematic approach to NOM characterization, and their applications to the study of NOM. We discuss some basics of how to acquire high-quality and quantitative solid-state ¹³C NMR spectra, and address some common technical mistakes that lead to unreliable spectra of NOM. The identification of specific functional groups in NOM, primarily based on ¹³C spectral-editing techniques, is described and the theoretical background of some recently-developed spectral-editing techniques is provided. Applications of solid-state NMR to investigating nitrogen (N) in NOM are described, focusing on limitations of the widely used ¹⁵N CP/MAS experiment and the potential of improved advanced NMR techniques for characterizing N forms in NOM. Then techniques used for identifying proximities, heterogeneities and domains are reviewed, and some examples provided. In addition, NMR techniques for studying segmental dynamics in NOM are reviewed. We also briefly discuss applications of solid-state NMR to NOM from various sources, including soil organic matter, aquatic organic matter, organic matter in atmospheric particulate matter, carbonaceous meteoritic organic matter, and fossil fuels. Finally, examples of NMR-based structural models and an outlook are provided.

A generalized theoretical framework for the description of spin decoupling in solid-state MAS NMR: Offset effect on decoupling performance

We present a generalized theoretical framework that allows the approximate but rapid analysis of residual couplings of arbitrary decoupling sequences in solid-state NMR under magic-angle spinning conditions. It is a generalization of the tri-modal Floquet analysis of TPPM decoupling [Scholz et al., J. Chem. Phys. 130, 114510 (2009)] where three characteristic frequencies are used to describe the pulse sequence. Such an approach can be used to describe arbitrary periodic decoupling sequences that differ only in the magnitude of the Fourier coefficients of the interaction-frame transformation. It allows a ∼100 times faster calculation of second-order residual couplings as a function of pulse sequence parameters than full spin-dynamics simulations. By comparing the theoretical calculations with full numerical simulations, we show the potential of the new approach to examine the performance of decoupling sequences. We exemplify the usefulness of this framework by analyzing the performance of commonly used high-power decoupling sequences and low-power decoupling sequences such as amplitude-modulated XiX (AM-XiX) and its super-cycled variant SC-AM-XiX. In addition, the effect of chemical-shift offset is examined for both high- and low-power decoupling sequences. The results show that the cross-terms between the dipolar couplings are the main contributions to the line broadening when offset is present. We also show that the SC-AM-XIX shows a better offset compensation.

Understanding Surface and Interfacial Chemistry in Functional Nanomaterials via Solid-State NMR

Surface and interfacial chemistry is of fundamental importance in functional nanomaterials applied in catalysis, energy storage and conversion, medicine, and other nanotechnologies. It has been a perpetual challenge for the scientific community to get an accurate and comprehensive picture of the structures, dynamics, and interactions at interfaces. Here, some recent examples in the major disciplines of nanomaterials are selected (e.g., nanoporous materials, battery materials, nanocrystals and quantum dots, supramolecular assemblies, drug-delivery systems, ionomers, and graphite oxides) and it is shown how interfacial chemistry can be addressed through the perspective of solid-state NMR characterization techniques.

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.

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.

Simulating spin dynamics in organic solids under heteronuclear decoupling

Although considerable progress has been made in simulating the dynamics of multiple coupled nuclear spins, predicting the evolution of nuclear magnetisation in the presence of radio-frequency decoupling remains challenging. We use exact numerical simulations of the spin dynamics under simultaneous magic-angle spinning and RF decoupling to determine the extent to which numerical simulations can be used to predict the experimental performance of heteronuclear decoupling for the CW, TPPM and XiX sequences, using the methylene group of glycine as a model system. The signal decay times are shown to be strongly dependent on the largest spin order simulated. Unexpectedly large differences are observed between the dynamics with and without spin echoes. Qualitative trends are well reproduced by modestly sized spin system simulations, and the effects of finite spin-system size can, in favourable cases, be mitigated by extrapolation. Quantitative prediction of the behaviour in complex parameter spaces is found, however, to be very challenging, suggesting that there are significant limits to the role of numerical simulations in RF decoupling problems, even when specialist techniques, such as state-space restriction, are used.

A unified heteronuclear decoupling strategy for magic-angle-spinning solid-state NMR spectroscopy

A unified strategy of two-pulse based heteronuclear decoupling for solid-state magic-angle spinning nuclear magnetic resonance is presented. The analysis presented here shows that different decoupling sequences like two-pulse phase-modulation (TPPM), X-inverse-X (XiX), and finite pulse refocused continuous wave (rCW(A)) are basically specific solutions of a more generalized decoupling scheme which incorporates the concept of time-modulation along with phase-modulation. A plethora of other good decoupling conditions apart from the standard, TPPM, XiX, and rCW(A) decoupling conditions are available from the unified decoupling approach. The importance of combined time- and phase-modulation in order to achieve the best decoupling conditions is delineated. The consequences of different indirect dipolar interactions arising from cross terms comprising of heteronuclear and homonuclear dipolar coupling terms and also those between heteronuclear dipolar coupling and chemical-shift anisotropy terms are presented in order to unfold the effects of anisotropic interactions under different decoupling conditions. Extensive numerical simulation results are corroborated with experiments on standard amino acids.

Efficient heteronuclear decoupling in MAS solid-state NMR using non-rotor-synchronized rCW irradiation

We present new non-rotor-synchronized variants of the recently introduced refocused continuous wave (rCW) heteronuclear decoupling method significantly improving the performance relative to the original rotor-synchronized variants. Under non-rotor-synchronized conditions the rCW decoupling sequences provide more efficient decoupling, are easier to setup, and prove more robust towards experimental parameters such as radio frequency (rf) field amplitude and spinning frequency. This is demonstrated through numerical simulations substantiated with experimental results under different sample spinning and rf field amplitude conditions for powder samples of U-(13)C-glycine and U-(13)C-L-histidine·HCl·H2O.

Computer-intensive simulation of solid-state NMR experiments using SIMPSON

Conducting large-scale solid-state NMR simulations requires fast computer software potentially in combination with efficient computational resources to complete within a reasonable time frame. Such simulations may involve large spin systems, multiple-parameter fitting of experimental spectra, or multiple-pulse experiment design using parameter scan, non-linear optimization, or optimal control procedures. To efficiently accommodate such simulations, we here present an improved version of the widely distributed open-source SIMPSON NMR simulation software package adapted to contemporary high performance hardware setups. The software is optimized for fast performance on standard stand-alone computers, multi-core processors, and large clusters of identical nodes. We describe the novel features for fast computation including internal matrix manipulations, propagator setups and acquisition strategies. For efficient calculation of powder averages, we implemented interpolation method of Alderman, Solum, and Grant, as well as recently introduced fast Wigner transform interpolation technique. The potential of the optimal control toolbox is greatly enhanced by higher precision gradients in combination with the efficient optimization algorithm known as limited memory Broyden-Fletcher-Goldfarb-Shanno. In addition, advanced parallelization can be used in all types of calculations, providing significant time reductions. SIMPSON is thus reflecting current knowledge in the field of numerical simulations of solid-state NMR experiments. The efficiency and novel features are demonstrated on the representative simulations.

r TPPM: towards improving solid-state NMR two-pulse phase-modulation heteronuclear dipolar decoupling sequence by refocusing

We present here a simple refocused modification, r TPPM, of the Two-Pulse Phase-Modulation (TPPM) heteronuclear decoupling method, which improves decoupling and makes the sequence much more robust with respect to essential experimental parameters. The modified sequence is compared with the established TPPM sequence and a variety of other decoupling sequences at low to moderate magic-angle spinning frequencies. Simulations are shown to compare TPPM and r TPPM with respect to various experimental parameters. The observations from simulations are corroborated with experimental findings at two spinning frequencies on U-(13)C-glycine and U-(13)C-L-histidine.HCl.H2O.

14N overtone NMR spectra under magic angle spinning: experiments and numerically exact simulations

It was recently shown that high resolution (14)N overtone NMR spectra can be obtained directly under magic angle spinning (MAS) conditions [L. A. O'Dell and C. I. Ratcliffe, Chem. Phys. Lett. 514, 168 (2011)]. Preliminary experimental results showed narrowed powder pattern widths, a frequency shift that is dependent on the MAS rate, and an apparent absence of spinning sidebands, observations which appeared to be inconsistent with previous theoretical treatments. Herein, we reproduce these effects using numerically exact simulations that take into account the full nuclear spin Hamiltonian. Under sample spinning, the (14)N overtone signal is split into five (0, ±1, ±2) overtone sidebands separated by the spinning frequency. For a powder sample spinning at the magic angle, the +2ω(r) sideband is dominant while the others show significantly lower signal intensities. The resultant MAS powder patterns show characteristic quadrupolar lineshapes from which the (14)N quadrupolar parameters and isotropic chemical shift can be determined. Spinning the sample at other angles is shown to alter both the shapes and relative intensities of the five overtone sidebands, with MAS providing the benefit of averaging dipolar couplings and shielding anisotropy. To demonstrate the advantages of this experimental approach, we present the (14)N overtone MAS spectrum obtained from L-histidine, in which powder patterns from all three nitrogen sites are clearly resolved.

Efficiency of heteronuclear dipolar decoupling schemes in solid-state NMR: investigation of effective transverse relaxation times

We here compare the T(2)(') values of various heteronuclear dipolar decoupling schemes commonly used in solid-state nuclear magnetic resonance experiments. Swept-frequency two-pulse phase modulation scheme is shown to give longer T(2)(') values for the majority of the magic-angle-spinning frequencies and radiofrequency amplitudes considered here. The longer T(2)(') values obtained are shown to yield spectra with higher resolution in experiments, such as INADEQUATE, which incorporate spin-echo blocks. Such blocks normally constitute the indirect dimension of a multidimensional experiment during which heteronuclear dipolar decoupling is applied, thereby making the relevance of T(2)(') manifest clearly. Experimental results are shown on samples of glycine, alanine, and Aβ(42).

Solid-state nuclear magnetic resonance structural studies of proteins using paramagnetic probes

Determination of three-dimensional structures of biological macromolecules by magic-angle spinning (MAS) solid-state NMR spectroscopy is hindered by the paucity of nuclear dipolar coupling-based restraints corresponding to distances exceeding 5 Å. Recent MAS NMR studies of uniformly (13)C,(15)N-enriched proteins containing paramagnetic centers have demonstrated the measurements of site-specific nuclear pseudocontact shifts and spin relaxation enhancements, which report on electron-nucleus distances up to ~20 Å. These studies pave the way for the application of such long-distance paramagnetic restraints to protein structure elucidation and analysis of protein-protein and protein-ligand interactions in the solid phase. Paramagnetic species also facilitate the rapid acquisition of high resolution and sensitivity multidimensional solid-state NMR spectra of biomacromolecules using condensed data collection schemes, and characterization of solvent-accessible surfaces of peptides and proteins. In this review we discuss some of the latest applications of magic-angle spinning NMR spectroscopy in conjunction with paramagnetic probes to the structural studies of proteins in the solid state.

Hydrogen-bonding interactions in T-2 toxin studied using solution and solid-state NMR

The structure of T-2 toxin in the solid-state is limited to X-ray crystallographic studies, which lack sufficient resolution to provide direct evidence for hydrogen-bonding interactions. Furthermore, its solution-structure, despite extensive Nuclear Magnetic Resonance (NMR) studies, has provided little insight into its hydrogen-bonding behavior, thus far. Hydrogen-bonding interactions are often an important part of biological activity. In order to study these interactions, the structure of T-2 toxin was compared in both the solution- and solid-state using NMR Spectroscopy. It was determined that the solution- and solid-state structure differ dramatically, as indicated by differences in their carbon chemical shifts, these observations are further supported by solution proton spectral parameters and exchange behavior. The slow chemical exchange process and cross-relaxation dynamics with water observed between the hydroxyl hydrogen on C-3 and water supports the existence of a preferential hydrogen bonding interaction on the opposite side of the molecule from the epoxide ring, which is known to be essential for trichothecene toxicity. This result implies that these hydrogen-bonding interactions could play an important role in the biological function of T-2 toxin and posits towards a possible interaction for the trichothecene class of toxins and the ribosome. These findings clearly illustrate the importance of utilizing solid-state NMR for the study of biological compounds, and suggest that a more detailed study of this whole class of toxins, namely trichothecenes, should be pursued using this methodology.

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.

19F-decoupling of half-integer spin quadrupolar nuclei in solid-state NMR: application of frequency-swept decoupling methods

In solid-state NMR studies of minerals and ion conductors, quadrupolar nuclei like (7)Li, (23)Na or (133)Cs are frequently situated in close proximity to fluorine, so that application of (19)F decoupling is beneficial for spectral resolution. Here, we compare the decoupling efficiency of various multi-pulse decoupling sequences by acquiring (19)F-decoupled (23)Na-NMR spectra of cryolite (Na(3)AlF(6)). Whereas the MAS spectrum is only marginally affected by application of (19)F decoupling, the 3Q-filtered (23)Na signal is very sensitive to it, as the de-phasing caused by the dipolar interaction between sodium and fluorine is three-fold magnified. Experimentally, we find that at moderate MAS speeds, the decoupling efficiencies of the frequency-swept decoupling schemes SW(f)-TPPM and SW(f)-SPINAL are significantly better than the conventional TPPM and SPINAL sequences. The frequency-swept sequences are therefore the methods of choice for efficient decoupling of quadrupolar nuclei with half-integer spin from fluorine.

The influence of the molecular system on the performance of heteronuclear decoupling in solid-state NMR

The intensity of the carbon signal in a CPMAS experiment has been measured for two CH and three CH(2) moieties in four test molecules under different phase-modulated proton decoupling conditions and as a function of the spinning rate. The proton decoupling schemes investigated were the golden standard TPPM and three of the GTn family. Aim of this analysis was to better describe experimentally the impact and limitations of phase-modulated decoupling. Sizeable differences in the response to decoupling were observed in otherwise chemically identical molecular fragments, such as the CHCH(2) found in tyrosine, phenyl-succinic acid or 9-Anthrylmethyl-malonate, probably due to differences in spin-diffusion rates. In keeping with known facts, the efficiency of the decoupling was observed to decrease with the MAS rate, but with somewhat different trends for the tested systems.