Spinning faster: protein NMR at MAS frequencies up to 126 kHz

Elimination of homogeneous broadening in 1H solid-state NMR

1H solid-state NMR spectra are plagued by low resolution, necessitating the use of complex pulse sequences or specialized equipment. We introduce a new resolution enhancement method, inspired by super-resolution microscopy, that uses a 2D Hahn-echo experiment to constrain deconvolution. The result is an effective doubling of the MAS frequency.

Selective Detection of Intermediate-Amplitude Motion by Solid-State NMR

The coexistence of rigid and mobile molecules or molecular segments abounds in biomolecular assemblies. Examples include the carbohydrate-rich cell walls of plants and intrinsically disordered proteins that contain rigid β-sheet cores. In solid-state nuclear magnetic resonance (NMR) spectroscopy, dipolar polarization transfer experiments are well suited for detecting rigid components, whereas scalar-coupling experiments are well suited for detecting highly mobile components. However, few NMR methods are available to detect the segments that undergo intermediate-amplitude fast motion. Here, we introduce two NMR experiments, a two-dimensional T2H-filtered CP-hCH correlation and a three-dimensional J-INADEQUATE CCH correlation, to observe this intermediate-amplitude motion. Both experiments involve 1H detection under fast magic-angle spinning (MAS). By combining 1H transverse relaxation (T2H) filters with dipolar polarization transfer, we suppress the signals of both highly rigid and highly mobile species, thus revealing the signals of intermediate mobile species. 1H detection under fast MAS is crucial for distinguishing the different motional amplitudes. We demonstrate these techniques on several plant cell wall samples and show that they allow the selective detection and resolution of certain hemicellulose and pectin signals, which are usually masked by the signals of the rigid cellulose and the highly dynamic pectins in purely dipolar and scalar NMR spectra.

Solid-state NMR MAS CryoProbe enables structural studies of human blood protein vitronectin bound to hydroxyapatite

The low sensitivity of nuclear magnetic resonance (NMR) is a major bottleneck for studying biomolecular structures of complex biomolecular assemblies. Cryogenically cooled probe technology overcomes the sensitivity limitations enabling NMR applications to challenging biomolecular systems. Here we describe solid-state NMR studies of the human blood protein vitronectin (Vn) bound to hydroxyapatite (HAP), the mineralized form of calcium phosphate, using a CryoProbe designed for magic angle spinning (MAS) experiments. Vn is a major blood protein that regulates many different physiological and pathological processes. The high sensitivity of the CryoProbe enabled us to acquire three-dimensional solid-state NMR spectra for sequential assignment and characterization of site-specific water-protein interactions that provide initial insights into the organization of the Vn-HAP complex. Vn associates with HAP in various pathological settings, including macular degeneration eyes and Alzheimer's disease brains. The ability to probe these assemblies at atomic detail paves the way for understanding their formation.

INEPT and CP transfer efficiencies of dynamic systems in MAS solid-state NMR

Hartmann-Hahn cross polarization and INEPT polarization transfer are the most popular sequences to increase the polarization of low-γ nuclei in magic-angle spinning solid-state NMR. It is well known that the two methods preferentially lead to polarization transfer in different parts of molecules. Cross polarization works best in rigid segments of the molecule while INEPT-based polarization transfer is efficient in highly mobile segments where (nearly) isotropic motion averages out the dipolar couplings. However, there have only been few attempts to define the time scales of motion that are compatible with cross polarization or INEPT transfer in a more quantitative way. We have used simple isotropic jump models in combination with simulations based on the stochastic Liouville equation to elucidate the time scales of motion that allow either cross polarization or INEPT-based polarization transfer. We investigate which motional time scales interfere with one or both polarization-transfer schemes. We have modeled isolated I-S two-spin systems, strongly-coupled I2S three-spin systems and more loosely coupled I-I-S three-spin systems as well as I3S groups. Such fragments can be used as models for typical environments in fully deuterated and back-exchanged molecules (I-S), for fully protonated molecules (I2S and I3S) or situations in between (I-I-S).

5D solid-state NMR spectroscopy for facilitated resonance assignment

1H-detected solid-state NMR spectroscopy has been becoming increasingly popular for the characterization of protein structure, dynamics, and function. Recently, we showed that higher-dimensionality solid-state NMR spectroscopy can aid resonance assignments in large micro-crystalline protein targets to combat ambiguity (Klein et al., Proc. Natl. Acad. Sci. U.S.A. 2022). However, assignments represent both, a time-limiting factor and one of the major practical disadvantages within solid-state NMR studies compared to other structural-biology techniques from a very general perspective. Here, we show that 5D solid-state NMR spectroscopy is not only justified for high-molecular-weight targets but will also be a realistic and practicable method to streamline resonance assignment in small to medium-sized protein targets, which such methodology might not have been expected to be of advantage for. Using a combination of non-uniform sampling and the signal separating algorithm for spectral reconstruction on a deuterated and proton back-exchanged micro-crystalline protein at fast magic-angle spinning, direct amide-to-amide correlations in five dimensions are obtained with competitive sensitivity compatible with common hardware and measurement time commitments. The self-sufficient backbone walks enable efficient assignment with very high confidence and can be combined with higher-dimensionality sidechain-to-backbone correlations from protonated preparations into minimal sets of experiments to be acquired for simultaneous backbone and sidechain assignment. The strategies present themselves as potent alternatives for efficient assignment compared to the traditional assignment approaches in 3D, avoiding user misassignments derived from ambiguity or loss of overview and facilitating automation. This will ease future access to NMR-based characterization for the typical solid-state NMR targets at fast MAS.

High-field and fast-spinning 1H MAS NMR spectroscopy for the characterization of two-dimensional covalent organic frameworks

Two-dimensional (2D) materials, like 2D covalent organic frameworks (COFs), have been attracting increasing research interest. They are usually obtained as polycrystalline powders. Solid-state NMR spectroscopy is capable of delivering structural information about such materials. Previous studies have applied, for example, 13C cross-polarization magic angle spinning (CP MAS) NMR experiments to characterize 2D COFs. Herein, we demonstrate the usefulness of high-field and fast-spinning 1H MAS NMR spectroscopy to resolve and quantify the signals of different 1H species within 2D COFs, including the edge sites and/or defects. Moreover, 1H-13C heteronuclear correlation (HETCOR) spectroscopy has also been applied and can provide improved resolution to obtain further information about stacking effects as well as edge sites/defects.

Simplified Preservation of Equivalent Pathways Spectroscopy

Inspired by the recently proposed transverse mixing optimal control pulses (TROP) approach for improving signal in multidimensional magic-angle spinning (MAS) NMR experiments, we present simplified preservation of equivalent pathways spectroscopy (SPEPS). It transfers both transverse components of magnetization that occur during indirect evolutions, theoretically enabling a √2 improvement in sensitivity for each such dimension. We compare SPEPS transfer with TROP and cross-polarization (CP) using membrane protein and fibril samples at MAS of 55 and 100 kHz. In three-dimensional (3D) (H)CANH spectra, SPEPS outperformed TROP and CP by factors of on average 1.16 and 1.69, respectively, for the membrane protein, but only a marginal improvement of 1.09 was observed for the fibril. These differences are discussed, making note of the longer transfer time used for CP, 14 ms, as compared with 2.9 and 3.6 ms for SPEPS and TROP, respectively. Using SPEPS for two transfers in the 3D (H)CANCO experiment resulted in an even larger benefit in signal intensity, with an average improvement of 1.82 as compared with CP. This results in multifold time savings, in particular considering the weaker peaks that are observed to benefit the most from SPEPS.

High and fast: NMR protein-proton side-chain assignments at 160 kHz and 1.2 GHz

The NMR spectra of side-chain protons in proteins provide important information, not only about their structure and dynamics, but also about the mechanisms that regulate interactions between macromolecules. However, in the solid-state, these resonances are particularly difficult to resolve, even in relatively small proteins. We show that magic-angle-spinning (MAS) frequencies of 160 kHz, combined with a high magnetic field of 1200 MHz proton Larmor frequency, significantly improve their spectral resolution. We investigate in detail the gain for MAS frequencies between 110 and 160 kHz MAS for a model sample as well as for the hepatitis B viral capsid assembled from 120 core-protein (Cp) dimers. For both systems, we found a significantly improved spectral resolution of the side-chain region in the 1H-13C 2D spectra. The combination of 160 kHz MAS frequency with a magnetic field of 1200 MHz, allowed us to assign 61% of the aliphatic protons of Cp. The side-chain proton assignment opens up new possibilities for structural studies and further characterization of protein-protein or protein-nucleic acid interactions.

Barriers to resolution in 1H NMR of rotating solids

The role of 1H solid-state NMR in structure elucidation of solids is becoming more preponderant, particularly as faster magic-angle spinning rates (MAS) become available which improve 1H detected assignment strategies. However, current 1H spectral resolution is still relatively poor, with linewidths of typically a few hundred Hz, even at the fastest rates available today. Here we detail and assess the factors limiting proton linewidths and line shapes in MAS experiments with five different samples, exemplifying the different sources of broadening that affect the residual linewidth. We disentangle the different contributions through one- and two-dimensional experiments: by using dilution to identify the contribution of ABMS; by using extensive deuteration to identify the dipolar contributions; and by using variable MAS rates to determine the ratio between homogeneous and inhomogeneous components. We find that the overall widths and the nature of the different contributions to the linewidths can vary very considerably. While we find that faster spinning always yields narrower lines and longer coherence lifetimes, we also find that for some resonances the dipolar contribution is no longer dominant at 100 kHz MAS. When the inhomogeneous sources of broadening, such as ABMS and chemical shift disorder, are dominant, two-dimensional 1H-1H correlation experiments yield better resolution for assignment. Particularly the extraction of the antidiagonal of a 2D peak will remove any correlated inhomogeneous broadening, giving substantially narrower 1H linewidths.

3D-Printable centrifugal devices for biomolecular solid state NMR rotors

The advent of magic angle spinning (MAS) rates exceeding 100 kHz has facilitated the acquisition of 1H-detected solid-state NMR spectra of biomolecules with high resolution. However, challenges can arise when preparing rotors for these experiments, due to the physical properties of biomolecular solid samples and the small dimensions of the rotors. In this study, we have designed 3D-printable centrifugal devices that facilitate efficient and consistent packing of crystalline protein slurries or viscous phospholipids into 0.7 mm rotors. We demonstrate the efficacy of these packing devices using 1H-detected solid state NMR at 105 kHz. In addition to devices for 0.7 mm rotors, we have also developed devices for other frequently employed rotor sizes and styles. We have made all our designs openly accessible, and we encourage their usage and ongoing development as a shared effort within the solid state NMR community.

Diamond rotors

The resolution of magic angle spinning (MAS) nuclear magnetic resonance (NMR) spectra remains bounded by the spinning frequency, which is limited by the material strength of MAS rotors. Since diamond is capable of withstanding 1.5-2.5x greater MAS frequencies, compared to state-of-the art zirconia, we fabricated rotors from single crystal diamond. When combined with bearings optimized for spinning with helium gas, diamond rotors could achieve the highest MAS frequencies to date. Furthermore, the excellent microwave transmission properties and thermal conductivity of diamond could improve sensitivity enhancements in dynamic nuclear polarization (DNP) experiments. The fabrication protocol we report involves novel laser micromachining and produced rotors that presently spin at ωr/2π = 111.000 ± 0.004 kHz, with stable spinning up to 124 kHz, using N2 gas as the driving fluid. We present the first proton-detected 13C/15N MAS spectra recorded using diamond rotors, a critical step towards studying currently inaccessible ex-vivo protein samples with MAS NMR. Previously, the high aspect ratio of MAS rotors (∼10:1) precluded fabrication of MAS rotors from diamond.

1H-detected characterization of carbon-carbon networks in highly flexible protonated biomolecules using MAS NMR

In the last three decades, the scope of solid-state NMR has expanded to exploring complex biomolecules, from large protein assemblies to intact cells at atomic-level resolution. This diversity in macromolecules frequently features highly flexible components whose insoluble environment precludes the use of solution NMR to study their structure and interactions. While High-resolution Magic-Angle Spinning (HR-MAS) probes offer the capacity for gradient-based ¹H-detected spectroscopy in solids, such probes are not commonly used for routine MAS NMR experiments. As a result, most exploration of the flexible regime entails either ¹³C-detected experiments, the use of partially perdeuterated systems, or ultra-fast MAS. Here we explore proton-detected pulse schemes probing through-bond ¹³C-¹³C networks to study mobile protein sidechains as well as polysaccharides in a broadband manner. We demonstrate the use of such schemes to study a mixture of microtubule-associated protein (MAP) tau and human microtubules (MTs), and the cell wall of the fungus Schizophyllum commune using 2D and 3D spectroscopy, to show its viability for obtaining unambiguous correlations using standard fast-spinning MAS probes at high and ultra-high magnetic fields.

Windowed cross polarization at 55 kHz magic-angle spinning

Cross polarization (CP) transfers via Hartmann-Hahn matching conditions are one of the cornerstones of solid-state magic-angle spinning NMR experiments. Here we investigate a windowed sequence for cross polarization (wCP) at 55 kHz magic-angle spinning, placing one window (and one pulse) per rotor period on one or both rf channels. The wCP sequence is known to have additional matching conditions. We observe a striking similarity between wCP and CP transfer conditions when considering the flip angle of the pulse rather than the rf-field strength applied during the pulse. Using fictitious spin-1/2 formalism and average Hamiltonian theory, we derive an analytical approximation that matches these observed transfer conditions. We recorded data at spectrometers with different external magnetic fields up to 1200 MHz, for strong and weak heteronuclear dipolar couplings. These transfers, and even the selectivity of CP were again found to relate to flip angle (average nutation).

A roadmap to high-resolution standard microcoil MAS NMR spectroscopy for metabolomics

Current microcoil probe technology has emerged as a significant advancement in NMR applications to biofluids research. It has continued to excel as a hyphenated tool with other prominent microdevices, opening many new possibilities in multiple omics fields. However, this does not hold for biological samples such as intact tissue or organisms, due to the considerable challenges of incorporating the microcoil in a magic-angle spinning (MAS) probe without relinquishing the high-resolution spectral data. Not until 2012 did a microcoil MAS probe show promise in profiling the metabolome in a submilligram tissue biopsy with spectral resolution on par with conventional high-resolution MAS (HR-MAS) NMR. This result subsequently triggered a great interest in the possibility of NMR analysis with microgram tissues and striving toward the probe development of "high-resolution" capable microcoil MAS NMR spectroscopy. This review gives an overview of the issues and challenges in the probe development and summarizes the advancements toward metabolomics.

Solid-state NMR studies of amyloids

Amyloids have special structural properties and are involved in many aspects of biological function. In particular, amyloids are the cause or hallmarks of a group of notorious and incurable neurodegenerative diseases. The extraordinary high molecular weight and aggregation states of amyloids have posed a challenge for researchers studying them. Solid-state NMR (SSNMR) has been extensively applied to study the structures and dynamics of amyloids for the past 20 or more years and brought us tremendous progress in understanding their structure and related diseases. These studies, at the same time, helped to push SSNMR technical developments in sensitivity and resolution. In this review, some interesting research studies and important technical developments are highlighted to give the reader an overview of the current state of this field.

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.

Ultrafast Magic Angle Spinning Solid-State NMR Spectroscopy: Advances in Methodology and Applications

Solid-state NMR spectroscopy is one of the most commonly used techniques to study the atomic-resolution structure and dynamics of various chemical, biological, material, and pharmaceutical systems spanning multiple forms, including crystalline, liquid crystalline, fibrous, and amorphous states. Despite the unique advantages of solid-state NMR spectroscopy, its poor spectral resolution and sensitivity have severely limited the scope of this technique. Fortunately, the recent developments in probe technology that mechanically rotate the sample fast (100 kHz and above) to obtain "solution-like" NMR spectra of solids with higher resolution and sensitivity have opened numerous avenues for the development of novel NMR techniques and their applications to study a plethora of solids including globular and membrane-associated proteins, self-assembled protein aggregates such as amyloid fibers, RNA, viral assemblies, polymorphic pharmaceuticals, metal-organic framework, bone materials, and inorganic materials. While the ultrafast-MAS continues to be developed, the minute sample quantity and radio frequency requirements, shorter recycle delays enabling fast data acquisition, the feasibility of employing proton detection, enhancement in proton spectral resolution and polarization transfer efficiency, and high sensitivity per unit sample are some of the remarkable benefits of the ultrafast-MAS technology as demonstrated by the reported studies in the literature. Although the very low sample volume and very high RF power could be limitations for some of the systems, the advantages have spurred solid-state NMR investigation into increasingly complex biological and material systems. As ultrafast-MAS NMR techniques are increasingly used in multidisciplinary research areas, further development of instrumentation, probes, and advanced methods are pursued in parallel to overcome the limitations and challenges for widespread applications. This review article is focused on providing timely comprehensive coverage of the major developments on instrumentation, theory, techniques, applications, limitations, and future scope of ultrafast-MAS technology.

Multiple acquisitions in a single scan: exhausting abundant 1H polarization at fast MAS

Proton-detected solid-state NMR spectroscopy is emerging as a unique tool for atomic characterization of organic solids due to the boost of resolution and sensitivity afforded by the combined use of high magnetic field and ultrafast magic angle spinning (MAS). Here, we proposed a new set of proton-detected solid-state NMR sequences that hybrid multi-dimensional ¹H-¹H homonuclear chemical shift correlation (HOMCOR) and two-dimensional ¹H-¹³C heteronuclear chemical shift correlation (HETCOR) sequences into a single experiment, enabling the simultaneous acquisition of multidimensional HOMCOR and HETCOR spectra and thus significant time savings. Based on the core idea of exhausting ¹H polarization in each transient scan, we firstly demonstrated that 3D ¹H multiple-quantum (MQ) HOMCOR sequence can be combined with 2D HETCOR sequence into a single experiment, leading to the simultaneous acquisition of a 3D ¹H MQ HOMCOR and a 2D ¹H-¹³C HETCOR spectrum. Besides, we also showed that 2D ¹H/¹H double-quantum/single-quantum (DQ/SQ) and single-quantum/single-quantum (SQ/SQ) HOMCOR sequence can be simultaneously combined with HETCOR sequence either, and thus three spectra can be simultaneously obtained from one experiment, including 2D ¹H DQ/SQ, 2D ¹H SQ/SQ and 2D ¹H-¹³C HETCOR spectra. Since there is only one recycle delay in each experiment, experimental time is substantially reduced compared to separate acquisition of each multi-dimensional solid-state NMR spectrum. Furthermore, those new sequences can be implemented on any standard solid-state spectrometer with only one receiver. Thus, we foresee that these approaches can be valuable for the study of a broad range of molecular systems, including polymers, pharmaceuticals, covalent-organic frameworks (COF) and so on.

Ultrafast magic angle spinning NMR characterization of pharmaceutical solid polymorphism: A posaconazole example

Protons represent the most NMR-sensitive nucleus in pharmaceutical compounds. Therefore, proton-detected solid-state NMR techniques under fast magic angle spinning are among the few solutions to overcome the challenge of low sensitivity to analyze natural abundant drug substances and products. In this study, we report the structural characterization of crystal polymorphs of a commercial drug molecule, posaconazole, with a relatively large molecular weight of 700.8 g·mol^-1 and at the natural abundance. The enhanced sensitivity and resolution at 100 kHz MAS enables the exploration of the distinct intermolecular packing in posaconazole forms I, III, and γ. These results demonstrate that proton-detected homo- and heteronuclear correlation methods can probe the structural details of pharmaceutical polymorphism.

Solid-state NMR methods for the characterization of bioconjugations and protein-material interactions

Protein solid-state NMR has evolved dramatically over the last two decades, with the development of new hardware and sample preparation methodologies. This technique is now ripe for complex applications, among which one can count bioconjugation, protein chemistry and functional biomaterials. In this review, we provide our account on this aspect of protein solid-state NMR.

Nucleic acid-protein interfaces studied by MAS solid-state NMR spectroscopy

Solid-state NMR (ssNMR) has become a well-established technique to study large and insoluble protein assemblies. However, its application to nucleic acid-protein complexes has remained scarce, mainly due to the challenges presented by overlapping nucleic acid signals. In the past decade, several efforts have led to the first structure determination of an RNA molecule by ssNMR. With the establishment of these tools, it has become possible to address the problem of structure determination of nucleic acid-protein complexes by ssNMR. Here we review first and more recent ssNMR methodologies that study nucleic acid-protein interfaces by means of chemical shift and peak intensity perturbations, direct distance measurements and paramagnetic effects. At the end, we review the first structure of an RNA-protein complex that has been determined from ssNMR-derived intermolecular restraints.

Fast Magic‐Angle‐Spinning NMR Reveals the Evasive Hepatitis B Virus Capsid C‐Terminal Domain**

Experimentally determined protein structures often feature missing domains. One example is the C‐terminal domain (CTD) of the hepatitis B virus capsid protein, a functionally central part of this assembly, crucial in regulating nucleic‐acid interactions, cellular trafficking, nuclear import, particle assembly and maturation. However, its structure remained elusive to all current techniques, including NMR. Here we show that the recently developed proton‐detected fast magic‐angle‐spinning solid‐state NMR at >100 kHz MAS allows one to detect this domain and unveil its structural and dynamic behavior. We describe the experimental framework used and compare the domain's behavior in different capsid states. The developed approaches extend solid‐state NMR observations to residues characterized by large‐amplitude motion on the microsecond timescale, and shall allow one to shed light on other flexible protein domains still lacking their structural and dynamic characterization.

Field and magic angle spinning frequency dependence of proton resonances in rotating solids

Proton detection in solid state NMR is continuously developing and allows one to gain new insights in structural biology. Overall, this progress is a result of the synergy between hardware development, new NMR methodology and new isotope labeling strategies, to name a few factors. Even though current developments are rapid, it is worthwhile to summarize what can currently be achieved employing proton detection in biological solids. We illustrate this by analysing the signal-to-noise ratio (SNR) for spectra obtained for a microcrystalline α-spectrin SH3 domain protein sample by (i) employing different degrees of chemical dilution to replace protons by incorporating deuterons in different sites, by (ii) variation of the magic angle spinning (MAS) frequencies between 20 and 110 kHz, and by (iii) variation of the static magnetic field B₀. The experimental SNR values are validated with numerical simulations employing up to 9 proton spins. Although in reality a protein would contain far more than 9 protons, in a deuterated environment this is a sufficient number to achieve satisfactory simulations consistent with the experimental data. The key results of this analysis are (i) with current hardware, deuteration is still necessary to record spectra of optimum quality; (ii) 13CH3 isotopomers for methyl groups yield the best SNR when MAS frequencies above 100 kHz are available; and (iii) sensitivity increases with a factor beyond B0 3/2 with the static magnetic field due to a transition of proton-proton dipolar interactions from a strong to a weak coupling limit.

1H-Detected Biomolecular NMR under Fast Magic-Angle Spinning

Since the first pioneering studies on small deuterated peptides dating more than 20 years ago, 1H detection has evolved into the most efficient approach for investigation of biomolecular structure, dynamics, and interactions by solid-state NMR. The development of faster and faster magic-angle spinning (MAS) rates (up to 150 kHz today) at ultrahigh magnetic fields has triggered a real revolution in the field. This new spinning regime reduces the 1H-1H dipolar couplings, so that a direct detection of 1H signals, for long impossible without proton dilution, has become possible at high resolution. The switch from the traditional MAS NMR approaches with 13C and 15N detection to 1H boosts the signal by more than an order of magnitude, accelerating the site-specific analysis and opening the way to more complex immobilized biological systems of higher molecular weight and available in limited amounts. This paper reviews the concepts underlying this recent leap forward in sensitivity and resolution, presents a detailed description of the experimental aspects of acquisition of multidimensional correlation spectra with fast MAS, and summarizes the most successful strategies for the assignment of the resonances and for the elucidation of protein structure and conformational dynamics. It finally outlines the many examples where 1H-detected MAS NMR has contributed to the detailed characterization of a variety of crystalline and noncrystalline biomolecular targets involved in biological processes ranging from catalysis through drug binding, viral infectivity, amyloid fibril formation, to transport across lipid membranes.

In-Cell Structural Biology by NMR: The Benefits of the Atomic Scale

In-cell structural biology aims at extracting structural information about proteins or nucleic acids in their native, cellular environment. This emerging field holds great promise and is already providing new facts and outlooks of interest at both fundamental and applied levels. NMR spectroscopy has important contributions on this stage: It brings information on a broad variety of nuclei at the atomic scale, which ensures its great versatility and uniqueness. Here, we detail the methods, the fundamental knowledge, and the applications in biomedical engineering related to in-cell structural biology by NMR. We finally propose a brief overview of the main other techniques in the field (EPR, smFRET, cryo-ET, etc.) to draw some advisable developments for in-cell NMR. In the era of large-scale screenings and deep learning, both accurate and qualitative experimental evidence are as essential as ever to understand the interior life of cells. In-cell structural biology by NMR spectroscopy can generate such a knowledge, and it does so at the atomic scale. This review is meant to deliver comprehensive but accessible information, with advanced technical details and reflections on the methods, the nature of the results, and the future of the field.

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.

Correction of field instabilities in biomolecular solid-state NMR by simultaneous acquisition of a frequency reference

With the advent of faster magic-angle spinning (MAS) and higher magnetic fields, the resolution of biomolecular solid-state nuclear magnetic resonance (NMR) spectra has been continuously increasing. As a direct consequence, the always narrower spectral lines, especially in proton-detected spectroscopy, are also becoming more sensitive to temporal instabilities of the magnetic field in the sample volume. Field drifts in the order of tenths of parts per million occur after probe insertion or temperature change, during cryogen refill, or are intrinsic to the superconducting high-field magnets, particularly in the months after charging. As an alternative to a field-frequency lock based on deuterium solvent resonance rarely available for solid-state NMR, we present a strategy to compensate non-linear field drifts using simultaneous acquisition of a frequency reference (SAFR). It is based on the acquisition of an auxiliary 1D spectrum in each scan of the experiment. Typically, a small-flip-angle pulse is added at the beginning of the pulse sequence. Based on the frequency of the maximum of the solvent signal, the field evolution in time is reconstructed and used to correct the raw data after acquisition, thereby acting in its principle as a digital lock system. The general applicability of our approach is demonstrated on 2D and 3D protein spectra during various situations with a non-linear field drift. SAFR with small-flip-angle pulses causes no significant loss in sensitivity or increase in experimental time in protein spectroscopy. The correction leads to the possibility of recording high-quality spectra in a typical biomolecular experiment even during non-linear field changes in the order of 0.1 ppm h- 1 without the need for hardware solutions, such as stabilizing the temperature of the magnet bore. The improvement of linewidths and peak shapes turns out to be especially important for 1 H-detected spectra under fast MAS, but the method is suitable for the detection of carbon or other nuclei as well.

Experimental Characterization of the Hepatitis B Virus Capsid Dynamics by Solid-State NMR

Protein plasticity and dynamics are important aspects of their function. Here we use solid-state NMR to experimentally characterize the dynamics of the 3.5 MDa hepatitis B virus (HBV) capsid, assembled from  240 copies of the Cp149 core protein. We measure both T₁ and T_1ρ relaxation times, which we use to establish detectors on the nanosecond and microsecond timescale. We compare our results to those from a 1 microsecond all-atom Molecular Dynamics (MD) simulation trajectory for the capsid. We show that, for the constituent residues, nanosecond dynamics are faithfully captured by the MD simulation. The calculated values can be used in good approximation for the NMR-non-detected residues, as well as to extrapolate into the range between the nanosecond and microsecond dynamics, where NMR has a blind spot at the current state of technology. Slower motions on the microsecond timescale are difficult to characterize by all-atom MD simulations owing to computational expense, but are readily accessed by NMR. The two methods are, thus, complementary, and a combination thereof can reliably characterize motions covering correlation times up to a few microseconds.

Solid-State NMR Dipolar and Chemical Shift Anisotropy Recoupling Techniques for Structural and Dynamical Studies in Biological Systems

With the development of NMR methodology and technology during the past decades, solid-state NMR (ssNMR) has become a particularly important tool for investigating structure and dynamics at atomic scale in biological systems, where the recoupling techniques play pivotal roles in modern high-resolution MAS NMR. In this review, following a brief introduction on the basic theory of recoupling in ssNMR, we highlight the recent advances in dipolar and chemical shift anisotropy recoupling methods, as well as their applications in structural determination and dynamical characterization at multiple time scales (i.e., fast-, intermediate-, and slow-motion). The performances of these prevalent recoupling techniques are compared and discussed in multiple aspects, together with the representative applications in biomolecules. Given the recent emerging advances in NMR technology, new challenges for recoupling methodology development and potential opportunities for biological systems are also discussed.

Proton-phosphorous connectivities revealed by high-resolution proton-detected solid-state NMR

Proton-detected solid-state NMR enables atomic-level insight in solid-state reactions, for instance in heterogeneous catalysis, which is fundamental for deciphering chemical reaction mechanisms. We herein introduce a phosphorus-31 radiofrequency channel in...

Dipolar Order Parameters in Large Systems With Fast Spinning

Order parameters are a useful tool for quantifying amplitudes of molecular motions. Here we measure dipolar order parameters by recoupling heteronuclear dipole-dipole couplings under fast spinning. We apply symmetry based recoupling methods to samples spinning under magic angle at 60 kHz by employing a variable flip angle compound inversion pulse. We validate the methods by measuring site-specific ¹⁵N-¹H order parameters of a microcrystalline protein over a small temperature range and the same protein in a large, precipitated complex with antibody. The measurements of the order parameters in the complex are consistent with the observed protein undergoing overall motion within the assembly.

Deuteration for High-Resolution Detection of Protons in Protein Magic Angle Spinning (MAS) Solid-State NMR

Proton detection developed in the last 20 years as the method of choice to study biomolecules in the solid state. In perdeuterated proteins, proton dipolar interactions are strongly attenuated, which allows yielding of high-resolution proton spectra. Perdeuteration and backsubstitution of exchangeable protons is essential if samples are rotated with MAS rotation frequencies below 60 kHz. Protonated samples can be investigated directly without spin dilution using proton detection methods in case the MAS frequency exceeds 110 kHz. This review summarizes labeling strategies and the spectroscopic methods to perform experiments that yield assignments, quantitative information on structure, and dynamics using perdeuterated samples. Techniques for solvent suppression, H/D exchange, and deuterium spectroscopy are discussed. Finally, experimental and theoretical results that allow estimation of the sensitivity of proton detected experiments as a function of the MAS frequency and the external B₀ field in a perdeuterated environment are compiled.

Towards a native environment: structure and function of membrane proteins in lipid bilayers by NMR

Solid-state NMR (ssNMR) is a versatile technique that can be used for the characterization of various materials, ranging from small molecules to biological samples, including membrane proteins. ssNMR can probe both the structure and dynamics of membrane proteins, revealing protein function in a near-native lipid bilayer environment. The main limitation of the method is spectral resolution and sensitivity, however recent developments in ssNMR hardware, including the commercialization of 28 T magnets (1.2 GHz proton frequency) and ultrafast MAS spinning (<100 kHz) promise to accelerate acquisition, while reducing sample requirement, both of which are critical to membrane protein studies. Here, we review recent advances in ssNMR methodology used for structure determination of membrane proteins in native and mimetic environments, as well as the study of protein functions such as protein dynamics, and interactions with ligands, lipids and cholesterol.

Strategies for RNA Resonance Assignment by 13C/15N- and 1H-Detected Solid-State NMR Spectroscopy

Magic angle spinning (MAS) solid-state NMR (ssNMR) is an established tool that can be applied to non-soluble or non-crystalline biomolecules of any size or complexity. The ssNMR method advances rapidly due to technical improvements and the development of advanced isotope labeling schemes. While ssNMR has shown significant progress in structural studies of proteins, the number of RNA studies remains limited due to ssNMR methodology that is still underdeveloped. Resonance assignment is the most critical and limiting step in the structure determination protocol that defines the feasibility of NMR studies. In this review, we summarize the recent progress in RNA resonance assignment methods and approaches for secondary structure determination by ssNMR. We critically discuss advantages and limitations of conventional 13C- and 15N-detected experiments and novel 1H-detected methods, identify optimal regimes for RNA studies by ssNMR, and provide our view on future ssNMR studies of RNA in large RNP complexes.

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.

Looking into the dynamics of molecular crystals of ibuprofen and terephthalic acid using 17 O and 2 H nuclear magnetic resonance analyses

Oxygen-17 and deuterium are two quadrupolar nuclei that are of interest for studying the structure and dynamics of materials by solid-state nuclear magnetic resonance (NMR). Here, 17 O and 2 H NMR analyses of crystalline ibuprofen and terephthalic acid are reported. First, improved 17 O-labelling protocols of these molecules are described using mechanochemistry. Then, dynamics occurring around the carboxylic groups of ibuprofen are studied considering variable temperature 17 O and 2 H NMR data, as well as computational modelling (including molecular dynamics simulations). More specifically, motions related to the concerted double proton jump and the 180° flip of the H-bonded (-COOH)2 unit in the crystal structure were looked into, and it was found that the merging of the C=O and C-OH 17 O resonances at high temperatures cannot be explained by the sole presence of one of these motions. Lastly, preliminary experiments were performed with a 2 H-17 O diplexer connected to the probe. Such configurations can allow, among others, 2 H and 17 O NMR spectra to be recorded at different temperatures without needing to tune or to change probe configurations. Overall, this work offers a few leads which could be of use in future studies of other materials using 17 O and 2 H NMR.

Theory and simulations of homonuclear three-spin systems in rotating solids

The homonuclear dipolar coupling is the internal spin interaction that contributes the most to the line shapes in magic-angle-spinning (MAS) ¹H NMR spectra of solids, and linewidths typically extend over several hundred Hertz, limiting the ¹H resolution. Understanding and reducing this contribution could provide rich structural information for organic solids. Here, we use average Hamiltonian theory to study two- and three-spin systems in the fast MAS regime. Specifically, we develop analytical expressions to third order in the case of two and three inequivalent spins (I = ½). The results show that the full third-order expression of the Hamiltonian, without secular approximations or truncation to second order, is the description that agrees the best, by far, with full numerical calculations. We determine the effect on the NMR spectrum of the different Hamiltonian terms, which are shown to produce both residual shifts and splittings in the three-spin systems. Both the shifts and splittings have a fairly complex dependence on the spinning rate with the eigenstates having a polynomial ω_r dependence. The effect on powder line shapes is also shown, and we find that the anisotropic residual shift does not have zero average so that the powder line shape is broadened and shifted from the isotropic position. This suggests that in ¹H MAS spectra, even at the fastest MAS rates attainable today, the positions observed are not exactly the isotropic shifts.

Pure Isotropic Proton Solid State NMR

Resolution in proton solid state magic angle sample spinning (MAS) NMR is limited by the intrinsically imperfect nature of coherent averaging induced by either MAS or multiple pulse sequence methods. Here, we suggest that instead of optimizing and perfecting a coherent averaging scheme, we could approach the problem by parametrically mapping the error terms due to imperfect averaging in a k-space representation, in such a way that they can be removed in a multidimensional correlation leaving only the desired pure isotropic signal. We illustrate the approach here by determining pure isotropic ¹H spectra from a series of MAS spectra acquired at different spinning rates. For six different organic solids, the approach is shown to produce pure isotropic ¹H spectra that are significantly narrower than the MAS spectrum acquired at the fastest possible rate, with linewidths down to as little as 48 Hz. On average, we observe a 7-fold increase in resolution, and up to a factor of 20, as compared with spectra acquired at 100 kHz MAS. The approach is directly applicable to a range of solids, and we anticipate that the same underlying principle for removing errors introduced here can be applied to other problems in NMR spectroscopy.

Biomolecular solid-state NMR spectroscopy at 1200 MHz: the gain in resolution

Progress in NMR in general and in biomolecular applications in particular is driven by increasing magnetic-field strengths leading to improved resolution and sensitivity of the NMR spectra. Recently, persistent superconducting magnets at a magnetic field strength (magnetic induction) of 28.2 T corresponding to 1200 MHz proton resonance frequency became commercially available. We present here a collection of high-field NMR spectra of a variety of proteins, including molecular machines, membrane proteins, viral capsids, fibrils and large molecular assemblies. We show this large panel in order to provide an overview over a range of representative systems under study, rather than a single best performing model system. We discuss both carbon-13 and proton-detected experiments, and show that in ¹³C spectra substantially higher numbers of peaks can be resolved compared to 850 MHz while for ¹H spectra the most impressive increase in resolution is observed for aliphatic side-chain resonances.

Residual dipolar line width in magic-angle spinning proton solid-state NMR

Magic-angle spinning is routinely used to average anisotropic interactions in solid-state nuclear magnetic resonance (NMR). Due to the fact that the homonuclear dipolar Hamiltonian of a strongly coupled spin system does not commute with itself at different time points during the rotation, second-order and higher-order terms lead to a residual dipolar line broadening in the observed resonances. Additional truncation of the residual broadening due to isotropic chemical-shift differences can be observed. We analyze the residual line broadening in coupled proton spin systems based on theoretical calculations of effective Hamiltonians up to third order using Floquet theory and compare these results to numerically obtained effective Hamiltonians in small spin systems. We show that at spinning frequencies beyond 75 kHz, second-order terms dominate the residual line width, leading to a 1 / ω r dependence of the second moment which we use to characterize the line width. However, chemical-shift truncation leads to a partial ω r - 2 dependence of the line width which looks as if third-order effective Hamiltonian terms are contributing significantly. At slower spinning frequencies, cross terms between the chemical shift and the dipolar coupling can contribute in third-order effective Hamiltonians. We show that second-order contributions not only broaden the line, but also lead to a shift of the center of gravity of the line. Experimental data reveal such spinning-frequency-dependent line shifts in proton spectra in model substances that can be explained by line shifts induced by the second-order dipolar Hamiltonian.

Structures of Pathological and Functional Amyloids and Prions, a Solid-State NMR Perspective

Infectious proteins or prions are a remarkable class of pathogens, where pathogenicity and infectious state correspond to conformational transition of a protein fold. The conformational change translates into the formation by the protein of insoluble amyloid aggregates, associated in humans with various neurodegenerative disorders and systemic protein-deposition diseases. The prion principle, however, is not limited to pathogenicity. While pathological amyloids (and prions) emerge from protein misfolding, a class of functional amyloids has been defined, consisting of amyloid-forming domains under natural selection and with diverse biological roles. Although of great importance, prion amyloid structures remain challenging for conventional structural biology techniques. Solid-state nuclear magnetic resonance (SSNMR) has been preferentially used to investigate these insoluble, morphologically heterogeneous aggregates with poor crystallinity. SSNMR methods have yielded a wealth of knowledge regarding the fundamentals of prion biology and have helped to solve the structures of several prion and prion-like fibrils. Here, we will review pathological and functional amyloid structures and will discuss some of the obtained structural models. We will finish the review with a perspective on integrative approaches combining solid-state NMR, electron paramagnetic resonance and cryo-electron microscopy, which can complement and extend our toolkit to structurally explore various facets of prion biology.

Proton Detected Solid-State NMR of Membrane Proteins at 28 Tesla (1.2 GHz) and 100 kHz Magic-Angle Spinning

The available magnetic field strength for high resolution NMR in persistent superconducting magnets has recently improved from 23.5 to 28 Tesla, increasing the proton resonance frequency from 1 to 1.2 GHz. For magic-angle spinning (MAS) NMR, this is expected to improve resolution, provided the sample preparation results in homogeneous broadening. We compare two-dimensional (2D) proton detected MAS NMR spectra of four membrane proteins at 950 and 1200 MHz. We find a consistent improvement in resolution that scales superlinearly with the increase in magnetic field for three of the four examples. In 3D and 4D spectra, which are now routinely acquired, this improvement indicates the ability to resolve at least 2 and 2.5 times as many signals, respectively.

Faster magic angle spinning reveals cellulose conformations in woods

We present a first report on the detection of three different C6 conformers of cellulose in spruce, as revealed by solid-state 1H-13C correlation spectra. The breakthrough in 1H resolution is achieved by magic-angle spinning in the regime of 150 kHz. The suppression of dense dipolar network of 1H provides inverse detected 13C spectra at a good sensitivity even in natural samples. We find that the glycosidic linkages are initially more ordered in spruce than maple, but a thermal treatment of spruce leads to a more heterogeneous packing order of the remaining cellulose fibrils.

Protein Side-Chain-DNA Contacts Probed by Fast Magic-Angle Spinning NMR

Protein–nucleic acid interactions are essential in a variety of biological events ranging from the replication of genomic DNA to the synthesis of proteins. Noncovalent interactions guide such molecular recognition events, and protons are often at the center of them, particularly due to their capability of forming hydrogen bonds to the nucleic acid phosphate groups. Fast magic-angle spinning experiments (100 kHz) reduce the proton NMR line width in solid-state NMR of fully protonated protein–DNA complexes to such an extent that resolved proton signals from side-chains coordinating the DNA can be detected. We describe a set of NMR experiments focusing on the detection of protein side-chains from lysine, arginine, and aromatic amino acids and discuss the conclusions that can be obtained on their role in DNA coordination. We studied the 39 kDa enzyme of the archaeal pRN1 primase complexed with DNA and characterize protein–DNA contacts in the presence and absence of bound ATP molecules.

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.

Asparagine and Glutamine Side-Chains and Ladders in HET-s(218-289) Amyloid Fibrils Studied by Fast Magic-Angle Spinning NMR

Asparagine and glutamine side-chains can form hydrogen-bonded ladders which contribute significantly to the stability of amyloid fibrils. We show, using the example of HET-s(218–289) fibrils, that the primary amide side-chain proton resonances can be detected in cross-polarization based solid-state NMR spectra at fast magic-angle spinning (MAS). J-coupling based experiments offer the possibility to distinguish them from backbone amide groups if the spin-echo lifetimes are long enough, which turned out to be the case for the glutamine side-chains, but not for the asparagine side-chains forming asparagine ladders. We explore the sensitivity of NMR observables to asparagine ladder formation. One of the two possible asparagine ladders in HET-s(218–289), the one comprising N226 and N262, is assigned by proton-detected 3D experiments at fast MAS and significant de-shielding of one of the NH₂ proton resonances indicative of hydrogen-bond formation is observed. Small rotating-frame ¹⁵N relaxation-rate constants point to rigidified asparagine side-chains in this ladder. The proton resonances are homogeneously broadened which could indicate chemical exchange, but is presently not fully understood. The second asparagine ladder (N243 and N279) in contrast remains more flexible.

Solid-State NMR for Studying the Structure and Dynamics of Viral Assemblies

Structural virology reveals the architecture underlying infection. While notably electron microscopy images have provided an atomic view on viruses which profoundly changed our understanding of these assemblies incapable of independent life, spectroscopic techniques like NMR enter the field with their strengths in detailed conformational analysis and investigation of dynamic behavior. Typically, the large assemblies represented by viral particles fall in the regime of biological high-resolution solid-state NMR, able to follow with high sensitivity the path of the viral proteins through their interactions and maturation steps during the viral life cycle. We here trace the way from first solid-state NMR investigations to the state-of-the-art approaches currently developing, including applications focused on HIV, HBV, HCV and influenza, and an outlook to the possibilities opening in the coming years.

Protein NMR Spectroscopy at 150 kHz Magic-Angle Spinning Continues To Improve Resolution and Mass Sensitivity

Spectral resolution is the key to unleashing the structural and dynamic information contained in NMR spectra. Fast magic-angle spinning (MAS) has recently revolutionized the spectroscopy of biomolecular solids. Herein, we report a further remarkable improvement in the resolution of the spectra of four fully protonated proteins and a small drug molecule by pushing the MAS rotation frequency higher (150 kHz) than the more routinely used 100 kHz. We observed a reduction in the average homogeneous linewidth by a factor of 1.5 and a decrease in the observed linewidth by a factor 1.25. We conclude that even faster MAS is highly attractive and increases mass sensitivity at a moderate price in overall sensitivity.