13C–13C dipolar recoupling under very fast magic angle spinning in solid-state nuclear magnetic resonance: Applications to distance measurements, spectral assignments, and high-throughput secondary-structure determination

Optimal control: From sensitivity improvement to alternative pulse-sequence design in solid-state NMR

Exciting developments in new experimental methods for multidimensional solid-state NMR spectroscopy have recently been achieved using optimal-control theory. These results, in turn, have triggered the development of new pulse sequences based on traditional analytical theories. This trend article summarises the key steps leading to these advancements. It also describes additional applications of optimal control beyond structural biology and envisions similar progress in the NMR of solid materials. Despite attractive features of optimal-control pulse sequences demonstrated in the proof-of-concept studies, their experimental utilization remains sparse, probably due to the lack of awareness among experimentalists. We hope this mini-review helps to spread optimal-control methods into routine experimental workflows. Furthermore, we offer a personal outlook on how numerical optimisations could in general enhance the experimental capabilities of solid-state NMR in the near future, with optimal control serving as a pioneer exploring new possibilities.

Analysis of the MODIST Sequence for Selective Proton-Proton Recoupling

Theoretical and simulated analyses of selective homonuclear dipolar recoupling sequences serve as primary tools for understanding and determining the robustness of these sequences under various conditions. In this article, we investigate the recently proposed first-order dipolar recoupling sequence known as MODIST (Modest Offset Difference Internuclear Selective Transfer). We evaluate the MODIST transfer efficiency, assessing its dependence on rf-field strengths and the number of simulated spins, extending up to 10 spins. This helps to identify conditions that enhance polarization transfer among spins that are nearby in frequency, particularly among aliphatic protons. The exploration uncovers a novel effect for first-order selective recoupling sequences that we term "facilitated dipolar recoupling". This effect amplifies the recoupled dipolar interaction between distant spins due to the presence of additional strongly dipolar-coupled spins. Unlike the third spin-assisted recoupling mechanism, facilitated dipolar recoupling only requires a coupling to one of the two distant spins of interest. Experimental demonstration of MODIST, including at different rf-field strengths, was carried out with the membrane protein influenza A M2 in lipid bilayers using 55 kHz magic-angle spinning (MAS). Reducing MODIST rf-field strength by a factor of 2 unveils possibilities for detecting Hα-Hα and HMeth-HMeth correlations with a 3D (H)C(H)(H)CH experiment under fast MAS rates, all achievable without specific spin labeling.

Dipolar Recoupling in Rotating Solids

Magic angle spinning (MAS) nuclear magnetic resonance (NMR) has evolved significantly over the past three decades and established itself as a vital tool for the structural analysis of biological macromolecules and materials. This review delves into the development and application of dipolar recoupling techniques in MAS NMR, which are crucial for obtaining detailed structural and dynamic information. We discuss a variety of homonuclear and heteronuclear recoupling methods which are essential for measuring spatial restraints and explain in detail the spin dynamics that these sequences generate. We also explore recent developments in high spinning frequency MAS, proton detection, and dynamic nuclear polarization, underscoring their importance in advancing biomolecular NMR. Our aim is to provide a comprehensive account of contemporary dipolar recoupling methods, their principles, and their application to structural biology and materials, highlighting significant contributions to the field and emerging techniques that enhance resolution and sensitivity in MAS NMR spectroscopy.

Selective Methods Promote Protein Solid-State NMR

Solid-state nuclear magnetic resonance (ssNMR) is indispensable for studying the structures, dynamics, and interactions of insoluble proteins in native or native-like environments. While ssNMR includes numerous nonselective techniques for general analysis, it also provides various selective methods that allow for the extraction of precise details about proteins. This perspective highlights three key aspects of selective methods: selective signals of protein segments, selective recoupling, and site-specific insights into proteins. These methods leverage protein topology, labeling strategies, and the tailored manipulation of spin interactions through radio frequency (RF) pulses, significantly promoting the field of protein ssNMR. With ongoing advancements in higher magnetic fields and faster magic angle spinning (MAS), there remains an ongoing need to enhance the selectivity and efficiency of selective ssNMR methods, facilitating deeper atomic-level insights into complex biological systems.

E22G Aβ40 fibril structure and kinetics illuminate how Aβ40 rather than Aβ42 triggers familial Alzheimer's

Arctic (E22G) mutation in amyloid-β (Aβ enhances Aβ40 fibril accumulation in Alzheimer's disease (AD). Unlike sporadic AD, familial AD (FAD) patients with the mutation exhibit more Aβ40 in the plaque core. However, structural details of E22G Aβ40 fibrils remain elusive, hindering therapeutic progress. Here, we determine a distinctive W-shaped parallel β-sheet structure through co-analysis by cryo-electron microscopy (cryoEM) and solid-state nuclear magnetic resonance (SSNMR) of in-vitro-prepared E22G Aβ40 fibrils. The E22G Aβ40 fibrils displays typical amyloid features in cotton-wool plaques in the FAD, such as low thioflavin-T fluorescence and a less compact unbundled morphology. Furthermore, kinetic and MD studies reveal previously unidentified in-vitro evidence that E22G Aβ40, rather than Aβ42, may trigger Aβ misfolding in the FAD, and prompt subsequent misfolding of wild-type (WT) Aβ40/Aβ42 via cross-seeding. The results provide insight into how the Arctic mutation promotes AD via Aβ40 accumulation and cross-propagation.

Selective correlations between aliphatic 13C nuclei in protein solid-state NMR

Solid-state nuclear magnetic resonance (NMR) is a potent tool for studying the structures and dynamics of insoluble proteins. It starts with signal assignment through multi-dimensional correlation experiments, where the aliphatic 13Cα-13Cβ correlation is indispensable for identifying specific residues. However, developing efficient methods for achieving this correlation is a challenge in solid-state NMR. We present a simple band-selective zero-quantum (ZQ) recoupling method, named POST-C4161 (PC4), which enhances 13Cα-13Cβ correlations under moderate magic-angle spinning (MAS) conditions. PC4 requires minimal 13C radio-frequency (RF) field and proton decoupling, exhibits high stability against RF variations, and achieves superior efficiency. Comparative tests on various samples, including the formyl-Met-Leu-Phe (fMLF) tripeptide, microcrystalline β1 immunoglobulin binding domain of protein G (GB1), and membrane protein of mechanosensitive channel of large conductance from Methanosarcina acetivorans (MaMscL), demonstrate that PC4 selectively enhances 13Cα-13Cβ correlations by up to 50 % while suppressing unwanted correlations, as compared to the popular dipolar-assisted rotational resonance (DARR). It has addressed the long-standing need for selective 13C-13C correlation methods. We anticipate that this simple but efficient PC4 method will have immediate applications in structural biology by solid-state NMR.

Structure of Amyloid Peptide Ribbons Characterized by Electron Microscopy, Atomic Force Microscopy, and Solid-State Nuclear Magnetic Resonance

Polypeptides often self-assemble to form amyloid fibrils, which contain cross-β structural motifs and are typically 5-15 nm in width and micrometers in length. In many cases, short segments of longer amyloid-forming protein or peptide sequences also form cross-β assemblies but with distinctive ribbon-like morphologies that are characterized by a well-defined thickness (on the order of 5 nm) in one lateral dimension and a variable width (typically 10-100 nm) in the other. Here, we use a novel combination of data from solid-state nuclear magnetic resonance (ssNMR), dark-field transmission electron microscopy (TEM), atomic force microscopy (AFM), and cryogenic electron microscopy (cryoEM) to investigate the structures within amyloid ribbons formed by residues 14-23 and residues 11-25 of the Alzheimer's disease-associated amyloid-β peptide (Aβ14-23 and Aβ11-25). The ssNMR data indicate antiparallel β-sheets with specific registries of intermolecular hydrogen bonds. Mass-per-area values are derived from dark-field TEM data. The ribbon thickness is determined from AFM images. For Aβ14-23 ribbons, averaged cryoEM images show a periodic spacing of β-sheets. The combined data support structures in which the amyloid ribbon growth direction is the direction of intermolecular hydrogen bonds between β-strands, the ribbon thickness corresponds to the width of one β-sheet (i.e., approximately the length of one molecule), and the variable ribbon width is a variable multiple of the thickness of one β-sheet (i.e., a multiple of the repeat distance in a stack of β-sheets). This architecture for a cross-β assembly may generally exist within amyloid ribbons.

Solid-State NMR Double-Quantum Dipolar Recoupling Enhanced by Additional Phase Modulation

Additional phase modulation (APM) is proposed to generally enhance the theoretical efficiency of homonuclear double-quantum (DQ) recoupling in solid-state NMR. APM applies an additional phase list to DQ recoupling in steps of an entire block. The sine-based phase list can enhance the theoretical efficiency by 15-30 %, from 0.52 to 0.68 (non-γ-encoded recoupling) or from 0.73 to 0.84 (γ-encoded recoupling), with doubled recoupling time. The genetic-algorithm (GA) optimized APM can adiabatically enhance the efficiency to ∼1.0 at longer times. The concept of APM has been tested on SPR-51 , BaBa, and SPR-31 , which represent γ-encoded recoupling, non-γ-encoded recoupling, and another kind beyond the former two, respectively. Simulations reveal that enhancements from APM are due to the activation of more crystallites in the powder. Experiments on 2,3-13 C labeled alanine are used to validate the APM recoupling. This new concept shall shed light on developing more efficient homonuclear recoupling methods.

Two structurally defined Aβ polymorphs promote different pathological changes in susceptible mice

Misfolded Aβ is involved in the progression of Alzheimer's disease (AD). However, the role of its polymorphic variants or conformational strains in AD pathogenesis is not fully understood. Here, we study the seeding properties of two structurally defined synthetic misfolded Aβ strains (termed 2F and 3F) using in vitro and in vivo assays. We show that 2F and 3F strains differ in their biochemical properties, including resistance to proteolysis, binding to strain-specific dyes, and in vitro seeding. Injection of these strains into a transgenic mouse model produces different pathological features, namely different rates of aggregation, formation of different plaque types, tropism to specific brain regions, differential recruitment of Aβ40 /Aβ42 peptides, and induction of microglial and astroglial responses. Importantly, the aggregates induced by 2F and 3F are structurally different as determined by ssNMR. Our study analyzes the biological properties of purified Aβ polymorphs that have been characterized at the atomic resolution level and provides relevant information on the pathological significance of misfolded Aβ strains.

Great Offset Difference Internuclear Selective Transfer

Carbon-carbon dipolar recoupling sequences are frequently used building blocks in routine magic-angle spinning NMR experiments. While broadband homonuclear first-order dipolar recoupling sequences mainly excite intra-residue correlations, selective methods can detect inter-residue transfers and long-range correlations. Here, we present the great offset difference internuclear selective transfer (GODIST) pulse sequence optimized for selective carbonyl or aliphatic recoupling at fast magic-angle spinning, here, 55 kHz. We observe a 3- to 5-fold increase in intensities compared with broadband RFDR recoupling for perdeuterated microcrystalline SH3 and for the membrane protein influenza A M2 in lipid bilayers. In 3D (H)COCO(N)H and (H)CO(CO)NH spectra, inter-residue carbonyl-carbonyl correlations up to about 5 Å are observed in uniformly 13C-labeled proteins.

Specific Signal Enhancement on an RNA-Protein Interface by Dynamic Nuclear Polarization

Sensitivity and specificity are both crucial for the efficient solid-state NMR structure determination of large biomolecules. We present an approach that features both advantages by site-specific enhancement of NMR spectroscopic signals from the protein-RNA binding site within a ribonucleoprotein (RNP) by dynamic nuclear polarization (DNP). This approach uses modern biochemical techniques for sparse isotope labeling and exploits the molecular dynamics of ¹³ C-labeled methyl groups exclusively present in the protein. These dynamics drive heteronuclear cross relaxation and thus allow specific hyperpolarization transfer across the biomolecular complex's interface. For the example of the L7Ae protein in complex with a 26mer guide RNA minimal construct from the box C/D complex in archaea, we demonstrate that a single methyl-nucleotide contact is responsible for most of the polarization transfer to the RNA, and that this specific transfer can be used to boost both NMR spectral sensitivity and specificity by DNP.

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.

19F fast MAS (60-111 kHz) dipolar and scalar based correlation spectroscopy of organic molecules and pharmaceutical formulations

¹⁹F magic angle spinning (MAS) NMR spectroscopy is a powerful tool for characterization of fluorinated solids. The recent development of ¹⁹F MAS NMR probes, operating at spinning frequencies of 60-111 kHz, enabled analysis of systems spanning from organic molecules to pharmaceutical formulations to biological assemblies, with unprecedented resolution. Herein, we systematically evaluate the benefits of high MAS frequencies (60-111 kHz) for 1D and 2D ¹⁹F-detected experiments in two pharmaceuticals, the antimalarial drug mefloquine and a formulation of the cholesterol-lowering drug atorvastatin calcium. We demonstrate that ¹H decoupling is essential and that scalar-based, heteronuclear single quantum coherence (HSQC) and heteronuclear multiple quantum coherence (HMQC) correlation experiments become feasible and efficient at the MAS frequency of 100 kHz. This study opens doors for the applications of high frequency ¹⁹F MAS NMR to a wide range of problems in chemistry and biology.

Sensitivity-Enhanced Multidimensional Solid-State NMR Spectroscopy by Optimal-Control-Based Transverse Mixing Sequences

Recently, proton-detected magic-angle spinning (MAS) solid-state nuclear magnetic resonance (NMR) spectroscopy has become an attractive tool to study the structure and dynamics of insoluble proteins at atomic resolution. The sensitivity of the employed multidimensional experiments can be systematically improved when both transversal components of the magnetization are transferred simultaneously after an evolution period. The method of preservation of equivalent pathways has been explored in solution-state NMR; however, it does not find widespread application due to relaxation issues connected with increased molecular size. We present here for the first time heteronuclear transverse mixing sequences for correlation experiments at moderate and fast MAS frequencies. Optimal control allows to boost the signal-to-noise ratio (SNR) beyond the expected factor of 2 for each indirect dimension. In addition to the carbon-detected sensitivity-enhanced 2D NCA experiment, we present a novel proton-detected, doubly sensitivity-enhanced 3D hCANH pulse sequence for which we observe a 3-fold improvement in SNR compared to the conventional experimental implementation. The sensitivity gain turned out to be essential to unambiguously characterize a minor fibril polymorph of a human lambda-III immunoglobulin light chain protein that escaped detection so far.

Pulse induced resonance with angular dependent total enhancement of multi-dimensional solid-state NMR correlation spectra

We demonstrate a new resonance condition that obeys the relation Δδ=nν_R/2, where Δδ is the chemical shift difference between two homonuclear-coupled spins, ν_R is the magic-angle spinning speed and n is an integer. This modulation on the rotational resonance recoupling condition is obtained by the application of rotor-synchronous ¹H pulses when at least one proton is dipolar-coupled to one of the homonuclear spins. We suggest a new experimental scheme entitled 'pulse induced resonance with angular dependent total enhancement' (PIRATE) that can enhance proton-driven spin diffusion by the application of a single ¹H pulse every rotor period. Experimental evidence is demonstrated on the two carbon spins of glycine and on the Y21M mutant of fd bacteriophage virus. Numerical simulations reveal the existence of the resonances and report on the important interactions governing these phenomena.

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.

Modest Offset Difference Internuclear Selective Transfer via Homonuclear Dipolar Coupling

Homonuclear dipolar recoupling is routinely used for magic-angle spinning NMR-based structure determination. In fully protonated samples, only short proton-proton distances are accessible to broadband recoupling approaches because of high proton density. Selective methods allow detection of longer distances by directing polarization to a subset of spins. Here we introduce the selective pulse sequence MODIST, which recouples spins that have a modest chemical shift offset difference, and demonstrate it to selectively record correlations between amide protons. The sequence was selected for good retention of total signal, leading to up to twice the intensity for proton-proton correlations compared with other selective methods. The sequence is effective across a range of spinning conditions and magnetic fields, here tested at 55.555 and 100 kHz magic-angle spinning and at proton Larmor frequencies from 600 to 1200 MHz. For influenza A M2 in lipid bilayers, cross-peaks characteristic of a helical conformation are observed.

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.

Rapid Structural Analysis of Minute Quantities of Organic Solids by Exhausting 1H Polarization in Solid-State NMR Spectroscopy Under Fast Magic Angle Spinning

Solid-state nuclear magnetic resonance (NMR) often suffers from significant limitations due to the inherent low signal sensitivity when low-γ nuclei are involved. Herein, we report an elegant solid-state NMR approach for rapid structural analysis of minute amounts of organic solids. By encoding staggered chemical shift evolution in the indirect dimension and staggered acquisition in the ¹H dimension, a proton-detected homonuclear ¹H/¹H and heteronuclear ¹³C/¹H chemical shift correlation (HETCOR) spectrum can be obtained simultaneously in a single experiment at a fast magic-angle-spinning (MAS) condition with barely increasing the experimental time. We further show that during the conventional ¹H-detected HETCOR experimental time, multiple homonuclear ¹H/¹H correlation spectra can be recorded in addition to the HETCOR spectrum, enabling the determination of ¹H-¹H distances. We establish that abundant ¹H polarization can be efficiently manipulated and fully utilized in proton-detected solid-state NMR spectroscopy for extraction of more critical structural information and thus reduction of the total experimental time.

Theory of frequency-selective homonuclear dipolar recoupling in solid-state NMR

In solid-state nuclear magnetic resonance, frequency-selective homonuclear dipolar recoupling is key to quantitative distance measurement or selective enhancement of correlations between atoms of interest in multiple-spin systems, which are not amenable to band-selective or broadband recoupling. Previous frequency-selective recoupling is mostly based on the so-called rotational resonance (R²) condition that restricts the application to spin pairs with resonance frequencies differing in integral multiples of the magic-angle spinning (MAS) frequency. Recently, we have proposed a series of frequency-selective homonuclear recoupling sequences called SPR (short for Selective Phase-optimized Recoupling), which have been successfully applied for selective ¹H-¹H or ¹³C-¹³C recoupling under from moderate (∼10 kHz) to ultra-fast (150 kHz) MAS frequencies. In this study, we fully analyze the average Hamiltonian theory of SPR sequences and reveal the origin of frequency selectivity in recoupling. The theoretical description, as well as numerical simulations and experiments, demonstrates that the frequency selectivity can be easily controlled by the flip angle (p) in the (p)_ϕk(p)_ϕk+π unit in the pSPR-N_n sequences. Small flip angles lead to frequency-selective recoupling, while large flip angles may lead to broadband recoupling in principle. The result shall shed new light on the design of homonuclear recoupling sequences with arbitrary frequency bandwidths.

From Angstroms to Nanometers: Measuring Interatomic Distances by Solid-State NMR

Internuclear distances represent one of the main structural constraints in molecular structure determination using solid-state NMR spectroscopy, complementing chemical shifts and orientational restraints. Although a large number of magic-angle-spinning (MAS) NMR techniques have been available for distance measurements, traditional ¹³C and ¹⁵N NMR experiments are inherently limited to distances of a few angstroms due to the low gyromagnetic ratios of these nuclei. Recent development of fast MAS triple-resonance ¹⁹F and ¹H NMR probes has stimulated the design of MAS NMR experiments that measure distances in the 1-2 nm range with high sensitivity. This review describes the principles and applications of these multiplexed multidimensional correlation distance NMR experiments, with an emphasis on ¹⁹F- and ¹H-based distance experiments. Representative applications of these long-distance NMR methods to biological macromolecules as well as small molecules are reviewed.

Heteronuclear and homonuclear radio-frequency-driven recoupling

The radio-frequency-driven recoupling (RFDR) pulse sequence is used in magic-angle spinning (MAS) NMR to recouple homonuclear dipolar interactions. Here we show simultaneous recoupling of both the heteronuclear and homonuclear dipolar interactions by applying RFDR pulses on two channels. We demonstrate the method, called HETeronuclear RFDR (HET-RFDR), on microcrystalline SH3 samples at 10 and 55.555 kHz MAS. Numerical simulations of both HET-RFDR and standard RFDR sequences allow for better understanding of the influence of offsets and paths of magnetization transfers for both HET-RFDR and RFDR experiments, as well as the crucial role of XY phase cycling.

Recent progress in dipolar recoupling techniques under fast MAS in solid-state NMR spectroscopy

With the recent advances in NMR hardware and probe design technology, magic-angle spinning (MAS) rates over 100 ​kHz are accessible now, even on commercial solid NMR probes. Under such fast MAS conditions, excellent spectral resolution has been achieved by efficient suppression of anisotropic interactions, which also opens an avenue to the proton-detected NMR experiments in solids. Numerous methods have been developed to take full advantage of fast MAS during the last decades. Among them, dipolar recoupling techniques under fast MAS play vital roles in the determination of the molecular structure and dynamics, and are also key elements in multi-dimensional correlation NMR experiments. Herein, we review the dipolar recoupling techniques, especially those developed in the past two decades for fast-to-ultrafast MAS conditions. A major focus for our discussion is the ratio of RF field strength (in frequency) to MAS frequency, ν₁/ν_r, in different pulse sequences, which determines whether these dipolar recoupling techniques are suitable for NMR experiments under fast MAS conditions. Systematic comparisons are made among both heteronuclear and homonuclear dipolar recoupling schemes. In addition, the schemes developed specially for proton-detection NMR experiments under ultrafast MAS conditions are highlighted as well.

Structural Arrangement within a Peptide Fibril Derived from the Glaucoma-Associated Myocilin Olfactomedin Domain

Myocilin-associated glaucoma is a new addition to the list of diseases linked to protein misfolding and amyloid formation. Single point variants of the ∼257-residue myocilin olfactomedin domain (mOLF) lead to mutant myocilin aggregation. Here, we analyze the 12-residue peptide P1 (GAVVYSGSLYFQ), corresponding to residues 326-337 of mOLF, previously shown to form amyloid fibrils in vitro and in silico. We applied solid-state NMR structural measurements to test the hypothesis that P1 fibrils adopt one of three predicted structures. Our data are consistent with a U-shaped fibril arrangement for P1, one that is related to the U-shape predicted previously in silico. Our data are also consistent with an antiparallel fibril arrangement, likely driven by terminal electrostatics. Our proposed structural model is reminiscent of fibrils formed by the Aβ(1-40) Iowa mutant peptide, but with a different arrangement of molecular turn regions. Taken together, our results strengthen the connection between mOLF fibrils and the broader amylome and contribute to our understanding of the fundamental molecular interactions governing fibril architecture and stability.

Solid-state NMR spectroscopy

Solid-state nuclear magnetic resonance (NMR) spectroscopy is an atomic-level method used to determine the chemical structure, three-dimensional structure, and dynamics of solids and semi-solids. This Primer summarizes the basic principles of NMR as applied to the wide range of solid systems. The fundamental nuclear spin interactions and the effects of magnetic fields and radiofrequency pulses on nuclear spins are the same as in liquid-state NMR. However, because of the anisotropy of the interactions in the solid state, the majority of high-resolution solid-state NMR spectra is measured under magic-angle spinning (MAS), which has profound effects on the types of radiofrequency pulse sequences required to extract structural and dynamical information. We describe the most common MAS NMR experiments and data analysis approaches for investigating biological macromolecules, organic materials, and inorganic solids. Continuing development of sensitivity-enhancement approaches, including 1H-detected fast MAS experiments, dynamic nuclear polarization, and experiments tailored to ultrahigh magnetic fields, is described. We highlight recent applications of solid-state NMR to biological and materials chemistry. The Primer ends with a discussion of current limitations of NMR to study solids, and points to future avenues of development to further enhance the capabilities of this sophisticated spectroscopy for new applications.

Atomic-level differences between brain parenchymal- and cerebrovascular-seeded Aβ fibrils

Alzheimer's disease is characterized by neuritic plaques, the main protein components of which are β-amyloid (Aβ) peptides deposited as β-sheet-rich amyloid fibrils. Cerebral Amyloid Angiopathy (CAA) consists of cerebrovascular deposits of Aβ peptides; it usually accompanies Alzheimer's disease, though it sometimes occurs in the absence of neuritic plaques, as AD also occurs without accompanying CAA. Although neuritic plaques and vascular deposits have similar protein compositions, one of the characteristic features of amyloids is polymorphism, i.e., the ability of a single pure peptide to adopt multiple conformations in fibrils, depending on fibrillization conditions. For this reason, we asked whether the Aβ fibrils in neuritic plaques differed structurally from those in cerebral blood vessels. To address this question, we used seeding techniques, starting with amyloid-enriched material from either brain parenchyma or cerebral blood vessels (using meninges as the source). These amyloid-enriched preparations were then added to fresh, disaggregated solutions of Aβ to make replicate fibrils, as described elsewhere. Such fibrils were then studied by solid-state NMR, fiber X-ray diffraction, and other biophysical techniques. We observed chemical shift differences between parenchymal vs. vascular-seeded replicate fibrils in select sites (in particular, Ala2, Phe4, Val12, and Gln15 side chains) in two-dimensional 13C-13C correlation solid-state NMR spectra, strongly indicating structural differences at these sites. X-ray diffraction studies also indicated that vascular-seeded fibrils displayed greater order than parenchyma-seeded fibrils in the "side-chain dimension" (~ 10 Å reflection), though the "hydrogen-bond dimensions" (~ 5 Å reflection) were alike. These results indicate that the different nucleation conditions at two sites in the brain, parenchyma and blood vessels, affect the fibril products that get formed at each site, possibly leading to distinct pathophysiological outcomes.

Local atomic and electronic structure in the LiVPO4 (F,O) tavorite-type materials from solid-state NMR combined with DFT calculations

⁷ Li, ³¹ P, and ¹⁹ F solid-state nuclear magnetic resonance (NMR) spectroscopy was used to investigate the local arrangement of oxygen and fluorine in LiVPO₄ F_1-y O_y materials, interesting as positive electrode materials for Li-ion batteries. From the evolution of the 1D spectra versus y, 2D ⁷ Li radiofrequency-driven recoupling (RFDR) experiments combined, and a tentative signal assignment based on density functional theory (DFT) calculations, it appears that F and O are not randomly dispersed on the bridging X position between two X-VO₄ -X octahedra (X = O or F) but tend to segregate at a local scale. Using DFT calculations, we analyzed the impact of the different local environments on the local electronic structure. Depending on the nature of the VO₄ X₂ environments, vanadium ions are either in the +III or in the +IV oxidation state and can exhibit different distributions of their unpaired electron(s) on the d orbitals. Based on those different local electronic structures and on the computed Fermi contact shifts, we discuss the impact on the spin transfer mechanism on adjacent nuclei and propose tentative signal assignments. The O/F clustering tendency is discussed in relation with the formation of short V^IV O vanadyl bonds with a very specific electronic structure and possible cooperative effect along the chain.

Selectively Enhanced 1H-1H Correlations in Proton-Detected Solid-State NMR under Ultrafast MAS Conditions

Proton-detected solid-state NMR has emerged as a powerful analytical technique in structural elucidation via ¹H-¹H correlations, which are mostly established by broadband methods. We propose a new class of frequency-selective homonuclear recoupling methods to selectively enhance ¹H-¹H correlations of interest under ultrafast magic-angle spinning (MAS). These methods, dubbed as selective phase-optimized recoupling (SPR), can provide a sensitivity enhancement by a factor of ∼3 over the widely used radio-frequency-driven recoupling (RFDR) to observe ¹H_N-¹H_N contacts in a protonated tripeptide N-formyl-Met-Leu-Phe (fMLF) under 150 kHz MAS and are successfully utilized to probe a long-range ¹H-¹H contact in a pharmaceutical molecule, the hydrochloride form of pioglitazone (PIO-HCl). SPR is not only highly efficient in frequency-selective recoupling but also easy to implement, imparting to it great potential to probe ¹H-¹H contacts for the structural elucidation of organic solids such as proteins and pharmaceuticals under ultrafast MAS conditions.

Can proton-proton recoupling in fully protonated solids provide quantitative, selective and efficient polarization transfer?

Dipolar recoupling sequences have been used to probe spatial proximity of nuclear spins and were traditionally designed to probe rare spins such as ¹³C and/or ¹⁵N nuclei. The multi-spin dipolar-coupling network of the rare spins is weak due to smaller couplings and large chemical shift dispersion. Therefore, the recoupling approaches were tailored to design offset compensated or broadband sequences. In contrast, protons have a substantially stronger dipolar-coupling network and much narrower chemical shift range. Broadband recoupling sequences such as radio-frequency driven recoupling (RFDR), back-to-back (BABA), and lab frame proton-proton spin diffusion have been routinely used to characterize the structures of protein/macromolecules and small molecules. Recently selective ¹H-¹H recoupling sequences have been proposed that combine chemical shift offset of the resolved proton spectrum (at fast MAS) with first- and second-order dipolar recoupling Hamiltonians to obtain quantitative and qualitative proton distances, respectively. Herein, we evaluate the performances of broadband and selective proton recoupling sequences such as finite pulse RFDR (fp-RFDR), band-selective spectral spin diffusion (BASS-SD), second-order cross-polarization (SOCP), and selective recoupling of proton (SERP) in terms of the selectivity and efficiency of ¹H-¹H polarization transfers in a dense network of proton spins and explore the possibility of measuring ¹H-¹H distances. We use theoretical considerations, numerical simulations, and experiments to support the distinct advantages and disadvantages of each recoupling sequence. Experiments were performed on L-histidine.HCl.H₂O at a MAS frequency of 71.43 kHz. This study rationalizes the proper selection of ¹H-¹H recoupling sequences when working with fully protonated solids.

Assessment of new symmetry-based dipolar recoupling schemes for homonuclear magnetization exchange between quadrupolar nuclei in two-dimensional correlation MAS NMR

We provide an extensive experimental and numerical evaluation of MQ-phase (S)M supercycles with M={3,4} of three groups of symmetry-based homonuclear dipolar recoupling rf-pulse sequences, [Formula: see text] , for establishing proximities among half-integer spin quadrupolar nuclei under moderately fast magic-angle-spinning (MAS) conditions in single-quantum-single-quantum (1Q-1Q) correlation NMR experiments. The relative merits of the (S)M schemes for variations in resonance offsets and rf-amplitude errors were assessed by numerically simulated magnetization transfers in spin-3/2 pairs with variable isotropic chemical shifts and quadrupolar coupling constants. Experimental demonstrations of ²³Na (spin-3/2) NMR on Na₂MoO₄·2H₂O and ²⁷Al (spin-5/2) NMR on AlPO-CJ19 [(NH₄)₂Al₄(PO₄)₄HPO₄·H₂O] are presented at 14.1 T and 24 kHz MAS. We recommend using the (SR2₂¹)3 or (SR2₂¹)4 supercycles for samples that exhibit small chemical-shift dispersions (<3 kHz), and any (SRN_N^N/2)3 scheme with N⩾10 for larger spreads of isotropic chemical shifts. However, because the (SRN_N^N/2)3 sequences recouple heteronuclear dipolar interactions, their application to proton-bearing samples requires high-power proton decoupling during the mixing period. Alternatively, the (SR2₄¹)3 and (SR2₄¹)4 schemes may be employed in the absence of proton decoupling, but with poorer compensation to resonance-offsets and rf-amplitude errors.

Out-of-Register Parallel β-Sheets and Antiparallel β-Sheets Coexist in 150-kDa Oligomers Formed by Amyloid-β(1-42)

We present solid-state NMR measurements of β-strand secondary structure and inter-strand organization within a 150-kDa oligomeric aggregate of the 42-residue variant of the Alzheimer's amyloid-β peptide (Aβ(1-42)). We build upon our previous report of a β-strand spanned by residues 30-42, which arranges into an antiparallel β-sheet. New results presented here indicate that there is a second β-strand formed by residues 11-24. Contrary to expectations, NMR data indicate that this second β-strand is organized into a parallel β-sheet despite the co-existence of an antiparallel β-sheet in the same structure. In addition, the in-register parallel β-sheet commonly observed for amyloid fibril structure does not apply to residues 11-24 in the 150-kDa oligomer. Rather, we present evidence for an inter-strand registry shift of three residues that likely alternate in direction between adjacent molecules along the β-sheet. We corroborated this unexpected scheme for β-strand organization using multiple two-dimensional NMR and ¹³C-¹³C dipolar recoupling experiments. Our findings indicate a previously unknown assembly pathway and inspire a suggestion as to why this aggregate does not grow to larger sizes.

High-resolution proton-detected MAS experiments on self-assembled diphenylalanine nanotubes enabled by fast MAS and high magnetic field

The advent of ultrahigh magnetic field and fast magic-angle-spinning (MAS) probe technology has led to dramatically enhanced spectral resolution and sensitivity in solid-state NMR spectroscopy. In particular, proton-based multidimensional solid-state NMR techniques have become feasible to investigate the structure and dynamics at atomic resolution, due to the increased chemical shift span and spectral resolution. Herein, the benefits of faster MAS and higher magnetic field are demonstrated on a self-assembled diphenylalanine (Phe-Phe) nanomaterial. Proton-detected 2D ¹H/¹H single-quantum/single-quantum (SQ/SQ) correlation, double-quantum/single-quantum (DQ/SQ) correlation, and ¹H chemical shift anisotropy/chemical shift (CSA/CS) correlation spectra obtained at two different spinning speeds (60 and 100 kHz) and two different magnetic fields (600 and 900 MHz) are reported. The dramatic enhancement of proton spectral resolution achieved with the use of a 900 MHz magnetic field and 100 kHz MAS is remarkable and enabled the measurement of proton CSA tensors, which will be useful to better understand the self-assembled structures of Phe-Phe nanotubes. We also show through numerical simulations that the unaveraged proton-proton dipolar couplings can result in broadening of CSA lines, leading to inaccurate determination of CSA tensors of protons. Thus, our results clearly show the insufficiency of a 600 MHz magnetic field to resolve ¹H spectra lines and the inability of a moderate spinning speed of 60 kHz to completely suppress ¹H-¹H dipolar couplings, which further justify the pursuit of ultrahigh magnetic field beyond 1 GHz and ultrafast MAS beyond 100 kHz.

Molecular complementarity and structural heterogeneity within co-assembled peptide β-sheet nanofibers

Self-assembling peptides have garnered an increasing amount of interest as a functional biomaterial for medical and biotechnological applications. Recently, β-sheet peptide designs utilizing complementary pairs of peptides composed of charged amino acids positioned to impart co-assembly behavior have expanded the portfolio of peptide aggregate structures. Structural characterization of these charge-complementary peptide co-assemblies has been limited. Thus, it is not known how the complementary peptides organize on the molecular level. Through a combination of solid-state NMR measurements and discontinuous molecular dynamics simulations, we investigate the molecular organization of King-Webb peptide nanofibers. KW+ and KW- peptides co-assemble into near stoichiometric two-component β-sheet structures as observed by computational simulations and ¹³C-¹³C dipolar couplings. A majority of β-strands are aligned with antiparallel nearest neighbors within the β-sheet as previously suggested by Fourier transform infrared spectroscopy measurements. Surprisingly, however, a significant proportion of β-strand neighbors are parallel. While charge-complementary peptides were previously assumed to organize in an ideal (AB)_n pattern, dipolar recoupling measurements on isotopically diluted nanofiber samples reveal a non-negligible amount of self-associated (AA and BB) pairs. Furthermore, computational simulations predict these different structures can coexist within the same nanofiber. Our results highlight structural disorder at the molecular level in a charge-complementary peptide system with implications on co-assembling peptide designs.

Improved Magnetization Transfers among Quadrupolar Nuclei in Two-Dimensional Homonuclear Correlation NMR Experiments Applied to Inorganic Network Structures

We demonstrate that supercycles of previously introduced two-fold symmetry dipolar recoupling schemes may be utilized successfully in homonuclear correlation nuclear magnetic resonance (NMR) spectroscopy for probing proximities among half-integer spin quadrupolar nuclei in network materials undergoing magic-angle-spinning (MAS). These (SR221)M, (SR241)M, and (SR281)M recoupling sequences with M=3 and M=4 offer comparably efficient magnetization transfers in single-quantum–single-quantum (1Q–1Q) correlation NMR experiments under moderately fast MAS conditions, as demonstrated at 14.1 T and 24 kHz MAS in the contexts of 11B NMR on a Na2O–CaO–B2O3–SiO2 glass and 27Al NMR on the open framework aluminophosphate AlPO-CJ19 [(NH4)2Al4(PO4)4HPO4·H2O]. Numerically simulated magnetization transfers in spin–3/2 pairs revealed a progressively enhanced tolerance to resonance offsets and rf-amplitude errors of the recoupling pulses along the series (SR221)M< (SR241)M< (SR281)M for increasing differences in chemical shifts between the two nuclei. Nonetheless, for scenarios of a relatively minor chemical-shift dispersions (≲3 kHz), the (SR221)M supercycles perform best both experimentally and in simulations.

Side Chain Hydrogen-Bonding Interactions within Amyloid-like Fibrils Formed by the Low-Complexity Domain of FUS: Evidence from Solid State Nuclear Magnetic Resonance Spectroscopy

In aqueous solutions, the 214-residue low-complexity domain of the FUS protein (FUS-LC) is known to undergo liquid-liquid phase separation and also to self-assemble into amyloid-like fibrils. In previous work based on solid state nuclear magnetic resonance (ssNMR) methods, a structural model for the FUS-LC fibril core was developed, showing that residues 39-95 form the fibril core. Unlike fibrils formed by amyloid-β peptides, α-synuclein, and other amyloid-forming proteins, the FUS-LC core is largely devoid of purely hydrophobic amino acid side chains. Instead, the core-forming segment contains numerous hydroxyl-bearing residues, including 18 serines, six threonines, and eight tyrosines, suggesting that the FUS-LC fibril structure may be stabilized in part by inter-residue hydrogen bonds among side chain hydroxyl groups. Here we describe ssNMR measurements, performed on ²H,¹⁵N,¹³C-labeled FUS-LC fibrils, that provide new information about the interactions of hydroxyl-bearing residues with one another and with water. The ssNMR data support the involvement of specific serine, threonine, and tyrosine residues in hydrogen-bonding interactions. The data also reveal differences in hydrogen exchange rates with water for different side chain hydroxyl groups, providing information about solvent exposure and penetration of water into the FUS-LC fibril core.

Measurement of Accurate Interfluorine Distances in Crystalline Organic Solids: A High-Frequency Magic Angle Spinning NMR Approach

Long-range interatomic distance restraints are critical for the determination of molecular structures by NMR spectroscopy, both in solution and in the solid state. Fluorine is a powerful NMR probe in a wide variety of contexts, owing to its favorable magnetic properties, ease of incorporation into biological molecules, and ubiquitous use in synthetic organic molecules designed for diverse applications. Because of the large gyromagnetic ratio of the 100% naturally abundant ¹⁹F isotope, interfluorine distances as long as 20 Å are accessible in magic-angle spinning (MAS) dipolar recoupling experiments. Herein, we present an approach for the determination of accurate interfluorine distances in multispin systems, using the finite pulse radio frequency driven recoupling (fpRFDR) at high MAS frequencies of 40-60 kHz. We use a series of crystalline "molecular ruler" solids, difluorobenzoic acids and 7F-L-tryptophan, for which the intra- and intermolecular interfluorine distances are known. We describe the optimal experimental conditions for accurate distance determinations, including the choice of a phase cycle, the relative advantages of selective inversion one-dimensional versus two-dimensional correlation experiments, and the appropriate numerical simulation protocols. An optimal strategy for the analysis of RFDR exchange curves in organic solids with extended spin interaction networks is presented, which, even in the absence of crystal structures, can be potentially incorporated into NMR structure determination.

Exploiting heterogeneous time scale of dynamics to enhance 2D HETCOR solid-state NMR sensitivity

Multidimensional solid-state NMR spectroscopy plays a significant role in offering atomic-level insights into molecular systems. In particular, heteronuclear chemical shift correlation (HETCOR) experiments could provide local chemical and structural information in terms of spatial heteronuclear proximity and through-bond connectivity. In solid state, the transfer of magnetization between heteronuclei, a key step in HETCOR experiments, is usually achieved using cross-polarization (CP) or insensitive nuclei enhanced by polarization transfer (INEPT) depending on the sample characteristics and magic-angle-spinning (MAS) frequency. But, for a multiphase system constituting molecular components that differ in their time scales of mobilities, CP efficiency is pretty low for mobile components because of the averaging of heteronuclear dipolar couplings whereas INEPT is inefficient for immobile components due to the short T2 and can yield through-space connectivity due to strong proton spin diffusion for immobile components especially under moderate spinning speeds. Herein, in this study we present two 2D pulse sequences that enable the sequential acquisition of 13C/1H HETCOR NMR spectra for the rigid and mobile components by taking full advantage of the abundant proton magnetization in a single experiment with barely increasing the overall experimental time. In particular, the 13C-detected HETCOR experiment could be applied under slow MAS conditions, where a multiple-pulse sequence is typically employed to enhance 1H spectral resolution in the indirect dimension. In contrast, the 1H-detected HETCOR experiment should be applied under ultrafast MAS, where CP and heteronuclear nuclear Overhauser effect (NOE) polarization transfer are combined to enhance 13C signal intensities for mobile components. These pulse sequences are experimentally demonstrated on two model systems to obtain 2D 13C/1H chemical shift correlation spectra of rigid and mobile components independently and separately. These pulse sequences can be used for dynamics based spectral editing and resonance assignments. Therefore, we believe the proposed 2D HETCOR NMR pulse sequences will be beneficial for the structural studies of heterogeneous systems containing molecular components that differ in their time scale of motions for understanding the interplay of structures and properties.

Structural characterization of bacteriophage viruses by NMR

Magic-angle spinning (MAS) solid-state NMR has provided structural insights into various bacteriophage systems including filamentous, spherical, and tailed bacteriophage viruses. A variety of methodologies have been utilized including elementary two and three-dimensional assignment experiments, proton-detection techniques at fast spinning speeds, non-uniform sampling, structure determination protocols, conformational dynamics revealed by recoupling of anisotropic interactions, and enhancement by dynamic nuclear polarization. This review summarizes most of the studies performed during the last decade by MAS techniques and makes comparisons with prior knowledge obtained from static and solution NMR techniques. Chemical shifts for the capsids of the various systems are reported and analyzed, and DNA shifts are reported and discussed in the context of general high molecular-weight DNA molecules. Chemical shift and torsion angle prediction techniques are compared and applied to the various phage systems. The structures of the intact M13 filamentous bacteriophage and that of the Acinetobacter phage AP205 capsid, determined using MAS-based experimental data, are presented. Finally, filamentous phages, which are highly rigid systems, show interesting dynamics at the interface of the capsid and DNA, and their mutual electrostatic interactions are shown to be mediated by highly mobile positively charged residues. Novel results obtained from recoupling the chemical shift anisotropy of a single arginine in IKe phage, which is in contact with its DNA, further demonstrate this point. MAS NMR thus provides many new insights into phage structure, and on the other hand the richness, complexity and variety of bacteriophage systems provide opportunities for new NMR methodologies and technique developments.

Homonuclear dipolar recoupling of arbitrary pairs in multi-spin systems under magic angle spinning: A double-frequency-selective ZQ-SEASHORE experiment

We describe a useful method for measuring the internuclear distances within arbitrarily selected pairs of like nuclei in dipolar-coupled multi-spin systems. The method uses a combination of the zero-quantum shift-evolution-assisted selective homonuclear recoupling (ZQ-SEASHORE) technique developed by Hu and Tycko [J. Chem. Phys. 2009, 131, 045101] and double-frequency-selective radio-frequency pulse. The double-frequency-selective pulse inverts polarizations of two spins simultaneously, and thus applications of the method presented here are only limited by the spectral resolution, and not by the number of interacting spins. Our experiments demonstrate the validity of the method and present analytical expressions for the dephasing curve.

Accuracy and precision of protein structures determined by magic angle spinning NMR spectroscopy: for some 'with a little help from a friend'

We present a systematic investigation into the attainable accuracy and precision of protein structures determined by heteronuclear magic angle spinning solid-state NMR for a set of four proteins of varied size and secondary structure content. Structures were calculated using synthetically generated random sets of C-C distances up to 7 Å at different degrees of completeness. For single-domain proteins, 9-15 restraints per residue are sufficient to derive an accurate model structure, while maximum accuracy and precision are reached with over 15 restraints per residue. For multi-domain proteins and protein assemblies, additional information on domain orientations, quaternary structure and/or protein shape is needed. As demonstrated for the HIV-1 capsid protein assembly, this can be accomplished by integrating MAS NMR with cryoEM data. In all cases, inclusion of TALOS-derived backbone torsion angles improves the accuracy for small number of restraints, while no further increases are noted for restraint completeness above 40%. In contrast, inclusion of TALOS-derived torsion angle restraints consistently increases the precision of the structural ensemble at all degrees of distance restraint completeness.

Exact distance measurements for structure and dynamics in solid proteins by fast-magic-angle-spinning NMR

Fast-magic-angle-spinning solid-state NMR is a developing technique for determination of protein structure and dynamics. Proton-proton correlations usually lead to rough distance restraints, a serious hurdle towards high-resolution structures. Analogous to the "eNOE" concept in solution, an integrative approach for more accurate restraints enables improved structural accuracy with minimal analytical effort.

Optimization of band-selective homonuclear dipolar recoupling in solid-state NMR by a numerical phase search

Spin polarization transfers among aliphatic ¹³C nuclei, especially ¹³Cα-¹³Cβ transfers, permit correlations of their nuclear magnetic resonance (NMR) frequencies that are essential for signal assignments in multidimensional solid-state NMR of proteins. We derive and demonstrate a new radio-frequency (RF) excitation sequence for homonuclear dipolar recoupling that enhances spin polarization transfers among aliphatic ¹³C nuclei at moderate magic-angle spinning (MAS) frequencies. The phase-optimized recoupling sequence with five π pulses per MAS rotation period (denoted as PR5) is derived initially from systematic numerical simulations in which only the RF phases are varied. Subsequent theoretical analysis by average Hamiltonian theory explains the favorable properties of numerically optimized phase schemes. The high efficiency of spin polarization transfers in simulations is preserved in experiments, in part because the RF field amplitude in PR5 is only 2.5 times the MAS frequency so that relatively low ¹H decoupling powers are required. Experiments on a microcrystalline sample of the β1 immunoglobulin binding domain of protein G demonstrate an average enhancement factor of 1.6 for ¹³Cα → ¹³Cβ polarization transfers, compared to the standard ¹³C-¹³C spin-diffusion method, implying a two-fold time saving in relevant 2D and 3D experiments.

A one-dimensional solid-state NMR approach for 14NH/14NH overtone correlation through 1H/1H mixing under fast MAS

Homonuclear correlations are key to structural studies using solid-state NMR. In this contribution, using 14N overtone transition (OT) as a selective excitation approach, we propose a proton-detected one-dimensional (1D) 14NOT/14NOT/1H correlation solid-state NMR method mediated through 1H/1H mixing at fast magic angle spinning to achieve NH/NH proximities in naturally abundant samples. The proposed method is time efficient by a factor of ∼7.5 in comparison to the existing fundamental 14N frequency-based three-dimensional (3D) 14N/14N/1H correlation method.

Forcing the 'lazy' protons to work

The combination of cross-polarization (CP) with flip-back (FB) pulse has enabled in NMR the enhancement of 13C sensitivity and the decrease of the recycling delay at both moderate and fast magic-angle spinning (MAS) frequencies. However, only continuous-wave (CW) decoupling is presently compatible with FB-pulse (FB-CW), and depending on the CW radio-frequency (rf) field, either an insignificant sensitivity gain or an acquisition time-dependent gain and a low 13C resolution are obtained. In this study, we propose a new FB-pulse method in which radio frequency-driven recoupling (RFDR) is used as the 1H-13C decoupling scheme to overcome these drawbacks. The performances of FB-RFDR in terms of decoupling efficiency and sensitivity gain are tested on both natural abundance (NA) and uniformly 13C-15N labeled l-histidine·HCl·H2O (Hist) samples at a MAS frequency of νR = 70 kHz. The results show the superiority of RFDR over the CW decoupling with respect to these criteria. Importantly, they reveal that the sensitivity gain offered by FB-RFDR is nearly independent of the decoupling/acquisition duration. The application of FB-RFDR on NA-Hist and sucrose yields a sensitivity gain between 60 and 100% compared to conventional FB-CW and CPMAS-SPINAL experiments. Moreover, we compare the 13C sensitivities of NA-Hist obtained by our 1D FB-RFDR method and 2D 1H-{13C} double-CP acquisition. Both methods provide similar 13C sensitivity and are complementary. Indeed, the 2D method has the advantage of also providing the 1H-13C spatial proximities, but its sensitivity for quaternary carbons is limited; whereas our 1D FB-RFDR method is more independent of the type of carbon, and can provide a 13C 1D spectrum in a shorter experimental time. We also test the feasibility of FB-RFDR at a moderate frequency of νR = 20 kHz, but the experimental results demonstrate a poor resolution as well as a negligible sensitivity gain.

Determination of Long-Range Distances by Fast Magic-Angle-Spinning Radiofrequency-Driven 19F-19F Dipolar Recoupling NMR

Nanometer-range distances are important for restraining the three-dimensional structure and oligomeric assembly of proteins and other biological molecules. Solid-state NMR determination of protein structures typically utilizes ¹³C-¹³C and ¹³C-¹⁵N distance restraints, which can only be measured up to ∼7 Å because of the low gyromagnetic ratios of these nuclear spins. To extend the distance reach of NMR, one can harvest the power of ¹⁹F, whose large gyromagnetic ratio in principle allows distances up to 2 nm to be measured. However, ¹⁹F possesses large chemical shift anisotropies (CSAs) as well as large isotropic chemical shift dispersions, which pose challenges to dipolar coupling measurements. Here, we demonstrate ¹⁹F-¹⁹F distance measurements at high magnetic fields under fast magic-angle spinning (MAS) using radiofrequency-driven dipolar recoupling (RFDR). We show that ¹⁹F-¹⁹F cross-peaks for distances up to 1 nm can be readily observed in two-dimensional ¹⁹F-¹⁹F correlation spectra using less than 5 ms of RFDR mixing. This efficient ¹⁹F-¹⁹F dipolar recoupling is achieved using practically accessible MAS frequencies of 15-55 kHz, moderate ¹⁹F radio frequency field strengths, and no ¹H decoupling. Experiments and simulations show that the fastest polarization transfer for aromatic fluorines with the highest distance accuracy is achieved using either fast MAS (e.g., 60 kHz) with large pulse duty cycles (>50%) or slow MAS with strong ¹⁹F pulses. Fast MAS considerably reduces relaxation losses during the RFDR π-pulse train, making finite-pulse RFDR under fast-MAS the method of choice. Under intermediate MAS frequencies (25-40 kHz) and intermediate pulse duty cycles (15-30%), the ¹⁹F CSA tensor orientation has a quantifiable effect on the polarization transfer rate; thus, the RFDR buildup curves encode both distance and orientation information. At fast MAS, the impact of CSA orientation is minimized, allowing pure distance restraints to be extracted. We further investigate how relayed transfer and dipolar truncation in multifluorine environments affect polarization transfer. This fast-MAS ¹⁹F RFDR approach is complementary to ¹⁹F spin diffusion for distance measurements and will be the method of choice under high-field fast-MAS conditions that are increasingly important for protein structure determination by solid-state NMR.

Efficient 15N-13C Polarization Transfer by Third-Spin-Assisted Pulsed Cross-Polarization Magic-Angle-Spinning NMR for Protein Structure Determination

We introduce a pulsed third-spin-assisted recoupling experiment that produces high-intensity long-range ¹⁵N-¹³C cross peaks using low radiofrequency (rf) energy. This Proton-Enhanced Rotor-echo Short-Pulse IRradiATION Cross-Polarization (^PERSPIRATIONCP) pulse sequence operates with the same principle as the Proton-Assisted Insensitive-Nuclei Cross-Polarization (^PAINCP) experiment but uses only a fraction of the rf energy by replacing continuous-wave ¹³C and ¹⁵N irradiation with rotor-echo 90° pulses. Using formyl-Met-Leu-Phe (f-MLF) and β1 immunoglobulin binding domain of protein G (GB1) as model proteins, we demonstrate experimentally how ^PERSPIRATIONCP polarization transfer depends on the CP contact time, rf power, pulse flip angle, and ¹³C carrier frequency and compare the ^PERSPIRATIONCP performance with the performances of ^PAINCP, ^RESPIRATIONCP, and ^SPECIFICCP for measuring ¹⁵N-¹³C cross peaks. ^PERSPIRATIONCP achieves long-range ¹⁵N-¹³C transfer and yields higher cross peak-intensities than that of the other techniques. Numerical simulations reproduce the experimental trends and moreover indicate that ^PERSPIRATIONCP relies on ¹⁵N-¹H and ¹³C-¹H dipolar couplings rather than ¹⁵N-¹³C dipolar coupling for polarization transfer. Therefore, ^PERSPIRATIONCP is an rf-efficient and higher-sensitivity alternative to ^PAINCP for measuring long-range ¹⁵N-¹³C correlations, which are essential for protein resonance assignment and structure determination. Using cross peaks from two ^PERSPIRATIONCP ¹⁵N-¹³C correlation spectra as the sole distance restraints, supplemented with (φ, ψ) torsion angles obtained from chemical shifts, we calculated the GB1 structure and obtained a backbone root-mean-square deviation of 2.0 Å from the high-resolution structure of the protein. Therefore, this rf-efficient ^PERSPIRATIONCP method is useful for obtaining many long-range distance restraints for protein structure determination.

Transient effects in π-pulse sequences in MAS solid-state NMR

Dipolar recoupling techniques that use isolated rotor-synchronized π pulses are commonly used in solid-state NMR spectroscopy to gain insight into the structure of biological molecules. These sequences excel through their simplicity, stability towards radio-frequency (rf) inhomogeneity, and low rf requirements. For a theoretical understanding of such sequences, we present a Floquet treatment based on an interaction-frame transformation including the chemical-shift offset dependence. This approach is applied to the homonuclear dipolar-recoupling sequence Radio-Frequency Driven Recoupling (RFDR) and the heteronuclear recoupling sequence Rotational Echo Double Resonance (REDOR). Based on the Floquet approach, we show the influence of effective fields caused by pulse transients and discuss the advantages of pulse-transient compensation. We demonstrate experimentally that the transfer efficiency for homonuclear recoupling can be doubled in some cases in model compounds as well as in simple peptides if pulse-transient compensation is applied to the π pulses. Additionally, we discuss the influence of various phase cycles on the recoupling efficiency in order to reduce the magnitude of effective fields. Based on the findings from RFDR, we are able to explain why the REDOR sequence does not suffer in the recoupling efficiency despite the presence of effective fields.

Sensitivity enhanced (14)N/(14)N correlations to probe inter-beta-sheet interactions using fast magic angle spinning solid-state NMR in biological solids

(14)N/(14)N correlations are vital for structural studies of solid samples, especially those in which (15)N isotopic enrichment is challenging, time-consuming and expensive. Although (14)N nuclei have high isotopic abundance (99.6%), there are inherent difficulties in observing (14)N/(14)N correlations due to limited resolution and sensitivity related to: (i) low (14)N gyromagnetic ratio (γ), (ii) large (14)N quadrupolar couplings, (iii) integer (14)N spin quantum number (I = 1), and (iv) very weak (14)N-(14)N dipolar couplings. Previously, we demonstrated a proton-detected 3D (14)N/(14)N/(1)H correlation experiment at fast magic angle spinning (MAS) on l-histidine·HCl·H2O utilizing a through-bond (J) and residual dipolar-splitting (RDS) based heteronuclear multiple quantum correlation (J-HMQC) sequence mediated through (1)H/(1)H radio-frequency driven recoupling (RFDR). As an extension of our previous work, in this study we show the utility of dipolar-based HMQC (D-HMQC) in combination with (1)H/(1)H RFDR mixing to obtain sensitivity enhanced (14)N/(14)N correlations in more complex biological solids such as a glycyl-l-alanine (Gly-l-Ala) dipeptide, and parallel (P) and antiparallel (AP) β-strand alanine tripeptides (P-(Ala)3 and AP-(Ala)3, respectively). These systems highlight the mandatory necessity of 3D (14)N/(14)N/(1)H measurements to get (14)N/(14)N correlations when the amide proton resonances are overlapped. Moreover, the application of long selective (14)N pulses, instead of short hard ones, is shown to improve the sensitivity. Globally, we demonstrate that replacing J-scalar with dipolar interaction and hard- with selective-(14)N pulses allows gaining a factor of ca. 360 in experimental time. On the basis of intermolecular NH/NH distances and (14)N quadrupolar tensor orientations, (14)N/(14)N correlations are effectively utilized to make a clear distinction between the parallel and antiparallel arrangements of the β-strands in (Ala)3 through the observation of inter-β-sheet correlations.