Double‐quantum homonuclear rotary resonance: Efficient dipolar recovery in magic‐angle spinning nuclear magnetic resonance

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.

Continuous Floquet theory in solid-state NMR

This article presents the application of continuous Floquet theory in solid-state nuclear magnetic resonance (NMR). Continuous Floquet theory extends the traditional Floquet theory to non-continuous Hamiltonians, enabling the description of observable effects not fully captured by the traditional Floquet theory due to its requirement for a periodic Hamiltonian. We present closed-form expressions for computing first- and second-order effective Hamiltonians, streamlining integration with the traditional Floquet theory and facilitating application in NMR experiments featuring multiple modulation frequencies. Subsequently, we show examples of the practical application of continuous Floquet theory by investigating several solid-state NMR experiments. These examples illustrate the importance of the duration of the pulse scheme regarding the width of the resonance conditions and the near-resonance behavior.

Advanced solid-state NMR spectroscopy and its applications in zeolite chemistry

Solid-state NMR spectroscopy (ssNMR) can provide details about the structure, host-guest/guest-guest interactions and dynamic behavior of materials at atomic length scales. A crucial use of ssNMR is for the characterization of zeolite catalysts that are extensively employed in industrial catalytic processes. This review aims to spotlight the recent advancements in ssNMR spectroscopy and its application to zeolite chemistry. We first review the current ssNMR methods and techniques that are relevant to characterize zeolite catalysts, including advanced multinuclear and multidimensional experiments, in situ NMR techniques and hyperpolarization methods. Of these, the methodology development on half-integer quadrupolar nuclei is emphasized, which represent about two-thirds of stable NMR-active nuclei and are widely present in catalytic materials. Subsequently, we introduce the recent progress in understanding zeolite chemistry with the aid of these ssNMR methods and techniques, with a specific focus on the investigation of zeolite framework structures, zeolite crystallization mechanisms, surface active/acidic sites, host-guest/guest-guest interactions, and catalytic reaction mechanisms.

Short and long range 2D 15N-15N NMR correlations among peptide groups by novel solid state dipolar mixing schemes

A recently developed homonuclear dipolar recoupling scheme, Adiabatic Linearly FREquency Swept reCOupling (AL FRESCO), was applied to record two-dimensional (2D) 15N-15N correlations on uniformly 15N-labeled GB1 powders. A major feature exploited in these 15N-15N correlations was AL FRESCO's remarkably low RF power demands, which enabled seconds-long mixing schemes when establishing direct correlations. These 15N-15N mixing schemes proved efficient regardless of the magic-angle spinning (MAS) rate and, being nearly free from dipolar truncation effects, they enabled the detection of long-range, weak dipolar couplings, even in the presence of strong short-range dipolar couplings. This led to a connectivity information that was significantly better than that obtained with spontaneously proton-driven, 15N spin-diffusion experiments. An indirect approach producing long-range 15N-15N correlations was also tested, relying on short (ms-long) 1HN-1HN mixings schemes while applying AL FRESCO chirped pulses along the 15N channel. These indirect mixing schemes produced numerous long-distance Ni-Ni±n (n = 2 - 5) correlations, that might be useful for characterizing three-dimensional arrangements in proteins. Once again, these AL FRESCO mediated experiments proved more informative than variants based on spin-diffusion-based 1HN-1HN counterparts.

A facile approach for estimating radio-frequency field strength of low-receptivity nuclei

Radio-frequency (RF) field calibration is essential in NMR spectroscopy. A common practice is to collect a nutation curve by varying the pulse length in a direct single-pulse excitation experiment or in a cross-polarization magic-angle spinning with a flip-back pulse experiment. From the null points on this curve, one can calculate the RF field strength. Nevertheless, the practical implementation is not always straightforward or can even be unrealizable, especially for low-receptivity nuclei owing to their associated low sensitivity. Several researchers used an approach that involves utilizing other nuclei with more sensitivity but nearly identical Larmor frequencies to that of the nucleus of interest. However, such an approach has not been a common practice so far. In this work, we have systematically revisited this approach using 3.2 mm rotors on different sets of nuclei covering a Larmor frequency range up to 80 MHz. The effect of solid- and solution-states on RF field strength measurements has been investigated. The detection of each set of nuclei is then carried out with a resonant circuit in the NMR probe consisting of identical coils and capacitors. Our methodology is illustrated by recording 135/137Ba NMR spectra of BaTiO3 without prior 135/137Ba RF field calibration.

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.

Satellite-transition double cross-polarization HETCOR under fast MAS

Double-cross polarization to the satellite-transitions (STs) of half-integer quadrupolar nuclei is demonstrated using proton-detected heteronuclear correlation (HETCOR) under fast magic-angle spinning (MAS). By placing the rf frequency away from the central-transition (CT) and selective to the STs, average Hamiltonian theory shows a scaled effective rf field with a phase equal to the complex ST spinning sideband being irradiated. Such an effective rf field can excite and spinlock STs but the phase spread usually leads to signal cancellation in one-step excitation or cross polarization experiments. The cancellation does not occur for two-step double cross-polarization (DCP) HETCOR experiments, therefore high efficiencies can be obtained. With careful magic-angle calibration, ST and double-quantum ST (DQST) HETCOR experiments are demonstrated with the ³⁵Cl nuclei in histidine·HCl·H₂O. These experiments provide additional information over the commonly observed CT spectra and near isotropic resolution in the case of DQST of spin S = 3/2 quadrupolar nuclei.

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.

Aromatic ring flips in differently packed ubiquitin protein crystals from MAS NMR and MD

Probing the dynamics of aromatic side chains provides important insights into the behavior of a protein because flips of aromatic rings in a protein's hydrophobic core report on breathing motion involving a large part of the protein. Inherently invisible to crystallography, aromatic motions have been primarily studied by solution NMR. The question how packing of proteins in crystals affects ring flips has, thus, remained largely unexplored. Here we apply magic-angle spinning NMR, advanced phenylalanine 1H-13C/2H isotope labeling and MD simulation to a protein in three different crystal packing environments to shed light onto possible impact of packing on ring flips. The flips of the two Phe residues in ubiquitin, both surface exposed, appear remarkably conserved in the different crystal forms, even though the intermolecular packing is quite different: Phe4 flips on a ca. 10-20 ns time scale, and Phe45 are broadened in all crystals, presumably due to µs motion. Our findings suggest that intramolecular influences are more important for ring flips than intermolecular (packing) effects.

Interaction frames in solid-state NMR: A case study for chemical-shift-selective irradiation schemes

Interaction frames play an important role in describing and understanding experimental schemes in magnetic resonance. They are often used to eliminate dominating parts of the spin Hamiltonian, e.g., the Zeeman Hamiltonian in the usual (Zeeman) rotating frame, or the radio-frequency-field (rf) Hamiltonian to describe the efficiency of decoupling or recoupling sequences. Going into an interaction frame can also make parts of a time-dependent Hamiltonian time independent like the rf-field Hamiltonian in the usual (Zeeman) rotating frame. Eliminating the dominant term often allows a better understanding of the details of the spin dynamics. Going into an interaction frame can also reduces the energy-level splitting in the Hamiltonian leading to a faster convergence of perturbation expansions, average Hamiltonian, or Floquet theory. Often, there is no obvious choice of the interaction frame to use but some can be more convenient than others. Using the example of frequency-selective dipolar recoupling, we discuss the differences, advantages, and disadvantages of different choices of interaction frames. They always include the complete radio-frequency Hamiltonian but can also contain the chemical shifts of the spins and may or may not contain the effective fields over one cycle of the pulse sequence.

Residue-Specific High-Resolution 17O Solid-State Nuclear Magnetic Resonance of Peptides: Multidimensional Indirect 1H Detection and Magic-Angle Spinning

Oxygen is an integral component of proteins but remains sparsely studied because its only NMR active isotope, ¹⁷O, has low sensitivity, low resolution, and large quadrupolar couplings. These issues are addressed here with efficient isotopic labeling, high magnetic fields, fast sample spinning, and ¹H detection in conjunction with multidimensional experiments to observe oxygen sites specific to each amino acid residue. Notably, cross-polarization at high sample spinning frequencies provides efficient ¹³C ↔ ¹⁷O polarization transfer. The use of ¹⁷O for initial polarization is found to provide better sensitivity per unit time compared to ¹H. Sharp isotropic ¹⁷O peaks are obtained by using a low-power multiple-quantum sequence, which in turn allows extraction of quadrupolar parameters for each oxygen site. Finally, the potential to determine sequential assignments and long-range distance restraints is demonstrated by using 3D ¹H/¹³C/¹⁷O experiments, suggesting that such methods can become an essential tool for biomolecular structure determination.

A unified description for polarization-transfer mechanisms in magnetic resonance in static solids: Cross polarization and DNP

Polarization transfers are crucial building blocks in magnetic resonance experiments, i.e., they can be used to polarize insensitive nuclei and correlate nuclear spins in multidimensional nuclear magnetic resonance (NMR) spectroscopy. The polarization can be transferred either across different nuclear spin species or from electron spins to the relatively low-polarized nuclear spins. The former route occurring in solid-state NMR can be performed via cross polarization (CP), while the latter route is known as dynamic nuclear polarization (DNP). Despite having different operating conditions, we opinionate that both mechanisms are theoretically similar processes in ideal conditions, i.e., the electron is merely another spin-1/2 particle with a much higher gyromagnetic ratio. Here, we show that the CP and DNP processes can be described using a unified theory based on average Hamiltonian theory combined with fictitious operators. The intuitive and unified approach has allowed new insights into the cross-effect DNP mechanism, leading to better design of DNP polarizing agents and extending the applications beyond just hyperpolarization. We explore the possibility of exploiting theoretically predicted DNP transients for electron–nucleus distance measurements—such as routine dipolar-recoupling experiments in solid-state NMR.

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.

Deuteron rotating frame relaxation for the detection of slow motions in rotating solids

We demonstrate experimental and computational approaches for measuring 2H rotating frame NMR relaxation for solid samples under magic angle spinning (MAS) conditions. The relaxation properties of the deuterium spin-1 system are dominated by the reorientation of the anisotropic quadrupolar tensors, with the effective quadrupolar coupling constant around 55 kHz for methyl groups. The technique is demonstrated using the model compound dimethyl-sulfone at MAS rates of 10 and 60 kHz as well as for an amyloid fibril sample comprising an amyloid-β (1-40) protein with a selective methyl group labeled in the disordered domain of the fibrils, at an MAS rate of 8 kHz. For both systems, the motional parameters fall well within the ranges determined by other techniques, thus validating its feasibility. Experimental and computational factors such as i) the probe's radio frequency inhomogeneity profiles, ii) rotary resonances at conditions for which the spin-lock field strength matches the half- or full-integer of the MAS rate, iii) the choice of MAS rates and spin-lock field strengths, and iv) simulations that account for the interconversion of multiple coherences for the spin-1 system under MAS and deviations from the analytical Redfield treatment are thoroughly considered.

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.

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.

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.

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.

Floquet theory in magnetic resonance: Formalism and applications

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

On the use of radio-frequency offsets for improving double-quantum homonuclear dipolar recoupling of half-integer-spin quadrupolar nuclei

Detecting proximities between nuclei is crucial for atomic-scale structure determination with nuclear magnetic resonance (NMR) spectroscopy. Different from spin-1/2 nuclei, the methodology for quadrupolar nuclei is limited for solids due to the complex spin dynamics under simultaneous magic-angle spinning (MAS) and radio-frequency irradiation. Herein, the performances of several homonuclear rotary recoupling (HORROR)-based homonuclear dipolar recoupling sequences are evaluated for ²⁷ Al (spin-5/2). It is shown numerically and experimentally on mesoporous alumina that BR 2 2 1 outperforms the supercycled S₃ sequence and its pure double-quantum (DQ) (bracketed) version, [S₃ ], both in terms of DQ transfer efficiency and bandwidth. This result is surprising since the S₃ sequence is among the best low-power recoupling schemes for spin-1/2. The superiority of BR 2 2 1 is thoroughly explained, and the crucial role of radio-frequency offsets during its spin dynamics is highlighted. The analytical approximation of BR 2 2 1 , derived in an offset-toggling frame, clarifies the interplay between offset and DQ efficiency, namely, the benefits of off-resonance irradiation and the trough in DQ efficiency for BR 2 2 1 when the irradiation is central between two resonances, both for spin-1/2 and half-integer-spin quadrupolar nuclei. Additionally, density matrix propagations show that the BR 2 2 1 sequence, applied to quadrupolar nuclei subject to quadrupolar interaction much larger than radio-frequency frequency field, can create single- and multiple-quantum coherences for near on-resonance irradiation. This significantly perturbs the creation of DQ coherences between central transitions of neighboring quadrupolar nuclei. This effect explains the DQ efficiency trough for near on-resonance irradiation, in the case of both cross-correlation and autocorrelation peaks. Overall, this work aids experimental acquisition of homonuclear dipolar correlation spectra of half-integer-spin quadrupolar nuclei and provides theoretical insights towards improving recoupling schemes at high magnetic field and fast MAS.

Deuteron Chemical Exchange Saturation Transfer for the Detection of Slow Motions in Rotating Solids

We utilized the ²H Chemical Exchange Saturation Transfer (CEST) technique under magic angle spinning (MAS) conditions to demonstrate the feasibility of the method for studies of slow motions in the solid state. For the quadrupolar anisotropic interaction, the essence of CEST is to scan the saturation pattern over a range of offsets corresponding to the entire spectral region(s) for all conformational states involved, which translates into a range of −60–+ 60 kHz for methyl groups. Rotary resonances occur when the offsets are at half-and full-integer of the MAS rates. The choice of the optimal MAS rate is governed by the condition to reduce the number of rotary resonances in the CEST profile patterns and retain a sufficiently large quadrupolar interaction active under MAS to maintain sensitivity to motions. As examples, we applied this technique to a well-known model compound dimethyl-sulfone (DMS) as well as amyloid-β fibrils selectively deuterated at a single methyl group of A2 belonging to the disordered domain. It is demonstrated that the obtained exchange rate between the two rotameric states of DMS at elevated temperatures fell within known ranges and the fitted model parameters for the fibrils agree well with the previously obtained value using static ²H NMR techniques. Additionally, for the fibrils we have observed characteristic broadening of rotary resonances in the presence of conformational exchange, which provides implications for model selection and refinement. This work sets the stage for future potential extensions of the ²H CEST under MAS technique to multiple-labeled samples in small molecules and proteins.

Spectral editing of alanine, serine, and threonine in uniformly labeled proteins based on frequency-selective homonuclear recoupling in solid-state NMR

Spectral editing is crucial to simplify the crowded solid-state NMR spectra of proteins. New techniques are introduced to edit ¹³C-¹³C correlations of uniformly labeled proteins under moderate magic-angle spinning (MAS), based on our recent frequency-selective homonuclear recoupling sequences [Zhang et al., J. Phys. Chem. Lett. 2020, 11, 8077-8083]. The signals of alanine, serine, or threonine residues are selected out by selective ¹³Cα-¹³Cβ double-quantum filtering (DQF). The ¹³Cα-¹³Cβ correlations of alanine residues are selectively established with efficiency up to ~ 1.8 times that by dipolar-assisted rotational resonance (DARR). The techniques are shown in 2D/3D NCCX experiments and applied to the uniformly ¹³C, ¹⁵N labeled Aquaporin Z (AqpZ) membrane protein, demonstrating their potential to simplify spectral analyses in biological solid-state NMR.

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.

Frequency-swept adiabatic pulses for broadband solid-state MAS NMR

We present a complete description of frequency-swept adiabatic pulses applied to isolated spin-1/2 nuclei with a shift anisotropy in solid materials under magic-angle spinning. Our theoretical framework unifies the existing descriptions of adiabatic pulses in the high-power regime, where the radiofrequency (RF) amplitude is greater than twice the spinning frequency, and the low-power regime, where the RF power is less than the spinning frequency, and so links the short high-powered adiabatic pulse (SHAP) and single-sideband-selective adiabatic pulses (S³AP) schemes used in paramagnetic solid-state NMR. We also identify a hitherto unidentified third regime intermediate between the low- and high-power regimes, and separated from them by rotary resonance conditions. We show that the prevailing benchmark of inversion performance based on (super) adiabatic factors is only applicable in the high- and intermediate-power regimes, but fails to account both for the poor performance at rotary resonance, and the impressive inversion seen in the low-power regime. For low-power pulses, which are non-adiabatic according to this definition of (super) adiabaticity, the effective Floquet Hamiltonian in the jolting frame reveals "hidden" (super) adiabaticity. The theory is demonstrated using a combination of simulation and experiment, and is used to refine the practical recommendations for the experimentalist who wishes to use these pulses.

Phase-sensitive γ-encoded recoupling of heteronuclear dipolar interactions and 1H chemical shift anisotropy

γ-encoded recoupling sequences are known to produce strong amplitude modulations that lead to sharp doublets when Fourier transformed. These doublets depend very little on the recoupled tensor asymmetry and thus enable for the straightforward determination of dynamic order parameters. It can, however, be difficult to measure small anisotropies, or small order parameters, using such sequences; the resonances from the doublet may overlap with each other, or with the zero-frequency glitch. This limitation has prevented the widespread use of ¹H chemical shift anisotropy (CSA) for the measurement of dynamics, particularly for CH protons which typically have CSAs of only a few ppm when immobile. Here, we introduce a simple modification to the traditional ¹H CSA and proton-detected local field pulse sequences that enables the acquisition of a hypercomplex dataset and the removal of the uncorrelated magnetization that results in the zero-frequency glitch. These new sequences then yield a frequency shift in the indirect dimension, rather than a splitting, which is easily identifiable even in cases of weak interactions.

ssNMRlib: a comprehensive library and tool box for acquisition of solid-state nuclear magnetic resonance experiments on Bruker spectrometers

We introduce ssNMRlib, a comprehensive suite of pulse sequences and jython scripts for user-friendly solid-state nuclear magnetic resonance (NMR) data acquisition, parameter optimization and storage on Bruker spectrometers. ssNMRlib allows the straightforward setup of even highly complex multi-dimensional solid-state NMR experiments with a few clicks from an intuitive graphical interface directly from the Bruker Topspin acquisition software. ssNMRlib allows the setup of experiments in a magnetic-field-independent manner and thus facilitates the workflow in a multi-spectrometer setting with a centralized library. Safety checks furthermore assist the user in experiment setup. Currently hosting more than 140 1D to 4D experiments, primarily for biomolecular solid-state NMR, the library can be easily customized and new experiments are readily added as new templates. ssNMRlib is part of the previously introduced NMRlib library, which comprises many solution-NMR pulse sequences and macros.

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.

Accuracy of 1H-1H distances measured using frequency selective recoupling and fast magic-angle spinning

Selective recoupling of protons (SERP) is a method to selectively and quantitatively measure magnetic dipole-dipole interaction between protons and, in turn, the proton-proton distance in solid-state samples at fast magic-angle spinning. We present a bimodal operator-based Floquet approach to describe the numerically optimized SERP recoupling sequence. The description calculates the allowed terms in the first-order effective Hamiltonian, explains the origin of selectivity during recoupling, and shows how different terms are modulated as a function of the radio frequency amplitude and the phase of the sequence. Analytical and numerical simulations have been used to evaluate the effect of higher-order terms and offsets on the polarization transfer efficiency and quantitative distance measurement. The experimentally measured ¹H-¹H distances on a fully protonated thymol sample are ∼10%-15% shorter than those reported from diffraction studies. A semi-quantitative model combined with extensive numerical simulations is used to rationalize the effect of the third-spin and the role of different parameters in the experimentally observed shorter distances. Measurements at high magnetic fields improve the match between experimental and diffraction distances. The measurement of ¹H-¹H couplings at offsets different from the SERP-offset has also been explored. Experiments were also performed on a perdeuterated ubiquitin sample to demonstrate the feasibility of simultaneously measuring multiple quantitative distances and to evaluate the accuracy of the measured distance in the absence of multispin effects. The estimation of proton-proton distances provides a boost to structural characterization of small pharmaceuticals and biomolecules, given that the positions of protons are generally not well defined in x-ray structures.

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.

Sensitivity enhancement in 2D Double Cross Polarization experiments under fast MAS by recycling unused protons

We demonstrate sensitivity enhancement via recycling of proton magnetization in 2D Double Cross Polarization (Double CP) experiments performed on fully protonated and uniformly labeled (¹³C, ¹⁵N) samples at a magic angle spinning rate of 60 kHz. Unused proton magnetization is preserved during t₁ evolution either by locking it with CW irradiation or by employing rotor-synchronized pi pulses. A flip-back pulse together with a modified second CP block preserves unused proton magnetization resulting in enhanced sensitivity. We have achieved sensitivity enhancements of 15-20% and 25-28% in ¹H-¹³C and ¹H-¹⁵N 2D Double CP experiments respectively. At shorter recycle delays (∼0.25T₁), relative sensitivity enhancements of 40-45% and 55% were obtained in ¹H-¹³C and ¹H-¹⁵N 2D Double CP experiments respectively. An analysis of the sensitivity enhancements and theoretical estimation of lineshapes in indirect dimension in the presence of proton recycling is provided.

Suppressing 1H Spin Diffusion in Fast MAS Proton Detected Heteronuclear Correlation Solid-State NMR Experiments

Fast magic angle spinning (MAS) and indirect detection by high gyromagnetic ratio (γ) nuclei such as proton or fluorine are increasingly utilized to obtain 2D heteronuclear correlation (HETCOR) solid-state NMR spectra of spin-1/2 nuclei by using cross polarization (CP) for coherence transfer. However, one major drawback of CP HETCOR pulse sequences is that ¹H spin diffusion during the back X→¹H CP transfer step may result in relayed correlations. This problem is particularly pronounced for the indirect detection of very low-γ nuclei such as ⁸⁹Y, ¹⁰³Rh, ¹⁰⁹Ag and ¹⁸³W where long contact times on the order of 10-30 ms are necessary for optimal CP transfer. Here we propose two methods that eliminate relayed correlations and allow more reliable distance information to be obtained from 2D HETCOR NMR spectra. The first method uses Lee-Goldburg (LG) CP during the X→¹H back-transfer step to suppress ¹H spin diffusion. We determine LG conditions compatible with fast MAS frequencies (ν_rot) of 40-95 kHz and show that ¹H spin diffusion can be efficiently suppressed at low effective radiofrequency (RF) fields (ν_1,eff ≪ 0.5ν_rot) and also at high effective RF fields (ν_1,eff ≫ 2ν_rot). We describe modified Hartmann-Hahn LG-CP match conditions compatible with fast MAS and suitable for indirect detection of moderate-γ nuclei such as ¹³C, and low-γ nuclei such as ⁸⁹Y. The second method uses D-RINEPT (dipolar refocused insensitive nuclei enhanced by polarization transfer) during the X→¹H back-transfer step of the HETCOR pulse sequence. The effectiveness of these methods for acquiring HETCOR spectra with reduced relayed signal intensities is demonstrated with ¹H{¹³C} HETCOR NMR experiments on l-histidine⋅HCl⋅H₂O and ¹H{⁸⁹Y} HETCOR NMR experiments on an organometallic yttrium complex.

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.

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.

Accurate 1H-14N distance measurements by phase-modulated RESPDOR at ultra-fast MAS

The combination of a phase-modulated (PM) saturation pulse and symmetry-based dipolar recoupling into a rotational-echo saturation-pulse double-resonance (RESPDOR) sequence has been employed to measure ¹H-¹⁴N distances. Such a measurement is challenging owing to the quadrupolar interaction of ¹⁴N nucleus and the intense ¹H-¹H homonuclear dipolar interactions. Thanks to the recent advances in probe technology, the homonuclear dipolar interaction can be sufficiently suppressed at a fast MAS frequency (ν_R ≥ 60 kHz). PM pulse is robust to large variations of parameters on quadrupolar spins, but it has not been demonstrated under very fast MAS conditions. On the other hand, the RESPDOR sequence is applicable to such condition when it employs symmetry-based pulses during the recoupling period, but a prior knowledge on the system is required. In this article, we demonstrated the PM-RESPDOR combination for providing accurate ¹H-¹⁴N distances at a very fast MAS frequency of 70 kHz on two samples, namely L-tyrosine⋅HCl and N-acetyl-L-alanine. This sequence, supported by simulations and experiments, has shown its feasibility at ν_R = 70 kHz as well as the robustness to the ¹⁴N quadrupolar interaction. It is applicable to a wide range of ¹H-¹⁴N dipolar coupling constants when a radio frequency field on the ¹⁴N channel is approximately 80 kHz or more, while the PM pulse length lasts 10 rotor periods. For the first time, multiple ¹H-¹⁴N heteronuclear dipolar couplings, thus multiple quantitative distances, are simultaneously and reliably extracted by fitting the experimental fraction curves with the analytical expression. The size of the ¹H-¹⁴N dipolar interaction is solely used as a fitting parameter. These determined distances are in excellent agreement with those derived from diffraction techniques.

Understanding the formation of apremilast cocrystals

Apremilast (APR), an anti-psoriatic agent, easily forms isostructural cocrystals and solvates with aromatic entities, often disobeying at the same time Kitaigorodsky's rule as to the saturation of possible hydrogen-bonding sites. In this paper the reasons for this peculiar behavior are investigated, employing a joint experimental and theoretical approach. This includes the design of cocrystals with coformers having a high propensity towards the formation of both aromatic-aromatic and hydrogen-bonding interactions, determination of their structure, using solid-state NMR spectroscopy and X-ray crystallography, as well as calculations of stabilization energies of formation of the obtained cocrystals, followed by crystal structure prediction calculations and solubility measurements. The findings indicate that the stabilization energies of cocrystal formation are positive in all cases, which results from strain in the APR conformation in these crystal forms. On the other hand, solubility measurements show that the Gibbs free energy of formation of the apremilast:picolinamide cocrystal is negative, suggesting that the formation of the studied cocrystals is entropy driven. This entropic stabilization is associated with the disorder observed in almost all known cocrystals and solvates of APR.

Perspectives on high-field and solid-state NMR methods of quadrupole nuclei

High magnetic field can dramatically increase the spectral resolution and sensitivity of quadrupole nuclei S > 1/2 by the reduction of the second-order quadrupole broadening. A brief overview and outlook on spectral acquisition, the importance of high magnetic field, inter-nuclei distance measurement, various 2D separation and correlation methods of quadrupole nuclei are presented. The complications and consequences of spin dynamics under rf irradiation for the (2S + 1) level system and level-crossing with the satellite transition frequencies under magic-angle spinning are discussed. There is a scaling down of (S + 1/2) to the efficiency of many experiments in comparison with a spin-1/2 due to the fact that only two central transition spin states out of the (2S + 1) levels contribute to polarization transfer and spin correlation.

Natural Isotopic Abundance 13C and 15N Multidimensional Solid-State NMR Enabled by Dynamic Nuclear Polarization

Dynamic nuclear polarization (DNP) has made feasible solid-state NMR experiments that were previously thought impractical due to sensitivity limitations. One such class of experiments is the structural characterization of organic and biological samples at natural isotopic abundance (NA). Herein, we describe the many advantages of DNP-enabled ssNMR at NA, including the extraction of long-range distance constraints using dipolar recoupling pulse sequences without the deleterious effects of dipolar truncation. In addition to the theoretical underpinnings in the analysis of these types of experiments, numerous applications of DNP-enabled ssNMR at NA are discussed.

Bone mineral: new insights into its chemical composition

Some compositional and structural features of mature bone mineral particles remain unclear. They have been described as calcium-deficient and hydroxyl-deficient carbonated hydroxyapatite particles in which a fraction of the PO₄^3- lattice sites are occupied by HPO₄^2- ions. The time has come to revise this description since it has now been proven that the surface of mature bone mineral particles is not in the form of hydroxyapatite but rather in the form of hydrated amorphous calcium phosphate. Using a combination of dedicated solid-state nuclear magnetic resonance techniques, the hydrogen-bearing species present in bone mineral and especially the HPO₄^2- ions were closely scrutinized. We show that these HPO₄^2- ions are concentrated at the surface of bone mineral particles in the so-called amorphous surface layer whose thickness was estimated here to be about 0.8 nm for a 4-nm thick particle. We also show that their molar proportion is much higher than previously estimated since they stand for about half of the overall amount of inorganic phosphate ions that compose bone mineral. As such, the mineral-mineral and mineral-biomolecule interfaces in bone tissue must be driven by metastable hydrated amorphous environments rich in HPO₄^2- ions rather than by stable crystalline environments of hydroxyapatite structure.

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.

Mechanistic Insights into Microsecond Time-Scale Motion of Solid Proteins Using Complementary 15N and 1H Relaxation Dispersion Techniques

NMR relaxation dispersion methods provide a holistic way to observe microsecond time-scale protein backbone motion both in solution and in the solid state. Different nuclei (¹H and ¹⁵N) and different relaxation dispersion techniques (Bloch-McConnell and near-rotary-resonance) give complementary information about the amplitudes and time scales of the conformational dynamics and provide comprehensive insights into the mechanistic details of the structural rearrangements. In this paper, we exemplify the benefits of the combination of various solution- and solid-state relaxation dispersion methods on a microcrystalline protein (α-spectrin SH3 domain), for which we are able to identify and model the functionally relevant conformational rearrangements around the ligand recognition loop occurring on multiple microsecond time scales. The observed loop motions suggest that the SH3 domain exists in a binding-competent conformation in dynamic equilibrium with a sterically impaired ground-state conformation both in solution and in crystalline form. This inherent plasticity between the interconverting macrostates is compatible with a conformational-preselection model and provides new insights into the recognition mechanisms of SH3 domains.

Structure determination of supra-molecular assemblies by solid-state NMR: Practical considerations

In the cellular environment, biomolecules assemble in large complexes which can act as molecular machines. Determining the structure of intact assemblies can reveal conformations and inter-molecular interactions that are only present in the context of the full assembly. Solid-state NMR (ssNMR) spectroscopy is a technique suitable for the study of samples with high molecular weight that allows the atomic structure determination of such large protein assemblies under nearly physiological conditions. This review provides a practical guide for the first steps of studying biological supra-molecular assemblies using ssNMR. The production of isotope-labeled samples is achievable via several means, which include recombinant expression, cell-free protein synthesis, extraction of assemblies directly from cells, or even the study of assemblies in whole cells in situ. Specialized isotope labeling schemes greatly facilitate the assignment of chemical shifts and the collection of structural data. Advanced strategies such as mixed, diluted, or segmental subunit labeling offer the possibility to study inter-molecular interfaces. Detailed and practical considerations are presented with respect to first setting up magic-angle spinning (MAS) ssNMR experiments, including the selection of the ssNMR rotor, different methods to best transfer the sample and prepare the rotor, as well as common and robust procedures for the calibration of the instrument. Diagnostic spectra to evaluate the resolution and sensitivity of the sample are presented. Possible improvements that can reduce sample heterogeneity and improve the quality of ssNMR spectra are reviewed.

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.

Measurement of proton chemical shift anisotropy in solid-state NMR spectroscopy

Proton chemical shift anisotropy (CSA) is significantly important as it provides the information of the dynamics and local environmental structure of the proton. The measurement of proton CSA keeps drawing the attention of NMR researchers, and great efforts have been expended. In the early years, measuring proton CSA in solid-state NMR, especially with the strong ¹H-¹H dipolar network, was hampered by ineffective decoupling or selectively recoupling techniques, and the applications were only limited to those with sparse proton sites or single crystals. Till the latest decades, the dramatic progress on NMR methodology and magic-angle spinning (MAS) technology enable accurate detection of proton CSA in complicated powder samples even proteins. In this review, following a brief description of the measurement of proton CSA in solution and LCs NMR, a retrospect of the experimental development of proton CSA measurement in solid state NMR is presented, from the continuous wave (CW) and multiple pulse sequences for static solid samples, to combined rotation and multiple pulse spectroscopy (CRAMPS), then to the latest methods including rotary resonance, CSA amplification and R-symmetry pulse sequences under MAS conditions.

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.

Protons as Versatile Reporters in Solid-State NMR Spectroscopy

Solid-state nuclear magnetic resonance (ssNMR) is a spectroscopic technique that is used for characterization of molecular properties in the solid phase at atomic resolution. In particular, using the approach of magic-angle spinning (MAS), ssNMR has seen widespread applications for topics ranging from material sciences to catalysis, metabolomics, and structural biology, where both isotropic and anisotropic parameters can be exploited for a detailed assessment of molecular properties. High-resolution detection of protons long represented the holy grail of the field. With its high natural abundance and high gyromagnetic ratio, ¹H has naturally been the most important nucleus type for the solution counterpart of NMR spectroscopy. In the solid state, similar benefits are obtained over detection of heteronuclei, however, a rocky road led to its success as their high gyromagnetic ratio has also been associated with various detrimental effects. Two exciting approaches have been developed in recent years that enable proton detection: After partial deuteration of the sample to reduce the proton spin density, the exploitation of protons could begin. Also, faster MAS, nowadays using tiny rotors with frequencies up to 130 kHz, has relieved the need for expensive deuteration. Apart from the sheer gain in sensitivity from choosing protons as the detection nucleus, the proton chemical shift and several other useful aspects of protons have revolutionized the field. In this Account, we are describing the fundamentals of proton detection as well as the arising possibilities for characterization of biomolecules as associated with the developments in our own lab. In particular, we focus on facilitated chemical-shift assignment, structure calculation based on protons, and on assessment of dynamics in solid proteins. For example, the proton chemical-shift dimension adds additional information for resonance assignments in the protein backbone and side chains. Chemical shifts and high gyromagnetic ratio of protons enable direct readout of spatial information over large distances. Dynamics in the protein backbone or side chains can be characterized efficiently using protons as reporters. For all of this, the sample amounts necessary for a given signal-to-noise have drastically shrunk, and new methodology enables assessment of molecules with increasing monomer molecular weight and complexity. Taken together, protons are able to overcome previous limitations, by speeding up processes, enhancing accuracies, and increasing the accessible ranges of ssNMR spectroscopy, as we shall discuss in detail in the following. In particular, these methodological developments have been pushing solid-state NMR into a new regime of biological topics as they realistically allow access to complex cellular molecules, elucidating their functions and interactions in a multitude of ways.

Microsecond motions probed by near-rotary-resonance R1ρ15N MAS NMR experiments: the model case of protein overall-rocking in crystals

Solid-state near-rotary-resonance measurements of the spin-lattice relaxation rate in the rotating frame (R_1ρ) is a powerful NMR technique for studying molecular dynamics in the microsecond time scale. The small difference between the spin-lock (SL) and magic-angle-spinning (MAS) frequencies allows sampling very slow motions, at the same time it brings up some methodological challenges. In this work, several issues affecting correct measurements and analysis of ¹⁵N R_1ρ data are considered in detail. Among them are signal amplitude as a function of the difference between SL and MAS frequencies, "dead time" in the initial part of the relaxation decay caused by transient spin-dynamic oscillations, measurements under HORROR condition and proper treatment of the multi-exponential relaxation decays. The multiple ¹⁵N R_1ρ measurements at different SL fields and temperatures have been conducted in 1D mode (i.e. without site-specific resolution) for a set of four different microcrystalline protein samples (GB1, SH3, MPD-ubiquitin and cubic-PEG-ubiquitin) to study the overall protein rocking in a crystal. While the amplitude of this motion varies very significantly, its correlation time for all four sample is practically the same, 30-50 μs. The amplitude of the rocking motion correlates with the packing density of a protein crystal. It has been suggested that the rocking motion is not diffusive but likely a jump-like dynamic process.

Efficient low-power TOBSY sequences for fast MAS

Through-bond J-coupling based experiments in solid-state NMR spectroscopy are challenging because the J couplings are typically much smaller than the dipolar couplings. This often leads to a lower transfer efficiency compared to dipolar-coupling based sequences. One of the reasons for the low transfer efficiency are the second-order cross terms involving the strong heteronuclear dipolar couplings leading to fast magnetization decay. Here, we show that by employing a symmetry-based C9 sequence, which was carefully selected to suppress second-order terms, efficient polarization transfers of up to 80% can be achieved without decoupling on fully protonated two-spin model systems at a MAS frequency of 55.5 kHz with rf-field amplitudes of about 25 kHz. In addition, we analyse the effects of rf inhomogeneity and crystallites selection due to the polarization preparation method on the TOBSY transfer efficiency. We demonstrate on small model substances as well as on deuterated and 100% back-exchanged ubiquitin that C9₃₉¹ and C9₄₈¹ are efficient and practical TOBSY sequences at experimental conditions ranging from proton Larmor frequencies of 400-850 MHz, and MAS frequencies ranging from 55.5 to 111.1 kHz.