MIRROR recoupling and its application to spin diffusion under fast magic-angle spinning

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.

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.

Barriers to resolution in 1H NMR of rotating solids

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

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.

Theoretical description of pulse induced resonances in the homonuclear PIRATE experiment

Rotor-synchronous π pulses applied to protons (S) enhance homonuclear polarisation transfer between two spins (I) such as ¹³C or ¹⁵N as long as at least a single I-S heteronuclear dipolar-coupling interaction exists. The enhancement is maximum when the chemical-shift difference Δν between two spins equals an integer multiple, n, of the pulse-modulation frequency, which is half the rotor frequency ν_r. This condition, applied in the Pulse Induced Resonance with Angular dependent Total Enhancement (PIRATE) experiment, can be generalised for any spacing of the pulses k/ν_r such that Δν=nν_r2k . We show, using average Hamiltonian theory (AHT) and Floquet theory, that the resonance conditions promote a second-order recoupling consisting of a cross-term between the homonuclear and heteronuclear dipolar interactions in a three-spin system. The minimum requirement is a coupling between the two I spins and a coupling of one of the I spins to the S spin. The effective Hamiltonian at the resonance conditions contains three-spin operators of the form 2I₁^±I₂^∓S_z with a non-zero effective dipolar coupling. Theoretical analysis shows that the effective strength of the resonance conditions decreases with increasing values of k and n. The theory is backed by numerical simulations, and experimental results on fully labelled ¹³C-glycine demonstrating the efficiency of the different resonance condition for k=1,2 at various spinning frequencies.

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.

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

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

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

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

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.

HORRENDOUS NMR: Establishing correlations in solution-state NMR by reinstating non-secular J-coupling terms

Homonuclear isotropic mixing modules allow J-coupled spins to exchange magnetization even when separated by chemical shift offsets that exceed their couplings. This is exploited in TOtal Correlation SpectroscopY (TOCSY) experiments and its variants, which facilitate these homonuclear polarization exchanges by applying broadband RF pulses. These then establish an effective Hamiltonian in which chemical shift offsets are erased, while J-coupling terms -including flip-flop components- remain active. The polarization that these non-secular terms will transfer among systems of chemically inequivalent sites over the course of a mixing period, are widely used modules in 1D and in multidimensional liquid-state NMR. Homonuclear correlation experiments are also common in solids NMR, particularly among X = ¹³C or ¹⁵N nuclei. Solids NMR experiments are often challenged by high-power RF demands which have led to a family of homonuclear solid-state correlation experiments that avoid pulsing on the nuclei of interest, and focus instead on the ¹Hs that are bonded to them. These solid experiments usually reintroduce/strengthen ¹H-X dipolar couplings; these, in conjunction with assistance from rotational resonance effects, bring back the truncated X-X dipolar interactions and facilitate the generation of cross peaks. The present study explores whether a similar goal can be achieved for solution-state counterparts, based on the reintroduction of truncated flip-flop terms in the J-coupling Hamiltonian via the pulsing on other, heteronuclear species. A proposal to achieve this is derived, and the resulting HOmonucleaR Recoupling by hEteroNuclear DecOUplingS (HORRENDOUS) approach to provide correlations between like nuclei without pulsing on them, is demonstrated.

NMR Assignment of Methyl Groups in Immobilized Proteins Using Multiple-Bond 13C Homonuclear Transfers, Proton Detection, and Very Fast MAS

In nuclear magnetic resonance spectroscopy of proteins, methyl protons play a particular role as extremely sensitive reporters on dynamics, allosteric effects, and protein–protein interactions, accessible even in high-molecular-weight systems approaching 1 MDa. The notorious issue of their chemical shift assignment is addressed here by a joint use of solid-state 1H-detected methods at very fast (nearly 100 kHz) magic-angle spinning, partial deuteration, and high-magnetic fields. The suitability of a series of RF schemes is evaluated for the efficient coherence transfer across entire 13C side chains of methyl-containing residues, which is key for establishing connection between methyl and backbone 1H resonances. The performance of ten methods for recoupling of either isotropic 13C–13C scalar or anisotropic dipolar interactions (five variants of TOBSY, FLOPSY, DIPSI, WALTZ, RFDR, and DREAM) is evaluated experimentally at two state-of-the-art magic-angle spinning (55 and 94.5 kHz) and static magnetic field conditions (18.8 and 23.5 T). Model isotopically labeled compounds (alanine and Met-Leu-Phe tripeptide) and ILV-methyl and amide-selectively protonated, and otherwise deuterated chicken α-spectrin SH3 protein are used as convenient reference systems. Spin dynamics simulations in SIMPSON are performed to determine optimal parameters of these RF schemes, up to recently experimentally attained spinning frequencies (200 kHz) and B0 field strengths (28.2 T). The concept of linearization of 13C side chain by appropriate isotope labeling is revisited and showed to significantly increase sensitivity of methyl-to-backbone correlations. A resolution enhancement provided by 4D spectroscopy with non-uniform (sparse) sampling is demonstrated to remove ambiguities in simultaneous resonance assignment of methyl proton and carbon chemical shifts.

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.

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

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

Floquet theory in magnetic resonance: Formalism and applications

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

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

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

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.

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.

Protein resonance assignment by BSH-CP-based 3D solid-state NMR experiments: A practical guide

Solid-state NMR (ssNMR) spectroscopy has evolved into a powerful method to obtain structural information and to study the dynamics of proteins at atomic resolution and under physiological conditions. The method is especially well suited to investigate insoluble and noncrystalline proteins that cannot be investigated easily by X-ray crystallography or solution NMR. To allow for detailed analysis of ssNMR data, the assignment of resonances to the protein atoms is essential. For this purpose, a set of three-dimensional (3D) spectra needs to be acquired. Band-selective homo-nuclear cross-polarization (BSH-CP) is an effective method for magnetization transfer between carbonyl carbon (CO) and alpha carbon (CA) atoms, which is an important transfer step in multidimensional ssNMR experiments. This tutorial describes the detailed procedure for the chemical shift assignment of the backbone atoms of ¹³ C-¹⁵ N-labeled proteins by BSH-CP-based ¹³ C-detected ssNMR experiments. A set of six 3D experiments is used for unambiguous assignment of the protein backbone as well as certain side-chain resonances. The tutorial especially addresses scientists with little experience in the field of ssNMR and provides all the necessary information for protein assignment in an efficient, time-saving approach.

The origin of negative cross-peaks in proton-spin diffusion spectrum of fully protonated solids at fast MAS: Coherent or incoherent effect?

Spin-diffusion (SD) is amongst the first methods proposed to spatially transfer polarization between dipolar-coupled nuclear spins. Lab-frame SD has proved particularly useful in structural characterization of a large variety of molecules. During SD, the rate of magnetization transfer between the two nuclei depends on the square of the dipolar coupling and the zero-quantum lineshape of the two spins. The relative sign of the diagonal and cross-peaks is determined by the spin part of the dipolar Hamiltonian. Practically, SD experiments are used in two ways: (a) SD transfer amongst only the protons (known as proton spin-diffusion or PSD) and b) SD amongst rare nuclei, coupled to a strong proton bath, known as proton driven spin-diffusion (PDSD). It is well established that the diagonal and cross-peaks have the same sign during SD based polarization transfer. 2D PSD experiments recorded on Histidine.HCl.H₂O sample at fast magic angle spinning (MAS) show that some of the cross-peaks in the 2D spectrum are negative with respect to the diagonal peaks. Cross-relaxation due to stochastic motion is generally believed to give rise to such negative peaks. Herein, we use theoretical calculations, numerical simulations and experiments to show that the origin of the negative cross-peaks in PSD spectrum is due to coherent interactions. The origin of negative peaks can be specifically ascribed to a four spin, double-flip-double flop term, in the third-order Hamiltonian. These terms become the dominant terms at fast spinning when additional - conditions are satisfied.

A suite of solid-state NMR experiments to utilize orphaned magnetization for assignment of proteins using parallel high and low gamma detection

We present a suite of two-receiver solid-state NMR experiments for backbone and side chain resonance assignment. The experiments rely on either dipolar coupling or scalar coupling for polarization transfer and are devised to acquire a ¹H-detected 3D experiment AND a nested ¹³C-detected 2D from a shared excitation pulse. In order to compensate for the lower sensitivity of detection on ¹³C nucleus, 2D rows are signal averaged during 3D planes. The 3D dual receiver experiments do not suffer from any appreciable signal loss compared to their single receiver versions and require no extra optimization. The resulting data is higher in information content with no additional experiment time. The approach is expected to become widespread as multiple receivers become standard for new NMR spectrometers.

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.

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.

Solid-state MAS NMR resonance assignment methods for proteins

The prerequisite to structural or functional studies of proteins by NMR is generally the assignment of resonances. Since the first assignment of proteins by solid-state MAS NMR was conducted almost two decades ago, a wide variety of different pulse sequences and methods have been proposed and continue to be developed. Traditionally, a variety of 2D and 3D ¹³C-detected experiments have been used for the assignment of backbone and side-chain ¹³C and ¹⁵N resonances. These methods have found widespread use across the field. But as the hardware has changed and higher spinning frequencies and magnetic fields are becoming available, the ability to use direct proton detection is opening up a new set of assignment methods based on triple-resonance experiments. This review describes solid-state MAS NMR assignment methods using carbon detection and proton detection at different deuteration levels. The use of different isotopic labelling schemes as an aid to assignment in difficult cases is discussed as well as the increasing number of software packages that support manual and automated resonance assignment.

Dynamic membrane interactions of antibacterial and antifungal biomolecules, and amyloid peptides, revealed by solid-state NMR spectroscopy

A variety of biomolecules acting on the cell membrane folds into a biologically active structure in the membrane environment. It is, therefore, important to determine the structures and dynamics of such biomolecules in a membrane environment. While several biophysical techniques are used to obtain low-resolution information, solid-state NMR spectroscopy is one of the most powerful means for determining the structure and dynamics of membrane bound biomolecules such as antibacterial biomolecules and amyloidogenic proteins; unlike X-ray crystallography and solution NMR spectroscopy, applications of solid-state NMR spectroscopy are not limited by non-crystalline, non-soluble nature or molecular size of membrane-associated biomolecules. This review article focuses on the applications of solid-state NMR techniques to study a few selected antibacterial and amyloid peptides. Solid-state NMR studies revealing the membrane inserted bent α-helical structure associated with the hemolytic activity of bee venom melittin and the chemical shift oscillation analysis used to determine the transmembrane structure (with α-helix and 310-helix in the N- and C-termini, respectively) of antibiotic peptide alamethicin are discussed in detail. Oligomerization of an amyloidogenic islet amyloid polypeptide (IAPP, or also known as amylin) resulting from its aggregation in a membrane environment, molecular interactions of the antifungal natural product amphotericin B with ergosterol in lipid bilayers, and the mechanism of lipid raft formation by sphingomyelin studied using solid state NMR methods are also discussed in this review article. This article is part of a Special Issue entitled "Biophysical Exploration of Dynamical Ordering of Biomolecular Systems" edited by Dr. Koichi Kato.

Bidirectional band-selective magnetization transfer along the protein backbone doubles the information content of solid-state NMR correlation experiments

Resonance assignment is the first stage towards solving the structure of a protein. This is normally achieved by the employment of separate inter and intra residue experiments. By utilising the mixed rotation and rotary recoupling (MIRROR) condition it is possible to double the information content through the efficient bidirectional transfer of magnetization from the CO to its adjacent Cα and the Cα of the subsequent amino acid. We have incorporated this into a 3D experiment, a 3D-MIRROR-NCOCA, where correlations present in the 3D spectrum permit the sequential assignment of the protein backbone from a single experiment as we have demonstrated on a microcrystalline preparation of GB3. Furthermore, the low-power requirements of the MIRROR recoupling sequence facilitate the development of a low-power 3D-NCOCA experiment. This has enabled us to realise significant reductions in acquisition times, allowing the acquisition of a single 3D-NCOCA spectrum suitable for a full backbone resonance assignment of GB3 in less than 24 h.

Emerging Structural Understanding of Amyloid Fibrils by Solid-State NMR

Amyloid structures at atomic resolution have remained elusive mainly because of their extensive polymorphism and because their polymeric properties have hampered structural studies by classical approaches. Progress in sample preparation, as well as solid-state NMR methods, recently enabled the determination of high-resolution 3D structures of fibrils such as the amyloid-β fibril, which is involved in Alzheimer's disease. Notably, the simultaneous but independent structure determination of Aβ1-42, a peptide that forms fibrillar deposits in the brain of Alzheimer patients, by two independent laboratories, which yielded virtually identical results, has highlighted how structures can be obtained that allow further functional investigation.

Selective 1H-1H Distance Restraints in Fully Protonated Proteins by Very Fast Magic-Angle Spinning Solid-State NMR

Very fast magic-angle spinning (MAS > 80 kHz) NMR combined with high-field magnets has enabled the acquisition of proton-detected spectra in fully protonated solid samples with sufficient resolution and sensitivity. One of the primary challenges in structure determination of protein is observing long-range ¹H-¹H contacts. Here we use band-selective spin-lock pulses to obtain selective ¹H-¹H contacts (e.g., H^N-H^N) on the order of 5-6 Å in fully protonated proteins at 111 kHz MAS. This approach is a major advancement in structural characterization of proteins given that magnetization can be selectively transferred between protons that are 5-6 Å apart despite the presence of other protons at shorter distance. The observed contacts are similar to those previously observed only in perdeuterated proteins with selective protonation. Simulations and experiments show the proposed method has performance that is superior to that of the currently used methods. The method is demonstrated on GB1 and a β-barrel membrane protein, AlkL.

Accelerating proton spin diffusion in perdeuterated proteins at 100 kHz MAS

Fast magic-angle spinning (>60 kHz) has many advantages but makes spin-diffusion-type proton-proton long-range polarization transfer inefficient and highly dependent on chemical-shift offset. Using 100%-HN-[²H,¹³C,¹⁵N]-ubiquitin as a model substance, we quantify the influence of the chemical-shift difference on the spin diffusion between proton spins and compare two experiments which lead to an improved chemical-shift compensation of the transfer: rotating-frame spin diffusion and a new experiment, reverse amplitude-modulated MIRROR. Both approaches enable broadband spin diffusion, but the application of the first variant is limited due to fast spin relaxation in the rotating frame. The reverse MIRROR experiment, in contrast, is a promising candidate for the determination of structurally relevant distance restraints. The applied tailored rf-irradiation schemes allow full control over the range of recoupled chemical shifts and efficiently drive spin diffusion. Here, the relevant relaxation time is the larger longitudinal relaxation time, which leads to a higher signal-to-noise ratio in the spectra.

Solid-state NMR chemical-shift perturbations indicate domain reorientation of the DnaG primase in the primosome of Helicobacter pylori

We here investigate the interactions between the DnaB helicase and the C-terminal domain of the corresponding DnaG primase of Helicobacter pylori using solid-state NMR. The difficult crystallization of this 387 kDa complex, where the two proteins interact in a six to three ratio, is circumvented by simple co-sedimentation of the two proteins directly into the MAS-NMR rotor. While the amount of information that can be extracted from such a large protein is still limited, we can assign a number of amino-acid residues experiencing significant chemical-shift perturbations upon helicase-primase complex formation. The location of these residues is used as a guide to model the interaction interface between the two proteins in the complex. Chemical-shift perturbations also reveal changes at the interaction interfaces of the hexameric HpDnaB assembly on HpDnaG binding. A structural model of the complex that explains the experimental findings is obtained.

Strategies for solid-state NMR investigations of supramolecular assemblies with large subunit sizes

Solid-state NMR is a versatile tool to study structure and dynamics of insoluble and non-crystalline biopolymers. Supramolecular protein assemblies are formed by self-association of multiple copies of single small-sized proteins. Because of their high degree of local order, solid-state NMR spectra of such systems exhibit an unusually high level of resolution, rendering them an ideal target for solid-state NMR investigations. Recently, our group has solved the structure of one particular supramolecular assembly, the type-iii-secretion-system needle. The needle subunit comprises around 80 residues. Many interesting supramolecular assemblies with unknown structure have subunits larger in size, which requires development of tailored solid-state NMR strategies to address their structures. In this "Perspective" article, we provide a view on different approaches to enhance sensitivity and resolution in biological solid-state NMR with a focus on the possible application to supramolecular assemblies with large subunit sizes.

Spinning proteins, the faster, the better?

Magic-angle spinning (MAS) is a technique that is a prerequisite for high-resolution solid-state NMR spectroscopy of proteins and other biomolecules. Recently, the 100 kHz limit for the rotation frequency has been broken, arguably making MAS rotors the man-made objects with the highest rotation frequency. This development is expected to have a significant impact on biomolecular NMR as it facilitates proton detection, which allows to partially compensate the loss in overall sensitivity associated with the small sample amounts that fit into MAS rotors with less than 1 mm outer diameter. Under these conditions, the mass-normalized sensitivity of a small rotor becomes much higher than that of larger-volume rotor.

Magic angle spinning NMR of proteins: high-frequency dynamic nuclear polarization and (1)H detection

Magic angle spinning (MAS) NMR studies of amyloid and membrane proteins and large macromolecular complexes are an important new approach to structural biology. However, the applicability of these experiments, which are based on (13)C- and (15)N-detected spectra, would be enhanced if the sensitivity were improved. Here we discuss two advances that address this problem: high-frequency dynamic nuclear polarization (DNP) and (1)H-detected MAS techniques. DNP is a sensitivity enhancement technique that transfers the high polarization of exogenous unpaired electrons to nuclear spins via microwave irradiation of electron-nuclear transitions. DNP boosts NMR signal intensities by factors of 10(2) to 10(3), thereby overcoming NMR's inherent low sensitivity. Alternatively, it permits structural investigations at the nanomolar scale. In addition, (1)H detection is feasible primarily because of the development of MAS rotors that spin at frequencies of 40 to 60 kHz or higher and the preparation of extensively (2)H-labeled proteins.

Combined zero-quantum and spin-diffusion mixing for efficient homonuclear correlation spectroscopy under fast MAS: broadband recoupling and detection of long-range correlations

Fast magic angle spinning (MAS) NMR spectroscopy is emerging as an essential analytical and structural biology technique. Large resolution and sensitivity enhancements observed under fast MAS conditions enable structural and dynamics analysis of challenging systems, such as large macromolecular assemblies and isotopically dilute samples, using only a fraction of material required for conventional experiments. Homonuclear dipolar-based correlation spectroscopy constitutes a centerpiece in the MAS NMR methodological toolbox, and is used essentially in every biological and organic system for deriving resonance assignments and distance restraints information necessary for structural analysis. Under fast MAS conditions (rotation frequencies above 35-40 kHz), dipolar-based techniques that yield multi-bond correlations and non-trivial distance information are ineffective and suffer from low polarization transfer efficiency. To overcome this limitation, we have developed a family of experiments, CORD-RFDR. These experiments exploit the advantages of both zero-quantum RFDR and spin-diffusion based CORD methods, and exhibit highly efficient and broadband dipolar recoupling across the entire spectrum, for both short-range and long-range correlations. We have verified the performance of the CORD-RFDR sequences experimentally on a U-(13)C,(15)N-MLF tripeptide and by numerical simulations. We demonstrate applications of 2D CORD-RFDR correlation spectroscopy in dynein light chain LC8 and HIV-1 CA tubular assemblies. In the CORD-RFDR spectra of LC8 acquired at the MAS frequency of 40 kHz, many new intra- and inter-residue correlations are detected, which were not observed with conventional dipolar recoupling sequences. At a moderate MAS frequency of 14 kHz, the CORD-RFDR experiment exhibits excellent performance as well, as demonstrated in the HIV-1 CA tubular assemblies. Taken together, the results indicate that CORD-RFDR experiment is beneficial in a broad range of conditions, including both high and moderate MAS frequencies and magnetic fields.

Recent advances in magic angle spinning solid state NMR of membrane proteins

Membrane proteins mediate many critical functions in cells. Determining their three-dimensional structures in the native lipid environment has been one of the main objectives in structural biology. There are two major NMR methodologies that allow this objective to be accomplished. Oriented sample NMR, which can be applied to membrane proteins that are uniformly aligned in the magnetic field, has been successful in determining the backbone structures of a handful of membrane proteins. Owing to methodological and technological developments, Magic Angle Spinning (MAS) solid-state NMR (ssNMR) spectroscopy has emerged as another major technique for the complete characterization of the structure and dynamics of membrane proteins. First developed on peptides and small microcrystalline proteins, MAS ssNMR has recently been successfully applied to large membrane proteins. In this review we describe recent progress in MAS ssNMR methodologies, which are now available for studies of membrane protein structure determination, and outline a few examples, which highlight the broad capability of ssNMR spectroscopy.

Efficient and stable reconstitution of the ABC transporter BmrA for solid-state NMR studies

We present solid-state NMR sample preparation and first 2D spectra of the Bacillus subtilis ATP-binding cassette (ABC) transporter BmrA, a membrane protein involved in multidrug resistance. The homodimeric 130-kDa protein is a challenge for structural characterization due to its membrane-bound nature, size, inherent flexibility and insolubility. We show that reconstitution of this protein in lipids from Bacillus subtilis at a lipid-protein ratio of 0.5 w/w allows for optimal protein insertion in lipid membranes with respect to two central NMR requirements, high signal-to-noise in the spectra and sample stability over a time period of months. The obtained spectra point to a well-folded protein and a highly homogenous preparation, as witnessed by the narrow resonance lines and the signal dispersion typical for the expected secondary structure distribution of BmrA. This opens the way for studies of the different conformational states of the transporter in the export cycle, as well as on interactions with substrates, via chemical-shift fingerprints and sequential resonance assignments.

BSH-CP based 3D solid-state NMR experiments for protein resonance assignment

We have recently presented band-selective homonuclear cross-polarization (BSH-CP) as an efficient method for CO-CA transfer in deuterated as well as protonated solid proteins. Here we show how the BSH-CP CO-CA transfer block can be incorporated in a set of three-dimensional (3D) solid-state NMR (ssNMR) pulse schemes tailored for resonance assignment of proteins at high static magnetic fields and moderate magic-angle spinning rates. Due to the achieved excellent transfer efficiency of 33 % for BSH-CP, a complete set of 3D spectra needed for unambiguous resonance assignment could be rapidly recorded within 1 week for the model protein ubiquitin. Thus we expect that BSH-CP could replace the typically used CO-CA transfer schemes in well-established 3D ssNMR approaches for resonance assignment of solid biomolecules.

Mechanism of dilute-spin-exchange in solid-state NMR

In the stationary, aligned samples used in oriented sample (OS) solid-state NMR, (1)H-(1)H homonuclear dipolar couplings are not attenuated as they are in magic angle spinning solid-state NMR; consequently, they are available for participation in dipolar coupling-based spin-exchange processes. Here we describe analytically the pathways of (15)N-(15)N spin-exchange mediated by (1)H-(1)H homonuclear dipolar couplings. The mixed-order proton-relay mechanism can be differentiated from the third spin assisted recoupling mechanism by setting the (1)H to an off-resonance frequency so that it is at the "magic angle" during the spin-exchange interval in the experiment, since the "magic angle" irradiation nearly quenches the former but only slightly attenuates the latter. Experimental spectra from a single crystal of N-acetyl leucine confirm that this proton-relay mechanism plays the dominant role in (15)N-(15)N dilute-spin-exchange in OS solid-state NMR in crystalline samples. Remarkably, the "forbidden" spin-exchange condition under "magic angle" irradiation results in (15)N-(15)N cross-peaks intensities that are comparable to those observed with on-resonance irradiation in applications to proteins. The mechanism of the proton relay in dilute-spin-exchange is crucial for the design of polarization transfer experiments.

Exploring various modulation-sideband recoupling conditions of SHA+ sequence at fast MAS

We explore modulation-sideband recoupling conditions of the (13)C-(13)C Second-order Hamiltonian among Analogous nuclei plus pulse sequence (SHA+), and found that this sequence can be used in two different recoupling regimes. The first regime, νR>Δνiso(max), is recommended for broad-band recoupling to avoid any rotational resonance broadening. In this regime, the spinning speed should be only slightly larger than Δνiso(max), to obtain the best transfer efficiency. The second regime, νR<Δνiso(max), can be used to observe long-range constraints with lower spinning speed, which increases the transfer efficiency, and may allow using bigger rotors to increase the S/N ratio.

A Floquet description of phase alternated sequences for efficient homonuclear recoupling in solid perdeuterated systems

A Floquet description of a phase alternated homonuclear recoupling scheme for perdeuterated systems is presented. As a result, we demonstrate improvements in the recoupling efficiency of the DOuble Nucleus Enhanced Recoupling [DONER; J. Am. Chem. Soc. 131 (2009) 17054] technique by utilizing Phase Alternated Recoupling Irradiation Schemes [PARIS; Chem. Phys. Lett. 469 (2009) 342]. The effect of proton and deuterium radio frequency irradiation during recoupling has been systematically studied and theoretical observations have been verified experimentally using a deuterated model compound, L-Alanine, at 10 and 20 kHz magic angle spinning frequency. Experimental results are well in agreement with theoretical observations, thereby significantly increasing the recoupling efficiency of conventional DONER in perdeuterated systems.

PAIN with and without PAR: variants for third-spin assisted heteronuclear polarization transfer

In this article, we describe third-spin assisted heteronuclear recoupling experiments, which play an increasingly important role in measuring long-range heteronuclear couplings, in particular (15)N-(13)C, in proteins. In the proton-assisted insensitive nuclei cross polarization (PAIN-CP) experiment (de Paëpe et al. in J Chem Phys 134:095101, 2011), heteronuclear polarization transfer is always accompanied by homonuclear transfer of the proton-assisted recoupling (PAR) type. We present a phase-alternating experiment that promotes heteronuclear (e.g. (15)N → (13)C) polarization transfer while simultaneously minimizing homonuclear (e.g.(13)C → (13)C) transfer (PAIN without PAR). This minimization of homonuclear polarization transfer is based on the principle of the resonant second-order transfer (RESORT) recoupling scheme where the passive proton spins are irradiated by a phase-alternating sequence and the modulation frequency is matched to an integer multiple of the spinning frequency. The similarities and differences between the PAIN-CP and this het-RESORT experiment are discussed here.

Efficient band-selective homonuclear CO-CA cross-polarization in protonated proteins

Previously introduced for highly deuterated proteins, band-selective magnetization transfer between CO and CA spins by dipolar-based homonuclear cross polarization is applied here to a protonated protein. Robust and efficient recoupling is achieved when the sum of effective radio-frequency fields on CO and CA resonances equals two times the spinning rate, yielding up to 33% of magnetization transfer efficiency in protonated ubiquitin. The approach is designed for moderate magic-angle spinning rates and high external magnetic fields when the isotropic chemical shift difference of CO and CA considerably exceeds the spinning rate. This method has been implemented in NiCOi-1CAi-1 and CAi(Ni)COi-1CAi-1 two-dimensional interresidual correlation experiments for fast and efficient resonance assignment of ubiquitin by solid-state NMR spectroscopy.

Broadband homonuclear correlation spectroscopy driven by combined R2(n)(v) sequences under fast magic angle spinning for NMR structural analysis of organic and biological solids

We recently described a family of experiments for R2n(v) Driven Spin Diffusion (RDSD) spectroscopy suitable for homonuclear correlation experiments under fast MAS conditions [G. Hou, S. Yan, S.J. Sun, Y. Han, I.J. Byeon, J. Ahn, J. Concel, A. Samoson, A.M. Gronenborn, T. Polenova, Spin diffusion drive by R-symmetry sequencs: applications to homonuclear correlation spectroscopy in MAS NMR of biological and organic solids, J. Am. Chem. Soc. 133 (2011) 3943-3953]. In these RDSD experiments, since the broadened second-order rotational resonance conditions are dominated by the radio frequency field strength and the phase shifts, as well as the size of reintroduced dipolar couplings, the different R2n(v) sequences display unique polarization transfer behaviors and different recoupling frequency bandwidths. Herein, we present a series of modified R2n(v) sequences, dubbed COmbined R2n(v)-Driven (CORD), that yield broadband homonuclear dipolar recoupling and give rise to uniform distribution of cross peak intensities across the entire correlation spectrum. We report NMR experiments and numerical simulations demonstrating that these CORD spin diffusion sequences are suitable for broadband recoupling at a wide range of magnetic fields and MAS frequencies, including fast-MAS conditions (νr=40 kHz and above). Since these CORD sequences are largely insensitive to dipolar truncation, they are well suited for the determination of long-range distance constraints, which are indispensable for the structural characterization of a broad range of systems. Using U-(13)C,(15)N-alanine and U-(13)C,(15)N-histidine, we show that under fast-MAS conditions, the CORD sequences display polarization transfer efficiencies within broadband frequency regions that are generally higher than those offered by other existing spin diffusion pulse schemes. A 89-residue U-(13)C,(15)N-dynein light chain (LC8) protein has also been used to demonstrate that the CORD sequences exhibit uniformly high cross peak intensities across the entire chemical shift range.