Homonuclear dipolar recoupling techniques for structure determination in uniformly 13C-labeled proteins

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.

Serial Polarization Transfer by Combination of Cross-Relaxation and Rotational Resonance for Sensitivity-Enhanced Solid-State NMR

Methods which induce site-specificity and sensitivity enhancement in solid-state magic-angle spinning NMR spectroscopy become more important for structural biology due to the increasing size of molecules under investigation. Recently, several strategies have been developed to increase site specificity and thus reduce signal overlap. Under dynamic nuclear polarization (DNP) for NMR signal enhancement, it is possible to use cross-relaxation transfer induced by select dynamic groups within the molecules which is exploited by SCREAM-DNP (Specific Cross Relaxation Enhancement by Active Motions under DNP). Here, we present an approach where we additionally reintroduce the homonuclear dipolar coupling with rotational resonance (R2 ) during SCREAM-DNP to further boost the selectivity of the experiment. Detailed analysis of the polarization buildup dynamics of 13 C-methyl polarization source and 13 C-carbonyl target in 2-13 C-ethyl 1-13 C-acetate provides information about the sought-after and spurious transfer pathways. We show that dipolar-recoupled transfer rates greatly exceed the DNP buildup dynamics in our model system, indicating that significantly larger distances can be selectively and efficiently hyperpolarized.

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.

Integrated Assessment of the Structure and Dynamics of Solid Proteins

Understanding macromolecular function, interactions, and stability hinges on detailed assessment of conformational ensembles. For solid proteins, accurate elucidation of the spatial aspects of dynamics at physiological temperatures is limited by the qualitative character or low abundance of solid-state nuclear magnetic resonance internuclear distance information. Here, we demonstrate access to abundant proton-proton internuclear distances for integrated structural biology and chemistry with unprecedented accuracy. Apart from highest-resolution single-state structures, the exact distances enable molecular dynamics (MD) ensemble simulations orchestrated by a dense network of experimental interproton distance boundaries gathered in the context of their physical lattices. This direct embedding of experimental ensemble distances into MD will provide access to representative, atomic-level spatial details of conformational dynamics in supramolecular assemblies, crystalline and lipid-embedded proteins, and beyond.

Supercycled R-symmetry sequences for robust heteronuclear polarization transfer in solid-state NMR

Herein, we introduce supercycle of R-symmetry sequences (SR-sequences) and incomplete supercycle schemes of R-symmetry sequences (iSR-I- and iSR-II-sequences) to improve the robustness of PRESTO for heteronuclear polarization transfer in MAS NMR. The constructions of SR- and iSR-I/II- sequences are based on the different phase-inverted supercycles of R-symmetry sequences, and such supercycles can suppress the influence of CSA, resonance offset and RF mismatch when incorporated into the PRESTO method. Moreover, the SR- and iSR-II-sequences are more efficient in suppressing the interference of homonuclear dipolar coupling. The improved robustness of SR-, iSR-I- and iSR-II-PRESTO over the original R-PRESTO has been verified by numerical simulations and NMR experiments on NH₄H₂PO₄ and gamma-alumina at fast MAS conditions. It is also important to note that the SR- and iSR-II-PRESTO can greatly lengthen the transverse relaxation times and lead to much higher polarization transfer efficiency compared to R-PRESTO, thanks to their superior tolerance to RF inhomogeneity and homonuclear dipolar coupling.

Mechanism of selective polarization exchange amongst chemically similar and distinct protons during weak rf irradiation at fast magic angle spinning

Band Selective Spectral Spin-Diffusion (BASS-SD) is a method to obtain selective ¹H-¹H contacts between chemically similar protons within a distance range of 5-6 Å in fully protonated proteins. BASS-SD combines low-amplitude proton spinlock radio frequency (rf) pulses with fast MAS frequency to enable selective polarization exchange in fully protonated molecules. The selectivity of transfer is dictated by the bandwidth of the spinlock pulse and has been used to observe selective H^N-H^N, H^α-Η^α and H^methyl-H^methyl correlations. These proton-proton spatial contacts are similar to those observed in perdeuterated samples and serve as useful structural restraints towards de novo protein structure determination. This study employs bimodal Floquet theory to derive the first- and second-order effective Hamiltonians necessary to understand the spin dynamics during BASS-SD. Analytical calculations combined with numerical simulations delineate two different mechanisms for polarization transfer amongst the proton spins. The BASS-SD recoupling condition has been reoptimized to observe selective correlations between chemically different protons (e.g., H^N-H^α) while retaining the spatial contacts between chemically similar protons (e.g., H^N-H^N). The new BASS-SD condition is integrated with simultaneous and sequential acquisition approaches to generate four different types of structural restraints (H^N-H^N, H^α-Η^α, H^N-H^α, H^α-H^N) in one experiment. The approach has been demonstrated on microcrystalline U-[¹³C,¹⁵N] labeled GB1 protein at ∼ 95-100 kHz MAS.

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.

Refined Structures of O-Phospho-l-serine and Its Calcium Salt by New Multinuclear Solid-State NMR Crystallography Methods

O-phospho-l-serine (Pser) and its Ca salt, Ca[O-phospho-l-serine]·H2O (CaPser), play important roles for bone mineralization and were recently also proposed to account for the markedly improved bone-adhesive properties of Pser-doped calcium phosphate-based cements for biomedical implants. However, the hitherto few proposed structural models of Pser and CaPser were obtained by X-ray diffraction, thereby leaving the proton positions poorly defined. Herein, we refine the Pser and CaPser structures by density functional theory (DFT) calculations and contrast them with direct interatomic-distance constraints from two-dimensional (2D) nuclear magnetic resonance (NMR) correlation experimentation at fast magic-angle spinning (MAS), encompassing double-quantum-single-quantum (2Q-1Q) 1H NMR along with heteronuclear 13C{1H} and 31P{1H} correlation NMR experiments. The Pser and CaPser structures before and after refinements by DFT were validated against sets of NMR-derived effective 1H-1H, 1H-31P, and 1H-13C distances, which confirmed the improved accuracy of the refined structures. Each distance set was derived from one sole 2D NMR experiment applied to a powder without isotopic enrichment. The distances were extracted without invoking numerical spin-dynamics simulations or approximate phenomenological models. We highlight the advantages and limitations of the new distance-extraction procedure. Isotropic 1H, 13C, and 31P chemical shifts obtained by DFT calculations using the gauge including projector augmented wave (GIPAW) method agreed very well with the experimental results. We discuss the isotropic and anisotropic 13C and 31P chemical-shift parameters in relation to the previous literature, where most data on CaPser are reported herein for the first time.

Selective 1H-1H recoupling via symmetry sequences in fully protonated samples at fast magic angle spinning

Proton-detected solid-state NMR at fast Magic Angle Spinning (MAS) is becoming the norm to characterize molecules. Routinely ¹H-¹H and ¹H-X dipolar couplings are used to characterize the structure and dynamics of molecules. Selective proton recoupling techniques are emerging as a method for structural characterization via estimation of qualitative and quantitative distances. In the present study, we demonstrate through numerical simulations and experiments that the well-characterized CN^v_n sequences can also be tailored for selective recoupling of proton spins by employing C elements of the type (β)_Φ(4β)_Φ+π(3β)_Φ. Herein, several CN^v_n sequences were examined through numerical simulations and experiments. C6¹₄ recoupling sequence with a modified POST-element ((β)_Φ(4β)_Φ+π(3β)_Φ) shows selective polarization transfer efficiencies on the order of 40-50% between various proton spin pairs in fully protonated samples at rf amplitudes ranging from 0.3 to 0.8 times the MAS frequency. These selective recoupling sequences have been labeled as frequency-selective-CN^v_n sequences. The extent of selectivity, polarization transfer efficiency and the feasibility of experimentally measuring proton-proton distances in fully protonated samples are explored here. The development of efficient and robust selective ¹H-¹H recoupling experiments is required to structurally characterize molecules without artificial isotope enrichment or the need for diffracting crystals.

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

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

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.

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

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

Reducing the computational cost of NMR crystallography of organic powders at natural isotopic abundance with the help of 13 C-13 C dipolar couplings

Structure determination of functional organic compounds remains a formidable challenge when the sample exists as a powder. Nuclear magnetic resonance crystallography approaches based on the comparison of experimental and Density Functional Theory (DFT)-computed ¹ H chemical shifts have already demonstrated great potential for structure determination of organic powders, but limitations still persist. In this study, we discuss the possibility of using ¹³ C-¹³ C dipolar couplings quantified on powdered theophylline at natural isotopic abundance with the help of dynamic nuclear polarization, to realize a DFT-free, rapid screening of a pool of structures predicted by ab initio random structure search. We show that although ¹³ C-¹³ C dipolar couplings can identify structures possessing long range structural motifs and unit cell parameters close to those of the true structure, it must be complemented with other data to recover information about the presence and the chemical nature of the supramolecular interactions.

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.

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.

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

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

Optimizing symmetry-based recoupling sequences in solid-state NMR by pulse-transient compensation and asynchronous implementation

Pulse imperfections like pulse transients and radio-frequency field maladjustment or inhomogeneity are the main sources of performance degradation and limited reproducibility in solid-state nuclear magnetic resonance experiments. We quantitatively analyze the influence of such imperfections on the performance of symmetry-based pulse sequences and describe how they can be compensated. Based on a triple-mode Floquet analysis, we develop a theoretical description of symmetry-based dipolar recoupling sequences, in particular, R26₄¹¹, calculating first- and second-order effective Hamiltonians using real pulse shapes. We discuss the various origins of effective fields, namely, pulse transients, deviation from the ideal flip angle, and fictitious fields, and develop strategies to counteract them for the restoration of full transfer efficiency. We compare experimental applications of transient-compensated pulses and an asynchronous implementation of the sequence to a supercycle, SR26, which is known to be efficient in compensating higher-order error terms. We are able to show the superiority of R26 compared to the supercycle, SR26, given the ability to reduce experimental error on the pulse sequence by pulse-transient compensation and a complete theoretical understanding of the sequence.

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.

Handling the influence of chemical shift in amplitude-modulated heteronuclear dipolar recoupling solid-state NMR

We present a theoretical analysis of the influence of chemical shifts on amplitude-modulated heteronuclear dipolar recoupling experiments in solid-state NMR spectroscopy. The method is demonstrated using the Rotor Echo Short Pulse IRrAdiaTION mediated Cross-Polarization ((RESPIRATION)CP) experiment as an example. By going into the pulse sequence rf interaction frame and employing a quintuple-mode operator-based Floquet approach, we describe how chemical shift offset and anisotropic chemical shift affect the efficiency of heteronuclear polarization transfer. In this description, it becomes transparent that the main attribute leading to non-ideal performance is a fictitious field along the rf field axis, which is generated from second-order cross terms arising mainly between chemical shift tensors and themselves. This insight is useful for the development of improved recoupling experiments. We discuss the validity of this approach and present quaternion calculations to determine the effective resonance conditions in a combined rf field and chemical shift offset interaction frame transformation. Based on this, we derive a broad-banded version of the (RESPIRATION)CP experiment. The new sequence is experimentally verified using SNNFGAILSS amyloid fibrils where simultaneous (15)N → (13)CO and (15)N → (13)Cα coherence transfer is demonstrated on high-field NMR instrumentation, requiring great offset stability.

Improved transfer efficiencies in radio-frequency-driven recoupling solid-state NMR by adiabatic sweep through the dipolar recoupling condition

The homonuclear radio-frequency driven recoupling (RFDR) experiment is commonly used in solid-state NMR spectroscopy to gain insight into the structure of biological samples due to its ease of implementation, stability towards fluctuations/missetting of radio-frequency (rf) field strength, and in general low rf requirements. A theoretical operator-based Floquet description is presented to appreciate the effect of having a temporal displacement of the π-pulses in the RFDR experiment. From this description, we demonstrate improved transfer efficiency for the RFDR experiment by generating an adiabatic passage through the zero-quantum recoupling condition. We have compared the performances of RFDR and the improved sequence to mediate efficient (13)CO to (13)Cα polarization transfer for uniformly (13)C,(15)N-labeled glycine and for the fibril forming peptide SNNFGAILSS (one-letter amino acid codes) uniformly (13)C,(15)N-labeled at the FGAIL residues. Using numerically optimized sweeps, we get experimental gains of approximately 20% for glycine where numerical simulations predict an improvement of 25% relative to the standard implementation. For the fibril forming peptide, using the same sweep parameters as found for glycine, we have gains in the order of 10%-20% depending on the spectral regions of interest.

Low-power broadband homonuclear dipolar recoupling in MAS NMR by two-fold symmetry pulse schemes for magnetization transfers and double-quantum excitation

We provide an experimental, numerical, and high-order average Hamiltonian evaluation of an open-ended series of homonuclear dipolar recoupling sequences, SR [Formula: see text] with p=1,2,3,…. While operating at a very low radio-frequency (rf) power, corresponding to a nutation frequency of 1/2 of the magic-angle spinning (MAS) rate (ωnut=ωr/2), these recursively generated double-quantum (2Q) dipolar recoupling schemes offer a progressively improved compensation to resonance offsets and rf inhomogeneity for increasing pulse-sequence order p. The excellent recoupling robustness to these experimental obstacles, as well as to CSA, is demonstrated for 2Q filtering (2QF) experiments and for driving magnetization transfers in 2D NMR correlation spectroscopy, where the sequences may provide either double or zero quantum dipolar Hamiltonians during mixing. Experimental and numerical demonstrations, which mostly target conditions of "ultra-fast" MAS (≳50kHz) and high magnetic fields, are provided for recoupling of (13)C across a wide range of isotropic and anisotropic chemical shifts, as well as dipolar coupling constants, encompassing [2,3-(13)C2]alanine, [1,3-(13)C2]alanine, diammonium [1,4-(13)C2]fumarate, and [U-(13)C]tyrosine. When compared at equal power levels, a superior performance is observed for the SR [Formula: see text] sequences with p⩾3 relative to existing and well-established 2Q recoupling techniques. At ultra-fast MAS, proton decoupling is redundant during the homonuclear dipolar recoupling of dilute spins in organic solids, which renders the family of SR [Formula: see text] schemes the first efficient 2Q recoupling option for general applications, such as 2Q-1Q correlation NMR and high-order multiple-quantum excitation, under truly low-power rf conditions.

Dynamics-based selective 2D (1)H/(1)H chemical shift correlation spectroscopy under ultrafast MAS conditions

Dynamics plays important roles in determining the physical, chemical, and functional properties of a variety of chemical and biological materials. However, a material (such as a polymer) generally has mobile and rigid regions in order to have high strength and toughness at the same time. Therefore, it is difficult to measure the role of mobile phase without being affected by the rigid components. Herein, we propose a highly sensitive solid-state NMR approach that utilizes a dipolar-coupling based filter (composed of 12 equally spaced 90° RF pulses) to selectively measure the correlation of (1)H chemical shifts from the mobile regions of a material. It is interesting to find that the rotor-synchronized dipolar filter strength decreases with increasing inter-pulse delay between the 90° pulses, whereas the dipolar filter strength increases with increasing inter-pulse delay under static conditions. In this study, we also demonstrate the unique advantages of proton-detection under ultrafast magic-angle-spinning conditions to enhance the spectral resolution and sensitivity for studies on small molecules as well as multi-phase polymers. Our results further demonstrate the use of finite-pulse radio-frequency driven recoupling pulse sequence to efficiently recouple weak proton-proton dipolar couplings in the dynamic regions of a molecule and to facilitate the fast acquisition of (1)H/(1)H correlation spectrum compared to the traditional 2D NOESY (Nuclear Overhauser effect spectroscopy) experiment. We believe that the proposed approach is beneficial to study mobile components in multi-phase systems, such as block copolymers, polymer blends, nanocomposites, heterogeneous amyloid mixture of oligomers and fibers, and other materials.

Quantitative structural constraints for organic powders at natural isotopic abundance using dynamic nuclear polarization solid-state NMR spectroscopy

A straightforward method is reported to quantitatively relate structural constraints based on (13)C-(13)C double-quantum build-up curves obtained by dynamic nuclear polarization (DNP) solid-state NMR to the crystal structure of organic powders at natural isotopic abundance. This method relies on the significant gain in NMR sensitivity provided by DNP (approximately 50-fold, lowering the experimental time from a few years to a few days), and is sensitive to the molecular conformation and crystal packing of the studied powder sample (in this case theophylline). This method allows trial crystal structures to be rapidly and effectively discriminated, and paves the way to three-dimensional structure elucidation of powders through combination with powder X-ray diffraction, crystal-structure prediction, and density functional theory computation of NMR chemical shifts.

Probing crystal packing of uniformly (13)C-enriched powder samples using homonuclear dipolar coupling measurements

The relationship between the crystal packing of powder samples and long-range (13)C-(13)C homonuclear dipolar couplings is presented and illustrated for the case of uniformly (13)C-enriched L-alanine and L-histidine·HCl·H2O. Dipolar coupling measurement is based on the partial reintroduction of dipolar interactions by spinning the sample slightly off-magic-angle, while the coupling of interest for a given spin pair is isolated with a frequency-selective pulse. A cost function is used to correlate the so-derived dipolar couplings to trial crystal structures of the samples under study. This procedure allowed for the investigation of the l-alanine space group and L-histidine·HCl·H2O space group and unit-cell parameters.

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.

Broad-Band DREAM Recoupling Sequence

We describe a more broad-banded version of the DREAM double-quantum dipolar-recoupling sequence, which is devised by superimposing a phase-alternating RF irradiation scheme, that is, XiX pulses, on top of the original DREAM sequence. We call this sequence XiX(CW) DREAM. The recoupling conditions and the corresponding first-order effective Hamiltonian are analyzed using triple-mode Floquet theory. The performance of the XiX(CW) DREAM sequence is compared to the original DREAM sequence by numerical simulations and experiments on small model substances and the model protein ubiquitin. The results confirm that XiX(CW) DREAM shows a wider recoupling bandwidth compared to that of DREAM, therefore making the choice for the position of the carrier frequency less critical.

Improved decoupling during symmetry-based C9-TOBSY sequences

We show that heteronuclear decoupling during symmetry-based C9 TOBSY sequences can be improved by using phase-alternating pulse sequences (XiX) instead of cw irradiation. The use of XiX sequences makes the optimization of the decoupling rf-field amplitude simpler and lowers the decoupling rf-field requirements to attain a comparable performance. A Floquet analysis of the first-order resonance conditions was used to determine the correct timing of the XiX sequence to avoid interference between the C sequence and the decoupling. The decoupling performance is analyzed analytically using Floquet theory and verified using numerical simulations as well as experimental results.

Central-transition double-quantum sideband NMR spectroscopy of half-integer quadrupolar nuclei: estimating internuclear distances and probing clusters within multi-spin networks

Clusters within quadrupolar spin networks are probed and internuclear distances between quadrupolar nuclei are estimated by central-transition double-quantum sideband NMR spectroscopy.

Selective inversion of 1H resonances in solid-state nuclear magnetic resonance: Use of double-DANTE pulse sequence

We here present a method based on DANTE pulses and homonuclear dipolar decoupling scheme to invert selectively any desired resonance in a proton spin system under magic-angle spinning. Experimental results are reported on a sample of L-histidine·HCl·H2O at magic-angle spinning frequencies of 15 and 60kHz. The results are also substantiated numerically.

Adiabatic Rotor-Echo-Short-Pulse-Irradiation mediated cross-polarization

We present a new dipolar recoupling method for efficient and robust heteronuclear polarization transfer in solid-state NMR under magic-angle-spinning (MAS) conditions. The method combines the recent (RESPIRATION)CP method with a modulation of the amplitude of the rotor-synchronized pulses at one of the involved rf channels through the recoupling condition. In this manner, it is possible to achieve high transfer efficiencies while maintaining robustness towards rf-field inhomogeneities and resonance offsets. The performance of the so-called adiabatic-(RESPIRATION)CP experiment is demonstrated numerically and experimentally using uniformly (13)C,(15)N-labeled samples of alanine and ubiquitin. In particular for cases with relatively high rf inhomogeneity, the scheme offers advantages over the commonly used dipolar recoupling pulse sequences.

Multiple-quantum spin counting in magic-angle-spinning NMR via low-power symmetry-based dipolar recoupling

By using a symmetry-based R2(8)(1)R2(8)(-1) double-quantum (2Q) dipolar recoupling sequence, we demonstrate high-order multiple-quantum coherence (MQC) excitation at fast magic-angle spinning (MAS) frequencies up to 34 kHz. This scheme combines several attractive features, such as a relatively high dipolar scaling factor, good compensation to rf-errors, isotropic and anisotropic chemical shifts, as well as an ultra-low radio-frequency (rf) power requirement. The latter translates into nutation frequencies below 30 kHz for MAS rates up to 60 kHz, thereby permitting rf application for very long excitation periods without risk of damaging the NMR probehead or sample, while the compensation to chemical shifts improves as the MAS rate increases. (31)P MQC spin counting is demonstrated on powders of calcium hydroxyapatite (Ca5(PO4)3OH) and anhydrous sodium diphosphate (Na4P2O7), from which all even coherence orders up to 30 and 14 were detected, respectively, over the respective MAS ranges of 15-24 kHz and 20-34 kHz. The amplitude distributions among the (31)P MQC orders depend on the precise nutation frequency during recoupling, despite that the highest detected order was relatively insensitive to this parameter. An observed gradual transition from a Gaussian to exponential functionality of the MQC amplitude-profile is discussed in relation to the prevailing approach to derive spin-cluster sizes by fitting the MQC amplitude-distribution to a Gaussian decay, where minor systematic deviations between the model and experimental data are frequently reported.

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.

Spinning-rate encoded chemical shift correlations from rotational resonance solid-state NMR experiments

Structural measurements in magic-angle-spinning (MAS) solid-state NMR rely heavily on (13)C-(13)C distance measurements. Broadbanded recoupling methods are used to generate many cross-peaks, but have complex polarization transfer mechanisms that limit the precision of distance constraints and can suffer from weak intensities for distant peaks due to relaxation, the broad distribution of polarization, as well as dipolar truncation. Frequency-selective methods that feature narrow-banded recoupling can reduce these effects. Indeed, rotational resonance (R(2)) experiments have found application in many different biological systems, where they have afforded improved precision and accuracy. Unfortunately, a highly selective transfer mechanism also leads to few cross-peaks in the resulting spectra, which complicates the extraction of multiple constraints. R(2)-width (R(2)W) measurements that scan a range of MAS rates to probe the R(2) matching conditions of one or more sites can improve precision, and also permit multiple simultaneous distance measurements. However, multidimensional R(2)W can be very time-consuming. Here, we present an approach that facilitates the acquisition of 2D-like spectra based on a series of 1D R(2)W experiments, by taking advantage of the chemical shift information encoded in the MAS rates where matching occurs. This yields a more time-efficient experiment with many of the benefits of more conventional multidimensional R(2)W measurements. The obtained spectra reveal long-distance (13)C-(13)C cross-peaks resulting from R(2)-mediated polarization transfer. This experiment also enables the efficient setup and targeted implementation of traditional R(2) or R(2)W experiments. Analogous applications may extend to other variable-MAS and frequency-selective solid-state NMR experiments.

(13)C-(13)c homonuclear recoupling in solid-state nuclear magnetic resonance at a moderately high magic-angle-spinning frequency

Two-dimensional (13)C-(13)C correlation experiments are widely employed in structure determination of protein assemblies using solid-state nuclear magnetic resonance. Here, we investigate the process of (13)C-(13)C magnetisation transfer at a moderate magic-angle-spinning frequency of 30 kHz using some of the prominent second-order dipolar recoupling schemes. The effect of isotropic chemical-shift difference and spatial distance between two carbons and amplitude of radio frequency on (1)H channel on the magnetisation transfer efficiency of these schemes is discussed in detail.

Solid-state NMR spectroscopy of proteins

Solid-state NMR spectroscopy proved to be a versatile tool for characterization of structure and dynamics of complex biochemical systems. In particular, magic angle spinning (MAS) solid-state NMR came to maturity for application towards structural elucidation of biological macromolecules. Current challenges in applying solid-state NMR as well as progress achieved recently will be discussed in the following chapter focusing on conceptual aspects important for structural elucidation of proteins.

Constant time tensor correlation experiments by non-gamma-encoded recoupling pulse sequences

Constant-time tensor correlation under magic-angle spinning conditions is an important technique in solid-state nuclear magnetic resonance spectroscopy for the measurements of backbone or side-chain torsion angles of polypeptides and proteins. We introduce a general method for the design of constant-time tensor correlation experiments under magic-angle spinning. Our method requires that the amplitude of the average Hamiltonian must depend on all the three Euler angles bringing the principal axis system to the rotor-fixed frame, which is commonly referred to as non-gamma encoding. We abbreviate this novel approach as COrrelation of Non-Gamma-Encoded Experiment (CONGEE), which exploits the orientation-dependence of non-gamma-encoded sequences with respect to the magic-angle rotation axis. By manipulating the relative orientation of the average Hamiltonians created by two non-gamma-encoded sequences, one can obtain a modulation of the detected signal, from which the structural information can be extracted when the tensor orientations relative to the molecular frame are known. CONGEE has a prominent feature that the number of rf pulses and the total pulse sequence duration can be maintained to be constant so that for torsion angle determination the effects of systematic errors owing to the experimental imperfections and/or T(2) effects could be minimized. As a proof of concept, we illustrate the utility of CONGEE in the correlation between the C' chemical shift tensor and the C(α)-H(α) dipolar tensor for the backbone psi angle determination. In addition to a detailed theoretical analysis, numerical simulations and experiments measured for [U-(13)C, (15)N]-L-alanine and N-acetyl-[U-(13)C, (15)N]-D,L-valine are used to validate our approach at a spinning frequency of 20 kHz.

Measurements of 13C multiple-quantum coherences in amyloid fibrils under magic-angle spinning

The excitation and detection of high-order multiple quantum coherences among (13)C nuclear spins are demonstrated in the samples of [1-(13)C]-L-alanine and (13)C labeled amyloid fibrils at a spinning frequency of 20 kHz. The technique is based on the double-quantum average Hamiltonian prepared by the DRAMA-XY4 pulse sequence. Empirically, we find that multiple supercycles are required to suppress the higher-order effects for real applications. Measurements for the fibril samples formed by the polypeptides of PrP(113-127) provide the first solid-state NMR evidence for the stacking of multiple β-sheet layers at the structural core of amyloid fibrils.