Theory and applications of supercycled symmetry-based recoupling sequences in solid-state nuclear magnetic resonance

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.

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.

t1-noise elimination by continuous chemical shift anisotropy refocusing

Due to their high gyromagnetic ratio, there is considerable interest in measuring distances and correlations involving protons, but such measurements are compounded by the simultaneous recoupling of chemical shift anisotropy (CSA). This secondary recoupling adds additional modulations to the signal intensities that ultimately lead to t₁-noise and signal decay. Recently, Venkatesh et al. demonstrated that the addition of CSA refocusing periods during ¹H-X dipolar recoupling led to sequences with far higher stability and performance. Herein, we describe a related effort and develop a symmetry-based recoupling sequence that continually refocuses the ¹H CSA. This sequence shows superior performance to the regular and t₁-noise eliminated D-HMQC sequences in the case of spin-1/2 nuclei and comparable performance to the later for half-integer quadrupoles.

Highly Efficient Polarizing Agents for MAS-DNP of Proton-Dense Molecular Solids

Efficiently hyperpolarizing proton-dense molecular solids through dynamic nuclear polarization (DNP) solid-state NMR is still an unmet challenge. Polarizing agents (PAs) developed so far do not perform well on proton-rich systems, such as organic microcrystals and biomolecular assemblies. Herein we introduce a new PA, cAsymPol-POK, and report outstanding hyperpolarization efficiency on 12.76 kDa U-¹³ C,¹⁵ N-labeled LecA protein and pharmaceutical drugs at high magnetic fields (up to 18.8 T) and fast magic angle spinning (MAS) frequencies (up to 40 kHz). The performance of cAsymPol-POK is rationalized by MAS-DNP simulations combined with electron paramagnetic resonance (EPR), density functional theory (DFT) and molecular dynamics (MD). This work shows that this new biradical is compatible with challenging biomolecular applications and unlocks the rapid acquisition of ¹³ C-¹³ C and ¹⁵ N-¹³ C correlations of pharmaceutical drugs at natural isotopic abundance, which are key experiments for structure determination.

A modification of γ-encoded RN symmetry pulses for increasing the scaling factor and more accurate measurements of the strong heteronuclear dipolar couplings

Symmetry based γ-encoded RN_n^ν elements are broadly used in magic-angle spinning solid-state NMR experiments to achieve selective recoupling of the heteronuclear dipolar interactions. The recoupled dipolar couplings in such experiments are scaled by a factor, K_sc, which theoretically depends on the chosen symmetry numbers N, n, and ν. However, the maximum theoretical value of K_sc for γ-encoded RN_n^ν pulses is limited to ~0.25, resulting in long RN_n^ν experiment times. Also, the dependence of K_sc on the experimental parameters can result in systematic errors in the experimental determination of the dipolar couplings, especially at low and moderate MAS rates. In this manuscript, we investigate the use of MODifiEd RN_n^ν symmetry (MODERN_n^ν(ϕ_M)) pulses that increase the dipolar scaling factor by at least 1.45 fold compared to γ-encoded RN_n^ν. The second advantage of MODERN_n^ν(ϕ_M) pulses with respect to traditional RN_n^ν pulses is the reduced influence of experimental parameters on K_sc, which allows for more accurate measurement of short-range distances. The robustness of MODERN_n^ν(ϕ_M) is compared with γ-encoded R14₂³ symmetry pulses. The enhanced performance is demonstrated on two uniformly-¹³C-enriched samples, N-acetyl valine and the microcrystalline protein GB1, at a 31.111 kHz MAS rate.

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

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

Enhanced 1H-X D-HMQC performance through improved 1H homonuclear decoupling

The sensitivity of solid-state NMR experiments that utilize ¹H zero-quantum heteronuclear dipolar recoupling, such as D-HMQC, is compromised by poor homonuclear decoupling. This leads to a rapid decay of recoupled magnetization and an inefficient recoupling of long-range dipolar interactions, especially for nuclides with low gyromagnetic ratios. We investigated the use, in symmetry-based ¹H heteronuclear recoupling sequences, of a basic R element that was principally designed for efficient homonuclear decoupling. By shortening the time required to suppress the effects of homonuclear dipolar interactions to the duration of a single inversion pulse, spin diffusion was effectively quenched and long-lived recoupled coherence lifetimes could be obtained. We show, both theoretically and experimentally, that these modified sequences can yield considerable sensitivity improvements over the current state-of-the-art methods and applied them to the indirect detection of ⁸⁹Y in a metal-organic framework.

Atomic-Scale Structure of Mesoporous Silica-Encapsulated Pt and PtSn Nanoparticles Revealed by Dynamic Nuclear Polarization- Enhanced 29Si MAS NMR Spectroscopy

Mesoporous silica encapsulated Pt (Pt@mSiO₂) and PtSn (PtSn@mSiO₂) nanoparticles (NPs) are representatives of a novel class of heterogeneous catalysts with uniform particle size, enhanced catalytic properties, and superior thermal stability. In the ship-in-a-bottle synthesis, PtSn@mSiO₂ intermetallic NPs are derived from Pt@mSiO₂ seeds where the mSiO₂ shell is formed by polymerization of tetraethyl orthosilicate around a tetradecyltrimethylammonium bromide template, a surfactant used to template MCM-41. Incorporation of Sn into the Pt@mSiO₂ seeds is accommodated by chemical etching of the mSiO₂ shell. The effect of this etching on the atomic-scale structure of the mSiO₂ has not been previously examined, nor has the extent of the structural similarity to MCM-41. Here, the quaternary Q², Q³ and Q⁴ sites corresponding to formulas Si(O_1/2)₂(OH)₂, Si(O_1/2)₃(OH)₁ and Si(O_1/2)₄, in MCM-41 and the mesoporous silica of Pt@mSiO₂ and PtSn@mSiO₂ NPs were identified and quantified by conventional and dynamic nuclear polarization enhanced Si-29 Magic Angle Spinning Nuclear Magnetic Resonance (DNP MAS NMR). The connectivity of the -Si-O-Si-network was revealed by DNP enhanced two-dimensional ²⁹Si-²⁹Si correlation spectroscopy.

Simple and Robust Study of Backbone Dynamics of Crystalline Proteins Employing 1H-15N Dipolar Coupling Dispersion

We report a new solid-state multidimensional NMR approach based on the cross-polarization with variable-contact pulse sequence [ Paluch , P. ; Pawlak , T. ; Amoureux , J.-P. ; Potrzebowski , M. J. J. Magn. Reson. 233 , 2013 , 56 ], with ¹H inverse detection and very fast magic angle spinning (ν_R = 60 kHz), dedicated to the measurement of local molecular motions of ¹H-¹⁵N vectors. The introduced three-dimensional experiments, ¹H-¹⁵N-¹H and hCA(N)H, are particularly useful for the study of molecular dynamics of proteins and other complex structures. The applicability and power of this methodology have been revealed by employing as a model sample the GB-1 small protein doped with Na₂CuEDTA. The results clearly prove that the dispersion of ¹H-¹⁵N dipolar coupling constants well correlates with higher order structure of the protein. Our approach complements the conventional studies and offers a fast and reasonably simple method.

Low-power broadband solid-state MAS NMR of 14N

We propose two broadband pulse schemes for ¹⁴N solid-state magic-angle-spinning (MAS) nuclear magnetic resonance (NMR) that achieves (i) complete population inversion and (ii) efficient excitation of the double-quantum spectrum using low-power single-sideband-selective pulses. We give a comprehensive theoretical description of both schemes using a common framework that is based on the jolting-frame formalism of Caravatti et al. [J. Magn. Reson. 55, 88 (1983)]. This formalism is used to determine for the first time that we can obtain complete population inversion of ¹⁴N under low-power conditions, which we do here using single-sideband-selective adiabatic pulses. It is then used to predict that double-quantum coherences can be excited using low-power single-sideband-selective pulses. We then proceed to design a new experimental scheme for double-quantum excitation. The final double-quantum excitation pulse scheme is easily incorporated into other NMR experiments, as demonstrated here for double quantum-single quantum ¹⁴N correlation spectroscopy, and ¹H-¹⁴N dipolar heteronuclear multiple-quantum correlation experiments. These pulses and irradiation schemes are evaluated numerically using simulations on single crystals and full powders, as well as experimentally on ammonium oxalate ((NH₄)₂C₂O₄) at moderate MAS and glycine at ultra-fast MAS. The performance of these new NMR methods is found to be very high, with population inversion efficiencies of 100% and double-quantum excitation efficiencies of 30%-50%, which are hitherto unprecedented for the low radiofrequency field amplitudes, up to the spinning frequency, that are used here.

Quantitative description of 1H SQ and DQ coherences for the hydroxyl disorder within hydrous ringwoodite

Proton-containing point defects in solid materials are important for a variety of properties ranging from ionic transport over thermal conductivity up to compressibility. Ultrafast magic-angle spinning techniques nowadays offer high-resolution solid-state NMR spectra, even for 1H, and thus open up possibilities to study the underlying defect chemistry. Nevertheless, disorder within such defects again leads to heavy spectral overlap of 1H resonances, which prevents quantitative analysis of defect concentrations, if several defect types are present. Here, we present a strategy to overcome this limitation by simulating the 1H lineshape as well as 1H-1H double-quantum buildup curves, which we then validate against the experimental data in a joint cost function. To mimic the local structural disorder, we use molecular dynamics simulations at the DFT level. It turned out to be advantageous for the joint refinement to put the computational effort into the structural optimisation to derive accurate proton positions and to use empirical correlations for the relation between isotropic and anisotropic 1H chemical shifts and structural elements. The expressiveness of this approach is demonstrated on ringwoodite's (γ-Mg2SiO4) OH defect chemistry containing four different defect types in octahedral and tetrahedral voids with both pure Mg and mixed Si and Mg cation environments. Still, we determine the ratio for each defect type with an accuracy of about 5% as a result of the minimization of the joint cost function. We expect that our approach is generally applicable for local proton disorder and might prove to be a valuable alternative to the established AIRSS and Monte Carlo methods, respectively.

Fast Magic-Angle-Spinning 19F Spin Exchange NMR for Determining Nanometer 19F-19F Distances in Proteins and Pharmaceutical Compounds

Internuclear distances measured using NMR provide crucial constraints of three-dimensional structures but are often restricted to about 5 Å due to the weakness of nuclear-spin dipolar couplings. For studying macromolecular assemblies in biology and materials science, distance constraints beyond 1 nm will be extremely valuable. Here we present an extensive and quantitative analysis of the feasibility of 19F spin exchange NMR for precise and robust measurements of interatomic distances up to 1.6 nm at a magnetic field of 14.1 T, under 20-40 kHz magic-angle spinning (MAS). The measured distances are comparable to those achievable from paramagnetic relaxation enhancement but have higher precision, which is better than ±1 Å for short distances and ±2 Å for long distances. For 19F spins with the same isotropic chemical shift but different anisotropic chemical shifts, intermediate MAS frequencies of 15-25 kHz without 1H irradiation accelerate spin exchange. For spectrally resolved 19F-19F spin exchange, 1H-19F dipolar recoupling significantly speeds up 19F-19F spin exchange. On the basis of data from five fluorinated synthetic, pharmaceutical, and biological compounds, we obtained two general curves for spin exchange between CF groups and between CF3 and CF groups. These curves allow 19F-19F distances to be extracted from the measured spin exchange rates after taking into account 19F chemical shifts. These results demonstrate the robustness of 19F spin exchange NMR for distance measurements in a wide range of biological and chemical systems.

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

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

Analysis of the Electronic Structure of the Special Pair of a Bacterial Photosynthetic Reaction Center by 13 C Photochemically Induced Dynamic Nuclear Polarization Magic-Angle Spinning NMR Using a Double-Quantum Axis

The origin of the functional symmetry break in bacterial photosynthesis challenges since several decades. Although structurally very similar, the two branches of cofactors in the reaction center (RC) protein complex act very differently. Upon photochemical excitation, an electron is transported along one branch, while the other remains inactive. Photochemically induced dynamic nuclear polarization (photo-CIDNP) magic-angle spinning (MAS) ¹³ C NMR revealed that the two bacteriochlorophyll cofactors forming the "Special Pair" donor dimer are already well distinguished in the electronic ground state. These previous studies are relying solely on ¹³ C-¹³ C correlation experiments as radio-frequency-driven recoupling (RFDR) and dipolar-assisted rotational resonance (DARR). Obviously, the chemical-shift assignment is difficult in a dimer of tetrapyrrole macrocycles, having eight pyrrole rings of similar chemical shifts. To overcome this problem, an INADEQUATE type of experiment using a POST C7 symmetry-based approach is applied to selectively isotope-labeled bacterial RC of Rhodobacter (R.) sphaeroides wild type (WT). We, therefore, were able to distinguish unresolved sites of the macromolecular dimer. The obtained chemical-shift pattern is in-line with a concentric assembly of negative charge within the common center of the Special Pair supermolecule in the electronic ground state.

Hidden Oceans? Unraveling the Structure of Hydrous Defects in the Earth's Deep Interior

High-pressure silicates making up the main proportion of the earth's interior can incorporate a significant amount of water in the form of OH defects. Generally, they are charge balanced by removing low-valent cations such as Mg²⁺. By combining high-resolution multidimensional single- and double-quantum ¹H solid-state NMR spectroscopy with density functional theory calculations, we show that, for ringwoodite (γ-Mg₂SiO₄), additionally, Si⁴⁺ vacancies are formed, even at a water content as low as 0.1 wt %. They are charge balanced by either four protons or one Mg²⁺ and two protons. Surprisingly, also a significant proportion of coupled Mg and Si vacancies are present. Furthermore, all defect types feature a pronounced orientational disorder of the OH groups, which results in a significant range of OH···O bond distributions. As such, we are able to present unique insight into the defect chemistry of ringwoodite's spinel structure, which not only accounts for a potentially large fraction of the earth's entire water budget, but will also control transport properties in the mantle. We expect that our results will even impact other hydrous spinel-type materials, helping to understand properties such as ion conduction and heterogeneous catalysis.

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.

Efficient 2D double-quantum solid-state NMR spectroscopy with large spectral widths

STiC phase shifts enable the use of supercycled recoupling sequences for recording 2D DQ–SQ correlation spectra with arbitrary spectral widths.

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.

Asynchronous through-bond homonuclear isotropic mixing: application to carbon-carbon transfer in perdeuterated proteins under MAS

Multiple-bond carbon-carbon homonuclear mixing is a hurdle in extensively deuterated proteins and under fast MAS due to the absence of an effective proton dipolar-coupling network. Such conditions are now commonly employed in solid-state NMR spectroscopy. Here, we introduce an isotropic homonuclear (13)C-(13)C through-bond mixing sequence, MOCCA, for the solid state. Even though applied under MAS, this scheme performs without rotor synchronization and thus does not pose the usual hurdles in terms of power dissipation for fast spinning. We compare its performance with existing homonuclear (13)C-(13)C mixing schemes using a perdeuterated and partially proton-backexchanged protein. Based on the analysis of side chain carbon-carbon correlations, we show that particularly MOCCA with standard 180-degree pulses and delays leading to non-rotor-synchronized spacing performs exceptionally well. This method provides high magnetization transfer efficiency for multiple-bond transfer in the aliphatic region compared with other tested mixing sequences. In addition, we show that this sequence can also be tailor-made for recoupling within a selected spectral region using band-selective pulses.

Investigating adsorption of organic compounds in metal-organic framework MIL-53

Metal-organic frameworks (MOFs) are versatile materials that incorporate metal centers along with organic linkers in highly ordered, intricate structures. MIL-53 is a MOF that exhibits a “breathing effect,” where the pore size and MOF topology are profoundly influenced by the identity and binding mechanism of guest molecules. This phenomenon renders MIL-53 a promising candidate for sensing applications. In this report, the adsorption of various organic compounds within MIL-53 is investigated using a combination of complementary techniques. Thermal gravimetric analysis experiments confirm loading of the guest molecules and yield insight into adsorption interactions and strengths. Significant guest-induced changes in the crystal structure of MIL-53 are revealed by powder X-ray diffraction experiments; specific unique phases of MIL-53 are related to the identity of the guest molecule and its binding mechanism to the framework. 27Al and 13C solid-state NMR experiments probe the interaction between guest molecules and MIL-53. The relationship between the nature of the guest, the structure of MIL-53, and 27Al NMR parameters is explored. 27Al NMR parameters are sensitive to the host-guest binding mechanism (i.e., hydrogen-bonding or π–π stacking interactions) and yield valuable information regarding the influence of the adsorbates on the local aluminum environment. This combination of physical characterization techniques is a useful probe of guest adsorption and the breathing effect within MIL-53 and should prove useful for investigation of related MOFs.

MAS NMR of HIV-1 protein assemblies

The negative global impact of the AIDS pandemic is well known. In this perspective article, the utility of magic angle spinning (MAS) NMR spectroscopy to answer pressing questions related to the structure and dynamics of HIV-1 protein assemblies is examined. In recent years, MAS NMR has undergone major technological developments enabling studies of large viral assemblies. We discuss some of these evolving methods and technologies and provide a perspective on the current state of MAS NMR as applied to the investigations into structure and dynamics of HIV-1 assemblies of CA capsid protein and of Gag maturation intermediates.

Influence of proton coupling on symmetry-based homonuclear (19)F dipolar recoupling experiments

We study the efficiency of two symmetry based homonuclear (19)F double-quantum recoupling sequences for moderate (R142(6)) and ultra-fast (R144(5)) MAS under the influence of strong (1)H-(1)H and (1)H-(19)F dipolar interactions and (1)H continuous wave decoupling. Simulations based on various spin systems derived from the organic solid 1,3,5-tris(2-fluoro-2-methylpropionylamino)benzene (F-BTA), used as a model system, reveal that the strong-decoupling limit is not accessible even for moderate spinning speeds. Additionally, for the no-decoupling limit improved DQ efficiencies are predicted for both moderate and ultra-fast MAS. Strong perturbations of build-up curves can be avoided by additional stabilisation through supercycling. Additional (1)H cw decoupling during (19)F recoupling rapidly reduces the maximum DQ efficiency when deviating from the no-decoupling limit. These effects were confirmed by experimental data on F-BTA. For moderate spinning the influence of (1)H-(1)H and (1)H-(19)F couplings is markedly stronger compared to ultra-fast MAS. For the latter case those influences reduce to a constant scaling if only short excitation times up to the first minimum are taken into account. Based on this analysis the experimental build-up curves of 1,3,5-tris(2-fluoro-2-methylpropionylamino)benzene can be refined with homonuclear (19)F spin systems which allow to probe even subtle structural differences for the fluorine atoms of F-BTA.

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.

Influence of fluorine side-group substitution on the crystal structure formation of benzene-1,3,5-trisamides

The crystal structure of 1,3,5-tris(2-fluoro-2-methylpropionylamino)benzene was solved by combining powder X-ray diffraction, solid-state NMR spectroscopy and quantum chemical calculations.

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.

Structure solution of network materials by solid-state NMR without knowledge of the crystallographic space group

An algorithm is presented for solving the structures of silicate network materials such as zeolites or layered silicates from solid-state (29)Si double-quantum NMR data for situations in which the crystallographic space group is not known. The algorithm is explained and illustrated in detail using a hypothetical two-dimensional network structure as a working example. The algorithm involves an atom-by-atom structure building process in which candidate partial structures are evaluated according to their agreement with Si-O-Si connectivity information, symmetry restraints, and fits to (29)Si double quantum NMR curves followed by minimization of a cost function that incorporates connectivity, symmetry, and quality of fit to the double quantum curves. The two-dimensional network material is successfully reconstructed from hypothetical NMR data that can be reasonably expected to be obtained for real samples. This advance in "NMR crystallography" is expected to be important for structure determination of partially ordered silicate materials for which diffraction provides very limited structural information.

Genetic algorithms and solid state NMR pulse sequences

The use of genetic algorithms for the optimisation of magic angle spinning NMR pulse sequences is discussed. The discussion uses as an example the optimisation of the C7(2)(1) dipolar recoupling pulse sequence, aiming to achieve improved efficiency for spin systems characterised by large chemical shielding anisotropies and/or small dipolar coupling interactions. The optimised pulse sequence is found to be robust over a wide range of parameters, requires only minimal a priori knowledge of the spin system for experimental implementations with buildup rates being solely determined by the magnitude of the dipolar coupling interaction, but is found to be less broadbanded than the original C7(2)(1) pulse sequence. The optimised pulse sequence breaks the synchronicity between r.f. pulses and sample spinning.

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.

Measurement of hetero-nuclear distances using a symmetry-based pulse sequence in solid-state NMR

A Symmetry-based Resonance-Echo DOuble-Resonance (S-REDOR) method is proposed for measuring hetero-nuclear dipolar couplings between two different spin-1/2 nuclei, under fast magic-angle spinning. The hetero-nuclear dipolar couplings are restored by employing the SR4 sequence, which requires the rf-field strength to be only twice the spinning frequency. The S-REDOR experiment is extended to S-RESPDOR (Symmetry-based Resonance-Echo Saturation-Pulse DOuble-Resonance) for determining dipolar coupling between a spin-1/2 nucleus (e.g.(13)C) and (14)N. It is demonstrated that S-REDOR and S-RESPDOR methods suppress efficiently the homo-nuclear dipolar interaction of the irradiated nucleus and benefit from high robustness to the rf-field inhomogeneity, chemical shielding and dipolar truncation. Therefore, these methods allow the measurement of (13)C/(14,15)N distances, with (13)C observation, in uniformly (13)C-labeled samples. Furthermore, we provide analytical solutions for the S-REDOR and S-RESPDOR dephasing curves. These solutions facilitate the measurement of hetero-nuclear distances from experimental data.

Homonuclear dipolar recoupling under ultra-fast magic-angle spinning: probing 19F-19F proximities by solid-state NMR

We describe dipolar recoupling methods that accomplish, at high magic-angle spinning (MAS) frequencies, the excitation of double-quantum (DQ) coherences between spin-1/2 nuclei. We employ rotor-synchronized symmetry-based pulse sequences which are either gamma-encoded or non-gamma-encoded. The sensitivity and the robustness to both chemical-shift anisotropy and offset are examined. We also compare different techniques to avoid signal folding in the indirect dimension of two-dimensional double-quantum<-->single-quantum (DQ-SQ) spectra. This comprehensive analysis results in the identification of satisfactory conditions for dipolar (19)F-(19)F recoupling at high magnetic fields and high MAS frequencies. The utility of these recoupling methods is demonstrated with high-resolution DQ-SQ NMR spectra, which allow probing (19)F-(19)F proximities in powered fluoroaluminates.

Double-quantum NMR spectroscopy of 31P species submitted to very large CSAs

We introduce an original pulse sequence, BR2(2)(1)(taupitau), which is a block super-cycled R2(2)(1) sequence employing as basic element a pi pulse sandwiched by 'window' intervals. This homonuclear dipolar recoupling method allows the efficient excitation of double-quantum coherences between spin-1/2 nuclei submitted to very large chemical shift anisotropy. We demonstrate that this technique can be employed in double-quantum<-->single-quantum (31)P homonuclear correlation experiment at high magnetic field (B(0)>or=14 T) and high MAS frequencies (nu(R)>or=30 kHz). The performances of BR2(2)(1)(taupitau) are compared to those of the double-quantum recoupling methods, such as BABA and bracketed fp-RFDR, which were already employed at fast MAS rates. The BR2(2)(1)(taupitau) sequence displays a higher robustness to CSA and offset than the other existing techniques.

Supercycled symmetry-based double-quantum dipolar recoupling of quadrupolar spins in MAS NMR: I. Theory

Using average Hamiltonian (AH) theory, we analyze recently introduced homonuclear dipolar recoupling pulse sequences for exciting central-transition double-quantum coherences (2QC) between half-integer spin quadrupolar nuclei undergoing magic-angle-spinning. Several previously observed differences among the recoupling schemes concerning their compensation to resonance offsets and radio-frequency (rf) inhomogeneity may qualitatively be rationalized by an AH analysis up to third perturbation order, despite its omission of first-order quadrupolar interactions. General aspects of the engineering of 2Q-recoupling pulse sequences applicable to half-integer spins are discussed, emphasizing the improvements offered from a diversity of supercycles providing enhanced suppression of undesirable AH cross-terms between resonance offsets and rf amplitude errors.

Accurate measurement of methyl 13C chemical shifts by solid-state NMR for the determination of protein side chain conformation: the influenza a M2 transmembrane peptide as an example

The use of side chain methyl (13)C chemical shifts for the determination of the rotameric conformation of Val and Leu residues in proteins by solid-state NMR spectroscopy is described. Examination of the solution NMR stereospecifically assigned methyl groups shows significant correlation between the difference in the two methyl carbons' chemical shifts and the side chain conformation. It is found that alpha-helical and beta-sheet backbones cause different side chain methyl chemical shift trends. In alpha-helical Leu's, a relatively large absolute methyl (13)C shift difference of 2.89 ppm is found for the most populated mt rotamer (chi(1) = -60 degrees, chi(2) = 180 degrees), while a much smaller value of 0.73 ppm is found for the next populated tp rotamer (chi(1) = 180 degrees, chi(2) = 60 degrees). For alpha-helical Val residues, the dominant t rotamer (chi(1) = 180 degrees) has more downfield Cgamma2 chemical shifts than Cgamma1 by 1.71 ppm, while the next populated m rotamer (chi(1) = -60 degrees) shows the opposite trend of more downfield Cgamma1 chemical shift by 1.23 ppm. These significantly different methyl (13)C chemical shifts exist despite the likelihood of partial rotameric averaging at ambient temperature. We show that these conformation-dependent methyl (13)C chemical shifts can be utilized for side chain structure determination once the methyl (13)C resonances are accurately measured by double-quantum (DQ) filtered 2D correlation experiments, most notably the dipolar DQ to single-quantum (SQ) correlation technique. The advantage of the DQ-SQ correlation experiment over simple 2D SQ-SQ correlation experiments is demonstrated on the transmembrane peptide of the influenza A M2 proton channel. The methyl chemical shifts led to predictions of the side chain rotameric states for several Val and Leu residues in this tetrameric helical bundle. The predicted Val rotamers were further verified by dipolar correlation experiments that directly measure the chi(1) torsion angles. It was found that the chemical-shift-predicted side chain conformations are fully consistent with the direct torsion angle results; moreover, the methyl (13)C chemical shifts are sensitive to approximately 5 degrees changes in the chi(1) torsion angle due to drug binding.

High-resolution 1H homonuclear dipolar recoupling NMR spectra of biological solids at MAS rates up to 67 kHz

Two-dimensional (1)H homonuclear correlation NMR spectra of solids of biological interest have been recorded at high magnetic fields (14.1 and 18.8 T) and MAS rates up to 67 kHz, using RN(n)(nu) symmetry-based homonuclear recoupling and CRAMPS decoupling; this method affords exceptional spectral resolution and is well suited to probe (1)H-(1)H proximities in powdered solids.

Dipolar truncation in magic-angle spinning NMR recoupling experiments

Quantitative solid-state NMR distance measurements in strongly coupled spin systems are often complicated due to the simultaneous presence of multiple noncommuting spin interactions. In the case of zeroth-order homonuclear dipolar recoupling experiments, the recoupled dipolar interaction between distant spins is attenuated by the presence of stronger couplings to nearby spins, an effect known as dipolar truncation. In this article, we quantitatively investigate the effect of dipolar truncation on the polarization-transfer efficiency of various homonuclear recoupling experiments with analytical theory, numerical simulations, and experiments. In particular, using selectively (13)C-labeled tripeptides, we compare the extent of dipolar truncation in model three-spin systems encountered in protein samples produced with uniform and alternating labeling. Our observations indicate that while the extent of dipolar truncation decreases in the absence of directly bonded nuclei, two-bond dipolar couplings can generate significant dipolar truncation of small, long-range couplings. Therefore, while alternating labeling alleviates the effects of dipolar truncation, and thus facilitates the application of recoupling experiments to large spin systems, it does not represent a complete solution to this outstanding problem.

Robust and efficient spin-locked symmetry-based double-quantum homonuclear dipolar recoupling for probing (1)H-(1)H proximity in the solid-state

We report a novel symmetry-based method, using inversion elements bracketed by spin locks, for exciting double-quantum (DQ) coherences between spin-1/2 nuclei, such as protons. Compared to previous DQ-recoupling techniques, this new pulse sequence requires moderate rf field, even at ultra-fast MAS speeds. Furthermore, it is easy to implement and it displays higher robustness to both chemical shift anisotropy and to spreads in resonance frequencies. These advances greatly facilitate the observation of (1)H-(1)H proximities at high fields and high MAS frequencies.