Multiple quantum NMR excitation with a one-quantum hamiltonian

Dynamic Nuclear Polarization Enhanced Multiple-Quantum Spin Counting of Molecular Assemblies in Vitrified Solutions

Crystallization pathways are essential to various industrial, geological, and biological processes. In nonclassical nucleation theory, prenucleation clusters (PNCs) form, aggregate, and crystallize to produce higher order assemblies. Microscopy and X-ray techniques have limited utility for PNC analysis due to the small size (0.5-3 nm) and time stability constraints. We present a new approach for analyzing PNC formation based on 31P nuclear magnetic resonance (NMR) spin counting of vitrified molecular assemblies. The use of glassing agents ensures that vitrification generates amorphous aqueous samples and offers conditions for performing dynamic nuclear polarization (DNP)-amplified NMR spectroscopy. We demonstrate that molecular adenosine triphosphate along with crystalline, amorphous, and clustered calcium phosphate materials formed via a nonclassical growth pathway can be differentiated from one another by the number of dipolar coupled 31P spins. We also present an innovative approach for examining spin counting data, demonstrating that a knowledge-based fitting of integer multiples of cosine wave functions, instead of the traditional Fourier transform, provides a more physically meaningful retrieval of the existing frequencies. This is the first report of multiquantum spin counting of assemblies formed in solution as captured under vitrified DNP conditions, which can be useful for future analysis of PNCs and other aqueous molecular clusters.

Combinatorial Enumeration of Isomers of Superaromatic Polysubstituted Cycloarenes and Coronoid Hydrocarbons with Applications to NMR

We have employed combinatorial techniques based on character cycle indices, Pólya's theory, and Euler totem function to enumerate isomers of polysubstituted cycloarenes and coronoid hydrocarbons which have been receiving considerable attention because of their superaromaticity, ring currents, and interesting magnetic properties. Systematic enumeration and construction of tables of polysubstituted isomers such as fluoro-chloro superaromatic hydrocarbons are considered as they are of interest in the study of environmental pollutants and toxicity. Isomers of fluoro-chloro polysubstituted donut shaped circumkekulenes, circumseptulenes, circumoctulenes, etc., are enumerated in addition to other cycloarenes, polycyclic circumcoronaphenes and coronoids. Applications to ¹³C NMR, proton NMR and multiple quantum NMR spectroscopies of these superaromatic species are considered.

Engineering spin Hamiltonians using multiple pulse sequences in solid state NMR spectroscopy

Multiple pulse sequences are often used to manipulate spin Hamiltonians in solid-state nuclear magnetic resonance spectroscopy. In this paper, we analyze multiple pulse sequences using the well-known average Hamiltonian theory. We first expand the resulting average Hamiltonian into a reachable set of sub-Hamiltonians and then develop a general procedure using both flip-angle and phase of the applied pulses as control variables to select any of those sub-Hamiltonians. We use this method to analyze solid-echo based sequences and to design new proton-proton homonuclear decoupling sequences in static solids. It is found that this newly designed decoupling scheme, in the presence of finite pulse length, effectively suppresses the ¹H-¹H homonuclear dipolar interactions while establishes variable scaling factors on the heteronuclear dipolar interactions and chemical shift interactions, depending on the flip-angle of the applied pulses. When the pulse flip-angle is close to 54.7°, this sequence possesses a large scaling factor with relatively low average decoupling field. When the pulse flip-angle becomes ∼120°, the scaling factor is almost zero. A static ¹⁵N-acetyl-valine crystal sample has been used as an example to confirm and validate the performance of this new decoupling scheme.

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.

Quantum simulation via filtered Hamiltonian engineering: application to perfect quantum transport in spin networks

We propose a method for Hamiltonian engineering that requires no local control but only relies on collective qubit rotations and field gradients. The technique achieves a spatial modulation of the coupling strengths via a dynamical construction of a weighting function combined with a Bragg grating. As an example, we demonstrate how to generate the ideal Hamiltonian for perfect quantum information transport between two separated nodes of a large spin network. We engineer a spin chain with optimal couplings starting from a large spin network, such as one naturally occurring in crystals, while decoupling all unwanted interactions. For realistic experimental parameters, our method can be used to drive almost perfect quantum information transport at room temperature. The Hamiltonian engineering method can be made more robust under decoherence and coupling disorder by a novel apodization scheme. Thus, the method is quite general and can be used to engineer the Hamiltonian of many complex spin lattices with different topologies and interactions.

Triple-quantum dynamics in multiple-spin systems undergoing magic-angle spinning: application to 13C homonuclear correlation spectroscopy

We analyze the multiple-quantum dynamics governed by a new homonuclear recoupling strategy effecting an average dipolar Hamiltonian comprising three-spin triple-quantum operators (e.g., S(p)+S(q)+S(r)+) under magic-angle spinning conditions. Analytical expressions are presented for polarization transfer processes in systems of three and four coupled spins-1/2 subject to triple-quantum filtration (3QF), and high-order multiple-quantum excitation is investigated numerically in moderately large clusters, comprising up to seven spins. This recoupling approach gives highly efficient excitation of triple-quantum coherences: ideally, up to 67% of the initial polarization may be recovered by 3QF in three-spin systems in polycrystalline powders. Two homonuclear 2D correlation strategies are demonstrated experimentally on powders of uniformly 13C-labeled alanine and tyrosine: the first correlates the single-quantum spectrum in the first dimension with the corresponding 3QF spectrum along the other. The second protocol correlates triple-quantum coherences with their corresponding single-quantum coherences within triplets of coupled spins.

Multiple quantum spin counting techniques with quadrupolar nuclei

Phase incremented and continuous irradiation multiple spin correlation methods are applied to spin [Formula: see text] nuclei with small quadrupole couplings such as (7)Li in LiCl and are shown to successfully produce a coherently coupled dipolar spin network. Application to the analogous Na salt shows successful spin correlation evolving at a slower rate due to the weaker homonuclear dipolar coupling strength between Na nuclei. The results are analysed using a statistical approach. Spin counting is non-trivial as not only multiple quantum coherences between spins are generated but also within the quadrupolar spin levels. Na(2)C(2)O(4) is investigated as a material with non-negligible quadrupole coupling and it is in this limit that the spin correlation techniques are found to break down.

NMR polarization echoes in a nematic liquid crystal

We have modified the polarization echo (PE) sequence through the incorporation of Lee-Goldburg cross polarization steps to quench the 1H-1H dipolar dynamics. In this way, the 13C becomes an ideal local probe to inject and detect polarization in the proton system. This improvement made possible the observation of the local polarization P(00)(t) and polarization echoes in the interphenyl proton of the liquid crystal N-(4-methoxybenzylidene)-4-butylaniline. The decay of P(00)(t) was well fitted to an exponential law with a characteristic time tau(C) approximately 310 micros. The hierarchy of the intramolecular dipolar couplings determines a dynamical bottleneck that justifies the use of the Fermi Golden Rule to obtain a spectral density consistent with the structural parameters. The time evolution of P(00)(t) was reversed by the PE sequence generating echoes at the time expected by the scaling of the dipolar Hamiltonian. This indicates that the reversible 1H-1H dipolar interaction is the main contribution to the local polarization decrease and that the exponential decay for P(00)(t) does not imply irreversibility. The attenuation of the echoes follows a Gaussian law with a characteristic time tau(phi) approximately 527 micros. The shape and magnitude of the characteristic time of the PE decay suggest that it is dominated by the unperturbed homonuclear dipolar Hamiltonian. This means that tau(phi) is an intrinsic property of the dipolar coupled network and not of other degrees of freedom. In this case, one cannot unambiguously identify the mechanism that produces the decoherence of the dipolar order. This is because even weak interactions are able to break the fragile multiple coherences originated on the dipolar evolution, hindering its reversal. Other schemes to investigate these underlying mechanisms are proposed.

Enhanced triple-quantum excitation in 13C magic-angle spinning NMR

We describe a new method for exciting triple-quantum coherences in 13C-labelled powder samples under MAS. The proposed method combines selective double-quantum excitation with rotational resonance and frequency-selective composite pulses. The spin dynamics of this new method are described theoretically. Numerical calculations of the spin dynamics are compared to experimental results on fully 13C-labelled L-alanine. The observed triple-quantum filtering efficiency is around 10% for the most intense spectral peak. The method is also demonstrated on other fully 13C-labelled compounds, including a uniformly 13C-labelled amino acid.

Biomolecular solid state NMR: advances in structural methodology and applications to peptide and protein fibrils

Solid state nuclear magnetic resonance (NMR) methods can provide atomic-level structural constraints on peptides and proteins in forms that are not amenable to characterization by other high-resolution structural techniques, owing to insolubility, high molecular weight, noncrystallinity, or other characteristics. Important examples include peptide and protein fibrils and membrane-bound peptides and proteins. Recent advances in solid state NMR methodology aimed at structural problems in biological systems are reviewed. The power of these methods is illustrated by experimental results on amyloid fibrils and other protein fibrils.

Multiple quantum solid-state NMR indicates a parallel, not antiparallel, organization of beta-sheets in Alzheimer's beta-amyloid fibrils

Senile plaques associated with Alzheimer's disease contain deposits of fibrils formed by 39- to 43-residue beta-amyloid peptides with possible neurotoxic effects. X-ray diffraction measurements on oriented fibril bundles have indicated an extended beta-sheet structure for Alzheimer's beta-amyloid fibrils and other amyloid fibrils, but the supramolecular organization of the beta-sheets and other structural details are not well established because of the intrinsically noncrystalline, insoluble nature of amyloid fibrils. Here we report solid-state NMR measurements, using a multiple quantum (MQ) (13)C NMR technique, that probe the beta-sheet organization in fibrils formed by the full-length, 40-residue beta-amyloid peptide (Abeta(1-40)). Although an antiparallel beta-sheet organization often is assumed and is invoked in recent structural models for full-length beta-amyloid fibrils, the MQNMR data indicate an in-register, parallel organization. This work provides site-specific, atomic-level structural constraints on full-length beta-amyloid fibrils and applies MQNMR to a significant problem in structural biology.

Solid-state NMR as a probe of amyloid fibril structure

Amyloid fibrils are intrinsically noncrystalline, insoluble, high-molecular-weight aggregates of peptides and proteins, with considerable biomedical and biophysical significance. Solid-state NMR techniques are uniquely capable of providing high-resolution, site-specific structural constraints for amyloid fibrils, at the level of specific interatomic distances and torsion angles. So far, a relatively small number of solid-state NMR studies of amyloid fibrils have been reported. These have addressed issues about the supramolecular organization of beta-sheets in the fibrils and the peptide conformation in the fibrils, and have concentrated on the beta-amyloid peptide of Alzheimer's disease. Many additional applications of solid-state NMR to amyloid fibrils from a variety of sources are anticipated in the near future, as these systems are ideally suited for the technique and are of widespread current interest.

Selection rules for multiple quantum NMR excitation in solids: derivation from time-reversal symmetry and comparison with simulations and (13)C NMR experiments

New derivations of selection rules for excitation and detection of multiple quantum coherences in coupled spin-1/2 systems are presented. The selection rules apply to experiments in which the effective coupling Hamiltonian used for multiple quantum excitation is both time-reversal invariant and time-reversible by a phase shift of the radiofrequency pulse sequence that generates the effective couplings. The selection rules are shown to be consequences of time-reversal invariance and time-reversibility and otherwise independent of the specific form of the effective coupling Hamiltonian. Numerical simulations of multiple quantum NMR signal amplitudes and experimental multiple quantum excitation spectra are presented for the case of a multiply (13)C-labeled helical polypeptide. The simulations and experiments confirm the selection rules and demonstrate their impact on multiple quantum (13)C NMR spectra in this biochemically relevant case.

Multiple-quantum nuclear magnetic resonance spectroscopy of coupled 1/2 spins in solids. Combination with cross-polarization and magic-angle spinning

Proton multiple-quantum coherence spectroscopy has been combined with magic-angle spinning (MAS) and cross-polarization (CP). This enables the detection of the proton (or any other abundant spin) multiple-quantum coherence spectrum via the high-resolution 13C (any other spin) nuclear magnetic resonance (NMR) spectrum. For this purpose multiple-quantum pulse sequences synchronised to sample rotation have been designed, and the average Hamiltonians of these sequences have been analysed. The analysis allows the design of optimal experimental conditions. As a demonstration of the technique, it has been applied to a mixture of adamantane and hexamethylethane. From earlier 13C spin diffusion experiments it was known that these two molecules form a mixed crystal. With our technique we detected two different phases with different molecular translational self-diffusion coefficients in this system.

Experimental detection of multiple-quantum coherence transfer in coupled spin solids by multi-dimensional NMR experiments

Three-dimensional multiple-quantum coherence experiments in coupled 1/2 spin solids have been designed to directly detect coherence transfers among all the accessible coherence orders during irradiation. The experiments have been performed on the coupled four-spin polycrystalline sample 1,2,3,4-tetrachloronaphthalene-bis(hexachlorocyclopentadiene) adduct. The experimental results reveal how the coherences transfer in this spin system, which support the theoretically deduced selection rules and can be used to assist more precise description of multiple-quantum coherence dynamics.