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

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.

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.

Spherical tensor analysis of nuclear magnetic resonance signals

In a nuclear magnetic-resonance (NMR) experiment, the spin density operator may be regarded as a superposition of irreducible spherical tensor operators. Each of these spin operators evolves during the NMR experiment and may give rise to an NMR signal at a later time. The NMR signal at the end of a pulse sequence may, therefore, be regarded as a superposition of spherical components, each derived from a different spherical tensor operator. We describe an experimental method, called spherical tensor analysis (STA), which allows the complete resolution of the NMR signal into its individual spherical components. The method is demonstrated on a powder of a (13)C-labeled amino acid, exposed to a pulse sequence generating a double-quantum effective Hamiltonian. The propagation of spin order through the space of spherical tensor operators is revealed by the STA procedure, both in static and rotating solids. Possible applications of STA to the NMR of liquids, liquid crystals, and solids are discussed.

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.

Line shapes of multiple quantum NMR coherences in one-dimensional quantum spin chains in solids

General formulae for intensities of multiple quantum (MQ) NMR coherences in systems of nuclear spins coupled by the dipole-dipole interactions are derived. The second moments of the MQ coherences of zero- and second orders are calculated for infinite linear chains in the approximation of the nearest neighbor interactions. Supercomputer simulations of intensities of MQ coherences of linear chains are performed at different times of preparation and evolution periods of MQ NMR experiments. The second moments obtained from the developed theory are compared with the results of the supercomputer analysis of MQ NMR dynamics. The linewidth information in MQ NMR experiments is discussed.

Amyloidosis of Alzheimer's Abeta peptides: solid-state nuclear magnetic resonance, electron paramagnetic resonance, transmission electron microscopy, scanning transmission electron microscopy and atomic force microscopy studies

Aggregation cascade for Alzheimer's amyloid-beta peptides, its relevance to neurotoxicity in the course of Alzheimer's disease and experimental methods useful for these studies are discussed. Details of the solid-phase peptide synthesis and sample preparation procedures for Alzheimer's beta-amyloid fibrils are given. Recent progress in obtaining structural constraints on Abeta-fibrils from solid-state NMR and scanning transmission electron microscopy (STEM) data is discussed. Polymorphism of amyloid fibrils and oligomers of the 'Arctic' mutant of Abeta(1-40) was studied by (1)H,(13)C solid-state NMR, transmission electron microscopy (TEM) and atomic force microscopy (AFM), and a real-time aggregation of different polymorphs of the peptide was observed with the aid of in situ AFM. Recent results on binding of Cu(II) ions and Al-citrate and Al-ATP complexes to amyloid fibrils, as studied by electron paramagnetic resonance (EPR) and solid-state (27)Al NMR techniques, are also presented.

Supramolecular structural constraints on Alzheimer's beta-amyloid fibrils from electron microscopy and solid-state nuclear magnetic resonance

We describe electron microscopy (EM), scanning transmission electron microscopy (STEM), and solid-state nuclear magnetic resonance (NMR) measurements on amyloid fibrils formed by the 42-residue beta-amyloid peptide associated with Alzheimer's disease (Abeta(1)(-)(42)) and by residues 10-35 of the full-length peptide (Abeta(10)(-)(35)). These measurements place constraints on the supramolecular structure of the amyloid fibrils, especially the type of beta-sheets present in the characteristic amyloid cross-beta structural motif and the assembly of these beta-sheets into a fibril. EM images of negatively stained Abeta(10)(-)(35) fibrils and measurements of fibril mass per length (MPL) by STEM show a strong dependence of fibril morphology and MPL on pH. Abeta(10)(-)(35) fibrils formed at pH 3.7 are single "protofilaments" with MPL equal to twice the value expected for a single cross-beta layer. Abeta(10)(-)(35) fibrils formed at pH 7.4 are apparently pairs of protofilaments or higher order bundles. EM and STEM data for Abeta(1)(-)(42) fibrils indicate that protofilaments with MPL equal to twice the value expected for a single cross-beta layer are also formed by Abeta(1)(-)(42) and that these protofilaments exist singly and in pairs at pH 7.4. Solid-state NMR measurements of intermolecular distances in Abeta(10)(-)(35) fibrils, using multiple-quantum (13)C NMR, (13)C-(13)C dipolar recoupling, and (15)N-(13)C dipolar recoupling techniques, support the in-register parallel beta-sheet organization previously established by Lynn, Meredith, Botto, and co-workers [Benzinger et al. (1998) Proc. Natl. Acad. Sci. U.S.A. 95, 13407-13412; Benzinger et al. (2000) Biochemistry 39, 3491-3499] and show that this beta-sheet organization is present at pH 3.7 as well as pH 7.4 despite the differences in fibril morphology and MPL. Solid-state NMR measurements of intermolecular distances in Abeta(1)(-)(42) fibrils, which represent the first NMR data on Abeta(1)(-)(42) fibrils, also indicate an in-register parallel beta-sheet organization. These results, along with previously reported data on Abeta(1)(-)(40) fibrils, suggest that the supramolecular structures of Abeta(10)(-)(35), Abeta(1)(-)(40), and Abeta(1)(-)(42) fibrils are quite similar. A schematic structural model of these fibrils, consistent with known experimental EM, STEM, and solid-state NMR data, is presented.

Structure and ionic interactions of organic-inorganic composite polymer electrolytes studied by solid-state NMR and Raman spectroscopy

Solid-state NMR studies of composite polymer electrolytes are reported. The materials consist of polyethylene oxide and an organic inorganic composite, together with a lithium salt, and are candidates for electrolytes in solid-state lithium ion batteries. Silicon and aluminum MAS and multiple quantum MAS are used to characterize the network character of the organic-inorganic composite, and spin diffusion measurements are used to determine the nanostructure of the polymer/composite blending. Multiple quantum spin counting is used to measure the ion aggregation. The NMR results are supported by Raman spectra, calorimetry, and impedance spectroscopy. From these experiments it is concluded that the composite suppresses polymer crystallization without suppressing its local mobility, and also suppresses the tendency for the ions to aggregate. This polymer composite thus appears very promising for application in lithium ion batteries.

NMR of multipolar spin states excitated in strongly inhomogeneous magnetic fields

The possibility of exciting and filtering various multipolar spin states in proton NMR like dipolar encoded longitudinal magnetization (LM), double-quantum (DQ) coherences, and dipolar order (DO) in strongly inhomogeneous static and radio-frequency magnetic fields is investigated. For this purpose pulse sequences which label and manipulate the multipolar spin states in a specific way were implemented on the NMR-MOUSE (mobile universal surface explorer). The performance of the pulse sequences was also tested in homogeneous fields on a solid-state high-field NMR spectrometer. The theoretical justification of these procedures was shown for a rigid two-spin 1/2 system coupled by dipolar interactions. Dipolar encoded longitudinal magnetization decay curves, double-quantum and dipolar-order buildup curves, as well as double-quantum decay curves were recorded with the NMR-MOUSE for natural rubber samples with different crosslink density. The possibility of using these multipolar spin states for investigations of strained elastomers by NMR-MOUSE is also shown. These curves give access to quantitative values of the ratio of the total residual dipolar couplings of the protons in the series of samples which are in good agreement with those measured in homogeneous fields.

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.

Amyloid fibril formation by A beta 16-22, a seven-residue fragment of the Alzheimer's beta-amyloid peptide, and structural characterization by solid state NMR

The seven-residue peptide N-acetyl-Lys-Leu-Val-Phe-Phe-Ala-Glu-NH(2), called A beta(16-22) and representing residues 16-22 of the full-length beta-amyloid peptide associated with Alzheimer's disease, is shown by electron microscopy to form highly ordered fibrils upon incubation of aqueous solutions. X-ray powder diffraction and optical birefringence measurements confirm that these are amyloid fibrils. The peptide conformation and supramolecular organization in A beta(16-22) fibrils are investigated by solid state (13)C NMR measurements. Two-dimensional magic-angle spinning (2D MAS) exchange and constant-time double-quantum-filtered dipolar recoupling (CTDQFD) measurements indicate a beta-strand conformation of the peptide backbone at the central phenylalanine. One-dimensional and two-dimensional spectra of selectively and uniformly labeled samples exhibit (13)C NMR line widths of <2 ppm, demonstrating that the peptide, including amino acid side chains, has a well-ordered conformation in the fibrils. Two-dimensional (13)C-(13)C chemical shift correlation spectroscopy permits a nearly complete assignment of backbone and side chain (13)C NMR signals and indicates that the beta-strand conformation extends across the entire hydrophobic segment from Leu17 through Ala21. (13)C multiple-quantum (MQ) NMR and (13)C/(15)N rotational echo double-resonance (REDOR) measurements indicate an antiparallel organization of beta-sheets in the A beta(16-22) fibrils. These results suggest that the degree of structural order at the molecular level in amyloid fibrils can approach that in peptide or protein crystals, suggest how the supramolecular organization of beta-sheets in amyloid fibrils can be dependent on the peptide sequence, and illustrate the utility of solid state NMR measurements as probes of the molecular structure of amyloid fibrils. A beta(16-22) is among the shortest fibril-forming fragments of full-length beta-amyloid reported to date, and hence serves as a useful model system for physical studies of amyloid fibril formation.

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.

Determination of molecular geometry by high-order multiple-quantum evolution in solid-state NMR

The principles of molecular geometry determination by high-quantum heteronuclear local field spectroscopy in solid-state NMR are discussed. The extreme multiple-quantum coherences in a cluster of nuclear spins are allowed to evolve in the presence of heteronuclear through-space couplings to two spins of a different type. The multiple-quantum dephasing curve is independent of the homonuclear spin-spin couplings and may be described in terms of geometric parameters. The triple-quantum version of the experiment is demonstrated by determining the psi torsion angle in a [(15)N(2), (13)C(3)]-labeled sample of the peptide ala-ala-gly. Two regions of torsion angle space fit the experimental data, one in the neighborhood of -152 degrees and one in the neighborhood of +161 degrees. The latter determination is in excellent agreement with the X-ray estimate of +160.5 degrees.