Principles and Applications of Multiple-Quantum Nmr

Dissipative dynamics of multiple-quantum NMR coherences in two-spin systems

Multiple-quantum (MQ) NMR experiments were performed at a special orientation of a hambergite (Be2BO3OH) single crystal, which consists of alternating zigzag proton chains. At the chosen orientation, one of the dipolar coupling constants in the chain becomes zero and the system becomes a set of well-isolated dipolar coupled spin pairs. The relaxation of the spin pairs in the MQ NMR experiment was studied on the basis of the Lindblad equation. Fermi's golden rule was used to investigate the relaxation mechanism. The agreement of the calculated relaxation time with the experimental value (125 μs) suggests that the dipole-dipole interactions with protons surrounding the pair are responsible for the relaxation of MQ coherences.

Schrödinger Cat State Spectroscopy-A New Frontier for Analytical Chemistry

The invention of the laser generated great excitement, because its ability to create quantum state coherences could form a new family of coherent spectroscopies that were the optical analogue of multidimensional nuclear magnetic resonance (NMR). The full realization of this promise has not yet been realized, but the pathway forward is clear. The path involves the use of multiple, tunable lasers that create a Schrödinger cat state, where the system is simultaneously in a mixture of vibrational and/or electronic states. The multiplicity of these states confers many advantages for analytical methods: high selectivity from the multiple spectral dimensions, line-narrowing, isolation of spectral features where quantum states are coupled, and spectral decongestion. Now that the feasibility of Schrödinger cat spectroscopy has been demonstrated, the future is open for the development of a new frontier in analytical chemistry that creates a new set of tools for studying the complex systems that form the heart of analytical chemistry.

A statistical approach for analyzing the development of 1H multiple-quantum coherence in solids

A novel statistical approach for analyzing (1)H multiple-quantum (MQ) spin dynamics in so-called spin-counting solid-state NMR experiments is presented. The statistical approach is based on the percolation theory with Monte Carlo methods and is examined by applying it to the experimental results of three solid samples having unique hydrogen arrangement for 1-3 dimensions: the n-alkane/d-urea inclusion complex as a one-dimensional (1D) system, whose (1)H nuclei align approximately in 1D, and magnesium hydroxide and adamantane as a two-dimensional (2D) and a three-dimensional (3D) system, respectively. Four lattice models, linear, honeycomb, square and cubic, are used to represent the (1)H arrangement of the three samples. It is shown that the MQ dynamics in adamantane is consistent with that calculated using the cubic lattice and that in Mg(OH)2 with that calculated using the honeycomb and the square lattices. For n-C20H42/d-urea, these 4 lattice models fail to express its result. It is shown that a more realistic model representing the (1)H arrangement of n-C20H42/d-urea can describe the result. The present approach can thus be used to determine (1)H arrangement in solids.

NMR method for amplification of single-spin state

Amplification of a single-spin state using nuclear magnetic resonance (NMR) techniques in a rotating frame is considered. The main aim is to investigate the efficiency of various schemes for quantum detection. Results of numerical simulation of the time dependence of individual and total nuclear polarizations for 1D, 2D, and 3D configurations of the spin systems are presented.

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.

Enhanced sensitivity to residual dipolar couplings of elastomers by higher-order multiple-quantum NMR

The homonuclear and heteronuclear residual dipolar couplings in elastomers reflect changes in the cross-link density, temperature, the uniaxial and biaxial extension or compression as well as the presence of penetrant molecules. It is shown theoretically that for an isolated methyl group the relative changes in the intensity of the homonuclear double-quantum buildup curves in the initial time regime due to variation of the residual dipolar coupling strength is less sensitive than the changes in the triple-quantum filtered NMR signal when considering the same excitation/reconversion time. For a quadrupolar nucleus with spin I=2 the sensitivity enhancement was simulated for four-quantum, triple-quantum, and double-quantum buildup curves. In this case the four-quantum build-up curve shows the highest sensitivity to changes of spin couplings. This enhanced sensitivity to the residual dipolar couplings was tested experimentally by measuring 1H double-quantum, triple-quantum, and four-quantum buildup curves of differently cross-linked natural rubber samples. In the initial excitation/reconversion time regime, where the residual dipolar couplings can be measured model free, the relative changes in the intensity of the four-quantum buildup curves are about five times higher than those of the double-quantum coherences. For the first time proton four-quantum coherences were recorded for cross-linked elastomers.

Second order average Hamiltonian theory of symmetry-based pulse schemes in the nuclear magnetic resonance of rotating solids: Application to triple-quantum dipolar recoupling

The average Hamiltonian theory (AHT) of several classes of symmetry-based radio-frequency pulse sequences is developed to second order, allowing quantitative analyses of a wide range of recoupling and decoupling applications in magic-angle-spinning solid state nuclear magnetic resonance. General closed analytical expressions are presented for a cross term between any two interactions recoupled to second order AHT. We classify them into different categories and show that some properties of the recoupling pulse sequence may be predicted directly from this classification. These results are applied to examine a novel homonuclear recoupling strategy, effecting a second order average dipolar Hamiltonian comprising trilinear triple quantum (3Q) spin operators. We discuss general features and design principles of such 3Q recoupling sequences and demonstrate by numerical simulations and experiments that they provide more efficient excitation of (13)C 3Q coherences compared to previous techniques. We passed up to 15% of the signal through a state of 3Q coherence in rotating powders of uniformly (13)C-labeled alanine and tyrosine. Second order recoupling-based (13)C homonuclear 3Q correlation spectroscopy is introduced and demonstrated on tyrosine.

Parameter maps of 1H residual dipolar couplings in tendon under mechanical load

Proton multipolar spin states associated with dipolar encoded longitudinal magnetization (DELM) and double-quantum (DQ) coherences of bound water are investigated for bovine and sheep Achilles tendon under mechanical load. DELM decay curves and DQ buildup and decay curves reveal changes of the 1H residual dipolar couplings for tendon at rest and under local compression forces. The multipolar spin states are used to design dipolar contrast filters for NMR 1H images of heterogeneous tendon. Heterogeneities in tendon samples were artificially generated by local compression parallel and perpendicular to the tendon plug axis. Quotient images obtained from DQ-filtered images by matched and mismatched excitation/reconversion periods are encoded only by the residual dipolar couplings. Semi-quantitative parameter maps of the residual dipolar couplings of bound water were obtained from these quotient images using a reference elastomer sample. This method can be used to quantify NMR imaging of injured ordered tissues.

Domain sizes in heterogeneous polymers by spin diffusion using single-quantum and double-quantum dipolar filters

1H spin-diffusion experiments employing a double-quantum (DQ) dipolar filter were performed for the characterization of the microdomain structure of heterogeneous samples. For this purpose the NMR spin-diffusion process was analysed based on a model morphology of three different domains with arbitrary sizes, diffusivities, and filter efficiency. General analytical solutions for z magnetization source and sink were obtained valid for a one-dimensional lamellar morphology in the full range of spin-diffusion times. These solutions of the spin-diffusion equations were used for determining the crystalline, interface, and amorphous domain sizes in polystyrene-poly(ethylene oxide) (PS-PEO) and poly(hydroxyethylmethacrylate)-poly(ethylene oxide) (PHEMA-PEO). The DQ dipolar filter has a good efficiency for PS-PEO but is only partially efficient in filtering the signal of the mobile domains in the PHEMA-PEO diblock copolymer. The domain sizes measured by the DQ filter method are compared to those obtained using the traditional dipolar filter creating z magnetization in the mobile domains.

Dipolar recoupling NMR of biomolecular self-assemblies: determining inter- and intrastrand distances in fibrilized Alzheimer's beta-amyloid peptide

We demonstrate a new method for investigating the structure of self-associating biopolymers using dipolar recoupling NMR techniques. This approach was applied to the study of fibrillar beta-amyloid (Abeta) peptides (the primary component of the plaques of Alzheimer's disease) containing only a single isotopic spin label (13C), by employing the DRAWS (dipolar recoupling with a windowless sequence) technique to measure 13C-13C distances. The 'single-label' approach simplified analysis of DRAWS data, since only interstrand contacts are present, without the possibility of any intrastrand contacts. As previously reported [T.L.S. Benzinger, D.M. Gregory, T.S. Burkoth, H. Miller-Auer, D.G. Lynn, R.E. Botto, S.C. Meredith, Proc. Natl. Acad. Sci. 95 (1998) 13407.], contacts of approximately 5 A were observed at all residues studied, consistent with an extended parallel beta-sheet structure with each amino acid in exact register. Here, we propose that our strategy is completely generalizable, and provides a new approach for characterizing any iterative, self-associating biopolymer. Towards the end of generalizing and refining our approach, in this paper we evaluate several issues raised by our previous analyses. First, we consider the effects of double-quantum (DQ) transverse relaxation processes. Next, we discuss the effects of various multiple-spin geometries on modeling of DRAWS data. Several practical issues are also discussed: these include (1) the use of DQ filtering experiments, either to corroborate DRAWS data, or as a rapid screening assessment of the proper placement of isotopic spin labels; and (2) the comparison of solid samples prepared by either lyophilization or freezing. Finally, data obtained from the use of single labels is compared with that obtained in doubly 13C-labeled model compounds of known crystal structure. It is shown that such data are obtainable in far more complex peptide molecules. These data,taken together, refine the DRAWS method, and demonstrate its precision and utility in obtaining high resolution structural data in complex biomolecular aggregates such as Abeta.

Selective residual dipolar couplings in cross-linked elastomers by 1H double-quantum NMR spectroscopy

1H double-quantum (DQ) solid-state NMR spectroscopy under fast magic-angle spinning (MAS) is introduced as a new spectroscopic tool for the investigation of the structure and local chain dynamics of elastomers. Dipolar connectivities between the protons of the various functional groups can be directly established from the highly resolved DQ solid-state NMR spectra as is shown for a series of cross-linked poly(styrene-co-butadiene). More quantitatively, residual dipolar couplings within and between the functional groups are evaluated selectively from the build-up curves of the double-quantum signals in the limit of the spin-pair approximation. In particular, the CH-CH and the CH2-CH couplings of butadiene, which both act predominantly along the chain-segment direction, have been measured relative to the CH2 coupling. The total build-up intensity is correlated with the cross-link density.