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

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.

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.

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.

Solid-state NMR techniques for the structural determination of amyloid fibrils

This review discusses the solid-state NMR techniques developed for the study of amyloid fibrils. Literature up to the end of 2010 has been surveyed and the materials are organized according to five categories, viz. homonuclear dipolar recoupling and polarization transfer via J-coupling, heteronuclear dipolar recoupling, correlation spectroscopy, recoupling of chemical shift anisotropy, and tensor correlation. Our emphasis is on the NMR techniques and their practical aspects. The biological implications of the results obtained for amyloid fibrils are only briefly discussed. Our main objective is to showcase the power of NMR in the study of biological unoriented solids.

Determination of the backbone torsion psi angle by tensor correlation of chemical shift anisotropy and heteronuclear dipole-dipole interaction

We demonstrate that the backbone torsion psi angle of a uniformly labeled residue can be determined accurately by correlating the chemical shift anisotropy of the carbonyl carbon and the 13C-1H heteronuclear dipole-dipole interaction of the alpha carbon. To obtain the highest sensitivity for the psi angle determination, the following conditions are desired: (i) the recoupling pulse sequences for the CSA and the heteronuclear dipolar interactions are gamma encoded, in which the spatial parts of m=2 are selected; (ii) the homonuclear polarization transfer is based on the scalar spin-spin coupling. Experimental data were obtained for [U-13C, 15N]-alanine and N-acetyl-[U-13C, 15N]-d,l-valine under magic-angle spinning at 25kHz. Only three data points are required for the measurements and the dihedral angles determined are in excellent agreement with the diffraction data.

Sensitivity considerations in polarization transfer and filtering using dipole-dipole couplings: implications for biomineral systems

The robustness and sensitivities of different polarization-transfer methods that exploit heteronuclear dipole-dipole couplings are compared for a series of heterogeneous solid systems, including polycrystalline tetrakis(trimethylsilyl)silane (TKS), adamantane, a physical mixture of doubly (13)C,(15)N-enriched and singly (13)C-enriched polycrystalline glycine, and a powder sample of siliceous marine diatoms, Thalossiosira pseudonana. The methods were analyzed according to their respective frequency-matching spectra or resultant signal intensities. For a series of (13)C{(1)H} cross-polarization experiments, adiabatic passage Hartmann-Hahn cross-polarization (APHH-CP) was shown to have several advantages over other methods, including Hartmann-Hahn cross-polarization (HHCP), variable-amplitude cross-polarization (VACP), and ramped-amplitude cross-polarization (RACP). For X-Y systems, such as (13)C{(15)N}, high and comparable sensitivities were obtained by using APHH-CP with Lee-Goldburg decoupling or by using the transferred-echo double resonance (TEDOR) experiment. The findings were applied to multinuclear (1)H, (13)C, (15)N, and (29)Si CP MAS characterization of a powder diatom sample, a challenging inorganic-organic hybrid solid that places high demands on NMR signal sensitivity.

A DOQSY approach for the elucidation of torsion angle distributions in biopolymers: application to silk

Silk from the wild silkworm Samia cynthia ricini with a molecular mass of about 300kDa consists of alternating repeats of nano-crystalline poly-(Ala) and non-crystalline glycine-rich domains. The backbone torsion angles between pairs of these two amino acids is determined by DOQSY solid-state NMR spectroscopy: the alanine-rich domains are predominantly in a beta-sheet conformation, whereas the glycine-rich domains are found to be partially in an extended beta-sheet conformation and partially in an approximately 3(1)-helical conformation. In the cast film from liquid silk significantly different secondary structures were found: the alanine-rich domains are alpha-helical conformation, whereas the results for glycine-labelled sample are explained by a random-coil state. A detailed error analysis of the technique is presented.

Heteronuclear decoupling interference during symmetry-based homonuclear recoupling in solid-state NMR

We examine the influence of continuous-wave heteronuclear decoupling on symmetry-based double-quantum homonuclear dipolar recoupling, using experimental measurements, numerical simulations, and average Hamiltonian theory. There are two distinct regimes in which the heteronuclear interference effects are minimized. The first regime utilizes a moderate homonuclear recoupling field and a strong heteronuclear decoupling field; the second regime utilizes a strong homonuclear recoupling field and a weak or absent heteronuclear decoupling field. The second regime is experimentally accessible at moderate or high magic-angle-spinning frequencies and is particularly relevant for many realistic applications of solid-state NMR recoupling experiments to organic or biological materials.

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.

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.

Solid-State NMR Spectroscopy Method for Determination of the Backbone Torsion Angle ψ in Peptides with Isolated Uniformly Labeled Residues

We demonstrate a solid-state nuclear magnetic resonance technique, with the acronym ROCSA-LG, for the determination of backbone torsion angles psi in peptides with multiple, but isolated, uniformly labeled residues. The method correlates the 13C' chemical shift anisotropy and the 13Calpha-1Halpha heteronuclear dipolar tensors within a single uniformly labeled residue in a two-dimensional (2D) experiment. The technique requires the measurement of only five 2D spectra and is compatible with high-speed magic-angle spinning. Experimental results are presented for the 17-residue alpha-helical peptide MB(i+4)EK and for amyloid fibrils formed by the 15-residue peptide Abeta11-25.

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.

A test for the number of coupled spins I = 1/2 in magic-angle-spinning solids: zero-quantum recoupling of multiple-quantum coherences

Current methodologies for estimating the number of coupled spins I = 1/2 in solids are based upon the maximum multiple-quantum order that can be observed. This strategy establishes a clear lower bound on the number of coupled spins I = 1/2. However, it is difficult to ascertain the exact number of coupled spins, since the absence of a peak could be due either to the limited size of the spin system or to the experimental difficulty of exciting high-quantum orders and recovering those coherences into detectable signals. Herein, a supplementary test is proposed that allows one to determine whether a given coherence has the highest possible order in the spin system. The sample is subjected to magic-angle spinning and the behaviour of the coherence under a rotor-synchronised spin-echo sequence is compared to its behaviour under a zero-quantum recoupling sequence. A similar decay of the coherence in these two experiments is strong evidence for the coherence order being the maximum possible. We propose applications to biomolecular solid-state NMR spectroscopy.

Solid-state NMR determination of sugar ring pucker in (13)C-labeled 2'-deoxynucleosides

The H3'-C3'-C4'-H4' torsional angles of two microcrystalline 2'-deoxynucleosides, thymidine and 2'-deoxycytidine.HCl, doubly (13)C-labeled at the C3' and C4' positions of the sugar ring, have been measured by solid-state magic-angle-spinning nuclear magnetic resonance (NMR). A double-quantum heteronuclear local field experiment with frequency-switched Lee-Goldberg homonuclear decoupling was used. The H3'-C3'-C4'-H4' torsional angles were obtained by comparing the experimental curves with numerical simulations, including the two (13)C nuclei, the directly bonded (1)H nuclei, and five remote protons. The H3'-C3'-C4'-H4' angles were converted into sugar pucker angles and compared with crystallographic data. The delta torsional angles determined by solid-state NMR and x-ray crystallography agree within experimental error. Evidence is also obtained that the proton positions may be unreliable in the x-ray structures. This work confirms that double-quantum solid-state NMR is a feasible tool for studying sugar pucker conformations in macromolecular complexes that are unsuitable for solution NMR or crystallography.

Determination of multiple torsion-angle constraints in U-(13)C,(15)N-labeled peptides: 3D (1)H-(15)N-(13)C-(1)H dipolar chemical shift NMR spectroscopy in rotating solids

We demonstrate constraint of peptide backbone and side-chain conformation with 3D (1)H-(15)N-(13)C-(1)H dipolar chemical shift, magic-angle spinning NMR experiments. In these experiments, polarization is transferred from (15)N[i] by ramped SPECIFIC cross polarization to the (13)C(alpha)[i], (13)C(beta)[i], and (13)C(alpha)[i - 1] resonances and evolves coherently under the correlated (1)H-(15)N and (1)H-(13)C dipolar couplings. The resulting set of frequency-labeled (15)N(1)H-(13)C(1)H dipolar spectra depend strongly upon the molecular torsion angles phi[i], chi1[i], and psi[i - 1]. To interpret the data with high precision, we considered the effects of weakly coupled protons and differential relaxation of proton coherences via an average Liouvillian theory formalism for multispin clusters and employed average Hamiltonian theory to describe the transfer of (15)N polarization to three coupled (13)C spins ((13)C(alpha)[i], (13)C(beta)[i], and (13)C(alpha)[i - 1]). Degeneracies in the conformational solution space were minimized by combining data from multiple (15)N(1)H-(13)C(1)H line shapes and analogous data from other 3D (1)H-(13)C(alpha)-(13)C(beta)-(1)H (chi1), (15)N-(13)C(alpha)-(13)C'-(15)N (psi), and (1)H-(15)N[i]-(15)N[i + 1]-(1)H (phi, psi) experiments. The method is demonstrated here with studies of the uniformly (13)C,(15)N-labeled solid tripeptide N-formyl-Met-Leu-Phe-OH, where the combined data constrains a total of eight torsion angles (three phi, three chi1, and two psi): phi(Met) = -146 degrees, psi(Met) = 159 degrees, chi1(Met) = -85 degrees, phi(Leu) = -90 degrees, psi(Leu) = -40 degrees, chi1(Leu) = -59 degrees, phi(Phe) = -166 degrees, and chi1(Phe) = 56 degrees. The high sensitivity and dynamic range of the 3D experiments and the data analysis methods provided here will permit immediate application to larger peptides and proteins when sufficient resolution is available in the (15)N-(13)C chemical shift correlation spectra.

Specification and visualization of anisotropic interaction tensors in polypeptides and numerical simulations in biological solid-state NMR

Software facilitating numerical simulation of solid-state NMR experiments on polypeptides is presented. The Tcl-controlled SIMMOL program reads in atomic coordinates in the PDB format from which it generates typical or user-defined parameters for the chemical shift, J coupling, quadrupolar coupling, and dipolar coupling tensors. The output is a spin system file for numerical simulations, e.g., using SIMPSON (Bak, Rasmussen, and Nielsen, J. Magn. Reson. 147, 296 (2000)), as well as a 3D visualization of the molecular structure, or selected parts of this, with user-controlled representation of relevant tensors, bonds, atoms, peptide planes, and coordinate systems. The combination of SIMPSON and SIMMOL allows straightforward simulation of the response of advanced solid-state NMR experiments on typical nuclear spin interactions present in polypeptides. Thus, SIMMOL may be considered a "sample changer" to the SIMPSON "computer spectrometer" and proves to be very useful for the design and optimization of pulse sequences for application on uniformly or extensively isotope-labeled peptides where multiple-spin interactions need to be considered. These aspects are demonstrated by optimization and simulation of novel DCP and C7 based 2D N(CO)CA, N(CA)CB, and N(CA)CX MAS correlation experiments for multiple-spin clusters in ubiquitin and by simulation of PISA wheels from PISEMA spectra of uniaxially oriented bacteriorhodopsin and rhodopsin under conditions of finite RF pulses and multiple spin interactions.

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.