CHHC and H–H magnetization exchange: Analysis by experimental solid-state NMR and 11-spin density-matrix simulations

A protocol is presented for correcting the effect of non-specific cross-polarization in CHHC solid-state MAS NMR experiments, thus allowing the recovery of the ¹H–¹H magnetization exchange functions from the mixing-time dependent buildup of experimental CHHC peak intensity. The presented protocol also incorporates a scaling procedure to take into account the effect of multiplicity of a CH₂ or CH₃ moiety. Experimental CHHC buildup curves are presented for l-tyrosine·HCl samples where either all or only one in 10 molecules are U–¹³C labeled. Good agreement between experiment and 11-spin SPINEVOLUTION simulation (including only isotropic ¹H chemical shifts) is demonstrated for the initial buildup (t_mix < 100 μs) of CHHC peak intensity corresponding to an intramolecular close (2.5 Å) H–H proximity. Differences in the initial CHHC buildup are observed between the one in 10 dilute and 100% samples for cases where there is a close intermolecular H–H proximity in addition to a close intramolecular H–H proximity. For the dilute sample, CHHC cross-peak intensities tended to significantly lower values for long mixing times (500 μs) as compared to the 100% sample. This difference is explained as being due to the dependence of the limiting total magnetization on the ratio N_obs/N_tot between the number of protons that are directly attached to a ¹³C nucleus and hence contribute significantly to the observed ¹³C CHHC NMR signal, and the total number of ¹H spins into the system. ¹H–¹H magnetization exchange curves extracted from CHHC spectra for the 100% l-tyrosine·HCl sample exhibit a clear sensitivity to the root sum squared dipolar coupling, with fast buildup being observed for the shortest intramolecular distances (2.5 Å) and slower, yet observable buildup for the longer intermolecular distances (up to 5 Å).     

3D 1H-13C-14N correlation solid-state NMR spectrum

Nitrogen-14 (spin I = 1) has always been a nucleus difficult to observe in solid-state NMR and until recently its observation was restricted to one-dimensional (1D) spectra. We present here the first 3D ¹H–¹³C–¹⁴N NMR correlation spectrum. This spectrum was acquired on a test sample l-histidine·HCl·H₂O using a recently developed technique, which consists in indirectly observing ¹⁴N nuclei via dipolar recoupling with an HMQC-type experiment.     

Accurate Measurement of Small Spin–Spin Couplings in Partially Aligned Molecules Using a Novel J-Mismatch Compensated Spin-State-Selection Filter

The accurate measurement of small spin–spin coupling constants in macromolecules dissolved in a liquid crystalline phase is important in the context of molecular structure investigation by modern liquid state NMR. A new spin-state-selection filter, DIPSAP, is presented with significantly reduced sensitivity to J-mismatch of the filter delays compared to previously proposed pulse sequences. DIPSAP presents an attractive new approach for the accurate measurement of small spin–spin coupling constants in molecules dissolved in anisotropic solution. Application to the measurement of ¹⁵N–¹³C′ and ¹H^N–¹³C′ coupling constants in the peptide planes of ¹³C, ¹⁵N labeled proteins demonstrates the high accuracy obtained by a DIPSAP-based experiment.     

The 2D {P} Spin-Echo-Difference Constant-Time [C, H]-HMQC Experiment for Simultaneous Determination of JH3′P and JC4′P in C-Labeled Nucleic Acids and Their Protein Complexes

A two-dimensional {³¹P} spin-echo-difference constant-time [¹³C, ¹H]-HMQC experiment (2D {³¹P}-sedct-[¹³C, ¹H]-HMQC) is introduced for measurements of ³J_C4′P and ³J_H3′P scalar couplings in large ¹³C-labeled nucleic acids and in DNA–protein complexes. This experiment makes use of the fact that ¹H–¹³C multiple-quantum coherences in macromolecules relax more slowly than the corresponding ¹³C single-quantum coherences. ³J_C4′P and ³J_H3′P are related via Karplus-type functions with the phosphodiester torsion angles β and ε, respectively, and their experimental assessment therefore contributes to further improved quality of NMR solution structures. Data are presented for a uniformly ¹³C, ¹⁵N-labeled 14-base-pair DNA duplex, both free in solution and in a 17-kDa protein–DNA complex.     

Separation of Anisotropy and Exchange Broadening Using N CSA–N–H Dipole–Dipole Relaxation Cross-Correlation Experiments

Based on the measurement of cross-correlation rates between ¹⁵N CSA and ¹⁵N–¹H dipole–dipole relaxation we propose a procedure for separating exchange contributions to transverse relaxation rates (R₂ = 1/T₂) from effects caused by anisotropic rotational diffusion of the protein molecule. This approach determines the influence of anisotropy and chemical exchange processes independently and therefore circumvents difficulties associated with the currently standard use of T₁/T₂ ratios to determine the rotational diffusion tensor. We find from computer simulations that, in the presence of even small amounts of internal flexibility, fitting T₁/T₂ ratios tends to underestimate the anisotropy of overall tumbling. An additional problem exists when the N–H bond vector directions are not distributed homogeneously over the surface of a unit sphere, such as in helix bundles or β-sheets. Such a case was found in segment 4 of the gelation factor (ABP 120), an F-actin cross-linking protein, in which the diffusion tensor cannot be calculated from T₁/T₂ ratios. The ¹⁵N CSA tensor of the residues for this β-sheet protein was found to vary even within secondary structure elements. The use of a common value for the whole protein molecule therefore might be an oversimplification. Using our approach it is immediately apparent that no exchange broadening exists for segment 4 although strongly reduced T₂ relaxation times for several residues could be mistaken as indications for exchange processes.     

Structural analysis of uniformly C-labelled solids from selective angle measurements at rotational resonance

We demonstrate that individual H–C–C–H torsional angles in uniformly labelled organic solids can be estimated by selective excitation of ¹³C double-quantum coherences under magic-angle spinning at rotational resonance. By adapting a straightforward one-dimensional experiment described earlier [T. Karlsson, M. Eden, H. Luhman, M.H. Levitt, J. Magn. Reson. 145 (2000) 95–107], a double-quantum filtered spectrum selective for Cα and Cβ of uniformly labelled l-[¹³C,¹⁵N]valine is obtained with 25% efficiency. The evolution of Cα–Cβ double-quantum coherence under the influence of the dipolar fields of bonded protons is monitored to provide a value of the Hα–Cα–Cβ–Hβ torsional angle that is consistent with the crystal structure. In addition, double-quantum filtration selective for C6 and C1′ of uniformly labelled [¹³C,¹⁵N]uridine is achieved with 12% efficiency for a ¹³C–¹³C distance of 2.5 Å, yielding a reliable estimate of the C6–H and C1′–H projection angle defining the relative orientations of the nucleoside pyrimidine and ribose rings. This procedure will be useful, in favourable cases, for structural analysis of fully labelled small molecules such as receptor ligands that are not readily synthesised with labels placed selectively at structurally diagnostic sites.     

Isotope Effects on theO,H Coupling Constant and theO–{H} Nuclear Overhauser Effect in Water

The NMR spectra of solutions of 30%¹⁷O-enriched H₂O and D₂O in nitromethane display the resonances of the three isotopomers H₂O, HDO, and D₂O. All¹⁷O,¹H and¹⁷O,²H coupling constants and the primary and secondary isotope effects onJ(¹⁷O,¹H) have been determined. The primary effect is −1.0 ± 0.2 Hz and the secondary effect is −0.07 ± 0.04 Hz. Using integrated intensities in the¹⁷O NMR spectra, the equilibrium constant for the reaction H₂O + D₂O 2HDO is found to be 3.68 ± 0.2 at 343 K. From the relative integrated intensities of proton-coupled and -decoupled spectra the¹⁷O–{¹H} NOE is estimated for the first time, resulting in values of 0.908 and 0.945 for H₂O and HDO, respectively. This means that dipole–dipole interactions contribute about 2.5% to the overall¹⁷O relaxation rate in H₂O dissolved in nitromethane.     

The factor of nonparaxial Hermite–Gaussian beams and related problems

On the basis of the second-order moment of the power density and in the use of the series expansion, the expressions for the beam width, far-field divergence angle and M² factor of nonparaxial Hermite–Gaussian (H–G) beams are derived and expressed in a sum of the series of the Gamma function. The theoretical results are illustrated with numerical examples. The M² factor of nonparaxial H–G beams depends not only on the beam order m, but also on the waist-width to wavelength ratio w₀/λ. The far-field divergence angles of nonparaxial H–G beams with even and odd orders approach their upper limits θ_max=63.435 and 73.898, respectively, which results in M²<1 as w₀/λ→0. For the special case of m=0 our results reduce to those of nonparaxial Gaussian beams. Some problems related to the characterization of the nonparaxial beam quality are also discussed.     

2H NMR of Deuterofullerites C60D x

Deuterofullerites C₆₀D _x have been studied by means of ²H NMR spectroscopy. It has been established that there are two types of carbon–deuterium bindings in the samples under study: tip C–D with quadrupole constant coupling (QCC) 171 kHz and bridge –C...D...C– with QCC 56 kHz. It is possible that the latter bond is a result of the rigidity of the lattice, which is unusual for fullerene compounds.     

Separating Structure and Dynamics in CSA/DD Cross-Correlated Relaxation: A Case Study on Trehalose and Ubiquitin

We present two new sensitivity enhanced gradient NMR experiments for measuring interference effects between chemical shift anisotropy (CSA) and dipolar coupling interactions in a scalar coupled two-spin system in both the laboratory and rotating frames. We apply these methods for quantitative measurement of longitudinal and transverse cross-correlation rates involving interference of ¹³C CSA and ¹³C–¹H dipolar coupling in a disaccharide, α,α- -trehalose, at natural abundance of ¹³C as well as interference of amide ¹⁵N CSA and ¹⁵N–¹H dipolar coupling in uniformly ¹⁵N-labeled ubiquitin. We demonstrate that the standard heteronuclear T₁, T₂, and steady-state NOE autocorrelation experiments augmented by cross-correlation measurements provide sufficient experimental data to quantitatively separate the structural and dynamic contributions to these relaxation rates when the simplifying assumptions of isotropic overall tumbling and an axially symmetric chemical shift tensor are valid.     

In Vivo Detection of N-Coupled Protons in Rat Brain by ISIS Localization and Multiple-Quantum Editing

Three-dimensional image-selected in vivo spectroscopy (ISIS) was combined with phase-cycled ¹H–¹⁵N heteronuclear multiple-quantum coherence (HMQC) transfer NMR for localized selective observation of protons J-coupled to ¹⁵N in phantoms and in vivo. The ISIS–HMQC sequence, supplemented by jump–return water suppression, permitted localized selective observation of 2–5 μmol of [¹⁵N_indole]tryptophan, a precursor of the neurotransmitter serotonin, through the ¹⁵N-coupled proton in 20–40 min of acquisition in vitro at 4.7 T. In vivo, the amide proton of [5-¹⁵N]glutamine was selectively observed in the brain of spontaneously breathing ¹⁵NH₄⁺-infused rats, using a volume probe with homogeneous ¹H and ¹⁵N fields. Signal recovery after three-dimensional localization was 72–82% in phantoms and 59 ± 4% in vivo. The result demonstrates that localized selective observation of ¹⁵N-coupled protons, with complete cancellation of all other protons except water, can be achieved in spontaneously breathing animals by the ISIS–HMQC sequence. This sequence performs both volume selection and heteronuclear editing through an addition/subtraction scheme and predicts the highest intrinsic sensitivity for detection of ¹⁵N-coupled protons in the selected volume. The advantages and limitations of this method for in vivo application are compared to those of other localized editing techniques currently in use for non-exchanging protons.     

J Coupling between C and H across Hydrogen Bonds in Proteins

Two new two- or three-dimensional NMR methods for measuring ^3hJ_C′N and ^2hJ_C′H coupling constants across hydrogen bonds in proteins are presented. They are tailored to suit the size of the TROSY effect, i.e., the degree of interference between dipolar and chemical shift anisotropy relaxation mechanisms. The methods edit 2D or 3D spectra into two separate subspectra corresponding to the two possible spin states of the ¹H^N spin during evolution of ¹³CO coherences. This allows ^2hJ_C′H to be measured in an E.COSY-type way while ^3hJ_C′N can be measured in the so-called quantitative way provided a reference spectrum is also recorded. A demonstration of the new methods is shown for the ¹⁵N,¹³C-labeled protein chymotrypsin inhibitor 2.     

N Chemical Shift Tensor Magnitude and Orientation in the Molecular Frame of Uracil Determined via MAS NMR

The potential of heteronuclear MAS NMR spectroscopy for the characterization of ¹⁵N chemical shift (CS) tensors in multiply labeled systems has been illustrated, in one of the first studies of this type, by a measurement of the chemical shift tensor magnitude and orientation in the molecular frame for the two ¹⁵N sites of uracil. Employing polycrystalline samples of ¹⁵N₂ and 2-¹³C,¹⁵N₂-labeled uracil, we have measured, via ¹⁵N–¹³C REDOR and ¹⁵N–¹H dipolar-shift experiments, the polar and azimuthal angles (θ, ψ) of orientation of the ¹⁵N–¹³C and ¹⁵N–¹H dipolar vectors in the ¹⁵N CS tensor frame. The (θ_NC, ψ_NC) angles are determined to be (92 ± 10°, 100 ± 5°) and (132 ± 3°, 88 ± 10°) for the N1 and N3 sites, respectively. Similarly, (θ_NH, ψ_NH) are found to be (15 ± 5°, −80 ± 10°) and (15 ± 5°, 90 ± 10°) for the N1 and N3 sites, respectively. These results obtained based only on MAS NMR measurements have been compared with the data reported in the literature.     

The First in Vivo Observation of C–N Coupling in Mammalian Brain

[5-¹³C,¹⁵N]Glutamine, with ¹J(¹³C–¹⁵N) of 16 Hz, was observed in vivo in the brain of spontaneously breathing rats by ¹³C MRS at 4.7 T. The brain [5-¹³C]glutamine peak consisted of the doublet from [5-¹³C,¹⁵N]glutamine and the center [5-¹³C,¹⁴N]glutamine peak, resulting in an apparent triplet with a separation of 8 Hz. The time course of formation of brain [5-¹³C,¹⁵N]glutamine was monitored in vivo with a time resolution of 20–35 min. This [5-¹³C,¹⁵N]glutamine was formed by glial uptake of released neurotransmitter [5-¹³C]glutamate and its reaction with ¹⁵NH₃ catalyzed by the glia-specific glutamine synthetase. The neurotransmitter glutamate C5 was selectively¹³C-enriched by intravenous [2,5-¹³C]glucose infusion to ¹³C-label whole-brain glutamate C5, followed by [¹²C]glucose infusion to chase ¹³C from the small and rapidly turning-over glial glutamate pool, leaving ¹³C mainly in the neurotransmitter [5-¹³C]glutamate pool, which is sequestered in vesicles until release. Hence, the observed [5-¹³C,¹⁵N]glutamine arises from a coupling between ¹³C of neuronal origin and ¹⁵N of glial origin. Measurement of the rate of brain [5-¹³C,¹⁵N]glutamine formation provides a novel noninvasive method of studying the kinetics of neurotransmitter uptake into glia in vivo, a process that is crucial for protecting the brain from glutamate excitotoxicity.     

Deuterium Nuclear Spin–Lattice Relaxation Times and Quadrupolar Coupling Constants in Isotopically Labeled Saccharides

¹³C and ²H spin–lattice relaxation times have been determined by inversion recovery in a range of site-specific ¹³C- and ²H-labeled saccharides under identical solution conditions, and the data were used to calculate deuterium nuclear quadrupolar coupling constants (²H NQCC) at specific sites within cyclic and acyclic forms in solution. ¹³C T₁ values ranged from 0.6 to 8.2 s, and ²H T₁ values ranged from 79 to 450 ms, depending on molecular structure (0.4 M sugar in 5 mM EDTA (disodium salt) in ²H₂O-depleted H₂O, pH 4.8, 30°C). In addition to providing new information on ¹³C and ²H relaxation behavior of saccharides in solution, the resulting ²H1 NQCC values reveal a dependency on anomeric configuration within aldopyranose rings, whereas ²H NQCC values at other ring sites appear less sensitive to configuration at C1. In contrast, ²H NQCC values at both anomeric and nonanomeric sites within aldofuranose rings appear to be influenced by anomeric configuration. These experimental observations were confirmed by density functional theory (DFT) calculations of ²H NQCC values in model aldopyranosyl and aldofuranosyl rings.     

Recoupled Polarization-Transfer Methods for Solid-State H–C Heteronuclear Correlation in the Limit of Fast MAS

An in-depth account of the effects of homonuclear couplings and multiple heteronuclear couplings is given for a recently published technique for ¹H–¹³C dipolar correlation in solids under very fast MAS, where the heteronuclear dipolar coupling is recoupled by means of REDOR π-pulse trains. The method bears similarities to well-known solution-state NMR techniques, which form the framework of a heteronuclear multiple-quantum experiment. The so-called recoupled polarization-transfer (REPT) technique is versatile in that rotor-synchronized ¹H–¹³C shift correlation spectra can be recorded. In addition, weak heteronuclear dipolar coupling constants can be extracted by means of spinning sideband analysis in the indirect dimension of the experiment. These sidebands are generated by rotor encoding of the reconversion Hamiltonian. We present generalized variants of the initially described heteronuclear multiple-quantum correlation (HMQC) experiment, which are better suited for certain applications. Using these techniques, measurements on model compounds with ¹³C in natural abundance, as well as simulations, confirm the very weak effect of ¹H–¹H homonuclear couplings on the spectra recorded with spinning frequencies of 25–30 kHz. The effect of remote heteronuclear couplings on the spinning-sideband patterns of CH_n groups is discussed, and ¹³C spectral editing of rigid organic solids is shown to be practicable with these techniques.     

Determination of Multiple φ-Torsion Angles in Proteins by Selective and Extensive C Labeling and Two-Dimensional Solid-State NMR

We describe an approach to efficiently determine the backbone conformation of solid proteins that utilizes selective and extensive ¹³C labeling in conjunction with two-dimensional magic-angle-spinning NMR. The selective ¹³C labeling approach aims to reduce line broadening and other multispin complications encountered in solid-state NMR of uniformly labeled proteins while still enhancing the sensitivity of NMR spectra. It is achieved by using specifically labeled glucose or glycerol as the sole carbon source in the protein expression medium. For amino acids synthesized in the linear part of the biosynthetic pathways, [1-¹³C]glucose preferentially labels the ends of the side chains, while [2-¹³C]glycerol labels the C^α of these residues. Amino acids produced from the citric-acid cycle are labeled in a more complex manner. Information on the secondary structure of such a labeled protein was obtained by measuring multiple backbone torsion angles φ simultaneously, using an isotropic–anisotropic 2D correlation technique, the HNCH experiment. Initial experiments for resonance assignment of a selectively ¹³C labeled protein were performed using ¹⁵N–¹³C 2D correlation spectroscopy. From the time dependence of the ¹⁵N–¹³C dipolar coherence transfer, both intraresidue and interresidue connectivities can be observed, thus yielding partial sequential assignment. We demonstrate the selective ¹³C labeling and these 2D NMR experiments on a 8.5-kDa model protein, ubiquitin. This isotope-edited NMR approach is expected to facilitate the structure determination of proteins in the solid state.     

C Chemical Shift and C–N Dipolar Coupling Tensors Determined by C Rotary Resonance Solid-State NMR

This work explores the utility of simple rotary resonance experiments for the determination of the magnitude and orientation of ¹³C chemical shift tensors relative to one or more ¹³C–¹⁴N internuclear axes from ¹³C magic-angle-spinning NMR experiments. The experiment relies on simultaneous recoupling of the anisotropic ¹³C chemical shift and ¹³C–¹⁴N dipole–dipole coupling interactions using 2D rotary resonance NMR with RF irradiation on the ¹³C spins only. The method is demonstrated by experiments and numerical simulations for the ¹³C^α spins in powder samples of -alanine and glycine with ¹³C in natural abundance. To investigate the potential of the experiment for determination of relative/absolute tensor orientations and backbone dihedral angles in peptides, the influence from long-range dipolar coupling to sequential ¹⁴N spins in a peptide chain (¹⁴N_i–¹³C^α_i–¹⁴N_i+1 and ¹⁴N_i+1–¹³C′_i–¹⁴N_i three-spin systems) as well as residual quadrupolar–dipolar coupling cross-terms is analyzed numerically.     

A core level and valence band photoemission study of the (1 1 1) and ( ) surfaces of 3C–SiC

A core level and valence band photoemission study of thick 3C–SiC(1 1 1) and 3C–SiC( ) epilayers grown by sublimation epitaxy is reported. The as introduced samples show threefold 1×1 low-energy electron diffraction patterns. For the Si face and reconstructed surfaces develop after in situ heating to 1100°C and 1300°C, respectively. For the C face a 3×3 reconstruction form after heating to 980°C. A semiconducting behavior is observed for the and 3×3 reconstructed surfaces while the reconstruction show a Fermi edge and thus a metallic-like behavior. The surface state on the surface is investigated and found to have Λ₁ symmetry and a total band width of 0.10 eV within the first surface Brillouin zone. For the Si 2p and C 1s core levels binding energies and surface shifted components are extracted and compared to earlier reported results for 6H– and 4H–SiC.     

Two- and Three-Dimensional H/C PISEMA Experiments and Their Application to Backbone and Side Chain Sites of Amino Acids and Peptides

Two-dimensional ¹H/¹³C polarization inversion spin exchange at the magic angle experiments were applied to single crystal samples of amino acids to demonstrate their potential utility on oriented samples of peptides and proteins. High resolution is achieved and structural information obtained on backbone and side chain sites from these spectra. A triple-resonance experiment that correlates the ¹H–¹³C_α dipolar coupling frequency with the chemical shift frequencies of the α-carbon, as well as the directly bonded amide ¹⁵N site, is also demonstrated. In this experiment the large ¹H–¹³C_α heteronuclear dipolar interaction provides an independent frequency dimension that significantly improves the resolution among overlapping ¹³C resonances of oriented polypeptides, while simultaneously providing measurements of the ¹³C_α chemical shift, ¹H–¹³C dipolar coupling, and ¹⁵N chemical shift frequencies and angular restraints for backbone structure determination.