Accurate measurement of H(N)-H(alpha) residual dipolar couplings in proteins.

A method for accurately measuring H(N)-H(alpha) residual dipolar couplings is described. Using this technique, both the sign and magnitude of the coupling can be determined easily. Residual dipolar coupling between H(N)(i)-H(alpha)(i) and H(N)(i)-H(alpha)(i-1) were measured for the FK506 binding protein complexed to FK506. The experimental values were in excellent agreement with predictions based on an X-ray crystal structure of the protein/ligand complex, suggesting that these residual dipolar couplings will provide accurate structural constraints for the refinement of protein structures determined by NMR.     

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.     

Measurement of one and two bond N–C couplings in large proteins by TROSY-based J-modulation experiments

Residual dipolar couplings (RDCs) between NC′ and NC^α atoms in polypeptide backbones of proteins contain information on the orientation of bond vectors that is complementary to that contained in NH RDCs. The ¹J_NC^α and ²J_NC^α scalar couplings between these atoms also display a Karplus relation with the backbone torsion angles and report on secondary structure. However, these N–C couplings tend to be small and they are frequently unresolvable in frequency domain spectra having the broad lines characteristic of large proteins. Here a TROSY-based J-modulated approach for the measurement of small ¹⁵N–¹³C couplings in large proteins is described. The cross-correlation interference effects inherent in TROSY methods improve resolution and signal to noise ratios for large proteins, and the use of J-modulation to encode couplings eliminates the need to remove frequency distortions from overlapping peaks during data analysis. The utility of the method is demonstrated by measurement of ¹J_NC′, ¹J_NC^α, and ²J_NC^α scalar couplings and ¹D_NC′ and ¹D_NC^α residual dipolar couplings for the myristoylated yeast ARF1·GTPγs protein bound to small lipid bicelles, a system with an effective molecule weight of 70 kDa.     

Determination of Backbone Angle ψ in Proteins Using a TROSY-Based α/β-HN(CO)CA-J Experiment

Transverse relaxation-optimized NMR experiment (TROSY) for the measurement of three-bond scalar coupling constant between ¹H^α_i−1 and ¹⁵N_i defining the dihedral angle ψ is described. The triple-spin-state-selective experiment allows measurement of ³J_H^αN from ¹³C^α, ¹⁵N, and ¹H^N correlation spectra H₂O with minimum resonance overlap. Transverse relaxation of ¹³C^α spin is minimized by using spin-state-selective filtering and by acquiring a signal longer in ¹⁵N-dimension in a manner of semi-constant-time TROSY evolution. The ³J_H^αN values obtained with the proposed α/β-HN(CO)CA-J TROSY scheme are in good agreement with the values measured earlier from ubiquitin in D₂O using the HCACO[N] experiment.     

Measurement of Small One-Bond Proton–Carbon Residual Dipolar Coupling Constants in Partially Oriented C Natural Abundance Oligosaccharide Samples: Analysis of Heteronuclear JCH-Modulated Spectra with the BIRD Inversion Pulse

Two 2D J-modulated HSQC-based experiments were designed for precise determination of small residual dipolar one-bond carbon–proton coupling constants in ¹³C natural abundance carbohydrates. Crucial to the precision of a few hundredths of Hz achieved by these methods was the use of long modulation intervals and BIRD pulses, which acted as semiselective inversion pulses. The BIRD pulses eliminated effective evolution of all but ¹J_CH couplings, resulting in signal modulation that can be described by simple modulation functions. A thorough analysis of such modulation functions for a typical four-spin carbohydrate spin system was performed for both experiments. The results showed that the evolution of the ¹H–¹H and long-range ¹H–¹³C couplings during the BIRD pulses did not necessitate the introduction of more complicated modulation functions. The effects of pulse imperfections were also inspected. While weakly coupled spin systems can be analyzed by simple fitting of cross peak intensities, in strongly coupled spin systems the evolution of the density matrix needs to be considered in order to analyse data accurately. However, if strong coupling effects are modest the errors in coupling constants determined by the “weak coupling” analysis are of similar magnitudes in oriented and isotropic samples and are partially cancelled during dipolar coupling calculation. Simple criteria have been established as to when the strong coupling treatment needs to be invoked.     

Molecular dynamics and information on possible sites of interaction of intramyocellular metabolites in vivo from resolved dipolar couplings in localized H NMR spectra

Proton NMR resonances of the endogenous metabolites creatine and phosphocreatine ((P)Cr), taurine (Tau), and carnosine (Cs, β-alanyl-l-histidine) were studied with regard to residual dipolar couplings and molecular mobility. We present an analysis of the direct ¹H–¹H interaction that provides information on motional reorientation of subgroups in these molecules in vivo. For this purpose, localized ¹H NMR experiments were performed on m. gastrocnemius of healthy volunteers using a 1.5-T clinical whole-body MR scanner. We evaluated the observable dipolar coupling strength SD₀ (S = order parameter) of the (P)Cr-methyl triplet and the Tau-methylene doublet by means of the apparent line splitting. These were compared to the dipolar coupling strength of the (P)Cr-methylene doublet. In contrast to the aliphatic protons of (P)Cr and Tau, the aromatic H2 (δ = 8 ppm) and H4 (δ = 7 ppm) protons of the imidazole ring of Cs exhibit second-order spectra at 1.5 T. This effect is the consequence of incomplete transition from Zeeman to Paschen-Back regime and allows a determination of SD₀ from H2 and H4 of Cs as an alternative to evaluating the multiplet splitting which can be measured directly in high-resolution ¹H NMR spectra. Experimental data showed striking differences in the mobility of the metabolites when the dipolar coupling constant D₀ (calculated with the internuclear distance known from molecular geometry in the case of complete absence of molecular dynamics and motion) is used for comparison. The aliphatic signals involve very small order parameters S ≈ (1.4 − 3) × 10⁻⁴ indicating rapid reorientation of the corresponding subgroups in these metabolites. In contrast, analysis of the Cs resonances yielded S ≈ (113 − 137) × 10⁻⁴. Thus, the immobilization of the Cs imidazole ring owing to an anisotropic cellular substructure in human m. gastrocnemius is much more effective than for (P)Cr and Tau subgroups. Furthermore, ¹H NMR experiments on aqueous model solutions of histidine and N-acetyl-l-aspartate (NAA) enabled the assignment of an additional signal component at δ = 8 ppm of Cs in vivo to the amide group at the peptide bond. The visibility of this proton could result from hydrogen bonding which would agree with the anticipated stronger motional restriction of Cs. Referring to the observation that all dipolar-coupled multiplets resolved in localized in vivo ¹H NMR spectra of human m. gastrocnemius collapse simultaneously when the fibre structure is tilted towards the magic angle (θ ≈ 55°), a common model for molecular confinement in muscle tissue is proposed on the basis of an interaction of the studied metabolites with myocellular membrane phospholipids.     

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.     

Direct Refinement against Proton–Proton Dipolar Couplings in NMR Structure Determination of Macromolecules

The computational tools necessary for making use of ¹H–¹H dipolar couplings in macromolecular structure refinement are presented. Potentials are described for direct refinement against ¹H–¹H dipolar couplings of known sign as well as of unknown sign. In addition, a multiple potential is developed for prochiral protons whose stereospecific assignments are unknown. The utility of direct ¹H–¹H dipolar coupling refinement is illustrated using the small protein ubiquitin. It is shown that direct ¹H–¹H dipolar coupling refinement leads to improvements in the precision, accuracy, and quality of the resulting structures.     

Reentrant transitions in the van Hemmen model of a spin glass

The van Hemmen model of a spin glass, which is an Ising model with random couplings J_ij between sites i and j equal to J₀ + J(ξ_iη_j + ξ_jη_i), where (ξ_i, η_i) are independent, identically distributed random variables, is studied in the pair approximation of the cluster variation method. For the family of probability distributions (1 − p)δ(ξ_i − a) + pδ(ξ_i) + (1 − p)δ(ξ_i + a), where p is varied, phase diagrams are constructed. They are qualitatively different from the mean-field phase diagrams and display a competition between tendencies towards spin-glass and towards ferromagnetic ordering, which results in reentrant transitions. It is argued that the observed effects are not accidental but are borne by the competition of bonds of the underlying lattice system.     

Dipolar Coupling Information in Multispin Systems: Application of a Compensated REDOR NMR Approach to Inorganic Phosphates

Anexperimental strategy has been developed for measuring multiple dipole–dipole interactions in inorganic compounds using the technique of rotational echo double resonance (REDOR) NMR. Geometry-independent information about the dipole couplings between the observe nuclear species S (arbitrary quantum number) and the heteronuclear species I (spin- ) can be conveniently obtained from the experimental curve of ΔS/S₀ versus dipolar evolution time by limiting the analysis to the initial data range 0 < ΔS/S₀ < 0.30. Numerical simulations have been carried out on a three-spin system of type SI₂ in order to assess the effect of the I–I homonuclear dipole–dipole coupling and the influence of experimental imperfections such as finite pulse length and misadjustments of the 180° pulses applied to the I-spin species. The simulations show further that within the initial data range the effects of such misadjustments can be internally compensated by a modified sequence having an additional 180° pulse on the I channel in the middle of the dipolar evolution periods. Experimental ²⁷Al{³¹P} REDOR results on the multispin systems Al(PO₃)₃, AlPO₄, [AlPO₄]₁₂(C₃H₇)₄NF, and Na₃PO₄ confirm the general utility of this approach. Thus, for applications to unknown systems the compensation strategy obviates calibration procedures with model compounds.     

On higher derivative corrections of tachyon action

We have examined the momentum expansion of the disk level S-matrix element of two tachyons and two gauge fields to find, up to on-shell ambiguity, the couplings of these fields in the world volume theory of N coincident non-BPS D-branes to all order of α^′. Using the proposal that the action of D-brane–anti-D-brane is given by the projection of the action of two non-BPS D-branes with (−1)^F_L, we find the corresponding couplings in the world volume theory of the brane–anti-brane system. Using these infinite tower of couplings, we then calculate the massless pole of the scattering amplitude of one RR field, two tachyons and one gauge field in the brane–anti-brane theory. We find that the massless pole of the field theory amplitude is exactly equal to the massless pole of the disk level S-matrix element of one RR, two tachyons and one gauge field to all order of α^′. We have also found the couplings of four tachyons to all order of α^′ by examining the S-matrix element of four tachyons.     

Contribution to the Analysis of theA2←XA1“Wulf” Transition of Ozone by High-Resolution Fourier Transform Spectrometry

The analysis of the rotational structure of the high-resolution Fourier transform 0⁰₀absorption spectrum of the³A₂←X¹A₁band system of the “Wulf” transition of the isotopomer¹⁶O₃of ozone is reported for the first time. With a near pure case (b) coupling model for the upper triplet state, we have assigned a significant portion of the spectrum, mainly theF₁(J=N+ 1) andF₂(J=N) spin components, primarily in the lower frequency region of the band. The lines corresponding to theF₃(J=N− 1) component are weak at lower frequencies and heavily congested in the central and higher frequency regions of the spectrum. Perturbations and predissociation phenomena have reduced the effective lifetime of the metastable³A₂state and have also limited the number of transitions included in the least-squares fit of the band. Approximately 100 lines have been assigned in the range from 9100–9550 cm⁻¹. Three rotational, three centrifugal distortion, three spin–rotation, and one spin–spin constant were varied. The geometry of the molecule in the³A₂state, as determined from these constants, isr= 1.345 Å and θ = 98.9°, in good agreement withab initioresults.     

Electrical transport, magnetic and thermal properties of icosahedral Al–Pd–Mn quasicrystals

We report measurements of electrical resistivity (ρ), Hall coefficient (R_H), magnetization (M) and specific heat (C_p(T)) of high-quality icosahedral Al_70.4Pd_20.8Mn_8.8 phases with different thermal treatment. An improvement in the quasi-crystallinity upon the annealing treatment caused a drastic increase in ρ up to 7000 μΩ cm accompanied by a very small electronic specific heat coefficient γ. The low temperature ρ(T) data has been analyzed in terms of weak localization and electron–electron interaction effects. The Hall resistivity (ρ_H) is found to be strongly temperature-dependent and varies linearly with the magnetization (M) for the same field and temperature. Magnetization measurement reveals that more conductive samples are more magnetic and vice versa. Magnetic susceptibility (χ) data of all the annealed samples agrees with the Curie–Weiss-like behavior implying the existence of localized moments. The negative Curie–Weiss temperature (θ) indicates strong antiferromagnetic coupling between individual Mn atoms. The magnetic Mn concentration is found to be small, ranging from 1.73×10^-4 for the less magnetic sample studied up to 3×10^-3 for the more magnetic one. The small electronic specific heat coefficient obtained for all the samples suggests a significant reduction in the electronic density of states (DOS) at the Fermi level (E_F) upon thermal annealing treatment.     

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.     

Noncommutative theories, the axial anomaly, Fujikawa's method and the Atiyah–Singer index

Fujikawa's method is employed to compute at first order in the noncommutative parameter the U(1)_A anomaly for noncommutative SU(N). We consider the most general Seiberg–Witten map which commutes with hermiticity and complex conjugation and a noncommutative matrix parameter, θ^μν, which is of “magnetic” type. Our results for SU(N) can be readily generalized to cover the case of general nonsemisimple gauge groups when the symmetric Seiberg–Witten map is used. Connection with the Atiyah–Singer index theorem is also made.     

Cosine Modulated HSQC: A Rapid Determination of JHNHα Scalar Couplings in N-labeled Proteins

A two-dimensional HSQC-based NMR method, ¹⁵N-COSMO-HSQC, is presented for the rapid determination of homonuclear ³J_HNHα couplings in ¹⁵N-labeled proteins in solution. Scalar couplings are extracted by comparing the intensity of two separate datasets recorded with and without decoupling of the ³J_HNHα during a preparation period. The scalar couplings are introduced through a cosine modulation of the peak intensities. The experiment relies on a BIRD sandwich to selectively invert all amide protons H^N and is very simple to implement. ³J_HNHα couplings were determined using both the ¹⁵N-COSMO-HSQC and quantitative-J on ¹⁵N-labeled chemokine RANTES. The two experiments show well-correlated values.     

Laser Spectroscopy of the CCO Radical in the 0.77-μm Region: Analysis of theÃ(020)κΠ andÃΠi(001) States

TheÃ(020)κ³Π–X³Σ⁻(000) andóΠ_i(001)–X³Σ⁻(000) bands of the CCO radical have been investigated by laser spectroscopy with two types of tunable laser system. An analysis was made simultaneously for both the bands to establish line assignments and determine molecular constants for both theÃ(020) andÃ(001) states. A coupling constant between these two states was also determined by assuming the interaction to be of Fermi type.     

A Study of Dipolar Interactions and Dynamic Processes of Water Molecules in Tendon byH andH Homonuclear and Heteronuclear Multiple-Quantum-Filtered NMR Spectroscopy

The effect of proton exchange on the measurement of¹H–¹H,¹H–²H, and²H–²H residual dipolar interactions in water molecules in bovine Achilles tendons was investigated using double-quantum-filtered (DQF) NMR and new pulse sequences based on heteronuclear and homonuclear multiple-quantum filtering (MQF). Derivation of theoretical expressions for these techniques allowed evaluation of the¹H–¹H and¹H–²H residual dipolar interactions and the proton exchange rate at a temperature of 24°C and above, where no dipolar splitting is evident. The values obtained for these parameters at 24°C were 300 and 50 Hz and 3000 s⁻¹, respectively. The results for the residual dipolar interactions were verified by repeating the above measurements at a temperature of 1.5°C, where the spectra of the H₂O molecules were well resolved, so that the¹H–¹H dipolar interaction could be determined directly from the observed splitting. Analysis of the MQF experiments at 1.5°C, where the proton exchange was in the intermediate regime for the¹H–²H dipolar interaction, confirmed the result obtained at 24°C for this interaction. A strong dependence of the intensities of the MQF signals on the proton exchange rate, in the intermediate and the fast exchange regimes, was observed and theoretically interpreted. This leads to the conclusion that the MQF techniques are mostly useful for tissues where the residual dipolar interaction is not significantly smaller than the proton exchange rate. Dependence of the relaxation times and signal intensities of the MQF experiments on the orientation of the tendon with respect to the magnetic field was observed and analyzed. One of the results of the theoretical analysis is that, in the fast exchange regime, the signal decay rates in the MQF experiments as well as in the spin echo or CPMG pulse sequences (T₂) depend on the orientation as the square of the second-rank Legendre polynomial.     

More line narrowing in TROSY by decoupling of long-range couplings: shift correlation and JNC′ coupling constant measurements

Since the introduction of RDCs in high-resolution NMR studies of macromolecules, there is a growing interest in the development of accurate, and sensitive methods for determining coupling constants. Most methods for extracting these couplings are based on the measurement of the splitting between multiplet components in J-coupled spectra. However, these methods are often unreliable since undesired multiple-bond couplings can considerably broaden the multiplet components and consequently make accurate determination of their position difficult. To demonstrate one approach to this problem, G-BIRD^(r) decoupled TROSY sequences are proposed for the measurement of ¹J_NH and ¹J_NC′ coupling constants. Resolved or unresolved splittings due to remote protons are removed by a G-BIRD^(r) module employed during t₁ and as a result, spectra with narrow, well-resolved peaks are obtained from which heteronuclear one-bond couplings can be accurately measured. Moreover, introduction of a spin-state-selective α/β-filter in the TROSY sequence allows the separation of the ¹J_NC′ doublet components into two subspectra which contain the same number of peaks as the regular TROSY spectrum. The ¹J_NC′ couplings are obtained from the displacement between the corresponding peaks in the subspectra.     

Determination of the effective strong coupling constant from CLAS spin structure function data

We present a new extraction of the effective strong coupling constant α_s,g1(Q²). The result agrees with a previous determination and extends the measurement of the low and high Q² behavior of α_s,g1(Q²) that was previously deduced from sum rules. In particular, it experimentally verifies the lack of Q²-dependence of α_s,g1(Q²) in the low Q² limit. This fact is necessary for application of the AdS/CFT correspondence to QCD calculations. We provide a parameterization of α_s,g1(Q²) that can equivalently be used to parameterize the Q²-dependence of the generalized Gerasimov–Drell–Hearn and Bjorken sums.