NMR determination of the torsion angle psi in alpha-helical peptides and proteins: the HCCN dipolar correlation experiment

Several existing methods permit measurement of the torsion angles phi, psi and chi in peptides and proteins with solid-state MAS NMR experiments. Currently, however, there is not an approach that is applicable to measurement of psi in the angular range -20 degree to -70 degree, commonly found in alpha-helical structures. Accordingly, we have developed a HCCN dipolar correlation MAS experiment that is sensitive and accurate in this regime. An initial REDOR driven (13)C'--(15)N dipolar evolution period is followed by the C' to C(alpha) polarization transfer and by Lee--Goldburg cross polarization recoupling of the (13)C(alpha)(1)H dipolar interaction. The difference between the effective (13)C(1)H and (13)C(15)N dipolar interaction strengths is balanced out by incrementing the (13)C--(15)N dipolar evolution period in steps that are a factor of R(R approximately omega(CH)/omega(CN)) larger than the (13)C--(1)H steps. The resulting dephasing curves are sensitive to variations in psi in the angular region associated with alpha-helical secondary structure. To demonstrate the validity of the technique, we apply it to N-formyl-[U-(13)C,(15)N] Met-Leu-Phe-OH (MLF). The value of psi extracted is consistent with the previous NMR measurements and close to that reported in diffraction studies for the methyl ester of MLF, N-formyl-[U-(13)C,(15)N]Met-Leu-Phe-OMe.     

Variable angle NMR spectroscopy and its application to the measurement of residual chemical shift anisotropy

The successful measurement of anisotropic NMR parameters like residual dipolar couplings (RDCs), residual quadrupolar couplings (RQCs), or residual chemical shift anisotropy (RCSA) involves the partial alignment of solute molecules in an alignment medium. To avoid any influence of the change of environment from the isotropic to the anisotropic sample, the measurement of both datasets with a single sample is highly desirable. Here, we introduce the scaling of alignment for mechanically stretched polymer gels by varying the angle of the director of alignment relative to the static magnetic field, which we call variable angle NMR spectroscopy (VA-NMR). The technique is closely related to variable angle sample spinning NMR spectroscopy (VASS-NMR) of liquid crystalline samples, but due to the mechanical fixation of the director of alignment no sample spinning is necessary. Also, in contrast to VASS-NMR, VA-NMR works for the full range of sample inclinations between 0° and 90°. Isotropic spectra are obtained at the magic angle. As a demonstration of the approach we measure 13C-RCSA values for strychnine in a stretched PDMS/CDCl? gel and show their usefulness for assignment purposes. In this context special care has been taken with respect to the exact calibration of chemical shift data, for which three approaches have been derived and tested.     

Determination of backbone angle psi in proteins using a TROSY-based alpha/beta-HN(CO)CA-J experiment

Transverse relaxation-optimized NMR experiment (TROSY) for the measurement of three-bond scalar coupling constant between (1)H(alpha)(i-1) and (15)N(i) defining the dihedral angle psi is described. The triple-spin-state-selective experiment allows measurement of (3)J(H(alpha)N) from (13)C(alpha), (15)N, and (1)H(N) correlation spectra H(2)O with minimum resonance overlap. Transverse relaxation of (13)C(alpha) spin is minimized by using spin-state-selective filtering and by acquiring a signal longer in (15)N-dimension in a manner of semi-constant-time TROSY evolution. The (3)J(H(alpha))(N) values obtained with the proposed alpha/beta-HN(CO)CA-J TROSY scheme are in good agreement with the values measured earlier from ubiquitin in D(2)O using the HCACO[N] experiment.     

Efficiency of purging sequences in the long-range heteronuclear shift correlation experiment

The efficiencies of a number of pulse sequences designed to remove directly bonded C-H correlations from long-range C-H shift correlation maps are evaluated. A two-step J filter sequence is shown to give good suppression in 1 D experiments. Its incorporation into the long-range C-H shift correlation experiment with a BIRD sequence at the center of the refocusing period gives the BIRDTRAP sequence, which is shown to yield 2D maps with a few very weak direct correlations and no artifacts. BIRDTRAP has a sensitivity higher than that of FLOCK.     

Two-dimensional chemical shift/heteronuclear dipolar coupling spectra obtained with polarization inversion spin exchange at the magic angle and magic-angle sample spinning (PISEMAMAS)

High-resolution two-dimensional ¹⁵N chemical shift/¹H-¹⁵N dipolar coupling polarization inversion spin exchange at the magic angle (PISEMA) spectra of a polycrystalline sample of ¹⁵N-acetylvaline were obtained with and without magic-angle sample spinning. These spectra demonstrate the advantages of the PISEMA experiment over conventional approaches to separated local-field spectroscopy, especially the high resolution in the dipolar dimension where the spinning sidebands have uniformly narrow linewidths.     

Cross correlation between the dipole-dipole interaction and the Curie spin relaxation: the effect of anisotropic magnetic susceptibility

Cross-correlated relaxation caused by the interference of nuclear dipole-dipole interaction and the Curie spin relaxation (DD-CSR cross relaxation) is generalized to treat the case of anisotropic magnetic susceptibility, including the important case where the latter originates from zero-field splitting. It is shown that the phenomenon of DD-CSR cross relaxation is absolutely general and to be expected under any electronic configuration. The results of the generalization are presented for a model system, and the consequences for paramagnetic metalloproteins are illustrated with an example of cerium(III)-substituted calbindin. The effects of the magnetic anisotropy are found to be substantial.     

Measurement of the principal values of the anisotropic diffusion tensor in an unoriented sample by exploiting the chemical shift anisotropy: (19)F PGSE NMR with homonuclear decoupling

NMR methods (S. V. Dvinskikh et al., J. Magn. Reson. 142, 102-110 (2000) and S. V. Dvinskikh and I. Furó, J. Magn. Reson. 144, 142-149 (2000)) that combine PGSE with dipolar decoupling are extended to polycrystalline solids and unoriented liquid crystals. Decoupling suppresses dipolar dephasing not only during the gradient pulses but also under signal acquisition so that the detected spectral shape is dominated by the chemical shift tensor of the selected nucleus. The decay of the spectral intensity at different positions in the powder spectrum provides the diffusion coefficient in sample regions with their crystal axes oriented differently with respect to the direction of the field gradient. Hence, one can obtain the principal values of the diffusion tensor. The method is demonstrated by (19)F PGSE NMR with homonuclear decoupling in a lyotropic lamellar liquid crystal.     

A 2D MAS solid-state NMR method to recover the amplified heteronuclear dipolar and chemical shift anisotropic interactions

A two-dimensional solid-state NMR method for the measurement of chemical shift anisotropy tensors of X nuclei (15N or 13C) from multiple sites of a polypeptide powder sample is presented. This method employs rotor-synchronized pi pulses to amplify the magnitude of the inhomogeneous X-CSA and 1H-X dipolar coupling interactions. A combination of on-resonance and magic angle rf irradiation of protons is used to vary the ratio of the magnitudes of the 1H-X dipolar and X-CSA interactions which are recovered under MAS, in addition to suppressing the 1H-1H dipolar interactions. The increased number of spinning sidebands in the recovered anisotropic interactions is useful to determine the CSA tensors accurately. The performance of this method is examined for powder samples of N-acetyl-(15)N-L-valine (NAV), N-acetyl-15N-L-valyl-15N-L-leucine (NAVL), and alpha-13C-L-leucine. The sources of experimental errors in the measurement of CSA tensors and the application of the pulse sequences under high-field fast MAS operations are discussed.     

Measurement of 15N chemical shift anisotropy in a protein dissolved in a dilute liquid crystalline medium with the application of magic angle sample spinning

The chemical shifts of nuclei that have chemical shielding anisotropy, such as the 15N amide in a protein, show significant changes in their chemical shifts when the sample is altered from an isotropic state to an aligned state. Such orientation-dependent chemical shift changes provide information on the magnitudes and orientation of the chemical shielding tensors relative to the molecule's alignment frame. Because of the extremely high sensitivity of the chemical shifts to the sample conditions, the changes in chemical shifts induced by adding aligned bicelles do not arise only from the protein alignment but should also include the accumulated effects of environmental changes including protein-bicelle interactions. With the aim of determining accurate 15N chemical shielding tensor values for solution proteins, here we have used magic angle sample spinning (MAS) to observe discriminately the orientation-dependent changes in the 15N chemical shift. The application of MAS to an aligned bicelle solution removes the torque that aligns the bicelles against the magnetic field. Thus, the application of MAS to a protein in a bicelle solution eliminates only the molecular alignment effect, while keeping all other sample conditions the same. The observed chemical shift differences between experiments with and without MAS therefore provide accurate values of the orientation-dependent 15N chemical shifts. From the values for ubiquitin in a 7.5% (w/v) bicelle medium, we determined the 15N chemical shielding anisotropy (CSA) tensor. For this evaluation, we considered uncertainties in measuring the 1H-15N dipolar couplings and the 15N chemical shifts and also structural noise present in the reference X-ray structure, assuming a random distribution of each NH bond vector in a cone with 5 degrees deviation from the original orientation. Taking into account these types of noise, we determined the average 15N CSA tensor for the residues in ubiquitin as Delta sigma=-162.0+/-4.3 ppm, eta=0.18+/-0.02, and beta=18.6+/-0.5 degrees, assuming a 1H-15N bond length of 1.02 A. These tensor values are consistent with those obtained from solid-state NMR experiments.     

Crystallographic magnetic anisotropy and the permeability tensor of a ferrite

Seidel and Boyet [1] first derive the magnetic-permeability tensor for a single crystal of a cubic ferrite of low energy; they gave explicit expressions for the components for a crystal magnetized in the (110) plane. Here I consider the more general case of magnetization in any direction; the components are averaged to deduce the permeability of a polycrystalline aggregate.     

15N 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 (15)N 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 (15)N sites of uracil. Employing polycrystalline samples of (15)N(2) and 2-(13)C, (15)N(2)-labeled uracil, we have measured, via (15)N-(13)C REDOR and (15)N-(1)H dipolar-shift experiments, the polar and azimuthal angles (θ, psi) of orientation of the (15)N-(13)C and (15)N-(1)H dipolar vectors in the (15)N CS tensor frame. The (θ(NC), psi(NC)) angles are determined to be (92 +/- 10 degrees, 100 +/- 5 degrees ) and (132 +/- 3 degrees, 88 +/- 10 degrees ) for the N1 and N3 sites, respectively. Similarly, (θ(NH), psi(NH)) are found to be (15 +/- 5 degrees, -80 +/- 10 degrees ) and (15 +/- 5 degrees, 90 +/- 10 degrees ) 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.     

H2O/OH ratio determination in hydrous aluminosilicate glasses by static proton NMR and the effect of chemical shift anisotropy

Static ¹H NMR spectra of hydrous NaAlSi₃O₈ glasses have been acquired at low temperature (140 K) in order to quantitatively determine OH and H₂O concentrations. Since both components overlap in the spectra, an unambiguous determination of the line shapes is required. The structurally bonded hydroxyl groups are well described by a Gaussian line and the water molecules exhibit a Pake doublet-like line shape due to the strong proton–proton dipolar interaction. However, at proton resonance frequencies used in this study (360 MHz), the Pake doublet has an asymmetric line shape due to chemical shift anisotropy (CSA), which is significant and must be included in any simulation in order to reproduce the experimental line shape successfully. The simulations for rigid water molecules dissolved in our hydrous aluminosilicate glasses result in a CSA of 30±5 ppm and a dipolar interaction constant of 63.8±2.5 kHz (i.e., dipolar coupling constant (DCC) of 42.6±1.7 kHz), corresponding to a proton–proton distance of r_ij=154±2 pm. In contrast to earlier work, water speciation obtained from the simulations of our ¹H NMR spectra are in excellent agreement with those obtained from infrared (IR) spectroscopy.     

Optical control of excitons in a pair of quantum dots coupled by the dipole-dipole interaction

We demonstrate coherent nonlinear-optical control of excitons in a pair of quantum dots (QDs) coupled via dipolar interaction. The single-exciton population in the first QD is controlled by resonant picosecond excitation, giving rise to Rabi oscillations. As a result, the exciton transition in the second QD is spectrally shifted and concomitant Rabi oscillations are observed. We identify coupling between permanent excitonic dipole moments as the dominant interaction mechanism, whereas quasiresonant (F?rster) energy transfer is weak. Such control schemes based on dipolar interaction are a prerequisite for realizing scalable quantum logic gates.     

Phonon frequency shift and effect of correlation on the electron-phonon interaction in heavy fermion systems

The electron-phonon interaction in the periodic Anderson model (PAM) is considered. The PAM incorporates the effect of onsite Coulomb interaction (U) between f-electrons. The influence of Coulomb correlation U on the phonon response of the system is studied by evaluating the phonon spectral function for various parameters of the model. The numerical evaluation of the spectral function is carried out in the long wavelength limit at finite temperatures keeping only linear terms in U. The observed behaviour is found to agree well with the general features obtained experimentally for some heavy fermion (HF) systems.     

The roles of homonuclear line narrowing and the1H amide chemical shift tensor in structure determination of proteins by solid-state NMR spectroscopy

The seminal contributions of Ulrich Haeberlen to homonuclear line narrowing and the determination of¹H chemical shift tensors are crucial for protein structure determination by solid-state nuclear magnetic resonance spectroscopy. The¹H chemical shift is particularly important in spectra obtained on oriented samples of membrane proteins as a mechanism for providing dispersion among resonances that are not resolved with the¹H-¹⁵N dipolar coupling and¹⁵N chemical shift frequencies. This is demonstrated with three-dimensional experiments on uniformly¹⁵N-labeled samples of Magainin antibiotic peptide and the protein Vpu from HIV-1 in oriented lipid bilayers. These experiments enable resonances in two-dimensional¹H-¹⁵N dipolar coupling/¹⁵N chemical shift planes separated by¹H chemical shift frequencies to be resolved and analyzed. These three-dimensional spectra are compared to one-dimensional spectra of full-length Vpu, the cytoplasmic domain of Vpu, and Magainin, as well as to two-dimensional spectra of fd coat protein and Colicin El polypeptide. The¹H amide chemical shift tensor provides valuable structural information, and this is demonstrated with its contributions to orientational restrictions to one of the in-plane helical residues of Magainin.     

Determination of the 19F NMR chemical shielding tensor and crystal structure of 5-fluoro-dl-tryptophan

5-Fluoro-dl-tryptophan (5F-Trp) is a very sensitive probe used to investigate orientation and dynamics of biomacromolecules at the in situ level. In order to establish a (19)F NMR strategy, the crystal structure and (19)F chemical shielding tensor of 5F-Trp are reported. A novel approach was developed to use F-F homonuclear dipole-dipole coupling information to analyze single-crystal NMR data without determining crystal orientations. The measured values for the principal components of the shielding tensor are sigma(11)=0.9, sigma(22)=-63.3, and sigma(33)=-82.9 ppm relative to TFA in D(2)O. The principal axes of the shielding tensors coincide with the indole ring symmetry, which makes it a straightforward and powerful tool to monitor protein alignment in oriented environments. Hartree-Fock (HF) and density functional theory (DFT) calculations of the chemical shielding tensors are also reported.     

Determination of chemical shift anisotropies of unresolved carbonyl sites by C-alpha detection under magic-angle spinning

We demonstrate that the static powder pattern line shape of chemical shift anisotropy (CSA) can be obtained for unresolved carbonyl sites of polypeptides under magic-angle spinning. The CSA interaction is first recoupled at the carbonyl site. The phase factors associated with the CSA recoupling are then transferred to the adjacent alpha carbon by an isotropic polarization transfer based on scalar spin-spin coupling. Because alpha carbons of polypeptides are usually better resolved, we can then obtain the CSA static powder pattern line shapes of the carbonyl sites after Fourier transformation in the second dimension. We validate our approach experimentally by measurements on [U-(13)C, (15)N]-l-alanine, [U-(13)C, (15)N]-l-valine and prion fibrils with uniform (13)C and (15)N labels on selected residues.     

Errors in chemical shift tensor components and orientation in the molecular frame as obtained from MAS NMR spinning sideband analysis

It is shown how to calculate random errors in chemical shift tensor components and in the Euler angles which fix the orientation of the σ tensor in the molecular frame, as obtained from spinning sideband analysis of MAS NMR spectra of powdered solids, when heteronuclear dipolar coupling interactions occur in a two spin system. The procedure was applied to experimental data corresponding to the chemical shift tensor of a carbon-13 bonded to a phosphorus-31 nucleus. Clues are given concerning the experimental variables to be set in order to obtain the desired accuracy in the orientation angles.