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.     

Selective dephasing of OH and NH proton magnetization based on (1)H chemical-shift anisotropy recoupling

A method for selectively suppressing the signals of OH and NH protons in (1)H combined rotation and multiple-pulse spectroscopy (CRAMPS) and in (1)H-(13)C heteronuclear correlation (HETCOR) solid-state NMR spectra is presented. It permits distinction of overlapping CH and OH/NH proton signals, based on the selective dephasing of the magnetization of OH and NH protons by their relatively large (1)H chemical-shift anisotropies. For NH protons, the (14)N-(1)H dipolar coupling also contributes significantly to this dephasing. The dephasing is achieved by a new combination of heteronuclear recoupling of these anisotropies with (1)H homonuclear dipolar decoupling. Since the 180 degrees pulses traditionally used for heteronuclear dipolar and chemical-shift anisotropy recoupling would result in undesirable homonuclear dephasing of proton magnetization, instead the necessary inversion of the chemical-shift Hamiltonian every half rotation period is achieved by inverting the phases of all the pulses in the HW8 multiple-pulse sequence. In the HETCOR experiments, carefully timed (13)C 180 degrees pulses remove the strong dipolar coupling to the nearby (13)C spin. The suppression of NH and OH peaks is demonstrated on crystalline model compounds. The technique in combination with HETCOR NMR is applied to identify the CONH and NH-CH groups in chitin and to distinguish NH and aromatic proton peaks in a peat humin.     

Cross-correlated relaxation for the measurement of angles between tensorial interactions

Theory,experimental aspects, and use in structure calculation of cross-correlated relaxation rates measured on zero- and double-quantum coherences in liquid state NMR are presented. The relative size of the interaction depends on the projection angle between the two tensorial interactions. The tensorial interaction can be either a dipolar interaction or a chemical shift anisotropy relaxation mechanism (CSA). Effects of additional sources of relaxation on the cross-correlated relaxation rates are analyzed. Also, an easy-to-use formalism is given to manipulate different cross-correlated relaxation interactions. The application addresses measurement of the backbone angle psi in a protein by measuring dipole((15)N-(1)H)-dipole((13)C(alpha)-(1)H(alpha)) and CSA((15)N)-dipole((13)C(alpha)-(1)H(alpha)) cross-correlated relaxation rates. It is shown that ambiguities due to the 3 cos(2)θ-1 dependence of one cross-correlated relaxation rate can be overcome by measuring additional cross-correlated relaxation rates. The use of cross-correlated relaxation rates is demonstrated in structure calculations.     

1H-1H MAS correlation spectroscopy and distance measurements in a deuterated peptide

In this Communication, we demonstrate the use of deuteration together with back substitution of exchangeable protons as a means of attenuating the strong 1H-1H couplings that broaden 1H magic angle spinning (MAS) spectra of solids. The approach facilitates 15N-1H correlation experiments as well as experiments for the measurement of 1H-1H distances. The distance measurement relies on the excellent resolution in the 1H MAS spectrum and homonuclear double quantum recoupling techniques. The 1H-1H dipolar recoupling can be analyzed in an analytical fashion by fitting the data to a 2- or 3-spin system. The experiments are performed on a sample of the dipeptide N-Ac-Val-Leu-OH, which was synthesized from uniformly [2H, 15N] labeled materials and back-exchanged in H2O.     

One- and two-dimensional 13C-1H/15N- 1H dipolar correlation experiments under fast magic-angle spinning for determining the peptide dihedral angle phi

A recently proposed 13C-1H recoupling sequence operative under fast magic-angle spinning (MAS) [K. Takegoshi, T. Terao, Solid State Nucl. Magn. Reson. 13 (1999) 203-212.] is applied to observe 13C-1H and 15N-1H dipolar powder patterns in the IH-15N- 3C- H system of a peptide bond. Both patterns are correlated by 15N-to-13C cross polarization to observe one- or two-dimensional (1D or 2D) correlation spectra, which can be simulated by using a simple analytical expression to determine the H-N-C-H dihedral angle. The 1D and 2D experiments were applied to N-acetyl[1,2-13C,15N] DL-valine, and the peptide q angle was determined with high precision by the 2D experiment to be +/- 155.0 degrees +/- 1.2 degrees. The positive one is in good agreement with the X-ray value of 154 degrees +/- 5 degrees. The 1D experiment provided the value of phi = +/- 156.0 degrees +/- 0.8 degrees.     

Conformally invariant fractals and potential theory

The multifractal (MF) distribution of the electrostatic potential near any conformally invariant fractal boundary, like a critical O(N) loop or a Q-state Potts cluster, is solved in two dimensions. The dimension &fcirc;(straight theta) of the boundary set with local wedge angle straight theta is &fcirc;(straight theta) = pi / straight theta-25-c / 12 (pi-straight theta)(2) / straight theta(2pi-straight theta), with c the central charge of the model. As a corollary, the dimensions D(EP) of the external perimeter and D(H) of the hull of a Potts cluster obey the duality equation (D(EP)-1) (D(H)-1) = 1 / 4. A related covariant MF spectrum is obtained for self-avoiding walks anchored at cluster boundaries.     

Frequency-selective heteronuclear dephasing and selective carbonyl labeling to deconvolute crowded spectra of membrane proteins by magic angle spinning NMR

We present a new method that combines carbonyl-selective labeling with frequency-selective heteronuclear recoupling to resolve the spectral overlap of magic angle spinning (MAS) NMR spectra of membrane proteins in fluid lipid membranes with broad lines and high redundancy in the primary sequence. We implemented this approach in both heteronuclear (15)N-(13)C(α) and homonuclear (13)C-(13)C dipolar assisted rotational resonance (DARR) correlation experiments. We demonstrate its efficacy for the membrane protein phospholamban reconstituted in fluid PC/PE/PA lipid bilayers. The main advantage of this method is to discriminate overlapped (13)C(α) resonances by strategically labeling the preceding residue. This method is highly complementary to (13)C(i-1)(')-(15)N(i)-(13)C(i)(α) and (13)C(i-1)(α)-(15)N(i-1)-(13)C(i)(') experiments to distinguish inter-residue spin systems at a minimal cost to signal-to-noise.     

Sensitivity enhancement in solid state (15)N NMR by indirect detection with high-speed magic angle spinning

Enhancement of sensitivity in solid state (15)N NMR by indirect detection through (1)H NMR signals under high-speed magic angle spinning and high-field conditions is demonstrated experimentally on two (15)N-labeled peptides, polycrystalline AlaGlyGly and the helix-forming, 17-residue peptide MB(i + 4)EK in lyophilized form. Sensitivity enhancement factors ranging from 2.0 to 3.2 are observed experimentally, depending on the (15)N and (1)H linewidths and polarization transfer efficiencies. The (1)H-detected two-dimensional (1)H/(15)N correlation spectrum of AlaGlyGly illustrates the possibility of increased spectral resolution and resonance assignments in indirectly detected experiments, in addition to the sensitivity enhancement.     

Characterization of 15N chemical shift tensors via 15N-13C REDOR and 1N-1H dipolar-shift CPMAS NMR spectroscopy

As part of our studies on the characterization of 15N chemical shift anisotropy (CSA) via magic angle spinning (MAS) NMR spectroscopy, we have investigated via numerical simulations the sensitivity of two different REDOR experimental protocols to the angles defining the orientation of the 15N-13C' bond vector in the principal axis system of the 15N CSA tensor of the amide nitrogen in a peptide bond. Additionally, employing polycrystalline samples of 15N and 13C', 15N-labeled acetanilide, we have obtained, in a first study of this type, the orientation of the 15N CSA tensor in the molecular frame by orienting the tensor with respect to the 15N-3C' and 15N-1H dipolar vectors via 15N-13C' REDOR and 15N-1H dipolar-shift MAS experiments, respectively.     

1H assisted 13C/15N heteronuclear correlation spectroscopy in oriented sample solid-state NMR of single crystal and magnetically aligned samples

(1)H-irradiation under mismatched Hartmann-Hahn conditions provides an alternative mechanism for carrying out (15)N/(13)C transfers in triple-resonance heteronuclear correlation spectroscopy (HETCOR) on stationary samples of single crystals and aligned samples of biopolymers, which improve the efficiency especially when the direct (15)N-(13)C dipolar couplings are small. In many cases, the sensitivity is improved by taking advantage of the (13)C(α) labeled sites in peptides and proteins with (13)C detection. The similarities between experimental and simulated spectra demonstrate the validity of the recoupling mechanism and identify the potential for applying these experiments to virus particles or membrane proteins in phospholipid bilayers; however, further development is needed in order to derive quantitative distance and angular constraints from these measurements.     

Evaluation of cross-correlation effects and measurement of one-bond couplings in proteins with short transverse relaxation times

Various strategies are described and compared for measurement of one-bond J(NH) and J(NC') splittings in larger proteins. In order to evaluate the inherent resolution obtainable in the various experiments, relaxation rates of (15)N-(1)H(N) coupled and heteronuclear decoupled resonances were measured at 600- and 800-MHz field strengths for both perdeuterated and protonated proteins. A comparison of decay rates for the two (15)N-?H(N)? doublet components shows average ratios of 4.8 and 3.5 at 800- and 600-MHz (1)H frequency, respectively, in the perdeuterated proteins. For the protonated proteins these ratios are 3.2 (800 MHz) and 2.4 (600 MHz). Relative to the regular HSQC experiment, the enhancement in TROSY (15)N resolution is 2.6 (perdeuterated; 800 MHz), 2.0 (perdeuterated; 600 MHz), 2.1 (protonated; 800 MHz), and 1.7 (protonated; 600 MHz). For the (1)H dimension, the upfield (1)H(N)-?(15)N? component on average relaxes slower than the downfield (1)H(N)-?(15)N? component by a factor of 1.8 (perdeuterated; 800 MHz) and 1.6 (perdeuterated; 600 MHz). The poor resolution for the upfield (15)N-?(1)H? doublet component in slowly tumbling proteins makes it advantageous to derive the J(NH) splitting from the difference in frequency between the narrow downfield (15)N doublet component and either the (1)H-decoupled (15)N resonance or the peak position in an experiment which J-scales the frequency of the upfield doublet component but maintains some of the advantages of the TROSY experiment.     

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.     

Study of CP(N-1) theta-vacua by cluster simulation of SU(N) quantum spin ladders

D-theory provides an alternative lattice regularization of the 2D CP(N-1) quantum field theory in which continuous classical fields emerge from the dimensional reduction of discrete SU(N) quantum spins. Spin ladders consisting of n transversely coupled spin chains lead to a CP(N-1) model with a vacuum angle theta=npi. In D-theory no sign problem arises and an efficient cluster algorithm is used to investigate theta-vacuum effects. At theta=pi there is a first order phase transition with spontaneous breaking of charge conjugation symmetry for CP(N-1) models with N>2.     

Sensitivity-enhanced static 15N NMR of solids by 1h indirect detection

A method for enhancing the sensitivity of 15N spectra of nonspinning solids through 1H indirect detection is introduced. By sampling the 1H signals in the windows of a pulsed spin-lock sequence, high-sensitivity 1H spectra can be obtained in two-dimensional (2D) spectra whose indirect dimension yields the 15N chemical shift pattern. By sacrificing the 1H chemical shift information, sensitivity gains of 1.8 to 2.5 for the 15N spectra were achieved experimentally. A similar sensitivity enhancement was also obtained for 2D (15)N-(1)H dipolar and 15N chemical shift correlation spectroscopy, by means of a 3D 1H/15N-1H/15N correlation experiment. We demonstrate this technique, termed PRINS for proton indirectly detected nitrogen static NMR, on a crystalline model compound with long 1H T(1rho) and on a 25-kDa protein with short 1H T(1rho). This 1H indirect detection approach should be useful for enhancing the sensitivity of 15N NMR of oriented membrane peptides. It can also be used to facilitate the empirical optimization of 15N-detected experiments where the inherent sensitivity of the sample is low.     

On the accurate measurement of amide one-bond 15N-1H couplings in proteins: effects of cross-correlated relaxation, selective pulses and dynamic frequency shifts

Amide one-bond 15N-1H scalar couplings of 15N- and [15N,2H]-isotopically enriched ubiquitin have been measured with the Quantitative J approach by monitoring NMR signal intensity modulation. Scalar couplings of the non-deuterated protein are in average approximately 0.6 Hz larger than values of deuterated ubiquitin. This deviation is 30 times the error derived from experiment reproducibility. Refocusing dipole/dipole cross-correlated relaxation decreases the discrepancy to approximately 0.1 Hz, suggesting that it likely originates from relaxation interference. Alternatively, the subtraction of J values obtained at different magnetic fields largely reduces the relaxation effects. In contrast, the dynamic frequency shift whose main contribution to 1J(15N-1H) arises from 15N chemical shielding anisotropy/NH dipole cross-correlation, is not eliminated by refocusing spin evolution under this interaction. Furthermore, the average difference of 1J(15N-1H) values at two magnetic fields closely agrees with the theoretical expected difference in the dynamic frequency shift.     

One- and two-dimensional C–H/N–H dipolar correlation experiments under fast magic-angle spinning for determining the peptide dihedral angle φ

A recently proposed ¹³C–¹H recoupling sequence operative under fast magic-angle spinning (MAS) [K. Takegoshi, T. Terao, Solid State Nucl. Magn. Reson. 13 (1999) 203–212.] is applied to observe ¹³C–¹H and ¹⁵N–¹H dipolar powder patterns in the ¹H–¹⁵N–¹³C–¹H system of a peptide bond. Both patterns are correlated by ¹⁵N-to-¹³C cross polarization to observe one- or two-dimensional (1D or 2D) correlation spectra, which can be simulated by using a simple analytical expression to determine the H–N–C–H dihedral angle. The 1D and 2D experiments were applied to N-acetyl[1,2-¹³C,¹⁵N] -valine, and the peptide φ angle was determined with high precision by the 2D experiment to be ±155.0°±1.2°. The positive one is in good agreement with the X-ray value of 154°±5°. The 1D experiment provided the value of φ=±156.0°±0.8°.     

Determination of membrane Peptide orientation by 1H-detected 2H NMR spectroscopy

We demonstrate the application of the proton inverse detected deuteron (PRIDE) NMR technique to the measurement of the orientation of membrane-bound peptides with enhanced sensitivity. Gramicidin D, a transmembrane peptide, and ovispirin, a surface-bound peptide, were used as model systems. The peptides were 2H-labeled by 1H/2H exchange and oriented uniaxially on glass plates. The directly detected 2H spectra of both peptides showed only a strong D(2)O signal and no large quadrupolar splittings. In contrast, the PRIDE spectrum of gramicidin exhibited quadrupolar splittings as large as 281 kHz, consistent with its transmembrane orientation. Moreover, the large D(2)O signal in the directly detected 2H spectra was cleanly suppressed in the PRIDE spectrum. For ovispirin, the 1H indirectly detected 2H spectrum revealed a 104 kHz splitting and a zero-frequency peak. The former reflects the in-plane orientation of most of the helix axis, while the latter results from residues with a magic-angle orientation of the N-D bonds. These are consistent with previous 15N NMR results on ovispirin. The combination of PRIDE and exchange labeling provides an economical and sensitive method of studying membrane peptide orientations in lipid bilayers without the influence of D(2)O and with the ability to detect N-D bonds at the magic angle from the bilayer normal.     

Effects of nonmagnetic impurities on spin-fluctuation induced superconductivity

We study the effects of nonmagnetic impurities on the phase diagram of a system of interacting electrons with a flat Fermi surface. The one-loop Wilsonian renormalization group flow of the angle dependent diffusion function D(theta;(1),theta;(2),theta;(3)) and interaction U(theta;(1),theta;(2),theta;(3)) determines the critical temperature and the nature of the low temperature state. As the imperfect nesting increases, the critical temperature decreases, and the low temperature phase changes from the spin-density wave (SDW) to the d-wave superconductivity (dSC) and finally, for bad nesting, to the charge-localized state. Both SDW and dSC phases are affected by disorder. The pair breaking depends on the imperfect nesting and is the most efficient when the critical temperature for superconductivity is maximal.     

REDOR-based heteronuclear dipolar correlation experiments in multi-spin systems: rotor-encoding,directing, and multiple distance and angle determination

We review a variety of recently developed 1H-X heteronuclear recoupling techniques, which rely only on the homonuclear decoupling efficiency of very-fast magic-angle spinning. All these techniques, which are based on the simple rotational-echo, double-resonance (REDOR) approach for heteronuclear recoupling, are presented in a common context. Advantages and possibilities with respect to the complementary application of conventionally X and 1H-inversely detected variants are discussed in relation to the separability and analysis of multiple couplings. We present an improved and more sensitive approach to the determination of 1H-X dipolar couplings by spinning-sideband analysis, termed REREDOR, which is applicable to XHn groups in rigid and mobile systems and bears some similarity to more elaborate separated local-field methods. The estimation of medium-range 1H-X distances by analyzing signal intensities in two-dimensional REDOR correlation spectra in a model-free way is also discussed. More specifically, we demonstrate the possibility of combined distance and angle determination in H-X-H or X-H-X three-spin systems by asymmetric recoupling schemes and spinning-sideband analysis. Finally, an 1H-X correlation experiment is introduced which accomplishes high sensitivity by inverse (1H) detection and is therefore applicable to samples with 15N in natural abundance.