Intensity and mosaic spread analysis from PISEMA tensors in solid-state NMR

The solid-state NMR experiment PISEMA, is a technique for determining structures of proteins, especially membrane proteins, from oriented samples. One method for determining the structure is to find orientations of local molecular frames (peptide planes) with respect to the unit magnetic field direction, B0. This is done using equations that compute the coordinates of this vector in the frames. This requires an analysis of the PISEMA function and its degeneracies. As a measure of the sensitivity of peptide plane orientations to the data, we use these equations to derive a formula for the intensity function in the powder pattern. With this function and other measures, we investigate the effect of small changes in peptide plane orientations depending on the location of the resonances in the powder pattern spectrum. This gives us an indication of the change in lineshape due to mosaic spread and a way to interpret these in terms of an orientational error bar.     

2D solid state NMR spectral simulation of 310, α, and π-helices

Transmembrane helices are more uniform in structure than similar helices in water soluble proteins. Solid state NMR of aligned bilayer samples is being increasingly used to characterize helical membrane protein structures. Traditional spectroscopic methods have difficulty distinguishing between helices with i to i + 3 (3(10)), i to i + 4 (alpha), and i to i + 5 (pi) hydrogen bonding topology. Here, we show that resonance patterns in PISEMA spectra simulated for these different helices show unique and striking features. The size and shape of these Polar Index Slant Angle (PISA) wheels, as well as the resonances per turn and clockwise versus counter-clockwise sequential connectivity of the resonances demonstrate how these different helical structures, if present as a uniform structure, will be readily distinguished, and characterized.     

2D solid state NMR spectral simulation of 3(10), alpha, and pi-helices

Transmembrane helices are more uniform in structure than similar helices in water soluble proteins. Solid state NMR of aligned bilayer samples is being increasingly used to characterize helical membrane protein structures. Traditional spectroscopic methods have difficulty distinguishing between helices with i to i + 3 (3(10)), i to i + 4 (alpha), and i to i + 5 (pi) hydrogen bonding topology. Here, we show that resonance patterns in PISEMA spectra simulated for these different helices show unique and striking features. The size and shape of these Polar Index Slant Angle (PISA) wheels, as well as the resonances per turn and clockwise versus counter-clockwise sequential connectivity of the resonances demonstrate how these different helical structures, if present as a uniform structure, will be readily distinguished, and characterized.     

A solid-state NMR index of helical membrane protein structure and topology

The secondary structure and topology of membrane proteins can be described by inspection of two-dimensional (1)H-(15)N dipolar coupling/(15)N chemical shift polarization inversion spin exchange at the magic angle spectra obtained from uniformly (15)N-labeled samples in oriented bilayers. The characteristic wheel-like patterns of resonances observed in these spectra reflect helical wheel projections of residues in both transmembrane and in-plane helices and hence provide direct indices of the secondary structure and topology of membrane proteins in phospholipid bilayers. We refer to these patterns as PISA (polarity index slant angle) wheels. The transmembrane helix of the M2 peptide corresponding to the pore-lining segment of the acetylcholine receptor and the membrane surface helix of the antibiotic peptide magainin are used as examples.     

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.     

2D separated-local-field spectra from projections of 1D experiments

A novel procedure for reconstruction of 2D separated-local-field (SLF) NMR spectra from projections of 1D NMR data is presented. The technique, dubbed SLF projection reconstruction from one-dimensional spectra (SLF-PRODI), is particularly useful for uniaxially oriented membrane protein samples and represents a fast and robust alternative to the popular PISEMA experiment which correlates (1)H-(15)N dipole-dipole couplings with (15)N chemical shifts. The different 1D projections in the SLF-PRODI experiment are obtained from 1D spectra recorded under influence of homonuclear decoupling sequences with different scaling factors for the heteronuclear dipolar couplings. We demonstrate experimentally and numerically that as few as 2-4 1D projections will normally be sufficient to reconstruct a 2D SLF-PRODI spectrum with a quality resembling typical PISEMA spectra, leading to significant reduction of the acquisition time.     

Spin dynamics of polarization inversion spin exchange at the magic angle in multiple spin systems

Polarization inversion spin exchange at the magic angle (PISEMA) [J. Magn. Reson. A 109, 270 (1994)] is an important experiment in NMR structural characterization of membrane proteins in oriented lipid bilayers. This paper presents a theoretical and experimental study of the spin dynamics in PISEMA to investigate the line-narrowing mechanism. The study focuses on the effect of neighboring protons on the spin exchange of a strongly coupled spin pair. The spin exchange is solved analytically for simple spin systems and is numerically simulated for many-spin systems. The results show that the dipolar couplings from the neighboring protons of a strongly coupled spin pair perturb the spin exchange only in the second order, therefore it has little contribution to the linewidth of PISEMA spectra in comparison to the separated-local-field spectra. The effects from proton resonance offset and the mismatch of the Hartmann-Hahn condition are also discussed along with experimental results using model single-crystal samples.     

Selective averaging for high-resolution solid-state NMR spectroscopy of aligned samples

Solid-state NMR experiments benefit from being performed at high fields, and this is essential in order to obtain spectra with the resolution and sensitivity required for applications to protein structure determination in aligned samples. Since the amount of rf power that can be applied is limited, especially for aqueous protein samples, the most important pulse sequences suffer from bandwidth limitations resulting from the same spread in chemical shift frequencies that aids resolution. SAMPI4 is a pulse sequence that addresses these limitations. It yields separated local field spectra with narrower and more uniform linewidths over the entire spectrum than the currently used PISEMA and SAMMY experiments. In addition, it is much easier to set up on commercial spectrometers and can be incorporated as a building block into other multidimensional pulse sequences. This is illustrated with a two-dimensional HETCOR experiment, where it is crucial to transfer polarization from the amide protons to their directly bonded nitrogens over a wide range of chemical shift frequencies. A quantum-mechanical treatment of the spin Hamiltonians under high-power rf pulses is presented which gives the scaling factor for SAMPI4 as well as the durations of the rf pulses to achieve optimal decoupling.     

2₄-SEMA as a sensitive and offset compensated SLF sequence

Separated Local Field (SLF) spectroscopy is a powerful tool for the determination of structure and dynamics of oriented systems such as membrane proteins oriented in lipid bilayers and liquid crystals. Of many SLF techniques available, Polarization Inversion Spin Exchange at Magic Angle (PISEMA) has found wide application due to its many favorable characteristics. However the pulse sequence suffers from its sensitivity to proton resonance frequency offset. Recently we have proposed a new sequence named 2(4)-SEMA (J. Chem. Phys. 132 (2010) 134301) that overcomes this problem of PISEMA. The present work demonstrates the advantage of 2(4)-SEMA as a highly sensitive SLF technique even for very large proton offset. 2(4)-SEMA has been designed for obtaining reliable dipolar couplings by switching the magic-angle spin-lock for protons over four quadrants as against the use of only two quadrants in PISEMA. It is observed that for on-resonance condition, 2(4)-SEMA gives rise to signal intensity comparable to or slightly higher than that from PISEMA. But under off-resonance conditions, intensities from 2(4)-SEMA are several fold higher than those from PISEMA. Comparison with another offset compensated pulse sequence, SAMPI4, also indicates a better intensity profile for 2(4)-SEMA. Experiments carried out on a single crystal of (15)N labeled N-acetyl-dl-valine and simulations have been used to study the relative performance of the pulse sequences considered.     

Application of two-dimensional pulsed EPR nutation spectroscopy to a disordered system with largeg-anisotropy

Two-dimensional (2-D) pulsed electron paramagnetic resonance (EPR) nutation spectroscopy is applied to a disordered system with strongly anisotropicg-factors. The analysis and interpretation of a 2-D nutation spectrum is performed by theoretical calculations appropriate for ferric myoglobin cyanide in frozen solution. The observed and calculated 2-D spectra show broad signals which correspond to the principalg-values. The advantage of nutation spectroscopy is demonstrated by measuring theg _x=0.93 signal, which cannot be observed in a conventional field-swept spectrum due to largeg strain broadening. It is shown that the 2-D nutation experiment can be considered as a sort of an angle-selected method but a nutation spectrum gives a powder pattern even for magnetic field settings at extreme field values of an EPR spectrum. This is in contrast to angle-selected electron nuclear double resonance, which gives a single-crystal type spectrum. The advantage of sine Fourier transform (FT) over complex FT is demonstrated for data processing in the nutation domain. Problems of experimental and data-processing procedures are also discussed.     

Initial conditions of closed classical orbits from quantum spectra

A method is presented for determining the initial conditions of classical orbits from the quantum spectra of the diamagnetic hydrogen atom. Each classical trajectory which is closed at the nucleus produces a sinusoidal fluctuation in the photoabsorption spectrum. The amplitude of each orbit's contribution appears in the Fourier transform of a spectrum computed at constant scaled energy. For a given initial state, closed-orbit theory gives the dependence of this recurrence amplitude on the initial angle of an orbit. By comparing the recurrence amplitudes for different initial states, the initial conditions of closed classical orbits are determined from quantum spectra. (c) 1996 American Institute of Physics.     

NMR spin locking of proton magnetization under a frequency-switched Lee-Goldburg pulse sequence

The spin dynamics of NMR spin locking of proton magnetization under a frequency-switched Lee-Goldburg (FSLG) pulse sequence is investigated for a better understanding of the line-narrowing mechanism in PISEMA experiments. For the sample of oriented 15N(1,3,5,7)-labeled gramicidin A in hydrated DMPC bilayers, it is found that the spin-lattice relaxation time T(1rho)(H) in the tilted rotating frame is about five times shorter when the 1H magnetization is spin locked at the magic angle by the FSLG sequence compared to the simple Lee-Goldburg sequence. It is believed that the rapid phase alternation of the effective fields during the FSLG cycles results in averaging of the spin lock field so that the spin lock becomes less efficient. A FSLG supercycle has been suggested here to slow the phase alternation. It has been demonstrated experimentally that a modified PISEMA pulse sequence with such supercycles gives rise to about 30% line narrowing in the dipolar dimension in the PISEMA spectra compared to a standard PISEMA pulse sequence.     

Complete theoretical ESR powder spectra by analytical and monte carlo methods

The theoretical ESR spectrum of spins in randomly oriented crystals is built from the distribution function, or powder pattern, of the spins in resonance magnetic field, the anisotropic transition probability and the elementary lineshape of the crystallites. It is shown to be given by the convolution of the product of the powder pattern and the transition probability function — the probability powder pattern — with the elementary lineshape function. Powder patterns in analytical forms, obtained by an isotimic method of integration, are shown to be a very convenient basis for building the theoretical spectra. For the axial field the powder pattern, being always the solution of an algebraic equation, is usually expressed in terms of algebraic irrational functions. Full analytical solutions are then shown to be always possible for Lorentzian elementary lineshapes. Some are derived and compared with full numerical solutions obtained in various fast PC's and supercomputers by a simple Monte Carlo method for synthesizing ESR powder spectra. Sample applications to known physical systems, Cr³⁺: anatase and Mn²⁺: calcite are also shown. An approximate method for first-derivative ESR spectra for the non-axial field is described and used on an orthorhombicg-system, for which an analytically exact powder pattern, recently derived by the isotimic method, is known. The result of its application to a suitable physical system, Cr³⁺: rutile, is also shown.     

Echolocation with bat buzz emissions: model and biomimetic sonar for elevation estimation

Just prior to capture the Buzz II emissions of some mouth-emitting bats, such as Eptesicus fuscus, are observed to exhibit spectra having multiple peaks. This paper proposes an echolocation strategy that uses such spectra with energy concentrated in specific frequency bands for determining target elevation. A biomimetic sonar was implemented to produce a tri-modal spectrum by driving a speaker with a signal rich in harmonics. The emission magnitudes at these harmonic frequencies measured as a function of elevation in the zero-azimuth plane form distinct beams. A template was formed from the ratio of the first harmonic and fundamental magnitudes to determine elevation. The elevation estimator exhibited a sub-degree accuracy (SD = 0.4° over a 20° interval centered at the elevation at which these two beams intersect in the zero-azimuth plane. Spectral cues from -40° to +10° elevation allow a qualitative non-linear control of sonar orientation to drive the target to the beam-intersection point where quantitative elevation estimates are available.     

Imaging membrane protein helical wheels

Resonance patterns have been observed in 2D solid-state NMR spectra of the transmembrane segment of M2 protein from Influenza A virus in oriented samples reflecting the helical wheel of this alpha-helix. The center of this pattern uniquely defines the helical tilt with respect to the bilayer normal without a need for resonance assignments. The distribution of resonances from amino acid specific labels around the "PISA wheel" defines the rotational orientation of the helix and yields preliminary site-specific assignments. With assignments high-resolution structural detail, such as differences in tilt and rotational orientation along the helical axis leading to an assessment of helical coiling, can be obtained.     

Structural fitting of PISEMA spectra of aligned proteins

An algorithm for fitting protein structures to PISEMA spectra is described, and its application to helical proteins in aligned samples is demonstrated using both simulated and experimental results. The formulation of the algorithm in terms of rotation operators yields compact recursion relations that provide a fast and effective way of obtaining peptide plane orientations from chemical and torsion angle constraints. The algorithm in combination with experimental solid-state NMR data results in a method for determining the backbone structures of proteins, since it yields the orientation of a helix as a whole, including its tilt and twist angles, and describes kinks and curves with atomic resolution. Although the algorithm can be applied in an "assignment-free" manner to spectra of uniformly labeled proteins, the precision of the structural fitting is improved by the addition of assignment information, for example the identification of resonances by residue type from spectra of selectively labeled proteins.     

Intensity of cross-peaks in hyscore spectra of S = 1/2, I = 1/2 spin systems

The cross-peak intensity for a S = 1/2, I = 1/2 spin system in two-dimensional HYSCORE spectra of single-crystals and powders is analyzed. There is a fundamental difference between these two cases. For single crystals, the cross-peak intensity is distributed between the two (+, +) and (+, -) quadrants of the hyperfine sublevel correlation (HYSCORE) spectrum by the ratio c(2):s(2) (C. Gemperle, G. Aebli, A. Schweiger, and R. R. Ernst, J. Magn. Reson. 88, 241 (1990)). However, for powder spectra another factor becomes dominant and governs cross-peak intensities in the two quadrants. This factor is the phase interference between modulation from different orientations of the paramagnetic species. This can lead to essentially complete disappearance of the cross-peak in one of the two (+, +) or (+, -) quadrants. In the (+, +) quadrant, cross-peaks oriented parallel to the main (positive) diagonal of the HYSCORE spectrum are suppressed, while the opposite is true in the (+, -) quadrant where cross-peaks nearly perpendicular to the main (negative) diagonal of HYSCORE spectra are suppressed. Analytical expressions are derived for the cross-peak intensity profiles in powder HYSCORE spectra for both axial and nonaxial hyperfine interactions (HFI). The intensity is a product of two terms, one depending only on experimental parameter (tau) and the other only on the spin Hamiltonian. This separation provides a rapid way to choose tau for maximum cross-peak intensity in a region of interest in the spectrum. For axial HFI, the Hamiltonian-dependent term has only one maximum and decreases to zero at the canonical orientations. For nonaxial HFI, this term produces three separate ridges which outline the whole powder lineshape. These three ridges have the majority of the intensity in the HYSCORE spectrum. The intensity profile of each ridge resembles that observed for axial HFI. Each ridge defines two principal values of the HFI similar to the ridges from an axial HFI.     

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.     

Shapes and shifts in the oxygen Auger spectra

The oxidation of silicon and platinum single crystal faces, of polycrystalline supported catalysts and of some alloy surfaces has been studied by AES and as far as possible by LEED. A comparison of the oxygen Auger spectra obtained during the oxidation process with those found on oxides has been made; it shows that the modification of the fine structure of the oxygen Auger peaks gives some information about the binding state of oxygen. Two different structures, which compete one with the other, are described. In one case, a spectrum where three lines dominate is obtained; in the other case, a “quasi-atomic” spectrum characterized by five features is observed: multiplet splitting in the two-hole final state is predominant. Besides these differences in the fine structure of the Auger spectra one can notice shifts of several eV for the main feature. They have been correlated with the various observed LEED patterns. Physisorption, chemisorption, solution of oxygen in the metal lattice, growth of ordered or amorphous oxides are the different possibilities which are discussed.     

烃在四种典型活性炭中吸附状态随温度变化的~1H NMR和~2H NMR的研究

本文观察了吸附在四种孔结构活性炭中苯,环已烷和正已烷的~1H NMR和笊代苯的~2H NMR谱线在297～195 κ温度范围内的变化。在室温下被吸附的上述各种化合物的~1H NMR及~2H NMR谱均为一条线宽不同的单峰,且随温度下降而增宽。在~2H NMR谱中发现,当以对数表示的谱线半高宽和绝对温度倒数的直线关系上出现拐点时,同时可观察到固体粉末谱线。除2~#活性炭外,最初出现固体粉末谱的温度大致相同。这暗示粉末谱是毛细管中三维类液体固化的结果。文内就所观察到的现象进行了初步讨论。