Dephasing of spin echoes by multiple heteronuclear dipolar interactions in rotational echo double resonance NMR experiments

The application of rotational echo double resonance (REDOR) nuclear magnetic resonance (NMR) for accurate distance measurements has thus far been largely restricted to isolated heteronuclear two-spin systems. In the present paper, the informational content of REDOR curves is explored for systems characterized by multi-spin interactions. To this end, numerical REDOR simulations are presented for cases in which single observe spins S are dipolarly coupled to groups of spins I in distinct geometries. To develop the utility of REDOR for characterizing dipolar couplings in unknown and/or ill-defined geometries, the validity ranges and systematic errors of certain analytical approximations are studied. In the limit of short dipolar evolution times where 0 < deltaS/S0 < or = 0.2 to 0.3, the REDOR difference signal intensity increases approximately proportional to the square of the dipolar evolution time. Here, the curvature depends simply on the second moment M2 characterizing the overall strength of the heterodipolar coupling, irrespective of specific molecular geometries. Fitting experimental REDOR data in this manner produces slight systematic underestimates of M2. However, these errors tend to be counterbalanced by additional systematic errors made by neglecting weak couplings to more remote spins and distribution effects caused by disorder. Based on these findings, the results suggest a convenient method of obtaining site-resolved second moment information in disordered materials.     

Compensating for pulse imperfections in REDOR

Rotational-echo double resonance (REDOR) is a magic-angle spinning technique for measuring heteronuclear dipolar couplings. Rotor-synchronized pi pulses recouple the dipolar interaction. The accuracy of a REDOR determination of distance or orientation depends totally on the quality of the dephased (recoupled) and full-echo spectra. We present a scheme for measuring and compensating for the effects of pulse imperfections in REDOR experiments. No assumptions are made about the quality of the pi pulses, and no pulses are added or taken away in implementing the compensation for incomplete REDOR dephasing by imperfect pi pulses.     

Measurement of internuclear distances in solid-state NMR by a background-filtered REDOR experiment

A background-filtered version of the rotational-echo double resonance (REDOR) experiment is demonstrated. The experiment combines a traditional REDOR pulse sequence with a double-cross-polarization (DCP) sequence to select only those signals coming from spin pairs of interest. The relatively inefficient DCP sequence, which transfers polarization from (1)H to (15)N and subsequently to (13)C, is improved by the use of adiabatic passages through the (-1) sideband of the Hartmann-Hahn matching condition. The result is an efficient 2D-REDOR pulse sequence that does not require a reference experiment for removal of background signals. The data produced by the experiment are ideally suited to analysis by newly developed dipolar transform methods, such as the REDOR transform. The relevant features of the experiment are demonstrated on simple labeled amino acids. Relative efficiencies of several other potential filtering methods are also compared. Copyright 2000 Academic Press.     

Measuring (13)C-(2)D dipolar couplings with a universal REDOR dephasing curve

A (13)C-observe REDOR experiment is described which allows (13)C-(2)D dipolar couplings to be obtained by a universal dipolar dephasing curve. Previous (13)C-observe REDOR experiments on (13)C-(2)D spin pairs generally relied on numerical simulations to obtain the dipolar coupling. The REDOR experiment described in this article is based on a deuterium composite pulse, and the data analysis eliminates the need for numerical simulations and is the same as the traditional REDOR analysis performed on pairs of spin-12 nuclei. Copyright 2000 Academic Press.     

"Development of REDOR rotational-echo double-resonance NMR" by Terry Gullion and Jacob Schaefer [J. Magn. Reson. 81 (1989) 196-200

The popularity of rotational-echo double-resonance (REDOR) NMR arises from its ability to measure weak dipolar couplings and long-range heteronuclear distances accurately. This ability was not anticipated in the first REDOR experiments and resulted from the effectiveness of a simple radiofrequency phase alternation scheme to suppress amplitude and phase distortions in echo trains even after hundreds of pi pulses.     

Analytical solutions to several magic-angle spinning NMR experiments

Using the Anderson–Weiss (AW) formalism, analytical expressions of the NMR signal are obtained for the following magic-angle spinning (MAS) experiments: total suppression of sidebands (TOSS); phase adjusted spinning sidebands (PASS); rotational-echo double-resonance (REDOR); rotor-encoded REDOR (REREDOR); cross-polarization magic-angle spinning (CPMAS); exchange induced sidebands (EIS); one-dimensional exchange spectroscopy by sideband alternation (ODESSA); time-reverse ODESSA (trODESSA); centerband-only detection of exchange (CODEX). In order to test the validity of the AW approach, the Gaussian powder approximation is compared with exact powder calculations. A quantitative study of the effect of molecular dynamics on the efficiency of the TOSS and REDOR pulse sequences is then presented.     

角锥棱镜用于激光直线度测量的特性分析

对角锥棱镜用于激光直线度测量时可使测量精度提高一倍的光学特性进行了分析。分析了角锥棱镜的制造角差、面形误差和测量过程中角锥棱镜的偏摆、俯仰、滚转对直线度测量的影响。用实验验证了分析结果。分析结果为角锥棱镜用作激光直线度测量时的误差分析和误差补偿提供了理论依据。     

Long-distance rotational echo double resonance measurements for the determination of secondary structure and conformational heterogeneity in peptides.

The utility of rotational echo double resonance (REDOR) NMR spectroscopy for determining the conformations of linear peptides has been examined critically using a series of crystalline and amorphous samples. The focus of the present work was the evaluation of long-distance (> 5 A) interactions using 13C-15N dephasing. Detailed studies of specifically labeled melanostatin and synthetic analogs of the alpha-factor yeast mating hormone show that nitrogen-dephased, carbon-observe REDOR measurements are reliable for distances up to 6.0 A, and that dipolar interactions can be detected for distances up to 7 A. By contrast, nitrogen-observe REDOR gives reliable results only for distances shorter than 5.0 A. To measure distances accurately, REDOR data must be corrected for the effects of natural-abundance spins. These corrections are particularly important for measuring long distances, which are of the greatest value for determining peptide secondary structure. We have developed a spherical shell model for calculating the effect of these background spins. The REDOR studies also indicate that in a lyophilized powder, the tridecapeptide alpha-factor mating pheromone from Saccharomyces cerevisiae (WHWLQLKPGQPMY) probably exists as a distribution of different turn structures around the KPGQ region. This finding revises previous solid-state NMR studies on this peptide, which concluded alpha-factor assumes a distorted type-I beta-turn in the Pro-Gly central region of the molecule [J.R. Garbow, M. Breslav, O. Antohi, F. Naider, Biochemistry, 33 (1994) 10094].     

13C-(27)Al TRAPDOR and REDOR experiments for the detection of (13)C-(27)Al dipolar interactions in solids.

We report (13)C-(27)Al double resonance experiments (REDOR and TRAPDOR) on several aluminum organic compounds with the aim of detecting (13)C-(27)Al dipolar couplings and distances in solids. The (13)C and (27)Al pulses are applied to the same probe channel because their resonance frequencies are in close proximity. The different possibilities of controlling the efficiency of the TRAPDOR approach (by varying the (27)Al RF amplitude and the MAS frequency) are investigated. The results indicate that TRAPDOR is superior to REDOR in resolving differences in (13)C-(27)Al distances when choosing the proper experimental conditions. Where known, the crystal structure data are in qualitative agreement with the distance information extracted from our experiments. The experiment should be very valuable in different fields of solid state chemistry, where the interaction of organic and inorganic sample fractions is of fundamental importance.     

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.     

REDOR with adiabatic dephasing pulses

The response of a spin (1/2) ensemble, at thermal equilibrium and experiencing chemical shift anisotropy (CSA), to the application of adiabatic inversion pulses has been studied under magic-angle spinning (MAS). Numerical simulations and experimental studies on such systems, carried out under slow spinning conditions, show that the response to adiabatic inversion pulses has much more favorable characteristics than the response to conventional rectangular pulses. We have also explored the possibilities of employing adiabatic 180 degrees pulses as dephasing pulses in rotational-echo double-resonance (REDOR) experiments. Our results show that it is indeed possible to employ such adiabatic inversion pulses conveniently in REDOR experiments to eliminate resonance offset and H(1) inhomogeneity effects which may arise from the usage of conventional rectangular 180 degrees pulses. Copyright 2000 Academic Press.     

19F/29Si rotational-echo double-resonance and heteronuclear spin counting under fast magic-angle spinning in fluoride-containing octadecasil

19F/29Si rotational-echo double-resonance (REDOR) and theta-REDOR NMR techniques have been applied under fast magic-angle spinning to a powder sample of fluoride-containing octadecasil. Efficient dipolar recoupling was observed and the effect of finite pulse lengths was found to be negligible using standard radiofrequency field strengths. Moreover, the determined internuclear distance of the 19F-29Si spin pairs formed by the silicons in the D4R units (T-1 site) and the fluoride anions is in very good agreement with previous REDOR and Hartmann-Hahn cross-polarization measurements. Numerical simulation of the REDOR dephasing curves at both the T-1 and T-2 sites considering all fluoride anions in the infinite solid lattice clearly confirm the X-ray crystal structure of octadecasil. Heteronuclear spin-counting theta-REDOR experiments are found to be very useful to obtain direct insight into the local network of dipolar interactions. Indeed, while 19F-29Si pair-like behavior is confirmed at the T-1 site, multiple dipolar interactions are clearly evidenced at the T-2 site.     

Recoupling of heteronuclear dipolar interactions with rotational-echo double-resonance at high magic-angle spinning frequencies

Heteronuclear dipolar recoupling with rotational-echo double-resonance (REDOR) is investigated in the rapid magic-angle spinning regime, where radiofrequency irradiation occupies a significant fraction of the rotor period (10-60%). We demonstrate, in two model (13)C-(15)N spin systems, [1-(13)C, (15)N] and [2-(13)C, (15)N]glycine, that REDOR DeltaS/S(0) curves acquired at high MAS rates and relatively low recoupling fields are nearly identical to the DeltaS/S(0) curve expected for REDOR with ideal delta-function pulses. The only noticeable effect of the finite pi pulse length on the recoupling is a minor scaling of the dipolar oscillation frequency. Experimental results are explained using both numerical calculations and average Hamiltonian theory, which is used to derive analytical expressions for evolution under REDOR recoupling sequences with different pi pulse phasing schemes. For xy-4 and extensions thereof, finite pulses scale only the dipolar oscillation frequency by a well-defined factor. For other phasing schemes (e.g., xx-4 and xx-4) both the frequency and amplitude of the oscillation are expected to change.     

Structure determination of aligned systems by solid-state NMR magic angle spinning methods

Single crystal rotational echo double resonance (REDOR) experiments can be used to determine the three-dimensional orientation of heteronuclear bond vectors in an amino acid, as well as the crystal's orientation relative to the rotor fixed frame (RFF). We also demonstrate that for samples uniaxially aligned along the rotor axis, the polar tilt angle of a bond vector relative to the RFF can be measured by use of an analytical expression that describes the REDOR curve for that system. These bond orientations were verified by X-ray indexing of the single crystal sample, and were shown to be as accurate as +/- 1 degrees .     

Double-quantum filtered rotational-echo double resonance

The homonuclear scalar coupling of a directly bonded 13C-13C pair has been used to create a double-quantum filter (DQF) to remove the natural-abundance 13C background in 13C{15N} rotational-echo double-resonance (REDOR) experiments. The DQF scalar and REDOR dipolar evolution periods are coincident which is important for sensitivity in the event of weak 13C-15N dipolar coupling. Calculated and observed 13C{15N} DQF-REDOR dephasings were in agreement for a test sample of mixed recrystallized labeled alanines. Glycine metabolism in a single uniform-15N soybean leaf labeled for 6 min by 13CO2 was measured quantitatively by 13C{15N} DQF-REDOR with no background interferences.     

Application of REDOR subtraction for filtered MAS observation of labeled backbone carbons of membrane-bound fusion peptides

Clean MAS observation of 13C-labeled carbons in membrane-bound HIV-1 and influenza fusion peptides was made by using a rotational-echo double-resonance spectroscopy (REDOR) filter of directly bonded 13C-15N pairs. The clean filtering achieved with the REDOR approach is superior to filtering done with sample difference spectroscopy. In one labeling approach, the peptide had labels at a single 13C carbonyl and its directly bonded 15N. The resulting chemical shift distribution of the filtered signal is used to assess the distribution of local secondary structures at the labeled carbonyl. For the influenza peptide, the Leu-2 carbonyl chemical shift distribution is shown to vary markedly with lipid and detergent composition, as well as peptide:lipid ratio, suggesting that the local peptide structure also has a strong dependence on these factors. Because most carboxylic- and amino-labeled amino acids are commercially available, this REDOR approach should have broad applicability to chemically synthesized peptides as well as bacterially synthesized proteins. In a second labeling approach, the HIV-1 fusion peptide had U-13C, 15N labeling over three sequential residues. When a 1.6 ms REDOR dephasing time is used, only backbone 13C signals are observed. The resulting spectra are used to determine spectral linewidths and to assess feasibility of assignment of uniformly labeled peptide.     

Relative CSA-dipolar orientation from REDOR sidebands

Algebraic expressions are given for the sideband intensities of REDOR dephasing experiments as a function of the relative orientation of the CSA and dipolar tensors. The expressions are straightforward to derive and implement and can be easily modified for variations in the spin systems, including distributions of distances and multiple dephasers. These expressions, along with the high sensitivity, resolution, and general robust nature of REDOR, make determining CSA-dipolar orientations from REDOR experiments reliable and, compared to full simulations, efficient and routine. Additionally, it is shown that even the +/-1 sidebands of fast-spinning samples may contain significant information about orientation. Finally, numerical integration of the expressions supports the intuitive notion that any difference in the sideband dephasing rates is evidence of preferred CSA-dipolar orientations. This fact can be used to gauge the extent of local molecular order in intermolecular dephasing experiments.     

Abnormal electron spin echo and multiple-quantum coherence in a spin-correlated radical pair system

The phenomena of the abnormal “out-of-phase” electron spin echo in a photo-induced spin-correlated radical pair system are examined theoretically. It is shown that such abnormal phenomena are a consequence of initial non-Boltzmann distribution and zero-quantum coherence produced by laser excitation. The analysis of echo amplitude versus the pulse-angle of the microwave pulse reveals two sources for the formation of the echo. The method of excitation and detection of multiple-quantum coherence using a phase-cycled 2-pulse sequence is also discussed. Such a technique is complementary to the ESE method.     

Comparison of several hetero-nuclear dipolar recoupling NMR methods to be used in MAS HMQC/HSQC

We compare several hetero-nuclear dipolar recoupling sequences available for HMQC or HSQC experiments applied to spin-1/2 and quadrupolar nuclei. These sequences, which are applied to a single channel, are based either on the rotary resonance recoupling (R3) irradiation, or on two continuous rotor-synchronized modulations (SFAM1 and SFAM2), or on four symmetry-based sequences (R2(1)1,SR4(1)2,R12(3)5,R20(5)9), or on the REDOR scheme. We analyze systems exhibiting purely hetero-nuclear dipolar interactions as well as systems where homo-nuclear dipolar interactions need to be canceled. A special attention is given to the behavior of these sequences at very fast MAS. It is shown that R3 methods behave poorly due to the narrowness of their rf-matching curves, and that the best methods are SR4(1)2 and SFAM (SFAM1 or SFAM2 if homo-nuclear interactions are not negligible). REDOR can also recouple efficiently hetero-nuclear dipolar interactions, provided the sequence is sent on the non-observed channel and homo-nuclear dipolar interactions are negligible. We anticipate that at ultra-fast spinning speed, SFAM1 and SFAM2 will be the most efficient methods.