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.     

"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.     

Time displacement rotational echo double resonance: heteronuclear dipolar recoupling with suppression of homonuclear interaction under fast magic-angle spinning

We have developed a novel variant of REDOR which is applicable to multiple-spin systems without proton decoupling. The pulse sequence is constructed based on a systematic time displacement of the pi pulses of the conventional REDOR sequence. This so-called time displacement REDOR (td-REDOR) is insensitive to the effect of homonuclear dipole-dipole interaction when the higher order effects are negligible. The validity of td-REDOR has been verified experimentally by the P-31{C-13} measurements on glyphosate at a spinning frequency of 25 kHz. The experimental dephasing curve is in favorable agreement with the simulation data without considering the homonuclear dipole-dipole interactions.     

Compensation for pulse imperfections in rotational-echo double-resonance NMR by composite pulses and EXORCYCLE

We describe a simple method to compensate for pulse-angle errors in rotational-echo double resonance (REDOR) experiments for determining heteronuclear distances in solids. By using composite 180 degrees pulses on the unobserved dephasing spin and EXORCYCLE for the single pi pulse on the observed channel, the REDOR curve becomes much less sensitive to pulse-angle errors. Both improvements are demonstrated by experiments on the model compound, (15)N, (13)Calpha -labeled N-t-BOC-glycine, and are confirmed by numerical simulations. The advantage of EXORCYCLE is also shown analytically using the product operator formalism. The proposed simple schemes compensate for unavoidable pulse-angle errors that arise, for example, from radiofrequency field inhomogeneity. They also make REDOR experiments more accurate and robust for low-sensitivity samples where direct pulse-length calibration is difficult.     

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.     

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.     

Dipolar coupling information in multispin systems: application of a compensated REDOR NMR approach to inorganic phosphates. Rotational echo double resonance

An experimental 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-12) can be conveniently obtained from the experimental curve of DeltaS/S(0) versus dipolar evolution time by limiting the analysis to the initial data range 0 < delta S/S(0) < 0.30. Numerical simulations have been carried out on a three-spin system of type SI(2) 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 degrees 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 degrees pulse on the I channel in the middle of the dipolar evolution periods. Experimental (27)Al?(31)P? REDOR results on the multispin systems Al(PO(3))(3), AlPO(4), [AlPO(4)](12)(C(3)H(7))(4)NF, and Na(3)PO(4) confirm the general utility of this approach. Thus, for applications to unknown systems the compensation strategy obviates calibration procedures with model compounds.     

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.     

Recoupling of residual dipolar couplings in single-domain polymer-stabilized liquid crystals undergoing magic-angle spinning

Measurement of dipolar couplings, chemical shift anisotropies, and quadrupole couplings in oriented media such as liquid crystals are of great importance for extraction of structural parameters in biological macromolecules. Here, we introduce a new technique, SAD-REDOR, that consists of recoupling heteronuclear dipolar couplings in molecules dissolved in a single-domain liquid crystal or other oriented medium through the combined use of magic-angle spinning and rotor-synchronized radiofrequency pulses. This application of the REDOR pulse sequence to oriented media offers several advantages such as selectivity over the type of coupling recovered and tunable scaling of the interaction. The effectiveness of the technique is demonstrated both theoretically and experimentally, using the recently developed polyacrylamide-stabilized Pf1 phage medium and 15N-labeled benzamide as the aligned molecule.     

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 with a relative full-echo reference

REDOR and REDOR-like 13C[19F] and 2H[19F] NMR experiments have been performed on lyophilized whole cells of Staphylococcus aureus. The bacteria were grown to maturity on media containing L-[13C(3)]alanine or L-[methyl-d(3)]alanine, and then complexed with the 4-fluorobiphenyl derivative of chloroeremomycin, an analogue of the widely used antibiotic, vancomycin. The position of the 19F of the drug bound in the bacterial cell wall was determined relative to L-alanine 13C and 2H labels in the peptidoglycan peptide stem that was closest to the fluorinated biphenyl moiety of the drug. These determinations were made by dipolar recoupling methods that do not require an absolute measurement of the REDOR full echo (the signal observed without rotor-synchronized dephasing pulses) of the labels in the peptide stem.     

1H/31P distance determination by solid state NMR in multiple-spin systems

The results of two techniques of dipolar recoupling, REDOR and CPMAS, are compared in the case of a coupled multiple-spin system. A fundamentally different behavior is observed for these two techniques. In REDOR, the terms associated with each interaction S-I(k) commute with each other and no truncation takes place so that each addition of spin I(k) causes a splitting with its dipolar frequency. In CPMAS, the flip-flop terms of the dipolar Hamiltonian do not commute with the dominant term from the strongly coupled spin pair so that the weak coupling terms from the neighboring spin I(k) are effectively truncated by the dominant pair interaction. Spin dynamics calculations are in agreement with the experimental data in a cubane shaped cluster.     

A frequency-selective REDOR experiment for an SI2 spin system

A frequency-selective REDOR experiment is described for SI₂ spin systems. The experiment causes the net dipolar dephasing of the S spin to evolve only under the influence of one of the I spins. The experiment is based on a single pair of appropriately phased 90° I-spin pulses, and the I spin causing the S-spin dipolar dephasing is determined by the relative phases between the two 90° pulses. The experiment is demonstrated on a sample of ¹⁵N₂-l-asparagine.     

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/14N heteronuclear multiple-quantum correlation with rotary resonance and REDOR dipolar recoupling

A two-dimensional (13)C/(14)N heteronuclear multiple quantum correlation (HMQC) experiment using dipolar recoupling under magic-angle spinning (MAS) is described. The experiment is an extension of the recent indirect (13)C detection scheme for measuring (14)N quadrupolar coupling under MAS. The recoupling allows the direct use of the much larger dipolar interaction instead of the small J and residual dipolar couplings for establishing (13)C/(14)N correlations. Two recoupling methods are incorporated into the HMQC sequence, both applying rf only to the observed (13)C spin. The first one uses the REDOR sequence with two pi-pulses per rotor cycle. The second one uses a cw rf field matching the spinning frequency, known as rotary resonance. The effects of CSA, T(2)(') signal loss, MAS frequency and stability and t(1)-noise are compared and discussed.     

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.     

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.     

Analysis of the REDOR Signal and Inversion

An inversion of the REDOR signal to recover the dipolar couplings has been recently proposed [K. T. Muelleret al., Chem. Phys. Lett.242, 535 (1995)]: The corresponding integral transform was performed by tabulation of the kernel followed by numerical integration. After explicit determination of the inverse REDOR kernel by the Mellin transform method, we propose an alternative inversion method based on Fourier transforms. Representation of the inverse REDOR kernel by its asymptotic expansion reveals that the inverse REDOR operator is essentially a weighted sum of a cosine transform and of its derivative. Consequently, known properties of Fourier transforms can easily be transposed to the REDOR inversion, allowing for a precise discussion of the value of the method. Moreover, the first term of the asymptotic expansion leading to a derivative of a cosine transform, the REDOR inversion is found to be extremely sensitive to noise, thus considerably reducing the useful part of the theoretical dipolar window.     

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.     

Achieving high resolution dipolar NMR information without fast sample spinning: Combining magic angle turning with dipolar based NMR methods

In this article we present a new approach to high resolution NMR combining the concepts of magic angle hopping (MAH)/magic angle turning (MAT) and dipolar based NMR methods such as SEDOR, REDOR or cross polarization (CP). Employing aluminophosphates as model systems we demonstrate that No MAS needed (NOMAS) is capable of supplying high resolution dipolar information without the need of fast MAS.