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.     

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 .     

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.     

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.     

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.     

Measuring oxygen-phosphorus distances and the orientation of electric field gradient tensors using 17O-[31P] REDOR in phosphate glasses

Rotational echo double resonance (REDOR) of spin-12 nuclei is an extremely useful tool for the determination of distances in solids as well as of relative orientations of chemical shift and dipole tensors. We present the corresponding version for measuring the relative orientation of electric quadrupole and dipole tensors and demonstrate its applicability for non-bridging oxygens in phosphate glasses using 17O-[31P] REDOR NMR. The orientational information is found in the changes of the second-order quadrupole patterns as a function of the echo delay. Results and numeric simulations are presented for 17O-[31P] REDOR NMR of 17O-enriched sodium phosphate glasses. For non-bridging oxygens, the symmetric quadrupole tensor is found to be aligned along the phosphorus-oxygen bond. The distance between P and the non-bridging oxygen is calculated for two glasses of different compositions.     

REDOR NMR on a hydrophobic peptide in oriented membranes

A method is presented for the calculation of REDOR dephasing for specifically labeled membrane-spanning peptides in uniformly aligned lipid bilayers under magic angle oriented sample spinning (MAOSS) conditions. Numerical simulations are performed for dephasing of (13)C signal by (15)N when the labels are placed in an alpha-helical peptide at the carbonyl of residue (i) and amide nitrogen of residue (i + 2) to show the dependency of REDOR echo intensity on the peptide tilt angle relative to the membrane normal. The approach was applied to the labeled transmembrane domain of phospholamban ([(15)N-Leu(37), (13)C-Leu(39)]PLBTM) incorporated into dimyristoylphosphatidylcholine bilayers. The dephasing observed for a random membrane dispersion showed that the peptide was alpha-helical in the region including the two labels, and dephasing in oriented membranes showed that the peptide helix was tilted by 25 degrees +/- 7 degrees relative to the bilayer normal. These results agree with those obtained by other spectroscopic methods.     

Internuclear distance determination of S = 1, I = 1/2 spin pairs using REAPDOR NMR

A universal function is proposed to describe REAPDOR dephasing curves of an observed spin-1/2 nucleus dipole-recoupled to a spin-1 quadrupolar nucleus ((2)H or (14)N). Previous work had shown that, in contrast to REDOR, the shape of the dephasing curve depends on a large number of parameters including the quadrupolar coupling constant and asymmetry parameter, the sample rotation speed, the RF amplitude, and the relative orientations of the quadrupole tensor and the internuclear vector. Here we demonstrate by numerical simulations that the actual dispersion of REAPDOR dephasing curves is quite small, provided the rotation speed and the RF amplitude applied to the quadrupolar nucleus satisfy an adiabaticity condition. The condition is easily met for (2)H and is also practically achievable for virtually any (14)N-containing compound. This allows the REAPDOR curves to be approximated by a simple universal gaussian-type function, comparison of which with experimental data yields internuclear distances with less than 4% error. The spin dynamics of the recoupling mechanism is discussed. The critical importance of a stable spinning speed for optimizing the signal-to-noise ratio of the (13)C echoes is demonstrated and practical suggestions for achieving high stability are presented. Examples of applications of the universal curve are given for (2)H/(13)C and (14)N/(13)C REAPDOR in alanine.     

REDOR Dephasing by Multiple Spins in the Presence of Molecular Motion

Closed-form, numerical algorithms are presented for calculating REDOR dephasing for three general cases: (i) collections of isolatedI–Sspin pairs; (ii) manySspins coupled to anIspin; and (iii) anI–Sspin pair in relative motion. For the case when more than oneSspin is dipolar coupled to anIspin, the calculation assumes that theS–Shomonuclear interaction does not affect REDOR dephasing. Full numerical simulations show that this assumption is true if theS-spin lineshapes are inhomogeneously broadened, theS-spin chemical shifts are far from rotational resonance, and a version of REDOR is used which minimizes the number ofS-spin π pulses. For the rapidly rotating –CF₃group of poly(trifluoroethyl methacrylate), the formalisms of (ii) and (iii) are combined to calculate the dephasing. The experimentally measured dephasing matches theory when the wiggling motion of the –OCH₂CF₃moiety of the polymer is taken into account.     

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.     

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.     

Relaxation-induced dipolar exchange with recoupling-An MAS NMR method for determining heteronuclear distances without irradiating the second spin

A new magic-angle spinning NMR method for distance determination between unlike spins, where one of the two spins in question is not irradiated at all, is introduced. Relaxation-induced dipolar exchange with recoupling (RIDER) experiments can be performed with conventional double-resonance equipment and utilize the familiar π-pulse trains to recouple the heteronuclear dipolar interaction under magic-angle spinning conditions. Longitudinal relaxation of the passive spin during a delay between two recoupling periods results in a dephasing of the heteronuclear coherence and consequently a dephasing of the magnetization detected after the second recoupling period. The information about the dipolar coupling is obtained by recording normalized dephasing curves in a fashion similar to the REDOR experiment. At intermediate mixing times, the dephasing curves also depend on the relaxation properties of the passive spin, i.e., on single- and double-quantum longitudinal relaxation times for the case of I = 1 nuclei, and these relaxation times can be estimated with this new method. To a good approximation, the experiment does not depend on possible quadrupolar interactions of the passive spin, which makes RIDER an attractive method when distances to quadrupolar nuclei are to be determined. The new method is demonstrated experimentally with ¹⁴N and ²H as heteronuclei and observation of ¹³C in natural abundance.     

Efficient deuterium-carbon REDOR NMR spectroscopy

Phase modulated pulses for deuterium recoupling in (2)H-(13)C REDOR NMR spectroscopy have been introduced to improve dephasing of the detected (13)C nuclei. The deuterium inversion properties of phase modulated recoupling pulses have been studied experimentally on l-alanine-2-d(1) and theoretically using average Hamiltonian theory and exact simulations of the equation of motion of the density matrix. The best (13)C dephasing was observed when XYXYX (PM5) deuterium recoupling pulses were applied. A comparison to the 90 degrees -180 degrees -90 degrees (CPL) composite pulse scheme revealed an improvement of recoupling on the order of 2.5. Simple CW recoupling pulses of the same length of PM5 and CPL pulses showed the weakest (13)C dephasing. Simulations have shown that the (2)H recoupling efficiency of PM5 REDOR experiments approach the very efficient REAPDOR results. However, in our case a REAPDOR study of l-alanine-2-d(1) resulted in a significant decrease of the (13)C signal intensity due to pulse imperfections of (13)C pi-pulses. The new PM5-REDOR technique has been employed to study the torsion angle between C1/2 and C5 in ethylmalonic acid-4-d(2).     

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.     

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].     

Application of the Floquet theory to multiple quantum NMR of dipolar-coupled multi-spin systems under magic angle spinning

A new analytical Liouville-space representation of the time-propagator under magic angle spinning (MAS) is introduced using the formalized quantum Floquet theory. This approach has the advantage that it is applicable to the analysis of any type of NMR experiment where MAS is combined with multiple-pulse excitation. General relationships describing the spectral parameters in multiple-quantum (MQ) MAS spectra are derived in this representation. Their use is illustrated with an application to double-quantum (DQ) NMR spectra of dipolar-coupled multi-spin systems. Corresponding to the separation of the MAS time-propagator into a rotor modulated and a dephasing component, two distinct mechanisms for DQ excitation are identified. One of them exploits the rotor-modulated component to excite DQ coherences through dipolar-recoupling techniques, which are familiar for spin pairs. Analytical expressions of the integral intensities and linewidths in the resulting DQ sideband pattern are derived in the form of power series expansions of the inverse rotor frequency, of which coefficients depend on structural parameters. In a multi-spin system they can most reliably be extracted in the fast spinning regime. The other mechanism exploits the dephasing component, which is characteristic to multi-spin systems only. This is shown to give rise to DQ coherences by free evolution at full rotor periods. The possibility to exploit it for selective excitation of higher order MQ coherences is discussed. In either case, the dephasing component also leads to residual broadening. The main results of the theoretical developments are demonstrated experimentally on adamantane.     

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.     

Measurement of the local 1H spin-diffusion coefficient in polymers

Proton spin diffusion is widely used to determine domain sizes in heterogeneous organic solids. For an accurate analysis, spin diffusion coefficients are required. However, in most cases they are not directly measured, but instead derived from model systems. The effects of magic-angle spinning (MAS), mobility, or spin-lock fields on spin-diffusion coefficients have also been difficult to quantify. In this work, direct measurement of local (1)H spin-diffusion coefficients in any rigid polymer is achieved in experiments with heteronuclear dephasing of the (1)H magnetization, a mixing time for (1)H spin diffusion, and (13)C detection after cross-polarization. In the presence of (1)H homonuclear decoupling and (13)C 180 degrees-pulse recoupling, each (13)C spin dephases a significant number (3-20) of protons, depending on the dephasing time. For (13)C and other sufficiently dilute heteronuclei, the dephasing of the protons is described by simple spin-pair REDOR curves. As a result, every (13)C nucleus will "burn" a spherical hole of known diameter and profile into the proton magnetization distribution. (1)H spin diffusion into the hole during the mixing time can be monitored and simulated accurately for every resolved (13)C site, with the spin-diffusion coefficient as the only significant unknown parameter. By varying the dephasing time, holes with diameters of 0.4-0.8 nm can be burned into the proton magnetization profile and thus the dependence of the local spin-diffusion coefficients on the proton density or partial mobility can be explored. The effects of transverse or magic-angle spin-lock fields on spin diffusion can be quantified conveniently by this method. Analytical and numerical fits yield short-range spin-diffusion coefficients of 0.2-0.5 nm(2)/ms on the 0.5-nm scale, which is smaller than the value of 0.8 nm(2)/ms for organic solids previously measured on the 10-nm scale.