Recoupled polarization-transfer methods for solid-state (1)H--(13)C heteronuclear correlation in the limit of fast MAS

An in-depth account of the effects of homonuclear couplings and multiple heteronuclear couplings is given for a recently published technique for (1)H--(13)C dipolar correlation in solids under very fast MAS, where the heteronuclear dipolar coupling is recoupled by means of REDOR pi-pulse trains. The method bears similarities to well-known solution-state NMR techniques, which form the framework of a heteronuclear multiple-quantum experiment. The so-called recoupled polarization-transfer (REPT) technique is versatile in that rotor-synchronized (1)H--(13)C shift correlation spectra can be recorded. In addition, weak heteronuclear dipolar coupling constants can be extracted by means of spinning sideband analysis in the indirect dimension of the experiment. These sidebands are generated by rotor encoding of the reconversion Hamiltonian. We present generalized variants of the initially described heteronuclear multiple-quantum correlation (HMQC) experiment, which are better suited for certain applications. Using these techniques, measurements on model compounds with (13)C in natural abundance, as well as simulations, confirm the very weak effect of (1)H--(1)H homonuclear couplings on the spectra recorded with spinning frequencies of 25--30 kHz. The effect of remote heteronuclear couplings on the spinning-sideband patterns of CH(n) groups is discussed, and (13)C spectral editing of rigid organic solids is shown to be practicable with these techniques.     

Heteronuclear local field NMR spectroscopy under fast magic-angle sample spinning conditions

The acquisition of bidimensional heteronuclear nuclear magnetic resonance local field spectra under moderately fast magic-angle spinning (MAS) conditions is discussed. It is shown both experimentally and with the aid of numerical simulations on multispin systems that when sufficiently fast MAS rates are employed, quantitative dipolar sideband patterns from directly bonded spin pairs can be acquired in the absence of ¹H–¹H multiple-pulse homonuclear decoupling even for “real” organic solids. The MAS speeds involved are well within the range of commercially available systems (10–14 kHz) and provide sidebands with sufficient intensity to enable a reliable quantification of heteronuclear dipolar couplings from methine groups. Simulations and experiments show that useful information can be extracted in this manner even from more tightly coupled –CH₂– moieties, although the agreement with the patterns simulated solely on the basis of heteronuclear interactions is not in this case as satisfactory as for methines. Preliminary applications of this simple approach to the analysis of molecular motions in solids are presented; characteristics and potential extensions of the method are also discussed.     

A Study of Dipolar Interactions and Dynamic Processes of Water Molecules in Tendon byH andH Homonuclear and Heteronuclear Multiple-Quantum-Filtered NMR Spectroscopy

The effect of proton exchange on the measurement of¹H–¹H,¹H–²H, and²H–²H residual dipolar interactions in water molecules in bovine Achilles tendons was investigated using double-quantum-filtered (DQF) NMR and new pulse sequences based on heteronuclear and homonuclear multiple-quantum filtering (MQF). Derivation of theoretical expressions for these techniques allowed evaluation of the¹H–¹H and¹H–²H residual dipolar interactions and the proton exchange rate at a temperature of 24°C and above, where no dipolar splitting is evident. The values obtained for these parameters at 24°C were 300 and 50 Hz and 3000 s⁻¹, respectively. The results for the residual dipolar interactions were verified by repeating the above measurements at a temperature of 1.5°C, where the spectra of the H₂O molecules were well resolved, so that the¹H–¹H dipolar interaction could be determined directly from the observed splitting. Analysis of the MQF experiments at 1.5°C, where the proton exchange was in the intermediate regime for the¹H–²H dipolar interaction, confirmed the result obtained at 24°C for this interaction. A strong dependence of the intensities of the MQF signals on the proton exchange rate, in the intermediate and the fast exchange regimes, was observed and theoretically interpreted. This leads to the conclusion that the MQF techniques are mostly useful for tissues where the residual dipolar interaction is not significantly smaller than the proton exchange rate. Dependence of the relaxation times and signal intensities of the MQF experiments on the orientation of the tendon with respect to the magnetic field was observed and analyzed. One of the results of the theoretical analysis is that, in the fast exchange regime, the signal decay rates in the MQF experiments as well as in the spin echo or CPMG pulse sequences (T₂) depend on the orientation as the square of the second-rank Legendre polynomial.     

Complete Dipolar Decoupling ofC and Its Use in Two-Dimensional Double-Quantum Solid-State NMR for Determining Polymer Conformations

A multiple-pulse technique for complete dipolar decoupling of directly bonded¹³C-labeled sites is described. It achieves significant spectral simplifications in a recently introduced two-dimensional double-quantum solid-state NMR experiment for determining torsion angles. Both homonuclear and heteronuclear dipolar couplings are removed by combining a¹³C multiple-pulse sequence with continuous-wave irradiation on the protons. The¹³C sequence has a fundamental 10-pulse cycle which is a significantly modified magic-sandwich-echo sequence. The crucial heteronuclear decoupling is achieved by breaking the 360° “inner” pulses in the magic sandwich into 90° pulses and spacing them by¹H 360° pulse lengths. Spectral artifacts typical of multiple-pulse sequences are eliminated by phase shifts between cycles. In contrast to many other multiple-pulse decoupling sequences, the long window in the cycle is the dwell time and can be longer than the inverse dipolar coupling, which makes the sequence practical for direct detection even with long pulse ring-down times. A modification of the sequence to scale the chemical shift and increase the effective spectral width is also presented. The 1D and double-quantum 2D experiments are demonstrated on polyethylene with 4%¹³C–¹³C spin pairs. The potential of this approach for distinguishing segmental conformations is illustrated by spectral simulations of the two-dimensional ridge patterns that correlate double-quantum and single-quantum chemical-shift anisotropies.     

Two- and Three-Dimensional H/C PISEMA Experiments and Their Application to Backbone and Side Chain Sites of Amino Acids and Peptides

Two-dimensional ¹H/¹³C polarization inversion spin exchange at the magic angle experiments were applied to single crystal samples of amino acids to demonstrate their potential utility on oriented samples of peptides and proteins. High resolution is achieved and structural information obtained on backbone and side chain sites from these spectra. A triple-resonance experiment that correlates the ¹H–¹³C_α dipolar coupling frequency with the chemical shift frequencies of the α-carbon, as well as the directly bonded amide ¹⁵N site, is also demonstrated. In this experiment the large ¹H–¹³C_α heteronuclear dipolar interaction provides an independent frequency dimension that significantly improves the resolution among overlapping ¹³C resonances of oriented polypeptides, while simultaneously providing measurements of the ¹³C_α chemical shift, ¹H–¹³C dipolar coupling, and ¹⁵N chemical shift frequencies and angular restraints for backbone structure determination.     

Magnetic field gradients in solid state magic angle spinning NMR.

Magnetic field gradients have proven useful in NMR for coherence pathway selection, diffusion studies, and imaging. Recently they have been combined with magic angle spinning to permit high-resolution measurements of semi-solids, where magic angle spinning averages any residual dipolar couplings and local variations in the bulk magnetic susceptibility. Here we show the first examples of coherence pathway selection by gradients in dipolar coupled solids. When the gradient evolution competes with dipolar evolution the experiment design must take into account both the strength of the dipolar couplings and the means to refocus it. Examples of both homonuclear and heteronuclear experiments are shown in which gradients have been used to eliminate the need for phase cycling.     

Structural analysis of uniformly C-labelled solids from selective angle measurements at rotational resonance

We demonstrate that individual H–C–C–H torsional angles in uniformly labelled organic solids can be estimated by selective excitation of ¹³C double-quantum coherences under magic-angle spinning at rotational resonance. By adapting a straightforward one-dimensional experiment described earlier [T. Karlsson, M. Eden, H. Luhman, M.H. Levitt, J. Magn. Reson. 145 (2000) 95–107], a double-quantum filtered spectrum selective for Cα and Cβ of uniformly labelled l-[¹³C,¹⁵N]valine is obtained with 25% efficiency. The evolution of Cα–Cβ double-quantum coherence under the influence of the dipolar fields of bonded protons is monitored to provide a value of the Hα–Cα–Cβ–Hβ torsional angle that is consistent with the crystal structure. In addition, double-quantum filtration selective for C6 and C1′ of uniformly labelled [¹³C,¹⁵N]uridine is achieved with 12% efficiency for a ¹³C–¹³C distance of 2.5 Å, yielding a reliable estimate of the C6–H and C1′–H projection angle defining the relative orientations of the nucleoside pyrimidine and ribose rings. This procedure will be useful, in favourable cases, for structural analysis of fully labelled small molecules such as receptor ligands that are not readily synthesised with labels placed selectively at structurally diagnostic sites.     

Direct Refinement against Proton–Proton Dipolar Couplings in NMR Structure Determination of Macromolecules

The computational tools necessary for making use of ¹H–¹H dipolar couplings in macromolecular structure refinement are presented. Potentials are described for direct refinement against ¹H–¹H dipolar couplings of known sign as well as of unknown sign. In addition, a multiple potential is developed for prochiral protons whose stereospecific assignments are unknown. The utility of direct ¹H–¹H dipolar coupling refinement is illustrated using the small protein ubiquitin. It is shown that direct ¹H–¹H dipolar coupling refinement leads to improvements in the precision, accuracy, and quality of the resulting structures.     

Deuterium—carbon multiple-quantum NMR in liquid crystals: polarization transfer and off-magic-angle spinning

The polarization transfer dynamics in a recently introduced deuterium—carbon NMR correlation method is studied, both theoretically and experimentally. The technique, which exploits heteronuclear multiple-quantum coherences, is useful for measuring and assigning ²H quad-rupolar couplings in ordered media. It is also shown that the experiment is suitable for implementation under off-magic-angle spinning conditions. The approach is demonstrated on a perdeuterated liquid crystal.     

Sideband patterns from rotor-encoded longitudinal magnetization in MAS recoupling experiments

Recent multiple-quantum MAS NMR experiments have shown that a change in the rotor phase (and, hence, in the Hamiltonian) between the excitation and reconversion periods can lead to informative spinning-sideband patterns. However, such "rotor encoding" is not limited to multiple-quantum experiments. Here it is shown that longitudinal magnetization can also be rotor-encoded. Both homonuclear and heteronuclear rotor encoding of longitudinal magnetization (RELM) experiments are performed on dipolar-coupled spin-1/2 systems, and the corresponding sideband patterns in the indirect dimension are analyzed. In both cases, only even-order sidebands are produced, and their intensity distribution depends on the durations of the recoupling periods. In heteronuclear experiments using REDOR-type recoupling, purely dipolar sideband patterns that are entirely free of effects due to the chemical-shielding anisotropy can be generated. Advantages and disadvantages of the heteronuclear RELM experiment are discussed in the context of other methods used to measure heteronuclear dipolar couplings.     

Fluorine-19 Solid-State NMR Magic-Angle-Turning Experiments Using Multiple-Pulse Homonuclear Decoupling

For compounds giving “crowded” 1-dimensional magic-angle-spinning spectra, information about the local atomic environment in the form of the chemical shift anisotropy (CSA) is sacrificed for high resolution of the less informative isotropic chemical shift. Magic-angle-turning (MAT) NMR pulse sequences preserve the CSA information by correlating it to the isotropic chemical shift in a 2-dimensional experiment. For low natural abundance nuclei such as ¹³C and ¹⁵N and under ¹H heteronuclear dipolar decoupling conditions, the dominant NMR interaction is the chemical shift. For abundant nuclei such as ¹H, ¹⁹F, and ³¹P, the homonuclear dipolar interaction becomes a significant contribution to the observed linewidth in both F₁ and F₂ dimensions. We incorporate MREV8 homonuclear multiple-pulse decoupling sequences into the MAT experiment to give a multiple-pulse MAT (MP-MAT) experiment in which the homonuclear dipolar interaction is suppressed while maintaining the chemical shift information. Extensive use of computer simulation using GAMMA has guided the pulse sequence development. In particular, we show how the MREV8 pulses can be incorporated into a quadrature-detected sequence such as MAT. The MP-MAT technique is demonstrated for a model two-site system containing a mixture of silver trifluoroacetate and calcium difluoride. The resolution in the isotropic evolution dimension is improved by faster sample spinning, shorter MREV8 cycle times in the evolution dimension, and modifications of the MAT component of the pulse sequence.     

Broadband Polarization Transfer under Magic-Angle Spinning: Application to Total Through-Space-Correlation NMR Spectroscopy

A pulse sequence is described that leads to a broadband recoupling of the dipolar interaction in magic-angle-spinning solid-state NMR experiments of¹³C spins. The sequence is based on a combination of rotating frame and laboratory frame transfer periods. The recovered dipolar interaction is only weakly dependent on spectral parameters but is a faithful measure for the internuclear distances. Furthermore, a pure zero-quantum term is recovered (of the type found in static “spin-diffusion” experiments). This makes the pulse sequence particularly suited for incorporation into two-dimensional total through-space correlation experiments that deliver simultaneous information about all dipolar couplings in a single 2D experiment. It is found that the necessary decoupling from abundant protons is best performed in two steps: first, the strong homonuclear couplings between the high-γ spins are averaged by Lee–Goldburg irradiation and, second, the heteronuclear dipolar interaction is averaged by the combined application of an RF field to the low-γ spins and magic-angle sample spinning. Phase-inversion and amplitude attenuation in the rotating frame and refocusing pulses in the laboratory frame part of the pulse sequence are introduced to achieve an optimum chemical-shift offset-independence and for the suppression of unwanted double-quantum transitions. The design principles are explained in detail. Finally, the pulse scheme is applied to total-correlation spectroscopy of a uniformly labeled amino acid. The experimental cross-peak intensities are in qualitative agreement with the known crystal structure of the model compound.     

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°.     

2-D homonuclear correlation and separated local field experiments for solids with strong homonuclear dipolar couplings

An experiment for acquiring two-dimensional homonuclear correlation spectra of nuclei in solids in the presence of strong homonuclear dipolar couplings is described. The experiment utilizes a multiple-pulse homonuclear decoupling sequence with an effective precession axis parallel to the rotating frame z-axis during the evolution and detection periods. A multiple-pulse sequence that suppresses chemical shift and heteronuclear dipolar coupling evolution and scales the static homonuclear dipolar coupling is proposed for the mixing period. The evolution during the mixing period is analogous to the dynamics of the mixing period in solution-state TOCSY experiments, and can be interpreted as the oscillatory exchange of longitudinal magnetization between coupled spins. For nuclides with large gyromagnetic ratios, the static homonuclear dipolar interaction will be substantially larger than the mechanisms used to develop internuclear correlations in solution state 2-D experiments, which should make it possible to establish correlations over much longer distances and with significantly shorter mixing times. Extensions to separated local field experiments are discussed.     

Three-Dimensional C Shift/H–N Coupling/N Shift Solid-State NMR Correlation Spectroscopy

Triple-resonance experiments capable of correlating directly bonded and proximate carbon and nitrogen backbone sites of uniformly ¹³C- and ¹⁵N-labeled peptides in stationary oriented samples are described. The pulse sequences integrate cross-polarization from ¹H to ¹³C and from ¹³C to ¹⁵N with flip-flop (phase and frequency switched) Lee–Goldburg irradiation for both ¹³C homonuclear decoupling and ¹H–¹⁵N spin exchange at the magic angle. Because heteronuclear decoupling is applied throughout, the three-dimensional pulse sequence yields ¹³C shift/¹H–¹⁵N coupling/¹⁵N shift correlation spectra with single-line resonances in all three frequency dimensions. Not only do the three-dimensional spectra correlate ¹³C and ¹⁵N resonances, they are well resolved due to the three independent frequency dimensions, and they can provide up to four orientationally dependent frequencies as input for structure determination. These experiments have the potential to make sequential backbone resonance assignments in uniformly ¹³C- and ¹⁵N-labeled proteins.     

Recoupled Polarization Transfer Heteronuclear H–C Multiple-Quantum Correlation in Solids under Ultra-fast MAS

A new approach for high-resolution solid-state heteronuclear multiple-quantum MAS NMR spectroscopy of dipolar-coupled spin- nuclei is introduced. The method is a heteronuclear chemical shift correlation technique of abundant spins, like ¹H with rare spins, like ¹³C in natural abundance. High resolution is provided by ultra-fast MAS and high magnetic fields, high sensitivity being ensured by a direct polarization transfer from the abundant protons to ¹³C. In a rotor-synchronized variant, the method can be used to probe heteronuclear through-space proximities, while the heteronuclear dipolar coupling constant can quantitatively be determined by measuring multiple-quantum spinning-sideband patterns. By means of recoupling, even weak heteronuclear dipolar interactions are accessible. The capabilities of the technique are demonstrated by measurements on crystalline -tyrosine hydrochloride salt.     

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.     

The Application of 2D NMR Techniques in the Structural Assignment of the Diterpenoid Alkaloid,Delphinine

The two dimensional inverse detected heteronuclear correlation experiment HMQC and the homonuclear correlation experiments COSY and ROESY were performed on the natural alkaloid, delphinine enabling complete assignments of the ¹H and ¹³C spectra. The stereochemistry of ring A and B have been determined in solution. The results suggest that the application of direct correlation multipulse NMR techniques allows for unambiguous structural assignment of delphinine.     

Quantum Treatment of Intermolecular Multiple-Quantum Coherences with IntramolecularJCoupling in Solution NMR

A recently introduced density matrix picture for dipolar effects in solution NMR (1996,J. Chem. Phys.105,874) gave complete solutions for intermolecular multiple-quantum coherences for single-component samples without scalar couplings. This paper, for the first time, shows that this quantum picture can lead to explicit signal expressions for multicomponent samples of molecules with internal scalar couplings (here assumed to generate a first-order spectrum) and long-range dipolar couplings. Experimental observation of a triplet in the indirectly detected dimension for a heteronuclear CRAZED sequence (¹³CHCl₃sample, ZQ or 2Q coherences) gives clear evidence that the coupling is due to the intermolecular dipolar coupling. We also make comparisons with classical pictures which introduce the dipolar demagnetization field in multicomponent spin systems.     

The 2D {P} Spin-Echo-Difference Constant-Time [C, H]-HMQC Experiment for Simultaneous Determination of JH3′P and JC4′P in C-Labeled Nucleic Acids and Their Protein Complexes

A two-dimensional {³¹P} spin-echo-difference constant-time [¹³C, ¹H]-HMQC experiment (2D {³¹P}-sedct-[¹³C, ¹H]-HMQC) is introduced for measurements of ³J_C4′P and ³J_H3′P scalar couplings in large ¹³C-labeled nucleic acids and in DNA–protein complexes. This experiment makes use of the fact that ¹H–¹³C multiple-quantum coherences in macromolecules relax more slowly than the corresponding ¹³C single-quantum coherences. ³J_C4′P and ³J_H3′P are related via Karplus-type functions with the phosphodiester torsion angles β and ε, respectively, and their experimental assessment therefore contributes to further improved quality of NMR solution structures. Data are presented for a uniformly ¹³C, ¹⁵N-labeled 14-base-pair DNA duplex, both free in solution and in a 17-kDa protein–DNA complex.