Dipolar and J encoded DQ MAS spectra under rotational resonance

A two-dimensional (2D) double-quantum (DQ) experiment under rotational resonance (R(2)) conditions is introduced for evaluating dipolar couplings in rotating solids. The contributions from the R(2)-recoupled dipolar interaction and the J coupling can be conveniently separated in the resulting 2D R(2)-DQ spectrum, so that the unknown dipolar coupling can readily be extracted, provided that the values of the involved J coupling constants are known. Since the measured parameters are integral intensity ratios between suitably chosen absorption peaks in the 2D spectrum, the proposed method is characterized by a reduced sensitivity to relaxation parameters. The effect of rotor-modulated terms, including chemical shift anisotropy, is efficiently averaged out by synchronizing the excitation/reconversion time with the rotor period. All of these features are demonstrated theoretically by the example of two model systems, namely, isolated spin-pairs and a three-spin system. The results of the theoretical models are applied to both (13)C and (1)H nuclei to extract dipolar couplings in uniformly (13)C labeled L-alanine and a crosslinked natural rubber.     

A maximum likelihood method for determining D(a)(PQ) and R for sets of dipolar coupling data

The algorithms available today that use dipolar coupling data for macromolecular structure determination require the independent determination of two parameters, D(a)(PQ) and R. Methods exist for obtaining these parameters when the set of dipolar couplings available is large and the orientations of the interatomic vectors on which they report is isotropically distributed. These methods are less satisfactory when the set is small and anisotropic. Described here is a maximum likelihood method that extracts accurate values for D(a)(PQ) and R from small, anisotropic data sets. Also demonstrated is a procedure for estimating the errors associated with the values of D(a)(PQ) and R obtained and for incorporating these errors into refinement protocols.     

Accurate measurement of H(N)-H(alpha) residual dipolar couplings in proteins.

A method for accurately measuring H(N)-H(alpha) residual dipolar couplings is described. Using this technique, both the sign and magnitude of the coupling can be determined easily. Residual dipolar coupling between H(N)(i)-H(alpha)(i) and H(N)(i)-H(alpha)(i-1) were measured for the FK506 binding protein complexed to FK506. The experimental values were in excellent agreement with predictions based on an X-ray crystal structure of the protein/ligand complex, suggesting that these residual dipolar couplings will provide accurate structural constraints for the refinement of protein structures determined by NMR.     

Field-dependent nuclear relaxation of spins 1/2 induced by dipole-dipole couplings to quadrupole spins: LaF3 crystals as an example

A general theory of spin-lattice nuclear relaxation of spins I=1/2 caused by dipole-dipole couplings to quadrupole spins S1, characterized by a non-zero averaged (static) quadrupole coupling, is presented. In multispin systems containing quadrupolar and dipolar nuclei, transitions of spins 1/2 leading to their relaxation are associated through dipole-dipole couplings with certain transitions of quadrupole spins. The averaged quadrupole coupling attributes to the energy level structure of the quadrupole spin and influences in this manner relaxation processes of the spin 1/2. Typically, quadrupole spins exhibit also a complex multiexponential relaxation sensed by the dipolar spin as an additional modulation of the mutual dipole-dipole coupling. The proposed model includes both effects and is valid for an arbitrary magnetic field and an arbitrary quadrupole spin quantum number. The theory is applied to interpret fluorine relaxation profiles in LaF3 ionic crystals. The obtained results are compared with predictions of the 'classical' Solomon relaxation theory.     

Water-proton-spin-lattice-relaxation dispersion of paramagnetic protein solutions

The paramagnetic contributions to water-proton-spin-lattice relaxation rate constants in protein systems spin-labeled with nitroxide radicals were re-examined. As noted by others, the strength of the dipolar coupling between water protons and the protein-bound nitroxide radical often appears to be larger than physically reasonable when the relaxation is assumed to be controlled by 3-dimensional diffusive processes in the vicinity of the spin label. We examine the effects of the surface in biasing the diffusive exploration of the radical region and derive a relaxation model that incorporates 2-dimensional dynamics at the interfacial layer. However, we find that the local 2-dimensional dynamics changes the shape of the relaxation dispersion profile but does not necessarily reproduce the low-field relaxation efficiency found by experiment. We examine the contributions of long-range dipolar couplings between the paramagnetic center and protein-bound-water molecules and find that the contributions from these several long range couplings may be competitive with translational contributions because the correlation time for global rotation of the protein is approximately 1000 times longer than that for the diffusive motion of water at the interfacial region. As a result the electron-proton dipolar coupling to rare protein-bound-water-molecule protons may be significant for protein systems that accommodate long-lived-water molecules. Although the estimate of local diffusion coefficients is not seriously compromised because it derives from the Larmor frequency dependence, these several contributions confound efforts to fit relaxation data quantitatively with unique models.     

Solid state NMR analysis of the dipolar couplings within and between distant CF3-groups in a membrane-bound peptide

Dipolar couplings contain information on internuclear distances as well as orientational constraints. To characterize the structure of the antimicrobial peptide gramicidin S when bound to model membranes, two rigid 4-CF3-phenylglycine labels were attached to the cyclic backbone such that they reflect the behavior of the entire peptide. By solid state 19F NMR we measured the homonuclear dipolar couplings of the two trifluoromethyl-groups in oriented membrane samples. Using the CPMG experiment, both the strong couplings within each CF3-group as well as the weak coupling between the two CF3-groups could be detected. An intra-CF3-group dipolar coupling of 86 Hz and a weak inter-group coupling of 20 Hz were obtained by lineshape simulation of the complex dipolar spectrum. It is thus possible to explore the large distance range provided by 19F-labels and to resolve weak dipolar couplings even in the presence of strong intra-CF3 couplings. We applied this approach to distinguish and assign two epimers of the labeled gramicidin S peptide on the basis of their distinct 19F dipolar coupling patterns.     

A simulation algorithm based on Bloch equations and product operator matrix: application to dipolar and scalar couplings

A product operator matrix is proposed to describe scalar couplings in liquid NMR. Combination of the product operator matrix and non-linear Bloch equations is employed to describe effects of chemical shift, translational diffusion, dipolar field, radiation damping, and relaxation in multiple spin systems with both scalar and dipolar couplings. A new simulation algorithm based on this approach is used to simulate NMR signals from dipolar field effects in the presence of scalar couplings. Several typical coupled spin systems with both intra-molecular scalar couplings and inter-molecular dipolar couplings are simulated. Monte Carlo methods are incorporated into simulations as well to analyze diffusion process in these complicated spin systems. The simulated results of diffusion and relaxation parameters and 2D NMR spectra are coincident with the experimental measurements, and agree with theoretical predictions as well. The simulation algorithm presented herein therefore provides a convenient means for designing pulse sequences and quantifying experimental results in complex coupled spin systems.     

Double-quantum dipolar recoupling at high magic-angle spinning rates

A full investigation of the possible homonuclear double-quantum recoupling sequences, based on the RN family of sequences with N < or = 20, is given. Several new RN sequences, R16(6)(5), R18(8)(5), and R18(10)(5), were applied at high magic-angle spinning rates and compared with theory. The R18(10)(5) technique can be used to recouple dipolar couplings at spinning rates up to 39 kHz, and the application of the sequence in an INADEQUATE experiment is shown for a spinning rate of 30 kHz.     

Evolution of solid state systems containing mutually coupled dipolar and quadrupole spins: perturbation treatment

Perturbation approach to time evolution of multi-spin systems containing quadrupole and dipolar spins has been presented and discussed. The treatment comprises polarization transfer effects, field-dependent relaxation processes of dipolar as well as quadrupole spins and combined results of both of them. Complete theories dealing with various aspects of the spin dynamic processes have been proposed. Because of an educational character of this paper, relevant assumptions, limitations and even particular steps of the proposed treatments have been discussed in detail. Special emphasis is put on understanding of validity regimes of the perturbation treatment, depending on relative strengths of spin interactions and timescales of relevant motional processes affecting them. Motional regimes required for spins to be involved in essentially different evolution pathways like polarization transfers or relaxation have been illustrated by experimental examples.     

Effective dipolar couplings determined by dipolar dephasing of double-quantum coherences

It is shown how homonuclear distances and homonuclear dipolar lattice sums between spin-1/2 nuclei can be measured by a pulsed solid-state NMR experiment under magic-angle spinning conditions. The presented technique is based on double-quantum coherence filtering. Instead of measuring a build-up of double-quantum coherence the pulse sequence is designed to dephase double-quantum coherence. This is achieved by exciting double-quantum coherence either with the help of the through-space dipolar coupling or the through-bond dipolar coupling while the dephasing relies on the through-space dipolar coupling as selected by a gamma-encoded pulse sequence from the C/R symmetry class. Since dephasing curves can be normalized on zero dephasing, it is possible to analyze the initial dephasing regime and hence determine dipolar lattice sums (effective dipolar couplings) in multiple-spin systems. A formula for the effective dipolar coupling is derived theoretically and validated by numerical calculations and experiments on crystalline model compounds for (13)C and (31)P spin systems. The double-quantum dephasing experiment can be combined with constant-time data sampling to compensate for relaxation effects, consequently only two experimental data points are necessary for a single distance measurement. The phase cycling overhead for the constant-time experiment is minimal because a short cogwheel phase cycle exists. A 2D implementation is demonstrated on [(13)C(3)]alanine.     

Protein dynamics using frequency-dependent order parameters from analysis of NMR relaxation data

A novel approach is described to analyze NMR relaxation data on proteins. This method introduces the frequency-dependent order parameter, S(2)(omega), in order to estimate contributions to the generalized order parameter S(2) from different motional frequencies occurring on the picosecond to nanosecond time scales. S(2)(omega) is defined as the sum of a specified set of weighting coefficients from the Lorentzian expansion of the spectral density function. 15N NMR relaxation data (500, 600, and 800 MHz) on protein GB1 exemplify the method. Using this approach provides information on motional restrictions over specific frequency or time scale ranges and provides a normalized comparison of motional restrictions between proteins having different overall tumbling correlation times.     

Measurement of Dipolar Cross Correlation in Scalar-Coupled Systems

In systems with dipolar relaxation in isotropic phase, it is possible to measure the extent of cross correlation of the fluctuations of two selected dipole–dipole interactions A–M and A–X by selectively exciting and spin-locking the transverse magnetization of spin A. If the system comprises only three spins A, M, and X, the conversion of in-phase magnetization[formula]into doubly antiphase magnetization[formula]during the spin-locking period occurs spontaneously through relaxation. The rate of this conversion is proportional to the spectral density of the cross correlation of the random fluctuations of the dipolar A–M and A–X interactions. In this paper, larger systems, comprising at least a fourth spin K, are investigated. The complexity of the situation is increased, since other forms of three-spin order such as[formula]or[formula]become accessible. Furthermore, this paper addresses the role of scalar couplings, which are a prerequisite for making three-spin order observable, but which are also a source of perturbations, since scalar couplings can contribute significantly to the creation of various three-spin-order terms. If the spin-locking field is too weak compared to the width of the multiplet under investigation, residual scalar interactions lead to the generation of three-spin order. If the spin-locking field is too strong compared to the relative offsets of other “passive” spins, further complications occur. These can be avoided most effectively by using very high static magnetic fields. If coherent contributions to three-spin order can be suppressed or accounted for through simulations, the remaining buildup of three-spin-order terms arising from dipolar cross-correlation effects can be interpreted in terms of structural and motional parameters.     

Protein backbone dynamics from N-HN dipolar couplings in partially aligned systems: a comparison of motional models in the presence of structural noise

Residual dipolar couplings (RDCs) provide excellent probes for the exploration of dynamics in biomolecules on biologically relevant time-scales. Applying geometric motional models in combination with high-resolution structures to fit experimental RDCs allows the extraction of local dynamic amplitudes of peptide planes in proteins using only a limited number of data points. Here we compare the behaviour of three simple and intuitive dynamic modes: the Gaussian axial fluctuation model (1D-GAF), the two-site jump model, and a model supposing axially symmetric motion about a mean orientation. The requirement of a structural model makes this kind of methodology potentially very sensitive to structural imprecision. Numerical simulations of RDC dynamic averaging under different regimes show that the anisotropic motional models are more geometrically stringent than the axially symmetric model making it more difficult to alias structural noise as artificial dynamic amplitudes. Indeed, it appears that the model extracts accurate motional amplitudes even in the presence of significant structural error. We also show that a two-site jump model, also assuming the (alpha)C(i-1)-(alpha)C(i) as rotation axis, can only be distinguished from the previously developed GAF model beyond amplitude/jumps of around 40 degrees. The importance of appropriate estimation of the molecular alignment tensor for determination of local motional amplitudes is also illustrated here. We demonstrate a systematic scaling of extracted dynamic amplitudes if a static structure is assumed when determining the alignment tensor from dynamically averaged RDCs. As an example an artificial increase of 0.14 (0.85 compared to the expected 0.71) is observed in the extracted S2 if a pervasive 20 degrees GAF motion is present that is ignored in the tensor determination. Finally we apply a combined approach using the most appropriate motional model, to complete the analysis of dynamic motions from protein G.     

Residual 2H quadrupolar couplings in weakly aligned carbohydrates.

We report a novel two-dimensional NMR pulse scheme for the 1H-detected observation of 2H in isotopically 13C, 2H-enriched carbohydrates. This scheme is used for the indirect observation of residual quadrupolar couplings in 13C, 2H-enriched methyl-beta-D-glucopyranoside weakly aligned in a dilute lyotropic liquid-crystalline medium comprising 20% (w/v) dihexanoyl-phosphatidylcholine/dimyristoyl-phosphatidylcholine (1:3 mol/mol) in D2O. The observed residual quadrupolar couplings are substantially larger than residual dipolar one-bond 13C-1H couplings under the same experimental conditions. These quadrupolar couplings are thus a useful alternative to dipolar couplings for the structural analysis of small molecules that align very weakly in dilute liquid-crystalline media. Moreover, since the quadrupolar coupling constant is very uniform throughout endocyclic deuterons of the carbohydrate, these data suggest that adoption of a single average value of this parameter in 2H relaxation studies on the glycan moieties of glycoproteins and glycopeptides is a valid assumption.     

Ordering in nematic liquid crystals from NMR cross-polarization studies

The measurement of dipolar couplings between nuclei is a convenient way of obtatining directly liquid crystalline ordering through NMR since the coupling is dependent on the average orientation of the dipolar vector in the magnetic field which also aligns the liquid crystal. However, measurement of the dipolar coupling between a pair of selected nuclei is beset with problems that require special solutions. In this article the use of cross polarization for measuring dipolar couplings in liquid crystals is illustrated. Transient oscillations observed during cross polarization provide the dipolar couplings between essentially isolated nearest neighbour spins which can be extracted for several sites simultaneously by employing two-dimensional NMR techniques. The use of the method for obtaining heteronuclear dipolar couplings and hence the order parameters of liquid crystals is presented. Several modifications to the basic experiment are considered and their utility illustrated. A method for obtaining proton-proton dipolar couplings, by utilizing cross polarization from the dipolar reservoir, is also presented.     

Experimental aspects of multidimensional solid-state NMR correlation spectroscopy.

The experimental parameters critical for the implementation of multidimensional solid-state NMR experiments that incorporate heteronuclear spin exchange at the magic angle are discussed. This family of experiments is exemplified by the three-dimensional experiment that correlates the (1)H chemical shift, (1)H-(15)N dipolar coupling, and (15)N chemical shift frequencies. The broadening effects of the homonuclear (1)H-(1)H dipolar couplings are suppressed using flip-flop (phase- and frequency-switched) Lee-Goldburg irradiations in both the (1)H chemical shift and the (1)H-(15)N dipolar coupling dimensions. The experiments are illustrated using the (1)H and (15)N chemical shift and dipolar couplings in a single crystal of (15)N-acetylleucine.     

Measurement of long range H,C couplings in natural products in orienting media: a tool for structure elucidation of natural products

In this paper we show that water insoluble compounds dissolved in poly-gamma-benzyl-glutamate are amenable to the measurement of a number of homo- and heteronuclear dipolar couplings. The sensitivity and experimental precision of dipolar couplings are sufficient to obtain a good match with the structure. In order to achieve the necessary precision for H,C dipolar couplings between protons and carbons that are not directly bound a new method for the measurement of heteronuclear long range couplings is introduced that allows a one-parameter fit to a HSQC-based experiment as reference experiment. The methodology is applied to menthol (1R, 3S, 4R).     

Homonuclear Hartmann-Hahn transfer with reduced relaxation losses by use of the MOCCA-XY16 multiple pulse sequence

Homonuclear Hartmann-Hahn transfer is one of the most important building blocks in modern high-resolution NMR. It constitutes a very efficient transfer element for the assignment of proteins, nucleic acids, and oligosaccharides. Nevertheless, in macromolecules exceeding approximately 10 kDa TOCSY-experiments can show decreasing sensitivity due to fast transverse relaxation processes that are active during the mixing periods. In this article we propose the MOCCA-XY16 multiple pulse sequence, originally developed for efficient TOCSY transfer through residual dipolar couplings, as a homonuclear Hartmann-Hahn sequence with improved relaxation properties. A theoretical analysis of the coherence transfer via scalar couplings and its relaxation behavior as well as experimental transfer curves for MOCCA-XY16 relative to the well-characterized DIPSI-2 multiple pulse sequence are given.     

Spinning-frequency-dependent narrowband RF-driven dipolar recoupling

Dipolar recoupling techniques of homonuclear spin pairs are commonly used for distance or orientation measurements in solids. Accurate measurements are interfered with by broadening mechanisms. In this publication narrowband RF-driven dipolar recoupling magnetization exchange experiments are performed as a function of the spinning frequency to reduce the effect of zero-quantum T(2) relaxation. To enhance the exchange of magnetization between the coupled spins, a fixed number of rotor-synchronous pi-pulses are applied at spinning frequencies approaching the rotational resonance (R(2)) conditions. The analysis of the powder averaged dipolar decay curves of the spin magnetizations as a function of the spinning frequency provides a quantitative measure of the dipolar coupling. An effective Hamiltonian for this experiment is derived, taking into account all chemical shift parameters of the spins. The length of the nbRFDR mixing time and the number of rotor cycles per pi-pulse are optimized by numerical simulations for sensitive probing of the dipolar coupling strength. The zero-quantum T(2) relaxation time can easily be taken into account in the data analysis, because the overall exchange time is almost constant in these experiments. Spinning-frequency-dependent nbRFDR experiments near the m = 1 and m = 2 R(2) condition are shown for doubly (13)C-labeled hydroxybutyric acid. Copyright 2000 Academic Press.