NMR relaxation in multipolar AX systems under spin locking conditions

A relaxation matrix has been calculated for a multipolar AX spin system under the on-resonance spin-locking condition. Auto- and cross-correlation terms between dipolar, quadrupolar, and CSA interactions are considered. It is shown that the spin-lock leads to many relaxation pathways being blocked, resulting in a considerably simplified relaxation network. The presence of spectral densities at zero frequency, associated with locked nuclei, allows efficient relaxation also in the absence of fast molecular motions.     

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.     

Molecular dynamics simulations of quadrupolar relaxation of 131Xe in carbon tetrachloride,acetonitrile, and methanol

The nuclear relaxation of ¹³¹Xe in different solvents (carbon tetrachloride, acetonitrile and methanol) has been studied by means of molecular dynamics simulations. The solvation structure around xenon is examined with radial and angular distribution functions. Electric field gradient time correlation functions (EFG-TCF) have been calculated for the electric field gradient at the site of xenon, and are discussed in terms of molecular self- and cross-correlations. The amplitudes of total EFG-TCF for acetonitrile are comparable for the two potentials, a 3-site and a 6-site model, although the self- and cross-correlation EFG-TCF differ significantly between the models. For all solvents, the simulations give quadrupolar relaxation rates close to the experimental results.     

Influence of moving dislocations on the nuclear spin-lattice relaxation time in the rotating frame

Dislocation motion at various velocities in Na²³Cl single crystals was studied using the spin-locking technique. The resulting spin-lattice relaxation time in the rotating frame, T_1?, is strongly dependent on the plastic deformation rate ?e, but not on the plastic strain ?. The experimental results are in accord with a theoretical expression for T_1? based on the relaxation model of Rowland and Fradin for atomic diffusion.     

Quantitative Measurement of Transverse and Longitudinal Cross-Correlation between13C–1H Dipolar Interaction and13C Chemical Shift Anisotropy: Application to a13C-Labeled DNA Duplex

Measurement of both longitudinal and transverse relaxation interference (cross-correlation) between¹³C chemical shift anisotropy and¹³C–¹H dipolar interactions is described. The ratio of the transverse to longitudinal cross-correlation rates readily yields the ratio of spectral densitiesJ(0)/J(ω_C), independent of any structural attributes such as internuclear distance or chemical shift tensor. The spectral density at zero frequencyJ(0) is also independent of chemical exchange effects. With limited internal motions, the ratio also enables an accurate evaluation of the correlation time for overall molecular tumbling. Applicability of this approach to investigating dynamics has been demonstrated by measurements made at three temperatures using a DNA decamer duplex with purines randomly enriched to 15% in¹³C.     

Cross-correlation effects in NMR spectra of a spin 1/2 scalar coupled to a spin S≥1

In the frame of the density matrix formalism the lineshapes and dynamic frequency shifts in the multiplet structure of a spinI = 1/2 scalar coupled to a quadrupolar nucleus with a spinS ≥ 1 undergoing dipolar (D), quadrupolar (Q) and chemical shift anisotropy (CSA) relaxation are studied. Analytic expressions for the cross-correlation spectral densities J^Q-CSA, J_D-Q, J^D-CSA and also for the real and imaginary Redfield elements of the relaxation matrix were obtained in the general case of noncoincident and nonaxial Q, D, and CSA tensors. On the assumption that CSA and Q interactions are comparable in magnitude the contributions of cross-correlation terms CSA-Q, CSA-D, Q-D in the linewidth and dynamic shifts of the multiplet pattern of a spinI = 1/2 were analyzed in a wide interval of correlation times (10⁻¹²-10⁻⁷ s) for a spin system¹³C-¹¹B and³¹P-⁵⁹Co as an example.     

Rotating frame analog of spin-locking and spin-lattice relaxation in the doubly rotating frame

The present paper reports the achievement of the rotating-frame analog of spin-locking and its application to the precise measurements of the spin-lattice relaxation time T(1DR) in the doubly rotating frame. After the magnetization is aligned along the resonant RF field H(1), a pulse sequence of a low-frequency oscillating magnetic field at exact resonance is applied perpendicular to H(1). We have overcome several technical difficulties arising from the fact that the rotating-wave approximation is not valid for the low-frequency field. We have theoretically derived an expression of T(-1)(1DR) due to fluctuating magnetic dipole interactions in the weak collision case and found an important relation among the spin-lattice relaxation rates T(-1)(1), T(-1)(1rho), and T(-1)(1DR). This relation can be used to ascertain whether the relaxation is only due to the fluctuating magnetic dipole interactions between like spins. The experiment was carried out on (1)H nuclei in tetramethylammonium iodide (CH(3))(4)NI and the temperature dependence of T(-1)(1DR) was measured together with that of T(-1)(1) and T(-1)(1rho). The activation energies and the preexponential factors of Arrhenius expressions of the correlation times are newly determined.     

A Simple Approach to Analyzing Protein Side-Chain Dynamics fromC NMR Relaxation Data

A simple approach to deriving motional dynamics information of protein and peptide side chains by using¹³C NMR relaxation data is presented. By using linear approximation of internal rotational correlation functions, simple equations for relating side-chain conformation, bond rotational amplitudes, and rotational correlation coefficients with different NMR relaxation parameters have been obtained. Auto- and cross-correlation spectral densities are considered, and it is shown that proton-coupled¹³C NMR relaxation measurements allow detailed motional information to be obtained.     

Quantitative Measurement of Transverse and Longitudinal Cross-Correlation betweenC–H Dipolar Interaction andC Chemical Shift Anisotropy: Application to aC-Labeled DNA Duplex

Measurement of both longitudinal and transverse relaxation interference (cross-correlation) between¹³C chemical shift anisotropy and¹³C–¹H dipolar interactions is described. The ratio of the transverse to longitudinal cross-correlation rates readily yields the ratio of spectral densitiesJ(0)/J(ω_C), independent of any structural attributes such as internuclear distance or chemical shift tensor. The spectral density at zero frequencyJ(0) is also independent of chemical exchange effects. With limited internal motions, the ratio also enables an accurate evaluation of the correlation time for overall molecular tumbling. Applicability of this approach to investigating dynamics has been demonstrated by measurements made at three temperatures using a DNA decamer duplex with purines randomly enriched to 15% in¹³C.     

Heteronuclear Polarization Transfer by Radiofrequency-Driven Dipolar Recoupling Under Magic-Angle Spinning

At high spinning speeds, standard cross polarization (CP) can be difficult due to the narrow sideband structure of the matching condition. Recent proposals have been made to broaden the matching condition with respect to the applied spin-locking field strengths through the use of simultaneous, rotor-synchronized phase inversions of the spin-locking fields (the SPICP pulse sequence), specifically as relevant to CP between ¹H and ¹³C at spinning speeds sufficient to modulate the relevant dipolar couplings. This has been shown to effectively reduce sensitivity to RF inhomogeneity and fluctuations in overall RF power; however, the sensitivity to chemical shift (offset and anisotropy) remains. Application of the technique to the problem of polarization transfer between low-γ nuclei with large bandwidths (e.g., ¹³C and ¹⁵N) is therefore problematic: the transfer efficiency varies across the spectrum and is optimized for only a narrow region around resonance. A solution to this problem is presented in the form of the RFDRCP (RF-driven recoupling in CP) sequence. In this new method, rotor-synchronized (composite) π pulses are placed between the simultaneous phase inversions of the SPICP sequence to periodically invert the chemical-shift terms in the Hamiltonian, thereby removing their effects to zero order. The zero-order average Hamiltonian for this sequence is analogous to the average Hamiltonian for the homonuclear RFDR sequence. The technique has successfully been used to acquire 2D ¹³C-¹⁵N correlation spectra of uniformly labeled amino acids.     

Rotating-frame spin—lattice relaxation measurements (T 1ρ) with weak spin-locking fields in the presence of homonuclear dipolar coupling

The rotating-frame spin-lattice relaxation time T_1ρ, for two identical protons in the presence of residual dipole-dipole coupling is examined both theoretically and experimentally. The measured T_1ρ, value as well as the amplitude and frequency of the dipolar oscillations are described by a theoretical framework involving three coupled rotating-frame magnetization modes. These modes include the magnetization along the spin-lock field, an antiphase magnetization, and an unobservable form of two-spin order. Inhomogeneity in the spin-locking field decouples the two latter modes resulting in the rapid damping of dipolar oscillations. Both theoretical considerations and experimental observations demonstrate conclusively that whenever the amplitude of the spin-locking field B₁ greatly exceeds the dipolar coupling, the measured T_1ρ, is independent of B₁. Conversely, if B₁ is on the order of the dipolar coupling, the measured T_1ρ, increases as B₁ increases. Dipolar oscillations that are important for times short compared to T_1ρ, are rapidly damped for larger magnitudes of B₁.     

Multidimensional Cross-Correlation Relaxometry of Aqueous Protein Systems

We report, for the first time, the application of multidimensional cross-correlation relaxometry to a model globular aqueous protein system (bovine serum albumin) over a wide range of water contents from the solution to glassy states. Off-diagonal cross-relaxation peaks are observed and lend support to the proton-exchange cross-relaxation model of water relaxation. The dependence of the water proton relaxation rates on water content is also consistent with the multistate theory of water dynamics in protein systems. Evidence for water compartmentation in bovine serum albumin gels is presented and the potential of multidimensional cross-correlation nuclear magnetic resonance relaxometry in elucidating water–biopolymer interactions in more complex heterogeneous biopolymer systems is discussed. Authors' address: Brian P. Hills, Institute of Food Research, Norwich Research Park, Colney, Norwich NR4 7UA, UK     

Spin-lock techniques and CPMG imaging sequences: a critical appraisal of T1p contrast at 0.15 T

The addition of a spin-lock preparatory sequence to a Carr-Purcell-Meiboom-Gill (CPMG) imaging sequence provides a method which allows an accurate and simple comparison of T1p and T2 contrast. Sagittal and axial brain images, produced with the application of a three pulse preparatory spin-lock sequence prior to a sixteen-echo CPMG imaging sequence, are compared with images acquired without the spin-lock sequence. The CPMG sequence uses non-selective refocusing pulses. Therefore, observed echo signals accurately reflect T2 relaxation. This allows a convenient method for assessing the degree to which T1p and T2 contrast differ. The spin-lock CPMG (SL-CPMG) images were acquired with a spin-locking field amplitude of 0.4 G and resemble heavily T2-weighted images at 0.15 T. Quantitative analyses of signal intensities from edema and normal brain tissue confirm the qualitative observations. This in vivo method should prove useful for determining when the additional RF power deposition associated with spin-locking techniques will provide an alternate form of tissue contrast than that available from additional echo collection.     

Separating Structure and Dynamics in CSA/DD Cross-Correlated Relaxation: A Case Study on Trehalose and Ubiquitin

We present two new sensitivity enhanced gradient NMR experiments for measuring interference effects between chemical shift anisotropy (CSA) and dipolar coupling interactions in a scalar coupled two-spin system in both the laboratory and rotating frames. We apply these methods for quantitative measurement of longitudinal and transverse cross-correlation rates involving interference of ¹³C CSA and ¹³C–¹H dipolar coupling in a disaccharide, α,α- -trehalose, at natural abundance of ¹³C as well as interference of amide ¹⁵N CSA and ¹⁵N–¹H dipolar coupling in uniformly ¹⁵N-labeled ubiquitin. We demonstrate that the standard heteronuclear T₁, T₂, and steady-state NOE autocorrelation experiments augmented by cross-correlation measurements provide sufficient experimental data to quantitatively separate the structural and dynamic contributions to these relaxation rates when the simplifying assumptions of isotropic overall tumbling and an axially symmetric chemical shift tensor are valid.     

Nuclear magnetic resonance studies of surface interactions between trifluoromethanesulfonic acid and silica

The nature of the interaction between trifluoromethanesulfonic acid (triflic acid) and the surface groups of silica as a support has been investigated by¹H and¹⁹F-NMR studies. The¹⁹F-NMR spin-lattice relaxation time (T ₁) dependence on temperature suggests that the dominant relaxation mechanism for¹⁹F is a combination of spin-rotation (SR) interactions, one of which seems to be quenched by cage-like structures. This mechanism is activated by the treatment followed to stabilize the acid on silica. Hydrogen proton relaxation seems instead to be driven by dipolar interactions and the formation of hydrogen bridges. Activation energies have been estimated for various cases, assuming an Arrhenius-type temperature dependence for the correlation times of molecular motion. A linear dependence of¹H chemical shift on inverse temperature was also found, which is interpreted as thermal weakening of hydrogen bonding. The results support the conclusion that the stability of triflic acid on silica is due to the formation of strong hydrogen bridges between the sulfonic groups of triflic acid and the silica surface hydroxyls, provided a network structure similar to that observed for pure acid is obtained in which strong interactions between acid molecules occur. The acid seems to be organized as solid-like “drops” on the silica surface, which accounts for the long residence time on the silica surface.     

Measurement of Cross Correlation between Dipolar Coupling and Chemical Shift Anisotropy in the Spin Relaxation ofC,N-Labeled Proteins

We present a simple method for extracting interference effects between chemical shift anisotropy (CSA) and dipolar coupling from spin relaxation measurements in macromolecules, and we apply this method to extracting cross-correlation rates involving interference of amide¹⁵N CSA and¹⁵N–¹H dipolar coupling and interference of carbonyl¹³C′ CSA and¹⁵N–¹³C′ dipolar coupling, in a small protein. A theoretical basis for the interpretation of these rates is presented. While it proves difficult to quantitatively separate the structural and dynamic contributions to these cross-correlation rates in the presence of anisotropic overall tumbling and a nonaxially symmetric chemical shift tensor, some useful qualitative correlations of data with protein structure can be seen when simplifying assumptions are made.     

13C NMR Study of the Natural Glycosides Vicine and Convicine

¹³C NMR parameters have been obtained for vicine and convicine in DMSO, D₂O/DMSO and D₂O. Complete assignment of the spectra has been achieved. Interpretation of spin-lattice relaxation rates and heteronu-clear NOES has yielded evidence of intramolecular structuring in the case of vicine and not in that of ronvirine and also of a complex network of solute-solvent interactions.     

Nuclear spin-lattice relaxation in the triply rotating frame and ultraslow molecular motions in solids

A method for measuring nuclear magnetic spin-lattice relaxation in solids in the effective field H_e3 acting in the triply rotating frame (TRF) is described. The method advances the previously described techniques whereby nuclear magnetic resonance and relaxation in the rotating (RF) and doubly rotating frames (DRF) are measured directly. In the present work, the RF and DRF are employed for suppressing the secular part of nuclear dipole-dipole (DD) interactions in the first two orders. As a result, the higher-order DD interactions (four- and five-particle ones) were separated, and their contribution to the nuclear spin-lattice relaxation in the TRF was studied experimentally. The experiments were carried out on protons in polycrystalline benzene. With the introduced technique, an overall spin-lattice relaxation decay in the TRF was recorded continuously during a single radio-frequency pulse with a length not exceeding 1 s. The contribution of multiproton nonsecular DD interactions to the proton spin-lattice relaxation in the TRF was observed selectively as a pronounced local minimum in the temperature dependence of the relaxation timeT _1ϱϱϱ. This contribution corresponds to ultraslow motion of benzene molecules with a rate about γH_e3 ≈ 2π · (10¹-10³) s^-1 and is determined quantitatively by specific correlation functions corresponding to the multiparticle nonsecular DD interactions of protons. The prospects of using this method for studying ultraslow atomic and molecular dynamics in solids are discussed.     

1H relaxation and dynamics of triphenylbismuth in deuterated solvents

ABSTRACT

¹H spin–lattice relaxation experiments have been performed for triphenylbismuth dissolved in fully deuterated glycerol and tetrahydrofuran. The experiments have been carried out in a broad frequency range, from 10?kHz to 40?MHz, versus temperature. The data have been analysed in terms of a relaxation model including two relaxation pathways: ¹H-¹H dipole–dipole interactions between intrinsic protons of triphenylbismuth molecule and ¹H-²H dipole–dipole interactions between the solvent and solute molecules. As a result of the analysis, rotational correlation times of triphenylbismuth molecules in the solutions and relative translational diffusion coefficient between the solvent and solute molecules have been determined. Moreover, the role of the intramolecular ¹H-¹H relaxation contribution has been revealed, depending on the motional parameters, as a result of decomposing the overall relaxation dispersion profile into contributions associated with the ¹H-¹H and ¹H-²H relaxation pathways. The possibility of accessing the contribution of the relaxation of the intrinsic protons is important from the perspective of exploiting Quadrupole Relaxation Enhancement effects as possible contrast mechanisms for Magnetic Resonance Imaging.