Quadrupole Echo Spectra Research Articles

Simulated Annealing Method for the Automated Simulation of DNA Dynamics in the HhaI Protein Binding Site

Solid-state deuterium NMR is well suited to the study of the conformational dynamics of DNA. Deuterium quadrupole echo spectra for a particular motional model can be calculated and matched to the experimental spectrum to extract information on the DNA dynamics; however, doing so can be very time-intensive. The two-axis motion used to model the dynamics of either 2″ or 5′/5″ furanose ring deuteron is particularly complex with up to ten independent variables that can be optimized. Here, we present a program which automates both the input script generation and searches the parameter space for the best fit using a simulated annealing algorithm. The parameter, χ red 2 , provides a relative measure of goodness of fit. This method reduces the overall time to determine the best fit of a line shape to a few days, in most cases, when running on a low-power desktop PC. The automated fitting program presented here can be easily modified to generate input scripts for new models, incorporate a weighting factor to the χ red 2 calculation to emphasize key line shape features, or fit nonsymmetrized data. This adaptable program will make simulation of solid-state deuterium spectra accessible to a broader audience.

Solid-state NMR spectroscopy uncovers internal dynamics of antiviral compounds.

In this study we analyzed the internal dynamics of antiviral compounds such as amantadine and rimantadine and the model compound hexamethylbenzene (HMB) using solid-state 2H NMR spectroscopy. Amantadine and rimantadine have been successfully used to treat influenza and dyskinesia, and their antiviral activity can be characterized using structural and dynamical information from solid-state 2H NMR relaxation. The relaxation data collected for a range of temperatures can be fit using analytical models for the internal dynamics of these compounds to yield physical parameters such as activation energies and diffusion constants that quantify the different modes of motion. Here, we performed quadrupolar-echo and relaxation experiments on powdered samples of deuterated amantadine, rimantadine, and HMB for temperatures between −150⁰C and 60⁰C. HMB displayed two rotational modes about its internal symmetry axes with vastly different timescales. Quadrupolar-echo spectra showed that rimantadine exhibits methyl rotation about its 3-fold axis with no rotation about the C-C axis linked to the cage, while amantadine undergoes slow rotation about the cage axis. The order parameters calculated from the residual quadrupolar couplings for all three compounds were large (>0.8), indicating restricted off-axial dynamics. Spin-lattice (T1Z) and quadrupolar-order relaxation times (T1Q) were calculated for different orientations within the polycrystalline samples. The temperature and angular dependences of these relaxation times were fit using three models: anisotropic rotational diffusion [1,2], axial diffusion, and discrete jumps, among which the anisotropic rotational diffusion model displayed universal applicability. Application of NMR relaxometry to these drugs within the membrane channel will further enable us to understand their activity and the effect of the lipid environment on their structural dynamics.

Molecular Motion of the Junction Points in Model Networks Prepared by Acyclic Triene Metathesis.

The junction dynamics in a selectively deuterated model polymer network containing junctions on every 21st chain carbon is studied by solid state (2) H echo NMR. Polymer networks are prepared via acyclic triene metathesis of deuteron-labeled symmetric trienes with deuteron probes precisely placed at the alpha carbon relative to the junction point. The effect of decreasing the cross-link density on the junction dynamics is studied by introduction of polybutadiene chains in-between junctions. The networks are characterized by swelling, gel content, and solid state (1) H MAS NMR. Line shape analysis of the (2) H quadrupolar echo spectra reveals that the degree of motion anisotropy and the distribution of motion correlation times depend on the cross-link density and structural heterogeneity of the polymer networks. A detailed model of the junction dynamics at different temperatures is proposed and explained in terms of the intermolecular cooperativity in densely-packed systems.

Deuteron Magnetic Resonance Studies of Anhydrous Caffeine

AbstractMethyl deuterated caffeine powder was studied using2H-NMR relaxometry and line shape analysis. In caffeine's low-temperature phase the spin-lattice relaxation times indicate a thermally activated CD3reorientation (activation energy ≈4 kJ/mol). Below theT1minimum near 35 K the quadrupolar echo spectra develop features indicative for quantum mechanical tunneling. Dielectric measurements indicate the presence of dipole moment fluctuations with times scales that follow an Arrhenius law (energy barrier ≈107 kJ/mol). It is argued that the underlying motion involves small-angle molecular excursions and therefore remains undetectedviastimulated-echo spectroscopy. The hysteresis accompanying the order/disorder transition taking place above 400 K was monitored using solid-echo line shapes as well asviaspin relaxation times. In the high-temperature phase indications for the onset of anisotropic large-angle motions were obtained.

Fitting of deuterium quadrupole echo spectra with multiple motional models

Dynamic information is generally extracted from deuterium quadrupole echo spectra by matching a spectrum calculated for a particular motional model to the experimental spectrum. In this work, a set of computer programs has been written to facilitate fitting of calculated spectra to experimental spectra that represent from one to five motional models. The fitting program requires pre-calculated libraries of spectra for the models of interest, and accomplishes the fitting either by a systematic method or by simulated annealing. The systematic method is convenient for fitting with one or two motional models, but the simulated annealing method is faster for two or more models, if the libraries are made up of hundreds of spectra. The parameter Q, with the standard deviation of the spectral points estimated as the standard deviation of the baseline noise, provides a stringent measure of goodness of fit. Acceptable fits of experimental data as judged by this criterion have not been found, even in the case of ring flip motion in phenylalanine- d 5 in which the fit may be judged acceptable by eye. An example of fitting with isotropic and methyl rotation motional models of alanine- d 3, which have distinct spectral patterns, shows that it is possible to obtain reasonably accurate estimates of the relative amounts of deuterium representing the different models, even from poorly fitted spectra.

Finite pulse width artifact suppression in spin-1 quadrupolar echo spectra by phase cycling

A phase cycling scheme for suppressing spectral artifacts introduced in quadrupolar echo spectroscopy of spin-1 nuclei due to finite pulse width effects is presented. The phase cycling scheme is developed using the formalism of average Hamiltonian theory and fictitious spin-1 operators. A simulation and experiment on deuterated polyethelene is performed highlighting the spectral artifact introduced by finite pulse widths and successful removal with the proposed phase cycling scheme.

Investigation of multiaxis molecular motion by off-magic angle spinning deuteron NMR

The relatively new deuteron NMR method of off-axis-magic angle spinning (OMAS) has been extended and used to investigate multiaxis rotational jump motion. Floquet theory is developed for simulating deuteron OMAS spectra with multisite jumps at different rates about noncoincident axes, and efficient procedures are presented for computing the sideband line shapes. It is demonstrated experimentally that reproducible adjustment of the angle between the rotor axis and the static magnetic field is feasible with precision approaching +/- 0.01 degrees. This leads to the reintroduction of a scaled, first-order quadrupole coupling that defines a new kinetic window and makes deuteron OMAS much more sensitive than ordinary magic angle spinning to motion on the kilohertz time scale. Temperature-dependent deuteron OMAS line shapes of octanoic acid/urea-d4 inclusion compound have been recorded and fitted, using least-squares procedures, to provide rates of rotation about both CN and CO bonds. The Arrhenius activation parameters for rotation about CN bonds, Ea = 60.4+/-2.4 kJ/mol and ln(A) = 24.9+/-0.3, agree well with previous values determined by selective inversion experiments. However, OMAS yields Ea = 26.3+/-0.4 kJ/mole and ln(A) = 24.9+/-0.3 for whole-body rotation about the CO bond axis in contrast to previous analysis of static quadrupole echo (QE) line shapes which gave Ea = 22.3+/-0.3 kJ/mole and ln(A) = 24.8+/-0.6 for the same sample. The underlying homogeneous linewidths of OMAS spectra are much smaller than those of QE spectra, and this provides higher precision and less systematic error in the determination of rates.

Room Temperature Solid Surface Water with Tetrahedral Jumps of 2H Nuclei Detected in 2H2O-Hydrated Porous Silicates

The nature of water adjacent to solid silicate surfaces in kanemite, rehydrated zeolite A, rehydrated highly porous glass, rehydrated high surface area silica gel, and the hydration products of tricalcium silicate has been investigated with 2H NMR techniques and calorimetry. The room temperature 2H NMR quadrupole echo spectra of all samples show a sharp central resonance that corresponds to 2H2O. The kanemite, porous glass, and silica gel spectra show in addition powder patterns that were assigned, based on previous findings for kanemite, to silanol −OH groups experiencing rapid 3-fold jumps or rotational diffusion about the Si−O bond. The spectrum of hydrated tricalcium silicate shows in addition to the aqueous peak a rigid powder pattern that is assigned to Ca(O2H)2. Spectra obtained at −120 and −150 °C for the kanemite sample show that the qcc values for the aqueous deuterons range from 180 to 210 kHz, as would be expected for the different water environments observed in the X-ray structure of kanemite...

Noise Reduction in Quadrupolar Echo Spectra at Short Echo Times

The phase cycling scheme Exorcycle embedded into the quadrupolar echo pulse sequence is presented as a tool for reducing ringing effects in broad quadrupolar spectra.

Iterative lineshape analysis of quadrupolar echo spectra of a damped CD(3) quantum rotor: preliminary evidence of a novel mechanism of stochastic spin exchange.

It is demonstrated that the wealth of information about damped quantum rotation of CD(3) groups, contained in quadrupolar echo spectra, can be fully explored in a broad temperature range using a method of iterative analysis of the spectral lineshapes. The recently reported lineshape equation which, apart from the quantum tunneling and the dissipative Alexander--Binsch terms, contains an additional dissipative term having no classical analog is shown to be capable of describing even subtle details of the spectra of a crystal of acetylsalicylic acid--CD(3) oriented specifically in the magnetic field. Preliminary evidence of the occurrence of this novel dissipative mechanism in the system studied is reported. The results obtained seem to suggest that there is no "classical limit" in the dissipative behavior of this system.

Models for molecular motions within polymer chains. Part 1. A solid-state NMR study of hexane-1,6-diyl bis( p-nitrobenzoate)

Solid-state NMR experiments on hexane-1,6-diyl bis(p-nitrobenzoate) and its 1,1,6,6- and 2,2,5,5-deuteriated derivatives present a coherent view of the molecular dynamics of the central alkyl chain. The techniques used include 13C CP/MAS spectra, 2H quadrupole echo spectra, associated with measurements of 13C T1ρ relaxation times, 2H and 13C T1 relaxation times and quadrupole echo reduction factors. Molecular dynamics in the central chain are dominated by librational motions at the CH2 groups that can best be approximated by a six-site conical model. The activation energies for these librations are ca. 35 kJ mol−1. gauche–trans flips in the chain can be ruled out as the origin of the effects observed.

NMR study of chain dynamics in the hexagonal high-pressure phase of polyethylene

At high pressure (>3300 bar) polyethylene shows a hexagonal phase between the orthorhombic phase and the liquid phase. This first NMR investigation of polyethylene in its hexagonal phase shows that the mobility of the molecular chains is very high. Deuteron quadrupole echo spectra have been used to determine the character and rate of local reorientations of the molecular chains. The chains perform rapid axial reorientations, similar to those observed in the rotator phases occurring in the long normal alkanes. From proton rotating frame relaxation data we derive a high rate of translational diffusion in the chain direction. These observations contribute to the understanding of the important role of the hexagonal phase in the growth of chain-extended polyethylene crystals.

Investigation of multiaxial molecular dynamics by [formula omitted] MAS NMR spectroscopy

The technique of 2 H MAS NMR spectroscopy is presented for the investigation of multiaxial molecular dynamics. To evaluate the effects of discrete random reorientation a Lie algebraic formalism based on the stochastic Liouville–von Neumann equation is developed. The solution to the stochastic Liouville–von Neumann equation is obtained both in the presence and absence of rf irradiation. This allows effects of molecular dynamics to be evaluated during rf pulses and extends the applicability of the formalism to arbitrary multiple pulse experiments. Theoretical methods are presented for the description of multiaxial dynamics with particular emphasis on the application of vector parameters to represent molecular rotations. Numerical time and powder integration algorithms are presented that are both efficient and easy to implement computationally. The applicability of 2 H MAS NMR spectroscopy for investigating molecular dynamics is evaluated from theoretical spectra. To demonstrate the potential of the technique the dynamics of thiourea– 2 H 4 is investigated experimentally. From a series of variable temperature MAS and quadrupole echo spectra it has been found that the dynamics can be described by composite rotation about the CS and CN bonds. Both experiments are sensitive to the fast CS rotation which is shown to be described by the Arrhenius parameters E CS=46.4±2.3 kJ mol −1 and ln( A CS)=32.6±0.9. The MAS experiment represents a significant improvement by simultaneously allowing the dynamics of the slow CN rotation to be fully characterized in terms of E CN=56.3±3.4 kJ mol −1 and ln( A CN)=25.3±1.1.

Quadrupolar Echo Spectra of the Tunneling CD3Group

Abstract Deuteron NMR spectra of both single crystal and powder samples of acetylsalicylic acid–CD3were measured using the quadrupolar-echo technique. The experiments were done in the temperature range 17–100 K, with a special emphasis on the range 20– 30 K, in which the observable tunneling frequency decreases rapidly from its low-temperature value of 2.7 down to 1.2 MHz. In the tunneling regime, modulations of the line intensities and phases as a function of the echo time τ are observed in the single-crystal spectra. The modulation frequency is equal to the orientation-dependent displacement of the inner satellite pairs (α lines) from the Larmor frequency. These effects were confirmed in numerical simulations and fully explain the phase-modulation effects observed previously in quadrupolar-echo spectra of methyl-deuterated methanol andpara-xylene guest molecules in some inclusion compounds. By measuring the temperature and orientation dependence of the quadrupolar lineshapes, it was found that the echo spectra are more sensitive to the value of the tunneling frequency than the spectra obtained from the free induction decay. It is pointed out that, because of the modulation effects, special care must be taken when structural parameters are to be extracted from quadrupolar-echo spectra, in particular from spectra of powder samples.

Static H-2-H-2 Dipole Interactions in a Lyotropic Liquid-Crystal - A 2Dqe Study

The 2H NMR two-dimensional quadrupolar-echo spectra of an α-deuterated surfactant in an aligned hexagonal lyotropic liquid crystal were recorded. Whereas only indications of 2H-1H and 2H-2H dipole splittings were observed in the F2 spectra, these residual interactions were displayed in the F1, spectra as an apparently Lorentzian peak. When gated 1H decoupling was used, the 2H-2H dipole splittings became visible in the F1 spectra as three (apparently Lorentzian) peaks. From a fit to the experimental lineshape the frequencies, relative amplitudes, line-widths, and phases of these peaks were determined. The ratio between the 2H-2H dipole and 2H quadrupole splittings was found to be |q| = 0.0041. Since q values of about −0.0040 have been obtained in lamellar phases, these results indicate that the α-methylene angular distribution function with respect to the local surface normal of the cylindrical aggregates may not deviate significantly from threefold symmetry.

2H n.m.r. study of high pressure effects on the molecular dynamics in polystyrene: 1. Main chain motion

The effect of high pressure on the main chain motion near the glass transition temperature ( T g) in amorphous chain-deuterated polystyrene is studied using deuteron n.m.r. spin alignment echo and quadrupole echo spectra. Comparison with simulated spectra yields information on the time-scale and the type of motion. In the vicinity of T g the main chain performs ultra-slow small angle diffusive motion. The temperature dependence of the mean correlation time shows a strongly non-Arrhenius behaviour, typical for the so-called α-process. The width of the correlation time distribution rapidly increases on approaching T g. The effect of pressure on the motion is found to be much weaker than could be expected from equation-of-state data.

Molecular motion and transitions in solid tripalmitin measured by deuterium nuclear magnetic resonance

Deuterium nuclear magnetic resonance (NMR) quadrupole echo spectra of deuterated acyl chains and the glyceryl moiety of tripalmitin were found to depend on the crystal form. At 20°C, which is below melting points, line shapes indicate that molecular motions in theβ form (triclinic subcell) are more restricted than inβ′ (orthorhombic) orα (hexagonal). Motional rates in excess of about 20 kHz are responsible for the line shapes. Spin‐lattice relaxation, sensitive to motional frequencies in the tens of megahertz range, is much faster for methyl (CD2) groups inα orβ′ than inβ, indicating that fast motions are also governed by crystal form. General theoretical considerations suggest that motion of methylene groups is dynamically heterogeneous and that motion of methyl (CD3) groups may be averaged by motions other than rotation about the terminal C‐C bond. The isothermal solid‐state transition fromα toβ, induced by increasing the temperature to 35°C, was accompanied by NMR lineshape changes consistent with immobilization. The reversible transition ofα to “sub‐α” upon cooling, accompanied by orthorhombic‐like Bragg spacings and other changes in the X‐ray pattern and by corresponding changes in the infrared spectrum, also produced a marked restriction in NMR‐detected mobility of the kind seen inβ′ relative toα. The advantages of2H NMR for studies of motions and transitions in solid glycerides are discussed.

Multiple quantum NMR spectroscopy onI> 1 nuclei in anisotropic systems

The response of half-integral spin I > 1 nuclei in anisotropic systems to pulse sequences exciting multiple quantum (MQ) coherences is investigated theoretically. Using the state multipole formalism, we calculate the 2-dimensional (2D) MQ spectrum obtained by the conventional three-pulse sequence and compare it to recent experimental results. Next we consider MQ filters for detecting the evolution of rank (2I - 1) single quantum coherences. Pulse sequences based on these filters can be used for revealing hidden anisotropy in a spectrum or for suppressing a dominant isotropic contribution. Finally, we develop 2D spinecho and quadrupolar echo experiments that refocus the inhomogeneous decay of various MQ coherences. These MQ echo techniques can be used to determine accurately the homogeneous line widths of various MQ transitions, as demonstrated by experimental results (including the first MQ quadrupolar echo spectra) on 23Na and 17O nuclei in a lyotropic liquid crystal.

Solid-state deuterium quadrupole echo NMR characterization of vinylene-deuterated poly(p-phenylenevinylene) films

2H quadrupole echo NMR spectra have been obtained from stacked films of stretched vinylene-deuterated poly(p-phenylenevinylene) with their draw axes ligned relative to the NMR magnetic field. The 2 H spectra show that the orientation of the vinylene C-D bonds of PPV-d 2 is similar to that of a structure based on trans-stilbene. Spectra obtained at high temperature reveal substantial chain motion and are consistent with a 180° rotational jump of portions of the PPV chain about the crystallographic c axis. Inversion-recovery quadrupole echo spectra were obtained for these films to determine tha anisotropy and magnitude of T 1 .

A solid-state deuterium NMR study of internal rotation in p-nitroaniline

Deuterium quadrupole echo spectra have been obtained at 55.3 MHz and several temperatures between 26 and 133°C for samples of solid p-nitroaniline, deuterated either in the amino group or in the 2,6 positions of the aromatic ring. At all temperatures, the aromatic deuterons exhibit a simple rigid lattice powder pattern which is accurately simulated using a quadrupole coupling constant of 174 ± 1 kHz and asymmetry parameter 0.06 ± 0.02. Quadrupole echo spectra for the amino deuterons show features characteristic of 180° flips about the D-N-D bisector, and the activation energy for this motion is found to be 49 ± 6 kJ/mol, with a rate k = (5.2 ± 0.3) × 10 5 s −1 at 133°C. For the amino deuterons, the dependence of echo amplitude and spectral lineshape on pulse spacing includes contributions from heteronuclear dipolar coupling as well as from internal rotation. This makes the extraction of accurate rates difficult, unless the lineshape data are supplemented by independent information. The spin-lattice relaxation rate, which is dominated by the flipping motion at high temperature, is very useful in this regard.