We conducted a detailed investigation of the dynamics of two phenylalanine side chains in the hydrophobic core of the villin headpiece subdomain protein (HP36) in the hydrated powder state over the 298-80 K temperature range. Our main tools were static deuteron NMR measurements of longitudinal relaxation and line shapes supplemented with computational modeling. The temperature dependence of the relaxation times reveals the presence of two main mechanisms that can be attributed to the ring-flips, dominating at high temperatures, and small-angle fluctuations, dominating at low temperatures. The relaxation is nonexponential at all temperatures with the extent of nonexponentiality increasing from higher to lower temperatures. This behavior suggests a distribution of conformers with unique values of activation energies. The central values of the activation energies for the ring-flipping motions are among the smallest reported for aromatic residues in peptides and proteins and point to a very mobile hydrophobic core. The analysis of the widths of the distributions, in combination with the earlier results on the dynamics of flanking methyl groups (Vugmeyster et al. J. Phys. Chem. B 2013, 117, 6129-6137), suggests that the hydrophobic core undergoes slow concerted fluctuations. There is a pronounced effect of dehydration on the ring-flipping motions, which shifts the distribution toward more rigid conformers. The crossover temperature between the regions of dominance of the small-angle fluctuations and ring-flips shifts from 195 K in the hydrated protein to 278 K in the dry one. This result points to the role of solvent in softening the core and highlights aromatic residues as markers of the protein dynamical transitions.

We investigated site-specific dynamics of key methyl groups in the hydrophobic core of chicken villin headpiece subdomain (HP36) over the temperature range between 298 and 140 K using deuteron solid-state NMR longitudinal relaxation measurements. The relaxation of the longitudinal magnetization is weakly nonexponential (glassy) at high temperatures and exhibits a stronger degree of nonexponentiality below about 175 K. In addition, the characteristic relaxation times deviate from the simple Arrhenius law. We interpret this behavior via the existence of distribution of activation energy barriers for the three-site methyl jumps, which originates from somewhat different methyl environments within the local energy landscape. The width of the distribution of the activation barriers for methyl jumps is rather significant, about 1.4 kJ/mol. Our experimental results and modeling allow for the description of the apparent change at about 175 K without invoking a specific transition temperature. For most residues in the core, the relaxation behavior at high temperatures points to the existence of conformational exchange between the substates of the landscape, and our model takes into account the kinetics of this process. The observed dynamics are the same for dry and hydrated protein. We also looked at the effect of F58L mutation inside the hydrophobic core on the dynamics of one of the residues and observed a significant increase in its conformational exchange rate constant at high temperatures.

We have investigated microsecond to millisecond time scale dynamics in several key hydrophobic core methyl groups of chicken villin headpiece subdomain protein (HP36) using a combination of single-site labeling, deuteron solid-state NMR line shape analysis, and computational modeling. Deuteron line shapes of hydrated powder samples are dominated by rotameric jumps and show a large variability of rate constants, activation energies, and rotameric populations. Site-specific activation energies vary from 6 to 38 kJ/mol. An additional mode of diffusion on a restricted arc is significant for some sites. In dry samples, the dynamics is quenched. Parameters of the motional models allow for calculations of configurational entropy and heat capacity, which, together with the rate constants, allow for observation of interplay between thermodynamic and kinetic picture of the landscape. Mutations at key phenylalanine residues at both distal (F47L&F51L) and proximal (F58L) locations to a relatively rigid side chain of L69 have a pronounced effect on alleviating the rigidity of this side chain at room temperature and demonstrate the sensitivity of the hydrophobic core environment to such perturbations.

Quantitative dynamics of methyl groups in 9-fluorenylmethyloxycarbonyl-leucine (FMOC-leu) have been analyzed and compared with earlier studies of methyl dynamics in chicken villin headpiece subdomain protein (HP36) labeled at L69, a key hydrophobic core position. A combination of deuteron solid-state nuclear magnetic resonance experiments over the temperature range of 7-324 K and computational modeling indicated that while the two compounds show the same modes of motions, there are marked differences in the best-fit parameters of these motions. One of the main results is that the crossover observed in the dynamics of the methyl groups in the HP36 sample at 170 K is absent in FMOC-leu. A second crossover at around 95-88 K is present in both samples. The differences in the behavior of the two compounds suggest that some of the features of methyl dynamics reflect the complexity of the protein hydrophobic core and are not determined solely by local interactions.

The molecular dynamics of [-SiDMe(2)] grafted on two amorphous silica materials, mesoporous SBA and non-porous Aerosil, was investigated by deuteron ((2)H) solid-state NMR spectroscopy. Quadrupole echo (QE), quadrupole Carr-Purcell-Meiboom-Gill (QCPMG) and magic angle spinning (MAS) spectra were recorded as a function of temperature. These were analyzed to determine the rates and trajectories of molecular motion of the surface species. The dynamics were modelled as a composite two frame motion with independent rotations around the two Si-O bonds. In the first frame there are fast three-site jumps of the -SiDMe(2) group described by a single rate (k(1)) and unequal populations of the tetrahedral sites, such that the ratio D : Me : Me is around 1 : 4 : 4. In the second frame, the Si-O axis makes small step, nearest-neighbour jumps at a rate k(2) along an arc defined by the rim of a cone with a fixed half-angle. Both rates were found to be in the fast motional regime (k(1,2) > 10(10) s(-1)) throughout the experimentally accessible temperature range, 190-350 K. The experimental data are compatible only with models that include a distribution of arc lengths, lambda, in the second frame. The best fit of the simulations to the experimental data yields the distributions of the arc length. The results unequivocally demonstrate that even though the sites all have the same average environment, as reported by the isotropic chemical shifts, the dynamics of the grafted species are microscopically spatially heterogeneous with different molecules on the surface having different ranges of motional trajectories and populations. Furthermore, a clear difference in dynamic behavior is observed between the two silica supports, the motion being more constrained on the mesoporous SBA. This differential mobility is possibly due to differences in surface roughness and to the pore structure of SBA compared with the smoother surface of Aerosil.

This paper describes EXPRESS (EXchange Program for RElaxing Spin Systems), a computer program that simulates the effects of Markovian jump dynamics for a wide variety of solid state nuclear magnetic resonance experiments. A graphical interface is described that facilitates the definition of rotational jumps around non-commuting axes that may occur at arbitrary, different rates. Solid state deuteron NMR is widely used to investigate such processes, and EXPRESS allows simulations of deuteron quadrupole echo and magic angle spinning line (MAS) shapes, as well as partially relaxed line shapes for measurements of anisotropic relaxation of Zeeman and quadrupolar order. Facilities are included for chemical shift tensors (at user-defined orientations relative to the quadrupole coupling tensors), so that EXPRESS is potentially useful for studies of paramagnetic systems where these interactions are of comparable magnitude. Many of the same techniques used for deuterons can be extended to half-integer quadrupolar nuclei. The same interface that specifies rotational “sites” for deuteron NMR studies is usable in EXPRESS to simulate static line shapes, MAS line shapes, and multiple pulse Carr–Purcell–Meiboom–Gill (CPMG) line shapes for the central transition of high spin quadrupoles with second order quadrupole coupling and chemical shift anisotropy. Representative simulations are displayed that show effects of slow libration on deuteron quadrupole echo line shapes and relaxation time anisotropies. EXPRESS is also used to investigate fundamental differences in the mechanism of echo formation in deuteron MAS and quadrupole CPMG experiments, and to illustrate significant differences between these techniques in the context of high spin quadrupolar nuclei. The program is modular and platform-independent, with facilities for users to add routines for experiments not yet envisioned.

The signal to noise ratio of solid state deuteron NMR line shapes can be significantly improved by recording multiple echoes, generated either by a quadrupole Carr-Purcell-Meiboom-Gill pulse train (QCPMG) or by magic angle spinning (MAS). It is shown in this article, theoretically and experimentally, that when these techniques are used to record partially relaxed spectra, the relaxation times of Zeeman order, T(1Z), and quadrupole order, T(1Q), measured for individual side bands in QCPMG experiments preserve relaxation time anisotropy, while rotational side bands in MAS spectra do not. The relaxation times of individual QCPMG sidebands are not identical to those measured at the same frequencies on partially relaxed quadrupole echo powder patterns, and must be computed by explicit simulation.

The multiple-quantum magic-angle spinning (MQMAS) and satellite-transition magic-angle spinning (STMAS) experiments refocus second-order quadrupolar broadening of half-integer quadrupolar spins in the form of two-dimensional experiments. Isotropic shearing is usually applied along the indirect dimension of the 2D spectra such that an isotropic projection free of anisotropic quadrupolar broadening can be obtained. An alternative shear transformation by a factor equal to the coherence level (quantum number) selected during the evolution period is proposed. Such a transformation eliminates chemical shift along the indirect dimension leaving only the second-order quadrupolar-induced shift and anisotropic broadening, and is expected to be particularly useful for disordered systems. This transformation, dubbed Q-shearing, can help avoid aliasing problems due to large chemical shift ranges and spinning sidebands. It can also be used as an intermediate step to the isotropic representation for expanding the spectral window of rotor-synchronized experiments.

With the goal of investigating dynamical features of hydrophobic cores of proteins over a wide range of temperatures, the chicken villin headpiece subdomain protein (HP36) was labeled at a "single" site corresponding to any one of the two C(delta)D(3) groups of leucine-69, which is located in a key position of the core. The main techniques employed are deuteron NMR quadrupolar echo line shape analysis, and T(1Z) (Zeeman) and T(1Q) (quadrupolar order) relaxation experiments performed at 11.7 and 17.6 T over the temperature range of 112 to 298 K. The experimental data are compared with computer simulations. The deuteron line shapes give an excellent fit to a three-mode motional model that consists of (a) fast three-site rotational jumps about the pseudo C(3) methyl spinning axis, (b) slower reorientation of the spinning axis, described by diffusion along a restricted arc, and (c) large angle jumps between traces of rotameric conformers. Relaxation behavior is described by a phenomenological distribution of activation energies for three-site hops at high temperatures that collapses to a single, distinctly smaller value for lower temperatures.

Spin-lattice relaxation rates of lead have been measured at 17.6 T (156.9 MHz) as a function of temperature in polycrystalline lead nitrate and lead molybdate. Comparing the results with relaxation rates measured at lower fields, it is found that at high fields and low temperature, chemical shift anisotropy (CSA) makes small but observable contributions to lead relaxation in both materials. At 17.6 T and 200 K, CSA accounts for about 15% of the observed relaxation rate. Above 300 K, the dominant relaxation mechanism even at 17.6 T is an indirect Raman process involving modulation of the (207)Pb spin-rotation tensor, as first proposed by Grutzner et al. [J. Am. Chem. Soc. 123, 7094 (2001)] and later treated theoretically in more detail by Vega et al. [Phys. Rev. B 74, 214420 (2006)]. The improved signal to noise ratio at high fields makes it possible to quantify relaxation time anisotropy by analyzing saturation-recovery functions for individual frequencies on the powder pattern line shape. No orientation dependence is found for the spin-lattice relaxation rate of either material. It is argued from examination of the appropriate theoretical expressions, derived here for the first time, that the lack of observable relaxation time anisotropy is probably a general feature of this indirect Raman mechanism.

Nuclear magnetic resonance (NMR) spectra of $^{93}\mathrm{Nb}$ in the ferroelectric relaxor, lead magnesium niobate, have been obtained as a function of temperature, from $200\phantom{\rule{0.3em}{0ex}}\mathrm{K}\phantom{\rule{0.3em}{0ex}}\text{to}\phantom{\rule{0.3em}{0ex}}370\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, at $17.6\phantom{\rule{0.3em}{0ex}}\mathrm{T}$ with magic angle spinning at $30\phantom{\rule{0.3em}{0ex}}\mathrm{kHz}$. The central transition region consists of three overlapping peaks, and deconvolution yields temperature-dependent distributions of isotropic chemical shift $({\ensuremath{\delta}}_{\mathrm{iso}}^{\mathrm{cs}})$ and quadrupole coupling parameters $({C}_{\mathrm{Q}},{\ensuremath{\eta}}_{\mathrm{Q}})$ for each peak. Variable-temperature multiple quantum magic angle spinning (MAS) experiments confirm the accuracy of the procedures used to fit MAS spectra. The three peaks have been assigned to ${\mathrm{Nb}}^{5+}$ cations with specific configurations of next-nearest B-site neighbors (nBn) in the perovskite structure. Analysis of the temperature dependence provides the first unambiguous observation of specific local nBn structures associated with the polar nanoclusters. At temperatures below the Burns temperature, ${T}_{\mathrm{B}}=620\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, but well above the onset of macroscopic remnant polarization $(270\phantom{\rule{0.3em}{0ex}}\mathrm{K})$, the polar nanoclusters have only zero or one ${\mathrm{Mg}}^{2+}$ ion in the nBn shell. As the temperature decreases, the cooperative ferroelectric distortion characteristic of polar nanoclusters accommodates configurations with progressively more ${\mathrm{Mg}}^{2+}$ nBn ions. Effectively, each specific configuration has a different transition temperature, which explains the observed relaxor behavior.

The sections in this article are 1 Introduction 2 Spin Dynamics 3 Experimental Design 4 Site Specific Spectral Densities 5 Sample Rotation Experiments 6 Conclusions 7 Biographical Sketches Related Articles

Nuclear magnetic resonance (NMR) spectra of Nb-93 in the ferroelectric relaxor, lead magnesium niobate, have been obtained as a function of temperature, from 200 K to 370 K, at 17.6 T with magic angle spinning at 30 kHz. The central transition region consists of three overlapping peaks, and deconvolution yields temperature-dependent distributions of isotropic chemical shift (delta(cs)(iso)) and quadrupole coupling parameters (C-Q,eta(Q)) for each peak. Variable-temperature multiple quantum magic angle spinning (MAS) experiments confirm the accuracy of the procedures used to fit MAS spectra. The three peaks have been assigned to Nb5+ cations with specific configurations of next-nearest B-site neighbors (nBn) in the perovskite structure. Analysis of the temperature dependence provides the first unambiguous observation of specific local nBn structures associated with the polar nanoclusters. At temperatures below the Burns temperature, T-B=620 K, but well above the onset of macroscopic remnant polarization (270 K), the polar nanoclusters have only zero or one Mg2+ ion in the nBn shell. As the temperature decreases, the cooperative ferroelectric distortion characteristic of polar nanoclusters accommodates configurations with progressively more Mg2+ nBn ions. Effectively, each specific configuration has a different transition temperature, which explains the observed relaxor behavior.

Nb-93 magic angle spinning (MAS) and three quantum magic angle spinning (3QMAS) NMR experiments have been performed on (1-x)PbMg1/3Nb2/3O3-xPb(1/2)Sc(1/2)NbO(3) [(1-x)PMN-xPSN] ordered samples, for compositions x=0.6 (a normal ferroelectric) and 0.2 (a relaxor). Deconvolution of the MAS spectra at several temperatures ranging from 245 to 375 K reveals seven narrow peaks, P0,P1,...,P6, and two broad components, D1 and D2, that are assigned to specific local Nb5+ environments defined by the identities of the six nearest B-site cations. For both sample compositions, the temperature dependence of peak positions, MAS intensities, and linewidths is weak for peaks P0,P1,...,P6 and D2. However, the peak position, linewidth, and integrated intensity of D1 show anomalies in the range of the paraelectric to ferroelectric phase transition, that are much sharper for x=0.6 than for x=0.2. These effects are associated with the local structure and dynamics of polar nanoclusters. Site-specific values of the quadrupole product and isotropic chemical shift are extracted from combined analysis variable temperature MAS and 3QMAS spectra of the 0.4PMN-0.6PSN sample.

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.

The nanocrystalline perovskite material Li0.15La0.28TaO3 has been synthesized by alkoxide-free Pechini type sol gel method. Li-7 NMR measurements were carried out using a Bruker Avance 300 spectrometer at 116 MHz over the temperature range 150 to 400 K. Longitudinal spin-lattice relaxation times (T-1) measured by saturation recovery and longitudinal relaxation times in the rotating frame (T-1 rho) measured using the pulse sequence (pi/2-spin lock tau acquisition) with lock radio-frequency field upsilon=62.5 kHz and the T-2 relaxation time measured by Hahn echo are presented. The static Hahn-echo spectra show two different lithium sites in this perovskite oxide. Further, the relaxation measurements T-1 and T-1 rho show two different types of lithium cations with fast and slow dynamics. (c) 2006 Elsevier B.V. All rights reserved.

The crystal structure of a triclinic 2:2 inclusion complex of beta-cyclodextrin with N-acetyl-L-phenylalanine methyl ester has been determined at several temperatures between 298 and 20 K to further study molecular recognition using solid-state supramolecular beta-cyclodextrin complexes. The study reveals kinetic energy dependent changes in guest molecule conformations, orientations, and positions in the binding pocket presented by the crystal lattice. Accompanying these changes are observable differences in guest-guest interactions and hydrogen-bonding interactions in the binding pocket that involve guest molecules, water of hydration molecules, and beta-cyclodextrin molecules. On the basis of the differences observed in the crystal structures, we present a solid-state example of a system that displays the properties of both classical and quantum chemical models. At higher temperatures, the structure conforms to a classical mechanical model with dynamic disorder. At lower temperatures, the observations conform to examples in which there is static disorder representative of models in which quantum states differing in conformation, position, and orientation of components in the crystal structure are occupied. Ab initio theoretical calculations on the different guest molecule conformations have been carried out. Superpositions of theoretical electrostatic surface potential diagrams on the observed molecular positions in the complexes provide confidence that the deconvolution of the guest molecule disorder is acceptable. Temperature-dependent solid-state magic angle spinning deuteron NMR measurements provide evidence for large-amplitude, diffusive motion on a microsecond time scale in the complex.