Robert L. Vold

Investigation of multiaxial molecular dynamics by 2H MAS NMR spectroscopy

The technique of 2H 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 2H MAS NMR spectroscopy for investigating molecular dynamics is evaluated from theoretical spectra. To demonstrate the potential of the technique the dynamics of thiourea-2H4 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.

Slow motions in the hydrophobic core of chicken villin headpiece subdomain and their contributions to configurational entropy and heat capacity from solid-state deuteron NMR measurements.

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.

Effects of restricted rotational diffusion on 2H magic angle spinning nuclear magnetic resonance spectra

A general formalism is developed for describing the effects of restricted rotational diffusion on deuteron (2H) magic angle spinning (MAS) nuclear magnetic resonance (NMR) spectra. The approach is based on the Smoluchowski model that describes restricted rotational diffusion in an arbitrary ordering potential with an arbitrary diffusion tensor. It is shown that the Smoluchowski model gives a physically more reasonable description of molecular motion than the discrete Markov (jump) model. The models are shown to be mutually consistent for high ordering potentials and (or) low temperatures provided the diffusion coefficient is sufficiently high. However, for low ordering potentials and (or) high temperatures the discrete Markov model is not a useful approximation and the spectra can only be simulated with restricted rotational diffusion. This is also the case for small diffusion coefficients independent of the ordering potential and the temperature. The formalism is based on finite difference solutions to t...

Individual spectral densities and molecular motion in polycrystalline hexamethylbenzene‐d18

Methods are described for obtaining the orientation dependence of individual motional spectral densities, J1(ω0) and J2(2ω0), from deuterium spin relaxation experiments on polycrystalline materials. Spectral density measurements provide detailed information in a motional regime too fast to be studied by the two‐dimensional (2D) exchange method. Their potential as a source of detailed kinetic and geometric information is illustrated for hexamethylbenzene‐d18 (HMB). The relaxation behavior of HMB cannot be explained exclusively by six‐site jumps around the C6v axis. Agreement between the experimentally determined spectral densities and simulations is improved if the methyl rotation is explicitly included. At ambient temperature the experimental data are best fitted with the simultaneous jump rates, k6=3.85×108 s−1 and k3=5.0×1011 s−1. This is significantly different from the rate determined using a simple six‐site jump model, k6=3.9×109 s−1. Geometric distortions of the methyl rotation axes can account for ...

Motional heterogeneity in single-site silica-supported species revealed by deuteron NMR

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.

Solid state deuteron relaxation time anisotropy measured with multiple echo acquisition

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.

DEUTERON NMR STUDIES OF GUEST MOTION IN ALKANOIC ACID UREA INCLUSION COMPOUNDS

The orientation dependence of deuteron relaxation times of Zeeman (T1Z) and quadrupole (T1Q) order have been measured in the temperature range −30 to +45 °C for polycrystalline urea inclusion compounds containing alkyl deuterated octanoic acid-d18, dodecanoic acid-d23, and hexadecanoic acid-d31. These data were fitted to a model, based on Redfield relaxation theory, which incorporates rapid rotation about the long molecular axis and slower, limited angle libration of individual CD bonds about a perpendicular axis. The activation energies for rotational diffusion about the long axis are 17.4±0.8 kJ/mol for octanoic acid-d18, 14.4±0.6 kJ/mol for dodecanoic acid-d23, and 22.5±0.4 kJ/mol for hexadecanoic acid-d31 guests. These values are larger than those for alkane guests with the same number of carbon atoms, and they increase more rapidly with increasing chain length. Quadrupole coupling constants, determined at room temperature from measurements on large single crystals, are consistent with a small gauche ...

Glassy dynamics of protein methyl groups revealed by deuteron NMR.

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.

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.

Q-shear transformation for MQMAS and STMAS NMR spectra.

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.