Meghan E. Halse

Direct observation of hierarchical protein dynamics

A hierarchy of protein motions Functioning proteins are not static but explore complex conformational energy landscapes. Lewandowski et al. used multinuclear solid-state nuclear magnetic resonance experiments to measure protein motion over a broad range of temperatures and time scales. Above 160 K there was a strong coupling between solvent and protein motion. The hierarchy of motions as the temperature increased revealed the dynamic modes that relate solvent, sidechain, and backbone motion. Science, this issue p. 578 The dynamic modes that relate solvent, side-chain, and backbone motions in a protein are determined from nuclear magnetic resonance relaxation. One of the fundamental challenges of physical biology is to understand the relationship between protein dynamics and function. At physiological temperatures, functional motions arise from the complex interplay of thermal motions of proteins and their environments. Here, we determine the hierarchy in the protein conformational energy landscape that underlies these motions, based on a series of temperature-dependent magic-angle spinning multinuclear nuclear-magnetic-resonance relaxation measurements in a hydrated nanocrystalline protein. The results support strong coupling between protein and solvent dynamics above 160 kelvin, with fast solvent motions, slow protein side-chain motions, and fast protein backbone motions being activated consecutively. Low activation energy, small-amplitude local motions dominate at low temperatures, with larger-amplitude, anisotropic, and functionally relevant motions involving entire peptide units becoming dominant at temperatures above 220 kelvin.

A dynamic nuclear polarization strategy for multi-dimensional Earth’s field NMR spectroscopy

Dynamic nuclear polarization (DNP) is introduced as a powerful tool for polarization enhancement in multi-dimensional Earths field NMR spectroscopy. Maximum polarization enhancements, relative to thermal equilibrium in the Earths magnetic field, are calculated theoretically and compared to the more traditional prepolarization approach for NMR sensitivity enhancement at ultra-low fields. Signal enhancement factors on the order of 3000 are demonstrated experimentally using DNP with a nitroxide free radical, TEMPO, which contains an unpaired electron which is strongly coupled to a neighboring (14)N nucleus via the hyperfine interaction. A high-quality 2D (19)F-(1)H COSY spectrum acquired in the Earths magnetic field with DNP enhancement is presented and compared to simulation.

Photochemical pump and NMR probe: chemically created NMR coherence on a microsecond time scale.

We report pump-probe experiments employing laser-synchronized reactions of para-hydrogen (para-H2) with transition metal dihydride complexes in conjunction with nuclear magnetic resonance (NMR) detection. The pump-probe experiment consists of a single nanosecond laser pump pulse followed, after a precisely defined delay, by a single radio frequency (rf) probe pulse. Laser irradiation eliminates H2 from either Ru(PPh3)3(CO)(H)2 1 or cis-Ru(dppe)2(H)2 2 in C6D6 solution. Reaction with para-H2 then regenerates 1 and 2 in a well-defined nuclear spin state. The rf probe pulse produces a high-resolution, single-scan (1)H NMR spectrum that can be recorded after a pump-probe delay of just 10 μs. The evolution of the spectra can be followed as the pump-probe delay is increased by micro- or millisecond increments. Due to the sensitivity of this para-H2 experiment, the resulting NMR spectra can have hydride signal-to-noise ratios exceeding 750:1. The spectra of 1 oscillate in amplitude with frequency 1101 ± 3 Hz, the chemical shift difference between the chemically inequivalent hydrides. The corresponding hydride signals of 2 oscillate with frequency 83 ± 5 Hz, which matches the difference between couplings of the hydrides to the equatorial (31)P nuclei. We use the product operator formalism to show that this oscillatory behavior arises from a magnetic coherence in the plane orthogonal to the magnetic field that is generated by use of the laser pulse without rf initialization. In addition, we demonstrate how chemical shift imaging can differentiate the region of laser irradiation thereby distinguishing between thermal and photochemical reactivity within the NMR tube.

A common theory for phase-modulated homonuclear decoupling in solid-state NMR

We propose a new framework for homonuclear dipolar decoupling in solid-state NMR that provides a theoretical link between the FSLG, PMLG and DUMBO families. We show that through the use of a Legendre polynomial basis, the phase modulation of these decoupling schemes can be described by the same set of parameters, permitting for the first time a direct theoretical comparison between these methods. Use of this common basis reveals that the central decoupling mechanism is the same for DUMBO and FSLG/PMLG and that a similar vector picture can be used to describe both methods. In addition to the common root of decoupling efficiency, this new analysis highlights two major points of difference between the methods. First, the DUMBO phase modulation consists not only of a linear change in phase with time à la PMLG but also smaller high-order oscillations, which act to improve line-narrowing performance. Second, we show how the DUMBO phase waveforms are generated from a four-step permutation of a single asymmetric unit, in contrast to the two-step permutation of PMLG. Numerical simulations and experimental results suggest that this latter point of difference is responsible for the superior performance of DUMBO in the presence of significant RF inhomogeneity.

A first-principles description of proton-driven spin diffusion

Herein we design a reduced Liouville space for the simulation of proton-driven spin diffusion. Using this approach, the experimentally observed carbon-13 polarisation transfer in a powder sample undergoing magic-angle spinning is quantitatively described, directly from crystal geometry and without any adjustable parameters.

Improved Phase-Modulated Homonuclear Dipolar Decoupling for Solid-State NMR Spectroscopy from Symmetry Considerations

We explore the effects of symmetry on the performance of phase-modulated homonuclear dipolar decoupling in (1)H solid-state NMR. We demonstrate that the symmetry of the DUMBO family of decoupling sequences is the result of two well-defined symmetry expansions. The first is an antipalindromic expansion that arises from the symmetrization step that was built into the original architecture of the DUMBO sequence. The second is a mirror-pair expansion that inverts the sign of the phase modulation in the second half of the pulse sequence relative to the first. The combination of these two symmetry expansions generates a sequence of four Lee-Goldburg-type rotations in the rotating frame. The axes of rotation, oriented at the magic angle, are separated in the transverse plane by 2α, where α is chosen to minimize the sensitivity of the sequence to instrument imperfections such as rf inhomogeneity. The efficiency of the DUMBO symmetry for decoupling is demonstrated experimentally, and the effect of the α-phase-shift parameter is investigated. A new decoupling sequence (LG4) that combines the DUMBO symmetry with α = 55° is introduced and is shown to produce very efficient decoupling as well as a nearly 2-fold increase in coherence lifetimes when compared to standard PMLG/FSLG decoupling.

Quasi-equilibria in reduced Liouville spaces

The quasi-equilibrium behaviour of isolated nuclear spin systems in full and reduced Liouville spaces is discussed. We focus in particular on the reduced Liouville spaces used in the low-order correlations in Liouville space (LCL) simulation method, a restricted-spin-space approach to efficiently modelling the dynamics of large networks of strongly coupled spins. General numerical methods for the calculation of quasi-equilibrium expectation values of observables in Liouville space are presented. In particular, we treat the cases of a time-independent Hamiltonian, a time-periodic Hamiltonian (with and without stroboscopic sampling) and powder averaging. These quasi-equilibrium calculation methods are applied to the example case of spin diffusion in solid-state nuclear magnetic resonance. We show that there are marked differences between the quasi-equilibrium behaviour of spin systems in the full and reduced spaces. These differences are particularly interesting in the time-periodic-Hamiltonian case, where simulations carried out in the reduced space demonstrate ergodic behaviour even for small spins systems (as few as five homonuclei). The implications of this ergodic property on the success of the LCL method in modelling the dynamics of spin diffusion in magic-angle spinning experiments of powders is discussed.

An accurate nonuniform fourier transform for SPRITE magnetic resonance imaging data

A new algorithm is proposed for computing the discrete Fourier Transform (DFT) of purely phase encoded data acquired during Magnetic Resonance Imaging (MRI) experiments. These experiments use the SPRITE (Single Point Ramped Imaging with T1 Enhancement) method and multiple-point acquisition, sampling data in a nonuniform manner that prohibits reconstruction by fast Fourier transform. The chirp z-transform algorithm of Rabiner, Schafer, and Rader can be combined with phase corrections to compute the DFT of this data to extremely high accuracy. This algorithm outperforms the interpolation methods that are traditionally used to process nonuniform data, both in terms of execution time and in terms of accuracy as compared to the DFT.

Macroscopic nuclear spin diffusion constants of rotating polycrystalline solids from first-principles simulation

A method for quantitatively calculating nuclear spin diffusion constants directly from crystal structures is introduced. This approach uses the first-principles low-order correlations in Liouville space (LCL) method to simulate spin diffusion in a box, starting from atomic geometry and including both magic-angle spinning (MAS) and powder averaging. The LCL simulations are fit to the 3D diffusion equation to extract quantitative nuclear spin diffusion constants. We demonstrate this method for the case of (1)H spin diffusion in ice and L-histidine, obtaining diffusion constants that are consistent with literature values for (1)H spin diffusion in polymers and that follow the expected trends with respect to magic-angle spinning rate and the density of nuclear spins. In addition, we show that this method can be used to model (13)C spin diffusion in diamond and therefore has the potential to provide insight into applications such as the transport of polarization in non-protonated systems.

Quantitative analysis of Earth's field NMR spectra of strongly-coupled heteronuclear systems.

In the Earths magnetic field, it is possible to observe spin systems consisting of unlike spins that exhibit strongly coupled second-order NMR spectra. Such spectra result when the J-coupling between two unlike spins is of the same order of magnitude as the difference in their Larmor precession frequencies. Although the analysis of second-order spectra involving only spin-(1/2) nuclei has been discussed since the early days of NMR spectroscopy, NMR spectra involving spin-(1/2) nuclei and quadrupolar (I>(1/2)) nuclei have rarely been treated. Two examples are presented here, the tetrahydroborate anion, BH4-, and the ammonium cation, NH4+. For the tetrahydroborate anion, (1)J((11)B,(1)H)=80.9Hz, and in an Earths field of 53.3microT, nu((1)H)=2269Hz and nu((11)B)=728Hz. The (1)H NMR spectra exhibit features that both first- and second-order perturbation theory are unable to reproduce. On the other hand, second-order perturbation theory adequately describes (1)H NMR spectra of the ammonium anion, (14)NH4+, where (1)J((14)N,(1)H)=52.75Hz when nu((1)H)=2269Hz and nu((14)N)=164Hz. Contrary to an early report, we find that the (1)H NMR spectra are independent of the sign of (1)J((14)N,(1)H). Exact analysis of two-spin systems consisting of quadrupolar nuclei and spin-(1/2) nuclei are also discussed.