Multiple-timescale dynamics of side-chain carboxyl and carbonyl groups in proteins by 13C nuclear spin relaxation

Side-chain carboxyl and carbonyl groups play a major role in protein interactions and enzyme catalysis. A series of (13)C relaxation experiments is introduced to study the dynamics of carboxyl and carbonyl groups in protein side chains on both fast (sub-ns) and slower (micros-ms) time scales. This approach is illustrated on the protein calbindin D(9k). Fast dynamics features correlate with hydrogen- and ion-binding patterns. We also identify chemical dynamics on micros time scales in solvent-exposed carboxyl groups, most probably due to exchange between the carboxylate and carboxylic acid forms.     

Electron and nuclear spin dynamics in the thermal mixing model of dynamic nuclear polarization

A novel mathematical treatment is proposed for computing the time evolution of dynamic nuclear polarization processes in the low temperature thermal mixing regime. Without assuming any a priori analytical form for the electron polarization, our approach provides a quantitative picture of the steady state that agrees with the well known Borghini prediction based on thermodynamic arguments, as long as the electrons-nuclei transition rates are fast compared to the other relevant time scales. Substantially different final polarization levels are achieved instead when the latter assumption is relaxed in the presence of a nuclear leakage term, even though very weak, suggesting a possible explanation for the deviation between the measured steady state polarizations and the Borghini prediction. The proposed methodology also allows us to calculate nuclear polarization and relaxation times, once the electrons/nuclei concentration ratio and the typical rates of the microscopic processes involving the two spin species are specified. Numerical results are shown to account for the manifold dynamic behaviours of typical DNP samples.     

Probing side-chain dynamics in high molecular weight proteins by deuterium NMR spin relaxation: an application to an 82-kDa enzyme

New NMR experiments for the measurement of side-chain dynamics in high molecular weight ( approximately 100 kDa) proteins are presented. The experiments quantify (2)H spin relaxation rates in (13)CH(2)D or (13)CHD(2) methyl isotopomers and, for applications to large systems, offer significant gains both in sensitivity (2-3-fold) and resolution over previously published HSQC schemes. The methodology has been applied to investigate Ile dynamics in the 723-residue, single polypeptide chain enzyme, malate synthase G. Methyl-axis order parameters, S(axis), characterizing the amplitudes of motion of the methyl groups, have been derived from both (13)CH(2)D and (13)CHD(2) probes and are in excellent agreement. The distribution of order parameters is trimodal, reflecting the range of dynamics that are available to Ile residues. A reasonable correlation is noted between and inverse temperature factors from X-ray studies of the enzyme. The proposed methodology significantly extends the range of protein systems for which side-chain dynamics can be studied.     

Deuterium spin probes of side-chain dynamics in proteins. 2. Spectral density mapping and identification of nanosecond time-scale side-chain motions

In the previous paper in this issue we have demonstrated that it is possible to measure the five different relaxation rates of a deuteron in (13)CH(2)D methyl groups of (13)C-labeled, fractionally deuterated proteins. The extensive set of data acquired in these experiments provides an opportunity to investigate side-chain dynamics in proteins at a level of detail that heretofore was not possible. The data, acquired on the B1 domain of peptostreptococcal protein L, include 16 (9) relaxation measurements at 4 (2) different magnetic field strengths, 25 degrees C (5 degrees C). These data are shown to be self-consistent and are analyzed using a spectral density mapping procedure which allows extraction of values of the spectral density function at a number of frequencies with no assumptions about the underlying dynamics. Dynamics data from 31 of 35 methyls in the protein for which data could be obtained were well-fitted using the two-parameter Lipari-Szabo model (Lipari, G.; Szabo, A. J. Am. Chem. Soc. 1982, 104, 4546). The data from the remaining 4 methyls can be fitted using a three-parameter version of the Lipari-Szabo model that takes into account, in a simple manner, additional nanosecond time-scale local dynamics. This interpretation is supported by analysis of a molecular dynamics trajectory where spectral density profiles calculated for side-chain methyl sites reflect the influence of slower (nanosecond) time-scale motions involving jumps between rotameric wells. A discussion of the minimum number of relaxation measurements that are necessary to extract the full complement of dynamics information is presented along with an interpretation of the extracted dynamics parameters.     

The effect of nuclear spin on the polarisation ratio of resonance fluorescence

The nuclear quadrupole interaction causes the rotational angular momentum of a molecule with nuclear spin to precess about the total angular momentum whose projection along a space fixed axis is conserved. This effects the degree of orientation in the excited state of molecules optically pumped with circularly polarised light and reduces the polarisation ratio of fluorescence from molecules with large nuclear spin. Calculations are presented for the circular polarisation ratio of the forward scattered fluorescence when the exciting radiation is sufficiently broad-banded that it excites the full manifold of quadrupole split components of a given J″ → J′ transition. Results are also presented for the variation of the polarisation ratio and intensity as a narrow excitation source is tuned across the absorption.     

Dynamic nuclear polarization assisted spin diffusion for the solid effect case

The dynamic nuclear polarization (DNP) process in solids depends on the magnitudes of hyperfine interactions between unpaired electrons and their neighboring (core) nuclei, and on the dipole-dipole interactions between all nuclei in the sample. The polarization enhancement of the bulk nuclei has been typically described in terms of a hyperfine-assisted polarization of a core nucleus by microwave irradiation followed by a dipolar-assisted spin diffusion process in the core-bulk nuclear system. This work presents a theoretical approach for the study of this combined process using a density matrix formalism. In particular, solid effect DNP on a single electron coupled to a nuclear spin system is considered, taking into account the interactions between the spins as well as the main relaxation mechanisms introduced via the electron, nuclear, and cross-relaxation rates. The basic principles of the DNP-assisted spin diffusion mechanism, polarizing the bulk nuclei, are presented, and it is shown that the polarization of the core nuclei and the spin diffusion process should not be treated separately. To emphasize this observation the coherent mechanism driving the pure spin diffusion process is also discussed. In order to demonstrate the effects of the interactions and relaxation mechanisms on the enhancement of the nuclear polarization, model systems of up to ten spins are considered and polarization buildup curves are simulated. A linear chain of spins consisting of a single electron coupled to a core nucleus, which in turn is dipolar coupled to a chain of bulk nuclei, is considered. The interaction and relaxation parameters of this model system were chosen in a way to enable a critical analysis of the polarization enhancement of all nuclei, and are not far from the values of (13)C nuclei in frozen (glassy) organic solutions containing radicals, typically used in DNP at high fields. Results from the simulations are shown, demonstrating the complex dependences of the DNP-assisted spin diffusion process on variations of the relevant parameters. In particular, the effect of the spin lattice relaxation times on the polarization buildup times and the resulting end polarization are discussed, and the quenching of the polarizations by the hyperfine interaction is demonstrated.     

Effect of side-chain length on the side-chain dynamics of alpha-helical poly(L-glutamic acid) as probed by a fluorescence blob model

Two series of pyrene-labeled poly(glutamic acid) (Py-PGA) were synthesized utilizing two different linkers for pyrene attachment, namely 1-pyrenemethylamine (PMA) and 1-pyrenebutylamine (PBA). Several Py-PGAs were synthesized for each series with pyrene contents ranging from 4 to 15 mol %. Py-PGA forms a rigid alpha-helix in DMF that effectively locks the backbone in place, thus enabling only side-chain or linker motions to be monitored by time-resolved fluorescence. Time-resolved fluorescence decays were acquired for the pyrene monomer of the Py-PGA constructs and the fluorescence blob model (FBM) was used to quantify the dynamics of the different linkers connecting pyrene to the backbone. Nitromethane was used to shorten the lifetime of the pyrene monomer, in effect controlling the probing time of the pyrene group, from 50 to 155 ns for PGA-PBA and from 50 to 215 ns for PGA-PMA. The FBM analysis of the fluorescence decays led to the conclusion that excimer formation around the rigid alpha-helix backbone takes place in a compact environment. The number of glutamic acid units within a blob, N blob, decreased only slightly with decreasing probing time for both Py-PGA constructs as a result of the compact distribution of the chromophores around the alpha-helix. The PGA alpha-helix was modeled using Hyperchem software and the ability of two pyrene groups to encounter was evaluated as they were separated by increasing numbers of amino acids along the alpha-helix. The number of amino acids required for two pyrenes to lose their ability to overlap and form excimer matched closely the N blob values retrieved using the FBM.     

Computer generation of nuclear spin species and nuclear spin statistical weights

This article develops computer programs for computer generation of nuclear spin species and nuclear spin statistical weights of rovibronic levels. The programs developed here generate nuclear spin species and statistical weights from the group structures known as generalized character cycle indices (GCCI s) which are computed easily from the character table of the PI group of the molecule under consideration. Procedures are illustrated with examples.     

Rotational dynamics in supercooled water from nuclear spin relaxation and molecular simulations

Structural dynamics in liquid water slow down dramatically in the supercooled regime. To shed further light on the origin of this super-Arrhenius temperature dependence, we report high-precision (17)O and (2)H NMR relaxation data for H(2)O and D(2)O, respectively, down to 37 K below the equilibrium freezing point. With the aid of molecular dynamics (MD) simulations, we provide a detailed analysis of the rotational motions probed by the NMR experiments. The NMR-derived rotational correlation time τ(R) is the integral of a time correlation function (TCF) that, after a subpicosecond librational decay, can be described as a sum of two exponentials. Using a coarse-graining algorithm to map the MD trajectory on a continuous-time random walk (CTRW) in angular space, we show that the slowest TCF component can be attributed to large-angle molecular jumps. The mean jump angle is ～48° at all temperatures and the waiting time distribution is non-exponential, implying dynamical heterogeneity. We have previously used an analogous CTRW model to analyze quasielastic neutron scattering data from supercooled water. Although the translational and rotational waiting times are of similar magnitude, most translational jumps are not synchronized with a rotational jump of the same molecule. The rotational waiting time has a stronger temperature dependence than the translation one, consistent with the strong increase of the experimentally derived product τ(R)?D(T) at low temperatures. The present CTRW jump model is related to, but differs in essential ways from the extended jump model proposed by Laage and co-workers. Our analysis traces the super-Arrhenius temperature dependence of τ(R) to the rotational waiting time. We present arguments against interpreting this temperature dependence in terms of mode-coupling theory or in terms of mixture models of water structure.     

An algorithm for the generation of nuclear spin species and nuclear spin statistical weights

This article develops a set of algorithms for the computer generation of nuclear spin species and nuclear spin statistical weights potentially useful in molecular spectroscopy. These algorithms generate the nuclear spin species from group structures known as generalized character cycle indices (GCCI s). Thus the required input for these algorithms is just the set of all GCCI s for the symmetry group of the molecule which can be computed easily from the character table. The algorithms are executed and illustrated with examples.     

Nuclear spin conversion to probe the methyl rotation effect on hydrogen-bond and vibrational dynamics

A noteworthy example of a molecule with coupled large-amplitude motions is provided by acetylacetone (methyl group torsions and intramolecular hydrogen bonds). The molecule was trapped in solid parahydrogen to investigate the complex proton tunneling processes. Nuclear spin conversion in methyl groups is observed and, combined with IR spectra, documents the coupling between high frequency modes and large amplitude motions.     

Understanding anion transport in an aminated trimethyl polyphenylene with high anionic conductivity

An alkaline exchange membrane (AEM) based on an aminated trimethyl poly(phenylene) is studied in detail. This article reports hydroxide ion conductivity through an in situ method that allows for a more accurate measurement. The ionic conductivities of the membrane in bromide and carbonate forms at 90 °C and 95% RH are found to be 13 and 17 mS cm⁻¹ respectively. When exchanged with hydroxide, conductivity improved to 86 mS cm⁻¹ under the same experimental conditions. The effect of relative humidity on water uptake and the SAXS patterns of the AEM membranes were investigated. SAXS analysis revealed a rigid aromatic structure of the AEM membrane with no microphase separation. The synthesized AEM is shown to be mechanically stable as seen from the water uptake and SAXS studies. Diffusion NMR studies demonstrated a steady state long-range diffusion constant, D_∞ of 9.8 × 10⁻⁶ cm² s⁻¹ after 50–100 ms. © 2012 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2013, 51, 1743–1750, 2013     

Molecular dynamics simulations of the interactions of kinin peptides with an anionic POPG bilayer

We have performed molecular dynamics simulations of peptide hormone bradykinin (BK) and its fragment des-Arg9-BK in the presence of an anionic lipid bilayer, with an aim toward delineating the mechanism of action related to their bioactivity. Starting from the initial aqueous environment, both of the peptides are quickly adsorbed and stabilized on the cell surface. Whereas BK exhibits a stronger interaction with the membrane and prefers to stay on the interface, des-Arg9-BK, with the loss of C-terminal Arg, penetrates further. The heterogeneous lipid-water interface induces β-turn-like structure in the otherwise inherently flexible peptides. In the membrane-bound state, we observed C-terminal β-turn formation in BK, whereas for des-Arg9-BK, with the deletion of Arg9, turn formation occurred in the middle of the peptide. The basic Arg residues anchor the peptide to the bilayer by strong electrostatic interactions with charged lipid headgroups. Simulations with different starting orientations of the peptides with respect to the bilayer surface lead to the same observations, namely, the relative positioning of the peptides on the membrane surface, deeper penetration of the des-Arg9-BK, and the formation of turn structures. The lipid headgroups adjacent to the bound peptides become substantially tilted, causing bilayer thinning near the peptide contact region and increase the degree of disorder in nearby lipids. Again, because of hydrogen bonding with the peptide, the neighboring lipid's polar heads exhibit considerably reduced flexibility. Corroborating findings from earlier experiments, our results provide important information about how the lipid environment promotes peptide orientation/conformation and how the peptide adapts to the environment.     

Effect of nuclear spin of a homonuclear molecule on the rate of ion capture

Calculations employing statistical adiabatic channel model show that the spin of a nucleus in a homonuclear molecule affects the rate of ion capture at low temperatures. Whereas for bosons in even electronic states with respect to permutation of the nuclear coordinates (Σ⁺_g,Σ⁻_u) the ion capture rate decreases as the spin increases, for fermions in such states the situation is reversed; the capture rate increases with increasing spin. For the odd Σ⁺_u,Σ⁻_g states the trends are reversed. Such trends are exhibited over the whole region of low temperatures. At very low temperatures the spin effects can become very large. If the effect of the reduced mass contributed by the Langevin rate constant can be ignored, the normal kinetic order at which the isotopomeric molecules capture an ion is reversed. For instance, C₂T₂+H⁺₃ occurs slower than does C₂D₂+H⁺₃.     

Microstructure and dynamics in lyotropic liquid crystals. Principles and applications of nuclear spin relaxation

Nuclear spin relaxation of quadrupolar nuclei provides access to a wide range of properties of lyotropic liquid crystals, ranging from the molecular ordering and dynamics at the interface to the macroscopic viscoelastic behaviour. We emphasize here the unique capability of the spin relaxation method to provide detailed geometric and dynamic information relating to the microstructure of lyotropic liquid crystals, i.e. the metric, curvature, and fluctuations of the dividing interface that separates polar and non-polar regions. This information is conveyed to the spin system via the translational diffusion of surfactants or counterions over the interface. The general principles of the spin relaxation method, as applied to lyotropic liquid crystals, are described, with emphasis on the model-independent information content of the relaxation observables and on the relation to microstructure. Specific results for lamellar, hexagonal, cubic, and nematic phases are also described.     

Microstructure and dynamics in lyotropic liquid crystals. Principles and applications of nuclear spin relaxation

Abstract

Nuclear spin relaxation of quadrupolar nuclei provides access to a wide range of properties of lyotropic liquid crystals, ranging from the molecular ordering and dynamics at the interface to the macroscopic viscoelastic behaviour. We emphasize here the unique capability of the spin relaxation method to provide detailed geometric and dynamic information relating to the microstructure of lyotropic liquid crystals, i.e. the metric, curvature, and fluctuations of the dividing interface that separates polar and non-polar regions. This information is conveyed to the spin system via the translational diffusion of surfactants or counterions over the interface. The general principles of the spin relaxation method, as applied to lyotropic liquid crystals, are described, with emphasis on the model-independent information content of the relaxation observables and on the relation to microstructure. Specific results for lamellar, hexagonal, cubic, and nematic phases are also described.