Response of lysozyme internal dynamics to hydration probed by13C and1H solid-state NMR relaxation

We have studied the hydration dependence of the internal protein dynamics of hen egg white lysozyme by naturally abundant¹³C and¹H nuclear magnetic resonance (NMR) relaxation. NMR relaxation timesT ₁, off-resonanceT _1p and proton-decoupled on-resonanceT _1p (only for carbon expriments) were measured in the temperature range from 0 to 50°C. The spectral resolution in carbon cross-polarization magic angle spinning spectrum allows to treat methine, methylene and methyl carbons separately, while proton experiments provide only one integral signal from all protons at a time. The relaxation times were quantitatively analyzed by the well-established correlation function formalism and model-free approach. The whole set of the data could be adequately described by a model assuming three types of motion having correlation times around 10^?4, 10^?9 and 10^?12 s. The slowest process originated from correlated conformational transitions between different energy minima, the intermediate process could be identified as librations within one energy minimum, and the fastest one is a fast rotation of methyl protons the symmetry axis of methyl groups. A comparison of the dynamic behavior of lysozyme and polylysine obtained from a previous study (A. Krushelnitsky, D. Faizullin, D. Reichert, Biopolymers 73, 1–15, 2004) reveals that in the dry state both biopolymers are rigid on both fast and slow time scales. Upon hydration, lysozyme and polylysine reveal a considerable enhancement of the internal mobility, however, in different ways. The side chains of polylysine are more mobile than those of lysozyme, whereas for the backbone a reversed picture is observed. This difference correlates with structural features of lysozyme and polylysine discussed in detail. Due to the presence of a fast spin diffusion, the analysis of proton relaxation data is a more difficult task. However, our data demonstrate that the correlation functions of motion obtained from carbon and proton experiments are substantially different. We explained this by the fact that these two types of NMR relaxation experiments probe the motion of different internuclear vectors. The comparison of the proton data with our previous results on proton relaxation timesT ₁ measured over a wide temperature range indicates that at low temperatures lysozyme undergoes structural rearrangements affecting the amplitudes and/or activation energies of motions.     

EPR study of the hemoglobin rotational correlation time and microviscosity during the polymerization of hemoglobin S

The microviscosity and the protein rotational correlation time are analyzed in samples of hemoglobin A and hemoglobin S with the intracellular concentration at 36°C and during spontaneous deoxygenation. With this purpose, we use glutathione and carbonmonoxy hemoglobin labeled with 4-maleimido-2,2,6,6-tetramethyl-piperidine-1-oxyl (TEMPO) as probes and 4-maleimido TEMPO bound to the hemoglobin (A and S) as a spin label. The saturation transfer electron paramagnetic resonance experiment showed a sigmoidal behavior, and an increase (about twice) of the hemoglobin rotational correlation time and microviscosity during the polymerization process of hemoglobin S. The delay time determined by this method coincides with that obtained in proton magnetic resonance experiments. These results help to explain the temporal behavior of the proton relaxation times obtained in samples of hemoglobin A and S under the same experimental conditions.     

Low-Frequency and d.c. Phenomena in Magnetic Resonance

A review is given of some low-frequency and d.c. magnetic resonance phenomena studied since 1970s up to date. The content includes: the enhanced longitudinal susceptibility effect (ELSE) based on the concept of the dipole–dipole reservoir in EPR; direct registration of NMR in rotating frames; modulation method of measuring extremely fast electron spin longitudinal relaxation; resonance magnetoresistance and resonance spin rectification (“spin dynamo”) in conducting ferromagnetic films. Physical mechanism of these effects, as well as applications in studying spin dynamics and relaxation in solids, including dynamic nuclear polarization, high-temperature superconductivity and properties of rare-earth manganites are considered.     

Rotating-Frame Proton Cross Relaxation in the Presence of Paramagnetic Metal Ions

Rotating-frame cross relaxation for a pair of protons rotating in a spherical molecule with external relaxation is examined theoretically. The results of this study allow us to model intensities in 1D ROE and 2D ROESY spectra of protons in the presence of a paramagnetic metal ion. External relaxation moves the threshold correlation time for spin diffusion to longer times. In contrast to the effect of external relaxation on longitudinal cross relaxation (NOESY), the range of observable transverse cross relaxation (ROESY) expands with increasing external relaxation. At the same time, external relaxation compresses the overall time scale for cross-peak evolution. The initial slopes of cross-peak evolution are unaffected by external relaxation, but are sensitive to the rotational correlation time of the proton pair. Very short mixing times are necessary for accurate estimation of the initial Slopes.     

Kinetics of a local “magnetic” moment and a non-stationary spin-polarized current in the single impurity Anderson model

We perform theoretical investigation of the localized state dynamics in the presence of interaction with the reservoir and Coulomb correlations. We analyze kinetic equations for electron occupation numbers with different spins taking into account high order correlation functions for the localized electrons. We reveal that in the stationary state electron occupation numbers with the opposite spins always have the same value: the stationary state is a “paramagnetic” one. “Magnetic” properties can appear only in the non-stationary characteristics of the single-impurity Anderson model and in the dynamics of the localized electrons second order correlation functions. We found that for deep energy levels and strong Coulomb correlations, relaxation time for initial “magnetic” state can be several orders larger than for “paramagnetic” one. So, long-living “magnetic” moment can exist in the system. We also found non-stationary spin polarized currents flowing in opposite directions for the different spins in the particular time interval.     

Subterahertz Longitudinal Phonon Modes Propagating in a Lipid Bilayer Immersed in an Aqueous Medium

The properties of subterahertz longitudinal acoustic phonon modes in the hydrophobic region of a lipid bilayer immersed in a compressible viscous aqueous medium are investigated theoretically. An approximate expression is obtained for the Mandelstam–Brillouin components of the dynamic structure factor of a bilayer. The analysis is based on a generalized hydrodynamic model of the “two-dimensional lipid bilayer + three-dimensional fluid medium” system, as well as on known sharp estimates for the frequencies and lifetimes of long-wavelength longitudinal acoustic phonons in a free hydrated lipid bilayer and in water, obtained from inelastic X-ray scattering experiments and molecular dynamics simulations. It is shown that, for characteristic values of the parameters of the membrane system, subterahertz longitudinal phonon-like excitations in the hydrophobic part of the bilayer are underdamped. In this case, the contribution of the viscous flow of the aqueous medium to the damping of a longitudinal membrane mode is small compared with the contribution of the lipid bilayer. Quantitative estimates of the damping ratio agree well with the experimental results for the vibration mode of the enzyme lysozyme in aqueous solution [1]. It is also shown that a coupling between longitudinal phonon modes of the bilayer and relaxation processes in its fluid environment gives rise to an additional peak in the scattering spectrum, which corresponds to a non-propagating mode.     

Discrete-time Glauber model as a generalized Ehrenfest urn model

Glauber's continuous-time stochastic model for relaxation of spin systems is “imbedded” in discrete time as a Markov chain. The chain is a generalization of the Ehrenfest urn model as formulated by Hess. Some properties of the chain are discussed.     

Evaluation of Conformational dynamics properties of spin-labelled proteins at different degrees of nitroxide radicals immobilization

Spin-labelling has found wide applications in elucidation of the dynamic behaviour of biological macromolecules in aqueous media and biomembranes. Most of the proposed methods aimed at estimation of macromolecular correlation times (τ_c) assume, however, spin label molecules rigidly bound within the protein matrix. To avoid this limitation theoretical models which involve additional dynamic parameters to characterize the spin label motion should be considered. We have used ESR spectra analysis technique which permits quantitative separation of slow macromolecular rotation (described by the rotational correlation time, τ_c) and fast anisotropic relative to protein nitroxyl radical motion (described by the “order parameter”,S). This method was applied to study: i) conformational dynamics of covalently and non-covalently spin-labelled human serum albumin (HSA) in solution; ii) protein-protein (antigen-antibody) interactions in a model system containing spin-labelled bovine serum albumin (BSA) and anti-BSA immunoglobulin (IgG) in solution; and iii) dynamic properties of membrane-bound proteins: H⁺-ATPase (CF₁-CF₀ coupling factor of photophosphorylation) and Photosystem I pigment-protein reaction centre complex (PSI RC) isolated from spinach chloroplasts and reconstituted in proteoliposomes.     

Determination of relaxation constants of a quadrupole spin system with many energy levels

The two-frequency nuclear quadrupole resonance method is used to determine the relaxation time for all single-quantum transitions in a quadrupole spin system with many energy levels from the results obtained for a single transition, which is impossible in a one-frequency method. The accuracy is the same as in the measurement of relaxation time in the case of one-frequency pumping of the transition chosen as the “basis.” The results of measurements are presented and determination of relaxation constants for KReO₄ and NaReO₄ as well as SbCl₃ and SbBr₃ and their complexes at various temperatures with the help of the two-frequency NQR method.     

Sensitivity of Saturation Transfer Electron Spin Resonance Extended to Extremely Slow Mobility in Glassy Materials

A novel extension of the saturation transfer (ST) ESR technique that enables the determination of extremely long rotational correlation times of nitroxide spin labels up to values around 10⁴s is proposed. The method is based on the observation that the integral of ST-ESR spectra is sensitive to the spin–lattice relaxation time of the electron of the spin label, which in turn is directly dependent upon the rotational correlation time. The method is applied to the spin label TEMPOL (4-hydroxy-2,2,6,6-tetramethylpiperidine-N-oxyl) in glycerol. From the known viscosity data and the related rotational correlation times of the TEMPOL spin label in glycerol, the rotational correlation times of unknown samples can be determined. The method is especially applicable to systems with a very high viscosity, such as glassy materials. The method is applied to a 20 wt% glucose–water mixture in the glassy state, giving a value for the highest limiting rotational correlation time of about 10³s at a temperature of 45 K below the glass transition temperature of this system. This is an extension by six decades for the rotational correlation time, as compared to the current application of ST-ESR.     

Internal dynamics and hydration of solid proteins by1H NMR relaxation and FTIR spectroscopy

Temperature dependences of¹H nonselective nuclear magnetic resonanceT ₁ andT ₂ relaxation times measured at 27 MHz have been studied on solid human serum albumin (HSA) samples at various hydrations. The data were interpreted in terms of three kinds of internal motions in a protein and microdynamic parameters of the motions were obtained by a “model-free” approach. Two fast motions with correlation times lying in the range of tens to hundreds picoseconds were shown to be essentially insensitive to hydration. Unlike lysozyme and bovine albumin, HSA reveals relaxation transition due to slow motion in the room temperature range thus allowing one to obtain microdynamic parameters more precisely. Hydration leads to a shortening of the correlation time from hundreds to tens nanoseconds and to a less restricted movement. The comparison of the hydration dependence of relaxation parameters with infrared spectra of HSA side chain groups clearly shows that methyl protons are evidently involved in a slow motion, following the saturation of the protein globule surface by water. The same dependence correlating with solvent accessible surface areas was shown to exist for some other proteins. In addition to the main set of protons performing a solidlike movement, a small amount of much more mobile protons is also present with its proportion rising steeply with hydration and temperature. The origin of these protons is discussed.     

Optical detection of spin transport in nonmagnetic metals

We determine the dynamic magnetization induced in nonmagnetic metal wedges composed of silver, copper, and platinum by means of Brillouin light scattering microscopy. The magnetization is transferred from a ferromagnetic Ni80Fe20 layer to the metal wedge via the spin pumping effect. The spin pumping efficiency can be controlled by adding an insulating interlayer between the magnetic and nonmagnetic layer. By comparing the experimental results to a dynamical macroscopic spin-transport model we determine the transverse relaxation time of the pumped spin current which is much smaller than the longitudinal relaxation time.     

Analysis of nitroxide spin label motion in a protein-protein complex using multiple frequency EPR spectroscopy

X- and W-band EPR spectra, at room and low temperatures, are reported for nitroxide spin labels attached to cysteine residues selectively introduced into two proteins, the DNase domain of colicin-E9 and its immunity protein, Im9. The dynamics of each site of attachment on the individual proteins and in the tight DNase-Im9 complex have been analysed by computer simulations of the spectra using a model of Brownian dynamics trajectories for the spin label and protein. Ordering potentials have been introduced to describe mobility of labels restricted by the protein domain. Label mobility varies with position from completely immobilised, to motionally restricted and to freely rotating. Bi-modal dynamics of the spin label have been observed for several sites. We show that W-band spectra are particularly useful for detection of anisotropy of spin label motion. On complex formation significant changes are observed in the dynamics of labels at the binding interface region. This work reveals multi-frequency EPR as a sensitive and valuable tool for detecting conformational changes in protein structure and dynamics especially in protein-protein complexes.     

A paramagnetic molecular voltmeter

We have developed a general electron paramagnetic resonance (EPR) method to measure electrostatic potential at spin labels on proteins to millivolt accuracy. Electrostatic potential is fundamental to energy-transducing proteins like myosin, because molecular energy storage and retrieval is primarily electrostatic. Quantitative analysis of protein electrostatics demands a site-specific spectroscopic method sensitive to millivolt changes. Previous electrostatic potential studies on macromolecules fell short in sensitivity, accuracy and/or specificity. Our approach uses fast-relaxing charged and neutral paramagnetic relaxation agents (PRAs) to increase nitroxide spin label relaxation rate solely through collisional spin exchange. These PRAs were calibrated in experiments on small nitroxides of known structure and charge to account for differences in their relaxation efficiency. Nitroxide longitudinal (R(1)) and transverse (R(2)) relaxation rates were separated by applying lineshape analysis to progressive saturation spectra. The ratio of measured R(1) increases for each pair of charged and neutral PRAs measures the shift in local PRA concentration due to electrostatic potential. Voltage at the spin label is then calculated using the Boltzmann equation. Measured voltages for two small charged nitroxides agree with Debye-Hückel calculations. Voltage for spin-labeled myosin fragment S1 also agrees with calculation based on the pK shift of the reacted cysteine.     

Atomic mobility in a ternary liquid Ga–In–Sn alloy of the eutectic composition

The nuclear spin–lattice relaxation and Knight shift of ⁷¹Ga, ⁶⁹Ga, and ¹¹⁵In nuclei in a ternary liquid gallium–indium–tin alloy of the eutectic composition, which was introduced into pores of an opal matrix and porous glasses with pore sizes of 18 and 7 nm, have been investigated and compared with those for the bulk melt. It has been found that longitudinal relaxation is accelerated and the Knight shift is decreased, depending on the size of pores. The correlation time of the atomic motion has been calculated for the nanostructured melt in porous matrices. It has been shown that the atomic mobility in the melt decreases with decreasing size of pores in the glasses.

     

Model independent features of the two-particle correlation function

The Hanbury-Brown Twiss correlation function for two identical particles is studied for systems with cylindrical symmetry. Its shape for small values of the relative momentum is derived in a model independent way. In addition to the usual quadratic “side”, “out” and “longitudinal” terms in the exponent of the correlator, a previously neglected “out-longitudinal” cross term is found and discussed. The model-independent expressions for the size parameters of the HBT correlation function are interpreted as lengths of homogeneity of the source, in distinction to its purely geometrical size. They are evaluated analytically and numerically for two specific thermal models featuring collective transverse and longitudinal flow. The analytic expressions derived allow one to establish qualitatively important connections between the space-time features of the source and the shape of the correlation function. New ways of parametrizing the correlation function and a new approach to the measurement of the duration of the emission process are suggested.     

Water-proton-spin-lattice-relaxation dispersion of paramagnetic protein solutions

The paramagnetic contributions to water-proton-spin-lattice relaxation rate constants in protein systems spin-labeled with nitroxide radicals were re-examined. As noted by others, the strength of the dipolar coupling between water protons and the protein-bound nitroxide radical often appears to be larger than physically reasonable when the relaxation is assumed to be controlled by 3-dimensional diffusive processes in the vicinity of the spin label. We examine the effects of the surface in biasing the diffusive exploration of the radical region and derive a relaxation model that incorporates 2-dimensional dynamics at the interfacial layer. However, we find that the local 2-dimensional dynamics changes the shape of the relaxation dispersion profile but does not necessarily reproduce the low-field relaxation efficiency found by experiment. We examine the contributions of long-range dipolar couplings between the paramagnetic center and protein-bound-water molecules and find that the contributions from these several long range couplings may be competitive with translational contributions because the correlation time for global rotation of the protein is approximately 1000 times longer than that for the diffusive motion of water at the interfacial region. As a result the electron-proton dipolar coupling to rare protein-bound-water-molecule protons may be significant for protein systems that accommodate long-lived-water molecules. Although the estimate of local diffusion coefficients is not seriously compromised because it derives from the Larmor frequency dependence, these several contributions confound efforts to fit relaxation data quantitatively with unique models.     

Calculation of the fluctuation-dissipation ratio for the nonequilibrium critical behavior of disordered systems

The values of a new universal parameter characterizing a nonequilibrium critical behavior, namely, the fluctuation-dissipation ratio specifying a fundamental relation between the dynamic response function and the correlation function, are calculated for the disordered three-dimensional Ising model. The analysis of the two-time dependence for autocorrelation functions and the ac susceptibility for the systems with spin densities p = 1.0, 0.8, and 0.6 shows the aging effects characterized by the anomalous slowing of relaxation in the system with the growth of the waiting time and the violation of the fluctuation-dissipation theorem. To improve the accuracy of the ac susceptibility calculations, the “thermal bath” technique has been used without introducing the applied magnetic field in the simulation. It has been shown that the structural defects lead to the pronounced enhancement of the aging effects.     

X-ray photoelectron spectra of iron complexes: Correlation of iron 2p satellite intensity with complex spin state

Metal and ligand core-level spectra have been obtained for 36 iron complexes which possess a variety of ligands including carbonyl, nitrosyl, triphenylphosphine,o-phenylenebis(dimethylarsine), halides and pseudohalides. Formal metal oxidation states range from ? 1 to + 3, and complex spin states represented in the series include 0, $\text{1}\text{2}$, $\text{3}\text{2}$, 2 and $\text{5}\text{2}$. A clear correlation between complex spin state and satellite intensity in the Fe 2p spectra is found. The satellite intensities observed experimentally are in approximate quantitative accord with those predicted by a “spin flipping” model. Although the present analysis does not provide a definitive choice between the “sudden approximation” and “spin flipping” models, the agreement between experimental satellite intensities and the intensities predicted by the “spin flipping” model suggests that such a mechanism can be important in the satellite process.