Recent progress on polymer dynamics by neutron scattering: From simple polymers to complex materials

The recent (from 2010 onward) contributions of quasielastic neutron scattering techniques (time of flight, backscattering, and neutron spin echo) to the characterization and understanding of dynamical processes in soft materials based on polymers are analyzed. The selectivity provided by the combination of neutron scattering and isotopic—in particular, proton/deuterium—labeling allows the isolated study of chosen molecular groups and/or components in a system. This opportunity, together with the capability of neutrons to provide space/time resolution at the relevant length scales in soft matter, allows unraveling the nature of the large variety of molecular motions taking place in materials of increasing complexity. As a result, recent relevant works can be found dealing with dynamical process which associated characteristic lengths and nature are as diverse as, for example, phenyl motions in a glassy linear homopolymer like polystyrene and the chain dynamics of a polymer adsorbed on dispersed clay platelets. © 2012 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2013     

Light‐induced Modulation of Protein Dynamics During the Photocycle of Bacteriorhodopsin†

Knowledge about the dynamical properties of a protein is of essential importance for understanding the structure–dynamics–function relationship at the atomic level. So far, however, the correlation between internal protein dynamics and functionality has only been studied indirectly in steady‐state experiments by variation of external parameters like temperature and hydration. In the present study we describe a novel type of (laser‐neutron) pump‐probe experiment, which combines in situ optical activation of the biological function of a membrane protein with a time‐dependent monitoring of the protein dynamics using quasielastic neutron scattering. As a first successful application we present data obtained selectively in the ground state and in the M‐intermediate of bacteriorhodopsin (BR). Temporary alterations in both localized reorientational protein motions and harmonic vibrational dynamics have been observed during the photocycle of BR. This observation is a direct proof for the functional significance of protein structural flexibility, which is correlated with the large‐scale structural changes in the protein structure occurring during the M‐intermediate. We anticipate that functionally important modulations of protein dynamics as observed here are of relevance for most other proteins exhibiting conformational transitions in the time course of functional operation.     

Modeling the effects of structure and dynamics of the nitroxide side chain on the ESR spectra of spin-labeled proteins

In the companion paper (J. Phys. Chem. B 2006, 110, jp0629487), a study of the conformational dynamics of methanethiosulfonate spin probes linked at a surface-exposed alpha-helix has been presented. Here, on the basis of this analysis, X-band ESR spectra of these spin labels are simulated within the framework of the Stochastic Liouville equation (SLE) methodology. Slow reorientations of the whole protein are superimposed on fast chain motions, which have been identified with conformational jumps and fluctuations in the minima of the chain torsional potential. Fast chain motions are introduced in the SLE for the protein reorientations through partially averaged magnetic tensors and relaxation times calculated according to the motional narrowing theory. The 72R1 and 72R2 mutants of T4 lysozyme, which bear the spin label at a solvent-exposed helix site, have been taken as test systems. For the side chain of the R2 spin label, only a few noninterconverting conformers are possible, whose mobility is limited to torsional fluctuations, yielding almost identical spectra, typical of slightly mobile nitroxides. In the case of R1, more complex spectra result from the simultaneous presence of constrained and mobile chain conformers, with relative weights that can depend on the local environment. The model provides an explanation for the experimentally observed dependence of the spectral line shapes on temperature, solvent, and pattern of substituents in the pyrroline ring. The relatively simple methodology presented here allows the introduction of realistic features of the spin probe dynamics into the simulation of ESR spectra of spin-labeled proteins; moreover, it provides suggestions for a proper account of such dynamics in more sophisticated approaches.     

Fast enzyme dynamics at the active site of formate dehydrogenase

The role of femtosecond-picosecond structural dynamics of proteins in enzyme-catalyzed reactions is a hotly debated topic. We report infrared photon echo measurement of the formate dehydrogenase-NAD+-azide ternary complex. In contrast to earlier studies of protein dynamics, the data show complete spectral diffusion on the femtosecond-picosecond time scale with no static heterogeneity. This result indicates that this transition-state analogue complex completely samples the distribution of structures that determine the distribution of azide vibrational frequencies within a few picoseconds and that there are no slower motions that perturb the H-bond network at the active site.     

The trehalose coating effect on the internal protein dynamics

(15)N and (13)C NMR experiments were applied to conduct a comparative study of a cold shock protein (Csp) in two states-lyophilized powder and a protein embedded in a glassy trehalose matrix. Both samples were studied at various levels of rehydration. The experiments used (measuring relaxation rates R(1) and R(1ρ), motionally averaged dipolar couplings and solid state exchange method detecting reorientation of the chemical shift anisotropy tensor) allow obtaining abundant information on the protein structural features and internal motions in a range of correlation times from nanoseconds to seconds. The main results are: (a) the trehalose coating makes the protein structure more native in comparison with the dehydrated lyophilized powder, however, trehalose still cannot remove all non-native hydrogen bonds which are present in a dehydrated protein; (b) trehalose has an appreciable effect on the internal dynamics: the motion of the backbone N-H groups in the nanosecond and microsecond time scales becomes slower while the motional amplitude remains constant; (c) upon adding water to the Csp-trehalose mixture, water molecules accumulate around proteins forming a layer between the protein surface and the trehalose matrix. The protein dynamics become faster, however, not as fast as in the fully hydrated state; (d) the hydration response of dynamics of the NH and CH(CH(2)) groups in a protein is qualitatively different: upon increasing protein hydration, the correlation times of the N-H motions become shorter and the amplitude remains stable, and for CH(CH(2)) groups the motional amplitude increases and the correlation times do not change. This can be explained by a different ability of the NH and CH(CH(2)) groups to form hydrogen bonds.     

Slow dynamics in protein fluctuations revealed by time-structure based independent component analysis: the case of domain motions

Protein dynamics on a long time scale was investigated using all-atom molecular dynamics (MD) simulation and time-structure based independent component analysis (tICA). We selected the lysine-, arginine-, ornithine-binding protein (LAO) as a target protein and focused on its domain motions in the open state. A MD simulation of the LAO in explicit water was performed for 600 ns, in which slow and large-amplitude domain motions of the LAO were observed. After extracting domain motions by rigid-body domain analysis, the tICA was applied to the obtained rigid-body trajectory, yielding slow modes of the LAO's domain motions in order of decreasing time scale. The slowest mode detected by the tICA represented not a closure motion described by a largest-amplitude mode determined by the principal component analysis but a twist motion with a time scale of tens of nanoseconds. The slow dynamics of the LAO were well described by only the slowest mode and were characterized by transitions between two basins. The results show that tICA is promising for describing and analyzing slow dynamics of proteins.     

Combining Neutron Scattering,Deuteration Technique,and Molecular Dynamics Simulations to Study Dynamics of Protein and Its Surface Water Molecules

Protein internal dynamics is essential for its function.Exploring the internal dynamics of protein molecules as well as its connection to protein structure and function is a central topic in biophysics.However,the atomic motions in protein molecules exhibit a great degree of complexities.These complexities arise from the complex chemical composition and superposition of different types of atomic motions on the similar time scales,and render it challenging to explicitly understand the microscopic mechanism governing protein motions,functions,and their connections.Here,we demonstrate that,by using neutron scattering,molecular dynamics simulation,and deuteration technique,one can address this challenge to a large extent.     

General framework for studying the dynamics of folded and nonfolded proteins by NMR relaxation spectroscopy and MD simulation

A general framework is presented for the interpretation of NMR relaxation data of proteins. The method, termed isotropic reorientational eigenmode dynamics (iRED), relies on a principal component analysis of the isotropically averaged covariance matrix of the lattice functions of the spin interactions responsible for spin relaxation. The covariance matrix, which is evaluated using a molecular dynamics (MD) simulation, is diagonalized yielding reorientational eigenmodes and amplitudes that reveal detailed information about correlated protein dynamics. The eigenvalue distribution allows one to quantitatively assess whether overall and internal motions are statistically separable. To each eigenmode belongs a correlation time that can be adjusted to optimally reproduce experimental relaxation parameters. A key feature of the method is that it does not require separability of overall tumbling and internal motions, which makes it applicable to a wide range of systems, such as folded, partially folded, and unfolded biomolecular systems and other macromolecules in solution. The approach was applied to NMR relaxation data of ubiquitin collected at multiple magnetic fields in the native form and in the partially folded A-state using MD trajectories with lengths of 6 and 70 ns. The relaxation data of native ubiquitin are well reproduced after adjustment of the correlation times of the 10 largest eigenmodes. For this state, a high degree of separability between internal and overall motions is present as is reflected in large amplitude and collectivity gaps between internal and overall reorientational modes. In contrast, no such separability exists for the A-state. Residual overall tumbling motion involving the N-terminal beta-sheet and the central helix is observed for two of the largest modes only. By adjusting the correlation times of the 10 largest modes, a high degree of consistency between the experimental relaxation data and the iRED model is reached for this highly flexible biomolecule.     

Stochastic dynamic simulation of a protein

The internal motions of a small protein, the bovine pancreatic trypsin inhibitor (BPTI) in solution, are investigated in the framework of the Langevin equation. In this approach, the effects of the solvent molecules are incorporated by suitably defining the friction and random forces. The friction coefficients are determined from a molecular dynamics simulation. The details of the rapid fluctuations of protein atoms obtained by stochastic and molecular dynamics simulation techniques are compared by calculating the generalized density of states obtained via an incoherent neutron scattering. Presently, our stochastic dynamics simulation is one order of magnitude faster than the molecular dynamics simulation with the explicit inclusion of the water molecules. Generalizations of the present stochastic dynamics approach for studying the large-scale motion in proteins are briefly outlined and the probability of a further speedup by an additional order of magnitude is discussed.     

Using Markov models to simulate electron spin resonance spectra from molecular dynamics trajectories

Simulating electron spin resonance (ESR) spectra directly from molecular dynamics simulations of a spin-labeled protein necessitates a large number (hundreds or thousands) of relatively long (hundreds of nanoseconds) trajectories. To meet this challenge, we explore the possibility of constructing accurate stochastic models of the spin label dynamics from atomistic trajectories. A systematic, two-step procedure, based on the probabilistic framework of hidden Markov models, is developed to build a discrete-time Markov chain process that faithfully captures the internal spin label dynamics on time scales longer than about 150 ps. The constructed Markov model is used both to gain insight into the long-lived conformations of the spin label and to generate the stochastic trajectories required for the simulation of ESR spectra. The methodology is illustrated with an application to the case of a spin-labeled poly alanine alpha helix in explicit solvent.     

Radical cations of branched alkanes as observed in irradiated solutions by the method of time-resolved magnetic field effect

Spin dynamics in radical ion pairs formed under ionizing irradiation of n-hexane solutions of two branched alkanes 2,3-dimethylbutane and 2,2,4-trimethylpentane has been studied by the method of time-resolved magnetic field effect in recombination fluorescence. Experimental curves of the magnetic field effect are satisfactorily described by assuming that the spin dynamics is determined by the hyperfine interactions in the radical cation (RC) of branched alkane under study with hyperfine coupling (HFC) constants averaged by internal rotations of RC fragments. The HFC constants determined from the magnetic field effect curves are close to those estimated within DFT B3LYP approach. Analysis of the results indicates that at room temperature the lifetimes of the RC of the studied branched alkanes amount to, at least, tens of nanoseconds.     

High‐Resolution NMR Determination of the Dynamic Structure of Membrane Proteins

¹⁵N spin‐relaxation rates are demonstrated to provide critical information about the long‐range structure and internal motions of membrane proteins. Combined with an improved calculation method, the relaxation‐rate‐derived structure of the 283‐residue human voltage‐dependent anion channel revealed an anisotropically shaped barrel with a rigidly attached N‐terminal helix. Our study thus establishes an NMR spectroscopic approach to determine the structure and dynamics of mammalian membrane proteins at high accuracy and resolution.     

Temperature dependence of anisotropic protein backbone dynamics

The measurement of (15)N NMR spin relaxation, which reports the (15)N-(1)H vector reorientational dynamics, is a widely used experimental method to assess the motion of the protein backbone. Here, we investigate whether the (15)N-(1)H vector motions are representative of the overall backbone motions, by analyzing the temperature dependence of the (15)N-(1)H and (13)CO-(13)C(alpha) reorientational dynamics for the small proteins binase and ubiquitin. The latter dynamics were measured using NMR cross-correlated relaxation experiments. The data show that, on average, the (15)N-(1)H order parameters decrease only by 2.5% between 5 and 30 degrees C. In contrast, the (13)CO-(13)C(alpha) order parameters decrease by 10% over the same temperature trajectory. This strongly indicates that there are polypeptide-backbone motions activated at room temperature that are not sensed by the (15)N-(1)H vector. Our findings are at variance with the common crank-shaft model for protein backbone dynamics, which predicts the opposite behavior. This study suggests that investigation of the (15)N relaxation alone would lead to underestimation of the dynamics of the protein backbone and the entropy contained therein.     

Elastic network normal modes provide a basis for protein structure refinement

It is well recognized that thermal motions of atoms in the protein native state, the fluctuations about the minimum of the global free energy, are well reproduced by the simple elastic network models (ENMs) such as the anisotropic network model (ANM). Elastic network models represent protein dynamics as vibrations of a network of nodes (usually represented by positions of the heavy atoms or by the C(α) atoms only for coarse-grained representations) in which the spatially close nodes are connected by harmonic springs. These models provide a reliable representation of the fluctuational dynamics of proteins and RNA, and explain various conformational changes in protein structures including those important for ligand binding. In the present paper, we study the problem of protein structure refinement by analyzing thermal motions of proteins in non-native states. We represent the conformational space close to the native state by a set of decoys generated by the I-TASSER protein structure prediction server utilizing template-free modeling. The protein substates are selected by hierarchical structure clustering. The main finding is that thermal motions for some substates, overlap significantly with the deformations necessary to reach the native state. Additionally, more mobile residues yield higher overlaps with the required deformations than do the less mobile ones. These findings suggest that structural refinement of poorly resolved protein models can be significantly enhanced by reduction of the conformational space to the motions imposed by the dominant normal modes.     

The dynamics of unfolded versus folded tRNA: the role of electrostatic interactions

The dynamics of RNA contributes to its biological functions such as ligand recognition and catalysis. Using quasielastic neutron scattering spectroscopy, we show that Mg(2+) greatly increases the picosecond to nanosecond dynamics of hydrated tRNA while stabilizing its folded structure. Analyses of the atomic mean-squared displacement, relaxation time, persistence length, and fraction of mobile atoms showed that unfolded tRNA is more rigid than folded tRNA. This same result was found for a sulfonated polystyrene, indicating that the increased dynamics in Mg(2+) arises from improved charge screening of the polyelectrolyte rather than specific interactions with the folded tRNA. These results are opposite to the relationship between structural compactness and internal dynamics for proteins in which the folded state is more rigid than the denatured state. We conclude that RNA dynamics are strongly influenced by the electrostatic environment, in addition to the motions of local waters.     

Restricted orientational motion of nitroxides in molecular glasses: direct estimation of the motional time scale basing on the comparative study of primary and stimulated electron spin echo decays

A comparative study of anisotropic relaxation in two-pulse primary and three-pulse stimulated electron spin echo decays provides a direct way to distinguish fast (correlation time tau(c)<10(-6) s) and slow (tau(c)>10(-6) s) motions. Anisotropic relaxation is detected as a difference of the decay rates for different resonance field positions in anisotropic electron paramagnetic resonance spectra. For fast motion anisotropic relaxation influences the primary echo decay and does not influence the stimulated echo decay. For slow motion it is seen in both two-pulse echo and three-pulse stimulated echo decays. For nitroxide spin probes dissolved in glassy glycerol only fast motion was found below 200 K. Increase of temperature above 200 K results in the appearance of slow motion. Its amplitude increases rapidly with temperature increase. While in glycerol glass slow motion appears above glass transition temperature T(g), in ethanol glass it is observable below T(g). The scenario of motional dynamics in glasses is proposed which involves the broadening of the correlation time distribution with increasing temperature.     

Molecular view of water dynamics near model peptides

Incoherent quasi-elastic neutron scattering (QENS) has been used to measure the dynamics of water molecules in solutions of a model protein backbone, N-acetyl-glycine-methylamide (NAGMA), as a function of concentration, for comparison with results for water dynamics in aqueous solutions of the N-acetyl-leucine-methylamide (NALMA) hydrophobic peptide at comparable concentrations. From the analysis of the elastic incoherent structure factor, we find significant fractions of elastic intensity at high and low concentrations for both solutes, which corresponds to a greater population of protons with rotational time scales outside the experimental resolution (>13 ps). The higher-concentration solutions show a component of the elastic fraction that we propose is due to water motions that are strongly coupled to the solute motions, while for low-concentration solutions an additional component is activated due to dynamic coupling between inner and outer hydration layers. An important difference between the solute types at the highest concentration studied is found from stretched exponential fits to their experimental intermediate scattering functions, showing more pronounced anomalous diffusion signatures for NALMA, including a smaller stretched exponent beta and a longer structural relaxation time tau than those found for NAGMA. The more normal water diffusion exhibited near the hydrophilic NAGMA provides experimental support for an explanation of the origin of the anomalous diffusion behavior of NALMA as arising from frustrated interactions between water molecules when a chemical interface is formed upon addition of a hydrophobic side chain, inducing spatial heterogeneity in the hydration dynamics in the two types of regions of the NALMA peptide. We place our QENS measurements on model biological solutes in the context of other spectroscopic techniques and provide both confirming as well as complementary dynamic information that attempts to give a unifying molecular view of hydration dynamics signatures near peptides and proteins.     

A polymer surfactant corona dynamically replaces water in solvent-free protein liquids and ensures macromolecular flexibility and activity

The observation of biological activity in solvent-free protein-polymer surfactant hybrids challenges the view of aqueous and nonaqueous solvents being unique promoters of protein dynamics linked to function. Here, we combine elastic incoherent neutron scattering and specific deuterium labeling to separately study protein and polymer motions in solvent-free hybrids. Myoglobin motions within the hybrid are found to closely resemble those of a hydrated protein, and motions of the polymer surfactant coating are similar to those of the hydration water, leading to the conclusion that the polymer surfactant coating plasticizes protein structures in a way similar to hydration water.     

The dynamics of polymer melts as seen by neutron spin echo spectroscopy

Using the neutron spin echo spectroscopy, the internal segmental diffusion of chain molecules in polymer melts and concentrated solutions was studied. These investigations show that beyond a characteristic length d_t and after a cross over time τ_e(d_t) the segmental diffusion of the single chains is strongly impeded and deviates from the Rouse dynamics. d_t is polymer specific and depends on the temperature as well as on the polymer concentration. Within the framework of the reptation concept, where d_t is identified with the mean distance between intermolecular entanglements or with the tube diameter, the microscopically determined d_t-values agree quite well with those derived from related macroscopic measurements of the plateau modulus. A similar good agreement is also found with respect to the segmental friction coefficients obtained either from the Rouse regime of the NSE spectra or from Theological data of corresponding short chain systems, where entanglements are not yet effective.