First-passage time distribution and non-Markovian diffusion dynamics of protein folding

We study the kinetics of protein folding via statistical energy landscape theory. We concentrate on the local-connectivity case, where the configurational changes can only occur among neighboring states, with the folding progress described in terms of an order parameter given by the fraction of native conformations. The non-Markovian diffusion dynamics is analyzed in detail and an expression for the mean first-passage time (MFPT) from non-native unfolded states to native folded state is obtained. It was found that the MFPT has a V-shaped dependence on the temperature. We also find that the MFPT is shortened as one increases the gap between the energy of the native and average non-native folded states relative to the fluctuations of the energy landscape. The second- and higher-order moments are studied to infer the first-passage time distribution. At high temperature, the distribution becomes close to a Poisson distribution, while at low temperatures the distribution becomes a Levy-type distribution with power-law tails, indicating a nonself-averaging intermittent behavior of folding dynamics. We note the likely relevance of this result to single-molecule dynamics experiments, where a power law (Levy) distribution of the relaxation time of the underlined protein energy landscape is observed.

IONIC-CONDUCTIVITY AND DYNAMIC MECHANICAL RELAXATION OF A 2-COMPONENT EPOXY NETWORK-LICLO4 ELECTROLYTE SYSTEM

The correlation between mechanical relaxation and ionic conductivity was investigated in a two-component epoxy network-LiClO4 electrolyte system. The network was composed of diglycidyl ether of polyethylene glycol (DGEPEG) and triglycidyl ether of glycerol (TGEG). The effects of salt concentration, molecular weight of PEG in DGEPEG and the proportion of DGEPEG (1000) in DGEPEG/TGEG ratio on the ionic conductivity and the mechanical relaxation of the system were studied. It was found that, among the three influential factors, the former reinforces the network chains, reduces the free volume fraction and thus increases the relaxation time of the segmental motion, which in turn lowers the ionic conductivity of the specimen. Conversely, the latter two increase the free volume and thus the chain flexibility, showing an opposite effect. From the iso-free-volume plot of the shift factor log at and reduced ionic conductivity, it is noted that the plot can be used to examine the temperature dependence of segmental mobility and seems to be useful to judge whether the incorporated salt has been dissociated completely. Besides, the ionic conductivity and relaxation time at constant reference temperature are linearly correlated with each other in all the three cases. This result gives an additional experimental confirmation of the coordinated motion model of the ionic hopping with the moving polymer chain segment, which is generally used to explain the ionic conduction in non-glassy amorphous polymer electrolytes.

Laser-heated high-temperature NMR - a time-resolution study

Submitted to Appl Magn Reson Sponsorship: EPSRC / EU

Stress Relaxation for Granular Materials near Jamming under Cyclic Compression.

We have explored isotropically jammed states of semi-2D granular materials through cyclic compression. In each compression cycle, systems of either identical ellipses or bidisperse disks transition between jammed and unjammed states. We determine the evolution of the average pressure P and structure through consecutive jammed states. We observe a transition point ϕ_{m} above which P persists over many cycles; below ϕ_{m}, P relaxes slowly. The relaxation time scale associated with P increases with packing fraction, while the relaxation time scale for collective particle motion remains constant. The collective motion of the ellipses is hindered compared to disks because of the rotational constraints on elliptical particles.

Measuring distributions of jump rates in disordered metal–hydrogen systems by nuclear magnetic relaxation

Monte Carlo calculations of the nuclear magnetic relaxation rate in a disordered metal–hydrogen system having a distribution of jump rates are reported. The calculations deal specifically with the spin-locked rotating-frame relaxation time T1ρ. The results demonstrate that the temperature variation of the rate is only weakly dependent on the distribution and it is therefore unlikely that the jump rate distribution can be extracted from relaxation measurements in which temperature is the main variable. It is shown that the alternative of measuring the relaxation rate over a wide range of spin-locking field strengths at a constant temperature can lead to an evaluation of the distribution.

Escape times for rigid Brownian rotators in a bistable potential from the time evolution of the Green function and the characteristic time of the probability evolution

The greatest relaxation time for an assembly of three- dimensional rigid rotators in an axially symmetric bistable potential is obtained exactly in terms of continued fractions as a sum of the zero frequency decay functions (averages of the Legendre polynomials) of the system. This is accomplished by studying the entire time evolution of the Green function (transition probability) by expanding the time dependent distribution as a Fourier series and proceeding to the zero frequency limit of the Laplace transform of that distribution. The procedure is entirely analogous to the calculation of the characteristic time of the probability evolution (the integral of the configuration space probability density function with respect to the position co-ordinate) for a particle undergoing translational diffusion in a potential; a concept originally used by Malakhov and Pankratov (Physica A 229 (1996) 109). This procedure allowed them to obtain exact solutions of the Kramers one-dimensional translational escape rate problem for piecewise parabolic potentials. The solution was accomplished by posing the problem in terms of the appropriate Sturm-Liouville equation which could be solved in terms of the parabolic cylinder functions. The method (as applied to rotational problems and posed in terms of recurrence relations for the decay functions, i.e., the Brinkman approach c.f. Blomberg, Physica A 86 (1977) 49, as opposed to the Sturm-Liouville one) demonstrates clearly that the greatest relaxation time unlike the integral relaxation time which is governed by a single decay function (albeit coupled to all the others in non-linear fashion via the underlying recurrence relation) is governed by a sum of decay functions. The method is easily generalized to multidimensional state spaces by matrix continued fraction methods allowing one to treat non-axially symmetric potentials, where the distribution function is governed by two state variables. (C) 2001 Elsevier Science B.V. All rights reserved.

A variational approach to the relaxation of single domain magnetic particles based on Brown's model

Brown's model for the relaxation of the magnetization of a single domain ferromagnetic particle is considered. This model results in the Fokker-Planck equation of the process. The solution of this equation in the cases of most interest is non- trivial. The probability density of orientations of the magnetization in the Fokker-Planck equation can be expanded in terms of an infinite set of eigenfunctions and their corresponding eigenvalues where these obey a Sturm-Liouville type equation. A variational principle is applied to the solution of this equation in the case of an axially symmetric potential. The first (non-zero) eigenvalue, corresponding to the largest time constant, is considered. From this we obtain two new results. Firstly, an approximate minimising trial function is obtained which allows calculation of a rigorous upper bound. Secondly, a new upper bound formula is derived based on the Euler-Lagrange condition. This leads to very accurate calculation of the eigenvalue but also, interestingly, from this, use of the simplest trial function yields an equivalent result to the correlation time of Coffey et at. and the integral relaxation time of Garanin. (C) 2004 Elsevier B.V. All rights reserved.

A29 NMR spin-lattice relaxation study of paramagnetics -doped orthosilictes

A ~si MAS NMR study of spin-lattice relaxation behaviour in paramagnetic-doped crystalline silicates was undertaken, using synthetic magnesium orthosilicate (forsterite) and synthetic zinc orthosilicate (willemite) doped with 0.1% to 20% of Co(II), Ni(II), or CU(II), as experimental systems. All of the samples studied exhibited a longitudinal magnetization return to the Boltzmann distribution of nuclear spin states which followed a stretched-exponential function of time: Y=exp [- (tjTn) n], Orelaxation time and paramagnetic dopant ion concentration, with Tni[M2+]i=Tnj[M2+]j for a given dopant and mineral. There are many cases where this correlation is not apparent, however, and this is attributed to the structural, phase, and ion distribution complexities inherent in many of these systems.

Significance of cross correlations in the stress relaxation of polymer melts

According to linear response theory, all relaxation functions in the linear regime can be obtained using time correlation functions calculated under equilibrium. In this paper, we demonstrate that the cross correlations make a significant contribution to the partial stress relaxation functions in polymer melts. We present two illustrations in the context of polymer rheology using (1) Brownian dynamics simulations of a single chain model for entangled polymers, the slip-spring model, and (2) molecular dynamics simulations of a multichain model. Using the single chain model, we analyze the contribution of the confining potential to the stress relaxation and the plateau modulus. Although the idea is illustrated with a particular model, it applies to any single chain model that uses a potential to confine the motion of the chains. This leads us to question some of the assumptions behind the tube theory, especially the meaning of the entanglement molecular weight obtained from the plateau modulus. To shed some light on this issue, we study the contribution of the nonbonded excluded-volume interactions to the stress relaxation using the multichain model. The proportionality of the bonded/nonbonded contributions to the total stress relaxation (after a density dependent "colloidal" relaxation time) provides some insight into the success of the tube theory in spite of using questionable assumptions. The proportionality indicates that the shape of the relaxation spectrum can indeed be reproduced using the tube theory and the problem is reduced to that of finding the correct prefactor. (c) 2007 American Institute of Physics

Relaxation of surface tension in the liquid-solid interfaces of Lennard-Jones liquids

We have established the surface tension relaxation time in the liquid-solid interfaces of Lennard-Jones (LJ) liquids by means of direct measurements in molecular dynamics (MD) simulations. The main result is that the relaxation time is found to be almost independent of the molecular structures and viscosity of the liquids (at seventy-fold change) used in our study and lies in such a range that in slow hydrodynamic motion the interfaces are expected to be at equilibrium. The implications of our results for the modelling of dynamic wetting processes and interpretation of dynamic contact angle data are discussed.

Short-time dynamics of percolation observables

We consider the critical short-time evolution of magnetic and droplet-percolation order parameters for the Ising model in two and three dimensions, through Monte Carlo simulations with the (local) heat-bath method. We find qualitatively different dynamic behaviors for the two types of order parameters. More precisely, we find that the percolation order parameter does not have a power-law behavior as encountered for the magnetization, but develops a scale (related to the relaxation time to equilibrium) in the Monte Carlo time. We argue that this difference is due to the difficulty in forming large clusters at the early stages of the evolution. Our results show that, although the descriptions in terms of magnetic and percolation order parameters may be equivalent in the equilibrium regime, greater care must be taken to interpret percolation observables at short times. In particular, this concerns the attempts to describe the dynamics of the deconfinement phase transition in QCD using cluster observables.

Dipole relaxation current in n-type AlxGa1-xAs

We report for the first time the thermally stimulated depolarization current (TSDC) spectrum for a direct band-gap AlGaAs sample, where the presence of DX centers is clearly observed by photoconductivity measurements. A TSDC band is obtained, revealing the presence of dipoles, which could be attributed to DX--d+ pairs as indeed predicted by O'Reilly [Appl. Phys. Lett. 55, 1409 (1989)]. The data are fitted by relaxation time distribution approach yielding an average activation energy of 0.108 eV. This is the most striking feature of our data, since this energy has approximately the same value of the DX center binding energy.

Chromophore relaxation in a side-chain methacrylate copolymer functionalized with 4-[N-ethyl-N-(2-hydroxyethyl)]amino-2 '-chloro-4 '-nitroazobenzene

A side-chain methacrylate copolymer functionalized with the nonlinear optical chromophore 4-[N-ethyl-N-(2-hydroxyethyl)]amino-2'-chloro-4'-nitroazobenzene, disperse red-13, was prepared and characterized. The chromophore relaxation was investigated measuring the decay of the electrooptic coefficient r(13) and the complex dielectric constant at different temperatures. Results obtained below and above T-g were analyzed using the Kohlrausch-Williams-Watts(KWW) equation, through the study of the temperature dependence of the KWW parameters. Above T-g the relaxation time experimental data were fitted to the Williams-Landel-Ferry (WLF) equation and its parameters determined. Chromophore relaxation leading to the decrease of electrooptic properties was found associated with a primary alpha relaxation. The obtained WLF equation parameters were introduced into the Adam-Gibbs-Tool-Narayanaswamy-Moynihan equation, and the overall relaxation time temperature dependence was successfully obtained in terms of the fictive temperature, accounting for the sample thermal treatment and allowing optimized thermal treatment to be found. The copolymer KWW stretching parameter at the glass transition temperature lies close to the limit value for short-range interactions, i.e., 0.6, suggesting that the chromophore group is participating in primary a relaxation.

Nuclear magnetic relaxation of F-19 in fluoride glasses

Temperature and frequency dependence of the F-19 nuclear spin relaxation of the fluoroindate glass, 40InF(3)-20ZnF(2)- 20SrF(2)-2GaF(3)-2NaF-16BaF(2) and the fluorozirconate glass, 50ZrF(4)-20BaF(2)-21LiF-5LaF(3)-4AlF(3); are reported. Measurements were undertaken on pure and Gd3+ doped samples, in the temperature range of 185-1000 K, covering the region below and above the glass transition temperature, T-g. The temperature and frequency dependence of the spin-lattice relaxation rate, T-1(-1), measured in the glassy state at temperature <300 K, is less than the observed dependence at higher temperatures. At temperatures >T-g, the fluorine mobility increases, leading to a more efficient spins lattice relaxation process. Activation energies, for F- motion, are 0.8 eV for the fluoroindate glass and 1 eV for the fluorozirconate glass. The addition of Gd3+ paramagnetic impurities;at 0.1-wt%, does not alter the temperature and frequency dependence of T-1(-1), but increases its magnitude more than one order of magnitude. At temperatures <400 K, the spin-spin relaxation time, T-2(-1), measured for all samples, is determined by the rigid-lattice nuclear dipole-dipole coupling, and it is temperature independent within the accuracy of the measurements. Results obtained for the pure glass, at temperatures >400 K, show that T-2(-1) decreases monotonically as the temperature increases. This decrease is explained as a consequence of the motional narrowing effect caused by the onset of the diffusive motion of the F- ions, with an activation energy around 0.8 eV. For the doped samples, the hyperfine interaction with the paramagnetic impurities is most effective in the relaxation of the nuclear spin, causing an increase in the T(2)(-1)s observed at temperatures >600 K. (C) 1999 Elsevier B.V. B.V. All rights reserved.

Interaction between poly(ethylene glycol) and C12E8 investigated by dynamic light scattering, time-resolved fluorescence quenching, and calorimetry

Dynamic light scattering (DLS), time-resolved fluorescence quenching (TRFQ), and isothermal titration microcalorimetry have been used to show that, in dilute solution, low molecular weight poly(ethylene glycol) (PEG, M-w = 12 kDa) interacts with the nonionic surfactant octaethylene glycol n-dodecyl monoether, C12E8, to form a complex. Whereas the relaxation time distributions for the binary C12E8/water and PEG/water systems are unimodal, in the ternary mixtures they may be either uni- or bimodal depending on the relative concentrations of the components. At low concentrations of PEG or surfactant, the components of the relaxation time distribution are unresolvable, but the distribution becomes bimodal at higher concentrations of either polymer or surfactant. For the ternary system in excess surfactant, we ascribe, on the basis of the changes in apparent hydrodynamic radii and the scattered intensities, the fast mode to a single micelle, the surface of which is associated with the polymer and the slow mode to a similar complex but containing two or three micelles per PEG chain. Titration microcalorimetry results show that the interaction between C12E8, and PEG is exothermic and about 1 kJ mol(-1) at concentrations higher than the CMC of C12E8. The aggregation number, obtained by TRFQ, is roughly constant when either the PEG or the C12E8 concentration is increased at a given concentration of the second component, owing to the increasing amount of surfactant micelles inside the complex.