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.

Diffusion dynamics, moments, and distribution of first-passage time on the protein-folding energy landscape, with applications to single molecules

We study the dynamics of protein folding via statistical energy-landscape theory. In particular, we concentrate on the local-connectivity case with the folding progress described by the fraction of native conformations. We found that the first passage-time (FPT) distribution undergoes a dynamic transition at a temperature below which the FPT distribution develops a power-law tail, a signature of the intermittent nonexponential kinetic phenomena for the folding dynamics. Possible applications to single-molecule dynamics experiments are discussed.

Branched crystal morphology of linear polyethylene crystallized in a two-dimensional diffusion-controlled growth field

The branched crystal morphology of linear polyethylene formed at various temperatures from thin films has been studied by atomic-force microscopy (AFM), transmission electron microscopy (TEM), electron diffraction (ED) pattern and polymer decoration technique. Two types of branched patterns, i.e. dendrite and seaweed patterns, have been visualized. The fractal dimension d(f) = 1.65 of both dendrite and some of seaweed patterns was obtained by using the box-counting method, although most of the seaweed patterns are compact. Selected-area ED patterns indicate that the fold stems tilt about 34.5degrees around the b-axis and polymer decoration patterns show that the chain folding direction and regularity in two (200). regions are quite different from each other. Because of chain tilting, branched crystals show three striking features: 1) the lamella-like branches show two (200) regions with different thickness; 2) the crystals usually bend towards the thin region; 3) the thick region grows faster by developing branches, thus branches usually occur outside the thick region. The branched patterns show a characteristic width w, which gives a linear relationship with the crystallization temperature on a semilogarithmic plot.

Diffusion-limited kinetics modeling of one-step polyimide formation

A diffusion-limited kinetic model was developed to describe the imidization of one-step polythioetherimide formation based on an endgroup diffusion model. The changes of conversion and viscosity during the imidization were monitored with thermogravimetric analysis and dynamic stress rheometry, respectively. It was observed that the imidization rate began to decelerate after a fast early stage, whereas the viscosity in the system increased dramatically after a period of low value. Amic acid and imide formations concurrently take place in the one-step polyimide formation, but the formation of amic acid is much slower than that of imide and is the rate-limiting step of imidization. When a second-order kinetic model was used to describe the imidization, the effect of viscosity on the diffusion resistance of reactive groups needed to be included. In order to predict the change of viscosity during the imidization, the Lipshitz-Macosko model was modified and introduced into the diffusion-limited kinetic model by the Stokes-Einstein equation. The comparison of the modeled results with experimental data indicated that the diffusion-limited kinetic model and the modified Lipshitz-Macosko model were able to efficiently predict the changes of conversion and viscosity with temperature and time during the one-step polythioetherimide formation. (C) 2001 John Wiley & Sons, Inc.

Preparation of the phosphor BaMgAl10O17 : Eu2+ by the surface diffusion method

A surface diffusion method was proposed and applied to prepare blue phosphor BaMgAl10O17:Eu2+. The results show that, compared with the direct synthesis method by common high temperature solid state, the concentration of Eu2+ in the phosphor BaMgAl10O17:Eu2+ prepared by the surface diffusion method can be greatly reduced owing to the activator Eu2+ ions distributed mainly over the surface of the phosphor. It is possible to reduce the cost of this kind of the luminescent materials with the aid of the surface diffusion method.

A study of dimethylferrocene diffusion and electrode kinetics using microelectrode voltammetry in poly(ethylene glycol) solvent

The heterogeneous electron transfer rate constant (k(s)) of dimethylferrocene (DMFc) was estimated using cyclic voltammetric peak potential separations taken typically in a mixed diffusion geometry regime in a polyelectrolyte, and the diffusion coefficient (D) of DMFc was obtained using a steady-state voltammogram. The heterogeneous electron transfer rate constant and diffusion coefficient are both smaller by about 100-fold in the polymeric solvent than in the monomeric solvent. The results are in agreement with the difference of longitudinal dielectric relaxation time (tau(L)) in the two kinds of solvents, poly(ethylene glycol) (PEG) and CH3CN, indicating that k(s) varies inversely with tau(L); k(s), is proportional to D of DMFc. Both D and k(s) of DMFc in PEG containing different supporting electrolytes and at different temperatures have been estimated. These results show that D and k(s) of DMFc increase with increasing temperature in the polyelectrolyte, whereas they vary only slightly with changing the supporting electrolyte.

A novel electrochemical method for simultaneously measuring diffusion coefficient and ion transference number

This paper introduces a new method to estimate the diffusion coefficient and transference number of a salt or an electroactive ion in a solution with little or no supporting electrolyte. The above two parameters can be obtained from a single potential step experiment without previous knowledge of either one. It would appear that the method could also be used in the study of ion transport in a high viscosity solvent or a solid electrolyte. (C) 1998 Elsevier Science S.A.

A study on the diffusion of quinhydrone in polymer electrolyte

The diffusion coefficients (D) of quinhydrone were estimated in polymer electrolytes by using non-steady-state chronoamperometry and steady-state current voltammetry. The D values have been estimated in polyethylene glycol (PEG) containing different concentrations, and cations of supporting electrolytes, and in different solvents over a range of temperatures. The dependencies of electroactive probe diffusion coefficients on temperature, supporting electrolyte concentration and polymer chain length are discussed. The results show that D increases with increasing temperature and decreasing concentration of supporting electrolyte. The diffusion coefficient depends strongly on the length of polymer chain and decreases sharply with increasing polymer chain length. The contribution of electron self-exchange has been explored and it seems to be negligible here. (C) 1998 Elsevier Science S.A.

Studies of ferrocene derivative diffusion and heterogeneous kinetics in polymer electrolyte by using microelectrode voltammetry

The heterogeneous electron transfer rate constants (k(s)) of seven ferrocene derivatives were estimated using cyclic voltammograms under mixed spherical/semi-infinite linear diffusion and steady-state voltammetry at a microdisk electrode in polymer electrolyte. The k(s) and diffusion coefficient (D) are both 100 to 1000-fold smaller in polymer solvent than in monomeric solvents, and the D and k(s) decrease with increasing polymer chain length. The results conform to the difference of viscosity (eta) or relaxation time (tau(L)) for these different solvents. The k(s) and D increase with increasing temperature, and the activation barriers of the electrode reaction are obtained. The influences of the substituting group in the ferrocene ring on k(s) and D are discussed. The k(s) are proportional to the D of the ferrocene derivatives, which indicates that solvent dynamics control the electrode reaction. (C) 1998 Elsevier Science S.A.

Physical diffusion and electron-transfer dynamics of electroactive solutes in polymer electrolytes .2. Effect of the ionic size of supporting electrolytes

The diffusion coefficients(D-app) and the heterogeneous electron-transfer rate constants(k(s)) for ferrocene in MPEG/salt electrolytes were determined by using steady-state voltammetry. The temperature dependence of the two parameters obeys the Arrhenius equation. The effect of the ionic size of six supporting electrolytes on diffusion and electron transfer dynamics of ferrocene was discussed.

Physical diffusion and electron-transfer dynamics of electroactive solutes in polymer electrolytes .3. Effect of the polymer solvents

The diffusion coefficients(D-app) and the heterogeneous electron transfer rate constants(k(s)) for ferrocene in several polymer solvents were determined by using steady-state voltammetry. The temperature dependence of the two parameters indicates Arrhenius behavior, The polymer solvent effects on diffusion and electron transfer dynamics of ferrocene were discussed.

Physical diffusion and electron-transfer dynamics of electroactive solutes in polymer electrolytes .1. Effect of the nature of electroactive solutes

The diffusion coefficients(D-app) and the heterogeneous electron-transfer rate constants(k(s)) for ferrocene and its seven derivatives in MPEG/LiClO4 electrolyte were determined by using steady-state voltammetry. The two parameters increase with increasing temperature, indicating Arrhenius behavior. The effects of the nature of electroactive solute molecules on D-app, k(s), and the half-wave potentials(E-1/2) are discussed.

An ultramicroelectrode study of ferrocene diffusion and heterogeneous electron transfer rate in polyelectrolyte

Steady-state voltammograms at a microdisk electrode are used to measure the diffusion coefficient (D) and standard heterogeneous rate constant (k(s)) of ferrocene in polyelectrolyte PEG.MClO(4). The diffusion coefficient and standard heterogeneous rate constant of ferrocene are both smaller in polymer solvents than in monomeric solvents. The D and k(s) of ferrocene have been estimated in PEG containing different concentrations and cations of supporting electrolytes, and the dependencies of D and k(s) on temperature have been observed. These results show that the D and k(s) of ferrocene increase with increasing temperature in polyelectrolyte, and with increasing cation radius of supporting electrolyte, eg D and k(s) increase in the order Bu(4)NClO(4) > NaClO4 > LiClO4. On the other hand, D and k(s) increase with decreasing concentration of supporting electrolyte. The dependence of the half-wave potential (E(1/2)) on the concentration of the supporting electrolyte is also observed. E(1/2) shifts in the negative direction as the concentration of supporting electrolyte increases. (C) 1997 Elsevier Science Ltd.