Short-time dynamics of proteins in solutions studied by neutron spin echo

Dynamics of proteins in solutions include translational, rotational, and internal motions that are linked to different protein properties. Because most proteins are small with the sizes of just a few nanometers, the timescale for their short-time dynamics usually ranges from a few nanoseconds to a few hundreds of nanoseconds, during which a protein usually does not rotate too much. Protein short-time dynamics has been shown to be useful to study liquid theories, protein cluster formation, gelation transitions of concentrated protein systems, and protein internal motions. Neutron spin echo, which is able to measure protein motions with the right correlation time at the appropriate length scale, is ideally suitable to study the short-time dynamics of proteins in solutions. Here, we review recent activities of using neutron spin echo to study the protein short-time motions. Despite all progresses, there are still both theoretical and experimental challenges to exploit the full capability of neutron spin echo to study protein dynamics.     

Short-time behavior of mixed diffusion-barrier controlled adsorption

This paper focuses on the short-time adsorption kinetics of nonionic surfactants onto water/air surfaces, analyzed in the context of the mixed diffusion-barrier controlled adsorption modeling framework. Specifically, we reconcile the apparent contradiction between theoretical prediction and experimental observations on the adsorption kinetics mechanism at short times: while the mixed diffusion-barrier controlled model predicts a barrier-controlled adsorption, as well as the impossibility of a diffusion-controlled adsorption at asymptotic short times, the short-time experimental dynamic surface tension (DST) behavior of many nonionic surfactants has been interpreted to result from diffusion-controlled adsorption at asymptotic short times. This is because the short-time experimental DST of these surfactants displays a t variation, which is considered as a fingerprint for the existence of diffusion-controlled adsorption, based on the short-time asymptotic behavior of the diffusion-controlled adsorption model. As a result of this interpretation, the fundamental physical nature of the energy barrier has been proposed to be associated with high surfactant surface concentrations. In this paper, we derive a new nonasymptotic short-time formalism of the mixed diffusion-barrier controlled model to describe surfactant adsorption onto a spherical pendant-bubble surface, including determining the ranges of time and surfactant surface concentration values where the short-time formalism is applicable. Based on this formalism, we find that one can expect to observe an apparent t variation of the DST at short times even for the mixed diffusion-barrier controlled adsorption model. We analyze the consequence of this finding by re-evaluating the existing notions of the energy barrier. We conclude that the energy barrier is associated with the adsorption of a single surfactant molecule onto a clean surface.     

Molecular dynamics of some crotonates using infrared band shapes

The dipole correlation function of three esters of crotonic acid have been computed from the infrared absorption bands. Both short-time and long-time behaviour of the correlation functions are computed and discussed. The correlation times are also calculated. The short-time behaviour was compared with the correlation functions generated as an even-power series with second and fourth moments. They were also compared with the correlation functions of the freely rotating molecule.     

Modeling velocity autocorrelation functions for confined fluids using gamma distributions

We propose a model for the short-time dynamics of fluids confined in slit-shaped pores. The model has been developed from the observation that the real lobe of the instantaneous normal mode density of states (INM DOS) closely follows a gamma distribution. By proposing that the density of states of the confined fluid can be represented by a gamma distribution, the resulting velocity autocorrelation function (VACF) is constructed such that it is accurate upto the fourth frequency moment. The proposed model results in an analytical expression for the VACF and relaxation times. The VACFs obtained from the model have been compared with the VACFs obtained from molecular dynamic simulations and INM analysis for fluids confined in slit-shaped pores over a wide range of confinement and temperatures. The model is seen to capture the short-time behavior of the VACF extremely accurately and in this region is superior to the predictions of the VACF obtained from the real lobe of the INM DOS. Although the model predicts a zero self-diffusivity, the predicted relaxation times are in better agreement with the molecular dynamics results when compared with those obtained from the INM theory.     

Highly optimized fourth-order short-time approximation for path integrals

We derive a fourth-order short-time approximation for use in imaginary-time path-integral simulations. The short-time approximation converges for all continuous and bounded-from-below potentials, attains quartic order of convergence for sufficiently smooth potentials, and utilizes statistically independent random variables for its construction. These properties recommend the approximation as a natural replacement of the trapezoidal Trotter-Suzuki approximation for physical systems with continuous distributions.     

On the Use of Atmospheric Pressure Plasma for the Bio-Decontamination of Polymers and Its Impact on Their Chemical and Morphological Surface Properties

Low temperature atmospheric pressure plasma processes can be applied to inactivate micro-organisms on products and devices made from synthetic and natural polymers. This study shows that even a short-time exposure to Ar or Ar/O₂ plasma of an atmospheric pressure plasma jet leads to an inactivation of Bacillus atrophaeus spores with a maximum reduction of 4 orders of magnitude. However, changes in the surface properties of the plasma exposed material have to be considered, too. Therefore, polyethylene and polystyrene are used as exemplary substrate materials to investigate the effect of plasma treatment in more detail. The influence of process parameters, such as type of operating gas or jet-nozzle to substrate distance, is examined. The results show that short-time plasma treatment with Ar and Ar/O₂ affects the surface wettability due to the introduction of polar groups as proofed by X-ray photoelectron spectroscopy. Furthermore, atomic force microscopy images reveal changes in the surface topography. Thus, nanostructures of different heights are observed on the polymeric surface depending on the treatment time and type of process gas.     

Investigation of vibronic energy relaxation of polymethin cyanine dyes by picosecond spectroscopy

The vibronic energy relaxation times of some polymethin cyanine dyes in dependence on temperature have been measured by using picosecond fluorescence spectroscopy. The results should be explained by means of the hypothesis of short-time conformation change during the relaxation process.     

Time-dependent step–step correlations in a self-avoiding random walk

The space–time step–step correlations of a polymer chain, described by a self-avoiding random walk on a cubic lattice, are studied by simulating its behavior on a computer. Chains of N = 16 and N = 32 beads are studied. The short-time behavior of the correlations is characterized by peaks, which become depressed and broadened with increasing interstep distance. The long-time behavior is characterized by extremely slow decay, which goes to zero in about the same time for all interstep distances. The short-time behavior is a consequence of the rotation of parts of the chain smaller than or equal to the static coherence length ζ. These short-time processes also seem to be responsible for the relaxation of the square of the end-to-end distance, since in both cases the relaxation is of the order of 6N². The long-time behavior of the correlations is a consequence of the rotations of parts of the chain greater than the coherence length. The correlations vanish when the entire chain has had time to rotate in space. Our results suggest that this corresponds to the relaxation of the end-to-end vector.     

Collective diffusion in charge-stabilized suspensions: concentration and salt effects

The authors present a joint experimental-theoretical study of collective diffusion properties in aqueous suspensions of charge-stabilized fluorinated latex spheres. Small-angle x-ray scattering and x-ray photon correlation spectroscopy have been used to explore the concentration and ionic-strength dependence of the static and short-time dynamic properties including the hydrodynamic function H(q), the wave-number-dependent collective diffusion coefficient D(q), and the intermediate scattering function over the entire accessible range. They show that all experimental data can be quantitatively described and explained by means of a recently developed accelerated Stokesian dynamics simulation method, in combination with a modified hydrodynamic many-body theory. In particular, the behavior of H(q) for de-ionized and dense suspensions can be attributed to the influence of many-body hydrodynamics, without any need for postulating hydrodynamic screening to be present, as it was done in earlier work. Upper and lower boundaries are provided for the peak height of the hydrodynamic function and for the short-time self-diffusion coefficient over the entire range of added salt concentrations.     

Short-time dynamics through conical intersections in macrosystems. I. Theory: effective-mode formulation

The short-time dynamics through a conical intersection of a macrosystem comprising a large number of nuclear degrees of freedom (modes) is investigated. The macrosystem is decomposed into a "system" part carrying a limited number of modes, and an "environment" part. An orthogonal transformation in the environment's space is introduced, as a result of which a subset of three effective modes can be identified which couple directly to the electronic subsystem. Together with the system's modes, these govern the short-time dynamics of the overall macrosystem. The remaining environmental modes couple, in turn, to the effective modes and become relevant at longer times. In this paper, we present the derivation of the effective Hamiltonian, first introduced by Cederbaum et al. [Phys. Rev. Lett. 94, 113003 (2005)], and analyze its properties in some detail. Several special cases and topological aspects are discussed.     

Study of UVA irradiation on hemoglobin in the presence of NADH

Reduction of ferric methemoglobin (metHb) to its ferrous form is observed by short-time ultraviolet A (UVA) irradiation of metHb together with nicotinamide adenine dinucleotide (NADH). And, severely structural destruction of metHb occurs when long-time UVA irradiation is exerted. However, neither reduction nor destruction can be observed in the absence of NADH under otherwise the same experimental conditions. Accordingly, the O2-binding ability of the protein increases by short-time UVA irradiation of metHb together with NADH, which corresponds with the reduction of metHb, while it decreases by long-time UVA irradiation, which corresponds with the structural destruction. Besides, it is found that the reduction reaction and the conformational destruction proceed more rapidly with higher concentrations of NADH.     

Hierarchy of effective modes for the dynamics through conical intersections in macrosystems

An extension of the effective-mode theory for the short-time dynamics through conical intersections in macrosystems [L. S. Cederbaum et al., Phys. Rev. Lett. 94, 113003 (2005)] is proposed. The macrosystem, containing a vast number of nuclear degrees of freedom (modes), is decomposed into a system part and an environment part. Only three effective modes are needed-together with the system's modes-to accurately calculate low resolution spectra and the short-time dynamics of the entire macrosystem. Here, the authors propose an iterative scheme to construct a hierarchy of additional triplets of effective modes. This naturally extends the effective-mode formulation. By taking into account more and more triplets, the dynamics are accurately predicted for longer and longer times, and more resolved spectra can be calculated. Numerical examples are presented, computed using various numbers of additional effective modes.     

Short-time transport properties in dense suspensions: from neutral to charge-stabilized colloidal spheres

We present a detailed study of short-time dynamic properties in concentrated suspensions of charge-stabilized and of neutral colloidal spheres. The particles in many of these systems are subject to significant many-body hydrodynamic interactions. A recently developed accelerated Stokesian dynamics (ASD) simulation method is used to calculate hydrodynamic functions, wave-number-dependent collective diffusion coefficients, self-diffusion and sedimentation coefficients, and high-frequency limiting viscosities. The dynamic properties are discussed in dependence on the particle concentration and salt content. Our ASD simulation results are compared with existing theoretical predictions, notably those of the renormalized density fluctuation expansion method of Beenakker and Mazur [Physica A 126, 349 (1984)], and earlier simulation data on hard spheres. The range of applicability and the accuracy of various theoretical expressions for short-time properties are explored through comparison with the simulation data. We analyze, in particular, the validity of generalized Stokes-Einstein relations relating short-time diffusion properties to the high-frequency limiting viscosity, and we point to the distinctly different behavior of de-ionized charge-stabilized systems in comparison to hard spheres.     

Time-dependent approaches for the calculation of intersystem crossing rates

We present three formulas for calculating intersystem crossing rates in the Condon approximation to the golden rule by means of a time-dependent approach: an expression using the full time correlation function which is exact for harmonic oscillators, a second-order cumulant expansion, and a short-time approximation of this expression. While the exact expression and the cumulant expansion require numerical integration of the time correlation function, the integration of the short-time expansion can be performed analytically. To ensure convergence in the presence of large oscillations of the correlation function, we use a Gaussian damping function. The strengths and weaknesses of these approaches as well as the dependence of the results on the choice of the technical parameters of the time integration are assessed on four test examples, i.e., the nonradiative S(1) ? T(1) transitions in thymine, phenalenone, flavone, and porphyrin. The obtained rate constants are compared with previous results of a time-independent approach. Very good agreement between the literature values and the integrals over the full time correlation functions are observed. Furthermore, the comparison suggests that the cumulant expansion approximates the exact expression very well while allowing the interval of the time integration to be significantly shorter. In cases with sufficiently high vibrational density of states also the short-time approximation yields rates in good agreement with the results of the exact formula. A great advantage of the time-dependent approach over the time-independent approach is its excellent computational efficiency making it the method of choice in cases of large energy gaps, large numbers of normal modes, and high densities of final vibrational states.     

New methodology to determine the rate-limiting adsorption kinetics mechanism from experimental dynamic surface tension data

We present a new methodology to determine the rate-limiting adsorption kinetics mechanism (diffusion-controlled vs mixed diffusion-barrier controlled), including deducing the kinetics parameters (the diffusion coefficient, D, and the energy-barrier parameter, beta), from the experimental short-time dynamic surface tension (DST) data. The new methodology has the following advantages over the existing procedure used to analyze the experimental DST data: (a) it does not require using a model for the equilibrium adsorption isotherm, and (b) it only requires using the experimental short-time DST data measured at two initial surfactant bulk solution concentrations. We apply the new methodology to analyze the experimental short-time DST data of the following alkyl poly(ethylene oxide), CiEj, nonionic surfactants: C12E4, C12E6, C12E8, and C10E8 measured using the pendant-bubble apparatus. We find that for C12E4 and C12E6, the effect of the energy barrier on the overall rate of surfactant adsorption can be neglected for surfactant bulk solution concentrations below their respective critical micelle concentrations (CMCs), and therefore, that the rate-limiting adsorption kinetics mechanism for C12E4 and C12E6 is diffusion-controlled at any of their premicellar surfactant bulk solution concentrations. On the other hand, for C12E8 and C10E8, we find that their respective CMC values are large enough to observe a significant effect of the energy barrier on the overall rate of surfactant adsorption. In other words, for C12E8 and C10E8, the rate-limiting adsorption kinetics mechanism shifts from diffusion-controlled to mixed diffusion-barrier controlled as their premicellar surfactant bulk solution concentrations increase. We test the new methodology by predicting the short-time DST profiles at other initial surfactant bulk solution concentrations, and then comparing the predicted DST profiles with those measured experimentally. Very good agreement is obtained for the four CiEj nonionic surfactants considered. We also compare the results of implementing the new methodology with those of implementing the existing procedure, and conclude that using a model for the equilibrium adsorption isotherm can lead not only to different values of D and beta, but it can also lead to a completely different determination of the rate-limiting adsorption kinetics mechanism. Since the new methodology proposed here does not require using a model for the equilibrium adsorption isotherm, we conclude that it should provide a more reliable determination of the rate-limiting adsorption kinetics mechanism, including the deduced kinetics parameters, D and beta.     

Transport properties of normal liquid helium: comparison of various methodologies

We revisit the problem of self-diffusion in normal liquid helium above the lambda transition. Several different methods are applied to compute the velocity autocorrelation function. Since it is still impossible to determine the exact result for the velocity autocorrelation function from simulation, we appeal to the computation of short-time moments to determine the accuracy of the different approaches at short times. The main conclusion reached from our study is that both the quantum mode-coupling theory and the numerical analytic continuation approach must be regarded as a viable and competitive methods for the computation of dynamical properties of quantum systems.     

Polar solvation dynamics in supercritical fluids: a mode-coupling treatment

A mode-coupling treatment of polar solvation dynamics in supercritical fluids is presented. The equilibrium solvation time correlation function for the solute fluctuating transition frequency is obtained from the mode-coupling theory method and from molecular-dynamics simulations. The theory is shown to be in good agreement with the simulation. The solvation time correlation function exhibits three distinct time scales, with rapid initial decay, followed by a recurrence at intermediate times, and a slowly decaying long-time tail. Our theoretical analysis shows that the short-time decay arises from the coupling of the solute energy gap to the solvent polarization modes, the recurrence at intermediate times is due to the energy modes, while the slow long-time decay reflects the coupling to the number density modes.     

T ≠ 0 K Multimode modeling of optical absorption spectra and resonance Raman profiles

We discuss the superiority of the time-correlator approach over conventional sum-over-states methods for exact multimode modeling of T ≠ 0 K optical absorption and resonance Raman profiles. Numerical illustrations of thermal broadening are given, and a short-time approximation is shown to be very convenient for modeling this effect.     

A Surrogate for Debye-Waller Factors from Dynamic Stokes Shifts

We show that the short-time behavior of time-resolved fluorescence Stokes shifts (TRSS) are similar to that of the intermediate scattering function obtained from neutron scattering at q near the peak in the static structure factor for glycerol. This allows us to extract a Debye-Waller (DW) factor analog from TRSS data at times as short as 1 ps in a relatively simple way. Using the time-domain relaxation data obtained by this method we show that DW factors evaluated at times ≥ 40 ps can be directly influenced by α relaxation and thus should be used with caution when evaluating relationships between fast and slow dynamics in glassforming systems.