Hierarchically constrained dynamics of the configurational coordinate for rate processes in complex systems

Recent Developments in Dispersive Kinetics

In general, chemical reactions proceeding on time scales comparable to, or shorter than, those of internal rearrangements in a reaction system renewing the environment of the reactants (mixing), are dispersive. For dispersive kinetics, as for dispersive transport and dispersive relaxation, many time scales coexist. The rate coefficients for dispersive processes depend on time. For a time-dependent specific reaction rate, using the concept of energy profile along the reaction path, one finds the potential energy barrier separating reactants from products to evolve in time during the course of reaction. The evolution of the energy barrier during the course of reaction is described in terms of energy distribution functions related directly to the distribution function of logarithms of lifetimes calculable from kinetic equations with a time-dependent specific reaction rate. This phenomenological approach is compared with that in which the kinetic equations with time-dependent specific reaction rates are interpreted in terms of the superposition of classical reaction patterns. Special attention is paid to renor-malization of rate coefficients following from the stochastic theory of renewals (structural relaxation) in the reaction system. This phenomenological approach to kinetics is taken as a convenient basis to present a number of comprehensive models of dispersive kinetics developed in the 1990s and to discuss some recently published experimental data to show what one derives directly from experimental data and what the detailed mechanistic models have to account for to be acceptable.

Wait-and-switch relaxation model: relationship between nonexponential relaxation patterns and random local properties of a complex system

The wait-and-switch stochastic model of relaxation is presented. Using the "random-variable" formalism of limit theorems of probability theory we explain the universality of the short- and long-time fractional-power laws in relaxation responses of complex systems. We show that the time evolution of the nonequilibrium state of a macroscopic system depends on two stochastic mechanisms: one, which determines the local statistical properties of the relaxing entities, and the other one, which determines the number (random or deterministic) of the microscopic and mesoscopic relaxation contributions. Within the proposed framework we derive the Havriliak-Negami and Kohlrausch-Williams-Watts functions. We also discuss the influence of the random-walk characteristics of migrating defects on the homogeneous and heterogeneous relaxation scenarios and show the origins of the stretched-exponential integral kernel in the integral representation of the ensemble-averaged relaxation function.

Trehalose effect on low temperature protein dynamics: fluctuation and relaxation phenomena

We performed spectral diffusion experiments in trehalose-enriched glycerol/buffer-glass on horseradish peroxidase where the heme was replaced by metal-free mesoporphyrin IX, and compared them with the respective behavior in a pure glycerol/buffer-glass (Schlichter et al., J. Chem. Phys. 2000, 112:3045-3050). Trehalose has a significant influence: spectral diffusion broadening speeds up compared to the trehalose-free glass. This speeding up is attributed to a shortening of the correlation time of the frequency fluctuations most probably by preventing water molecules from leaving the protein interior. Superimposed to the frequency fluctuation dynamics is a relaxation dynamics that manifests itself as an aging process in the spectral diffusion broadening. Although the trehalose environment speeds up the fluctuations, it does not have any influence on the relaxation. Both relaxation and fluctuations are governed by power laws in time. The respective exponents do not seem to change with the protein environment. From the spectral dynamics, the mean square displacement in conformation space can be determined. It is governed by anomalous diffusion. The associated frequency correlation time is incredibly long, demonstrating that proteins at low temperatures are truly nonergodic systems.