Disordered Kinetic Systems

In the usual mass action chemical kinetics the rate coefficients are parameters with fixed values; these values may change with temperature, pressure, and possibly ionic strength for reactions among ions. In the field of disordered kinetics we broaden the study to systems in which the rate coefficients may vary. For some prior reviews on disordered kinetics, see [1–5].

Rate coefficients may vary due to environmental fluctuations and there are two categories of disorder: static and dynamic. In systems with static disorder the fluctuations of the environment are frozen and one fluctuation, once it occurs, lasts forever. For these systems, the fluctuations are introduced in the theoretical description by using random initial or random boundary conditions. (Thermal fluctuations are usually too small to be considered.) A typical example of a chemical reaction in a system with static disorder is a combination of an active intermediate in radiation chemistry in a disordered material, such as the sulphuric acid glass [6, 7]. The radiation of the active intermediate produces a reaction and the rate of that reaction differs at different sites in the glass. In systems with dynamical disorder the structure of the environment changes as the reaction progresses and the rate coefficients are random in time. An example of dynamic disorder is that of an enzyme in which a catalyzed reaction takes place at the active site of the enzyme and the rate of that reaction may depend on the configuration of the enzyme. As that configuration changes in time so does the rate coefficient of the catalytic reaction [8, 9].

The same system can display both types of disorder, depending on external conditions. For example, in the case of protein–ligand interactions [8, 9], the reaction rates are random because a protein can exist in many different molecular conformations, each conformation being characterized by a different reaction rate. At low temperatures, the transitions among the different conformations can be neglected, and the system displays static disorder. For higher temperatures, however, the transitions among the different conformations cannot be neglected, and the system displays dynamical disorder.