Complexity and Self-Organization in Enzyme Catalysis: Non-Kramers Behaviour of the Reaction Rate

In this paper we are mainly concerned with investigating the major qualitative predictions of a family of stochastic models which are claimed to represent the essential behaviour of the key-variables of a fairly broad class of enzyme systems. The most significant observable in this context is the reaction rate and particular attention is devoted to the predicted dependence of the rate on the solvent viscosity. We focus on the breakdown of Kramers theory to ascertain whether it is to be ascribed to the complexity of the enzyme macromolecule or to the dissipative properties of the solvent. Only some features of the non-Kramers behaviour have been previously accounted for by the coupling of intramolecular degrees of freedom. Here, variants of the original multidimensional model are discussed to shed light on the still unexplained saturation of the barrier crossing rate at very high solvent viscosities. Preliminary results indicate that this effect ensues from the non-Markov nature of the dynamics and the viscoelastic properties of the solvent irrespective of the dimensionality of the model (i.e. even in one-dimensional models).