A rate expression for enzymatic reactions. The dynamical relation between coupled oscillators at the active site and the rate enhancement of enzyme-catalysed processes

Abstract

The barriers for decarboxylation of various forms of the biotin analogue N-carboxy-2-imidazolidinone (1) and related systems have been discussed. None of the systems exhibits a significant reduction in classical barrier with respect to the gas phase process that might account for the enzymatic activity. The role of dynamical effects at the active site of the enzymes has been examined by stochastic dynamic simulation. The microscopic parameters for interparticle interactions have been obtained through ab initio and density functional theory calculations at the MP2 and B3LYP levels. The numerical analysis of a model system embedded in a harmonic bath shows how the vibrational density of states of the bath significantly affects its response factor. A statistical treatment of a system with more than one critical oscillator cooperating with the reaction coordinate exhibits a dramatic increase in rate with respect to the corresponding system with only one active critical oscillator. A quantitative interpretation of enzymatic activity in this hypothesis and its relationship with a classical Arrhenius analysis are offered.