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

The barriers for decarboxylation of various. forms of the biotin analogue N -carboxy-2-imidazolidinone (1) and related systems have been discussed. Non e of the systems exhibits a significant reduction in classical barrier with respect to the gas phase process that might account for the enzymatic acti vity. The role of dynamical effects at the active site of the enzymes has b een examined by stochastic dynamic simulation. The microscopic parameters f or interparticle interactions have been obtained through ab initio and dens ity functional theory calculations at the MP2 and B3LYP levels. The numeric al analysis of a model system embedded in a harmonic bath shows how the vib rational density of states of the bath significantly affects its response f actor. A statistical treatment of a system with more than one critical osci llator cooperating with the reaction coordinate exhibits a dramatic increas e in rate with respect to the corresponding system with only one active cri tical oscillator.. A quantitative interpretation of enzymatic activity in t his hypothesis and its relationship with a classical Arrhenius analysis are offered.