Enzyme kinetics, self-organized molecular machines, and parametric resonance

Abstract

Different models of enzymatic reactions are discussed and compared with experiments (a cytochrome P-450-dependent mono-oxygenase system). The following results are obtained. (i) Every chemical step in the reaction cycle contains approximately 5–7 substeps (approximately 40–60 steps in the cycle). (ii) In the case of too many substeps, the reaction cycle can be approximated by a continuous model. A Fokker-Planck equation is derived with drift and diffusion. The drift coefficient is determined by the measured cycle time (1.54 s) and the diffusion term by the measured memory time (2.8 times the cycle time). (iii) The enzymatic reaction can be influenced by periodic external signals. The action spectrum is described by a stochastic and parametric resonance.