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Abstract

This work contains theoretical investigations of the kinetics of enzymic reactions under the conditions of small spatial volumes, and taking into account the internal dynamics of single molecular enzymatic cycles. In such confined micro reactors typical for compartments of living cells the characteristic diffusive transport and mixing times of substrate and product molecules can be much shorter than the characteristic times of conformational transformations in single enzyme molecules. Experiments with the photosensitive cytochrome P-450 dependent monooxygenase system have shown, that the turnover cycles of individual enzymes can be externally synchronized by applying periodic light flashes. The aim of this work is to investigate theoretically, whether such a synchronization of molecular enzymatic cycles, can spontaneous appear without any external forcing, only because of internal interactions. To answer this question, three different enzymatic reaction mechanisms are considered. For each mechanism a separate stochastic model is introduced and numerically investigated. Additionally, the master equations describing the evolution of the probability functions of the system states are used to derive the equations for the mean values of the molecule numbers. These equations are further studied by a linear stability analysis. For a wide range of system parameters a spontaneous synchronization of the molecular enzymatic cycle, as a kind of microscopic self-organization is found.