A full stochastic description of the Michaelis-Menten reaction for small systems

A method is presented to solve the Komogorov-equations for the stochastic model of the Michaelis-Menten reaction. The results are given for the case when only one enzyme molecule is involved in the reaction and can be extended to the case when a few enzyme molecules react. The important differences between the results of stochastic and deterministic treatment are emphasized, and their possible biological implications are discussed. Beside the exact solution of the time course of the irreversible reaction also the equilibrium is described for the reversible reaction. The method provides means for studying other biologically important reactions assuming stochastic behaviour. A comparison is made also with the steady state approximation.