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A generic single gene cell model as an extension of a "standard" single enzyme (Monod) model is proposed. The model is structured at three levels: 1) gene transcription, 2) enzyme synthesis, and 3) metabolite and protein production. It accounts for a limiting substrate consumption, metabolite and biomass component production, gene transcription and enzyme synthesis. Control interactions between the key components at each level based on catalytic effects are assumed. Induction of gene transcription and enzyme synthesis as a cell response to step change of extracellular medium composition is simulated. In view of the small number of key molecules stochastic simulation is applied.