Mathematical model for diauxic growth of microorganisms in mixed substrate medium.

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The mathematical model for diauxic growth of microorganisms in the presence of two substrates, such as glucose and maltose, was proposed, being constructed in due consideration of catabolite repression and enzyme induction. In the model, it was assumed that the first substrate is metabolized by a constitutively synthesized enzyme system, while the second substrate is utilized by an inducibly synthesized enzyme. The synthesis of the inducible enzyme is dually controlled by catabolite repression, which is caused by the first substrate, and induction which is triggered by the second substrate as an inducer. The extent of catabolite repression was expressed as the inhibition of promoter activity of inducible gene. The promotor of inducible gene was assumed to be activated by a cofactor, the synthesis of which is inhibited by the first substrate. The extent of induction was expressed as the activity of the operator, which is activated by the second substrate. The equations introduced from the model were applied to experiments carried out with a batch culture, with glucose and maltose as carbon sources. The calculated values were in satisfactory agreement with the experimental data, especially in the estimation of lag time between the first log phase state and the second one.