Computation of the fraction of induced cells in enzyme induction systems

A theoretical model is developed for continuous multistage enzymed production systems, which consist of a growth fermentor used for growing microorganisms rapidly without enzyme production and a subsequent system of induction reactors in which enzyme induction and production occurs. The model allows the computation of the fraction of induced cells residing in the induction reactors for organisms exhibiting a lag phase in enzyme induction. For this model a general analytical solution was obtained for the cumulative internal residence time distribution of a series of n well-sterred vessels with a recycle. The theoretical results are compared in a preliminary way with experimentally measured cellulase productivities of continuous multistage cellulose fermentations with Trichoderma viride QM 9414.