Simple models are of great value in order to simulate cell dynamics, and a class of potentially useful models are the so-called compartment models, which are a simple extension of the unstructured approach. Compartment models have earlier been used with great success to describe cell dynamics. In this article the authors present a 4-compartment model that is able to describe a majority of the observations that have been made through fermentations with recombinant microorganisms. The compartment model is especially suited for description of dynamic changes in plasmid copy number, e.g., runaway replication. Simulation of batch fermentation with runaway conditions corresponds very well with experimental results. Finally the model is used in the design of an optimal fermentation strategy in a CSTR.