A kinetic model for product formation in unstable recombinant populations

A mathematical model has been formulated for product formation by unstable recombinant organisms in batch and in continuous flow reactors. The cell population is characterized by three different genotypes according to the absence or presence of plasmids (segregational instability) and of active cloned gene (structural instability). Empirical growth inhibition factors due to plasmids and to product protein are assigned to the corresponding strains. Product formation kinetics are based upon a quasi-steady-state transcription-translation expression model. An approximate form of these mechanism-based product formation kinetics is identical to the traditional, empirically based Leudeking-Piret formula. Alternative models which consider inhibition based on overall product concentration and based on intracellular product concentration are posed, and their implications are compared. Simulation results based on these models indicate (1) overall plasmid stability depends on product expression and reactor operating conditions as well as on intrinsic segregation and mutation rate parameters; (2) there exists an optimum combination of plasmid copy number and cloned-gene transcription and translation efficiencies to maximize reactor productivity; and (3) continuous reactor dilution rate influences the fraction of productive cells. General trends and substrate, product, and cell concentration time trajectories obtained from model simulation agree well qualitatively with currently available experimental information.