Optimal bacterial resource allocation: metabolite production in continuous bioreactors.

We show novel results addressing the problem of synthesizing a metabolite of interest in continuous bioreactors through resource allocation control. Our approach is based on a coarse-grained self-replicator dynamical model that accounts for microbial culture growth inside the bioreactor, and incorporates a synthetic growth switch that allows to externally modify the RNA polymerase concentration of the bacterial population, thus disrupting the natural process of allocation of available resources in bacteria. Further on, we study its asymptotic behavior using dynamical systems theory, and we provide conditions for the persistence of the bacterial population.