  Dynamic flux balance analysis of a bioreactor is based on the coupling
between a dynamic problem, which models the evolution of biomass, feeding
substrates and metabolites, and a linear program, which encodes the metabolic
activity inside cells. We cast the problem in the language of optimal control
and propose a hybrid formulation to model the full coupling between macroscopic
and microscopic level. On a given location of the hybrid system we analyze
necessary conditions given by the Pontryagin Maximum Principle and discuss the
presence of singular arcs. In particular, for the single-input case we prove
that optimal controls are bang-bang. For the multi-input case, under suitable
assumptions, we prove that generically with respect to initial conditions
optimal controls are bang-bang.
