In nature, microorganisms are continuously facing nutrient availability changes in the environment, and thus they have evolved to dynamically adapt their physiology to cope with this phenomena. This is achieved through reorganization of the gene expression machinery, by dynamically allocating resources to different cellular functions. Among all possible allocation strategies, only few will guarantee the survival of the fittest when competing for nutrient, leading to complex and highly optimized organisms. In contrast to previous steady-state growth studies, this line of research seeks to study the bacterial resource allocation problem in dynamical environments through self-replicator models. The fitness of the microorganism is represented as a dynamical growth maximization strategy, which is formulated as an optimal control problem. By means of the Pontryagin Maximum Principle, this theoretical approach allows us to obtain gold standard strategies, that can be then compared to feasible growth control implementations in bacterial cells. These results provide a baseline understanding upon which it is possible to re-engineer the underlying behaviors of the cell in order to improve certain productivity measures. In the framework of the ANR Project Maximic, we aim at maximizing the production of a metabolite of interest in E. coli by means of both analytical and computational techniques. First results show that optimal solutions for the biomass and product maximization problems are similar in scenarios with unlimited nutrient supply, but differ when the latter is scarce. Ultimately, we will explore the metabolite production scheme in the most relevant condition in biotechnological processes: the chemostat, a type of bioreactor highly conducive to industrial fermentation, but also a powerful tool in biological research.