Optimal control of bacterial growth for the maximization of metabolite production

Abstract

Microorganisms have evolved complex strategies for controlling the distribution of available resources over cellular functions. Biotechnology aims at interfering with these strategies, so as to optimize the production of metabolites and other compounds of interest, by (re)engineering the underlying regulatory networks of the cell. The resulting reallocation of resources can be described by simple so-called selfreplicator models and the maximization of the synthesis of a product of interest formulated as a dynamic optimal control problem. Motivated by recent experimental work, we are specifically interested in the maximization of metabolite production in cases where growth can be switched off through an external control signal. We study various optimal control problems for the corresponding self-replicator models by means of a combination of analytical and computational techniques. We show that the optimal solutions for biomass maximization and product maximization are very similar in the case of unlimited nutrient supply, but diverge when nutrients are limited. Moreover, external growth control overrides natural feedback growth control and leads to an optimal scheme consisting of a first phase of growth maximization followed by a second phase of product maximization. This two-phase scheme agrees with strategies that have been proposed in metabolic engineering. More generally, our work shows the potential of optimal control theory for better understanding and improving biotechnological production processes.

Singular regimes for the maximization of metabolite production

“…In this context, natural biomass maximization was achieved through a bangsingular strategy. In [5], authors showed that the same kind of strategy is necessary in order to maximize the synthetic production of a metabolite. In line with this work, we have proposed a metabolite production scheme in a CSTR Bioreactor, with the particularity that it encompasses previously studied models in the field.…”

“…The optimal product maximization problem was already analyzed for this particular case in [5] where, due to the complexity of the computations in the PMP, most of the analysis was performed through a numerical approach. To allow an analytical study, we further simplify the system by assuming there is substrate in excess and the depletion occurs slowly enough (if, for example, V V ext ).…”

“…with µ = pr K+p being the growth rate defined in (5). Given the state ϕ = (p, r), and according to Pontryagin Maximum Principle, the Hamiltonian is defined as…”

“…These results have provided a baseline understanding upon which it is possible to re-engineer the naturally-evolved behaviors of the cell in order to improve certain productivity measures. In particular, we consider the problem of producing a certain metabolite of interest, as considered in [5], for its relevance in biotechnological processes. In this regard, Optimal Control theory can not only shed light on the natural bacterial intracellular behaviours, but also help enhance industrial processes, as well as provide guidance in biotechnological research.…”

“…In this work, we present a general coarse-grained model for a self-replicating system extended with the metabolite production pathway based on [4], [5]. We start, in Section II, by considering the case of the CSTR (Continuous Stirred-Tank Reactor) Bioreactor scheme as our baseline, and we show that is it possible to derive the models previously analyzed in the field (fed-batch, constant substrate, no production of metabolites) as an initial step towards a full analysis of the new system.…”