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Journal of Mathematical Biology

, Volume 78, Issue 4, pp 985–1032 | Cite as

Optimal control of bacterial growth for the maximization of metabolite production

  • Ivan YegorovEmail author
  • Francis Mairet
  • Hidde de Jong
  • Jean-Luc Gouzé
Article
  • 208 Downloads

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 self-replicator 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.

Keywords

Optimal control Nonlinear dynamical systems Mathematical modelling Bacterial growth Biotechnology 

Notes

Acknowledgements

This work was supported in part by the PIA project Reset (ANR-11-BINF-0005), ANR project Maximic (ANR-17-CE40-0024-01), Inria IPL AlgaeInSilico, and Labex SIGNALIFE (ANR-11-LABX-0028-01). The authors thank Johannes Geiselmann and Eugenio Cinquemani for discussions and comments on the manuscript.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.North Dakota State UniversityFargoUSA
  2. 2.Ifremer PBANantesFrance
  3. 3.InriaUniv. Grenoble AlpesGrenobleFrance
  4. 4.BIOCORE team, Inria Sophia-Antipolis Méditerranée, Univ. Côte d’Azur, Inria, INRA, CNRS2004 Route des LuciolesValbonneFrance

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