Optimal feedback strategies for bacterial growth with degradation, recycling, and effect of temperature

• Published in: Optimal control applications & methods 2018-03, Vol.39 (2), p.1084-1109
• Main Authors: Yegorov, Ivan, Mairet, Francis, Gouzé, Jean‐Luc
• Format: Article
• Language: English
• Subjects: Amino acids; Automatic Control Engineering; Bacteria; bacterial growth; chattering regime; Computer Science; Control systems; Degradation; effect of temperature; Engineering Sciences; Feedback control; feedback strategy; Gene expression; Life Sciences; Mathematical models; Mathematics; Maximum principle; Numerical analysis; Optimal control; Pontryagin's maximum principle; protein degradation; Proteins; recycling; Replication; Resource allocation; singular regime; switching curve; Temperature effects
• ISSN: 0143-2087; 1099-1514
• DOI: 10.1002/oca.2398

Summary Mechanisms of bacterial adaptation to environmental changes are of great interest for both fundamental biology and engineering applications. In this work, we consider a continuous‐time dynamic problem of resource allocation between metabolic and gene expression machineries for a self‐replicating prokaryotic cell population. In compliance with evolutionary principles, the criterion is to maximize the accumulated structural biomass. In the model, we include both the degradation of proteins into amino acids and the recycling of the latter (ie, using as precursors again). On the basis of the analytical investigation of our problem by Pontryagin's maximum principle, we develop a numerical method to approximate the switching curve of the optimal feedback control strategy. The obtained field of extremal state trajectories consists of chattering arcs and 1 steady‐state singular arc. The constructed feedback control law can serve as a benchmark for comparing actual bacterial strategies of resource allocation. We also study the influence of temperature, whose increase intensifies protein degradation. While the growth rate suddenly decreases with the increase in temperature in a certain range, the optimal control synthesis appears to be essentially less sensitive.