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

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‐replica...

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Bibliographic Details
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
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Summary: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.
ISSN:0143-2087
1099-1514
DOI:10.1002/oca.2398