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

Type Article
Date 2018-03
Language English
Author(s) Yegorov Ivan1, Mairet FrancisORCID2, Gouze Jean-Luc1
Affiliation(s) 1 : UPMC Univ Paris 06, Univ Cote dAzur, CNRS, Inria,INRA,BIOCORE Team, F-06902 Sophia Antipolis, France.
2 : IFREMER PBA, Nantes, France.
Source Optimal Control Applications & Methods (0143-2087) (Wiley), 2018-03 , Vol. 39 , N. 2 , P. 1084-1109
DOI 10.1002/oca.2398
WOS© Times Cited 9
Note Special Issue: Global and Robust Optimization of Dynamic Systems
Keyword(s) bacterial growth, chattering regime, effect of temperature, feedback strategy, optimal control, Pontryagin's maximum principle, protein degradation, recycling, resource allocation, singular regime, switching curve
Abstract

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.

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