Dynamical Analysis and Optimization of a Generalized Resource Allocation Model of Microbial Growth

Type Article
Date 2022
Language English
Author(s) Yabo Agustin G.1, Caillau Jean-Baptiste2, Gouze Jean-Luc1, de Jong Hidde3, Mairet FrancisORCID4
Affiliation(s) 1 : Universite C^ote d'Azur, Inria, INRAE, CNRS, Sorbonne Universite, Biocore Team, Sophia Antipolis, France.
2 : Universite C^ote d'Azur, CNRS, Inria, LJAD, France
3 : Universite Grenoble Alpes, Inria, 38000 Grenoble, France
4 : Ifremer, Physiology and Biotechnology of Algae laboratory, rue de l'Ile d'Yeu, 44311 Nantes, France
Source Siam Journal On Applied Dynamical Systems (1536-0040) (Siam Publications), 2022 , Vol. 21 , N. 1 , P. 137-165
DOI 10.1137/21M141097X
WOS© Times Cited 1
Keyword(s) systems biology, bacterial growth laws, resource allocation, nutritional shifts, optimal control, turnpike

Gaining a better comprehension of the growth of microorganisms is a major scientific challenge, which has often been approached from a resource allocation perspective. Simple mathematical self-replicator models based on resource allocation principles have been surprisingly effective in accounting for experimental observations of the growth of microorganisms. Previous work, using a three-variable resource allocation model, predicted an optimal resource allocation scheme for the adaptation of microbial cells to a sudden nutrient change in the environment. We here propose an extended version of this model considering also proteins responsible for basic housekeeping functions, and we study their impact on predicted optimal strategies for resource allocation following changes in the environment. A full dynamical analysis of the system shows there is a single globally attractive equilibrium, which can be related to steady-state growth conditions of bacteria observed in experiments. We then explore the optimal allocation strategies using optimization and optimal control theory. We show that the solutions to this dynamical problem have a complicated structure that includes a second-order singular arc given in feedback form and characterized by (i) Fuller's phenomenon and (ii) the turnpike effect, producing a very particular asymptotic behavior towards the solution of the static optimization problem. Our work thus provides a generalized perspective on the analysis of microbial growth by means of simple self-replicator models.

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Yabo Agustin G., Caillau Jean-Baptiste, Gouze Jean-Luc, de Jong Hidde, Mairet Francis (2022). Dynamical Analysis and Optimization of a Generalized Resource Allocation Model of Microbial Growth. Siam Journal On Applied Dynamical Systems, 21(1), 137-165. Publisher's official version : https://doi.org/10.1137/21M141097X , Open Access version : https://archimer.ifremer.fr/doc/00756/86825/