Parameter Estimation for Dynamic Resource Allocation in Microorganisms: A Bi-level Optimization Problem

Type Article
Date 2020
Language English
Author(s) Mairet FrancisORCID1, Bayen Térence2
Affiliation(s) 1 : Ifremer, Physiology and Biotechnology of Algae laboratory, rue de l’Ile d’Yeu, 44311 Nantes, France
2 : Avignon Université, Laboratoire de Mathématiques d’ Avignon (EA2151) F-84018 ,France
Source Ifac Papersonline (2405-8963) (Elsevier BV), 2020 , Vol. 53 , N. 2 , P. 16814-16819
DOI 10.1016/j.ifacol.2020.12.1163
Keyword(s) Bi-level optimization, Optimal control, Pontryagin's principle, Chattering, Microbial growth, Microalgae

Given their key roles in almost all ecosystems and in several industries, understanding and predicting microorganism growth is of utmost importance. In compliance with evolutionary principles, coarse-grained or genome-scale models of microbial growth can be used to determine optimal resource allocation scheme under dynamic environmental conditions. Resource allocation approaches have given important qualitative results, but it still remains a gap towards quantitiative predictions. The first step in this direction is parameter calibration with experimental data. But fitting these models results in a bi-level optimization problem, whose numerical resolution involves complex optimization issues. As a case study, we present here a coarse-grained model describing how microalgae acclimate to a change in light intensity. We first determine using the Pontryagin maximum principle and numerical simulations the optimal strategy, corresponding to a turnpike with a chattering arc. Then, a bi-level optimization problem is proposed to calibrate the model with experimental data. To solve it, a classical parameter identification routine is used, calling at each iteration the bocop solver to solve the optimal control problem (by a direct method). The calibrated model is able to represent the photoacclimation dynamics of the microalga Dunaliella tertiolecta facing a down-shift of light intensity.

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