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

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. Copyright (C) 2020 The Authors.