Can optimal control explain the microbial heat-shock response? A bilevel optimization approach
Résumé
This paper presents preliminary results seeking to explain the microbial heat-shock response from a dynamical resource allocation perspective, under the hypothesis that microorganisms have been shaped by natural selection to maximize growth. Within this framework, natural regulatory mechanisms can potentially be predicted as solutions of an optimal control problem. While the optimal trajectories of such problems are inherently able to reproduce the main qualitative features of the desired transient response, we also address the problem of matching experimental measurements of E. coli exposed to a heat-shock. To this end, we seek to estimate the parameters of a bacterial growth model, so that the corresponding optimal trajectories match the experimental data. This nested formulation defines a bilevel optimization problem, that we solve with a two-level numerical approach: a global evolutionary algorithm for the upper-level calibration problem and a nonlinear optimal control solver for the lower-level problem. Our results show good agreement between data and predictions, and provide a promising perspective for better understanding stress-response mechanisms in microorganisms.
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