The promise of dawn: microalgae photoacclimation as an optimal control problem of resource allocation
Résumé
Photosynthetic microorganisms are known to adjust their photosynthetic capacity according to light intensity. This so-called photoacclimation process may correspond at equilibrium to the optimal behavior in order to maximize growth. But its dynamics under varying condition remains less understood. To tackle this problem, we propose here a resource allocation model, at coarse-grained, to represent microalgae growth and photoacclimation. Using the Pontryagin maximum principle and numerical simulations, we determine the optimal strategy of resource allocation in order to optimize microalgal growth rate over a time horizon. We show that, after a transient, the optimal trajectory approaches the optimal steady state, a behavior known as the turnpike property. Then, the model is fitted with experimental data, resulting in a bi-level optimization problem which is solved numerically. The fitted trajectory represents well a Dunaliella tertiolecta culture facing a light down-shift. Finally, we compute the optimal trajectory under day/night cycle and show that the synthesis of the photosynthetic apparatus starts a few hours before dawn. This anticipatory behavior has actually been observed both in the laboratory and in the field. This shows the algal predictive capacity and the interest of our method which predicts this phenomenon.
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