The promise of dawn: Microalgae photoacclimation as an optimal control problem of resource allocation

Photosynthetic microorganisms are known to adjust their photosynthetic capacity according to light intensity. This so-called photoacclimation process is thought to maximize growth at equilibrium, but its dynamics under varying conditions remains less understood. To tackle this problem, microalgae growth and photoacclimation are represented by a (coarse-grained) resource allocation model. Using optimal control theory (the Pontryagin maximum principle) and numerical simulations, we determine the optimal strategy of resource allocation to maximize 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, a bi-level optimization problem is solved numerically to estimate model parameters from experimental data. The fitted trajectory represents well a Dunaliella tertiolecta culture facing a light down-shift. Finally, we study photoacclimation dynamics under day/night cycle. In the optimal trajectory, the synthesis of the photosynthetic apparatus surprisingly 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.