Bang–Bang Optimal Light Control for Maximum Protein Production in Yeast ^*

This study revisits the optogenetic control strategy introduced in [1], which showed that proportional-integral-derivative (PID) feedback can enhance the production of folded amylase (FA) in Saccharomyces cerevisiae by using light to modulate the unfolded protein response. While effective, the PID approach does not guarantee optimal outcomes. In this preliminary work, we theoretically investigate optimal light input strategies to maximize the terminal amount of FA at the final time of a batch process. We first reformulate the original model, then state and solve an optimal control problem with the optogenetic light as the control input. By applying Pontryagin’s Maximum Principle (PMP), we derive necessary conditions for optimality. A complementary direct numerical approach yields results that align with the PMP analysis. The resulting optimal control is of bang–bang type, offering practical advantages for implementation. These results provide a basis for extended studies focusing on experimentally feasible feedback strategies.