Flatness-based control of PER protein oscillations in a drosophila model

Rhythms, and specially circadian rhythms governed by an oscillating set of genes called the central clock, and their incidence on therapeutics, have become an important concern in biology and medicine. Restoration of altered rhythms for therapeutic purpose can be viewed as an open-loop control problem. We study in this paper a nonlinear oscillator modeling the central clock mechanism through the synthesis cycle of PER protein for fruit fly Drosophila. Its particularly robust bifurcation structure makes it representative for a wide number of oscillating biological systems. We show how classical flatness-based motion planning techniques allow for fast design of chronomodulated injection schemes achieving circadian rhythm restoration.