Control theoretic views on circadian rhythms

Circadian rhythms, which are observed in most of living things, e.g. bacteria, fungi, plants, and animals, are self-sustained oscillations with about 24 hours period, and have the following properties: The first property is that the oscillation is entrained by light/dark cycles; the second one is that the oscillation, especially the period of the oscillation, is robust against changes of environment. In this paper, we investigate these two properties from control theoretic viewpoints. First, considering light/dark cycle as periodic control input, we try to explain how periodic control inputs can entrain one self-sustained circadian oscillator described by a core molecular model for Drosophila by Goldbeter (1995). Second, for structural understanding of robustness of circadian rhythms, we propose an evaluation method of the robustness based on period sensitivity, and try to design some rate parameters, which are regarded as control parameters, based on some optimizations using a robustness measure, when a rate parameter is moved to outside of normal area by environmental changes