Mathematical modeling of circadian rhythm: temperature compensation and after effect

Almost all organisms have a circadian clock. This circadian clock consists of negative transcriptional-translational feedback loops (TTFLs) between various circadian clock genes in cells. Collective gene expression rhythms in the central circadian pacemaker tissue regulate nearly 24-hour behavioral rhythms of organisms. The circadian clock has three characteristics: (1) autonomous oscillation, (2) temperature compensation of the period, and (3) entrainment to external cycles such as a light-dark cycle. In this presentation, I will talk about theoretical studies on temperature compensation, and the entrainment to light-dark cycles. For temperature compensation, I will show that only a few temperature-insensitive reactions in the complex TTFLs of the circadian clock are sufficient to maintain the circadian period under increasing temperature. For entrainment to the light-dark cycle, I will show the mechanism for after-effect where the period of the circadian clock in constant darkness correlates with that of a previously entrained light-dark cycle for several months.