[POS] Physiology and Biorhythms

[POS-12] Mathematical Analysis of the Temperature Compensation of the Drosophila Circadian Clock

*Hideyuki Kumano¹ (1. Institute of Science Tokyo (Japan))

Keywords:

Circadian Clock,Drosophila,PER,temperature compensation

The circadian clock of organisms is composed of transcription-translation feedback loops (TTFLs) where mRNA and protein levels increase and decrease with a nearly 24-hour period. In general, biochemical reaction rates in cells increase with temperature. However, the period of the circadian clock remains unchanged even when the temperature changes, which is known as the temperature compensation of the circadian period. One hypothesis to explain the temperature compensation of the circadian period is the “critical reaction hypothesis,” which proposes that the rates of some reactions in the TTFLs are independent of temperature, allowing period stabilization. However, it is still unclear (1) how many temperature-independent reactions are required and (2) which reactions should be temperature-independent to compensate the circadian period. To address these questions, here we analyze a mathematical model of the Drosophila circadian clock proposed by Ueda et al. 2001 with a few temperature-independent reaction rates. The model describes the two coupled negative feedback loops (NFLs) of the circadian clock genes period (per), timeless (tim), and clock (clk). PER and TIM form a complex and repress their own transcription, while induce clk transcription. CLK represses its own transcription, while induces the transcription of per and tim. The temperature dependence of reaction rates are modeled by the Arrhenius equation. We show that the circadian period shortens with temperature if only one reaction rate in the coupled NFLs is temperature-independent. However, we find that the circadian period is compensated if the nuclear translocation rate of the PER-TIM complex and the clk mRNA degradation rate are temperature-independent. The temperature-independent clk mRNA degradation rate causes a 2-fold increase of the amplitude of nuclear CLK protein. The accumulated CLK protein amounts balance the increased degradation rate, compensating the period of CLK. Furthermore, the temperature-independent nuclear translocation of the PER-TIM complex becomes a rate-limiting step, maintaining the period of PER and TIM. Thus, our analysis suggests that for period compensation, a single temperature-independent reaction rate is required in each negative feedback loop.