Circadian rhythms are constantly repetitive physiological phenomena with c.a. 24 hours period and observed in almost all organisms. One of the key characteristics of all circadian rhythms is that the free-running period remains stable under a relatively broad range of ambient temperatures, referred to as “temperature compensation” of the period. Temperature at which temperature compensation is effective typically lies well within the physiological range, that is, the range permissive for growth. Outside of the range of temperature compensation, circadian clocks stop running and are arrested at a certain phase.
Behaviour of self-sustained oscillator such as circadian clocks has been studied in the field of nonlinear dynamics. Altering parameters in a system can lead to qualitative changes of the dynamics reffered to as bifurcation. Based on the bifurcation theory, Hopf bifurcation and saddle-node bifurcation are plausible scenarios for nullification of self-sustained oscillations. Just by examining which bifurcation is adopted in circadian rhythms, the theory allows us to predict the behavior and its characteristics of circadian oscillator around low temperature limit and discuss the mechanisms of temperature compensation of the period.
The cyanobacterial circadian timing in Synechococcus elongatus PCC 7942 requires neither de novo transcription nor translation, and the posttranslational oscillation can be reconstituted in a test tube using only three clock proteins, KaiA, KaiB, and KaiC. The KaiC phosphorylation rhythm in vitro is best to observe directly and precisely dynamics of circadian oscillator, because there are little or no masking effects on the rhythmic profile of KaiC phosphorylation. We found that the phenomena of nullification of KaiC phosphorylation rhythm by low temperature was explained by theory of Hopf bifurcation. In this presentation, we will report damping oscillations and resonance of the in vitro clock , which can be predicted from the theory, and discuss fitness and physiological implications of circadian clock under lower temperature conditions.