Bifurcation analyses in the cyanobacterial circadian clock model

A conspicuous property of the circadian clock in cyanobacteria is that endogenous rhythm continues when protein abundances are kept constant either in the presence of translation and transcription inhibitors. Here we extend the study of a model recently proposed for the cyanobacterial circadian clock. We theoretically show that balanced ratio among KaiA, KaiB, and KaiC proteins is required for the generation of oscillations by using our model recently proposed. Bifurcation analyses show that cooperativity for the mutual inhibitory process in the model does not always enhance the generation of oscillations though cooperativity for the inhibition of transcription and in the nuclear transport of clock proteins in Goodwin type models extensively studied is known to always enhance the generation of oscillations