Mathematical Understanding for the Molecular Mechanism of Cyanobacterial Circadian Rhythms

Abstract

A cyanobacterial clock protein KaiC shows circadian cycling of the phosphorylation level in vitro. We first developed an observation-based model. The KaiC-KaiA complex formation consequently reduces free KaiA molecules, thereby may exert a negative feedback effect toward KaiC phosphorylation. However, this model was shown not to be adequate to generate the KaiC phosphorylation cycle. Then, we analyzed generalized models and determined necessary conditions to generate the cycle. Based on the result, we realized the observed pattern of the KaiC phosphorylation cycle and predicted an unknown state that lies between KaiC phosphorylation and the formation of the KaiC/KaiA complex.