Modelling circadian rhythms of protein KaiA, KaiB and KaiC interactions in cyanobacteria

Cyanobacteria are the simplest organisms known that exhibit circadian rhythms. The mechanism of circadian rhythm generation in cyanobacteria is different from eukaryotes. Based on the recent experiments about the interaction of KaiA, KaiB, and KaiC proteins with the generation of circadian rhythms in vitro, we developed a mathematical model to describe post-translational oscillations and the possible chemical reactions involved in the circadian clock mechanism of cyanobacteria. In this model, a series of differential equations, with linear kinetics for binding of proteins, Michaelis - Menten kinetics for enzymatic processes and a term including an explicit delay for dissociation of the KaiA/KaiB/phospho-KaiC complex, are proposed describing the dynamics of the chemistry. It is demonstrated that the mathematical system can lead to circadian oscillation within a range of parameter values.