  By incubating the mixture of three cyanobacterial proteins, KaiA, KaiB, and
KaiC, with ATP in vitro, Kondo and his colleagues reconstituted the robust
circadian rhythm of the phosphorylation level of KaiC (Science, 308; 414-415
(2005)). This finding indicates that protein-protein interactions and the
associated hydrolysis of ATP suffice to generate the circadian rhythm. Several
theoretical models have been proposed to explain the rhythm generated in this
"protein-only" system, but the clear criterion to discern different possible
mechanisms was not known. In this paper, we discuss a model based on the two
basic assumptions: The assumption of the allosteric transition of a KaiC
hexamer and the assumption of the monomer exchange between KaiC hexamers. The
model shows a stable rhythmic oscillation of the phosphorylation level of KaiC,
which is robust against changes in concentration of Kai proteins. We show that
this robustness gives a clue to distinguish different possible mechanisms. We
also discuss the robustness of oscillation against the change in the system
size. Behaviors of the system with the cellular or subcellular size should shed
light on the role of the protein-protein interactions in in vivo circadian
oscillation.
