A Mathematical Model for the Kai-Protein–Based Chemical Oscillator and Clock Gene Expression Rhythms in Cyanobacteria

Abstract

In the cyanobacterium, Synechococcus elongatus, most promoters are regulated by a circadian clock under continuous light (LL) conditions. Nevertheless, the basic circadian oscillation is primarily generated by alternating KaiC phosphorylation/dephosphorylation reactions at the posttranslational level. Indeed, the KaiC phosphorylation cycle was recently reconstituted in vitro by incubating KaiA, KaiB, and KaiC proteins with ATP. However, the molecular dynamics of this chemical oscillation and the mechanism that drives the circadian transcription/translation rhythms remain unknown. In this report, the KaiC phosphorylation cycle and the gene regulatory network in the cyanobacterial circadian system have been modeled. The model reproduces the robust KaiC phosphorylation cycle in the absence of de novo gene expression as is observed in vitro, as well as its coupling to transcriptional/translational feedback in LL conditions in vivo. Moreover, the model is consistent with most previous experiments, including various combinations of genetic knockout or overexpression of kai genes. It also predicts that multiple KaiC phosphorylation states and dynamic Kai protein interactions may be required for the cyanobacterial circadian system.