Predicting Regulation of the Phosphorylation Cycle of KaiC Clock Protein Using Mathematical Analysis

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Abstract
The cyanobacterial clock protein KaiC regulates the circadian cycle by exhibiting rhythms in transcription, translation, and phosphorylation. KaiC phosphorylation persists in circadian cycling even under transcription-less conditions and was reconstituted in vitro by incubating KaiC, KaiA, and KaiB. This presents a novel perspective for circadian oscillation occurring due to interactions between clock proteins. Using mathematical models, the authors investigated the mechanism for the transcription-less KaiC phosphorylation cycle. They developed a simple model based on the possible KaiC behavior, which is experimentally suggested by Kitayama et al. (2003, EMBO J, 22:2127–2134). They hypothesized that the KaiC-KaiA complex formation, followed by a decrease in free KaiA molecules, may attenuate the KaiC phosphorylation rate, and it acts as negative feedback in the system. However, this model was shown not to be adequate to generate the KaiC phosphorylation cycle. The authors developed the general version of the model and determined the necessary condition to generate the KaiC phosphorylation cycle. Linear stability analysis revealed that oscillations can occur when the distance of feedback between the recipient reaction and the effector is far enough. Furthermore, they classified negative feedback regulations in the closed system into 2 types: destabilizing inhibition and stabilizing inhibition. Based on this result, the authors predicted that, in addition to the identified states of KaiC, another unknown state must be present between KaiC phosphorylation and the complex formation. By incorporating the unknown state into the previous model, they realized the periodic pattern reminiscent of the KaiC phosphorylation cycle in computer simulation. This result implies that the KaiC-KaiA complex formation requires more than 1 step of posttranslational modification, including phosphorylation or conformational change of KaiC.