Circadian Rhythmicity by Autocatalysis

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Abstract
The temperature compensated in vitro oscillation of cyanobacterial KaiC phosphorylation, the first example of a thermodynamically closed system showing circadian rhythmicity, only involves the three Kai proteins (KaiA, KaiB, and KaiC) and ATP. In this paper, we describe a model in which the KaiA- and KaiB-assisted autocatalytic phosphorylation and dephosphorylation of KaiC are the source for circadian rhythmicity. This model, based upon autocatalysis instead of transcription-translation negative feedback, shows temperature-compensated circadian limit-cycle oscillations with KaiC phosphorylation profiles and has period lengths and rate constant values that are consistent with experimental observations. Circadian rhythms are a central feature of biological systems. In cyanobacteria, the clock involves three major proteins: KaiA, KaiB, and KaiC, with KaiC showing autophosphorylation in the presence of ATP. Remarkably, by incubating the purified Kai proteins with ATP, the clock can be reconstituted in vitro. The authors were intrigued by the simplicity of this oscillator and its connection to chemical oscillatory reactions, and saw the possibility for a realistic reaction kinetic representation. Their study represents a synthetic, predictive, and dynamic explanation for the in vitro KaiC circadian clock based on the self-amplifying response (“autocatalysis”) of autophosphorylating kinases. The presented model is based on existing biological and biochemical observations and recapitulates observed experimental features, including temperature compensation, which has been notably recalcitrant to explanation. The model provides several predictions including that period length and the ratio between phosphorylated and unphosphorylated KaiC in clock mutants are closely linked and related to the stability of the ternary complex formed between the three Kai proteins. The model also predicts the occurrence of bistability and that evolution can move simple bistable systems into oscillatory systems by changing only one rate constant.