An underlying bistability sets amplitude and explains temperature compensation in the cyanobacterial circadian clock

Circadian clocks create free-running biological rhythms with a period close to 24 hours. A universal property of these systems is temperature compensation, where the period of oscillation remains nearly invariant even as the amplitude changes with temperature. In the cyanobacterial system, where the core oscillator can be reconstituted from purified KaiABC proteins, we identify a key temperature-dependent positive feedback process: antagonism between KaiA and KaiB creates a bistable switch in protein-protein interaction. The region of bistability is strongly temperature dependent and correlated with oscillator amplitude. Combining this bistable mechanism with the temperature scaling of phosphorylation and dephosphorylation rates in a mathematical model recapitulates the overall temperature compensation of the oscillator. This capacity for history-dependent switching suggests that bistable dynamics underpin the generation of circadian rhythms. Significance StatementCircadian clocks are biological oscillators that anticipate the day-night cycle. The 24-hour time scale of the clock is remarkably insensitive to temperature owing to compensatory changes in amplitude and speed with temperature. In the cyanobacterial clock, we identify a bistability of the protein interaction network which determines oscillator amplitude and depends strongly on temperature, balancing the temperature dependence of dephosphorylation rates. This bistability indicates that oscillations arise from a combination of positive and negative feedback loops, a design principle used to maintain temperature compensation.