Circadian clock is an essential molecular regulatory mechanism that coordinates daily biological processes. Toward understanding the design principles of the circadian mechanism in cyanobacteria, the only prokaryotes reported to possess circadian rhythmicity, mathematical models have been used as important tools to help elucidate the complicated biochemical processes. In this study, we focus on elucidating the underlying systems properties that drive the oscillation of the cyanobacterial clockwork. We apply combined methods of time scale separation, phase space analysis, bifurcation analysis and sensitivity analysis to a model of the in vitro cyanobacterial circadian clock proposed by us recently. The original model is reduced to a three-dimensional slow subsystem by time scale separation. Phase space analysis of the reduced subsystem shows that the null-surface of the Serine-phosphorylated state (S-state) of KaiC is a bistable surface, and that the characteristic of the phase portrait indicates that the kernel mechanism of the clockwork behaves as a relaxation oscillator induced by interlinked positive and negative feedback loops. Phase space analysis together with perturbation analysis supports our previous viewpoint that the S-state of KaiC is plausibly a key component for the protein regulatory network of the cyanobacterial circadian clock.
Keywords: Circadian clock; Mathematical model; Phase space; Relaxation oscillator.
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