A wide range of organisms features molecular machines, circadian clocks, which generate endogenous oscillations with ~24 h periodicity and thereby synchronize biological processes to diurnal environmental fluctuations. Recently, it has become clear that plants harbor more complex gene regulatory circuits within the core circadian clocks than other organisms, inspiring a fundamental question: are all these regulatory interactions between clock genes equally crucial for the establishment and maintenance of circadian rhythms? Our mechanistic simulation for Arabidopsis thaliana demonstrates that at least half of the total regulatory interactions must be present to express the circadian molecular profiles observed in wild-type plants. A set of those essential interactions is called herein a kernel of the circadian system. The kernel structure unbiasedly reveals four interlocked negative feedback loops contributing to circadian rhythms, and three feedback loops among them drive the autonomous oscillation itself. Strikingly, the kernel structure, as well as the whole clock circuitry, is overwhelmingly composed of inhibitory, rather than activating, interactions between genes. We found that this tendency underlies plant circadian molecular profiles which often exhibit sharply-shaped, cuspidate waveforms. Through the generation of these cuspidate profiles, inhibitory interactions may facilitate the global coordination of temporally-distant clock events that are markedly peaked at very specific times of day. Our systematic approach resulting in experimentally-testable predictions provides insights into a design principle of biological clockwork, with implications for synthetic biology.
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Circadian clocks play a pivotal role in orchestrating numerous physiological and developmental events. Waveform shapes of the oscillations of protein abundances can be informative about the underlying biochemical processes of circadian clocks. We derive a mathematical framework where waveforms do reveal hidden biochemical mechanisms of circadian timekeeping. We find that the cost of synthesizing proteins with particular waveforms can be substantially reduced by rhythmic protein half-lives over time, as supported by previous plant and mammalian data, as well as our own seedling experiment. We also find that previously enigmatic, cyclic expression of positive arm components within the mammalian and insect clocks allows both a broad range of peak time differences between protein waveforms and the symmetries of the waveforms about the peak times. Such various peak-time differences may facilitate tissue-specific or developmental stage-specific multicellular processes. Our waveform-guided approach can be extended to various biological oscillators, including cell-cycle and synthetic genetic oscillators.
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