Abstract
BackgroundElectronic clocks exhibit undesirable jitter or time variations in periodic signals. The circadian clocks of humans, some animals, and plants consist of oscillating molecular networks with peak-to-peak time of approximately 24 hours. Clockwork orange (CWO) is a transcriptional repressor of Drosophila direct target genes.Methodology/Principal FindingsTheory and data from a model of the Drosophila circadian clock support the idea that CWO controls anti-jitter negative circuits that stabilize peak-to-peak time in light-dark cycles (LD). The orbit is confined to chaotic attractors in both LD and dark cycles and is almost periodic in LD; furthermore, CWO diminishes the Euclidean dimension of the chaotic attractor in LD. Light resets the clock each day by restricting each molecular peak to the proximity of a prescribed time.Conclusions/SignificanceThe theoretical results suggest that chaos plays a central role in the dynamics of the Drosophila circadian clock and that a single molecule, CWO, may sense jitter and repress it by its negative loops.
Highlights
Humans, most animals and plants, have a biological clock that exhibits circadian rhythms that control the timing of sleep, alertness, and appetite
Phase-space graphs in light-dark cycles (LD) conditions reveal trajectories of the wt and cwo-mutant models that are attracted to stable limit cycles (Figures 3b–c, S6, S7, S8, and S9), which are consistent with chaotic attractors in the sense that the orbits are confined to small subsets of the space
The theory and results detailed in this paper support the conclusion that Clockwork orange (CWO) appears to control negative circuits that reduce jitter in the Drosophila circadian clock leading to stabilization of peak-to-peak time
Summary
Most animals and plants, have a biological clock that exhibits circadian rhythms that control the timing of sleep, alertness, and appetite. Circadian clocks exhibit 24-hr recurring behavioral and transcriptional oscillations, generated by interconnected transcriptional feedback loops (see File S1). The Drosophila circadian clock has one positive and two negative loops that interconnect at CLK-CYC, a heterodimer of the CLOCK (CLK) and CYCLE (CYC) proteins. CWO is a recently defined negative transcriptional regulator of the same direct targets as those of CLK-CYC (Figure 1a). A recent report describes a mathematical model of the Drosophila circadian clock. This model is faithful in the sense that it replicates biological results (see File S1 and [10]). Like digital clocks and unlike the wt model, the cwo-mutant model of the Drosophila circadian clock exhibits jitter or variations in recurring signal (see Figures 1b–c). I investigate the idea that CWO regulates an anti-jitter control system and study its contribution to the dynamics of the circadian model
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