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Previous studies showed that a single negative feedback structure should be sufficient for robust circadian oscillations.
This is the case explicitly analyzed in Scenario 3 that results to be most robust and tunable as compared to Scenario 2, in which the topology of the network is reduced to a single negative feedback loop.
The first one consists of a single negative feedback circuit, the repressilator model described in [ 16].
The architecture of a single negative feedback loop in which the first regulator is an activator and the second is a repressor is shown in Figure 1a.
This circuit contains a single negative feedback loop implemented with scaffold proteins and operates on the time scale of one cell cycle.
This is based on a single negative feedback loop in which the gene FREQUENCY (FRQ) is repressed by its protein product.
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For instance, the single-cell green alga Ostreococcus tauri possesses a clock simpler than that in Arabidopsis in which CCA1 and TOC1 homologues form a single negative-feedback loop, and thus, it became the model for analyzing the minimal requirements for circadian oscillation.
Moreover, unlike the single negative feedback topology, the topology of Scenario 3 allows to tune the amplitude of the oscillations independently from the period (Figure S4, E and F).
The single negative feedback loop in the circuit represses overproduction of antiscaffold, but there is no mechanism for feedback in the case of an excess of scaffold or antiscaffold.
More interestingly, equations (12) and (17) show that and share the same analytical form for B. Further generalisations, therefore, can be made for variants of the general Goodwin systems: the systems with single negative feedback loop in which any step in the biochemical pathway can be potentially inhibited by the end-product (i.e. systems with 1 <= k <= I - Figure 8a).
Some simple and easily verified criteria are given for the stabilization of impulsive dynamical networks under a single impulsive controller and/or a single negative state-feedback control.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com