A stochastic model for circadian rhythms from coupled ultradian oscillators
Date
2007-01-09
Authors
Edwards, Roderick
Gibson, Richard
Illner, Reinhard
Paetkau, Verner
Journal Title
Journal ISSN
Volume Title
Publisher
BioMed Central
Abstract
Background: Circadian rhythms with varying components exist in organisms ranging from
humans to cyanobacteria. A simple evolutionarily plausible mechanism for the origin of such a
variety of circadian oscillators, proposed in earlier work, involves the non-disruptive coupling of
pre-existing ultradian transcriptional-translational oscillators (TTOs), producing "beats," in
individual cells. However, like other TTO models of circadian rhythms, it is important to establish
that the inherent stochasticity of the protein binding and unbinding does not invalidate the finding
of clear oscillations with circadian period.
Results: The TTOs of our model are described in two versions: 1) a version in which the activation
or inhibition of genes is regulated stochastically, where the 'unoccupied" (or "free") time of the site
under consideration depends on the concentration of a protein complex produced by another site,
and 2) a deterministic, "time-averaged" version in which the switching between the "free" and
"occupied" states of the sites occurs so rapidly that the stochastic effects average out. The second
case is proved to emerge from the first in a mathematically rigorous way. Numerical results for
both scenarios are presented and compared.
Conclusion: Our model proves to be robust to the stochasticity of protein binding/unbinding at
experimentally determined rates and even at rates several orders of magnitude slower. We have
not only confirmed this by numerical simulation, but have shown in a mathematically rigorous way
that the time-averaged deterministic system is indeed the fast-binding-rate limit of the full
stochastic model.
Description
BioMed Central
Keywords
Citation
Edwards R, Gibson R, Illner R, Paetkau V. A stochastic model for circadian rhythms from coupled ultradian oscillators. Theor Biol Med Model. 2007 Jan 9;4:1. doi:10.1186/1742-4682-4-1