Research
A stochastic model for circadian rhythms from coupled ultradian oscillators
-
* Corresponding author: Roderick Edwards edwards@math.uvic.ca
1 Department of Mathematics and Statistics, University of Victoria, P.O. Box 3045 STN CSC, Victoria, BC, V8W 3P4, Canada
2 Department of Biochemistry and Microbiology, University of Victoria, P.O. Box 3055 STN CSC, Victoria, BC, V8W 3P6, Canada
Theoretical Biology and Medical Modelling 2007, 4:1 doi:10.1186/1742-4682-4-1
Published: 9 January 2007Abstract
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.