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Theoretical Biology and Medical Modelling

, 4:1

First Online: 09 January 2007Received: 15 September 2006Accepted: 09 January 2007DOI: 10.1186-1742-4682-4-1

Cite this article as: Edwards, R., Gibson, R., Illner, R. et al. Theor Biol Med Model 2007 4: 1. doi:10.1186-1742-4682-4-1

Abstract

BackgroundCircadian 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.

ResultsThe 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.

ConclusionOur 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.

Electronic supplementary materialThe online version of this article doi:10.1186-1742-4682-4-1 contains supplementary material, which is available to authorized users.

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Autor: Roderick Edwards - Richard Gibson - Reinhard Illner - Verner Paetkau

Fuente: https://link.springer.com/







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