[Deterministic and stochastic models for circadian rhythms].
Circadian rhythms, characterized by a period of about 24h, are generated in nearly all living organisms by the negative autoregulation of clock gene expression. Deterministic models based on this genetic regulation account for circadian oscillations in constant environmental conditions (e.g., in constant darkness) and for entrainment of these rhythms by light-dark cycles. When the number of clock mRNA and protein molecules is low, it is necessary to resort to stochastic simulations to assess the influence of molecular noise on circadian oscillations. Indeed, it is possible that the autoregulatory mechanism of gene expression might not produce stable rhythms due to fluctuations if the number of molecules involved in the clock mechanism remains too low. We have compared the deterministic and stochastic approaches for a model based on the negative autoregulation of a clock gene. We show by means of stochastic simulations that robust circadian oscillations can already occur when the maximum number of mRNA and protein molecules is of the order of a few tens or hundreds, respectively. Furthermore, the results indicate that the cooperativity characterizing the repression of the transcription process strenghtens the robustness of circadian rhythms and that entrainment by light-dark cycles stabilizes the phase of the oscillations.
Gonze
D
D
Unité de chronobiologie théorique, faculté des sciences, université libre de Bruxelles, Campus Plaine, CP 231, B-1050, Bruxelles, Belgique. dgonze@ulb.ac.be
Halloy
J
J
Goldbeter
A
A
D002940:Circadian Rhythm / Q000235:genetics; D005786:Gene Expression Regulation; D008954:Models, Biological; D013269:Stochastic Processes