This model descibres the circadian oscillator. Below follows an excerpt of the abstract from the paper describing the model by S. Becker-Weimann et al (2004).

"The suprachiasmatic nucleus governs daily variations of physiology and behavior in mammals. Within single neurons, interlocked transcriptional/translational feedback loops generate circadian rhythms on the molecular level. We present a mathematical model that reflects the essential features of the mammalian circadian oscillator to characterize the differential roles of negative and positive feedback loops. The oscillations that are obtained have a 24-hour period and are robust toward parameter variations even when the positive feedback is replaced by a constantly expressed activator. This demonstrates the crucial role of the negative feedback for rhythm generation. Moreover, it explains the rhythmic phenotype of Rev-erbalpha-/- mutant mice, where a positive feedback is missing. The interplay of negative and positive feedback reveals a complex dynamic. In particular, the model explains the unexpected rescue of circadian oscillations in Per2Brdm1/Cry2-/- double-mutant mice (Per2Brdm1 single-mutant mice are arrhythmic). Here, a decrease of positive feedback strength associated with mutating the Per2 gene is compensated by the Cry2-/- mutation that simultaneously decreases the negative feedback strength. Finally, this model leads us to a testable prediction of a molecular and behavioral phenotype: circadian oscillations should be rescued when arrhythmic Per2Brdm1 mutant mice are crossed with Rev-erbalpha -/- mutant mice."

Fig. 1 show the simulation results and corresponds to Fig. 3(a) in the paper (S. Becker-Weimann et al 2004).


Fig. 1 the model predictions for the oscillations of clock gene mRNAs an proteins.

References

S. Becker-Weimann, J. Wolf, H. Herzel, A. Kramer, "Modeling Feedback Loops of the Mammalian Circadian Oscillator," Biophysical Journal, 87(5), 2004, pp. 3023-3034 doi:10.1529/biophysj.104.040824

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