Circadian Oscillator
This example is the modelica version of the model presented in
Modeling feedback loops of the Mammalian circadian oscillator by
Becker-Weimann S, Wolf J, Herzel H, Kramer A. (Biophysical Journal Volume 87 November 2004 3023-3034)
Abstract
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-h 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 dynamics. 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.
Simulations
The simulation results are shown in the
Figure 1. This plot corresponds to Fig 3A from the paper (Becker-Weimann, 2004).
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