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Modeling Feedback Loops of the Mammalian Circadian Oscillator

Sabine Becker-Weimann ^*, Jana Wolf ^*, Hanspeter Herzel ^* and Achim Kramer 

^* Institute for Theoretical Biology, and Laboratory of Chronobiology - Institute of Medical Immunology (Charité), Humboldt-University Berlin, 10115 Berlin, Germany

Correspondence: Address reprint requests to Dr. Achim Kramer, Laboratory of Chronobiology, Institute of Medical Immunology (Charité), Humboldt-University Berlin, Hessische Str. 3-4, 10115 Berlin, Germany. Tel.: +49-30-450-524263; Fax: +49-30-450-524942; E-mail: achim.kramer{at}charite.de.

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-erb^–/– 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 Per2^Brdm1/Cry2^–/– double-mutant mice (Per2^Brdm1 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 Per2^Brdm1 mutant mice are crossed with Rev- erb ^–/– mutant mice.

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