Modeling feedback loops of the mammalian circadian oscillator

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 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-erbalpha(-/-) mutant mice.