Modeling circadian oscillations with interlocking positive and negative feedback loops

Both positive and negative feedback loops of transcriptional regulation hav e been proposed to be important for the generation of circadian rhythms. To test the sufficiency of the proposed mechanisms, two differential equation -based models were constructed to describe the Neurospora crassa and Drosop hila melanogaster circadian oscillators. In the model of the Neurospora osc illator, FRQ suppresses frq transcription by binding to a complex of the tr anscriptional activators WC-1 and WC-2, thus yielding negative feedback. FR Q also activates synthesis of WC-1, which in turn activates frq transcripti on, yielding positive feedback. In the model of the Drosophila oscillator, PER and TIM are represented by a "lumped" variable, "PER." PER suppresses i ts own transcription by binding to the transcriptional regulator dCLOCK, th us yielding negative feedback. PER also binds to dCLOCK to de-repress dcloc k, and dCLOCK in turn activates per transcription, yielding positive feedba ck. Both models displayed circadian oscillations that were robust to parame ter variations and to noise and that entrained to simulated light/dark cycl es. Circadian oscillations were only obtained if time delays were included to represent processes not modeled in detail (e.g., transcription and trans lation). In both models, oscillations were preserved when positive feedback was removed.