Limit cycle models for circadian rhythms based on transcriptional regulation in Drosophila and Neurospora

We examine theoretical models for circadian oscillations based on transcrip tional regulation in Drosophila and Neurospora. For Drosophila, the molecul ar model is based on the negative feedback exerted on the expression of the per and tim genes by the complex formed between the PER and TIM proteins. For Neurospora, similarly, the model relies on the feedback exerted on the expression of the frq gene by its protein product FRQ. In both models, sust ained rhythmic variations in protein and mRNA levels occur in continuous da rkness, in the form of limit cycle oscillations. The effect of light on cir cadian rhythms is taken into account in the models by considering that it t riggers degradation of the TIM protein in Drosophila, and frq transcription in Neurospora. When incorporating the control exerted by light at the mole cular level, we show that the models can account for the entrainment of cir cadian rhythms by light-dark cycles and for the damping of the oscillations in constant Light, though such damping occurs more readily in the Drosophi la model. The models account for the phase shifts induced by light pulses a nd allow the construction of phase response curves. These compare well with experimental results obtained in Drosophila. The model for Drosophila show s that when applied at the appropriate phase, light pulses of appropriate d uration and magnitude can permanently or transiently suppress circadian rhy thmicity. We investigate the effects of the magnitude of light-induced chan ges on oscillatory behavior. Finally, we discuss the common and distinctive features of circadian oscillations in the two organisms.