JOURNAL OF BIOLOGICAL RHYTHMS / December 1999Leloup et al. / L MIT CY LE MODELS FOR CIRCADIAN RHYTHMS Limit Cycle Models for Circadian Rhythms Based on Transcriptional Regulation in Drosophila and Neurospora

Abstract We examine theoretical models for circadian oscillations based on transcriptional regulation in Drosophila and Neurospora. For Drosophila, the molecular 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 expres-sion of the frq gene by its protein product FRQ. In both models, sustained rhyth-mic variations in protein and mRNA levels occur in continuous darkness, in the form of limit cycle oscillations. The effect of light on circadian rhythms is taken into account in the models by considering that it triggers degradation of the TIM protein in Drosophila, and frq transcription in Neurospora. When incorporating the control exerted by light at the molecular level, we show that the models can account for the entrainment of circadian rhythms by light-dark cycles and for the damping of the oscillations in constant light, though such damping occurs more readily in the Drosophila model. The models account for the phase shifts induced by light pulses and allow the construction of phase response curves. These com