A MODEL FOR CIRCADIAN-RHYTHMS IN DROSOPHILA INCORPORATING THE FORMATION OF A COMPLEX BETWEEN THE PER AND TIM PROTEINS

The authors present a model for circadian oscillations of the Period ( PER) and Timeless (TIM) proteins in Drosophila. The model for the circ adian clock is based on multiple phosphorylation of PER and TIM and on the negative feedback exerted by a nuclear PER-TIM complex on the tra nscription of the per and tim genes. Periodic behavior occurs in a lar ge domain of parameter space in the form of limit cycle oscillations. These sustained oscillations occur in conditions corresponding to cont inuous darkness or to entrainment by light-dark cycles and are in good agreement with experimental observations on the temporal variations o f PER and TIM and of per and tim mRNAs. Birhythmicity (coexistence of two periodic regimes) and aperiodic oscillations (chaos) occur in a re stricted range of parameter values. The results are compared to the pr edictions of a model based on the sole regulation by PER. Both the for mation of a complex between PER and TIM and protein phosphorylation ar e found to favor oscillatory behavior. Determining how the period depe nds on several key parameters allows us to test possible molecular exp lanations proposed for the altered period in the per(1) and per(s) mut ants. The extended model further allows the construction of phase-resp onse curves based on the light-induced triggering of TIM degradation. These curves, established as a function of both the duration and magni tude of the effect of a light pulse, match the phase-response curves o btained experimentally in the wild type and per(s) mutant of Drosophil a.