Jc. Leloup et A. Goldbeter, A MODEL FOR CIRCADIAN-RHYTHMS IN DROSOPHILA INCORPORATING THE FORMATION OF A COMPLEX BETWEEN THE PER AND TIM PROTEINS, Journal of biological rhythms, 13(1), 1998, pp. 70-87
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.