Chaos and birhythmicity in a model for circadian oscillations of the PER and TIM proteins in Drosophila

In Drosophila, circadian oscillations in the levels of two proteins, PER and TIMI result from the negative feedback exerted by a PER-TIM complex on the expression of the per and tim genes which code for these two proteins. On the basis of these experimental observations, we have recently proposed a theoretical model for circadian oscillations of the PER and TIM proteins in Drosophila. Here we show that for constant environmental conditions this model is capable of generating autonomous chaotic oscillations. For other parameter values, the model can also display birhythmicity, i.e. the coexistence between two stable regimes of limit cycle oscillations. We analyse the occurrence of chaos and birhythmicity by means of bifurcation diagrams and locate the different domains of complex oscillatory behavior in parameter space. The relative smallness of these domains raises doubts as to the possible physiological significance of chaos and birhythmicity in regard to circadian rhythm generation. Beyond the particular context of circadian rhythms we discuss the results in the light of other mechanisms underlying chaos and birhythmicity in regulated biological systems. (C) 1999 Academic Press.