A PROPOSAL FOR TEMPERATURE COMPENSATION OF THE CIRCADIAN-RHYTHM IN DROSOPHILA BASED ON DIMERIZATION OF THE PER PROTEIN

Recently Goldbeter suggested an interesting model of circadian rhythms based on feedback inhibition by the PER protein on its own rate of tr anscription. In his model, the long delay necessary for generating 24h periodicity is associated with slow phosphorylations of PER protein i n the cytoplasm, assuming that only highly phosphorylated forms of PER are able to enter the nucleus and there interfere with transcription of the per gene. By casting this molecular mechanism in mathematical f orm, Goldbeter showed that it is consistent with many known features o f circadian oscillations in PER abundance. However, he did not address one of the most important characteristics of the circadian rhythm: th e near constancy of the 24h period over a broad temperature range. Hua ng, Curtin, and Rosbash have recently suggested that dimerization of t he PER protein is involved in temperature compensation of the circadia n rhythm in Drosophila, because in mutant flies lacking the PER dimeri zation domain, the period is strongly dependent on temperature. We inc orporate this idea into Goldbeter's model by introducing parallel path ways of phosphorylation of PER monomers and dimers. We assume that bot h monomers and dimers can be transported into the nucleus as long as a t least one PER subunit is multiply phosphorylated. Temperature compen sation in our model arises from opposing effects of temperature (T) on the rate of association of PER monomers and the rate of nuclear impor t of PER protein. In mutant flies, when PER subunits cannot dimerize, the period of the oscillation increases with T, so we assume that the rate constant for nuclear import is a decreasing function of T To comp ensate for this effect in wild-type flies, we assume that the rate of association of PER subunits is an increasing function of T. The mathem atical model reveals the relationship between these opposing tendencie s that must be satisfied to achieve effective temperature compensation .