A mathematical model of the Drosophila circadian clock with emphasis on posttranslational mechanisms.

Experimental evidence points increasingly to the importance of posttranslational processes such as phosphorylation and translocation in the molecular circadian clocks of many organisms. We develop a mathematical model of the Drosophila circadian clock that incorporates the emerging details of the timing of nuclear translocation of the PERIOD and TIMELESS proteins. Most models assume that these proteins enter the nucleus as a complex, but recent experiments suggest that they in fact enter the nucleus separately. Our model reproduces observed patterns of intracellular localization of PERIOD and TIMELESS during light-dark cycles and in constant darkness, as well as phenotypes of several clock mutants. We also use the model to demonstrate how the Drosophila clock can exhibit robust oscillations with constant mRNA levels of period or timeless, and propose a possible mechanism for oscillations in double-rescue experiments of per(01)-tim(01) mutants. The model also explains (via posttranslational processes) the counter-intuitive observation that total dCLOCK levels are at their lowest at the circadian time when active nuclear dCLOCK must be peaking in order to activate transcription of other clock genes, implying that for dCLOCK a posttranslationally generated rhythm is more important than the transcriptionally generated rhythm. These results support the idea that posttranslational processes play key roles in generating as well as modulating robust circadian oscillations. While it appears that posttranslational mechanisms alone are not sufficient to generate rhythms in Drosophila, posttranslational mechanisms can greatly amplify a very weak transcriptional rhythm.