PER/TIM-mediated amplification, gene dosage effects and temperature compensation in an interlocking-feedback loop model of the Drosophila circadian clock

We have analysed a first-order kinetic representation of a interlocking-feedback loop model for the Drosophila circadian clock. In this model, the transcription factor Drosophila CLOCK (dCLK) which activates the clock genes period (per) and timeless (tim) is subjected to positive and negative regulations by the proteins 'PAR Domain Protein 1' (PDP1) and VRILLE (VRI), whose transcription is activated by dCLK. The PER/TIM complex binds to dCLK and in this way reduces the activity of dCLK. The results of our simulations suggest that the positive and negative feedback loops of Pdp1 and vri are essential for the overall oscillations. Although self sustained oscillations can be obtained without per/tim, the model shows that the PER/TIM complex plays an important role in amplification and stabilization of the oscillations generated by the Pdp1/vri positive/negative feedback loops. We further show that in contrast to a single (per/tim) negative feedback loop oscillator, the interlocking-feedback loop model can readily account for the effect of gene dosages of per, vri, and Pdp1 on the period length. Calculations of phase resetting on a temperature compensated version of the model shows good agreement with experimental phase response curves for high and low temperature pulses. Also, the partial losses of temperature compensation in perS and perL mutants can be described, which are related to decreased stabilities of the PER/TIM complex in perS and the stronger/more stable inhibitory complex between dCLK and PER/TIM in perL, respectively. The model shows (somewhat surprisingly) poor entrainment properties, especially under extended light/dark (L/D) cycles, which suggests that parts of the L/D tracking or sensing system are not well represented.