Modelling Circadian Rhythms in Drosophila and Investigation of VRI and PDP1 Feedback Loops Using a New Mathematical Model

We present a brief review of molecular biological basis and mathematical modelling of circadian rhythms in Drosophila. We discuss pertinent aspects of a new model that incorporates the transcriptional feedback loops revealed so far in the network of the circadian clock (PER/TIM and VRI/PDP1 loops). Conventional Hill functions are not used to describe the regulation of genes, instead the explicit reactions of binding and unbinding processes of transcription factors to promoters are probabilistically modelled. The model is described by a set of ordinary differential equations, and the parameters are estimated from the in vitro experimental data of the clocks' components. The model is robust over a wide range of parameter variations. Through the sensitivity analysis of the model, roles of VRI and PDP1 feedback loops are investigated, and it is proposed that they increase the robustness of the clock.