The Ueda et al. Drosophila Model

 

This model is taken from Ueda et al. (J. theor. Biol. 210: 401-406, 2001). It consists of two interlocked feedback loops.

The PER-TIM loop

Both these genes are activated by the dCLK-CYC complex, and are repressed by the PER-TIM     complex. There is also an additional activation / repression factor included in this model, independent of these factors. Transcription is modelled in a linear manner. The two proteins form a complex in a reversible manner, which moves between the cytoplasm and nucleus by active transport, modelled in a Michalis Menten manner.

Degradation of mRNAs and proteins consists of enzymatic (Michaelis Menten) and linear components. The rate of enzymatic degradation of PER protein is dependant on the concentration of the DOUBLETIME enzyme, which is set to a constant level. The maximum rate of enzymatic degradation of TIM protein is enhanced by light, providing model entrainment to the light dark cycle.

The dCLK-CYC loop

The dCLK gene is activated by the PER-TIM complex, and is repressed by the dCLK-CYC complex. There is also an additional activation / repression factor included in this model, independent of these factors. Transcription is modelled in a linear manner. The CYC protein is set at a constant level and the gene is not modelled. The two proteins form a complex in a reversible manner, which moves between the cytoplasm and nucleus by active transport, modelled in a Michaelis Menten manner.

Degradation of mRNA and protein again consists of enzymatic (Michaelis Menten) and linear components.

 

Note that in our model we have replaced the single parameter D0, representing the rate constant of linear degradation of all RNAs and proteins, with separate constants for each equation (D0Pm, D0Pc, D0Tm, D0Tc, D0PTc, D0PTn, D0Cm, D0Cc, D0CCc, D0CCn).