Example: Circadian Rhythms

This is an example of a mathematical model of circadian rhythms simulated using SigTran. Circadian rhythm refers to the periodical oscillation that occurs in gene activity, physiology, and behavior of nearly all living organism within a period of 24 hours. The model presented here is based on the mathematical model of circadian rhythms proposed by Gonze et al [1].

In this model production of the regulatory protein PER starts a pathway that leads to the formation of a complex that decreases production of PER by inhibiting the activity of gene promoter of PER. This negative feedback system therefore causes any increase in the population of PER to be followed by a decrease, hence causing the oscillatory pattern observed. A through description of this model is provided in [1], also a schematic representation of the model, the reaction description and the value of kinetic constants are supplemented in the work of Gonze and colleagues. The initial populations of the different molecular species in this model are not provided in the article mentioned.

In this model the mRNA that produces PER is denoted as Mp, and the oscillation in the concentration of Mp is taken as a representation of the level of production of PER. The above graph is the plot of the simulation results representing the temporal fluctuation in the population of Mp.

[1] Gonze, D., Halloy, J., Goldbeter, A. (2002) PNAS 99, 673-678