Stochastic kinetic analysis of transcriptional feedback models for circadian rhythms

Rhythmic levels of activity with nearly twenty-four hour periods in the absence of environmental cues have been observed in species across four kingdoms. For the fly and the mouse it is established that these circadian rhythms arise from cellular genetic networks containing delayed transcriptional feedback mechanisms. This origination of physiologically relevant rhythms from dynamic feedback has inspired many mathematical models of this process. In the present work, the ability of four models from the literature to produce reliable oscillations in the face of stochastic disturbances is explored. The results show that there is a trade off of resistance to some disturbances for increased sensitivity to others, which allows an analogy to the Bode sensitivity integral to be made.