Organisms show physiological rhythms such as sleep-wake whose period is roughly 24hrs even in an environment without any information for time. Recent studies of molecular biology have revealed that oscillation in the abundance of specific cellular proteins generates this autonomous rhythm, called "circadian clock".
By analyzing nonlinear models for circadian clock, we derived the conditions necessary for the generation of oscillation. In the models, clock genes are transcribed and from mRNAs, clock proteins are produced. These inhibit the transcription of own genes through some modifications. When all reactions except for the inhibition of transcription are Michaelis-Menten type, reaction speed for these saturates for very large abundance of substrates. We identified that effect of saturation at reaction step on the tendency of the dynamics to oscillate depends critically on the location and direction of the reaction step in the gene-protein network.
Period of circadian clock remains unchanged with temperature increase, though reaction speed for biochemical process involved in feedback regulation for circadian clock (is unknown but it) should increase with temperature increase. By analyzing the effect of each process in gene-protein network on circadian period, we consider plausible sensitivity of each reaction to temperature, which generate robust period against ambient temperature.