Organisms show physiological rhythms such as sleep-wake and body temperature whose period is roughly 24hrs even in a constant dark condition. Recent studies of molecular biology has identified genes (clock genes) necessary for this autonomous rhythms, called "circadian rhythms". Clock genes are transcribed and from mRNAs, clock proteins are produced. These enter the nucleus through some modifications and inhibit the transcription of own genes. This negative feedback regulation of gene expression generates the oscillation in the abundance of clock proteins and this oscillation of proteins causes circadian rhythm for behavioral level.

[1] "Can an assemblage of those genes and proteins generate a sustained autonomous rhythm?" In this talk, we discuss this question mathematically, by analyzing the stability of nonlinear model, including transcription, modification of proteins, proteins transport and so on.

[2] Period of circadian rhythm remains unchanged with temperature increase (called temperature compensation). It is surprising because negative feedback regulation for clock genes is an assemblage of biochemical reactions and reaction speed for biochemical process generally increases with temperature increase. By analyzing the effect of each reaction step on circadian period in a systematical manner, we consider "why organisms are able to generate robust period against ambient temperature".