Mathematical Modeling and Progress in Test of Mammalian Biological Clock

  • Yiren Chen


This study aims to use mathematical models to integrate experimental data and analyze the unique advantages of gene regulation network dynamics, combine the results of the mathematical model in the field of biological rhythm research. The circadian rhythm of mammals is controlled by neurons located in the visually intersecting upper jaw, each neuron contains its own biological clock. This paper establishes a computational model of a 16-dimensional ordinary differential equation, in this model, the circadian clock mRNA (X) produces a circadian clock protein (Y), protein (Y) promotes transcription of the inhibitor (Z), which inhibits transcription of the circadian clock gene, thus forming a negative feedback loop, this model is an autonomous sustaining oscillator. The autonomous sustaining oscillator can be obtained by selecting a sharply rising Hill function (with a relatively large Hill coefficient).This limitation is mainly caused by the linear term used to describe the attenuation. In addition, studied the effect of light on the circadian clock, analyze the perspectives in mathematical methods combined with network. By controlling a single variable, comparing the recorded data and analysis of the results, the results show that there is a mathematical model relationship between the mammalian clock and the existence of the self-sustaining vibrator and illumination. The results show that the daily illumination with a 24-hour period has a resetting effect on the vibrator cycle; the relevant microRNA also has an effect on the circadian clock at the post-transcriptional level. This paper summarizes the mathematical modeling and dynamics of the biological clock and predicts the prospects for future hot research.