Analysis of Biological Smooth Oscillators Inspired by the Relay Control Tuning Method

Biological oscillation is generated by different genetic circuit structures, such as the smooth oscillator and the relaxation oscillator. Studies on the complex interactions among genes and proteins are essential for understanding the generating mechanism underlying the circadian clock or other biological oscillators. In this paper, the biological oscillation is investigated from a new perspective. It is studied here, through principles in the nonlinear system and control theory, the important factors for the existence of oscillation in the smooth oscillation system. Conclusions have been drawn that both the degradation rates of genes and proteins and the switch-like behavior of the translation process are essential for generating oscillation. The prediction in the Goodwin oscillators model, that the degradations of the clock mRNA and clock protein play important roles in regulating the oscillation period, is discussed here through classic control theory, i.e., the relay control tuning method.