Effects of miRNAs on Dynamics of the Circadian Rhythms Model in Drosophila

Experimental evidence points increasingly to the importance of miRNA on circadian rhythms. MiRNA can regulate some key clock genes' expression by stimulating degradation of mRNA and/or repression of translation. In this paper, miRNA is incorporated into a simple model of Drosophila circadian clock with dimerization and proteolysis of PER and TIM. We analytically derive the theoretical results of globally asymptotic stability and provide the conditions for oscillation of the system. Furthermore, the influences of miRNA on the amplitude and period of oscillation are examined by simulation. It is shown that distinct period profiles as a function of miRNA production rate occur.