A Mathematical Model Of The Light Adaptation In The Mammalian Circadian Clock

The circadian clock refers to the physical and biological behavior of cyclical changes with time. Behind these periodic behaviors, some molecular concentrations are changing with 24 hours period inside cells.Light regulates the biological rhythm through the retinohypothalamic tract(RHT) pathway. The latest biology research(published in the Cell 2013) showed that the negative CRTC1-SIK1 feedback loop represses the expression of per1 through RHT and in turn suppresses the responds of circadian clock on light stimulation. So this pathway provides a light adaptation mechanism of circadian clock. The following are our main results and contributions:(1) Based on the experimental results, we developed the first mathematical model of the CRTC1-SIK1 module. Then we coupled this module with a previous model of the cell-autonomous mammalian circadian clock, which was developed by Andrew C. Liu et. al.. Thus, we built a full mathematical model which includes the details of light entrainment of the mammalian circadian clock.(2)By the comparison of wild type(WT) and knock down(KD), we revealed that the SIK1 negative feedback pathway provides light adapta-tion mechanism of circadian clock. We simplify our model and proof that the steady solution of the simplified model is unique and local stability.(3) We illustrated the light adaptation is a crucial issue in circadian clock system.(a) Light adaptation provides the phase robustness to light stimulation in circadian clock.(b) Light adaptation can reduce the probability of the singularity behavior, which refers to the complete loss of biological rhythm by proper stimulation. Singularity behavior is one of the worst situations in circadian clock system.