A mathematical model for the mammalian melatonin rhythm

We propose and analyse a model for the mammalian melatonin rhythm consisting of first order equations describing the underlying biochemical reactions and pathways. The model includes activation through the secondary messenger system and end product inhibition of activator molecules through cooperative binding of melatonin to the light sensitive suprachiasmatic nucleus (SCN). The model has robust free-running limit-cycle solutions for a range of parameter values. Assuming light sensitivity of parameters describing the binding of melatonin to the SCN we show that the limit-cycle solutions become entrained to the imposed day/night cycle when the period of the cycle is not too far from the free-running period. Higher order cycles and "irregular" behaviour results when the period of the day/night cycle is above or below certain thresholds relative to the free-running period