Analyzing the Interactions of Light and Melatonin Forcing in a Mathematical Model of the Human Circadian Oscillator

The pineal secretion of the hormone melatonin demonstrates a circadian (~24 h) rhythm with the onset of melatonin production at night and offset each morning under tight circadian control for entrained individuals. Melatonin exerts both acute sleep-promoting effects and phase-shifting effects on the circadian clock. Due to its hypnotic and chronobiotic (phase shifting) effects, exogenous melatonin supplements are increasingly being used as a treatment for a variety of sleep and circadian diseases and disorders. Phase shifting of the circadian clock can also be accomplished through ocular exposure to light. However, the interacting effects of light and melatonin on the circadian clock are not well understood. To analyze the dynamic behavior of both endogenous and exogenous melatonin's influence on the circadian clock, we extend a previously published mathematical model of the circadian clock to account for forcing due to both endogenous melatonin produced by the pineal gland and exogenous melatonin entering the system through ingested oral supplements. We fit model parameters using published melatonin pharmacokinetics, a melatonin suppression illuminance-response curve, and a 3-pulse 3 mg melatonin phase response curve (PRC). Simulated microscopic PRCs to light and melatonin are determined by the model fits and demonstrate a relative phase difference consistent with previous observations in experimental PRC data. Finally, we simulate a phase advancing experimental protocol utilizing both light exposure and exogenous melatonin to generate model predictions for the effects of interacting inputs to the clock. This modeling framework allows for the study of melatonin's dynamic properties and interaction with the circadian clock. Furthermore, it provides a framework for determining optimal light exposure and exogenous melatonin administration schedules to induce desired phase shifting of the circadian clock.