Delay model of the circadian pacemaker

We present a simple and realistic model of the circadian pacemaker that can be interpreted in molecular terms. The model, which consists of a single t ime-delay differential equation, simulates the expression of a generic cloc k protein that inhibits its own expression through a feedback mechanism. De spite its simplicity, this model fulfils most of the necessary characterist ics of a realistic representation of natural circadian clocks: robust and s table oscillations with circadian free-running periods, typical phase respo nse curves and entrainment to environmental zeitgebers. The present model r educes the molecular mechanism necessary to sustain stable oscillations to its bare bones, suggesting that the essential factor is the time-delayed ne gative feedback of the oscillating protein on its own expression. (C) 2000 Academic Press.