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 time-delay differential equation, simulates the expression of a generic clock protein that inhibits its own expression through a feedback mechanism. Despite its simplicity, this model fulfils most of the necessary characteristics of a realistic representation of natural circadian clocks: robust and stable oscillations with circadian free-running periods, typical phase response curves and entrainment to environmental zeitgebers. The present model reduces the molecular mechanism necessary to sustain stable oscillations to its bare bones, suggesting that the essential factor is the time-delayed negative feedback of the oscillating protein on its own expression.