Amplitude of circadian oscillations entrained by 24-h light–dark cycles

An intriguing property of circadian clocks is that their free-running period is not exactly 24 h. Using models for circadian rhythms in Neurospora and Drosophila, we determine how the entrainment of these rhythms is affected by the free-running period and by the amplitude of the external light–dark cycle. We first consider the model for Neurospora, in which light acts by inducing the expression of a clock gene. We show that the amplitude of the oscillations of the clock protein entrained by light–dark cycles is maximized when the free-running period is smaller than 24 h. Moreover, if the amplitude of the light–dark cycle is very strong, complex oscillations occur when the free-running period is close to 24 h. In the model for circadian rhythms in Drosophila, light acts by enhancing the degradation of a clock protein. We show that while the amplitude of circadian oscillations entrained by light–dark cycles is also maximized if the free-running period is smaller than 24 h, the range of entrainment is centered around 24 h in this model. We discuss the physiological relevance of these results in regard to the setting of the free-running period of the circadian clock.