Constant Light Alters Both the Period and the Amplitude in a Goodwin Oscillator

Abstract

Light is the most important zeitgeber (time-giver) of the external environment for the circadian rhythms of the organisms. The alternation of the light condition can alter the rhythmic behaviors of the organisms. Exposed to the constant light, the amplitude suppression was observed in the wild-type strains, whereas the period of the circadian rhythms was shortened in the vvd strains of Neurospora. In this study, an explanation was given for this alternation by the Goodwin model. We found that this alternation depends on the degradation rate of the circadian oscillator in Neurospora. Specifically, with a small degradation rate, the constant light leads to the suppression of the amplitude. The small or moderate degradation rate results in a negative relationship between the period of the oscillator and the intensity of constant light. In addition, the analytical solutions explored by the asymptotic techniques confirm our simulation results. This article provides the insights for the mechanisms of light affecting the circadian clock, and the analytical solutions for the period and the amplitude of the clock.

Keywords: circadian rhythm, Goodwin model, constant light, period, amplitude