A temperature-compensated model for circadian rhythms that can be entrained by temperature cycles

From the viewpoint that reaction rates will change with temperature, we present a general method to build circadian clock models that generate circadian oscillations with almost constant period under different constant ambient temperature, and propose an algorithm estimating the parameter condition for compensated period against the change of temperature based on the PER single-feedback loop model of Goldbeter [1995. A model for circadian oscillations in the Drosophila period protein (PER). Proc. R. Soc. London Ser. B 261, 319-324] for Drosophila. We show that the model with derived parameters can realize the temperature compensation over a wide range of temperature, and simultaneously can realize the entrainment to temperature cycles.