Temperature compensation and entrainment in cyanobacteria circadian rhythm

Circadian rhythm is an endogenous rhythmic behavior of organisms used to adapt to the external environment. Although most biochemical reactions accelerate with increasing temperature, the period of circadian rhythms remains relatively stable across a range of temperature, a phenomenon known as temperature compensation. Meanwhile, circadian rhythms can be reset by environmental signals, such as daily periodic light or temperature, a phenomenon known as entrainment. Cyanobacteria are the simplest organisms to have circadian rhythms. The effect of light on cyanobacteria circadian rhythm has been widely studied with mathematical models. However, the effect of temperature on cyanobacteria circadian rhythm and the mechanisms of temperature compensation and entrainment are far from clear. In this paper, we apply a recent model to incorporate temperature dependence by Van't Hoff rule. With numerical simulation, we study the temperature compensation and entrainment in detail. The results show that the system can exhibit temperature compensation when the post-transcription process is insensitive to temperature. The temperature compensation is caused by the cancellation of the increase of amplitude and the acceleration of speed, resulting in the stable period, when the temperature rises. The system can also exhibit temperature entrainment in constant light in a very limited temperature range. When the periodic light is added simultaneously to simulate more realistic environment, the temperature range of entrainment is greatly improved. The results also suggest that long-day condition is conducive to entrainment. The findings of this paper provide a theoretical reference for biological research and help us understand the dynamical mechanisms of cyanobacteria circadian rhythm.