The circadian clock is a self-sustained biological oscillator which can be entrained by environmental signals.The cyanobacteria circadian clock is the simplest one,which is composed of the proteins KaiA,KaiB and KaiC.The phosphorylation/dephosphorylation state of KaiC exhibits a circadian oscillator.KaiA and KaiB activate KaiC phosphorylation and dephosphorylation respectively.CikA competing with KaiA for the same binding site on KaiB affects the phosphorylation state of KaiC.Quinone is a signaling molecule for entraining the cyanobacterial circadian clock which is oxidized at the onset of darkness and reduced at the onset of light,reflecting the environmental light-dark cycle.KaiA and CikA can sense external signals by detecting the oxidation state of quinone.However,the entrainment mechanism is far from clear.We develop an enhanced mathematical model including oxidized quinone sensed by KaiA and CikA,with which we present a detailed study on the entrainment of the cyanobacteria circadian clock induced by quinone signals.We find that KaiA and CikA sensing oxidized quinone pulse are related to phase advance and delay,respectively.The time of oxidized quinone pulse addition plays a key role in the phase shifts.The combination of KaiA and CikA is beneficial to the generation of entrainment,and the increase of signal intensity reduces the entrainment phase.This study provides a theoretical reference for biological research and helps us understand the dynamical mechanisms of cyanobacteria circadian clock.