Research On The Effects Of Time Delay On The Dynamic Of Quorum Sensing System

Recently,experimental evidence has shown that the oscillating behavior of quorum sensing system plays an important role in the biological field,such as in the rapid and tunable coupling process of genetic circuits,in the control of protein synthesis in prokary-otic and eukaryotic systems,the biological control of plant diseases and insect pests and in the process of drug delivery.Importantly,the amplitude and oscillation period of the quorum sensing system determine the dose and time of the drug delivered by the bacteria.Therefore,the dynamic behavior of quorum sensing system has become a frontier topic in the field of systems biology,which has attracted the attention of many scholars and ex-perts.However,little attention has been paid to the effect of time delay in bacterial gene expression on the stability,Hopf bifurcation and periodic oscillation of bacterial quorum sensing system.Therefore,it is a very significance subject to study the influence of time delay on the oscillatory mechanism of quorum sensing system.This paper mainly studied the effects of protein synthesis time delay on dynamic behaviors of quorum sensing system and quorum sensing system with H₂O₂regulation.Firstly,the research background of this topic,the development status of bacterial quorum sensing and the main work of this paper are expounded.Secondly,based on the gene regulatory network model of the bacterial quorum sensing system proposed by Prindle et al.,we studied how the time delay of protein synthesis affects the oscillation behavior of the bacterial quorum sensing system.The model is linearized at the positive equilibrium point.According to the corresponding characteristic equations,the stability at the equilibrium point and the existence condition of the Hopf bifurcation are determined.The center's popular theorem and normative theory are used to determine the properties of the Hopf bifurcation periodic solution.Numerical simulation is carried out to support theoretical results.Numerical simulation results are consistence with theoretical analysis.Thirdly,we apply the same method in Chapter 2 to study the effects of time delay,model parameters and H₂O₂on the gene regulatory network of the bacterial quorum sensing system with H₂O₂regulation proposed by Prindle et al.Finally,the main content and innovation of the full text are summarized,and looked forward to further research directions.