Bifurcation Analysis Of Gene Oscillations In Escherichia Coli With Negative Feedback And Time Delay Regulation

Gene regulation is the mechanism of regulation of gene expression in cells.The main process of gene expression is the transcription of genes and the translation of mRNA.The main research contents of gene regulation network include the discussion of stability,periodic oscillation behavior,bifurcation and chaos.Escherichia coli is the most common type of bacteria in the gut of humans and animals.The interaction of sRNA,mRNA and protein in Escherichia coli plays an crucial role in almost all cellular processes.In addition,the feedback regulation of sRNA on mRNA is most important.That is,when participating in cellular processes,sRNA mainly mediate mRNA degradation or translational repression.The first chapter,briefly described the significance of research,gene regulation research status,gene expression process,regulatory mechanisms.The second chapter discusses the use of negative feedback regulation of the kinetic behavior of E.coli gene vibrator study found that in the original with delay control model,the transcription delay and the translation delay increases to a certain critical value,the occurrence of bifurcation.Interestingly,after the introduction of negative feedback control in the model,the bounds of transcript delay and translation delay increase and bifurcation delays occurs,that is,the model can remain stable over a larger time delay.The numerical simulation is given at the end of the article.The third chapter,we develop a model by adding a delay to time delay model aim to understand the delay affects the kinetic behavior of E.coli gene network.A better knowledge of the sRNA mediated motifs is also of interest for bio-engineering and artificial control.Firstly,we study the asymptotic stability at the positive equilibrium point of the model and the conditions for determining the existence of Hopf bifurcation by using the time delay as a bifurcation parameter.Then,the bifurcation properties are determined by applying normative theory and central manifold theorem.Finally,the results show that time delay can change the system state and supercritical Hopf bifurcation occurs when the time delay crosses a criticalvalue.Furthermore,the results also show the new time delay exceeding the critical value,the system appear multi-peak periodic solution and chaos.