Qualitative Study Of Quorum Sensing On The Discontinuous Model Of Signal Molecules Concentration Regulation

As one of the indispensable regulatory mechanisms in organisms,quorum sensing has attracted extensive attention from experts and scholars at home and abroad.It is of great significance for the prevention and treatment of related diseases caused by quorum sensing to study the relationship between biological factors in the process of quorum sensing and explore the changing law of biological factors.Based on the strong discontinuity of the occurrence process of quorum sensing,the discontinuous function is introduced in this thesis.By studying the regulating effect of quortum sensing on the concentration of signal molecules,a mathematical model with discontinuous function is established.Using the theory of non-smooth system and time-delay system,the dynamic properties of the model are systematically studied and verified by numerical simulation experiments.Taking the concentration of signal molecules as an index,a discontinuous model describing the regulation of signal molecules concentration by quorum sensing mechanism is established,and the interaction between signal molecules and their decomposing enzymes are depicted.By using the theory of non-smooth systems,the existence and stability of the sliding module region,the true(false)equilibrium points and the pseudo-equilibrium points of the model are studied,and the existence of the traversing limit cycle around the sliding mode region is proved.In addition,numerical experiments are carried out to verify the theoretical results and explain their biological significance.Based on the fact that the production of signal molecule decomposition enzymes has a certain time delay compared with the production of signal molecules,a discontinuous mathematical model of bacterial quorum sensing mechanism with time delay for signal molecules concentration regulation is established.The dynamic properties of discontinuous systems with time delay are studied by using the theory of non-smooth system and time-delay system,and the direction and stability of periodic solutions are studied by Hopf bifurcation frequency domain method.Then the theoretical results are verified by numerical experiments with relevant softwareIn this thesis,discontinuous function is introduced to provide a new modeling idea for the theoretical study of quorum sensing mechanism in the future.The theoretical and experimental results show that the concentration of signal molecules and its decomposing enzymes can finally reach a stable state under the regulation of quorum sensing.It is of great significance to further study the prevention and treatment of related diseases caused by quorum sensing mechanism.