Study On The Oscillation Dynamics Of NF-?B Signaling Pathway

The NF-?B signaling system is an important gene regulatory network that regulates the expression of many genes,including the cell cycle,immune response,cell and tissue differentiation,inflammation,and apoptosis.Studies have shown that active NF-?B promotes cell proliferation and the survival and growth of cancer cells,thereby inducing cancer.At the same time,the oscillation can repeatedly transport newly activated NF-?B to the nucleus,thereby maintaining a higher proportion of active and inactive NF-?B in the nucleus.In other words,the oscillation of nuclear NF-?B is not good for cancer treatment.Thus,the study of the dynamics of the NF-?B signaling system has aroused the interests of many scholars.However,previous studies on the NF-?B signaling system have only considered the effects of delay and diffusion separately.So far,the combined effects of delay and diffusion effects have not been considered at the same time.Therefore,it is of great significance to study the dynamics of the delayed NF-?B signaling system with reaction-diffusion terms.This article focuses on the regulatory effects of time delay and diffusion on the oscillating mechanism of the NF-?B signaling system.In Chapter 1,the research background,current status of the NF-?B pathway and its main work are briefly introduced.In Chapter 2,aiming at the core NF-?B three-dimensional model proposed by Krishna et al.,we first consider the influences of the important parameter on the dynamic properties of the system.Second,we consider the effects of transcription and translation delays on the dynamic properties of the system.Then,using time delay as the bifurcation parameter,the stability of the system and the existence of the Hopf bifurcation are studied.Finally,the canonical theory and central manifold theorem are used to determine the properties of the Hopf bifurcation periodic solution,and numerical simulations are performed to verify the theoretical results.We find that the transmission rate of NF-?B from the cytoplasm to the nucleus has a great impact on the dynamic behaviors of the system.Its increase makes the system change from oscillatory to stable,which is beneficial for the treatment of cancer.The time delay can drive the oscillating expression of the system,which is not conducive to the treatment of cancer.In Chapter 3,based on Chapter 2,we consider the effects of diffusion on the complex dynamic behaviors of the system.It is find that the introduction of the reaction diffusion terms can lead to the occurrence of spatially inhomogeneous oscillation periodic solutions.Moreover,the system may occur different spatial patterns with different initial values.In Chapter 4,the seven-dimensional model of NF-?B with A20 proposed by Mengel et al.is studied.The regulatory effects of time delay,important biological factor A20,and several important parameters on the NF-?B signaling system are discussed separately.Similarly,with time delay as the bifurcation parameter,the stability of this dimensional model and the existence of Hopf bifurcation are studied,and some important parameters are analyzed by single-parameter and dualparameter bifurcation.The results show that shortening the time delay,repairing and maintaining the function of A20 protein,and increasing the transcription rate of I?B?may provide new clues for the treatment of related diseases.In Chapter 5,we summarize the full text and look forward to the next research work.