Oscillatory Dynamic Study Of Genetic Regulatory Networks With Transcriptional And Translational Time Delays

Oscillation of genetic regulatory networks represents a ubiquitous mechanism in biology,occurring in many biological events,and controlling every aspect of cell physiology from signaling,motility and development to growth,division and death.Over the years,however,the generation mechanism of such vital periodic behavior in cells and its physiological functions played in vivo,still are important scientific problems that need to be answered urgently.Extensive experimental and theo-retical evidence indicates that gene expression,is a time-consuming process,and inevitably involves time delays resulting from transcription,transcript splicing and processing,and protein synthesis.In particular,such delays can result in oscillato-ry expression of mRXA and protein,having important consequences on dynamies of genetic regulatory networks and consequently on biological functions.Not sur-prisingly,the issues of how to identify such delays and their function mechanisms,and of understanding how they are regulated,have caught the attention of many molecular biologists,systems biologists and computational biologists.From the nonlinear dynamic perspective,this dissertation is mainly concerned with the oscil-latory dynamics of several typical genetic regulatory networks with transcriptional and translational time delays.The main contents of this thesis are summarized as follows:1.Oscillatory dynamics of p38 activity with transcriptional and translational time delays.Recent experimental evidence reports that oscillations of p38 MAPK(p38)activity would efficiently induce pro-inflammatory gene expression,and can allow cells to respond optimally to continuous cytokine stimulation,thereby pre-venting cell damage and apoptosis that can be caused by continuous and excessive p38 activation.Because transcriptional and translational delays are ubiquitous in gene expression,delay-driven sustained oscillations in p38 activity(p38*)could in principle be commonplace.Nevertheless,so far the studies of the impact of such delays on p38*have been lacking both experimentally and theoretically.Here,we use experimental data to develop a delayed mathematical model,with the aim of understanding how such delays aflfect oscillatory behaviour on p38.We analyze the stability and oscillation of the model with and without explicit time delays.We show that a sufficiently input stimulation strength is prerequisite for generating p38*oscillations,and that an optimal rate of model parameters is also essential to these oscillations.Moreover,we find that the time delays required for transcription and translation in mitogen-activated protein kinase phosphatase-1(MKP-1)gene expression can drive p38*to be oscillatory even when the concentration of p38*level is at a stable state.Furthermore,the length of these delays can determine the amplitude and period of the oscillations and can enormously extend the oscillatory ranges of model parameters.These results indicate that time delays in MKP-1 synthesis are required,albeit not sufficient,for p38*oscillations,which may lead to new insights related to p38 oscillations.2.Oscillatory dynamics of p53-Mdm2 circuit with delay effects in response to DNA damage caused by ionizing radiation.The p53-Mdm2 feedback loop,which plays an essential role in the coordination of cellular responses to various stress signals through regulating the activation of p53 protein,is emerging as a potential and validated circuit for cancer therapy.Although the dynamical behavior of the p53-Mdm2 loop has been extensively studied,the understanding of the mechanism underlying the regulation of this pathway still remains limited.Herein,we devel-oped an integrated model with five basic components and three ubiquitous time delays for the p53-Mdm2 interaction in response to DNA damage following ioniz-ing radiation(IR).We showed that a sufficient amount of activated ATM level can initiate the p53 oscillations with nearly the same amplitude over a wide range of the ATM level;a proper range of p53 level is also required for generating the oscil-lations,for too high or too low levels it would fail to generate the oscillations;and increased Mdm2 level leads to decreased amplitude of the p53 oscillation and re-duced expression of the p53 activity.Moreover,we found that the negative feedback loop formed between p53 and nuclear Mdm2 plays a dominant role in determining the p53 dynamics,whereas when interaction strength of the negative feedback loop becormes weaker,the positive feedback loop formed between p53 and cytoplasmatic Mdm2 can induce different types of dynamics.Furthermore,we demonstrated that the total time delay required for protein production and nuclear translocation of Mdm2 can induce p53 oscillations even when the p53 level is at a certain stable high steady state or at a certain stable low steady state.In addition,the two important features of the oscillatory dynamics—amplitude and period—can be controlled by the time delay.Our results are in agreement with multiple experimental observa-tions and may provide clues to p53-Mdm2-based cancer therapy.3.Oscillatory behaviors in Escherichia coli genetic regulatory networks medi-ated by microRNA with time delays and reaction-diffusion terms.Escherichia coli is the first host strain that is used to product recombinant protein production,and is currently being developed to be one of the most widely used protein expression systems.However,our ability to understand dynamics of gene expression of Es-cherichia coli is still limited.Here,the oscillatory expression in Escherichia coli mediated by microRNA with time delays and reaction-diffusion terms is investigat-ed.First,of all,the integrated effects of delays and diffusions are first introduced into the genetic regulatory networks involving microRNAs,and a general model of genetic regulatory networks is then formulated.Secondly,two functional issues on gene regulatory networks,i.e.stability and oscillation of such model,are addressed in detail,and an explicit algorithm determining the properties of periodic oscilla-tion is also presented.We demonstrate that oscillatory expression of Escherichia coli is not only crucially dependent on the transcriptional and translational delays,but also heavily influenced by the diffusion coefficients.The conclusion is prac-tically verified by a lot of biological experiments and observations.We also find that if the diffusion coefficients of miRNA,mRNA and protein are suitably small,it can predict that inhomogeneous periodic oscillations can occur unless there only exhibits spatially homogencous peeriodic oscillations.The obtained results indicate that the effects of transcriptional and translational delays are essential factors for designing or controlling genetic regulatory networks,in the meantime the functions of reaction-diffusion must be taken into account.Finally,numerical examples are presented to illustrate and visualize theoretical results.