Dynamics Analysis Of The Coupled Synthetic Gene Networks

Gene regulatory network is an important research content of systems biology. Becauseof the complexity of the real gene regulatory networks, it is very difcult to carried outon system level, no matter about qualitative analysis or about quantitative analysis.However, there are a quantity of regulatory networks with a particular biological functionindependently in the biological systems, which are called network motifs, such as positivefeedback loops, negative feedback loops, feedforward loops. Research on these simplenetwork motifs’ ability of processing signal, fltering noise, forming spatiotemporal patternhas become the issue at home and abroad. Since real genetic regulatory network is usuallycomposed of many simple control loops, Research on the integration of simple control loopsfacilitates understanding the more complex real network biophysical mechanisms.This thesis mainly studies the dynamics of the synthetic coupled negative feedbackloops, such as oscillation, double rhythms and hard excitation. with the same parametervalues, the system could show birhythmicity, namely the coexistence between two stableregimes of limit cycle oscillations; and hard excitation, namely the coexistence of stablesteady state and the periodic orbits. These two kinds of dynamical phenomena both havebeen proved existing in biological experiments.By adding one component and two regulations, the coupled two negative feedbackloops are formed an integral networks. Using the standard quasi-steady-state approxi-mation assumption, it is easy to obtain the mathematical model. With the support ofthe software, XPPAUT, how the additional negative feedback loop and the main param-eters infuence the dynamics are discussed. Numerical analysis show the rich dynamicalphenomena. These results are signifcant for understanding the rich phenomenon in bi-ology experiments. It is possible to provide guidance for some corresponding biologicalexperiments.