Dynamic Evolution Mechanism And Control Of Genetic Regulatory Networks

Genetic regulatory networks refer to complex dynamic systems which describe the inhibition or activation functions between RNA, DNA, protein and other gene substances in cells (or in a particular genome). The study of genetic regulatory networks exploits the dynamic behaviors of biosystem at the molecular level. As we all know, diversity is a basic feature of biological systems. The organism diversity is essentially caused by the multi-attractor dynamic behaviors of genetic regulatory networks. From the perspective of complex networks, each cell is a complex dynamical system. These intracellular gene substances interact each other. The system has the ability to show the multi-attractor dynamical evolution, i.e., it can present or coexist various different dynamical behaviors such as stable states, bifurcations, limit cycles, chaos, pulses, synchronization, collective behaviors, and so on. It is of great significance to study the diversity of biological systems from the perspective of complex networks, as well as to explore the mechanism behind the evolution of biological systems.This dissertation studies the multi-attractor dynamic behavior through several kinds of genetic regulatory networks, including cyclic genetic regulatory networks with mixed time delays, double negative feedback loop with autoregulation, coupled repressorlators, coupled cyclic genetic regulatory networks and a multi-attractor motif. A new definition of multi-synchronization of complex networks is also proposed. A partial impulsive control strategy is developed, which can realize the multi-synchronization of coupled heterogeneous gene oscillator networks. The main contents and innovations of this dissertation are summarized as follows:Stability and bifurcation analysis of cyclic genetic regulatory networks with mixed time delays. Cyclic genetic regulatory network is an important gene structure. This dissertation studies the stability and bifurcation behavior of cyclic genetic regulatory networks with mixed delays (distributed and discrete time delays) under different positive and negative gains. The functions of the network gain, network size, and biochemical parameters on the system stability are explained. The conditions for the system to present saddle-node bifurcation and Hopf bifurcation behaviors are established.Dynamic analysis of two typical gene networks. This dissertation exploits the bistability of double negative feedback loop with autoregulation. The necessary and sufficient conditions for the equilibrium existence and local stability of the system at arbitrary equilibrium are obtained. The effects of various biochemical parameters and initial conditions on the system stability are explained. At the same time, this dissertation also studies the Hopf bifurcation sequence caused by coupling delays in coupled repressorlators. The effects of coupling mechanism and coupling time delays on the multiperiodicity behaviors of complex genetic regulatory networks are illustrated, which deepen our understanding of the complex mechanism of gene dynamic behaviors.Multi-attractor analysis of coupled cyclic genetic regulatory networks with discrete time delays. The dissertation uses cyclic genetic regulatory networks to construct a complex genetic regulatory network with discrete time delay. When the gain of the basic cyclic gene unit is negative, the coupled system only has a unique equilibrium, and is likely to occur a series of Hopf bifurcation behaviors. When the gain of the basic gene unit is positive, the coupled system may have multiple equilibria, and presents the phenomenon of multistability dynamics.Coexistence of multi-attractor in the simple gene motif. Motif is the basic unit of complex networks. Its frequency of emergence is higher than that of a random network, and it has important significance for the realization of a specific biological function. This dissertation studies a multi-attractor gene motif which is composed of two negative feedback loops and a self-autoregulatory function. Under different parameters and initial conditions, the gene motif has the ability to present complex dynamical behaviors, such as the point attractor (which is also a structure switching attractor), periodic attractor and chaotic attractor. Gene motifs are easy to be realized by artificial gene loop, which is helpful to deepen the understanding of the dynamic evolutionary process of genetic regulatory networks.Multi-synchronization of heterogeneous genetic oscillator networks via partial impulsive control. This dissertation proposes a definition of multi-synchronization based on other existing synchronization behaviors. This definition contains complete synchronization, group synchronization, quasi-synchronization and other complex dynamic behaviors. A new partial impulsive control protocol is introduced which combines the advantages of pinning control and the traditional impulsive control. Only a fraction of gene molecules in each oscillator is controlled by impulsive signals. The effectiveness of partial impulsive control for multi-synchronization in heterogeneous coupled genetic oscillator networks is proved by Lyapunov stability theory. Sufficient conditions about the impulsive control intensity, the number of controlled molecules and the impulsive time interval are established.Finally, this dissertation summarizes the main work and the innovative points of the whole text, and points out some meaningful issues to be exploited in the future.