Dynamical Analysis Of Two Types Of Synthetic Genetic Regulatory Networks

This thesis studies the dynamical behaviors of two types of synthetic genetic regulatory networks:one takes composite oscillators which are repressilators and hystersis-based relaxation oscillators as the core elements and it is used to analyze the influence of parameter detuning among oscillators on system collective dynamics.The other takes repressilators as the core components and it is used to investigate the effect of integration of intracellular and extracellular signals i.e.combinatorial regulation,on the population behaviors of the system.The following results have been achieved:(1)The effect of parameter detuning on multi-stability and multi-rhythmicity of a multicellular com-munication system are studied.Among them,single systems are composite oscillators,which are coupled by a quorum sensing mechanism.This study takes the maximum transcription rate as the bifurcation pa-rameter,and uses bifurcation analysis and numerical simulation.It is found that when the constituents of the system change from homogenous oscillators to inhomogenous oscillators,and the degree of detuning gradually increases,the characteristics of stable steady-state solution and stable periodic solution of the system are remarkably changed:the homogenous steady state is replaced by a new inhomogenous steady state,and two inhomogenous steady states coexist and form bistability.In-phase period 1 oscillation be-comes quasi-in-phase period 1 or asymmetric period 1 oscillation;the existent intervals of the left and right branches of the stable periodic 2 solution decrease and even the right branch disappears completely.When the detuning increases to a certain extent,a stable periodic 4 solution appears,the coexistence mode of the stable periodic solution and the stable periodic solution is also changed.Our results provide a basis for understanding the population behavior of multicellular systems.(2)The effect of integration of intracellular and extracellular signals on the population behavior of a multicellular communication system is studied.The repressilators are coupled by quorum sensing mech-anism.Taking the parameter v in cis-regulation input function as the bifurcation parameter and using numerical simulation and detailed bifurcation analysis,we find that when the Hill coefficient n increases,the steady-state solution of the system will be replaced by the new oscillation solution;when Hill coef-ficient is appropriately large and v changes from small to large,the oscillation of the system will evolve from non-balance cluster to balance cluster;finally,the increase in the number of oscillators will make the manifestations and the coexisting modes of oscillating clustering in the system more abundant the system.Stable steady states and stable oscillation are two common dynamical behaviors in biological systems.For the stable steady states,we mainly pay attention to monostability,bistability and multi-stability;for the oscillating solution,we mainly studies the periodic oscillation,quasi-periodic oscillation and chaotic oscillation of the system.Meanwhile,we pay close attention to the synchronization and clustering of multiple oscillators and the coexistence of different dynamical regimes,which provides us with theoretical support to understand the rhythmical behaviors and the adaptation to external environment of multicellular organisms.In the above two models,the systems are all composed of oscillators coupled by quorum sensing mechanism.In order to study the dynamical behavior of the systems,we adopt the bifurcation theory and chaos theory for theoretical analysis,and use XPPAUTand MATLAB software for numerical simulation,thus obtain the results of this paper.