| Gene regulatory network is an important research content of system biology,for which re-searchers have proposed a variety of effective research methods.Among these methods,the forward engineering technology method,which is based on the mathematical model and applies biological engineering methods to build a biological function of gene regulatory network,has been widely used at home and abroad.Multicellular system composed of gene oscillators is a kind of important gene regulatory network,which attracts the attention of researchers and technicians in different fields.These systems can often exhibit a variety of interesting dynamic phenomena,such as synchro-nization,clustering,multistability coexistence,multiryhthmicity and chaos,etc..Revealing the mechanism of these phenomena is of important significance for understanding the collaborative behaviors of multicellular organisms and summarizing the design principles of biological networks.In this paper,the population dynamics of a multicellular system composed of composite oscillators coupled by quorum sensing mechanism is studied.Through mathematical modeling,bifurcation analysis and numerical simulation,the effects of some realistic biological factors on the population dynamics behavior are investigated.The main content of this paper is as follows:Firstly,considering that the complex dynamics phenomena such as bifurcation and chaos occur in many gene regulatory networks,two important theories in nonlinear field,bifurcation theory and chaos theory,are introduced.Bifurcation theory is a mathematical theory that studies the characteristics and mechanism of bifurcation.Bifurcation analysis can help us to understand the formation mechanism of some complex dynamic phenomena and provide theoretical basis for our further numerical simulation.Chaos is a new form of existence in nonlinear systems,and it is a solution with inherent randomness in deterministic nonlinear systems.The appearance of chaos enriches the dynamic state of multicellular systems.Secondly,the effects of parameter detuning on the dynamic behavior of multicellular systems of combinatorial gene vibrators were studied.Bifurcation analysis and numerical simulation show that detuning can not only completely eliminate the stable homogeneous equilibrium state,but also generate a new stable heterogeneous equilibrium state.When the parameter detuning is less than 1 and gradually decreases to 0.93,the highly stable heterogeneous equilibrium state will be eliminated.On the other hand,when the parameter detuning is greater than 1,the low-stable heterogeneous equilibrium state will be eliminated,and when the parameter detuning increases to 1.06,part of the periodic solution will be eliminated.In addition,the stable heterogeneous equilibrium state and the asymmetric quasi-homogenous period 1 oscillation always coexist in the case of small detuning,which is quite different from the same vibration subsystem.These results suggest that parameter detuning may be a powerful regulator of genetic network dynamics.Thirdly,the multicellular systems of the above combinatorial gene vibrator was further studied to show the influence of time-scale separation on system dynamics under parameter detuning.The bifurcation analysis and numerical simulation of XPPAUT show that the number of stable equilibrium states,the existence interval and the vibration dynamics of the system will change obviously when the combined vibration subsystem changes from inclined to relaxed vibration to inclined to smooth vibration(ε increases).The number of stable equilibrium state increases from 2 bar to 3 bar,and the new stable heterogeneous equilibrium state will completely coexist with the original low concentration stable heterogeneous equilibrium state;The stable existence range of IHSS with high concentration decreased,while the stable existence range of IHSS with low concentration increased;Stable vibration dynamic changes not only show the existence of interval increase,the interval size from 0.0154 when ε=0.205 to 0.2241 when ε=0.7,more importantly,the system dynamics behavior will become more abundant,even appear chaotic phenomenon,for the cell differentiation and versatility in complex biochemical environment provides a good foundation.On the other hand,multiple dynamic states can coexist,which provides a greater possibility for organisms to adapt to the changing environment.At last,summarizes the research results of this paper,and puts forward some problems worth further study,pointing out the direction for future research. |
