Research On Macro-dynamics Of Gene Regulatory Networks Based On Individual Entrop

In the living world,each cell is a complex system containing a large number of genes and molecular components,which are regulated by molecules to form a complex gene regulatory network,resulting in different kinetic patterns of gene expression to determine the phenotype and behaviour of the cell.It is essential to establish appropriate macroscopic indicators to describe the kinetic properties of such a complex system.In this paper,we introduce the concept of individual entropy as a macroscopic variable to quantify transcriptional dynamics of complex gene regulatory networks and to investigate the macroscopic state change process of system in response to changes in random perturbations and/or network structures.In this paper,the proposed individual entropy is used to characterize the macroscopic orderliness of a system by the entropy of information about the change of the system at each moment with respect to the basic reference state,and to establish a indicator to characterise the evolution of the network structure.The results show that the proposed individual entropy can be a valuable macroscopic variable for complex systems,which can be used to describe the state transition from order to disorder in the system dynamics and to identify key events in the transition process,as well as to provide early warning of the moment of change in the system dynamics.The main results include the following:1.Establish the gene regulatory network model studied in this article and perform quantitative analysis.Perform dynamic bifurcation analysis on the low-dimensional system in the case of three genes,and determine the parameter range of the system with multi-stable behavior.For the high-dimensional system with multiple genes,the bifurcation analysis of the low-dimensional system is used to study the dependence of the steady-state behaviour on the initial value,and to determine the conditions under which the system converges to the same value for each component,converges to different values for each component,and oscillates.2.To construct individual entropy as a macroscopic indicator to study the dynamics of gene regulatory networks.By designing the change process of noise intensity and network structure,we study the state switching dynamics of the system with the change of noise disturbance or network structure,and identify the key time points that can be used to effectively reveal the sudden change of macroscopic dynamical behavior of complex systems through the dynamic change of individual entropy,and propose early warning conditions for possible state switching.3.The applicability of individual entropy is investigated.Defining different individual entropy indicators for macroscopic systems by choosing different reference states.In order to dynamically track the system state change process,the individual entropy defined by the dynamic reference state is used to quantify the difference between oscillatory modes,and the results obtained show that the individual entropy is more applicable than the traditional information entropy and relative entropy.This study takes a special gene regulatory network as an example,and proposes individual entropy as an indicator to describe the macroscopic dynamical behaviour of complex systems to quantify the switching process of dynamical modes,and the proposed concept of individual entropy can be extended to more general complex system dynamics,giving a new idea for the study of complex systems.