A Research On Combinatorial Regulation And Control Strategies Of Nonlinear Dynamical Networks

Most of the daily activities in nature are made up of nonlinear systems.When the various parts of these systems interfere,cooperate or compete with each other,nonlinear interactions will occur.Therefore,a nonlinear system is a system in which the change in output is not proportional to the change in input.Because this important property that nonlinear problems have aroused the interest of engineers,biologists,physicists,mathematicians and other researchers.The common dynamical behavior of nonlinear systems includes chaos,multistable,soliton,limit cycle,self-oscillation and so on.These common dynamical behaviors are very important for studying the combinatorial regulation or control strategies of the dynamical network of biomolecules.The theoretical methods used to analyze these dynamical behaviors mainly include bifurcation theory,perturbation theory,catastrophe theory,dissipation theory and so on.In this paper,the theoretical knowledge of these nonlinear systems is used to study the combinatorial regulation and control strategies of nonlinear systems.The works of this article focus on the following four issues(the first two issues are about combinatorial regulation,and the latter two issues are about control strategies):1)Firstly,we study the detection of synergistic combinatorial perturbation based on bifurcation theory.For nonlinear systems,we propose a method to quantitatively detect the synergistic combinatorial perturbation by using bifurcation theory.In this method,we regard the input of external drugs as a perturbation to the parameters in the system,and then according to the response of the dynamical system to the perturbation,all the parameters in the system can be divided into two groups.We combine parameters in the two groups in pairs to obtain three types of combinations,and the synergy of each combination can be detected by the relative position of the two parameters bifurcation curve and the isobole.In order to prove the effectiveness of the method,we apply the method to the epithelial-mesenchymal transition(EMT)network,and it has been well verified.This method has certain guiding significance for the rational design of combination drugs and other types of combinatorial regulation.2)Secondly,we study how to screen synergistic drug target combinations in disease-related molecular networks.Compared with drugs based on a single target,drugs based on a combination targets can not only overcome many limitations of drugs based on a single drug target,but also treat diseases more effectively and safely.We propose a new strategy to screen the synergistic combinations of two drug targets in the disease network based on the classification of single drug targets.This method attempts to determine the sensitivity of a single perturbation measure,and then determine the combinatorial perturbation that can switch the disease state to the normal state,and further detect the synergy of the drug target combinations corresponding to the combinatorial perturbation.We apply this strategy to the arachidonic acid metabolism(AA)network.In this network,we have discovered 18 pairs of synergistic drug target combinations,of which five pairs have been proven to be feasible in biological or medical experiments.3)Then,we study the impulse control of nonlinear dynamical network.By constructing an impulse control function,we propose a discrete control strategy for a nonlinear dynamical system.The appropriate input of the controllable system is crucial.This strategy controls the appropriate nodes in the network in a discrete manner to realize the switch from the disease state to the healthy state.In order to prove the effectiveness of this strategy,we applied it to two biomolecular networks with multi-stable states:the epithelial-mesenchymal transition(EMT)network and the Notch-Delta-Jagged signaling pathway.In theory,this strategy can not only be used to guide more feasible pharmacological design,but also can be applied to the dynamical analysis of multi-stable systems in biology,medicine and other fields.4)Finally,we study the influence of external drug intake on the threshold of the COVID-19 infection model.We analyze the impact of antiviral drugs on COVID-19 infection by establishing a mathematical model between uninfected healthy cells,infected cells and COVID-19.Antiviral drug intake functions include periodic functions and impulse functions in here.Through theoretical analysis,we prove that when the basic reproduction number R₀is less than 1,the disease-free equilibrium point of the system is globally asymptotically stable,which means that the patient can recover from the disease.When R₀is greater than1,COVID-19 infection will persist.Since the expression of R₀is closely related to the parameters in the drug intake function,we can use the relationship between R₀and drug intake parameters,as well as the relationship between R₀and COVID-19 infection status to find a way to regulate the COVID-19 disease status.This research can provide theoretical guidance on how to control COVID-19 infection with drugs,and can also help us further understand the dynamical complexity of the viral infection system.