Research On Optimal Strategy For State Transition Of Gene Regulatory Network

Biological systems are generally multi-stable systems,in which different stable states,ie attractors,represent different manifestations of the organism.Generally speaking,biological organisms are either working around an attractor or are moving towards a certain stable state.Recent studies have shown that the transformation of biological systems from one state to another can be achieved,such as the transition of cells from an early cancer state to a normal state.Therefore,this provides new opportunities for clinical treatment of many diseases.The molecules of biological systems have intricate regulatory relationships,so biological networks are highly complex and highly nonlinear.Because gene regulatory network is of great significance in biological systems,with the extensive development of gene sequencing technology in the past decade,a lot of research has been conducted to explore the controllability and state transition of gene regulatory networks from the perspective of control theory or physical energy.However,most of the current researches focus on Boolean network models or linear differential equation models,and ignore the continuous or nonlinear dynamic characteristics of gene regulatory network.In addition,some scholars have tried to perturb all the parameters in the nonlinear differential equation model of gene network in order to find the control variables that can achieve the state transition.But this method will consume huge time cost and computational costs for gene network with numerous regulatory parameters.Also it is impossible to find the optimal control strategy by parameter perturbation.It is a challenge to identify the minimum set of control variables from numerous control parameters and design the control signals for the current research on state transition strategies of gene network.Based on the idea of optimization,this paper extended the dynamic optimization algorithm and the mixed integer dynamic optimization algorithm,and implements the optimal control for the state transition of the gene regulatory network.The main contents include the following points:1.In this paper,an extended quasi-sequential algorithm is used to optimally design the control signals for the state transition of gene network.On the one hand,the trajectory of the control signal is optimized.On the other hand,based on the requirements of time optimization,the discrete finite element length is treated as the control variable,and time is added to the objective function.This method is applied to a two-node gene network and a T-LGL signal network,where the results proved the effectiveness of the quasi-sequential method in the optimal control of biological systems.2.In order to identify the control variables from numerous regulatory parameters of gene network,this paper formulates this problem as a mixed-integer dynamic optimization problem,and solve it with the mixed integer dynamic optimization algorithm.Due to the difficulty of selecting initial value and the instability of the MINLP slgorithm,this paper converts the mixed-integer dynamic optimization problem into a nonlinear programming problem through the discretization of variables and integer processing.This method is applied to a myeloid differentiation regulatory network,a cancer gene regulatory network,and a T-LGL signaling network,simultaneously realizing the identification of control variables for state transition,optimal design of signal paths,and minimization of transition time.A number of feasible strategies besides the optimal scheme have also been obtained.3.Considering that the disordered periodic rhythm will lead to the dysfunction of the biological system,this paper optimized the biological system with abnormal periodic rhythm.Due to the complex dynamic characteristics of such biological systems,this paper adopts a time-segmented strategy to achieve the state transition and periodic phase resets of the periodic rhythm in biological systems.This method was applied to chaotic systems,mammalian circadian rhythm systems,and gastric cancer gene regulatory networks,verifying the effectiveness of the optimization method.Although the optimal control of gene networks in this paper is implemented based on mathematical models,many practical factors of clinical treatment of diseases are taken into consideration,thus the method in this paper has practical guiding significance.In addition to gene regulatory networks,the method can also be used for state transition problems in other complex process systems.