Research On Optimal Control Of Genetic Regulatory Networks Based On Probabilistic Model Checking

Genetic regulatory networks(GRNs)are fundamental and important biological network and its control can realize the regulation of the biological system function.One of the significant topics in the field of system biology is to construct the control theory of genetic regulatory networks by applying external intervention control.The control theory can contribute to development of gene therapy technologies in the future and the resolution of some life science questions.Currently,Boolean network and probabilistic Boolean network as important network model have been widely used for the research on the optimal control problem of GRNs.Optimal control problem of GRNs is to find an effective control policy to make the evolution of network in the desirable fashion,while minimizing control costs.Because of the different control duration,the optimal control problem is divided into finite-horizon optimal control and infinite-horizon optimal control.According to the definition of two kinds of optimal control problems,this paper proposed the related solution based on probabilistic model checking technology.With respect to the finite-horizon optimal control problem,this paper proposed an approach based on probabilistic model checking which used to obtain the optimal total expected cost and corresponding optimal control policy.Firstly,the approach used the modeling language provided by probabilistic model checker PRISM to describe the context-sensitive PBN with perturbation(CS-PBNp)in the case of control input.Then,the optimal total expected cost defined in optimal control was reduced to the minimum reachability reward in a Markov decision processes.Finally,the reward structure was used to describe quantitative information in the optimal control,and the minimum reachability reward property was expressed by probabilistic computation tree logic formula and solved automatically by model checking algorithm in PRISM.The obtained finite-horizon optimal control policy can beneficially alter short-term behavior of the network.The proposed approach was applied to the cell apoptosis network and WNT5 A network.The experimental results illustrated the correctness and effectiveness of the approach.Further,this paper also considered using the approach to solve the finite-horizon optimal control problem with hard constraints and illustrated the flexibility of the approach in the experiment.With respect to the infinite-horizon optimal control problem,this paper proposed an approach based on the combination of genetic algorithm and probabilistic model checker PRISM which used to obtain the optimal total expected cost and corresponding optimal control policy.The infinite-horizon optimal control policy is a stationary control policy which determines the control decision in each network state independent of control time.Firstly,the total expected cost defined in infinite-horizon control was reduced to the steady-state reward in a discrete-time Markov chain.Next,the PRISM model of CS-PBNp containing stationary control policy should be constructed.Then,for solving infinite-horizon optimal control problem,stationary control policy was encoded as an individual in the solution space of genetic algorithm.The fitness of the individual could be computed by PRISM.Finally,the genetic algorithm executed genetic operations iteratively in order to obtain the optimal solution.The obtained infinite-horizon optimal control policy can beneficially alter long-run behavior of the network.The proposed approach was applied to the WNT5 A network.The experimental results illustrated the correctness and effectiveness of the approach.