Analysis And Control Of Gene Regulation Networks Subject To Function Perturbation

With the introduction and implementation of human genome project,the study of gene regulatory networks has received extensive attention in the post-genome era.In order to better describe gene regulatory networks,Boolean network model was proposed.Considering the influence of gene mutation or external uncertainties in organisms,it is particularly important to study the function perturbation impact on Boolean networks(BNs).Using algebraic state space representation method,this paper studies the function perturbation impact on the stability,state feedback stabilization and controllability of gene regulatory networks.Firstly,the considered BN and Boolean control network(BCN)are converted to equivalent algebraic forms by using algebraic state space representation method,so that the classical control theory can be used to study the function perturbation impact on gene regulatory networks.Secondly,the concepts of state feedback stabilization and controllability of BCNs,stability in distribution of probabilistic Boolean network(PBN)are given.By the method of reachable set of fixed point,some sufficient conditions are proposed for judging whether the considered BCN can still be stabilized after function perturbation.In addition,the state feedback gain matrix is modified to ensure the considered BCN can still be stabilized after function perturbation.Some conditions for judging whether the considered BCN can still be controllable after function perturbation are proposed by using the idea of graph theory.By defining some probabilistic reachable sets,some necessary and sufficient conditions are proposed for judging whether the considered PBN can still be stable in distribution after function perturbation.Finally,the obtained results are applied to some actual models such as the lac operon model in the bacterium Escherichia coli and the apoptosis network to verify the validity of the theoretical results.