Reachability Of Multiplex Boolean Control Networks

As a discrete model of time and state,Boolean networks can efficiently study the dynamic characteristics of gene regulatory networks.The control problem of gene regulatory networks has received considerable attention in the past few years,which has provided great help to solve problems in life science,such as the intervention and treatment of disease.Meanwhile,with the development of system biology,the integration study of various biology system has also become a hot topic in this filed.Therefore,it is necessary to study the reachability of multiplex Boolean control network.In this paper,the reachability of multiplex Boolean control network is concerned.First,we introduce the model of multiplex Boolean control network.Based on semi-tensor product of matrix method,the multiplex Boolean control network has been converted into an algebraic form.We introduce the definition for the reachability of multiplex Boolean control network.Furthermore,the necessary and sufficient condition for the reachability of multiplex Boolean control network is given.Second,considering the uncertain of the real biology system,On the basis of multiplex Boolean control network,we propose multiplex probabilistic Boolean control network.Furthermore,the necessary and sufficient condition for the reachability of multiplex Boolean control network is given.Finally,the model of multiplex Boolean control network is used to simulate the actual abscisic acid-induced stomatal closure signal transfer sub-network and the mammalian G1 /S phase gene regulatory sub-network.Based on semi-tensor product of matrix method,the two networks have been converted into an algebraic representation,and the reachability analysis of two networks is given.The validity of the conclusion is further illustrated by these two examples.