Symbolic Steady States and Dynamically Essential Subnetworks of Discrete Regulatory Networks

Analyzing complex networks is a difficult task, regardless of the chosen modeling framework. For a discrete regulatory network, even if the number of components is in some sense manageable, we have to deal with the problem of analyzing the dynamics in an exponentially large state space. A well known idea to approach this difficulty is to identify smaller building blocks of the system the study of which in isolation still renders information on the dynamics of the whole network. In this talk, we introduce the notion of symbolic steady state which allows us to identify such building blocks. We state explicit rules how to derive attractors of the network from subnetwork attractors valid for synchronous as well as asynchronous dynamics. Illustrating those rules, we derive general conditions for circuits embedded in the network to transfer their behavioral characteristics pertaining number and size of attractors observed in isolation to the complex network.