Global Robustness and Identifiability of Random, Scale-Free, and Small-World Networks

Abstract

We are interested in the relationships among network topology, robustness, and identifiability, and their implications in improving network reconstruction. We used three different types of artificial gene networks (AGNs) with distinct topologies: topologies random (RND), scale-free (SF), and small-world (SW), to investigate their robustness and identifiability. The robustness of a network is represented by structural reachability (existence of pathways between two nodes) and dynamic reachability (response on one node upon perturbation on another node). The identifiability of the network edges is assessed in silico with an established reverse-engineering algorithm. We found that (1) structural reachability does not always lead to dynamic reachability; (2) network robustness is high and identifiability is low in all surveyed AGNs; (3) robustness is more sensitive to network topologies than is identifiability. We also devised a method for network dissection in which three subnets (set of alternative pathways or feedbacks, referred to as pathnet) are related to each node pair. This method allows us to identify the fine structural features underlying the distinct behaviors of the networks. For example, pathnet of the edge tail negatively contributes to the edge identifiability, and it is likely that extra perturbation at this pathnet would improve edge identifiability. We provide a case study to prove that double perturbations decrease the edge robustness and increase structural identifiability with a T helper cell-differentiation network model.