Identification of a topological characteristic responsible for the biological robustness of regulatory networks

Attribution of biological robustness to the specific structural properties of a regulatory network is an important yet unsolved problem in systems biology. It is widely believed that the topological characteristics of a biological control network largely determine its dynamic behavior, yet the actual mechanism is still poorly understood. Here, we define a novel structural feature of biological networks, termed 'regulation entropy', to quantitatively assess the influence of network topology on the robustness of the systems. Using the cell-cycle control networks of the budding yeast (Saccharomyces cerevisiae) and the fission yeast (Schizosaccharomyces pombe) as examples, we first demonstrate the correlation of this quantity with the dynamic stability of biological control networks, and then we establish a significant association between this quantity and the structural stability of the networks. And we further substantiate the generality of this approach with a broad spectrum of biological and random networks. We conclude that the regulation entropy is an effective order parameter in evaluating the robustness of biological control networks. Our work suggests a novel connection between the topological feature and the dynamic property of biological regulatory networks.