Convergence behaviour and Control in Non-Linear Biological Networks.

Control of genetic regulatory networks is challenging to define and quantify. Previous control centrality metrics, which aim to capture the ability of individual nodes to control the system, have been found to suffer from plausibility and applicability problems. Here we present a new approach to control centrality based on network convergence behaviour, implemented as an extension of our genetic regulatory network simulation framework Jimena ( http://stefan-karl.de/jimena). We distinguish three types of network control, and show how these mathematical concepts correspond to experimentally verified node functions and signalling pathways in immunity and cell differentiation: Total control centrality quantifies the impact of node mutations and identifies potential pharmacological targets such as genes involved in oncogenesis (e.g. zinc finger protein GLI2 or bone morphogenetic proteins in chondrocytes). Dynamic control centrality describes relaying functions as observed in signalling cascades (e.g. src kinase or Jak/Stat pathways). Value control centrality measures the direct influence of the value of the node on the network (e.g. Indian hedgehog as an essential regulator of proliferation in chondrocytes). Surveying random scale-free networks and biological networks, we find that control of the network resides in few high degree driver nodes and networks can be controlled best if they are sparsely connected.