Figure 1

Illustrative examples for essentiality of components in signaling networks. I is the input node and O is the output node. All other nodes are intermediate nodes. → denotes activating regulations and ---| represents inhibitory regulations. We use three existing measures of node centrality: betweenness centrality, based on the node's participation in shortest paths between node pairs [18], pairwise disconnectivity index, based on the fraction of initially connected node pairs becoming disconnected after the node's deletion [27], and SigFlux, based on the path sets between input and output [29]. (a) E and F are independently activating O, but both of them require the synergy of D to be effective. C (rectangle) has higher betweenness centrality, pairwise disconnectivity index and SigFlux value than D. However, D (hexagon) is essential to the signal output, because the disruption of D blocks all signaling paths from I to O. (b) The three regulatory interactions regulating C are conditionally independent. C (rectangle) has very high betweenness centrality, pairwise disconnectivity index and SigFlux value. However, knockout of C interrupts its negative action on D, enabling D to activate O. (c) The activation of C requires the presence of both A and B. The SigFlux measure is not able to evaluate the importance of components not located on paths from input to output and thus SigFlux(A) = 0. However, the regulation of C by A (hexagon) is essential, as the disruption of A blocks the whole signal transduction process.