Impact of individual nodes in Boolean network dynamics

Boolean networks serve as discrete models of regulation and signaling in biological cells. Identifying the key controllers of such processes is important for their understanding and planning further analysis. We quantify the dynamical impact of a node as the probability of damage spreading after switching the node's state. The leading eigenvector of the adjacency matrix is a good predictor of dynamical impact in case of long-term spreading. Quality of prediction is further improved when eigenvector centrality is based on the weighted matrix of activities rather than the unweighted adjacency matrix. Simulations are performed with random Boolean networks and a model of signaling in fibroblasts. The findings are supported by analytic arguments from a linear approximation of damage spreading.