Measures for information propagation in Boolean networks

Boolean networks provide a large-scale model of gene regulatory and neuronal networks. In this paper, we study what kinds of Boolean networks best propagate and process signals, i.e. information, in the presence of stochasticity and noise. We first examine two existing approaches that use mutual information and find that these approaches do not capture well the phenomenon studied. We propose a new measure for information propagation based on perturbation avalanches in Boolean networks and find that the measure is maximized in dynamically critical networks and in subcritical networks if noise is present.