Determinative power and perturbations in Boolean networks

Authors

Reinhard Heckel, Steffen Schober, and Martin Bossert

Reference

9th International Workshop on Computational Systems Biology, 31–34, June 2012.

Abstract

Consider a large Boolean network with a feed forward structure. Given a probability distribution for the inputs, can one find—possibly small—collections of input nodes that determine the states of most other nodes in the network? To identify these nodes, a notion that quantifies the determinative power of an input over states in the network is needed. We argue that the mutual information (MI) be- tween a subset of the inputs X = {X_1, ..., X_n} of node i and the function f_i(X) associated with node i quantifies the determinative power of this subset of inputs over node i. We study the relation of determinative power to sensitivity to perturbations, and find that, maybe surprisingly, an input that has a large sensitivity to perturbations does not necessarily have large determinative power. For unate functions which play an important role in genetic regulatory networks, we find an particular relation between MI and sensitivity to perturbations. As an application of our methods, we analyze the large-scale regulatory network of E. coli numerically: We identify the most determinative nodes and show that a small set of those reduces the overall uncertainty of network states significantly.

Comments

Best student paper award

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