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Node-independent elementary signaling modes: A measure of redundancy in Boolean signaling transduction networks

Published online by Cambridge University Press:  21 April 2016

Department of Physics, The Pennsylvania State University, University Park, PA 16802, USA (e-mail:
Department of Physics, The Pennsylvania State University, University Park, PA 16802, USA (e-mail: Department of Biology, The Pennsylvania State University, University Park, PA 16802, USA (e-mail:


The redundancy of a system denotes the amount of duplicate components or mechanisms in it. For a network, especially one in which mass or information is being transferred from an origin to a destination, redundancy is related to the robustness of the system. Existing network measures of redundancy rely on local connectivity (e.g. clustering coefficients) or the existence of multiple paths. As in many systems there are functional dependencies between components and paths, a measure that not only characterizes the topology of a network, but also takes into account these functional dependencies, becomes most desirable.

We propose a network redundancy measure in a prototypical model that contains functionally dependent directed paths: a Boolean model of a signal transduction network. The functional dependencies are made explicit by using an expanded network and the concept of elementary signaling modes (ESMs). We define the redundancy of a Boolean signal transduction network as the maximum number of node-independent ESMs and develop a methodology for identifying all maximal node-independent ESM combinations. We apply our measure to a number of signal transduction network models and show that it successfully distills known properties of the systems and offers new functional insights. The concept can be easily extended to similar related forms, e.g. edge-independent ESMs.

Research Article
Network Science , Volume 4 , Issue 3 , September 2016 , pp. 273 - 292
Copyright © Cambridge University Press 2016 

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