

Preprint 14/2006
Geometric robustness theory and biological networks
Nihat Ay and David C. Krakauer
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Submission date: 03. Feb. 2006 (revised version: October 2006)
Pages: 41
published in: Theory in biosciences, 125 (2007) 2, p. 93-121
DOI number (of the published article): 10.1016/j.thbio.2006.06.002
Bibtex
MSC-Numbers: 93A10, 94A17, 92B05
Keywords and phrases: robustness, complexity, network information flow, entropy, causality
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Abstract:
We provide a geometric framework for investigating the robustness
of biological networks. We use information measures to quantify the
impact of knockout perturbations to simple networks. Robustness has
two components, a measure of the causal contribution of a node or
nodes, and a measure of the change or exclusion dependence, of the
network following node removal. Causality is measured as statistical
contribution of a node to network function, whereas exclusion
dependence measures the difference between the distribution of
unperturbed network functions and the reconfigured network function.
We explore the role that redundancy plays in increasing robustness,
and how redundacy can be exploited by an error correcting code
implemented by a network. We provide examples of the robustness
measure when applied to familiar boolean functions such as the AND,
OR amd XOR functions. We discuss the relationship between robustness
measures and related measures of complexity.