Theory in Biosciences

, Volume 125, Issue 2, pp 93–121 | Cite as

Geometric robustness theory and biological networks

  • Nihat Ay
  • David C. Krakauer


We provide a geometric framework for investigating the robustness of information flows over biological networks. We use information measures to quantify the impact of knockout perturbations on 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, wheras exclusion dependence measures a distance between unperturbed network and reconfigured network function. We explore the role that redundancy plays in increasing robustness, and how redundacy can be exploited through error-correcting codes implemented by networks. We provide examples of the robustness measure when applied to familiar boolean functions such as the AND, OR and XOR functions. We discuss the relationship between robustness measures and related measures of complexity and how robustness always implies a minimal level of complexity.


Robustness Complexity Networks Information Geometry Knockouts 


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Copyright information

© Elsevier GmbH. All rights reserved 2006

Authors and Affiliations

  1. 1.Max Planck Institute for Mathematics in the SciencesLeipzigGermany
  2. 2.Santa Fe InstituteSante FeUSA

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