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Nested Canalyzing Depth and Network Stability

Bulletin of Mathematical Biology volume 74, pages 422–433 (2012)Cite this article

Abstract

We introduce the nested canalyzing depth of a function, which measures the extent to which it retains a nested canalyzing structure. We characterize the structure of functions with a given depth and compute the expected activities and sensitivities of the variables. This analysis quantifies how canalyzation leads to higher stability in Boolean networks. It generalizes the notion of nested canalyzing functions (NCFs), which are precisely the functions with maximum depth. NCFs have been proposed as gene regulatory network models, but their structure is frequently too restrictive and they are extremely sparse. We find that functions become decreasingly sensitive to input perturbations as the canalyzing depth increases, but exhibit rapidly diminishing returns in stability. Additionally, we show that as depth increases, the dynamics of networks using these functions quickly approach the critical regime, suggesting that real networks exhibit some degree of canalyzing depth, and that NCFs are not significantly better than functions of sufficient depth for many applications of the modeling and reverse engineering of biological networks.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Clemson University, Clemson, SC, 29634, USA

    Lori Layne, Elena Dimitrova & Matthew Macauley

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  1. Lori Layne
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  2. Elena Dimitrova
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  3. Matthew Macauley
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Correspondence to Lori Layne.

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Layne, L., Dimitrova, E. & Macauley, M. Nested Canalyzing Depth and Network Stability. Bull Math Biol 74, 422–433 (2012). https://doi.org/10.1007/s11538-011-9692-y

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  • DOI: https://doi.org/10.1007/s11538-011-9692-y

Keywords

  • Boolean networks
  • Stability
  • Gene networks
  • Canalyzation