title: Exact quantification of cellular robustness in genome-scale metabolic networks.
abstract: Robustness, the ability of biological networks to uphold their functionality in spite of perturbations, is a key characteristic of all living systems. Although several theoretical approaches have been developed to formalize robustness, it still eludes an exact quantification. Here, we present a rigorous and quantitative approach for the structural robustness of metabolic networks by measuring their ability to tolerate random reaction (or gene) knockouts.
  
  
  
  In analogy to reliability theory, based on an explicit consideration of all possible knockout sets, we exactly quantify the probability of failure for a given network function (e.g. growth). This measure can be computed if the network's minimal cut sets (MSCs) are known. We show that even in genome-scale metabolic networks the probability of (network) failure can be reliably estimated from MSCs with lowest cardinalities. We demonstrate the applicability of our theory by analyzing the structural robustness of multiple Enterobacteriaceae and Blattibacteriaceae and show a dramatically low structural robustness for the latter. We find that structural robustness develops from the ability to proliferate in multiple growth environments consistent with experimentally found knowledge.
  
  
  
  The probability of (network) failure provides thus a reliable and easily computable measure of structural robustness and redundancy in (genome-scale) metabolic networks.
  
  
  
  Source code is available under the GNU General Public License at https://github.com/mpgerstl/networkRobustnessToolbox
  
  
  
  juergen.zanghellini@boku.ac.at
  
  
  
  Supplementary data are available at Bioinformatics online.
authors.affiliation: Austrian Centre of Industrial Biotechnology, Vienna, Austria, Department of Biotechnology, University of Natural Resources and Life Sciences, Vienna, Austria, and.
authors.forename: Matthias P
authors.initials: MP
authors.lastname: Gerstl
authors.affiliation: Max Planck Institute for Dynamics of Complex Technical Systems, Magdeburg, Germany.
authors.forename: Steffen
authors.initials: S
authors.lastname: Klamt
authors.affiliation: Austrian Centre of Industrial Biotechnology, Vienna, Austria, Department of Biotechnology, University of Natural Resources and Life Sciences, Vienna, Austria, and.
authors.forename: Christian
authors.initials: C
authors.lastname: Jungreuthmayer
authors.affiliation: Austrian Centre of Industrial Biotechnology, Vienna, Austria, Department of Biotechnology, University of Natural Resources and Life Sciences, Vienna, Austria, and.
authors.forename: Jürgen
authors.initials: J
authors.lastname: Zanghellini
mesh_terms: D016678:Genome; D053858:Metabolic Networks and Pathways; D011381:Programming Languages; D015203:Reproducibility of Results