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Detecting Structural Invariants in Biological Reaction Networks

  • Jörn Behre
  • Luís Filipe de Figueiredo
  • Stefan Schuster
  • Christoph KaletaEmail author
Protocol
Part of the Methods in Molecular Biology book series (MIMB, volume 804)

Abstract

The detection and analysis of structural invariants in cellular reaction networks is of central importance to achieve a more comprehensive understanding of metabolism. In this work, we review different kinds of structural invariants in reaction networks and their Petri net-based representation. In particular, we discuss invariants that can be obtained from the left and right null spaces of the stoichiometric matrix which correspond to conserved moieties (P-invariants) and elementary flux modes (EFMs, minimal T-invariants). While conserved moieties can be used to detect stoichiometric inconsistencies in reaction networks, EFMs correspond to a mathematically rigorous definition of the concept of a biochemical pathway. As outlined here, EFMs allow to devise strategies for strain improvement, to assess the robustness of metabolic networks subject to perturbations, and to analyze the information flow in regulatory and signaling networks. Another important aspect addressed by this review is the limitation of metabolic pathway analysis using EFMs to small or medium-scale reaction networks. We discuss two recently introduced approaches to circumvent these limitations. The first is an algorithm to enumerate a subset of EFMs in genome-scale metabolic networks starting from the EFM with the least number of reactions. The second approach, elementary flux pattern analysis, allows to analyze pathways through specific subsystems of genome-scale metabolic networks. In contrast to EFMs, elementary flux patterns much more accurately reflect the metabolic capabilities of a subsystem of metabolism as well as its integration into the entire system.

Key words

Elementary flux modes Elementary flux patterns K-Shortest elementary flux modes Petri nets Signal transduction Stoichiometric network analysis Structural robustness 

Notes

Acknowledgments

We thank Ines Heiland for the reconstruction of the medium-scale model of arginine metabolism in E. coli and for valuable discussions. Financial support from the German Ministry for Research and Education (BMBF) to C.K. and J.B. within the frameworks of the Forsys Partner initiative and the HepatoSys project, respectively, and from the Fundação Calouste Gulbenkian, Fundação para a Ciência e a Tecnologia (FCT) and Siemens SA Portugal (PhD grant SFRH/BD/32961/2006) to L.F.F. is gratefully acknowledged.

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Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  • Jörn Behre
    • 1
  • Luís Filipe de Figueiredo
    • 2
  • Stefan Schuster
    • 3
  • Christoph Kaleta
    • 3
    Email author
  1. 1.Theoretical Systems BiologyInstitute of Food Research (IFR), Norwich Research ParkNorwichUK
  2. 2.Chemoinformatics and Metabolism TeamEuropean Bioinformatics Institute (EBI)CambridgeshireUK
  3. 3.Department of BioinformaticsFriedrich Schiller University JenaJenaGermany

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