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Analysis of Metabolic Subnetworks by Flux Cone Projection

Sayed-Amir Marashi12*, Laszlo David234 and Alexander Bockmayr23*

Author Affiliations

1 International Max Planck Research School for Computational Biology and Scientic Computing (IMPRS-CBSC), Max Planck Institute for Molecular Genetics, Ihnestr. 63-73, D-14195 Berlin, Germany

2 FB Mathematik und Informatik, Freie Universität Berlin, Arnimallee 6, D-14195 Berlin, Germany

3 DFG-Research Center Matheon, Berlin, Germany

4 Berlin Mathematical School (BMS), Berlin, Germany

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Algorithms for Molecular Biology 2012, 7:17  doi:10.1186/1748-7188-7-17

Published: 29 May 2012



Analysis of elementary modes (EMs) is proven to be a powerful constraint-based method in the study of metabolic networks. However, enumeration of EMs is a hard computational task. Additionally, due to their large number, EMs cannot be simply used as an input for subsequent analysis. One possibility is to limit the analysis to a subset of interesting reactions. However, analysing an isolated subnetwork can result in finding incorrect EMs which are not part of any steady-state flux distribution of the original network. The ideal set to describe the reaction activity in a subnetwork would be the set of all EMs projected to the reactions of interest. Recently, the concept of "elementary flux patterns" (EFPs) has been proposed. Each EFP is a subset of the support (i.e., non-zero elements) of at least one EM.


We introduce the concept of ProCEMs (Projected Cone Elementary Modes). The ProCEM set can be computed by projecting the flux cone onto a lower-dimensional subspace and enumerating the extreme rays of the projected cone. In contrast to EFPs, ProCEMs are not merely a set of reactions, but projected EMs. We additionally prove that the set of EFPs is included in the set of ProCEM supports. Finally, ProCEMs and EFPs are compared for studying substructures of biological networks.


We introduce the concept of ProCEMs and recommend its use for the analysis of substructures of metabolic networks for which the set of EMs cannot be computed.