Analysis of Metabolic Subnetworks by Flux Cone Projection

doi:10.1186/1748-7188-7-17

Algorithms Mol Biol. 2012; 7: 17.

Published online 2012 May 29. doi: 10.1186/1748-7188-7-17

PMCID: PMC3408373

Analysis of Metabolic Subnetworks by Flux Cone Projection

Sayed-Amir Marashi,^#^1,² Laszlo David,^#^2,^3,⁴ and Alexander Bockmayr^2,³

¹International 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

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

³DFG-Research Center Matheon, Berlin, Germany

⁴Berlin Mathematical School (BMS), Berlin, Germany

Corresponding author.

^#Contributed equally.

Sayed-Amir Marashi: marashi/at/molgen.mpg.de; Laszlo David: Laszlo.David/at/fu-berlin.de; Alexander Bockmayr: Alexander.Bockmayr/at/fu-berlin.de

Received May 3, 2011; Accepted May 29, 2012.

This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Background

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.

Results

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.

Conclusions

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.

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