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Muller A.C.,Free University of Berlin | Muller A.C.,Max Planck Institute for Molecular Genetics | Bockmayr A.,Free University of Berlin | Bockmayr A.,Research Center Matheon
Bioinformatics | Year: 2013

Motivation: Flux variability analysis (FVA) is an important tool to further analyse the results obtained by flux balance analysis (FBA) on genome-scale metabolic networks. For many constraint-based models, FVA identifies unboundedness of the optimal flux space. This reveals that optimal flux solutions with net flux through internal biochemical loops are feasible, which violates the second law of thermodynamics. Such unbounded fluxes may be eliminated by extending FVA with thermodynamic constraints.Results: We present a new algorithm for efficient flux variability (and flux balance) analysis with thermodynamic constraints, suitable for analysing genome-scale metabolic networks. We first show that FBA with thermodynamic constraints is NP-hard. Then we derive a theoretical tractability result, which can be applied to metabolic networks in practice. We use this result to develop a new constraint programming algorithm Fast-tFVA for fast FVA with thermodynamic constraints (tFVA). Computational comparisons with previous methods demonstrate the efficiency of the new method. For tFVA, a speed-up of factor 30-300 is achieved. In an analysis of genome-scale metabolic networks in the BioModels database, we found that in 485 of 716 networks, additional irreversible or fixed reactions could be detected. © 2013 The Author. Published by Oxford University Press. All rights reserved. Source


Muller A.C.,Free University of Berlin | Muller A.C.,Max Planck Institute for Molecular Genetics | Bockmayr A.,Free University of Berlin | Bockmayr A.,Research Center Matheon
Journal of Mathematical Biology | Year: 2013

The huge number of elementary flux modes in genome-scale metabolic networks makes analysis based on elementary flux modes intrinsically difficult. However, it has been shown that the elementary flux modes with optimal yield often contain highly redundant information. The set of optimal-yield elementary flux modes can be compressed using modules. Up to now, this compression was only possible by first enumerating the whole set of all optimal-yield elementary flux modes. We present a direct method for computing modules of the thermodynamically constrained optimal flux space of a metabolic network. This method can be used to decompose the set of optimal-yield elementary flux modes in a modular way and to speed up their computation. In addition, it provides a new form of coupling information that is not obtained by classical flux coupling analysis. We illustrate our approach on a set of model organisms. © 2013 Springer-Verlag Berlin Heidelberg. Source


Marashi S.-A.,Free University of Berlin | Marashi S.-A.,Max Planck Institute for Molecular Genetics | David L.,Free University of Berlin | David L.,Research Center Matheon | And 2 more authors.
Journal of Theoretical Biology | Year: 2012

Genome-scale metabolic networks are useful tools for achieving a system-level understanding of metabolism. However, due to their large size, analysis of such networks may be difficult and algorithms can be very slow. Therefore, some authors have suggested to analyze subsystems instead of the original genome-scale models. Flux coupling analysis (FCA) is a well-known method for detecting functionally related reactions in metabolic networks. In this paper, we study how flux coupling relations may change if we analyze a subsystem instead of the original network. We show mathematically that a pair of fully, partially or directionally coupled reactions may be detected as uncoupled in certain subsystems. Interestingly, this behavior is the opposite of the flux coupling changes that may occur due to missing reactions, or equivalently, deletion of reactions. Computational experiments suggest that the analysis of plastid (but not mitochondrial) subsystems may significantly influence the results of FCA. Therefore, the results of FCA for subsystems, especially plastid subsystems, should be interpreted with care. © 2012 Elsevier Ltd. Source


Marashi S.-A.,Max Planck Institute for Molecular Genetics | Marashi S.-A.,Free University of Berlin | David L.,Free University of Berlin | David L.,Research Center Matheon | And 2 more authors.
Algorithms for Molecular Biology | Year: 2012

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. © 2012 Marashi et al; licensee BioMed Central Ltd. Source


David L.,Research Center Matheon | David L.,Free University of Berlin | Marashi S.,Free University of Berlin | Marashi S.,Max Planck Institute for Molecular Genetics | And 5 more authors.
BMC Bioinformatics | Year: 2011

Background: Flux coupling analysis (FCA) is a useful method for finding dependencies between fluxes of a metabolic network at steady-state. FCA classifies reactions into subsets (called coupled reaction sets) in which activity of one reaction implies activity of another reaction. Several approaches for FCA have been proposed in the literature.Results: We introduce a new FCA algorithm, FFCA (Feasibility-based Flux Coupling Analysis), which is based on checking the feasibility of a system of linear inequalities. We show on a set of benchmarks that for genome-scale networks FFCA is faster than other existing FCA methods.Conclusions: We present FFCA as a new method for flux coupling analysis and prove it to be faster than existing approaches. A corresponding software tool is freely available for non-commercial use at http://www.bioinformatics.org/ffca/. © 2011 David et al; licensee BioMed Central Ltd. Source

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