Algorithmic approaches for computing elementary modes in large biochemical reaction networks

Max Planck Institute for Dynamics of Complex Technical Systems, Magdeburg, Saxony-Anhalt, Germany
IEE Proceedings - Systems Biology (Impact Factor: 2.05). 01/2006; 152(4):249-55. DOI: 10.1049/ip-syb:20050035
Source: PubMed


The concept of elementary (flux) modes provides a rigorous description of pathways in metabolic networks and proved to be valuable in a number of applications. However, the computation of elementary modes is a hard computational task that gave rise to several variants of algorithms during the last years. This work brings substantial progresses to this issue. The authors start with a brief review of results obtained from previous work regarding (a) a unified framework for elementary-mode computation, (b) network compression and redundancy removal and (c) the binary approach by which elementary modes are determined as binary patterns reducing the memory demand drastically without loss of speed. Then the authors will address herein further issues. First, a new way to perform the elementarity tests required during the computation of elementary modes which empirically improves significantly the computation time in large networks is proposed. Second, a method to compute only those elementary modes where certain reactions are involved is derived. Relying on this method, a promising approach for computing EMs in a completely distributed manner by decomposing the full problem in arbitrarity many sub-tasks is presented. The new methods have been implemented in the freely available software tools FluxAnalyzer and Metatool and benchmark tests in realistic networks emphasise the potential of our proposed algorithms.

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    • "). Although more reactions may be available for subnetwork definition when compression is not used, compression greatly reduces computational burden during the enumeration process, vastly outweighing the benefit of additional potential reactions for splitting (data not shown; Klamt et al., 2005). A fourth type of reaction to avoid has poorly scaled coefficients that can lead to numerical instability. "
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    ABSTRACT: Elementary flux mode analysis (EFMA) decomposes complex metabolic network models into tractable biochemical pathways, which have been used for rational design and analysis of metabolic and regulatory networks. However, application of EFMA has often been limited to targeted or simplified metabolic network representations due to computational demands of the method. Division of biological networks into subnetworks enables the complete enumeration of elementary flux modes (EFMs) for metabolic models of a broad range of complexities, including genome-scale. Here, subnetworks are defined using serial dichotomous suppression and enforcement of flux through model reactions. Rules for selecting appropriate reactions to generate subnetworks are proposed and tested; three test cases, including both prokaryotic and eukaryotic network models, verify the efficacy of these rules and demonstrate completeness and reproducibility of EFM enumeration. Division of models into subnetworks is demand-based and automated; computationally intractable subnetworks are further divided until the entire solution space is enumerated. To demonstrate the strategy's scalability, the splitting algorithm was implemented using an EFMA software package (EFMTool) and Windows PowerShell on a 50 node Microsoft HPC cluster. Enumeration of the EFMs in a genome-scale metabolic model of a diatom, Phaeodactylum tricornutum, identified approximately two billion EFMs. The output represents an order of magnitude increase in EFMs computed compared to other published algorithms and demonstrates a scalable framework for EFMA of most systems., SUPPLEMENTARY INFORMATION: Supplemental materials are available at Bioinformatics online.
    Bioinformatics 06/2014; 30(11):1569-1578. DOI:10.1093/bioinformatics/btu021 · 4.98 Impact Factor
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    • "The mathematical representation of the model encompasses all thermodynamically relevant system fl ux distributions. The complete set of enzymatically unique, minimal steady-state pathways spanning this permissible space is known as the elementary fl ux modes (EFMs) (Gagneur and Klamt 2004 ; Klamt et al. 2005 ; Schuster and Hilgetag 1994 ; Schuster et al. 2000 ) . EFMs allow straightforward investigation of a network's metabolic potential from the bottom up (Klamt and Stelling 2003 ; Llaneras and Picó 2010 ; Papin et al. 2004 ; Trinh et al. 2009 ) . "
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    ABSTRACT: Microbes live in multi-factorial environments and have evolved under a variety of concurrent stresses including resource scarcity. Their metabolic organization is a reflection of their evolutionary histories and, in spite of decades of research, there is still a need for improved theoretical tools to explain fundamental aspects of microbial physiology. Using ecological and economic concepts, this chapter explores a resource-ratio based theory to elucidate microbial strategies for extracting and channeling mass and energy. The theory assumes cellular fitness is maximized by allocating scarce resources in appropriate proportions to multiple stress responses. Presented case studies deconstruct metabolic networks into a complete set of minimal biochemical pathways known as elementary flux modes. An economic analysis of the elementary flux modes tabulates enzyme atomic synthesis requirements from amino acid sequences and pathway operating costs from catabolic efficiencies, permitting characterization of inherent tradeoffs between resource investment and phenotype. A set of elementary flux modes with competitive tradeoffs properties can be mathe-matically projected onto experimental fluxomics datasets to decompose measured phenotypes into metabolic adaptations, interpreted as cellular responses proportional to the experienced culturing stresses. The resource-ratio based method describes the experimental phenotypes with greater accuracy than other contemporary approaches and further analysis suggests the results are both statistically and biologically significant. The insight into metabolic network design principles including tradeoffs associated with concurrent stress adaptation provides a foundation for interpreting physiology as well as for rational control and engineering of medically, environmentally, and industrially relevant microbes.
    Sub-cellular biochemistry 10/2012; 64:139-57. DOI:10.1007/978-94-007-5055-5_7
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    • "Thus, it is not surprising that the algorithms for computation of EMs and t-invariants have evolved closely [see Schuster et al. (2002) for a comparison of both concepts]. Despite recent improvements in the algorithms for computation of EMs (Klamt et al., 2005; Terzer and Stelling, 2008), their application to real world metabolic networks has been hampered by the combinatorial explosion in the number of modes as the size of the networks increase. The enumeration of the complete set of EMs for genome-scale networks has been infeasible so far, and perhaps even undesirable due to the hardly manageable number of modes that would be generated. "
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    ABSTRACT: The description of a metabolic network in terms of elementary (flux) modes (EMs) provides an important framework for metabolic pathway analysis. However, their application to large networks has been hampered by the combinatorial explosion in the number of modes. In this work, we develop a method for generating random samples of EMs without computing the whole set. Our algorithm is an adaptation of the canonical basis approach, where we add an additional filtering step which, at each iteration, selects a random subset of the new combinations of modes. In order to obtain an unbiased sample, all candidates are assigned the same probability of getting selected. This approach avoids the exponential growth of the number of modes during computation, thus generating a random sample of the complete set of EMs within reasonable time. We generated samples of different sizes for a metabolic network of Escherichia coli, and observed that they preserve several properties of the full EM set. It is also shown that EM sampling can be used for rational strain design. A well distributed sample, that is representative of the complete set of EMs, should be suitable to most EM-based methods for analysis and optimization of metabolic networks. Source code for a cross-platform implementation in Python is freely available at Supplementary data are available at Bioinformatics online.
    Bioinformatics 09/2012; 28(18):i515-i521. DOI:10.1093/bioinformatics/bts401 · 4.98 Impact Factor
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