Large-scale computation of elementary flux modes with bit pattern trees
Motivation: Elementary flux modes (EFMs)—non-decomposable minimal pathways—are commonly accepted tools for metabolic network analysis under steady state conditions. Valid states of the network are linear superpositions of elementary modes shaping a polyhedral cone (the flux cone), which is a well-st...
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| Vydáno v: | Bioinformatics Ročník 24; číslo 19; s. 2229 - 2235 |
|---|---|
| Hlavní autoři: | , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
Oxford
Oxford University Press
01.10.2008
Oxford Publishing Limited (England) |
| Témata: | |
| ISSN: | 1367-4803, 1367-4811, 1460-2059, 1367-4811 |
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| Abstract | Motivation: Elementary flux modes (EFMs)—non-decomposable minimal pathways—are commonly accepted tools for metabolic network analysis under steady state conditions. Valid states of the network are linear superpositions of elementary modes shaping a polyhedral cone (the flux cone), which is a well-studied convex set in computational geometry. Computing EFMs is thus basically equivalent to extreme ray enumeration of polyhedral cones. This is a combinatorial problem with poorly scaling algorithms, preventing the large-scale analysis of metabolic networks so far. Results: Here, we introduce new algorithmic concepts that enable large-scale computation of EFMs. Distinguishing extreme rays from normal (composite) vectors is one critical aspect of the algorithm. We present a new recursive enumeration strategy with bit pattern trees for adjacent rays—the ancestors of extreme rays—that is roughly one order of magnitude faster than previous methods. Additionally, we introduce a rank updating method that is particularly well suited for parallel computation and a residue arithmetic method for matrix rank computations, which circumvents potential numerical instability problems. Multi-core architectures of modern CPUs can be exploited for further performance improvements. The methods are applied to a central metabolism network of Escherichia coli, resulting in ≈26 Mio. EFMs. Within the top 2% modes considering biomass production, most of the gain in flux variability is achieved. In addition, we compute ≈5 Mio. EFMs for the production of non-essential amino acids for a genome-scale metabolic network of Helicobacter pylori. Only large-scale EFM analysis reveals the >85% of modes that generate several amino acids simultaneously. Availability: An implementation in Java, with integration into MATLAB and support of various input formats, including SBML, is available at http://www.csb.ethz.ch in the tools section; sources are available from the authors upon request. Contact: joerg.stelling@inf.ethz.ch Supplementary information: Supplementary data are available at Bioinformatics online. |
|---|---|
| AbstractList | Motivation: Elementary flux modes (EFMs)--non-decomposable minimal pathways--are commonly accepted tools for metabolic network analysis under steady state conditions. Valid states of the network are linear superpositions of elementary modes shaping a polyhedral cone (the flux cone), which is a well-studied convex set in computational geometry. Computing EFMs is thus basically equivalent to extreme ray enumeration of polyhedral cones. This is a combinatorial problem with poorly scaling algorithms, preventing the large-scale analysis of metabolic networks so far. Results: Here, we introduce new algorithmic concepts that enable large-scale computation of EFMs. Distinguishing extreme rays from normal (composite) vectors is one critical aspect of the algorithm. We present a new recursive enumeration strategy with bit pattern trees for adjacent rays--the ancestors of extreme rays--that is roughly one order of magnitude faster than previous methods. Additionally, we introduce a rank updating method that is particularly well suited for parallel computation and a residue arithmetic method for matrix rank computations, which circumvents potential numerical instability problems. Multi-core architectures of modern CPUs can be exploited for further performance improvements. The methods are applied to a central metabolism network of Escherichia coli, resulting in [approximate]26 Mio. EFMs. Within the top 2% modes considering biomass production, most of the gain in flux variability is achieved. In addition, we compute [approximate]5 Mio. EFMs for the production of non-essential amino acids for a genome-scale metabolic network of Helicobacter pylori. Only large-scale EFM analysis reveals the >85% of modes that generate several amino acids simultaneously. Availability: An implementation in Java, with integration into MATLAB and support of various input formats, including SBML, is available at http://www.csb.ethz.ch in the tools section; sources are available from the authors upon request. Contact: joerg.stelling@inf.ethz.ch Supplementary information: Supplementary data are available at Bioinformatics online. Elementary flux modes (EFMs)--non-decomposable minimal pathways--are commonly accepted tools for metabolic network analysis under steady state conditions. Valid states of the network are linear superpositions of elementary modes shaping a polyhedral cone (the flux cone), which is a well-studied convex set in computational geometry. Computing EFMs is thus basically equivalent to extreme ray enumeration of polyhedral cones. This is a combinatorial problem with poorly scaling algorithms, preventing the large-scale analysis of metabolic networks so far. Here, we introduce new algorithmic concepts that enable large-scale computation of EFMs. Distinguishing extreme rays from normal (composite) vectors is one critical aspect of the algorithm. We present a new recursive enumeration strategy with bit pattern trees for adjacent rays--the ancestors of extreme rays--that is roughly one order of magnitude faster than previous methods. Additionally, we introduce a rank updating method that is particularly well suited for parallel computation and a residue arithmetic method for matrix rank computations, which circumvents potential numerical instability problems. Multi-core architectures of modern CPUs can be exploited for further performance improvements. The methods are applied to a central metabolism network of Escherichia coli, resulting in approximately 26 Mio. EFMs. Within the top 2% modes considering biomass production, most of the gain in flux variability is achieved. In addition, we compute approximately 5 Mio. EFMs for the production of non-essential amino acids for a genome-scale metabolic network of Helicobacter pylori. Only large-scale EFM analysis reveals the >85% of modes that generate several amino acids simultaneously. An implementation in Java, with integration into MATLAB and support of various input formats, including SBML, is available at http://www.csb.ethz.ch in the tools section; sources are available from the authors upon request. Motivation: Elementary flux modes (EFMs)—non-decomposable minimal pathways—are commonly accepted tools for metabolic network analysis under steady state conditions. Valid states of the network are linear superpositions of elementary modes shaping a polyhedral cone (the flux cone), which is a well-studied convex set in computational geometry. Computing EFMs is thus basically equivalent to extreme ray enumeration of polyhedral cones. This is a combinatorial problem with poorly scaling algorithms, preventing the large-scale analysis of metabolic networks so far. Results: Here, we introduce new algorithmic concepts that enable large-scale computation of EFMs. Distinguishing extreme rays from normal (composite) vectors is one critical aspect of the algorithm. We present a new recursive enumeration strategy with bit pattern trees for adjacent rays—the ancestors of extreme rays—that is roughly one order of magnitude faster than previous methods. Additionally, we introduce a rank updating method that is particularly well suited for parallel computation and a residue arithmetic method for matrix rank computations, which circumvents potential numerical instability problems. Multi-core architectures of modern CPUs can be exploited for further performance improvements. The methods are applied to a central metabolism network of Escherichia coli, resulting in ≈26 Mio. EFMs. Within the top 2% modes considering biomass production, most of the gain in flux variability is achieved. In addition, we compute ≈5 Mio. EFMs for the production of non-essential amino acids for a genome-scale metabolic network of Helicobacter pylori. Only large-scale EFM analysis reveals the >85% of modes that generate several amino acids simultaneously. Availability: An implementation in Java, with integration into MATLAB and support of various input formats, including SBML, is available at http://www.csb.ethz.ch in the tools section; sources are available from the authors upon request. Contact: joerg.stelling@inf.ethz.ch Supplementary information: Supplementary data are available at Bioinformatics online. Elementary flux modes (EFMs)--non-decomposable minimal pathways--are commonly accepted tools for metabolic network analysis under steady state conditions. Valid states of the network are linear superpositions of elementary modes shaping a polyhedral cone (the flux cone), which is a well-studied convex set in computational geometry. Computing EFMs is thus basically equivalent to extreme ray enumeration of polyhedral cones. This is a combinatorial problem with poorly scaling algorithms, preventing the large-scale analysis of metabolic networks so far.MOTIVATIONElementary flux modes (EFMs)--non-decomposable minimal pathways--are commonly accepted tools for metabolic network analysis under steady state conditions. Valid states of the network are linear superpositions of elementary modes shaping a polyhedral cone (the flux cone), which is a well-studied convex set in computational geometry. Computing EFMs is thus basically equivalent to extreme ray enumeration of polyhedral cones. This is a combinatorial problem with poorly scaling algorithms, preventing the large-scale analysis of metabolic networks so far.Here, we introduce new algorithmic concepts that enable large-scale computation of EFMs. Distinguishing extreme rays from normal (composite) vectors is one critical aspect of the algorithm. We present a new recursive enumeration strategy with bit pattern trees for adjacent rays--the ancestors of extreme rays--that is roughly one order of magnitude faster than previous methods. Additionally, we introduce a rank updating method that is particularly well suited for parallel computation and a residue arithmetic method for matrix rank computations, which circumvents potential numerical instability problems. Multi-core architectures of modern CPUs can be exploited for further performance improvements. The methods are applied to a central metabolism network of Escherichia coli, resulting in approximately 26 Mio. EFMs. Within the top 2% modes considering biomass production, most of the gain in flux variability is achieved. In addition, we compute approximately 5 Mio. EFMs for the production of non-essential amino acids for a genome-scale metabolic network of Helicobacter pylori. Only large-scale EFM analysis reveals the >85% of modes that generate several amino acids simultaneously.RESULTSHere, we introduce new algorithmic concepts that enable large-scale computation of EFMs. Distinguishing extreme rays from normal (composite) vectors is one critical aspect of the algorithm. We present a new recursive enumeration strategy with bit pattern trees for adjacent rays--the ancestors of extreme rays--that is roughly one order of magnitude faster than previous methods. Additionally, we introduce a rank updating method that is particularly well suited for parallel computation and a residue arithmetic method for matrix rank computations, which circumvents potential numerical instability problems. Multi-core architectures of modern CPUs can be exploited for further performance improvements. The methods are applied to a central metabolism network of Escherichia coli, resulting in approximately 26 Mio. EFMs. Within the top 2% modes considering biomass production, most of the gain in flux variability is achieved. In addition, we compute approximately 5 Mio. EFMs for the production of non-essential amino acids for a genome-scale metabolic network of Helicobacter pylori. Only large-scale EFM analysis reveals the >85% of modes that generate several amino acids simultaneously.An implementation in Java, with integration into MATLAB and support of various input formats, including SBML, is available at http://www.csb.ethz.ch in the tools section; sources are available from the authors upon request.AVAILABILITYAn implementation in Java, with integration into MATLAB and support of various input formats, including SBML, is available at http://www.csb.ethz.ch in the tools section; sources are available from the authors upon request. Motivation: Elementary flux modes (EFMs)—non-decomposable minimal pathways—are commonly accepted tools for metabolic network analysis under steady state conditions. Valid states of the network are linear superpositions of elementary modes shaping a polyhedral cone (the flux cone), which is a well-studied convex set in computational geometry. Computing EFMs is thus basically equivalent to extreme ray enumeration of polyhedral cones. This is a combinatorial problem with poorly scaling algorithms, preventing the large-scale analysis of metabolic networks so far. Results: Here, we introduce new algorithmic concepts that enable large-scale computation of EFMs. Distinguishing extreme rays from normal (composite) vectors is one critical aspect of the algorithm. We present a new recursive enumeration strategy with bit pattern trees for adjacent rays—the ancestors of extreme rays—that is roughly one order of magnitude faster than previous methods. Additionally, we introduce a rank updating method that is particularly well suited for parallel computation and a residue arithmetic method for matrix rank computations, which circumvents potential numerical instability problems. Multi-core architectures of modern CPUs can be exploited for further performance improvements. The methods are applied to a central metabolism network of Escherichia coli, resulting in ≈26 Mio. EFMs. Within the top 2% modes considering biomass production, most of the gain in flux variability is achieved. In addition, we compute ≈5 Mio. EFMs for the production of non-essential amino acids for a genome-scale metabolic network of Helicobacter pylori. Only large-scale EFM analysis reveals the >85% of modes that generate several amino acids simultaneously. Availability: An implementation in Java, with integration into MATLAB and support of various input formats, including SBML, is available at http://www.csb.ethz.ch in the tools section; sources are available from the authors upon request. Contact: joerg.stelling@inf.ethz.ch Supplementary information: Supplementary data are available at Bioinformatics online. Motivation: Elementary flux modes (EFMs)-non-decomposable minimal pathways-are commonly accepted tools for metabolic network analysis under steady state conditions. Valid states of the network are linear superpositions of elementary modes shaping a polyhedral cone (the flux cone), which is a well-studied convex set in computational geometry. Computing EFMs is thus basically equivalent to extreme ray enumeration of polyhedral cones. This is a combinatorial problem with poorly scaling algorithms, preventing the large-scale analysis of metabolic networks so far. Results: Here, we introduce new algorithmic concepts that enable large-scale computation of EFMs. Distinguishing extreme rays from normal (composite) vectors is one critical aspect of the algorithm. We present a new recursive enumeration strategy with bit pattern trees for adjacent rays-the ancestors of extreme rays-that is roughly one order of magnitude faster than previous methods. Additionally, we introduce a rank updating method that is particularly well suited for parallel computation and a residue arithmetic method for matrix rank computations, which circumvents potential numerical instability problems. Multi-core architectures of modern CPUs can be exploited for further performance improvements. The methods are applied to a central metabolism network of Escherichia coli, resulting in ≈26 Mio. EFMs. Within the top 2% modes considering biomass production, most of the gain in flux variability is achieved. In addition, we compute ≈5 Mio. EFMs for the production of non-essential amino acids for a genome-scale metabolic network of Helicobacter pylori. Only large-scale EFM analysis reveals the >85% of modes that generate several amino acids simultaneously. Availability: An implementation in Java, with integration into MATLAB and support of various input formats, including SBML, is available at http://www.csb.ethz.ch in the tools section; sources are available from the authors upon request. Contact: joerg.stelling@inf.ethz.ch Supplementary information: Supplementary data are available at Bioinformatics online. |
| Author | Stelling, Jörg Terzer, Marco |
| Author_xml | – sequence: 1 givenname: Marco surname: Terzer fullname: Terzer, Marco organization: Institute of Computational Science and Swiss Institute of Bioinformatics, ETH Zurich, 8092 Zurich, Switzerland – sequence: 2 givenname: Jörg surname: Stelling fullname: Stelling, Jörg organization: To whom correspondence should be addressed |
| BackLink | http://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=20686170$$DView record in Pascal Francis https://www.ncbi.nlm.nih.gov/pubmed/18676417$$D View this record in MEDLINE/PubMed |
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| ContentType | Journal Article |
| Copyright | The Author 2008. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org 2008 2008 INIST-CNRS The Author 2008. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org |
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| References | Knuth (2023020211111611700_B7) 1997 Terzer (2023020211111611700_B15) 2006 Wagner (2023020211111611700_B17) 2004; 108 Urbanczik (2023020211111611700_B16) 2005; 21 Fukuda (2023020211111611700_B3) 1995 Klamt (2023020211111611700_B5) 2006 Schuetz (2023020211111611700_B11) 2007; 3 Segré (2023020211111611700_B13) 2002 Klamt (2023020211111611700_B6) 2005; 152 Stelling (2023020211111611700_B14) 2002; 420 Bentley (2023020211111611700_B2) 1975; 18 Price (2023020211111611700_B9) 2002; 12 Arita (2023020211111611700_B1) 2004; 101 Gagneur (2023020211111611700_B4) 2004; 5 Schuster (2023020211111611700_B12) 1994; 2 Price (2023020211111611700_B10) 2004; 2 Motzkin (2023020211111611700_B8) 1953 Wagner (2023020211111611700_B18) 2005; 89 |
| References_xml | – volume: 21 start-page: 4176 year: 2005 ident: 2023020211111611700_B16 article-title: Functional stoichiometric analysis of metabolic networks publication-title: Bioinformatics doi: 10.1093/bioinformatics/bti674 – volume: 18 start-page: 509 year: 1975 ident: 2023020211111611700_B2 article-title: Multidimensional binary search trees used for associative searching publication-title: Commun. ACM doi: 10.1145/361002.361007 – volume: 2 start-page: 165 year: 1994 ident: 2023020211111611700_B12 article-title: On elementary flux modes in biochemical reaction systems at steady state publication-title: J. Biol. Syst doi: 10.1142/S0218339094000131 – volume: 420 start-page: 190 year: 2002 ident: 2023020211111611700_B14 article-title: Metabolic network structure determines key aspects of functionality and regulation publication-title: Nature doi: 10.1038/nature01166 – volume: 89 start-page: 3837 year: 2005 ident: 2023020211111611700_B18 article-title: The geometry of the flux cone of a metabolic network publication-title: Biophys. J doi: 10.1529/biophysj.104.055129 – start-page: 333 volume-title: Lecture Notes in Computer Science. year: 2006 ident: 2023020211111611700_B15 article-title: Accelerating the computation of elementary modes using pattern trees – start-page: 73 volume-title: System Modeling in Cellular Biology. year: 2006 ident: 2023020211111611700_B5 article-title: Stoichiometric and constraint-based modeling doi: 10.7551/mitpress/9780262195485.003.0005 – volume: 2 start-page: 886 year: 2004 ident: 2023020211111611700_B10 article-title: Genome-scale models of microbial cells: evaluating the consequences of constraints publication-title: Nat. Rev. Microbiol doi: 10.1038/nrmicro1023 – volume: 5 start-page: 175 year: 2004 ident: 2023020211111611700_B4 article-title: Computation of elementary modes: a unifying framework and the new binary approach publication-title: BMC Bioinformatics doi: 10.1186/1471-2105-5-175 – volume: 108 start-page: 2425 year: 2004 ident: 2023020211111611700_B17 article-title: Nullspace approach to determine the elementary modes of chemical reaction systems publication-title: J. Phys. Chem. B doi: 10.1021/jp034523f – volume: 101 start-page: 1543 year: 2004 ident: 2023020211111611700_B1 article-title: The metabolic world ofEscherichia coliis not small publication-title: Proc. Natl Acad. Sci. USA doi: 10.1073/pnas.0306458101 – start-page: 91 volume-title: Combinatorics and Computer Science. year: 1995 ident: 2023020211111611700_B3 article-title: Double description method revisited – volume: 12 start-page: 760 year: 2002 ident: 2023020211111611700_B9 article-title: Determination of redundancy and systems properties of the metabolic network ofHelicobacter Pyloriusing genome-scale extreme pathway analysis publication-title: Genetics Res – start-page: 15112 volume-title: Proc. Natl Acad. Sci. USA. year: 2002 ident: 2023020211111611700_B13 article-title: Analysis of optimality in natural and perturbed metabolic networks – volume-title: The Art of Computer Programming3rd edn. year: 1997 ident: 2023020211111611700_B7 article-title: Seminumerical Algorithms – volume: 152 start-page: 249 year: 2005 ident: 2023020211111611700_B6 article-title: Algorithmic approaches for computing elementary modes in large biochemical reaction networks publication-title: IEE Proc. Syst. Biol doi: 10.1049/ip-syb:20050035 – volume: 3 year: 2007 ident: 2023020211111611700_B11 article-title: Systematic evaluation of objective functions for predicting intracellular fluxes inEscherichia coli publication-title: Mol. Syst. Biol doi: 10.1038/msb4100162 – start-page: 51 volume-title: Contributions to the Theory of Games II of Annals of Math. Studies. year: 1953 ident: 2023020211111611700_B8 article-title: The double description method |
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| Snippet | Motivation: Elementary flux modes (EFMs)—non-decomposable minimal pathways—are commonly accepted tools for metabolic network analysis under steady state... Motivation: Elementary flux modes (EFMs)-non-decomposable minimal pathways-are commonly accepted tools for metabolic network analysis under steady state... Elementary flux modes (EFMs)--non-decomposable minimal pathways--are commonly accepted tools for metabolic network analysis under steady state conditions.... Motivation: Elementary flux modes (EFMs)--non-decomposable minimal pathways--are commonly accepted tools for metabolic network analysis under steady state... |
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| SubjectTerms | Algorithms Amino acids Bioinformatics Biological and medical sciences Cell Physiological Phenomena Combinatorial analysis Computational geometry Computer applications Computer architecture Computer Simulation E coli Enumeration Escherichia coli - genetics Escherichia coli - metabolism Fluctuations Fundamental and applied biological sciences. Psychology General aspects Genomes Geometry Mathematics Mathematics in biology. Statistical analysis. Models. Metrology. Data processing in biology (general aspects) Metabolic networks Metabolism Metabolites Methods Network analysis Optimization techniques Parallel processing Proteome - analysis Proteome - metabolism Residue number systems Systems Biology - methods |
| Title | Large-scale computation of elementary flux modes with bit pattern trees |
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