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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description | 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. |
doi_str_mv | 10.1093/bioinformatics/btn401 |
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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.</description><identifier>ISSN: 1367-4803</identifier><identifier>ISSN: 0266-7061</identifier><identifier>EISSN: 1460-2059</identifier><identifier>EISSN: 1367-4811</identifier><identifier>DOI: 10.1093/bioinformatics/btn401</identifier><identifier>PMID: 18676417</identifier><identifier>CODEN: BOINFP</identifier><language>eng</language><publisher>Oxford: Oxford University Press</publisher><subject>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 ; Escherichia coli - genetics ; Escherichia coli - metabolism ; Fluctuations ; Fundamental and applied biological sciences. Psychology ; General aspects ; Genomes ; Geometry ; Helicobacter pylori ; 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</subject><ispartof>Bioinformatics, 2008-10, Vol.24 (19), p.2229-2235</ispartof><rights>The Author 2008. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org 2008</rights><rights>2008 INIST-CNRS</rights><rights>The Author 2008. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c521t-74760067746ae18a6fdb7faab33f3a43bcbff22ecfdc47a9e4a9ccec03081ca93</citedby><cites>FETCH-LOGICAL-c521t-74760067746ae18a6fdb7faab33f3a43bcbff22ecfdc47a9e4a9ccec03081ca93</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,776,780,1598,27903,27904</link.rule.ids><linktorsrc>$$Uhttps://dx.doi.org/10.1093/bioinformatics/btn401$$EView_record_in_Oxford_University_Press$$FView_record_in_$$GOxford_University_Press</linktorsrc><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=20686170$$DView record in Pascal Francis$$Hfree_for_read</backlink><backlink>$$Uhttps://www.ncbi.nlm.nih.gov/pubmed/18676417$$D View this record in MEDLINE/PubMed$$Hfree_for_read</backlink></links><search><creatorcontrib>Terzer, Marco</creatorcontrib><creatorcontrib>Stelling, Jörg</creatorcontrib><title>Large-scale computation of elementary flux modes with bit pattern trees</title><title>Bioinformatics</title><addtitle>Bioinformatics</addtitle><description>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.</description><subject>Algorithms</subject><subject>Amino acids</subject><subject>Bioinformatics</subject><subject>Biological and medical sciences</subject><subject>Cell Physiological Phenomena</subject><subject>Combinatorial analysis</subject><subject>Computational geometry</subject><subject>Computer applications</subject><subject>Computer architecture</subject><subject>Computer Simulation</subject><subject>E coli</subject><subject>Enumeration</subject><subject>Escherichia coli</subject><subject>Escherichia coli - genetics</subject><subject>Escherichia coli - metabolism</subject><subject>Fluctuations</subject><subject>Fundamental and applied biological sciences. Psychology</subject><subject>General aspects</subject><subject>Genomes</subject><subject>Geometry</subject><subject>Helicobacter pylori</subject><subject>Mathematics</subject><subject>Mathematics in biology. Statistical analysis. Models. Metrology. Data processing in biology (general aspects)</subject><subject>Metabolic networks</subject><subject>Metabolism</subject><subject>Metabolites</subject><subject>Methods</subject><subject>Network analysis</subject><subject>Optimization techniques</subject><subject>Parallel processing</subject><subject>Proteome - analysis</subject><subject>Proteome - metabolism</subject><subject>Residue number systems</subject><subject>Systems Biology - methods</subject><issn>1367-4803</issn><issn>0266-7061</issn><issn>1460-2059</issn><issn>1367-4811</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2008</creationdate><recordtype>article</recordtype><sourceid>EIF</sourceid><recordid>eNqNkcFqFTEUhoMotlYfQQmC7saeTDLJzFKKbZULpdCCdBMyuSeaOjMZkwytb99c5lLRja6Sxff_yTkfIa8ZfGDQ8ePeBz-5EEeTvU3HfZ4EsCfkkAkJVQ1N97TcuVSVaIEfkBcp3QI0TAjxnBywViopmDokZxsTv2GVrBmQ2jDOSy6FYaLBURxwxCmb-Iu6YbmnY9hionc-f6e9z3Q2OWOcaI6I6SV55syQ8NX-PCLXp5-uTs6rzcXZ55OPm8o2NcuVEkoCSKWENMhaI922V86YnnPHjeC97Z2ra7Rua4UyHQrTWYsWOLTMmo4fkfdr7xzDzwVT1qNPFofBTBiWpGUngctW_hNkXQtM8baAb_8Cb8MSpzLEjilfVbCDmhWyMaQU0ek5-rFsRjPQOx_6Tx969VFyb_blSz_i9ndqL6AA7_aA2Tlw0UzWp0euhjILU1A4WLmwzP_9drVGfMp4_xgy8YeWiqtGn3-90afdJbu5hCv9hT8AZZC6Ig</recordid><startdate>20081001</startdate><enddate>20081001</enddate><creator>Terzer, Marco</creator><creator>Stelling, Jörg</creator><general>Oxford University Press</general><general>Oxford Publishing Limited (England)</general><scope>BSCLL</scope><scope>IQODW</scope><scope>CGR</scope><scope>CUY</scope><scope>CVF</scope><scope>ECM</scope><scope>EIF</scope><scope>NPM</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7QF</scope><scope>7QO</scope><scope>7QQ</scope><scope>7SC</scope><scope>7SE</scope><scope>7SP</scope><scope>7SR</scope><scope>7TA</scope><scope>7TB</scope><scope>7TM</scope><scope>7TO</scope><scope>7U5</scope><scope>8BQ</scope><scope>8FD</scope><scope>F28</scope><scope>FR3</scope><scope>H8D</scope><scope>H8G</scope><scope>H94</scope><scope>JG9</scope><scope>JQ2</scope><scope>K9.</scope><scope>KR7</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope><scope>P64</scope><scope>7QL</scope><scope>C1K</scope><scope>7X8</scope></search><sort><creationdate>20081001</creationdate><title>Large-scale computation of elementary flux modes with bit pattern trees</title><author>Terzer, Marco ; Stelling, Jörg</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c521t-74760067746ae18a6fdb7faab33f3a43bcbff22ecfdc47a9e4a9ccec03081ca93</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2008</creationdate><topic>Algorithms</topic><topic>Amino acids</topic><topic>Bioinformatics</topic><topic>Biological and medical sciences</topic><topic>Cell Physiological Phenomena</topic><topic>Combinatorial analysis</topic><topic>Computational geometry</topic><topic>Computer applications</topic><topic>Computer architecture</topic><topic>Computer Simulation</topic><topic>E coli</topic><topic>Enumeration</topic><topic>Escherichia coli</topic><topic>Escherichia coli - genetics</topic><topic>Escherichia coli - metabolism</topic><topic>Fluctuations</topic><topic>Fundamental and applied biological sciences. Psychology</topic><topic>General aspects</topic><topic>Genomes</topic><topic>Geometry</topic><topic>Helicobacter pylori</topic><topic>Mathematics</topic><topic>Mathematics in biology. Statistical analysis. Models. Metrology. Data processing in biology (general aspects)</topic><topic>Metabolic networks</topic><topic>Metabolism</topic><topic>Metabolites</topic><topic>Methods</topic><topic>Network analysis</topic><topic>Optimization techniques</topic><topic>Parallel processing</topic><topic>Proteome - analysis</topic><topic>Proteome - metabolism</topic><topic>Residue number systems</topic><topic>Systems Biology - methods</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Terzer, Marco</creatorcontrib><creatorcontrib>Stelling, Jörg</creatorcontrib><collection>Istex</collection><collection>Pascal-Francis</collection><collection>Medline</collection><collection>MEDLINE</collection><collection>MEDLINE (Ovid)</collection><collection>MEDLINE</collection><collection>MEDLINE</collection><collection>PubMed</collection><collection>CrossRef</collection><collection>Aluminium Industry Abstracts</collection><collection>Biotechnology Research Abstracts</collection><collection>Ceramic Abstracts</collection><collection>Computer and Information Systems Abstracts</collection><collection>Corrosion Abstracts</collection><collection>Electronics & Communications Abstracts</collection><collection>Engineered Materials Abstracts</collection><collection>Materials Business File</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Nucleic Acids Abstracts</collection><collection>Oncogenes and Growth Factors Abstracts</collection><collection>Solid State and Superconductivity Abstracts</collection><collection>METADEX</collection><collection>Technology Research Database</collection><collection>ANTE: Abstracts in New Technology & Engineering</collection><collection>Engineering Research Database</collection><collection>Aerospace Database</collection><collection>Copper Technical Reference Library</collection><collection>AIDS and Cancer Research Abstracts</collection><collection>Materials Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>ProQuest Health & Medical Complete (Alumni)</collection><collection>Civil Engineering Abstracts</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><collection>Biotechnology and BioEngineering Abstracts</collection><collection>Bacteriology Abstracts (Microbiology B)</collection><collection>Environmental Sciences and Pollution Management</collection><collection>MEDLINE - Academic</collection><jtitle>Bioinformatics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Terzer, Marco</au><au>Stelling, Jörg</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Large-scale computation of elementary flux modes with bit pattern trees</atitle><jtitle>Bioinformatics</jtitle><addtitle>Bioinformatics</addtitle><date>2008-10-01</date><risdate>2008</risdate><volume>24</volume><issue>19</issue><spage>2229</spage><epage>2235</epage><pages>2229-2235</pages><issn>1367-4803</issn><issn>0266-7061</issn><eissn>1460-2059</eissn><eissn>1367-4811</eissn><coden>BOINFP</coden><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.</abstract><cop>Oxford</cop><pub>Oxford University Press</pub><pmid>18676417</pmid><doi>10.1093/bioinformatics/btn401</doi><tpages>7</tpages><oa>free_for_read</oa></addata></record> |
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subjects | 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 Escherichia coli - genetics Escherichia coli - metabolism Fluctuations Fundamental and applied biological sciences. Psychology General aspects Genomes Geometry Helicobacter pylori 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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