<?xml version="1.0" encoding="iso-8859-1"?>


<!--  FILE :  BPGS_P_1999.xml

CREATED :  4th March 2002

LAST MODIFIED :20th April 2005

AUTHOR :  Catherine Lloyd
         Department of Engineering Science
         The University of Auckland

MODEL STATUS :  This model conforms to the CellML 1.0 Specification released on
10th August 2001, and the 16/01/2002 CellML Metadata 1.0 Specification.

DESCRIPTION :  This file contains a CellML description of the 1999 Mulquiney,
Bubb and Kuchel mathematical model of the 2,3-bisphosphoglycerate shunt in
erythrocytes.

CHANGES:
 18/07/2002 - CML - Added more metadata.  
 09/04/2003 - AAC - Added publication date information.  
 20/04/2005 - PJV - Modified syntax to comply with cellml1.1 specs
-->

<model name="BPGS_P_1999" cmeta:id="BPGS_P_1999" pathway_editor:rendering_config_file="BGPS P 1999render.xml" xmlns="http://www.cellml.org/cellml/1.0#" xmlns:cellml="http://www.cellml.org/cellml/1.0#" xmlns:cmeta="http://www.cellml.org/metadata/1.0#" xmlns:pathway_editor="http://www.physiome.com/pathway_editor/1.0#">
  <rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:bqs="http://www.cellml.org/bqs/1.0#" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:dcterms="http://purl.org/dc/terms/" xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#">
    <!--
      The following RDF block contains metadata that applies to this document
      as a whole, as indicated by the empty about attribute on the 
      <rdf:Description> element.
    -->
    <rdf:Description rdf:about="">
      <!--
        The Model Builder Metadata.  The Dublin Core "creator" element is used  
        to indicate the person who translated the model into CellML.
      -->
      <dc:creator rdf:parseType="Resource">
        <vCard:N rdf:parseType="Resource">
          <vCard:Family>Lloyd</vCard:Family>
          <vCard:Given>Catherine</vCard:Given>
          <vCard:Other>May</vCard:Other>
        </vCard:N>
        <vCard:EMAIL rdf:parseType="Resource">
          <rdf:value>c.lloyd@auckland.ac.nz</rdf:value>
          <rdf:type rdf:resource="http://imc.org/vCard/3.0#internet" />
        </vCard:EMAIL>
        <vCard:ORG rdf:parseType="Resource">
          <vCard:Orgname>The University of Auckland</vCard:Orgname>
          <vCard:Orgunit>The Bioengineering Institute</vCard:Orgunit>
        </vCard:ORG>
      </dc:creator>

      <!--
        The Creation Date metadata. This is the date on which the model
        was translated into CellML.
      -->
      <dcterms:created rdf:parseType="Resource">
        <dcterms:W3CDTF>2002-03-04</dcterms:W3CDTF>
      </dcterms:created>

      <!--
        The Modification History metadata. This lists the changes that have been
        made to the document, who made the changes, and when they were made.
      -->

      <!-- The Publisher metadata. -->
      <dc:publisher>
        The University of Auckland, Bioengineering Research Group
      </dc:publisher>
    </rdf:Description>

    <!--
      The following metadata refers to the model itself, as indicated by the
      reference to the ID "BPGS_P_1999", which is declared on
      the <model> element.
    -->
    <rdf:Description rdf:about="#BPGS_P_1999">
      <!-- A human readable name for the model. -->
      <dc:title>
        A model of the 2,3-BPG shunt in human erythrocytes.
      </dc:title>

      <!-- A comment regarding the model. -->
      <cmeta:comment rdf:parseType="Resource">
        <rdf:value>
          This is the CellML description of Mulquiney, Bubb and Kuchel's 
          mathematical model of the 2,3-BPG shunt in human erythrocytes (1999).
        </rdf:value>
        <!-- The creator of the comment. -->
        <dc:creator rdf:parseType="Resource">
          <vCard:FN>Catherine Lloyd</vCard:FN>
        </dc:creator>
      </cmeta:comment>

      <!-- The model is relevant to human erythrocytes. -->
      <cmeta:species>Homo Sapiens</cmeta:species>

      <!--  This model is specific to erythrocytes. -->
      <cmeta:bio_entity>erythrocyte</cmeta:bio_entity>
      
      <!--  Keyword(s) -->
      <bqs:reference rdf:parseType="Resource">
        <dc:subject rdf:parseType="Resource">
          <bqs:subject_type>keyword</bqs:subject_type>
          <rdf:value>metabolism</rdf:value>
        </dc:subject>
      </bqs:reference>

      <!-- 
        The CellML Metadata Specification recommends that bibliographic metadata
        is used to provide information about the original model reference.  The 
        "identifier" attribute on the "BibliographicReference" class provides an
        elegant way to identify a cited reference using a database identifier            such as Pubmed.  All associated data such as author, journal title,     
        date, etc can be looked up on the database.
      -->
      <bqs:reference rdf:parseType="Resource">
        <bqs:Pubmed_id>10477268</bqs:Pubmed_id>
        <bqs:JournalArticle rdf:parseType="Resource">
          <dc:creator>
            <rdf:Seq>
              <rdf:li rdf:parseType="Resource">
                <bqs:Person rdf:parseType="Resource">
                  <vCard:N rdf:parseType="Resource">
                    <vCard:Family>Mulquiney</vCard:Family>
                    <vCard:Given>Peter</vCard:Given>
                    <vCard:Other>J</vCard:Other>
                  </vCard:N>
                </bqs:Person>
              </rdf:li>
              <rdf:li rdf:parseType="Resource">
                <bqs:Person rdf:parseType="Resource">
                  <vCard:N rdf:parseType="Resource">
                    <vCard:Family>Bubb</vCard:Family>
                    <vCard:Given>William</vCard:Given>
                    <vCard:Other>A</vCard:Other>
                  </vCard:N>
                </bqs:Person>
              </rdf:li>
              <rdf:li rdf:parseType="Resource">
                <bqs:Person rdf:parseType="Resource">
                  <vCard:N rdf:parseType="Resource">
                    <vCard:Family>Kuchel</vCard:Family>
                    <vCard:Given>Philip</vCard:Given>
                    <vCard:Other>W</vCard:Other>
                  </vCard:N>
                </bqs:Person>
              </rdf:li>
            </rdf:Seq>
          </dc:creator>
          <dc:title>
            Model of 2,3-bisphosphoglycerate metabolism in the human erythrocyte             based on detailed enzyme kinetic equations: in vivo kinetic 
            characterisation of 2,3-bisphosphoglycerate synthase/phosphatase 
            using 13C and 31P NMR
          </dc:title>
          <dcterms:issued rdf:parseType="Resource">
            <dcterms:W3CDTF>1999-09-15</dcterms:W3CDTF>
          </dcterms:issued>
          <bqs:Journal rdf:parseType="Resource">
            <dc:title>Biochemical Journal</dc:title>
          </bqs:Journal>
          <bqs:volume>342</bqs:volume>
          <bqs:first_page>567</bqs:first_page>
          <bqs:last_page>580</bqs:last_page>
        </bqs:JournalArticle>
      </bqs:reference>
    </rdf:Description>
  </rdf:RDF>

 <!--
   We start the model definition with a definition of some named
   sets of units for use throughout the model.
 -->

 <units name="molar">
   <unit units="mole" />
   <unit units="litre" exponent="-1" />
 </units>

 <units name="millimolar">
   <unit prefix="milli" units="molar" />
 </units>

 <units name="flux">
   <unit prefix="milli" units="mole" />
   <unit units="second" exponent="-1" />
 </units>

 <units name="first_order_rate_constant">
   <unit units="second" exponent="-1" />
 </units>

 <units name="second_order_rate_constant">
   <unit units="molar" exponent="-1" />
   <unit units="second" exponent="-1" />
 </units>

 <!--  
   The following component is defined for modelling convenience.  It contains 
   all the universal variables, in this case, only time.
 -->
 <component name="global_variables">
   <variable name="time" public_interface="out" units="second" />
 </component>

 <!--  
   The following components describe all the substrates, enzymes, 
   enzyme-substrate complexes and products in the 2,3-BPG shunt.
 -->

  <component name="E" cmeta:id="E">
    <rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:dcterms="http://purl.org/dc/terms/">
      <rdf:Description rdf:about="E">
        <dc:title>E</dc:title>
        <dcterms:alternative> 
          free BPGS/P
        </dcterms:alternative>
      </rdf:Description>
    </rdf:RDF>
    <variable name="E" public_interface="out" units="millimolar" />
    <variable name="delta_E_rxn3" public_interface="in" units="flux" />
    <variable name="delta_E_rxn3a" public_interface="in" units="flux" />
    <variable name="delta_E_rxn4" public_interface="in" units="flux" />
    <variable name="delta_E_rxn0" public_interface="in" units="flux" />
    <variable name="time" public_interface="in" units="second" />
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply><eq />
        <apply><diff />
          <bvar>
            <ci>time</ci>
          </bvar>
          <ci>E</ci>
        </apply>
        <apply><plus />
          <ci>delta_E_rxn3</ci>
          <ci>delta_E_rxn3a</ci>
          <ci>delta_E_rxn4</ci>
          <ci>delta_E_rxn0</ci>
        </apply>
      </apply>
    </math>
  </component>

  <component name="A" cmeta:id="A">
    <rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:dcterms="http://purl.org/dc/terms/">
      <rdf:Description rdf:about="A">
        <dc:title>A</dc:title>
        <dcterms:alternative> 
          1,3-BPG
        </dcterms:alternative>
      </rdf:Description>
    </rdf:RDF>
    <variable name="A" public_interface="out" units="millimolar" />
    <variable name="delta_A_rxn0" public_interface="in" units="flux" />
    <variable name="time" public_interface="in" units="second" />
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply><eq />
        <apply><diff />
          <bvar>
            <ci>time</ci>
          </bvar>
          <ci>A</ci>
        </apply>
        <ci>delta_A_rxn0</ci>
      </apply>
    </math>
  </component>

  <component name="EA">
    <variable name="EA" public_interface="out" units="millimolar" />
    <variable name="delta_EA_rxn0" public_interface="in" units="flux" />
    <variable name="delta_EA_rxn1" public_interface="in" units="flux" />
    <variable name="time" public_interface="in" units="second" />
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply><eq />
        <apply><diff />
          <bvar>
            <ci>time</ci>
          </bvar>
          <ci>EA</ci>
        </apply>
        <apply><plus />
          <ci>delta_EA_rxn0</ci>
          <ci>delta_EA_rxn1</ci>
        </apply>
      </apply>
    </math>
  </component>

  <component name="F" cmeta:id="F">
    <rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:dcterms="http://purl.org/dc/terms/">
      <rdf:Description rdf:about="F">
        <dc:title>F</dc:title>
        <dcterms:alternative> 
          phosphorylated BPGS/P
        </dcterms:alternative>
      </rdf:Description>
    </rdf:RDF>
    <variable name="F" public_interface="out" units="millimolar" />
    <variable name="delta_F_rxn1" public_interface="in" units="flux" />
    <variable name="delta_F_rxn2" public_interface="in" units="flux" />
    <variable name="delta_F_rxn2a" public_interface="in" units="flux" />
    <variable name="delta_F_rxn5" public_interface="in" units="flux" />
    <variable name="delta_F_rxn6" public_interface="in" units="flux" />
    <variable name="time" public_interface="in" units="second" />
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply><eq />
        <apply><diff />
          <bvar>
            <ci>time</ci>
          </bvar>
          <ci>F</ci>
        </apply>
        <apply><plus />
          <ci>delta_F_rxn1</ci>
          <ci>delta_F_rxn2</ci>
          <ci>delta_F_rxn2a</ci>
          <ci>delta_F_rxn5</ci>
          <ci>delta_F_rxn6</ci>
        </apply>
      </apply>
    </math>
  </component>

  <component name="Pi" cmeta:id="Pi">
    <rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:dcterms="http://purl.org/dc/terms/">
      <rdf:Description rdf:about="Pi">
        <dc:title>Pi</dc:title>
        <dcterms:alternative> 
          inorganic phosphate
        </dcterms:alternative>
      </rdf:Description>
    </rdf:RDF>
    <variable name="Pi" public_interface="out" units="millimolar" />
    <variable name="delta_Pi_rxn2" public_interface="in" units="flux" />
    <variable name="time" public_interface="in" units="second" />
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply><eq />
        <apply><diff />
          <bvar>
            <ci>time</ci>
          </bvar>
          <ci>Pi</ci>
        </apply>
        <ci>delta_Pi_rxn2</ci>
      </apply>
    </math>
  </component>

  <component name="two_PGly">
    <variable name="two_PGly" public_interface="out" units="millimolar" />
    <variable name="delta_2_PGly_rxn2a" public_interface="in" units="flux" />
    <variable name="time" public_interface="in" units="second" />
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply><eq />
        <apply><diff />
          <bvar>
            <ci>time</ci>
          </bvar>
          <ci>two_PGly</ci>
        </apply>
        <ci>delta_2_PGly_rxn2a</ci>
      </apply>
    </math>
  </component>

  <component name="FPi">
    <variable name="FPi" public_interface="out" units="millimolar" />
    <variable name="delta_FPi_rxn2" public_interface="in" units="flux" />
    <variable name="delta_FPi_rxn3" public_interface="in" units="flux" />
    <variable name="time" public_interface="in" units="second" />
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply><eq />
        <apply><diff />
          <bvar>
            <ci>time</ci>
          </bvar>
          <ci>FPi</ci>
        </apply>
        <apply><plus />
          <ci>delta_FPi_rxn2</ci>
          <ci>delta_FPi_rxn3</ci>
        </apply>
      </apply>
    </math>
  </component>

  <component name="F2_PGly">
    <variable name="F2_PGly" public_interface="out" units="millimolar" />
    <variable name="delta_F2_PGly_rxn2a" public_interface="in" units="flux" />
    <variable name="delta_F2_PGly_rxn3a" public_interface="in" units="flux" />
    <variable name="time" public_interface="in" units="second" />
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply><eq />
        <apply><diff />
          <bvar>
            <ci>time</ci>
          </bvar>
          <ci>F2_PGly</ci>
        </apply>
        <apply><plus />
          <ci>delta_F2_PGly_rxn2a</ci>
          <ci>delta_F2_PGly_rxn3a</ci>
        </apply>
      </apply>
    </math>
  </component>

  <component name="D" cmeta:id="D">
    <rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:dcterms="http://purl.org/dc/terms/">
      <rdf:Description rdf:about="D">
        <dc:title>D</dc:title>
        <dcterms:alternative> 
          2,3-BPG
        </dcterms:alternative>
      </rdf:Description>
    </rdf:RDF>
    <variable name="D" public_interface="out" units="millimolar" />
    <variable name="delta_D_rxn4" public_interface="in" units="flux" />
    <variable name="time" public_interface="in" units="second" />
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply><eq />
        <apply><diff />
          <bvar>
            <ci>time</ci>
          </bvar>
          <ci>D</ci>
        </apply>
        <ci>delta_D_rxn4</ci>
      </apply>
    </math>
  </component>

  <component name="ED">
    <variable name="ED" public_interface="out" units="millimolar" />
    <variable name="delta_ED_rxn7" public_interface="in" units="flux" />
    <variable name="delta_ED_rxn8" public_interface="in" units="flux" />
    <variable name="delta_ED_rxn4" public_interface="in" units="flux" />
    <variable name="time" public_interface="in" units="second" />
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply><eq />
        <apply><diff />
          <bvar>
            <ci>time</ci>
          </bvar>
          <ci>ED</ci>
        </apply>
        <apply><plus />
          <ci>delta_ED_rxn7</ci>
          <ci>delta_ED_rxn8</ci>
          <ci>delta_ED_rxn4</ci>
        </apply>
      </apply>
    </math>
  </component>

  <component name="B" cmeta:id="B">
    <rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:dcterms="http://purl.org/dc/terms/">
      <rdf:Description rdf:about="B">
        <dc:title>B</dc:title>
        <dcterms:alternative> 
          3-PGA
        </dcterms:alternative>
      </rdf:Description>
    </rdf:RDF>
    <variable name="B" public_interface="out" units="millimolar" />
    <variable name="delta_B_rxn5" public_interface="in" units="flux" />
    <variable name="time" public_interface="in" units="second" />
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply><eq />
        <apply><diff />
          <bvar>
            <ci>time</ci>
          </bvar>
          <ci>B</ci>
        </apply>
        <ci>delta_B_rxn5</ci>
      </apply>
    </math>
  </component>

  <component name="FB">
    <variable name="FB" public_interface="out" units="millimolar" />
    <variable name="delta_FB_rxn5" public_interface="in" units="flux" />
    <variable name="delta_FB_rxn7" public_interface="in" units="flux" />
    <variable name="time" public_interface="in" units="second" />
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply><eq />
        <apply><diff />
          <bvar>
            <ci>time</ci>
          </bvar>
          <ci>FB</ci>
        </apply>
        <apply><plus />
          <ci>delta_FB_rxn5</ci>
          <ci>delta_FB_rxn7</ci>
        </apply>
      </apply>
    </math>
  </component>

  <component name="C" cmeta:id="C">
    <rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:dcterms="http://purl.org/dc/terms/">
      <rdf:Description rdf:about="C">
        <dc:title>C</dc:title>
        <dcterms:alternative> 
          2-PGA
        </dcterms:alternative>
      </rdf:Description>
    </rdf:RDF>
    <variable name="C" public_interface="out" units="millimolar" />
    <variable name="delta_C_rxn6" public_interface="in" units="flux" />
    <variable name="time" public_interface="in" units="second" />
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply><eq />
        <apply><diff />
          <bvar>
            <ci>time</ci>
          </bvar>
          <ci>C</ci>
        </apply>
        <ci>delta_C_rxn6</ci>
      </apply>
    </math>
  </component>

  <component name="FC">
    <variable name="FC" public_interface="out" units="millimolar" />
    <variable name="delta_FC_rxn6" public_interface="in" units="flux" />
    <variable name="delta_FC_rxn8" public_interface="in" units="flux" />
    <variable name="time" public_interface="in" units="second" />
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply><eq />
        <apply><diff />
          <bvar>
            <ci>time</ci>
          </bvar>
          <ci>FC</ci>
        </apply>
        <apply><plus />
          <ci>delta_FC_rxn6</ci>
          <ci>delta_FC_rxn8</ci>
        </apply>
      </apply>
    </math>
  </component>

  <!--
   The following components represent the individual reaction steps of the 
   2,3-BPG shunt.
 -->

  <component name="reaction0">
    <variable name="A" public_interface="in" units="millimolar" />
    <variable name="E" public_interface="in" units="millimolar" />
    <variable name="EA" public_interface="in" units="millimolar" />
    <variable name="delta_A_rxn0" public_interface="out" units="flux" />
    <variable name="delta_E_rxn0" public_interface="out" units="flux" />
    <variable name="delta_EA_rxn0" public_interface="out" units="flux" />
    <variable name="k0" initial_value="8000000.0" units="second_order_rate_constant" />
    <variable name="k0_" initial_value="400.0" units="first_order_rate_constant" />
    <variable name="rate" units="flux" />
    <reaction reversible="yes">
      <variable_ref variable="A">
        <role role="reactant" direction="forward" delta_variable="delta_A_rxn0" stoichiometry="1" />
      </variable_ref>
      <variable_ref variable="E">
        <role role="reactant" direction="forward" delta_variable="delta_E_rxn0" stoichiometry="1" />
      </variable_ref>
      <variable_ref variable="EA">
        <role role="product" direction="forward" delta_variable="delta_EA_rxn0" stoichiometry="1" />
      </variable_ref>
      <variable_ref variable="rate">
        <role role="rate">
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply><eq />
              <ci>rate</ci>
              <apply><plus />
                <apply><times />
                  <ci>k0</ci>
                  <ci>A</ci>
                  <ci>E</ci>
                </apply>
                <apply><minus />
                  <apply><times />
                    <ci>k0_</ci>
                    <ci>EA</ci>
                  </apply>
                </apply>
              </apply>
            </apply>
          </math>
        </role>
      </variable_ref>
    </reaction>
  </component>

  <component name="reaction1">
    <variable name="EA" public_interface="in" units="millimolar" />
    <variable name="F" public_interface="in" units="millimolar" />
    <variable name="delta_EA_rxn1" public_interface="out" units="flux" />
    <variable name="delta_F_rxn1" public_interface="out" units="flux" />
    <variable name="k1" initial_value="9.9" units="first_order_rate_constant" />
    <variable name="rate" units="flux" />
    <reaction reversible="no">
      <variable_ref variable="EA">
        <role role="reactant" delta_variable="delta_EA_rxn1" stoichiometry="1" />
      </variable_ref>
      <variable_ref variable="F">
        <role role="product" delta_variable="delta_F_rxn1" stoichiometry="1" />
      </variable_ref>
      <variable_ref variable="rate">
        <role role="rate">
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply><eq />
              <ci>rate</ci>
              <apply><times />
                <ci>k1</ci>
                <ci>EA</ci>
              </apply>
            </apply>
          </math>
        </role>
      </variable_ref>
    </reaction>
  </component>

  <component name="reaction2">
    <variable name="Pi" public_interface="in" units="millimolar" />
    <variable name="F" public_interface="in" units="millimolar" />
    <variable name="FPi" public_interface="in" units="millimolar" />
    <variable name="delta_Pi_rxn2" public_interface="out" units="flux" />
    <variable name="delta_F_rxn2" public_interface="out" units="flux" />
    <variable name="delta_FPi_rxn2" public_interface="out" units="flux" />
    <variable name="k2" initial_value="1000000000.0" units="second_order_rate_constant" />
    <variable name="k2_" initial_value="610000.0" units="first_order_rate_constant" />
    <variable name="rate" units="flux" />
    <reaction reversible="yes">
      <variable_ref variable="Pi">
        <role role="reactant" direction="forward" delta_variable="delta_Pi_rxn2" stoichiometry="1" />
      </variable_ref>
      <variable_ref variable="F">
        <role role="reactant" direction="forward" delta_variable="delta_F_rxn2" stoichiometry="1" />
      </variable_ref>
      <variable_ref variable="FPi">
        <role role="product" direction="forward" delta_variable="delta_FPi_rxn2" stoichiometry="1" />
      </variable_ref>
      <variable_ref variable="rate">
        <role role="rate">
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply><eq />
              <ci>rate</ci>
              <apply><plus />
                <apply><times />
                  <ci>k2</ci>
                  <ci>Pi</ci>
                  <ci>F</ci>
                </apply>
                <apply><minus />
                  <apply><times />
                    <ci>k2_</ci>
                    <ci>FPi</ci>
                  </apply>
                </apply>
              </apply>
            </apply>
          </math>
        </role>
      </variable_ref>
    </reaction>
  </component>

  <component name="reaction2a">
    <variable name="two_PGly" public_interface="in" units="millimolar" />
    <variable name="F" public_interface="in" units="millimolar" />
    <variable name="F2_PGly" public_interface="in" units="millimolar" />
    <variable name="delta_2_PGly_rxn2a" public_interface="out" units="flux" />
    <variable name="delta_F_rxn2a" public_interface="out" units="flux" />
    <variable name="delta_F2_PGly_rxn2a" public_interface="out" units="flux" />
    <variable name="k2a" initial_value="1000000000.0" units="second_order_rate_constant" />
    <variable name="k2a_" initial_value="89000.0" units="first_order_rate_constant" />
    <variable name="rate" units="flux" />
    <reaction reversible="yes">
      <variable_ref variable="two_PGly">
        <role role="reactant" direction="forward" delta_variable="delta_2_PGly_rxn2a" stoichiometry="1" />
      </variable_ref>
      <variable_ref variable="F">
        <role role="reactant" direction="forward" delta_variable="delta_F_rxn2a" stoichiometry="1" />
      </variable_ref>
      <variable_ref variable="F2_PGly">
        <role role="product" direction="forward" delta_variable="delta_F2_PGly_rxn2a" stoichiometry="1" />
      </variable_ref>
      <variable_ref variable="rate">
        <role role="rate">
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply><eq />
              <ci>rate</ci>
              <apply><plus />
                <apply><times />
                  <ci>k2a</ci>
                  <ci>two_PGly</ci>
                  <ci>F</ci>
                </apply>
                <apply><minus />
                  <apply><times />
                    <ci>k2a_</ci>
                    <ci>F2_PGly</ci>
                  </apply>
                </apply>
              </apply>
            </apply>
          </math>
        </role>
      </variable_ref>
    </reaction>
  </component>

  <component name="reaction3">
    <variable name="FPi" public_interface="in" units="millimolar" />
    <variable name="E" public_interface="in" units="millimolar" />
    <variable name="delta_FPi_rxn3" public_interface="out" units="flux" />
    <variable name="delta_E_rxn3" public_interface="out" units="flux" />
    <variable name="k3" initial_value="0.19" units="first_order_rate_constant" />
    <variable name="rate" units="flux" />
    <reaction reversible="no">
      <variable_ref variable="FPi">
        <role role="reactant" delta_variable="delta_FPi_rxn3" stoichiometry="1" />
      </variable_ref>
      <variable_ref variable="E">
        <role role="product" delta_variable="delta_E_rxn3" stoichiometry="1" />
      </variable_ref>
      <variable_ref variable="rate">
        <role role="rate">
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply><eq />
              <ci>rate</ci>
              <apply><times />
                <ci>k3</ci>
                <ci>FPi</ci>
              </apply>
            </apply>
          </math>
        </role>
      </variable_ref>
    </reaction>
  </component>

  <component name="reaction3a">
    <variable name="F2_PGly" public_interface="in" units="millimolar" />
    <variable name="E" public_interface="in" units="millimolar" />
    <variable name="delta_F2_PGly_rxn3a" public_interface="out" units="flux" />
    <variable name="delta_E_rxn3a" public_interface="out" units="flux" />
    <variable name="k3a" initial_value="4.03" units="first_order_rate_constant" />
    <variable name="rate" units="flux" />
    <reaction reversible="no">
      <variable_ref variable="F2_PGly">
        <role role="reactant" delta_variable="delta_F2_PGly_rxn3a" stoichiometry="1" />
      </variable_ref>
      <variable_ref variable="E">
        <role role="product" delta_variable="delta_E_rxn3a" stoichiometry="1" />
      </variable_ref>
      <variable_ref variable="rate">
        <role role="rate">
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply><eq />
              <ci>rate</ci>
              <apply><times />
                <ci>k3a</ci>
                <ci>F2_PGly</ci>
              </apply>
            </apply>
          </math>
        </role>
      </variable_ref>
    </reaction>
  </component>

  <component name="reaction4">
    <variable name="ED" public_interface="in" units="millimolar" />
    <variable name="D" public_interface="in" units="millimolar" />
    <variable name="E" public_interface="in" units="millimolar" />
    <variable name="delta_ED_rxn4" public_interface="out" units="flux" />
    <variable name="delta_D_rxn4" public_interface="out" units="flux" />
    <variable name="delta_E_rxn4" public_interface="out" units="flux" />
    <variable name="k4" initial_value="1000.0" units="first_order_rate_constant" />
    <variable name="k4_" initial_value="1800000.0" units="second_order_rate_constant" />
    <variable name="rate" units="flux" />
    <reaction reversible="yes">
      <variable_ref variable="ED">
        <role role="reactant" direction="forward" delta_variable="delta_ED_rxn4" stoichiometry="1" />
      </variable_ref>
      <variable_ref variable="D">
        <role role="product" direction="forward" delta_variable="delta_D_rxn4" stoichiometry="1" />
      </variable_ref>
      <variable_ref variable="E">
        <role role="product" direction="forward" delta_variable="delta_E_rxn4" stoichiometry="1" />
      </variable_ref>
      <variable_ref variable="rate">
        <role role="rate">
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply><eq />
              <ci>rate</ci>
              <apply><plus />
                <apply><times />
                  <ci>k4</ci>
                  <ci>ED</ci>
                </apply>
                <apply><minus />
                  <apply><times />
                    <ci>k4_</ci>
                    <ci>D</ci>
                    <ci>E</ci>
                  </apply>
                </apply>
              </apply>
            </apply>
          </math>
        </role>
      </variable_ref>
    </reaction>
  </component>

  <component name="reaction5">
    <variable name="B" public_interface="in" units="millimolar" />
    <variable name="F" public_interface="in" units="millimolar" />
    <variable name="FB" public_interface="in" units="millimolar" />
    <variable name="delta_B_rxn5" public_interface="out" units="flux" />
    <variable name="delta_F_rxn5" public_interface="out" units="flux" />
    <variable name="delta_FB_rxn5" public_interface="out" units="flux" />
    <variable name="k5" initial_value="185000000.0" units="second_order_rate_constant" />
    <variable name="k5_" initial_value="100000000.0" units="first_order_rate_constant" />
    <variable name="rate" units="flux" />
    <reaction reversible="yes">
      <variable_ref variable="B">
        <role role="reactant" direction="forward" delta_variable="delta_B_rxn5" stoichiometry="1" />
      </variable_ref>
      <variable_ref variable="F">
        <role role="reactant" direction="forward" delta_variable="delta_F_rxn5" stoichiometry="1" />
      </variable_ref>
      <variable_ref variable="FB">
        <role role="product" direction="forward" delta_variable="delta_FB_rxn5" stoichiometry="1" />
      </variable_ref>
      <variable_ref variable="rate">
        <role role="rate">
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply><eq />
              <ci>rate</ci>
              <apply><plus />
                <apply><times />
                  <ci>k5</ci>
                  <ci>B</ci>
                  <ci>F</ci>
                </apply>
                <apply><minus />
                  <apply><times />
                    <ci>k5_</ci>
                    <ci>FB</ci>
                  </apply>
                </apply>
              </apply>
            </apply>
          </math>
        </role>
      </variable_ref>
    </reaction>
  </component>

  <component name="reaction6">
    <variable name="C" public_interface="in" units="millimolar" />
    <variable name="F" public_interface="in" units="millimolar" />
    <variable name="FC" public_interface="in" units="millimolar" />
    <variable name="delta_C_rxn6" public_interface="out" units="flux" />
    <variable name="delta_F_rxn6" public_interface="out" units="flux" />
    <variable name="delta_FC_rxn6" public_interface="out" units="flux" />
    <variable name="k6" initial_value="1000.0" units="second_order_rate_constant" />
    <variable name="k6_" initial_value="100000000.0" units="first_order_rate_constant" />
    <variable name="rate" units="flux" />
    <reaction reversible="yes">
      <variable_ref variable="C">
        <role role="reactant" direction="forward" delta_variable="delta_C_rxn6" stoichiometry="1" />
      </variable_ref>
      <variable_ref variable="F">
        <role role="reactant" direction="forward" delta_variable="delta_F_rxn6" stoichiometry="1" /> 
      </variable_ref>
      <variable_ref variable="FC">
        <role role="product" direction="forward" delta_variable="delta_FC_rxn6" stoichiometry="1" />
      </variable_ref>
      <variable_ref variable="rate">
        <role role="rate">
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply><eq />
              <ci>rate</ci>
              <apply><plus />
                <apply><times />
                  <ci>k6</ci>
                  <ci>C</ci>
                  <ci>F</ci>
                </apply>
                <apply><minus />
                  <apply><times />
                    <ci>k6_</ci>
                    <ci>FC</ci>
                  </apply>
                </apply>
              </apply>
            </apply>
          </math>
        </role>
      </variable_ref>
    </reaction>
  </component>

  <component name="reaction7">
    <variable name="FB" public_interface="in" units="millimolar" />
    <variable name="ED" public_interface="in" units="millimolar" />
    <variable name="delta_FB_rxn7" public_interface="out" units="flux" />
    <variable name="delta_ED_rxn7" public_interface="out" units="flux" />
    <variable name="k7" initial_value="10000.0" units="first_order_rate_constant" />
    <variable name="k7_" initial_value="0.55" units="first_order_rate_constant" />
    <variable name="rate" units="flux" />
    <reaction reversible="yes">
      <variable_ref variable="FB">
        <role role="reactant" direction="forward" delta_variable="delta_FB_rxn7" stoichiometry="1" />
      </variable_ref>
      <variable_ref variable="ED">
        <role role="product" direction="forward" delta_variable="delta_ED_rxn7" stoichiometry="1" />
      </variable_ref>
      <variable_ref variable="rate">
        <role role="rate">
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply><eq />
              <ci>rate</ci>
              <apply><plus />
                <apply><times />
                  <ci>k7</ci>
                  <ci>FB</ci>
                </apply>
                <apply><minus />
                  <apply><times />
                    <ci>k7_</ci>
                    <ci>ED</ci>
                  </apply>
                </apply>
              </apply>
            </apply>
          </math>
        </role>
      </variable_ref>
    </reaction>
  </component>

  <component name="reaction8">
    <variable name="FC" public_interface="in" units="millimolar" />
    <variable name="ED" public_interface="in" units="millimolar" />
    <variable name="delta_FC_rxn8" public_interface="out" units="flux" />
    <variable name="delta_ED_rxn8" public_interface="out" units="flux" />
    <variable name="k8" initial_value="1980.0" units="first_order_rate_constant" />
    <variable name="k8_" initial_value="0.01" units="first_order_rate_constant" />
    <variable name="rate" units="flux" />
    <reaction reversible="yes">
      <variable_ref variable="FC">
        <role role="reactant" direction="forward" delta_variable="delta_FC_rxn8" stoichiometry="1" />
      </variable_ref>
      <variable_ref variable="ED">
        <role role="product" direction="forward" delta_variable="delta_ED_rxn8" stoichiometry="1" />
      </variable_ref>
      <variable_ref variable="rate">
        <role role="rate">
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply><eq />
              <ci>rate</ci>
              <apply><plus />
                <apply><times />
                  <ci>k8</ci>
                  <ci>FC</ci>
                </apply>
                <apply><minus />
                  <apply><times />
                    <ci>k8_</ci>
                    <ci>ED</ci>
                  </apply>
                </apply>
              </apply>
            </apply>
          </math>
        </role>
      </variable_ref>
    </reaction>
  </component>

  <connection>
    <map_components component_1="E" component_2="reaction3" />
    <map_variables variable_1="E" variable_2="E" />
    <map_variables variable_1="delta_E_rxn3" variable_2="delta_E_rxn3" />
  </connection>

  <connection>
    <map_components component_1="E" component_2="reaction3a" />
    <map_variables variable_1="E" variable_2="E" />
    <map_variables variable_1="delta_E_rxn3a" variable_2="delta_E_rxn3a" />
  </connection>

  <connection>
    <map_components component_1="E" component_2="reaction4" />
    <map_variables variable_1="E" variable_2="E" />
    <map_variables variable_1="delta_E_rxn4" variable_2="delta_E_rxn4" />
  </connection>

  <connection>
    <map_components component_1="E" component_2="reaction0" />
    <map_variables variable_1="E" variable_2="E" />
    <map_variables variable_1="delta_E_rxn0" variable_2="delta_E_rxn0" />
  </connection>

  <connection>
    <map_components component_1="A" component_2="reaction0" />
    <map_variables variable_1="A" variable_2="A" />
    <map_variables variable_1="delta_A_rxn0" variable_2="delta_A_rxn0" />
  </connection>

  <connection>
    <map_components component_1="EA" component_2="reaction0" />
    <map_variables variable_1="EA" variable_2="EA" />
    <map_variables variable_1="delta_EA_rxn0" variable_2="delta_EA_rxn0" />
  </connection>

  <connection>
    <map_components component_1="EA" component_2="reaction1" />
    <map_variables variable_1="EA" variable_2="EA" />
    <map_variables variable_1="delta_EA_rxn1" variable_2="delta_EA_rxn1" />
  </connection>

  <connection>
    <map_components component_1="F" component_2="reaction1" />
    <map_variables variable_1="F" variable_2="F" />
    <map_variables variable_1="delta_F_rxn1" variable_2="delta_F_rxn1" />
  </connection>

  <connection>
    <map_components component_1="F" component_2="reaction2" />
    <map_variables variable_1="F" variable_2="F" />
    <map_variables variable_1="delta_F_rxn2" variable_2="delta_F_rxn2" />
  </connection>

  <connection>
    <map_components component_1="F" component_2="reaction2a" />
    <map_variables variable_1="F" variable_2="F" />
    <map_variables variable_1="delta_F_rxn2a" variable_2="delta_F_rxn2a" />
  </connection>

  <connection>
    <map_components component_1="F" component_2="reaction5" />
    <map_variables variable_1="F" variable_2="F" />
    <map_variables variable_1="delta_F_rxn5" variable_2="delta_F_rxn5" />
  </connection>

  <connection>
    <map_components component_1="F" component_2="reaction6" />
    <map_variables variable_1="F" variable_2="F" />
    <map_variables variable_1="delta_F_rxn6" variable_2="delta_F_rxn6" />
  </connection>

  <connection>
    <map_components component_1="Pi" component_2="reaction2" />
    <map_variables variable_1="Pi" variable_2="Pi" />
    <map_variables variable_1="delta_Pi_rxn2" variable_2="delta_Pi_rxn2" />
  </connection>

  <connection>
    <map_components component_1="FPi" component_2="reaction2" />
    <map_variables variable_1="FPi" variable_2="FPi" />
    <map_variables variable_1="delta_FPi_rxn2" variable_2="delta_FPi_rxn2" />
  </connection>

  <connection>
    <map_components component_1="FPi" component_2="reaction3" />
    <map_variables variable_1="FPi" variable_2="FPi" />
    <map_variables variable_1="delta_FPi_rxn3" variable_2="delta_FPi_rxn3" />
  </connection>

  <connection>
    <map_components component_1="two_PGly" component_2="reaction2a" />
    <map_variables variable_1="two_PGly" variable_2="two_PGly" />
    <map_variables variable_1="delta_2_PGly_rxn2a" variable_2="delta_2_PGly_rxn2a" />
  </connection>

  <connection>
    <map_components component_1="F2_PGly" component_2="reaction2a" />
    <map_variables variable_1="F2_PGly" variable_2="F2_PGly" />
    <map_variables variable_1="delta_F2_PGly_rxn2a" variable_2="delta_F2_PGly_rxn2a" />
  </connection>

  <connection>
    <map_components component_1="F2_PGly" component_2="reaction3a" />
    <map_variables variable_1="F2_PGly" variable_2="F2_PGly" />
    <map_variables variable_1="delta_F2_PGly_rxn3a" variable_2="delta_F2_PGly_rxn3a" />
  </connection>

  <connection>
    <map_components component_1="D" component_2="reaction4" />
    <map_variables variable_1="D" variable_2="D" />
    <map_variables variable_1="delta_D_rxn4" variable_2="delta_D_rxn4" />
  </connection>

  <connection>
    <map_components component_1="ED" component_2="reaction7" />
    <map_variables variable_1="ED" variable_2="ED" />
    <map_variables variable_1="delta_ED_rxn7" variable_2="delta_ED_rxn7" />
  </connection>

  <connection>
    <map_components component_1="ED" component_2="reaction8" />
    <map_variables variable_1="ED" variable_2="ED" />
    <map_variables variable_1="delta_ED_rxn8" variable_2="delta_ED_rxn8" />
  </connection>

  <connection>
    <map_components component_1="ED" component_2="reaction4" />
    <map_variables variable_1="ED" variable_2="ED" />
    <map_variables variable_1="delta_ED_rxn4" variable_2="delta_ED_rxn4" />
  </connection>

  <connection>
    <map_components component_1="B" component_2="reaction5" />
    <map_variables variable_1="B" variable_2="B" />
    <map_variables variable_1="delta_B_rxn5" variable_2="delta_B_rxn5" />
  </connection>

  <connection>
    <map_components component_1="FB" component_2="reaction5" />
    <map_variables variable_1="FB" variable_2="FB" />
    <map_variables variable_1="delta_FB_rxn5" variable_2="delta_FB_rxn5" />
  </connection>

  <connection>
    <map_components component_1="FB" component_2="reaction7" />
    <map_variables variable_1="FB" variable_2="FB" />
    <map_variables variable_1="delta_FB_rxn7" variable_2="delta_FB_rxn7" />
  </connection>

  <connection>
    <map_components component_1="C" component_2="reaction6" />
    <map_variables variable_1="C" variable_2="C" />
    <map_variables variable_1="delta_C_rxn6" variable_2="delta_C_rxn6" />
  </connection>

  <connection>
    <map_components component_1="FC" component_2="reaction6" />
    <map_variables variable_1="FC" variable_2="FC" />
    <map_variables variable_1="delta_FC_rxn6" variable_2="delta_FC_rxn6" />
  </connection>

  <connection>
    <map_components component_1="FC" component_2="reaction8" />
    <map_variables variable_1="FC" variable_2="FC" />
    <map_variables variable_1="delta_FC_rxn8" variable_2="delta_FC_rxn8" />
  </connection>

  <connection>
    <map_components component_1="E" component_2="global_variables" />
    <map_variables variable_1="time" variable_2="time" />
  </connection>

  <connection>
    <map_components component_1="A" component_2="global_variables" />
    <map_variables variable_1="time" variable_2="time" />
  </connection>

  <connection>
    <map_components component_1="EA" component_2="global_variables" />
    <map_variables variable_1="time" variable_2="time" />
  </connection>

  <connection>
    <map_components component_1="F" component_2="global_variables" />
    <map_variables variable_1="time" variable_2="time" />
  </connection>

  <connection>
    <map_components component_1="Pi" component_2="global_variables" />
    <map_variables variable_1="time" variable_2="time" />
  </connection>

  <connection>
    <map_components component_1="FPi" component_2="global_variables" />
    <map_variables variable_1="time" variable_2="time" />
  </connection>

  <connection>
    <map_components component_1="two_PGly" component_2="global_variables" />
    <map_variables variable_1="time" variable_2="time" />
  </connection>

  <connection>
    <map_components component_1="F2_PGly" component_2="global_variables" />
    <map_variables variable_1="time" variable_2="time" />
  </connection>

  <connection>
    <map_components component_1="D" component_2="global_variables" />
    <map_variables variable_1="time" variable_2="time" />
  </connection>

  <connection>
    <map_components component_1="ED" component_2="global_variables" />
    <map_variables variable_1="time" variable_2="time" />
  </connection>

  <connection>
    <map_components component_1="B" component_2="global_variables" />
    <map_variables variable_1="time" variable_2="time" />
  </connection>

  <connection>
    <map_components component_1="FB" component_2="global_variables" />
    <map_variables variable_1="time" variable_2="time" />
  </connection>

  <connection>
    <map_components component_1="C" component_2="global_variables" />
    <map_variables variable_1="time" variable_2="time" />
  </connection>

  <connection>
    <map_components component_1="FC" component_2="global_variables" />
    <map_variables variable_1="time" variable_2="time" />
  </connection>

</model>
