Location: Teusink, Passarge, Reijenga, Esgalhado, Vanderweijden, Schepper, Walsh, Bakker, Vandam, Westerhoff, Snoep, 2000 @ ddd08a236d99 / teusink_passarge_reijenga_esgalhado_vanderweijden_schepper_walsh_bakker_vandam_westerhoff_snoep_2000.cellml

Author:
pmr2.import <nobody@models.cellml.org>
Date:
2006-07-09 07:18:32+12:00
Desc:
committing version01 of teusink_passarge_reijenga_esgalhado_vanderweijden_schepper_walsh_bakker_vandam_westerhoff_snoep_2000
Permanent Source URI:
https://models.physiomeproject.org/workspace/teusink_passarge_reijenga_esgalhado_vanderweijden_schepper_walsh_bakker_vandam_westerhoff_snoep_2000/rawfile/ddd08a236d9938d437f877ceeb2cc2ec10d2956b/teusink_passarge_reijenga_esgalhado_vanderweijden_schepper_walsh_bakker_vandam_westerhoff_snoep_2000.cellml

<?xml version='1.0' encoding='utf-8'?>
<!--  FILE :  teusink_model_2000.xml

CREATED :  7th May 2003

LAST MODIFIED : 20th April 2005

AUTHOR :  Catherine Lloyd
          Bioengineering Institute
          The University of Auckland
          
MODEL STATUS :  This model conforms to the CellML 1.0 Specification released on
10th August 2001, and the 16/1/02 CellML Metadata 1.0 Specification.

DESCRIPTION :  This file contains a CellML description of Teusink et al.'s 2000 model for glycolysis in yeast.

CHANGES:  
  20/04/2005 - PJV - Updated syntax to conform with Cellml1.1 specs
  
--><model xmlns="http://www.cellml.org/cellml/1.0#" xmlns:cmeta="http://www.cellml.org/metadata/1.0#" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:bqs="http://www.cellml.org/bqs/1.0#" xmlns:cellml="http://www.cellml.org/cellml/1.0#" xmlns:dcterms="http://purl.org/dc/terms/" xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" cmeta:id="schepper_2000_version01" name="schepper_2000_version01">
<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
  <articleinfo>
  <title>Understanding Yeast Glycolysis in Terms of the in vitro Kinetics of the Constituent Enzymes</title>
  <author>
    <firstname>Catherine</firstname>
          <surname>Lloyd</surname>
    <affiliation>
      <shortaffil>Bioengineering Institute, University of Auckland</shortaffil>
    </affiliation>
  </author>
</articleinfo>
  <section id="sec_status">
    <title>Model Status</title>
    <para>
            This is the original unchecked version of the model imported from the previous
            CellML model repository, 24-Jan-2006.
          </para>
  </section>
  <sect1 id="sec_structure">
<title>Model Structure</title>

<para>
In April 2003 the human genome sequence was completed.  One of the greatest challenges currently facing biologists is the elucidation of the molecular function of the proteins encoded by the genes.  Traditionally, the approach has been to isolate these proteins and then characterise them <emphasis>in vitro</emphasis>.  More recently, scientists have begun to question whether this will generate an accurate picture of how these proteins behave within a functional cell (<emphasis>in vivo</emphasis>).  It is highly likely that the environment within a living cell is very different from the conditions within a test tube.  Interacting metabolites, intracellular compartmentation, and enzyme concentrations are all likely to differ.  The question to be asked is whether these differences between <emphasis>in vitro</emphasis> and <emphasis>in vivo</emphasis> conditions seriously affect scientists' understanding of the functional behaviour of the living cell.  
</para>

<para>
The paper described here by Teusink <emphasis>et al.</emphasis> (2000) asks the question: can the behaviour of biochemical pathways be described by simply combining the properties of the components in isolation?  In other words, can the <emphasis>in vivo</emphasis> behaviour of yeast glycolysis be understood in terms of the <emphasis>in vitro</emphasis> kinetic properties of the constituent enzymes? Based on <emphasis>in vitro</emphasis>, experimentally determined enzyme kinetics data, they developed a mathematical model of the glycolysis pathway in the yeast <emphasis>Saccharomyces cerevisiae</emphasis>.  The simulation results from this model were then compared with recorded fluxes and metabolite levels in living cells under similar conditions.  They employed mathematical modelling to test whether knowledge of the <emphasis>in vitro</emphasis> kinetic properties of the glycolytic enzymes allows a good understanding of the overall pathway behaviour <emphasis>in vivo</emphasis>.  
</para>

<para>
The model includes most enzymes in the glycolysis pathway (see <xref linkend="fig_reaction_diagram"/> below).  A set of ordinary differential equations was used to represent the time-dependence of the metabolite concentrations.  Reversible Michaelis-Menten and irreversible Hill kinetics were amongst the types of enzymes kinetics included in the model equations. 
</para>

<para>
The complete original paper reference is cited below:
</para>

<para>
<ulink url="http://www.blackwell-synergy.com/openurl?genre=article&amp;sid=nlm:pubmed&amp;issn=0014-2956&amp;date=2000&amp;volume=267&amp;issue=17&amp;spage=5313">Can yeast glycolysis be understood in terms of <emphasis>in vitro</emphasis> kinetics of the constituent enzymes? Testing biochemistry</ulink>, Bas Teusink, Jutta Passarge, Corinne A. Reijenga, Eugenia Esgalhado, Coen C. van der Weijden, Mike Schepper, Michael C. Walsh, Barbara M. Bakker, Karel van Dam, Hans V. Westerhoff, and Jacky L. Snoep, 2000, <ulink url="http://www.blackwell-synergy.com/servlet/useragent?func=showIssues&amp;code=ejb">
            <emphasis>European Journal of Biochemistry</emphasis>
          </ulink>, 267, 5313-5329. <ulink url="http://www.blackwell-synergy.com/links/doi/10.1046/j.1432-1327.2000.01527.x/full/">Full text</ulink> and PDF versions of the article are available to journal subscribers.)  <ulink url="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&amp;db=PubMed&amp;list_uids=10951190&amp;dopt=Abstract">PubMed ID: 10951190</ulink>
</para>

<informalfigure float="0" id="fig_reaction_diagram">
<mediaobject>
  <imageobject>
    <objectinfo>
      <title>reaction diagram</title>
    </objectinfo>
    <imagedata fileref="teusink_2000.png"/>
  </imageobject>
</mediaobject>
<caption>A schematic diagram of the reactions included in the Teusink <emphasis>et al.</emphasis> 2000 model of the glycolysis pathway in the yeast <emphasis>Saccharomyces cerevisiae</emphasis>.</caption>
</informalfigure>

<para>
Model simulations revealed that the orginal question posed does not have a simple answer.  For half of the enzymes studied, the <emphasis>in vitro</emphasis> kinetics did describe the <emphasis>in vivo</emphasis> activity.  However, the other half of the enzymes analysed, they were larger deviations between their <emphasis>in vitro</emphasis> and <emphasis>in vivo</emphasis> characteristics.
</para>

</sect1>
</article>
</documentation>
  
  
  <!--
    Below, we define some additional units for association with variables and
    constants within the model. 
  -->
  
  <units name="molar">
    <unit units="mole"/>
    <unit units="litre" exponent="-1"/>
  </units>
  
  <units name="millimolar">
    <unit units="mole" prefix="milli"/>
    <unit units="litre" exponent="-1"/>
  </units>
  
  <units name="minute">
    <unit units="second" multiplier="60.0"/>
  </units>
  
  <units name="flux">
    <unit units="molar"/>
    <unit units="minute" exponent="-1"/>
  </units>
  
  <units name="first_order_rate_constant">
    <unit units="minute" exponent="-1"/>
  </units>
  
  
  <component name="environment">
    <variable units="minute" public_interface="out" name="time"/>
  </component>
  
  <!--
    The following components describe all the reactants and products involved in
    reactions. 
  -->
  
  <component name="Glc_out" cmeta:id="Glc_out">
    <rdf:RDF>
      <rdf:Description rdf:about="Glc_out">
        <dc:title>Glc_out</dc:title>
        <dcterms:alternative>extracellular glucose</dcterms:alternative>  
      </rdf:Description>
    </rdf:RDF> 
    <variable units="millimolar" public_interface="out" name="Glc_out"/> 
    <variable units="flux" public_interface="in" name="V_transport"/>
    <variable units="minute" public_interface="in" name="time"/> 
    <math xmlns="http://www.w3.org/1998/Math/MathML"> 
      <apply>
        <eq/> 
        <apply>
          <diff/> 
          <bvar>
            <ci>time</ci>
          </bvar> 
          <ci>Glc_out</ci> 
        </apply>
        <apply>
          <minus/> 
          <ci>V_transport</ci>
        </apply> 
      </apply> 
    </math> 
  </component>
  
  <component name="Glc_in" cmeta:id="Glc_in">
    <rdf:RDF>
      <rdf:Description rdf:about="Glc_in">
        <dc:title>Glc_in</dc:title>
        <dcterms:alternative>intracellular glucose</dcterms:alternative>  
      </rdf:Description>
    </rdf:RDF> 
    <variable units="millimolar" public_interface="out" name="Glc_in"/> 
    <variable units="flux" public_interface="in" name="V_transport"/>
    <variable units="flux" public_interface="in" name="V_HK"/>
    <variable units="minute" public_interface="in" name="time"/> 
    <math xmlns="http://www.w3.org/1998/Math/MathML"> 
      <apply>
        <eq/> 
        <apply>
          <diff/> 
          <bvar>
            <ci>time</ci>
          </bvar> 
          <ci>Glc_in</ci> 
        </apply>
        <apply>
          <minus/> 
          <ci>V_transport</ci>
          <ci>V_HK</ci>
        </apply> 
      </apply> 
    </math> 
  </component>
  
  <component name="G6P" cmeta:id="G6P">
    <rdf:RDF>
      <rdf:Description rdf:about="G6P">
        <dc:title>G6P</dc:title>
        <dcterms:alternative>glucose 6-phosphate</dcterms:alternative>  
      </rdf:Description>
    </rdf:RDF> 
    <variable units="millimolar" public_interface="out" name="G6P" initial_value="2.45"/>
    <variable units="flux" public_interface="in" name="V_HK"/> 
    <variable units="flux" public_interface="in" name="V_glycogen"/>
    <variable units="flux" public_interface="in" name="V_trehalose"/>
    <variable units="flux" public_interface="in" name="V_PGI"/>
    <variable units="minute" public_interface="in" name="time"/> 
    <math xmlns="http://www.w3.org/1998/Math/MathML"> 
      <apply>
        <eq/> 
        <apply>
          <diff/> 
          <bvar>
            <ci>time</ci>
          </bvar> 
          <ci>G6P</ci> 
        </apply>
        <apply>
          <minus/>
          <ci>V_HK</ci>
          <apply>
            <plus/>
            <ci>V_PGI</ci>
            <apply>
              <times/>
              <cn cellml:units="dimensionless"> 2.0 </cn> 
              <ci>V_trehalose</ci>
            </apply> 
            <ci>V_glycogen</ci>
          </apply>
        </apply> 
      </apply> 
    </math> 
  </component>
  
  <component name="F6P" cmeta:id="F6P">
    <rdf:RDF>
      <rdf:Description rdf:about="F6P">
        <dc:title>F6P</dc:title>
        <dcterms:alternative>fructose 6-phosphate</dcterms:alternative>  
      </rdf:Description>
    </rdf:RDF> 
    <variable units="millimolar" public_interface="out" name="F6P" initial_value="0.62"/> 
    <variable units="flux" public_interface="in" name="V_PFK"/>
    <variable units="flux" public_interface="in" name="V_PGI"/>
    <variable units="minute" public_interface="in" name="time"/> 
    <math xmlns="http://www.w3.org/1998/Math/MathML"> 
      <apply>
        <eq/> 
        <apply>
          <diff/> 
          <bvar>
            <ci>time</ci>
          </bvar> 
          <ci>F6P</ci> 
        </apply>
        <apply>
          <minus/> 
          <ci>V_PGI</ci>
          <ci>V_PFK</ci>
        </apply> 
      </apply> 
    </math> 
  </component>
  
  <component name="F16bP2" cmeta:id="F16bP2">
    <rdf:RDF>
      <rdf:Description rdf:about="F16bP2">
        <dc:title>F16bP2</dc:title>
        <dcterms:alternative>fructose 1,6-bisphosphate</dcterms:alternative>  
      </rdf:Description>
    </rdf:RDF> 
    <variable units="millimolar" public_interface="out" name="F16bP2" initial_value="5.51"/> 
    <variable units="flux" public_interface="in" name="V_PFK"/>
    <variable units="flux" public_interface="in" name="V_ALD"/>
    <variable units="minute" public_interface="in" name="time"/> 
    <math xmlns="http://www.w3.org/1998/Math/MathML"> 
      <apply>
        <eq/> 
        <apply>
          <diff/> 
          <bvar>
            <ci>time</ci>
          </bvar> 
          <ci>F16bP2</ci> 
        </apply>
        <apply>
          <minus/> 
          <ci>V_PFK</ci>
          <ci>V_ALD</ci>
        </apply> 
      </apply> 
    </math> 
  </component>
  
  <component name="F26bP2" cmeta:id="F26bP2">
    <rdf:RDF>
      <rdf:Description rdf:about="F26bP2">
        <dc:title>F26bP2</dc:title>
        <dcterms:alternative>fructose 2,6-bisphosphate</dcterms:alternative>  
      </rdf:Description>
    </rdf:RDF> 
    <variable units="millimolar" public_interface="out" name="F26bP2"/> 
    <variable units="flux" public_interface="in" name="V_PFK"/>
    <variable units="minute" public_interface="in" name="time"/> 
    <math xmlns="http://www.w3.org/1998/Math/MathML"> 
      <apply>
        <eq/> 
        <apply>
          <diff/> 
          <bvar>
            <ci>time</ci>
          </bvar> 
          <ci>F26bP2</ci> 
        </apply>
        <ci>V_PFK</ci>
      </apply> 
    </math> 
  </component>
  
  <component name="Trio_P" cmeta:id="Trio_P">
    <rdf:RDF>
      <rdf:Description rdf:about="Trio_P">
        <dc:title>Trio_P</dc:title>
        <dcterms:alternative>triophosphate</dcterms:alternative>  
      </rdf:Description>
    </rdf:RDF> 
    <variable units="millimolar" public_interface="out" name="Trio_P"/>
    <variable units="flux" public_interface="in" name="V_ALD"/>
    <variable units="flux" public_interface="in" name="V_GraPDH"/>
    <variable units="flux" public_interface="in" name="V_glycerol"/>
    <variable units="minute" public_interface="in" name="time"/> 
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply>
        <eq/> 
        <apply>
          <diff/> 
          <bvar>
            <ci>time</ci>
          </bvar> 
          <ci>Trio_P</ci> 
        </apply>
        <apply>
          <minus/>
          <apply>
            <times/>
            <cn cellml:units="dimensionless"> 2.0 </cn> 
            <ci>V_ALD</ci>
          </apply>
          <apply>
            <plus/> 
            <ci>V_GraPDH</ci>
            <ci>V_glycerol</ci>
          </apply> 
        </apply> 
      </apply> 
    </math> 
  </component>
  
  <component name="TPI" cmeta:id="TPI">
    <rdf:RDF>
      <rdf:Description rdf:about="TPI">
        <dc:title>TPI</dc:title>
        <dcterms:alternative>triosephosphate</dcterms:alternative>  
      </rdf:Description>
    </rdf:RDF> 
    <variable units="millimolar" public_interface="out" name="glycerone_phosphate" initial_value="0.81"/>
    <variable units="millimolar" public_interface="in" name="Trio_P"/>
    <variable units="millimolar" public_interface="out" name="GraP"/>
    <variable units="dimensionless" name="Keq_TPI"/>
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply id="Keq_TPI_calculation">
        <eq/>
        <ci> Keq_TPI </ci>
        <apply>
          <divide/>
          <ci>GraP</ci> 
          <ci>glycerone_phosphate</ci> 
        </apply>
      </apply>

      <apply id="glycerone_phosphate_calculation">
        <eq/>
        <ci> glycerone_phosphate </ci>
        <apply>
          <divide/>
          <ci>Trio_P</ci>
          <apply>
            <plus/>
            <cn cellml:units="dimensionless"> 1.0 </cn>
            <ci> Keq_TPI </ci> 
          </apply>
        </apply>
      </apply>

      <apply id="GraP_calculation">
        <eq/>
        <ci> GraP </ci>
        <apply>
          <divide/>
          <apply>
            <times/>
            <ci>Trio_P</ci>
            <ci> Keq_TPI </ci>
          </apply>
          <apply>
            <plus/>
            <cn cellml:units="dimensionless"> 1.0 </cn>
            <ci> Keq_TPI </ci> 
          </apply>
        </apply>
      </apply> 
    </math> 
  </component>
  
  <component name="BPG" cmeta:id="BPG">
    <rdf:RDF>
      <rdf:Description rdf:about="BPG">
        <dc:title>BPG</dc:title>
        <dcterms:alternative>bisphosphoglycerate</dcterms:alternative>  
      </rdf:Description>
    </rdf:RDF> 
    <variable units="millimolar" public_interface="out" name="BPG"/> 
    <variable units="flux" public_interface="in" name="V_GraPDH"/>
    <variable units="flux" public_interface="in" name="V_PGK"/>
    <variable units="minute" public_interface="in" name="time"/> 
    <math xmlns="http://www.w3.org/1998/Math/MathML"> 
      <apply>
        <eq/> 
        <apply>
          <diff/> 
          <bvar>
            <ci>time</ci>
          </bvar> 
          <ci>BPG</ci> 
        </apply>
        <apply>
          <minus/> 
          <ci>V_GraPDH</ci>
          <ci>V_PGK</ci>
        </apply> 
      </apply> 
    </math> 
  </component>
  
  <component name="three_GriP" cmeta:id="three_GriP">
    <rdf:RDF>
      <rdf:Description rdf:about="three_GriP">
        <dc:title>three_GriP</dc:title>
        <dcterms:alternative>3-phosphoglycerate</dcterms:alternative>  
      </rdf:Description>
    </rdf:RDF> 
    <variable units="millimolar" public_interface="out" name="three_GriP" initial_value="0.90"/> 
    <variable units="flux" public_interface="in" name="V_PGM"/>
    <variable units="flux" public_interface="in" name="V_PGK"/>
    <variable units="minute" public_interface="in" name="time"/> 
    <math xmlns="http://www.w3.org/1998/Math/MathML"> 
      <apply>
        <eq/> 
        <apply>
          <diff/> 
          <bvar>
            <ci>time</ci>
          </bvar> 
          <ci>three_GriP</ci> 
        </apply>
        <apply>
          <minus/> 
          <ci>V_PGK</ci>
          <ci>V_PGM</ci>
        </apply> 
      </apply> 
    </math> 
  </component>
  
  <component name="two_GriP" cmeta:id="two_GriP">
    <rdf:RDF>
      <rdf:Description rdf:about="two_GriP">
        <dc:title>two_GriP</dc:title>
        <dcterms:alternative>2-phosphoglycerate</dcterms:alternative>  
      </rdf:Description>
    </rdf:RDF> 
    <variable units="millimolar" public_interface="out" name="two_GriP" initial_value="0.12"/> 
    <variable units="flux" public_interface="in" name="V_PGM"/>
    <variable units="flux" public_interface="in" name="V_ENO"/>
    <variable units="minute" public_interface="in" name="time"/> 
    <math xmlns="http://www.w3.org/1998/Math/MathML"> 
      <apply>
        <eq/> 
        <apply>
          <diff/> 
          <bvar>
            <ci>time</ci>
          </bvar> 
          <ci>two_GriP</ci> 
        </apply>
        <apply>
          <minus/> 
          <ci>V_PGM</ci>
          <ci>V_ENO</ci>
        </apply> 
      </apply> 
    </math> 
  </component>
  
  <component name="PEP" cmeta:id="PEP">
    <rdf:RDF>
      <rdf:Description rdf:about="PEP">
        <dc:title>PEP</dc:title>
        <dcterms:alternative>phosphoenolpyruvate</dcterms:alternative>  
      </rdf:Description>
    </rdf:RDF> 
    <variable units="millimolar" public_interface="out" name="PEP" initial_value="0.07"/> 
    <variable units="flux" public_interface="in" name="V_ENO"/>
    <variable units="flux" public_interface="in" name="V_PYK"/>
    <variable units="minute" public_interface="in" name="time"/> 
    <math xmlns="http://www.w3.org/1998/Math/MathML"> 
      <apply>
        <eq/> 
        <apply>
          <diff/> 
          <bvar>
            <ci>time</ci>
          </bvar> 
          <ci>PEP</ci> 
        </apply>
        <apply>
          <minus/> 
          <ci>V_ENO</ci>
          <ci>V_PYK</ci>
        </apply> 
      </apply> 
    </math> 
  </component>
  
  <component name="PYR" cmeta:id="PYR">
    <rdf:RDF>
      <rdf:Description rdf:about="PYR">
        <dc:title>PYR</dc:title>
        <dcterms:alternative>pyruvate</dcterms:alternative>  
      </rdf:Description>
    </rdf:RDF> 
    <variable units="millimolar" public_interface="out" name="PYR" initial_value="1.85"/> 
    <variable units="flux" public_interface="in" name="V_PYK"/>
    <variable units="flux" public_interface="in" name="V_PDC"/>
    <variable units="minute" public_interface="in" name="time"/> 
    <math xmlns="http://www.w3.org/1998/Math/MathML"> 
      <apply>
        <eq/> 
        <apply>
          <diff/> 
          <bvar>
            <ci>time</ci>
          </bvar> 
          <ci>PYR</ci> 
        </apply>
        <apply>
          <minus/> 
          <ci>V_PYK</ci>
          <ci>V_PDC</ci>
        </apply> 
      </apply> 
    </math> 
  </component>
  
  <component name="AcAld" cmeta:id="AcAld">
    <rdf:RDF>
      <rdf:Description rdf:about="AcAld">
        <dc:title>AcAld</dc:title>
        <dcterms:alternative>acetaldehyde</dcterms:alternative>  
      </rdf:Description>
    </rdf:RDF> 
    <variable units="millimolar" public_interface="out" name="AcAld" initial_value="0.17"/> 
    <variable units="flux" public_interface="in" name="V_PDC"/>
    <variable units="flux" public_interface="in" name="V_ADH"/>
    <variable units="flux" public_interface="in" name="V_succinate"/>
    <variable units="minute" public_interface="in" name="time"/> 
    <math xmlns="http://www.w3.org/1998/Math/MathML"> 
      <apply>
        <eq/> 
        <apply>
          <diff/> 
          <bvar>
            <ci>time</ci>
          </bvar> 
          <ci>AcAld</ci> 
        </apply>
        <apply>
          <minus/> 
          <ci>V_PDC</ci>
          <apply>
            <plus/>
            <ci>V_ADH</ci>
            <apply>
              <times/>
              <cn cellml:units="dimensionless"> 2.0 </cn>
              <ci>V_succinate</ci>
            </apply>
          </apply>
        </apply> 
      </apply> 
    </math> 
  </component>
  
  <component name="ADP" cmeta:id="ADP">
    <rdf:RDF>
      <rdf:Description rdf:about="ADP">
        <dc:title>ADP</dc:title>
        <dcterms:alternative>adenosine diphosphate</dcterms:alternative>  
      </rdf:Description>
    </rdf:RDF> 
    <variable units="millimolar" public_interface="out" name="ADP" initial_value="1.32"/> 
  </component>
  
  <component name="ATP" cmeta:id="ATP">
    <rdf:RDF>
      <rdf:Description rdf:about="ATP">
        <dc:title>ATP</dc:title>
        <dcterms:alternative>adenosine triphosphate</dcterms:alternative>  
      </rdf:Description>
    </rdf:RDF> 
    <variable units="millimolar" public_interface="out" name="ATP" initial_value="2.52"/>
    <variable units="millimolar" public_interface="in" name="AMP"/>
    <variable units="millimolar" public_interface="in" name="ADP"/>
    <variable units="millimolar" public_interface="in" name="P"/>
    <variable units="dimensionless" name="Keq_AK"/>
    <variable units="dimensionless" name="a"/>
    <variable units="dimensionless" name="b"/>
    <variable units="dimensionless" name="c"/>
    <variable units="minute" public_interface="in" name="time"/> 
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply id="Keq_AK_calculation">
        <eq/>
        <ci> Keq_AK </ci>
        <apply>
          <divide/>
          <apply>
            <times/>
            <ci>AMP</ci>
            <ci>ATP</ci>
          </apply>
          <apply>
            <power/> 
            <ci>ADP</ci>
            <cn cellml:units="dimensionless"> 2.0 </cn>
          </apply> 
        </apply>
      </apply>

      <apply id="ATP_calculation">
        <eq/>
        <ci> ATP </ci>
        <apply>
          <divide/>
          <apply>
            <plus/>
            <apply>
              <minus/>
              <ci> b </ci>
            </apply>
            <apply>
              <power/>
              <apply>
                <minus/>
                <apply>
                  <power/> 
                  <ci>b</ci>
                  <cn cellml:units="dimensionless"> 2.0 </cn>
                </apply>
                <apply>
                  <times/>  
                  <cn cellml:units="dimensionless"> 4.0 </cn>
                  <ci>a</ci>
                  <ci>c</ci>
                </apply>
              </apply>
              <cn cellml:units="dimensionless"> 0.5 </cn>
            </apply>
          </apply>
          <apply>
            <times/>  
            <cn cellml:units="dimensionless"> 2.0 </cn>
            <ci>a</ci>
          </apply>
        </apply>
      </apply>

      <apply id="a_calculation">
        <eq/>
        <ci> a </ci>
        <apply>
          <minus/>
          <cn cellml:units="dimensionless"> 1.0 </cn>
          <apply>
            <times/>
            <cn cellml:units="dimensionless"> 4.0 </cn>
            <ci> Keq_AK </ci>
          </apply>
        </apply>
      </apply>
      
      <apply id="b_calculation">
        <eq/>
        <ci> b </ci>
        <apply>
          <minus/>
          <apply>
            <plus/>
            <ci> ATP </ci>
            <ci> ADP </ci>
            <ci> AMP </ci>
          </apply>
          <apply>
            <times/>
            <ci> P </ci>
            <apply>
              <minus/>
              <cn cellml:units="dimensionless"> 1.0 </cn>
              <apply>
                <times/>
                <cn cellml:units="dimensionless"> 4.0 </cn>
                <ci> Keq_AK </ci>
              </apply>
            </apply>
          </apply>
        </apply> 
      </apply>
      
      <apply id="c_calculation">
        <eq/>
        <ci> c </ci>
        <apply>
          <minus/>
          <apply>
            <times/>
            <ci> Keq_AK </ci>
            <apply>
              <power/> 
              <ci>P</ci>
              <cn cellml:units="dimensionless"> 2.0 </cn>
            </apply>
          </apply>
        </apply>
      </apply>
    </math> 
  </component>
  
  <component name="AMP" cmeta:id="AMP">
    <rdf:RDF>
      <rdf:Description rdf:about="AMP">
        <dc:title>AMP</dc:title>
        <dcterms:alternative>adenosine monophoshate</dcterms:alternative>  
      </rdf:Description>
    </rdf:RDF> 
    <variable units="millimolar" public_interface="out" name="AMP" initial_value="0.25"/>
  </component>
  
  <component name="ethanol"> 
    <variable units="millimolar" public_interface="out" name="ethanol"/>
  </component>
  
  <component name="glycerol"> 
    <variable units="millimolar" public_interface="out" name="glycerol"/>
  </component>
  
  <component name="P" cmeta:id="P">
    <rdf:RDF>
      <rdf:Description rdf:about="P">
        <dc:title>P</dc:title>
        <dcterms:alternative>phosphate</dcterms:alternative>  
      </rdf:Description>
    </rdf:RDF> 
    <variable units="millimolar" public_interface="out" name="P"/> 
    <variable units="flux" public_interface="in" name="V_PFK"/>
    <variable units="flux" public_interface="in" name="V_PGK"/>
    <variable units="flux" public_interface="in" name="V_HK"/>
    <variable units="flux" public_interface="in" name="V_PYK"/>
    <variable units="flux" public_interface="in" name="V_trehalose"/>
    <variable units="flux" public_interface="in" name="V_ATPase"/>
    <variable units="flux" public_interface="in" name="V_glycogen"/> 
    <variable units="flux" public_interface="in" name="V_succinate"/>
    <variable units="minute" public_interface="in" name="time"/> 
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply>
        <eq/> 
        <apply>
          <diff/> 
          <bvar>
            <ci>time</ci>
          </bvar> 
          <ci>P</ci> 
        </apply>
        <apply>
          <plus/>
          <ci>V_PGK</ci>
          <ci>V_PYK</ci>
          <apply>
            <minus/>
            <apply>
              <plus/> 
              <ci>V_HK</ci>
              <ci>V_PFK</ci>
              <ci>V_ATPase</ci>
              <ci>V_trehalose</ci>
              <ci>V_glycogen</ci>
              <apply>
                <times/>
                <cn cellml:units="dimensionless"> 4.0 </cn>
                <ci>V_succinate</ci>
              </apply>
            </apply>
          </apply>
        </apply> 
      </apply> 
    </math> 
  </component>
  
  <component name="NADH" cmeta:id="NADH">
    <rdf:RDF>
      <rdf:Description rdf:about="NADH">
        <dc:title>NADH</dc:title>
        <dcterms:alternative>
          nicotinamide adenine dinucleotide
        </dcterms:alternative>  
      </rdf:Description>
    </rdf:RDF> 
    <variable units="millimolar" public_interface="out" name="NADH" initial_value="0.39"/> 
    <variable units="flux" public_interface="out" name="dt_NADH"/> 
    <variable units="flux" public_interface="in" name="V_GraPDH"/>
    <variable units="flux" public_interface="in" name="V_ADH"/>
    <variable units="flux" public_interface="in" name="V_succinate"/>
    <variable units="flux" public_interface="in" name="V_glycerol"/>
    <variable units="minute" public_interface="in" name="time"/> 
    <math xmlns="http://www.w3.org/1998/Math/MathML"> 
      <apply>
        <eq/> 
        <apply>
          <diff/> 
          <bvar>
            <ci>time</ci>
          </bvar> 
          <ci>NADH</ci> 
        </apply> 
        <ci>dt_NADH</ci>
      </apply>
        
      <apply id="dt_NADH_calculation">
        <eq/>
        <ci> dt_NADH </ci>  
        <apply>
          <plus/>
          <ci>V_GraPDH</ci>
          <apply>
            <times/>
            <cn cellml:units="dimensionless"> 3.0 </cn>
            <ci>V_succinate</ci>
          </apply>
          <apply>
            <minus/>
            <apply>
              <plus/> 
              <ci>V_ADH</ci>
              <ci>V_glycerol</ci>
            </apply>
          </apply>
        </apply> 
      </apply>
    </math> 
  </component>
  
  <component name="NAD" cmeta:id="NAD">
    <rdf:RDF>
      <rdf:Description rdf:about="NAD">
        <dc:title>NAD</dc:title>
        <dcterms:alternative>
          charged nicotinamide adenine dinucleotide
        </dcterms:alternative>  
      </rdf:Description>
    </rdf:RDF> 
    <variable units="millimolar" public_interface="out" name="NAD" initial_value="1.20"/>
    <variable units="flux" public_interface="in" name="dt_NADH"/>
    <variable units="minute" public_interface="in" name="time"/>  
    <math xmlns="http://www.w3.org/1998/Math/MathML"> 
      <apply>
        <eq/> 
        <apply>
          <diff/> 
          <bvar>
            <ci>time</ci>
          </bvar> 
          <ci>NAD</ci> 
        </apply>
        <ci>dt_NADH</ci>
      </apply>
    </math> 
  </component>
  
  <!--
    The following components describe the reactions of the main model.
  -->
  
  <component name="V_PGI">
    <variable units="flux" public_interface="out" name="V_PGI"/>
    
    <variable units="millimolar" public_interface="in" name="F6P"/>
    <variable units="millimolar" public_interface="in" name="G6P"/>
    
    <variable units="millimolar" name="K_G6P" initial_value="1.4"/>
    <variable units="millimolar" name="K_F6P" initial_value="0.3"/>
    <variable units="dimensionless" name="Keq_PGI" initial_value="0.314"/>
    <variable units="flux" name="V_max" initial_value="1.26"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply id="V_PGI_calculation">
        <eq/>
        <ci> V_PGI </ci>
        <apply>
          <times/>
          <ci> V_max </ci>
          <apply>
            <divide/>
            <apply>
              <times/>
              <apply>
                <divide/>
                <ci> G6P </ci>
                <ci> K_G6P </ci>
              </apply>
              <apply>
                <minus/>
                <cn cellml:units="dimensionless"> 1.0 </cn>
                <apply>
                  <divide/>
                  <apply>
                    <divide/>
                    <ci> F6P </ci>
                    <ci> G6P </ci>
                  </apply>
                  <ci> Keq_PGI </ci>
                </apply>
              </apply>
            </apply>
            <apply>
              <plus/>
              <cn cellml:units="dimensionless"> 1.0 </cn>
              <apply>
                <divide/>
                <ci> G6P </ci>
                <ci> K_G6P </ci>
              </apply>
              <apply>
                <divide/>
                <ci> F6P </ci>
                <ci> K_F6P </ci>
              </apply>
            </apply>
          </apply>
        </apply>
      </apply>
    </math>
  </component>
  
  <component name="V_PGM">
    <variable units="flux" public_interface="out" name="V_PGM"/>
    
    <variable units="millimolar" public_interface="in" name="two_GriP"/>
    <variable units="millimolar" public_interface="in" name="three_GriP"/>
    
    <variable units="millimolar" name="K_three_GriP" initial_value="1.2"/>
    <variable units="millimolar" name="K_two_GriP" initial_value="0.1"/>
    <variable units="dimensionless" name="Keq_PGM" initial_value="0.19"/>
    <variable units="flux" name="V_max" initial_value="9.4"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply id="V_PGM_calculation">
        <eq/>
        <ci> V_PGM </ci>
        <apply>
          <times/>
          <ci> V_max </ci>
          <apply>
            <divide/>
            <apply>
              <times/>
              <apply>
                <divide/>
                <ci> three_GriP </ci>
                <ci> K_three_GriP </ci>
              </apply>
              <apply>
                <minus/>
                <cn cellml:units="dimensionless"> 1.0 </cn>
                <apply>
                  <divide/>
                  <apply>
                    <divide/>
                    <ci> two_GriP </ci>
                    <ci> three_GriP </ci>
                  </apply>
                  <ci> Keq_PGM </ci>
                </apply>
              </apply>
            </apply>
            <apply>
              <plus/>
              <cn cellml:units="dimensionless"> 1.0 </cn>
              <apply>
                <divide/>
                <ci> three_GriP </ci>
                <ci> K_three_GriP </ci>
              </apply>
              <apply>
                <divide/>
                <ci> two_GriP </ci>
                <ci> K_two_GriP </ci>
              </apply>
            </apply>
          </apply>
        </apply>
      </apply>
    </math>
  </component>
  
  <component name="V_ENO">
    <variable units="flux" public_interface="out" name="V_ENO"/>
    
    <variable units="millimolar" public_interface="in" name="PEP"/>
    <variable units="millimolar" public_interface="in" name="two_GriP"/>
    
    <variable units="millimolar" name="K_two_GriP" initial_value="0.04"/>
    <variable units="millimolar" name="K_PEP" initial_value="0.5"/>
    <variable units="dimensionless" name="Keq_ENO" initial_value="6.7"/>
    <variable units="flux" name="V_max" initial_value="1.35"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply id="V_ENO_calculation">
        <eq/>
        <ci> V_ENO </ci>
        <apply>
          <times/>
          <ci> V_max </ci>
          <apply>
            <divide/>
            <apply>
              <times/>
              <apply>
                <divide/>
                <ci> two_GriP </ci>
                <ci> K_two_GriP </ci>
              </apply>
              <apply>
                <minus/>
                <cn cellml:units="dimensionless"> 1.0 </cn>
                <apply>
                  <divide/>
                  <apply>
                    <divide/>
                    <ci> PEP </ci>
                    <ci> two_GriP </ci>
                  </apply>
                  <ci> Keq_ENO </ci>
                </apply>
              </apply>
            </apply>
            <apply>
              <plus/>
              <cn cellml:units="dimensionless"> 1.0 </cn>
              <apply>
                <divide/>
                <ci> two_GriP </ci>
                <ci> K_two_GriP </ci>
              </apply>
              <apply>
                <divide/>
                <ci> PEP </ci>
                <ci> K_PEP </ci>
              </apply>
            </apply>
          </apply>
        </apply>
      </apply>
    </math>
  </component>
  
  <component name="V_HK">
    <variable units="flux" public_interface="out" name="V_HK"/>
    
    <variable units="millimolar" public_interface="in" name="G6P"/>
    <variable units="millimolar" public_interface="in" name="Glc_in"/>
    <variable units="millimolar" public_interface="in" name="ATP"/>
    <variable units="millimolar" public_interface="in" name="ADP"/>
    
    <variable units="millimolar" name="K_Glc_in" initial_value="0.08"/>
    <variable units="millimolar" name="K_G6P" initial_value="30.0"/>
    <variable units="millimolar" name="K_ATP" initial_value="0.15"/>
    <variable units="millimolar" name="K_ADP" initial_value="0.23"/>
    <variable units="dimensionless" name="Keq_HK" initial_value="3.8E3"/>
    <variable units="flux" name="V_max" initial_value="0.84"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply id="V_HK_calculation">
        <eq/>
        <ci> V_HK </ci>
        <apply>
          <times/>
          <ci> V_max </ci>
          <apply>
            <divide/>
            <apply>
              <times/>
              <apply>
                <divide/>
                <apply>
                  <times/>
                  <ci> Glc_in </ci>
                  <ci> ATP </ci>
                </apply>
                <apply>
                  <times/>
                  <ci> K_Glc_in </ci>
                  <ci> K_ATP </ci>
                </apply>
              </apply>
              <apply>
                <minus/>
                <cn cellml:units="dimensionless"> 1.0 </cn>
                <apply>
                  <divide/>
                  <apply>
                    <divide/>
                    <apply>
                      <times/>
                      <ci> G6P </ci>
                      <ci> ADP </ci>
                    </apply>
                    <apply>
                      <times/>
                      <ci> Glc_in </ci>
                      <ci> ATP </ci>
                    </apply>
                  </apply>
                  <ci> Keq_HK </ci>
                </apply>
              </apply>
            </apply>
            <apply>
              <times/>
              <apply>
                <plus/>
                <cn cellml:units="dimensionless"> 1.0 </cn>
                <apply>
                  <divide/>
                  <ci> Glc_in </ci>
                  <ci> K_Glc_in </ci>
                </apply>
                <apply>
                  <divide/>
                  <ci> G6P </ci>
                  <ci> K_G6P </ci>
                </apply>
              </apply>
              <apply>
                <plus/>
                <cn cellml:units="dimensionless"> 1.0 </cn>
                <apply>
                  <divide/>
                  <ci> ATP </ci>
                  <ci> K_ATP </ci>
                </apply>
                <apply>
                  <divide/>
                  <ci> ADP </ci>
                  <ci> K_ADP </ci>
                </apply>
              </apply>
            </apply>
          </apply>
        </apply>
      </apply>
    </math>
  </component>
  
  <component name="V_GraPDH">
    <variable units="flux" public_interface="out" name="V_GraPDH"/>
    
    <variable units="millimolar" public_interface="in" name="BPG"/>
    <variable units="millimolar" public_interface="in" name="GraP"/>
    <variable units="millimolar" public_interface="in" name="NADH"/>
    <variable units="millimolar" public_interface="in" name="NAD"/>
    
    <variable units="millimolar" name="K_GraP" initial_value="0.21"/>
    <variable units="millimolar" name="K_BPG" initial_value="9.8E-3"/>
    <variable units="millimolar" name="K_NAD" initial_value="0.09"/>
    <variable units="millimolar" name="K_NADH" initial_value="0.06"/>
    <variable units="dimensionless" name="Keq_GraPDH" initial_value="0.0056"/>
    <variable units="flux" name="V_max" initial_value="0.181"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply id="V_GraPDH_calculation">
        <eq/>
        <ci> V_GraPDH </ci>
        <apply>
          <times/>
          <ci> V_max </ci>
          <apply>
            <divide/>
            <apply>
              <times/>
              <apply>
                <divide/>
                <apply>
                  <times/>
                  <ci> GraP </ci>
                  <ci> NAD </ci>
                </apply>
                <apply>
                  <times/>
                  <ci> K_GraP </ci>
                  <ci> K_NAD </ci>
                </apply>
              </apply>
              <apply>
                <minus/>
                <cn cellml:units="dimensionless"> 1.0 </cn>
                <apply>
                  <divide/>
                  <apply>
                    <divide/>
                    <apply>
                      <times/>
                      <ci> BPG </ci>
                      <ci> NADH </ci>
                    </apply>
                    <apply>
                      <times/>
                      <ci> GraP </ci>
                      <ci> NAD </ci>
                    </apply>
                  </apply>
                  <ci> Keq_GraPDH </ci>
                </apply>
              </apply>
            </apply>
            <apply>
              <times/>
              <apply>
                <plus/>
                <cn cellml:units="dimensionless"> 1.0 </cn>
                <apply>
                  <divide/>
                  <ci> GraP </ci>
                  <ci> K_GraP </ci>
                </apply>
                <apply>
                  <divide/>
                  <ci> BPG </ci>
                  <ci> K_BPG </ci>
                </apply>
              </apply>
              <apply>
                <plus/>
                <cn cellml:units="dimensionless"> 1.0 </cn>
                <apply>
                  <divide/>
                  <ci> NAD </ci>
                  <ci> K_NAD </ci>
                </apply>
                <apply>
                  <divide/>
                  <ci> NADH </ci>
                  <ci> K_NADH </ci>
                </apply>
              </apply>
            </apply>
          </apply>
        </apply>
      </apply>
    </math>
  </component>
  
  <component name="V_PGK">
    <variable units="flux" public_interface="out" name="V_PGK"/>
    
    <variable units="millimolar" public_interface="in" name="three_GriP"/>
    <variable units="millimolar" public_interface="in" name="BPG"/>
    <variable units="millimolar" public_interface="in" name="ADP"/>
    <variable units="millimolar" public_interface="in" name="ATP"/>
    
    <variable units="millimolar" name="K_BPG" initial_value="3E-3"/>
    <variable units="millimolar" name="K_three_GriP" initial_value="0.53"/>
    <variable units="millimolar" name="K_ADP" initial_value="0.2"/>
    <variable units="millimolar" name="K_ATP" initial_value="0.3"/>
    <variable units="dimensionless" name="Keq_PGK" initial_value="3.2E3"/>
    <variable units="flux" name="V_max" initial_value="4.8"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply id="V_PGK_calculation">
        <eq/>
        <ci> V_PGK </ci>
        <apply>
          <times/>
          <ci> V_max </ci>
          <apply>
            <divide/>
            <apply>
              <times/>
              <apply>
                <divide/>
                <apply>
                  <times/>
                  <ci> BPG </ci>
                  <ci> ADP </ci>
                </apply>
                <apply>
                  <times/>
                  <ci> K_BPG </ci>
                  <ci> K_ADP </ci>
                </apply>
              </apply>
              <apply>
                <minus/>
                <cn cellml:units="dimensionless"> 1.0 </cn>
                <apply>
                  <divide/>
                  <apply>
                    <divide/>
                    <apply>
                      <times/>
                      <ci> three_GriP </ci>
                      <ci> ATP </ci>
                    </apply>
                    <apply>
                      <times/>
                      <ci> BPG </ci>
                      <ci> ADP </ci>
                    </apply>
                  </apply>
                  <ci> Keq_PGK </ci>
                </apply>
              </apply>
            </apply>
            <apply>
              <times/>
              <apply>
                <plus/>
                <cn cellml:units="dimensionless"> 1.0 </cn>
                <apply>
                  <divide/>
                  <ci> BPG </ci>
                  <ci> K_BPG </ci>
                </apply>
                <apply>
                  <divide/>
                  <ci> three_GriP </ci>
                  <ci> K_three_GriP </ci>
                </apply>
              </apply>
              <apply>
                <plus/>
                <cn cellml:units="dimensionless"> 1.0 </cn>
                <apply>
                  <divide/>
                  <ci> ADP </ci>
                  <ci> K_ADP </ci>
                </apply>
                <apply>
                  <divide/>
                  <ci> ATP </ci>
                  <ci> K_ATP </ci>
                </apply>
              </apply>
            </apply>
          </apply>
        </apply>
      </apply>
    </math>
  </component>
  
  <component name="V_PYK">
    <variable units="flux" public_interface="out" name="V_PYK"/>
    
    <variable units="millimolar" public_interface="in" name="PYR"/>
    <variable units="millimolar" public_interface="in" name="PEP"/>
    <variable units="millimolar" public_interface="in" name="ADP"/>
    <variable units="millimolar" public_interface="in" name="ATP"/>
    
    <variable units="millimolar" name="K_PEP" initial_value="0.14"/>
    <variable units="millimolar" name="K_PYR" initial_value="21.0"/>
    <variable units="millimolar" name="K_ADP" initial_value="0.53"/>
    <variable units="millimolar" name="K_ATP" initial_value="1.5"/>
    <variable units="dimensionless" name="Keq_PYK" initial_value="6.5E3"/>
    <variable units="flux" name="V_max" initial_value="4.05"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply id="V_PYK_calculation">
        <eq/>
        <ci> V_PYK </ci>
        <apply>
          <times/>
          <ci> V_max </ci>
          <apply>
            <divide/>
            <apply>
              <times/>
              <apply>
                <divide/>
                <apply>
                  <times/>
                  <ci> PEP </ci>
                  <ci> ADP </ci>
                </apply>
                <apply>
                  <times/>
                  <ci> K_PEP </ci>
                  <ci> K_ADP </ci>
                </apply>
              </apply>
              <apply>
                <minus/>
                <cn cellml:units="dimensionless"> 1.0 </cn>
                <apply>
                  <divide/>
                  <apply>
                    <divide/>
                    <apply>
                      <times/>
                      <ci> PYR </ci>
                      <ci> ATP </ci>
                    </apply>
                    <apply>
                      <times/>
                      <ci> PEP </ci>
                      <ci> ADP </ci>
                    </apply>
                  </apply>
                  <ci> Keq_PYK </ci>
                </apply>
              </apply>
            </apply>
            <apply>
              <times/>
              <apply>
                <plus/>
                <cn cellml:units="dimensionless"> 1.0 </cn>
                <apply>
                  <divide/>
                  <ci> PEP </ci>
                  <ci> K_PEP </ci>
                </apply>
                <apply>
                  <divide/>
                  <ci> PYR </ci>
                  <ci> K_PYR </ci>
                </apply>
              </apply>
              <apply>
                <plus/>
                <cn cellml:units="dimensionless"> 1.0 </cn>
                <apply>
                  <divide/>
                  <ci> ADP </ci>
                  <ci> K_ADP </ci>
                </apply>
                <apply>
                  <divide/>
                  <ci> ATP </ci>
                  <ci> K_ATP </ci>
                </apply>
              </apply>
            </apply>
          </apply>
        </apply>
      </apply>
    </math>
  </component>
  
  <component name="V_transport">
    <variable units="flux" public_interface="out" name="V_transport"/>
    
    <variable units="millimolar" public_interface="in" name="Glc_out"/>
    <variable units="millimolar" public_interface="in" name="Glc_in"/>
    
    <variable units="millimolar" name="Ki" initial_value="2.0"/>
    <variable units="millimolar" name="K_Glc" initial_value="1.19"/>
    <variable units="flux" name="V_max" initial_value="0.36"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply id="V_transport_calculation">
        <eq/>
        <ci> V_transport </ci>
        <apply>
          <times/>
          <ci> V_max </ci>
          <apply>
            <divide/>
            <apply>
              <divide/>
              <apply>
                <minus/>
                <ci> Glc_out </ci>
                <ci> Glc_in </ci>
              </apply>
              <ci> K_Glc </ci>
            </apply>
            <apply>
              <plus/>
              <cn cellml:units="dimensionless"> 1.0 </cn>
              <apply>
                <divide/>
                <ci> Glc_out </ci>
                <ci> K_Glc </ci>
              </apply>
              <apply>
                <divide/>
                <ci> Glc_in </ci>
                <ci> K_Glc </ci>
              </apply>
              <apply>
                <times/>
                <ci> Ki </ci>
                <apply>
                  <divide/>
                  <ci> Glc_out </ci>
                  <ci> K_Glc </ci>
                </apply>
                <apply>
                  <divide/>
                  <ci> Glc_in </ci>
                  <ci> K_Glc </ci>
                </apply>
              </apply>
            </apply>
          </apply>
        </apply>
      </apply>
    </math>
  </component>
  
  <component name="V_ALD">
    <variable units="flux" public_interface="out" name="V_ALD"/>
    
    <variable units="millimolar" public_interface="in" name="glycerone_phosphate"/>
    <variable units="millimolar" public_interface="in" name="F16bP2"/>
    <variable units="millimolar" public_interface="in" name="GraP"/>
    
    <variable units="millimolar" name="K_F16bP2" initial_value="0.3"/>
    <variable units="millimolar" name="K_GraP" initial_value="2.0"/>
    <variable units="millimolar" name="Ki_GraP" initial_value="10.0"/>
    <variable units="millimolar" name="K_glycerone_phosphate" initial_value="2.4"/>
    <variable units="dimensionless" name="Keq_ALD" initial_value="0.069"/>
    <variable units="flux" name="V_max" initial_value="1.19"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply id="V_ALD_calculation">
        <eq/>
        <ci> V_ALD </ci>
        <apply>
          <times/>
          <ci> V_max </ci>
          <apply>
            <divide/>
            <apply>
              <times/>
              <apply>
                <divide/>
                <ci> F16bP2 </ci>
                <ci> K_F16bP2 </ci>
              </apply>
              <apply>
                <minus/>
                <cn cellml:units="dimensionless"> 1.0 </cn>
                <apply>
                  <divide/>
                  <apply>
                    <divide/>
                    <apply>
                      <times/>
                      <ci> glycerone_phosphate </ci>
                      <ci> GraP </ci>
                    </apply>
                    <ci> F16bP2 </ci>
                  </apply>
                  <ci> Keq_ALD </ci>
                </apply>
              </apply>
            </apply>
            <apply>
              <plus/>
              <cn cellml:units="dimensionless"> 1.0 </cn>
              <apply>
                <divide/>
                <ci> F16bP2 </ci>
                <ci> K_F16bP2 </ci>
              </apply>
              <apply>
                <divide/>
                <ci> glycerone_phosphate </ci>
                <ci> K_glycerone_phosphate </ci>
              </apply>
              <apply>
                <divide/>
                <ci> GraP </ci>
                <ci> K_GraP </ci>
              </apply>
              <apply>
                <divide/>
                <apply>
                  <times/>
                  <ci> F16bP2 </ci>
                  <ci> GraP </ci>
                </apply>
                <apply>
                  <times/>
                  <ci> K_F16bP2 </ci>
                  <ci> Ki_GraP </ci>
                </apply>
              </apply>
              <apply>
                <divide/>
                <apply>
                  <times/>
                  <ci> glycerone_phosphate </ci>
                  <ci> GraP </ci>
                </apply>
                <apply>
                  <times/>
                  <ci> K_glycerone_phosphate </ci>
                  <ci> K_GraP </ci>
                </apply>
              </apply>
            </apply>
          </apply>
        </apply>
      </apply>
    </math>
  </component>
  
  <component name="V_PDC">
    <variable units="flux" public_interface="out" name="V_PDC"/>
    
    <variable units="millimolar" public_interface="in" name="PYR"/>
    
    <variable units="millimolar" name="nH" initial_value="1.9"/>
    <variable units="millimolar" name="K_0_5" initial_value="4.3"/>
    <variable units="flux" name="V_max" initial_value="0.65"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply id="V_PDC_calculation">
        <eq/>
        <ci> V_PDC </ci>
        <apply>
          <times/>
          <ci> V_max </ci>
          <apply>
            <divide/>
            <apply>
              <power/>
              <apply>
                <divide/>
                <ci> PYR </ci>
                <ci> K_0_5 </ci>
              </apply>
              <ci> nH </ci>
            </apply>
            <apply>
              <plus/>
              <cn cellml:units="dimensionless"> 1.0 </cn>
              <apply>
                <power/>
                <apply>
                  <divide/>
                  <ci> PYR </ci>
                  <ci> K_0_5 </ci>
                </apply>
                <ci> nH </ci>
              </apply>
            </apply>
          </apply>
        </apply>
      </apply>
    </math>
  </component>
  
  <component name="V_ADH">
    <variable units="flux" public_interface="out" name="V_ADH"/>
    
    <variable units="millimolar" public_interface="in" name="NAD"/>
    <variable units="millimolar" public_interface="in" name="NADH"/>
    <variable units="millimolar" public_interface="in" name="AcAld"/>
    <variable units="millimolar" public_interface="in" name="ethanol"/>
    
    <variable units="millimolar" name="K_NAD" initial_value="0.17"/>
    <variable units="millimolar" name="K_NADH" initial_value="0.11"/>
    <variable units="millimolar" name="K_AcAld" initial_value="1.11"/>
    <variable units="millimolar" name="K_ethanol" initial_value="17.0"/>
    <variable units="millimolar" name="Ki_NADH" initial_value="0.031"/>
    <variable units="millimolar" name="Ki_AcAld" initial_value="1.1"/>
    <variable units="millimolar" name="Ki_ethanol" initial_value="90.0"/>
    <variable units="millimolar" name="Keq_ADH" initial_value="2.21"/>
    <variable units="flux" name="V_max" initial_value="3.0"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply id="V_ADH_calculation">
        <eq/>
        <ci> V_ADH </ci>
        <apply>
          <divide/>
          <apply>
            <minus/>
            <apply>
              <times/>
              <ci> V_max </ci>
              <apply>
                <divide/>
                <apply>
                  <times/>
                  <ci> ethanol </ci>
                  <ci> NAD </ci>
                </apply>
                <apply>
                  <times/>
                  <ci> Ki_ethanol </ci>
                  <ci> K_NAD </ci>
                </apply>
              </apply>
            </apply>
            <apply>
              <times/>
              <ci> V_max </ci>
              <apply>
                <divide/>
                <apply>
                  <times/>
                  <ci> AcAld </ci>
                  <ci> NADH </ci>
                </apply>
                <apply>
                  <times/>
                  <ci> K_AcAld </ci>
                  <ci> Ki_NADH </ci>
                </apply>
              </apply>
            </apply>
          </apply>
          <apply>
            <plus/>
            <cn cellml:units="dimensionless"> 1.0 </cn>
            <apply>
              <divide/>
              <ci> ethanol </ci>
              <ci> Ki_ethanol </ci>
            </apply>
            <apply>
              <divide/>
              <apply>
                <times/>
                <ci> K_ethanol </ci>
                <ci> NAD </ci>
              </apply>
              <apply>
                <times/>
                <ci> Ki_ethanol </ci>
                <ci> K_NAD </ci>
              </apply>
            </apply>
            <apply>
              <divide/>
              <apply>
                <times/>
                <ci> K_NADH </ci>
                <ci> AcAld </ci>
              </apply>
              <apply>
                <times/>
                <ci> K_AcAld </ci>
                <ci> Ki_NADH </ci>
              </apply>
            </apply>
            <apply>
              <divide/>
              <ci> NADH </ci>
              <ci> Ki_NADH </ci>
            </apply>
            <apply>
              <divide/>
              <apply>
                <times/>
                <ci> ethanol </ci>
                <ci> NAD </ci>
              </apply>
              <apply>
                <times/>
                <ci> Ki_ethanol </ci>
                <ci> K_NAD </ci>
              </apply>
            </apply>
            <apply>
              <divide/>
              <apply>
                <times/>
                <ci> K_NADH </ci>
                <ci> ethanol </ci>
                <ci> AcAld </ci>
              </apply>
              <apply>
                <times/>
                <ci> Ki_ethanol </ci>
                <ci> K_AcAld </ci>
                <ci> Ki_NADH </ci>
              </apply>
            </apply>
            <apply>
              <divide/>
              <apply>
                <times/>
                <ci> K_ethanol </ci>
                <ci> NAD </ci>
                <ci> NADH </ci>
              </apply>
              <apply>
                <times/>
                <ci> Ki_ethanol </ci>
                <ci> K_NAD </ci>
                <ci> Ki_NADH </ci>
              </apply>
            </apply>
            <apply>
              <divide/>
              <apply>
                <times/>
                <ci> AcAld </ci>
                <ci> NADH </ci>
              </apply>
              <apply>
                <times/>
                <ci> K_AcAld </ci>
                <ci> Ki_NADH </ci>
              </apply>
            </apply>
            <apply>
              <divide/>
              <apply>
                <times/>
                <ci> ethanol </ci>
                <ci> NAD </ci>
                <ci> AcAld </ci>
              </apply>
              <apply>
                <times/>
                <ci> Ki_ethanol </ci>
                <ci> K_NAD </ci>
                <ci> Ki_AcAld </ci>
              </apply>
            </apply>
            <apply>
              <divide/>
              <apply>
                <times/>
                <ci> NAD </ci>
                <ci> AcAld </ci>
                <ci> NADH </ci>
              </apply>
              <apply>
                <times/>
                <ci> Ki_ethanol </ci>
                <ci> K_NAD </ci>
                <ci> Ki_NADH </ci>
              </apply>
            </apply>
          </apply>
        </apply>
      </apply>
    </math>
  </component>
  
  <component name="V_ATPase">
    <variable units="flux" public_interface="out" name="V_ATPase"/>
    
    <variable units="first_order_rate_constant" name="k_ATPase"/>
    
    <variable units="millimolar" public_interface="in" name="ATP"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply id="V_ATPase_calculation">
        <eq/>
        <ci> V_ATPase </ci>
        <apply>
          <times/>
          <ci> k_ATPase </ci>
          <ci> ATP </ci>
        </apply>
      </apply>
    </math>
  </component>
  
  <component name="V_PFK">
    <variable units="flux" public_interface="out" name="V_PFK"/>
    
    <variable units="millimolar" public_interface="in" name="F6P"/>
    <variable units="millimolar" public_interface="in" name="F16bP2"/>
    <variable units="millimolar" public_interface="in" name="F26bP2"/>
    <variable units="millimolar" public_interface="in" name="ATP"/>
    <variable units="millimolar" public_interface="in" name="AMP"/>
    
    <variable units="millimolar" name="K_F26bP2" initial_value="6.82E-4"/>
    <variable units="millimolar" name="K_F16bP2" initial_value="0.111"/>
    <variable units="millimolar" name="K_F6P" initial_value="0.18"/>
    <variable units="millimolar" name="K_ATP" initial_value="0.65"/>
    <variable units="millimolar" name="K_AMP" initial_value="0.0995"/>
    <variable units="millimolar" name="KR_ATP" initial_value="2.7"/>
    <variable units="millimolar" name="KR_F6P" initial_value="0.1"/>
    <variable units="dimensionless" name="Ci_ATP" initial_value="100.0"/>
    <variable units="dimensionless" name="Ci_AMP" initial_value="0.0845"/>
    <variable units="dimensionless" name="Ci_F26bP2" initial_value="0.0174"/>
    <variable units="dimensionless" name="Ci_F16bP2" initial_value="0.397"/>
    <variable units="millimolar" name="cATP" initial_value="3.0"/>
    <variable units="flux" name="V_max" initial_value="0.68"/>
    <variable units="dimensionless" name="lamda_1"/>
    <variable units="dimensionless" name="lamda_2"/>
    <variable units="millimolar" name="L"/>
    <variable units="millimolar" name="Lo" initial_value="0.66"/>
    <variable units="dimensionless" name="R"/>
    <variable units="dimensionless" name="T"/>
    <variable units="millimolar" name="gR" initial_value="5.12"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply id="V_PFK_calculation">
        <eq/>
        <ci> V_PFK </ci>
        <apply>
          <times/>
          <ci> V_max   </ci>
          <apply>
            <divide/>
            <apply>
              <times/>
              <ci> gR </ci>
              <ci> lamda_1 </ci>
              <ci> lamda_2 </ci>
              <ci> R </ci>
            </apply>
            <apply>
              <plus/>
              <apply>
                <power/>
                <ci> R </ci>
                <cn cellml:units="dimensionless"> 2.0 </cn>
              </apply>
              <apply>
                <times/>
                <ci> L </ci>
                <apply>
                  <power/>
                  <ci> T </ci>
                  <cn cellml:units="dimensionless"> 2.0 </cn>
                </apply>
              </apply>
            </apply>
          </apply>
        </apply>
      </apply>
      
      <apply id="lamda_1_calculation">
        <eq/>
        <ci> lamda_1 </ci>
        <apply>
          <divide/>
          <ci> F6P </ci>
          <ci> KR_F6P </ci>
        </apply>
      </apply>
      
      <apply id="lamda_2_calculation">
        <eq/>
        <ci> lamda_2 </ci>
        <apply>
          <divide/>
          <ci> ATP </ci>
          <ci> KR_ATP </ci>
        </apply>
      </apply>
      
      <apply id="R_calculation">
        <eq/>
        <ci> R </ci>
        <apply>
          <plus/>
          <cn cellml:units="dimensionless"> 1.0 </cn>
          <apply>
            <times/>
            <ci> lamda_1 </ci>
            <ci> lamda_2 </ci>
          </apply>
          <apply>
            <times/>
            <ci> gR </ci>
            <ci> lamda_1 </ci>
            <ci> lamda_2 </ci>
          </apply>
        </apply>
      </apply>
      
      <apply id="T_calculation">
        <eq/>
        <ci> T </ci>
        <apply>
          <plus/>
          <cn cellml:units="dimensionless"> 1.0 </cn>
          <apply>
            <times/>
            <ci> cATP </ci>
            <ci> lamda_2 </ci>
          </apply>
        </apply>
      </apply>
      
      <apply id="L_calculation">
        <eq/>
        <ci> L </ci>
        <apply>
          <times/>
          <ci> Lo </ci>
          <apply>
            <power/>
            <apply>
              <divide/>
              <apply>
                <plus/>
                <cn cellml:units="dimensionless"> 1.0 </cn>
                <apply>
                  <divide/>
                  <apply>
                    <times/>
                    <ci> Ci_ATP </ci>
                    <ci> ATP </ci>
                  </apply>
                  <ci> K_ATP </ci>
                </apply>
              </apply>
              <apply>
                <plus/>
                <cn cellml:units="dimensionless"> 1.0 </cn>
                <apply>
                  <divide/>
                  <ci> ATP </ci>
                  <ci> K_ATP </ci>
                </apply>
              </apply>
            </apply>
            <cn cellml:units="dimensionless"> 2.0 </cn>
          </apply>
          <apply>
            <power/>
            <apply>
              <divide/>
              <apply>
                <plus/>
                <cn cellml:units="dimensionless"> 1.0 </cn>
                <apply>
                  <divide/>
                  <apply>
                    <times/>
                    <ci> Ci_AMP </ci>
                    <ci> AMP </ci>
                  </apply>
                  <ci> K_AMP </ci>
                </apply>
              </apply>
              <apply>
                <plus/>
                <cn cellml:units="dimensionless"> 1.0 </cn>
                <apply>
                  <divide/>
                  <ci> AMP </ci>
                  <ci> K_AMP </ci>
                </apply>
              </apply>
            </apply>
            <cn cellml:units="dimensionless"> 2.0 </cn>
          </apply>
          <apply>
            <divide/>
            <apply>
              <plus/>
              <cn cellml:units="dimensionless"> 1.0 </cn>
              <apply>
                <divide/>
                <apply>
                  <times/>
                  <ci> Ci_F26bP2 </ci>
                  <ci> F26bP2 </ci>
                </apply>
                <ci> K_F26bP2 </ci>
              </apply>
              <apply>
                <divide/>
                <apply>
                  <times/>
                  <ci> Ci_F16bP2 </ci>
                  <ci> F16bP2 </ci>
                </apply>
                <ci> K_F16bP2 </ci>
              </apply>
            </apply>
            <apply>
              <plus/>
              <cn cellml:units="dimensionless"> 1.0 </cn>
              <apply>
                <divide/>
                <ci> F26bP2 </ci>
                <ci> K_F26bP2 </ci>
              </apply>
              <apply>
                <divide/>
                <ci> F16bP2 </ci>
                <ci> K_F16bP2 </ci>
              </apply>
            </apply>
          </apply>
        </apply>
      </apply> 
    </math>
  </component>
  
  <!--
    The following components describe the reactions of the branches introduced in the extended model.  For simplicity, fluxes to glycogen and trehalose are introduced as experimentally derived constants.
  -->
  
  <component name="V_glycogen">
    <variable units="flux" public_interface="out" name="V_glycogen" initial_value="6.0"/>
  </component>
  
  <component name="V_trehalose">
    <variable units="flux" public_interface="out" name="V_trehalose" initial_value="4.8"/>
  </component>
  
  <component name="V_glycerol">
    <variable units="flux" public_interface="out" name="V_glycerol"/>
    
    <variable units="millimolar" public_interface="in" name="glycerol"/>
    <variable units="millimolar" public_interface="in" name="glycerone_phosphate"/>
    <variable units="millimolar" public_interface="in" name="NADH"/>
    <variable units="millimolar" public_interface="in" name="NAD"/>
    
    <variable units="millimolar" name="K_glycerone_phosphate" initial_value="0.18"/>
    <variable units="millimolar" name="K_glycerol" initial_value="0.119"/>
    <variable units="millimolar" name="K_NADH" initial_value="0.18"/>
    <variable units="millimolar" name="K_NAD" initial_value="0.119"/>
    <variable units="dimensionless" name="Keq_glycerol" initial_value="0.45"/>
    <variable units="flux" name="V_max" initial_value="0.88"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply id="V_glycerol_calculation">
        <eq/>
        <ci> V_glycerol </ci>
        <apply>
          <times/>
          <ci> V_max </ci>
          <apply>
            <divide/>
            <apply>
              <times/>
              <apply>
                <divide/>
                <apply>
                  <times/>
                  <ci> glycerone_phosphate </ci>
                  <ci> NADH </ci>
                </apply>
                <apply>
                  <times/>
                  <ci> K_glycerone_phosphate </ci>
                  <ci> K_NADH </ci>
                </apply>
              </apply>
              <apply>
                <minus/>
                <cn cellml:units="dimensionless"> 1.0 </cn>
                <apply>
                  <divide/>
                  <apply>
                    <divide/>
                    <apply>
                      <times/>
                      <ci> glycerol </ci>
                      <ci> NAD </ci>
                    </apply>
                    <apply>
                      <times/>
                      <ci> glycerone_phosphate </ci>
                      <ci> NADH </ci>
                    </apply>
                  </apply>
                  <ci> Keq_glycerol </ci>
                </apply>
              </apply>
            </apply>
            <apply>
              <times/>
              <apply>
                <plus/>
                <cn cellml:units="dimensionless"> 1.0 </cn>
                <apply>
                  <divide/>
                  <ci> glycerone_phosphate </ci>
                  <ci> K_glycerone_phosphate </ci>
                </apply>
                <apply>
                  <divide/>
                  <ci> glycerol </ci>
                  <ci> K_glycerol </ci>
                </apply>
              </apply>
              <apply>
                <plus/>
                <cn cellml:units="dimensionless"> 1.0 </cn>
                <apply>
                  <divide/>
                  <ci> NADH </ci>
                  <ci> K_NADH </ci>
                </apply>
                <apply>
                  <divide/>
                  <ci> NAD </ci>
                  <ci> K_NAD </ci>
                </apply>
              </apply>
            </apply>
          </apply>
        </apply>
      </apply>
    </math>
  </component>
  
  <component name="V_succinate">
    <variable units="flux" public_interface="out" name="V_succinate"/>
    
    <variable units="first_order_rate_constant" name="k_succinate"/>
    
    <variable units="millimolar" public_interface="in" name="AcAld"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply id="V_succinate_calculation">
        <eq/>
        <ci> V_succinate </ci>
        <apply>
          <times/>
          <ci> k_succinate </ci>
          <ci> AcAld </ci>
        </apply>
      </apply>
    </math>
  </component>
  
  <connection>
    <map_components component_2="V_transport" component_1="Glc_out"/>
    <map_variables variable_2="Glc_out" variable_1="Glc_out"/>
    <map_variables variable_2="V_transport" variable_1="V_transport"/>
  </connection>
  
  <connection>
    <map_components component_2="V_transport" component_1="Glc_in"/>
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    <dc:title>Can yeast glycolysis be understood in terms of in vitro kinetics of &#13;
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