Location: Cortassa, Aon, Marban, Winslow, Orourke, 2003 @ a126ab075023 / cortassa_aon_marban_winslow_orourke_2003.cellml

Author:
pmr2.import <nobody@models.cellml.org>
Date:
2009-04-29 22:20:22+12:00
Desc:
committing version02 of cortassa_aon_marban_winslow_orourke_2003
Permanent Source URI:
https://models.cellml.org/workspace/cortassa_aon_marban_winslow_orourke_2003/rawfile/a126ab0750236d6b24146fad455cccaa39d6f087/cortassa_aon_marban_winslow_orourke_2003.cellml

<?xml version='1.0' encoding='utf-8'?>
<!--  FILE :  cortassa_model_2003.xml

CREATED :  13th May 2003

LAST MODIFIED : 13th May 2003

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 Cortassa et al.'s 2003 integrated model of cardiac mitochondrial energy metabolism and calcium dynamics.

CHANGES:  
  
--><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="cortassa_aon_marban_winslow_orourke_2003_version01" name="cortassa_aon_marban_winslow_orourke_2003_version01">
<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
  <articleinfo>
  <title>Modelling Mitochondrial Energy Metabolism</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 CellML model has been checked in both OpenCell and COR and the units are consistent.  Unfortunately the model will not integrate at the moment.  We are working with the model author to complete the curation of this model.
          </para>
  </section>
  <sect1 id="sec_structure">
<title>Model Structure</title>

<para>
The high metabolic rate of cardiac tissue necessitates close agreement between the rates of energy production and consumption.  About 2 percent of cellular ATP is consumed per heartbeat, and under normal conditions, almost all of this energy is provided by mitochondrial oxidative phosphorylation.  Although the chemiosmotic theory of energy transduction was developed by Michell in 1961, remarkably little has since been elucidated about the mechanisms underlying the control of mitochondrial metabolism.  
</para>

<para>
The thermokinetic model describes the tricarboxylic acid (TCA) cycle, oxidative phosphorylation, and mitochondrial Ca<superscript>2+</superscript> dynamics (see <xref linkend="fig_reaction_diagram"/> below).  The kinetic portion of the model includes effectors of the TCA cycle enzymes regulating production of NADH and FADH<subscript>2</subscript>.  In turn, these are used by the electron transport chain to establish a proton motive force driving the F<subscript>1</subscript>F<subscript>0</subscript>-ATPase.  In addition, mitochondrial matrix Ca<superscript>2+</superscript>, determined by Ca<superscript>2+</superscript> uniporter and Ca<superscript>2+</superscript>/Na<superscript>+</superscript> exchanger activities, controls the activity of the TCA cycle enzymes isocitrate dehydrogenase and alpha-ketoglutarate dehydrogenase.  Model simulations are used to predict the response of mitochondria to changes in substrate delivery, metabolic inhibition, the rate of ATP/ADP exchange, and Ca<superscript>2+</superscript> concentration.  Model simulations are able to reproduce experimental data, which was taken as supporting evidence for the validity of the model.  The steady-state and time-dependent behaviour of the model supports the hypothesis that mitochondrial matrix Ca<superscript>2+</superscript> plays an important role in matching energy supply with demand in cardiac myocytes.     
</para>

<para>
Previously published models of mitochondrial energetics include the models of pancreatic beta-cell mitochondrial metabolism by Magnus and Keizer (see <ulink url="${HTML_EXMPL_MITOCHONDRIAL_CA_HANDLING}">Mitochondrial Ca<superscript>2+</superscript> Handling Model, 1997</ulink>).  An oxidative phosphorylation model has been developed by Korzeniewski (see <ulink url="${HTML_EXMPL_OXIDATIVE_PHOSPHORYLATION}">The Oxidative Phosphorylation Pathway, 2001</ulink>).  However, these models, in common with other previously developed models of mitochondrial energetics, fail to include all the necessary variables.  Together with the desire to improve understanding of mitochondrial metabolism, this has led Cortassa <emphasis>et al.</emphasis> to develop an integrated kinetic and thermodynamic model of cardiac mitochondrial energy metabolism.  Their model has been described here in CellML (the raw CellML description of the Cortassa <emphasis>et al.</emphasis> model can be downloaded in various formats as described in <xref linkend="sec_download_this_model"/>).     
</para>

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

<para>
<ulink url="http://www.biophysj.org/cgi/content/abstract/84/4/2734">An Integrated Model of Cardiac Mitochondrial Energy Metabolism and Calcium Dynamics</ulink>, Sonia Cortassa, Miguel A. Aon, Eduardo Marban, Raimond L. Winslow, and Brian O'Rourke, 2003, <ulink url="http://www.biophysj.org/">
            <emphasis>Biophysical Journal</emphasis>
          </ulink>, 84, 2734-2755.  (<ulink url="http://www.biophysj.org/cgi/content/full/84/4/2734">Full text (HTML)</ulink> and <ulink url="http://www.biophysj.org/cgi/reprint/84/4/2734.pdf">PDF</ulink> versions of the article are available on the <emphasis>Biophysical Journal</emphasis> website.)  <ulink url="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&amp;db=PubMed&amp;list_uids=12668482&amp;dopt=Abstract">PubMed ID: 12668482</ulink>
</para>

<informalfigure float="0" id="fig_reaction_diagram">
<mediaobject>
  <imageobject>
    <objectinfo>
      <title>reaction diagram</title>
    </objectinfo>
    <imagedata fileref="cortassa_2003.png"/>
  </imageobject>
</mediaobject>
<caption>A schematic diagram of the reactions used in the model of the glycogenolysis pathway in skeletal muscle.</caption>
</informalfigure>

</sect1>
</article>
</documentation>
  

 
  <units name="millimolar">
    <unit units="mole" prefix="milli"/>
    <unit units="litre" exponent="-1"/>
  </units>
  
  <units name="millimolar_per_volt">
    <unit units="millimolar"/>
    <unit units="volt" exponent="-1"/>
  </units>
  
  <units name="micromolar">
    <unit units="mole" prefix="micro"/>
    <unit units="litre" exponent="-1"/>
  </units>
  
  <units name="micromolar_per_second">
    <unit units="micromolar"/>
    <unit units="second" exponent="-1"/>
  </units>
  
  <units name="micromolar_per_millimolar">
    <unit units="micromolar"/>
    <unit units="millimolar" exponent="-1"/>
  </units>
  
  <units name="flux">
    <unit units="millimolar"/>
    <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="millimolar" exponent="-1"/>
    <unit units="second" exponent="-1"/>
  </units>
  
  <units name="millimolar_per_second_volt">
    <unit units="millimolar"/>
	<unit units="second" exponent="-1"/>
    <unit units="volt" exponent="-1"/>
  </units>
  
  <units name="volt_coulomb_per_mole_kelvin">
    <unit units="volt"/>
	<unit units="coulomb"/>
    <unit units="mole" exponent="-1"/>
    <unit units="kelvin" exponent="-1"/>
  </units>
  
  <units name="coulomb_per_mole">
    <unit units="coulomb"/>
    <unit units="mole" exponent="-1"/>
  </units>
  
  
  <component name="environment">
    <variable units="second" public_interface="out" name="time"/>
  </component>

  
  <component cmeta:id="ADP_m" name="ADP_m">
    <rdf:RDF>
      <rdf:Description rdf:about="#ADP_m">
        <dc:title>ADP_m</dc:title>
        <dcterms:alternative>
          mitochondrial adenosine diphosphate
        </dcterms:alternative>  
      </rdf:Description>
    </rdf:RDF> 
    <variable units="millimolar" public_interface="out" name="ADP_m" initial_value="0.1"/>
    <variable units="flux" public_interface="in" name="V_ANT"/> 
    <variable units="flux" public_interface="in" name="V_ATPase"/>
    <variable units="flux" public_interface="in" name="V_SL"/>
    <variable units="second" public_interface="in" name="time"/> 
    <math xmlns="http://www.w3.org/1998/Math/MathML"> 
      <apply>
        <eq/> 
        <apply>
          <diff/> 
          <bvar>
            <ci>time</ci>
          </bvar> 
          <ci>ADP_m</ci> 
        </apply>
        <apply>
          <minus/>
          <ci>V_ANT</ci>
          <apply>
            <plus/>
            <ci>V_ATPase</ci>
            <ci>V_SL</ci>
          </apply>
        </apply> 
      </apply> 
    </math> 
  </component>
  
  <component cmeta:id="NADH" name="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="0.01"/> 
    <variable units="flux" public_interface="in" name="V_O2"/>
    <variable units="flux" public_interface="in" name="V_IDH"/>
    <variable units="flux" public_interface="in" name="V_KGDH"/>
    <variable units="flux" public_interface="in" name="V_MDH"/>
    <variable units="second" 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>
        <apply>
          <plus/>
          <apply>
            <minus/> 
            <ci>V_O2</ci>
          </apply> 
          <ci>V_IDH</ci>
          <ci>V_KGDH</ci>
          <ci>V_MDH</ci>
        </apply> 
      </apply> 
    </math> 
  </component>
  
  <component cmeta:id="ISOC" name="ISOC">
    <rdf:RDF>
      <rdf:Description rdf:about="#ISOC">
        <dc:title>ISOC</dc:title>
        <dcterms:alternative>isocitrate</dcterms:alternative>  
      </rdf:Description>
    </rdf:RDF> 
    <variable units="millimolar" public_interface="out" name="ISOC" initial_value="0.01"/> 
    <variable units="flux" public_interface="in" name="V_ACO"/>
    <variable units="flux" public_interface="in" name="V_IDH"/>
    <variable units="second" public_interface="in" name="time"/> 
    <math xmlns="http://www.w3.org/1998/Math/MathML"> 
      <apply>
        <eq/> 
        <apply>
          <diff/> 
          <bvar>
            <ci>time</ci>
          </bvar> 
          <ci>ISOC</ci> 
        </apply>
        <apply>
          <minus/> 
          <ci>V_ACO</ci>
          <ci>V_IDH</ci>
        </apply> 
      </apply> 
    </math> 
  </component>
  
  <component cmeta:id="alpha_KG" name="alpha_KG">
    <rdf:RDF>
      <rdf:Description rdf:about="#alpha_KG">
        <dc:title>alpha_KG</dc:title>
        <dcterms:alternative>alpha-ketoglutarate</dcterms:alternative>  
      </rdf:Description>
    </rdf:RDF> 
    <variable units="millimolar" public_interface="out" name="alpha_KG" initial_value="0.01"/> 
    <variable units="flux" public_interface="in" name="V_IDH"/>
    <variable units="flux" public_interface="in" name="V_KGDH"/>
    <variable units="flux" public_interface="in" name="V_AAT"/>
    <variable units="second" public_interface="in" name="time"/> 
    <math xmlns="http://www.w3.org/1998/Math/MathML"> 
      <apply>
        <eq/> 
        <apply>
          <diff/> 
          <bvar>
            <ci>time</ci>
          </bvar> 
          <ci>alpha_KG</ci> 
        </apply>
        <apply>
          <plus/>
          <ci>V_AAT</ci>
          <ci>V_IDH</ci>
          <apply>
            <minus/> 
            <ci>V_KGDH</ci>
          </apply>
        </apply>
      </apply> 
    </math> 
  </component>
  
  <component cmeta:id="SCoA" name="SCoA">
    <rdf:RDF>
      <rdf:Description rdf:about="#SCoA">
        <dc:title>SCoA</dc:title>
        <dcterms:alternative>succinyl CoA</dcterms:alternative>  
      </rdf:Description>
    </rdf:RDF> 
    <variable units="millimolar" public_interface="out" name="SCoA" initial_value="0.01"/>
    <variable units="flux" public_interface="in" name="V_KGDH"/>
    <variable units="flux" public_interface="in" name="V_SL"/>
    <variable units="second" public_interface="in" name="time"/> 
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply>
        <eq/> 
        <apply>
          <diff/> 
          <bvar>
            <ci>time</ci>
          </bvar> 
          <ci>SCoA</ci> 
        </apply>
        <apply>
          <minus/>
          <ci>V_KGDH</ci>
          <ci>V_SL</ci>
        </apply> 
      </apply> 
    </math> 
  </component>
  
  <component cmeta:id="Suc" name="Suc">
    <rdf:RDF>
      <rdf:Description rdf:about="#Suc">
        <dc:title>Suc</dc:title>
        <dcterms:alternative>succinate</dcterms:alternative>  
      </rdf:Description>
    </rdf:RDF> 
    <variable units="millimolar" public_interface="out" name="Suc" initial_value="0.01"/> 
    <variable units="flux" public_interface="in" name="V_SL"/>
    <variable units="flux" public_interface="in" name="V_SDH"/>
    <variable units="second" public_interface="in" name="time"/> 
    <math xmlns="http://www.w3.org/1998/Math/MathML"> 
      <apply>
        <eq/> 
        <apply>
          <diff/> 
          <bvar>
            <ci>time</ci>
          </bvar> 
          <ci>Suc</ci> 
        </apply>
        <apply>
          <minus/> 
          <ci>V_SL</ci>
          <ci>V_SDH</ci>
        </apply> 
      </apply> 
    </math> 
  </component>
  
  <component cmeta:id="FUM" name="FUM">
    <rdf:RDF>
      <rdf:Description rdf:about="#FUM">
        <dc:title>FUM</dc:title>
        <dcterms:alternative>fumarate</dcterms:alternative>  
      </rdf:Description>
    </rdf:RDF> 
    <variable units="millimolar" public_interface="out" name="FUM" initial_value="0.01"/> 
    <variable units="flux" public_interface="in" name="V_SDH"/>
    <variable units="flux" public_interface="in" name="V_FH"/>
    <variable units="second" public_interface="in" name="time"/> 
    <math xmlns="http://www.w3.org/1998/Math/MathML"> 
      <apply>
        <eq/> 
        <apply>
          <diff/> 
          <bvar>
            <ci>time</ci>
          </bvar> 
          <ci>FUM</ci> 
        </apply>
        <apply>
          <minus/> 
          <ci>V_SDH</ci>
          <ci>V_FH</ci>
        </apply> 
      </apply> 
    </math> 
  </component>
  
  <component cmeta:id="MAL" name="MAL">
    <rdf:RDF>
      <rdf:Description rdf:about="#MAL">
        <dc:title>MAL</dc:title>
        <dcterms:alternative>malate</dcterms:alternative>  
      </rdf:Description>
    </rdf:RDF> 
    <variable units="millimolar" public_interface="out" name="MAL" initial_value="0.01"/> 
    <variable units="flux" public_interface="in" name="V_FH"/>
    <variable units="flux" public_interface="in" name="V_MDH"/>
    <variable units="second" public_interface="in" name="time"/> 
    <math xmlns="http://www.w3.org/1998/Math/MathML"> 
      <apply>
        <eq/> 
        <apply>
          <diff/> 
          <bvar>
            <ci>time</ci>
          </bvar> 
          <ci>MAL</ci> 
        </apply>
        <apply>
          <minus/> 
          <ci>V_FH</ci>
          <ci>V_MDH</ci>
        </apply> 
      </apply> 
    </math> 
  </component>
  
  <component cmeta:id="OAA" name="OAA">
    <rdf:RDF>
      <rdf:Description rdf:about="#OAA">
        <dc:title>OAA</dc:title>
        <dcterms:alternative>oxaloacetate</dcterms:alternative>  
      </rdf:Description>
    </rdf:RDF> 
    <variable units="millimolar" public_interface="out" name="OAA" initial_value="0.01"/> 
    <variable units="flux" public_interface="in" name="V_MDH"/>
    <variable units="flux" public_interface="in" name="V_CS"/>
    <variable units="flux" public_interface="in" name="V_AAT"/>
    <variable units="second" public_interface="in" name="time"/> 
    <math xmlns="http://www.w3.org/1998/Math/MathML"> 
      <apply>
        <eq/> 
        <apply>
          <diff/> 
          <bvar>
            <ci>time</ci>
          </bvar> 
          <ci>OAA</ci> 
        </apply>
        <apply>
          <minus/> 
          <ci>V_MDH</ci>
          <apply>
            <plus/> 
            <ci>V_CS</ci>
            <ci>V_AAT</ci>
          </apply>
        </apply> 
      </apply> 
    </math> 
  </component>
  
  <component cmeta:id="ASP" name="ASP">
    <rdf:RDF>
      <rdf:Description rdf:about="#ASP">
        <dc:title>ASP</dc:title>
        <dcterms:alternative>aspartate</dcterms:alternative>  
      </rdf:Description>
    </rdf:RDF> 
    <variable units="millimolar" public_interface="out" name="ASP" initial_value="0.01"/> 
    <variable units="flux" public_interface="in" name="V_AAT"/>
    <variable units="flux" public_interface="in" name="V_C_ASP"/>
    <variable units="second" public_interface="in" name="time"/> 
    <math xmlns="http://www.w3.org/1998/Math/MathML"> 
      <apply>
        <eq/> 
        <apply>
          <diff/> 
          <bvar>
            <ci>time</ci>
          </bvar> 
          <ci>ASP</ci> 
        </apply>
        <apply>
          <minus/> 
          <ci>V_AAT</ci>
          <ci>V_C_ASP</ci>
        </apply> 
      </apply> 
    </math> 
  </component>
  
  <component cmeta:id="Ca_m" name="Ca_m">
    <rdf:RDF>
      <rdf:Description rdf:about="#Ca_m">
        <dc:title>Ca_m</dc:title>
        <dcterms:alternative>mitochondrial calcium</dcterms:alternative>  
      </rdf:Description>
    </rdf:RDF> 
    <variable units="micromolar" public_interface="out" name="Ca_m" initial_value="0.01"/>
    <variable units="dimensionless" name="f" initial_value="0.0003"/> 
    <variable units="flux" public_interface="in" name="V_uni"/>
    <variable units="flux" public_interface="in" name="V_NaCa"/>
    <variable units="second" public_interface="in" name="time"/> 
    <math xmlns="http://www.w3.org/1998/Math/MathML"> 
      <apply>
        <eq/> 
        <apply>
          <diff/> 
          <bvar>
            <ci>time</ci>
          </bvar> 
          <ci>Ca_m</ci> 
        </apply>
        <apply>
          <times/>
          <ci>f</ci>
		  <cn cellml:units="micromolar_per_millimolar">1</cn>
          <apply>
            <minus/> 
            <ci>V_uni</ci>
            <ci>V_NaCa</ci>
          </apply>
        </apply> 
      </apply> 
    </math> 
  </component>
  
  <component cmeta:id="Ca_i" name="Ca_i">
    <rdf:RDF>
      <rdf:Description rdf:about="#Ca_i">
        <dc:title>Ca_i</dc:title>
        <dcterms:alternative>cytosolic calcium</dcterms:alternative>  
      </rdf:Description>
    </rdf:RDF> 
    <variable units="micromolar" public_interface="out" name="Ca_i"/>
	
	<variable units="second" name="stim_start" initial_value="0"/>
    <variable units="second" name="stim_end" initial_value="10000"/>
    <variable units="second" name="stim_period"/>
	<variable units="second" name="stim_duration" initial_value="0.4"/>
    <variable units="micromolar" name="pulse_value" initial_value="1"/>
	
	<variable units="second" public_interface="in" name="time"/> 
    <math xmlns="http://www.w3.org/1998/Math/MathML"> 
      <apply>
        <eq/> 
        <ci>Ca_i</ci> 
        <piecewise>
          <piece>
		    <ci>pulse_value</ci>
            <apply>
              <and/>
              <apply>
                <geq/>
                <ci>time</ci>
                <ci>stim_start</ci>
              </apply>
              <apply>
                <leq/>
                <ci>time</ci>
                <ci>stim_end</ci>
              </apply>
              <apply>
                <leq/>
                <apply>
                  <minus/>
                  <apply>
                    <minus/>
                    <ci>time</ci>
                    <ci>stim_start</ci>
                  </apply>
                  <apply>
                    <times/>
                    <apply>
                      <floor/>
                      <apply>
                        <divide/>
                        <apply>
                          <minus/>
                          <ci>time</ci>
                          <ci>stim_start</ci>
                        </apply>
                        <ci>stim_period</ci>
                      </apply>
                    </apply>
                    <ci>stim_period</ci>
                  </apply>
                </apply>
                <ci>stim_duration</ci>
              </apply>
            </apply>
          </piece>
          <otherwise>
            <cn cellml:units="micromolar">0.1</cn>
          </otherwise>
        </piecewise>
      </apply>
	  
	  <apply>
        <eq/> 
        <ci>stim_period</ci> 
        <piecewise>
          <piece>
		    <cn cellml:units="second">0.5</cn>
            <apply>
              <and/>
              <apply>
                <geq/>
                <ci>time</ci>
                <cn cellml:units="second">100</cn>
              </apply>
              <apply>
                <lt/>
                <ci>time</ci>
                <cn cellml:units="second">300</cn>
              </apply>
            </apply>
          </piece>
          <otherwise>
            <cn cellml:units="second">4</cn>
          </otherwise>
        </piecewise>
      </apply>
	</math> 
  </component>
  
  <component cmeta:id="Na_i" name="Na_i">
    <rdf:RDF>
      <rdf:Description rdf:about="#Na_i">
        <dc:title>Na_i</dc:title>
        <dcterms:alternative>cytosolic sodium</dcterms:alternative>  
      </rdf:Description>
    </rdf:RDF> 
    <variable units="millimolar" public_interface="out" name="Na_i" initial_value="10.0"/>
  </component>
  
  <component cmeta:id="ATP_i" name="ATP_i">
    <rdf:RDF>
      <rdf:Description rdf:about="#ATP_i">
        <dc:title>ATP_i</dc:title>
        <dcterms:alternative>
          cytosolic adenosine triphosphate
        </dcterms:alternative>  
      </rdf:Description>
    </rdf:RDF> 
    <variable units="millimolar" public_interface="out" name="ATP_i" initial_value="6.5"/>
  </component>
  
  <component cmeta:id="ATP_m" name="ATP_m">
    <rdf:RDF>
      <rdf:Description rdf:about="#ATP_m">
        <dc:title>ATP_m</dc:title>
        <dcterms:alternative>
          mitochondrial adenosine triphosphate
        </dcterms:alternative>  
      </rdf:Description>
    </rdf:RDF> 
    <variable units="millimolar" public_interface="out" name="ATP_m"/>
    <variable units="millimolar" name="Cm" initial_value="15.0"/>
    <variable units="millimolar" public_interface="in" name="ADP_m"/>
    <math xmlns="http://www.w3.org/1998/Math/MathML"> 
      <apply>
        <eq/> 
        <ci>ATP_m</ci> 
        <apply>
          <minus/>
          <ci>Cm</ci>
          <ci>ADP_m</ci>
        </apply> 
      </apply> 
    </math> 
  </component>
  
  <component cmeta:id="ADP_i" name="ADP_i">
    <rdf:RDF>
      <rdf:Description rdf:about="#ADP_i">
        <dc:title>ADP_i</dc:title>
        <dcterms:alternative>
          cytosolic adenosine diphosphate
        </dcterms:alternative>  
      </rdf:Description>
    </rdf:RDF> 
    <variable units="millimolar" public_interface="out" name="ADP_i"/>
	
	<variable units="millimolar" name="pulse_value" initial_value="0.15"/>
	
	<variable units="second" public_interface="in" name="time"/> 
    <math xmlns="http://www.w3.org/1998/Math/MathML"> 
      <apply>
        <eq/> 
        <ci>ADP_i</ci> 
        <piecewise>
          <piece>
		    <ci>pulse_value</ci>
            <apply>
              <and/>
              <apply>
                <geq/>
                <ci>time</ci>
                <cn cellml:units="second">100</cn>
              </apply>
              <apply>
                <lt/>
                <ci>time</ci>
                <cn cellml:units="second">300</cn>
              </apply>
            </apply>
          </piece>
          <otherwise>
            <cn cellml:units="millimolar">0.05</cn>
          </otherwise>
        </piecewise>
      </apply>
	</math> 
  </component>
 
  <component cmeta:id="GLU" name="GLU">
    <rdf:RDF>
      <rdf:Description rdf:about="#GLU">
        <dc:title>GLU</dc:title>
        <dcterms:alternative>glutamate</dcterms:alternative>  
      </rdf:Description>
    </rdf:RDF> 
    <variable units="millimolar" public_interface="out" name="GLU" initial_value="20"/>
  </component>
  
  <component cmeta:id="Mg" name="Mg">
    <rdf:RDF>
      <rdf:Description rdf:about="#Mg">
        <dc:title>Mg</dc:title>
        <dcterms:alternative>magnesium</dcterms:alternative>  
      </rdf:Description>
    </rdf:RDF> 
    <variable units="millimolar" public_interface="out" name="Mg" initial_value="0.4"/>
  </component>
  
  <component cmeta:id="H" name="H">
    <rdf:RDF>
      <rdf:Description rdf:about="#H">
        <dc:title>H</dc:title>
        <dcterms:alternative>proton</dcterms:alternative>  
      </rdf:Description>
    </rdf:RDF> 
    <variable units="millimolar" public_interface="out" name="H" initial_value="2.5E-5"/>
  </component>
  
  <component cmeta:id="Pi" name="Pi">
    <rdf:RDF>
      <rdf:Description rdf:about="#Pi">
        <dc:title>Pi</dc:title>
        <dcterms:alternative>inorganic phosphate</dcterms:alternative>  
      </rdf:Description>
    </rdf:RDF> 
    <variable units="millimolar" public_interface="out" name="Pi" initial_value="20.0"/>
  </component>
  
  <component cmeta:id="CoA" name="CoA">
    <rdf:RDF>
      <rdf:Description rdf:about="#CoA">
        <dc:title>CoA</dc:title>
        <dcterms:alternative>Coenzyme A</dcterms:alternative>  
      </rdf:Description>
    </rdf:RDF> 
    <variable units="millimolar" public_interface="out" name="CoA" initial_value="0.02"/>
  </component>
  
  <component cmeta:id="AcCoA" name="AcCoA">
    <rdf:RDF>
      <rdf:Description rdf:about="#AcCoA">
        <dc:title>AcCoA</dc:title>
        <dcterms:alternative>acetyl Coenzyme A</dcterms:alternative>  
      </rdf:Description>
    </rdf:RDF> 
    <variable units="millimolar" public_interface="out" name="AcCoA" initial_value="0.0002"/>
  </component>
  
  <component cmeta:id="FAD" name="FAD">
    <rdf:RDF>
      <rdf:Description rdf:about="#FAD">
        <dc:title>FAD</dc:title>
        <dcterms:alternative>
          flavin adenine dinucleotide (oxidised)
        </dcterms:alternative>  
      </rdf:Description>
    </rdf:RDF> 
    <variable units="millimolar" public_interface="out" name="FAD" initial_value="0.01"/>
  </component>
  
  <component cmeta:id="FADH2" name="FADH2">
    <rdf:RDF>
      <rdf:Description rdf:about="#FADH2">
        <dc:title>FADH2</dc:title>
        <dcterms:alternative>
          flavin adenine dinucleotide (reduced)
        </dcterms:alternative>  
      </rdf:Description>
    </rdf:RDF> 
    <variable units="millimolar" public_interface="out" name="FADH2" initial_value="1.24"/>
  </component>
  
  <component cmeta:id="NAD" name="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"/>
    <variable units="millimolar" public_interface="in" name="NADH"/>
    <variable units="millimolar" name="C_PN" initial_value="10.0"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply id="NAD_calculation">
        <eq/>
        <ci> NAD </ci>
        <apply>
          <minus/>
          <ci> C_PN </ci>
          <ci> NADH </ci>
        </apply>
      </apply>
    </math>
  </component>
  
  <component cmeta:id="CIT" name="CIT">
    <rdf:RDF>
      <rdf:Description rdf:about="#CIT">
        <dc:title>CIT</dc:title>
        <dcterms:alternative>citric acid</dcterms:alternative>  
      </rdf:Description>
    </rdf:RDF> 
    <variable units="millimolar" public_interface="out" name="CIT"/>
    <variable units="millimolar" public_interface="in" name="ISOC"/>
    <variable units="millimolar" public_interface="in" name="alpha_KG"/>
    <variable units="millimolar" public_interface="in" name="SCoA"/>
    <variable units="millimolar" public_interface="in" name="Suc"/>
    <variable units="millimolar" public_interface="in" name="FUM"/>
    <variable units="millimolar" public_interface="in" name="MAL"/>
    <variable units="millimolar" public_interface="in" name="OAA"/>
    <variable units="millimolar" name="C_Kint" initial_value="1.0"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply id="CIT_calculation">
        <eq/>
        <ci> CIT </ci>
        <apply>
          <minus/>
          <ci> C_Kint </ci>
          <apply>
            <plus/>
            <ci> ISOC </ci>
            <ci> alpha_KG </ci>
            <ci> SCoA </ci>
            <ci> Suc </ci>
            <ci> FUM </ci>
            <ci> MAL </ci>
            <ci> OAA </ci>
          </apply>
        </apply>
      </apply>
    </math>
  </component>
  
  <component name="mitochondrial_membrane">
    <variable units="volt" public_interface="out" name="delta_psi_m" initial_value="0.01"/>
    <variable units="volt_coulomb_per_mole_kelvin" public_interface="out" name="R" initial_value="8.315"/>
    <variable units="kelvin" public_interface="out" name="T" initial_value="310.16"/>
    <variable units="coulomb_per_mole" public_interface="out" name="F" initial_value="96480"/>
	
    <variable units="millimolar_per_volt" name="C_mito" initial_value="1.812"/>
    
    <variable units="flux" public_interface="in" name="V_He"/>
    <variable units="flux" public_interface="in" name="V_He_F"/>
    <variable units="flux" public_interface="in" name="V_Hu"/>
    <variable units="flux" public_interface="in" name="V_ANT"/>
    <variable units="flux" public_interface="in" name="V_Hleak"/>
    <variable units="flux" public_interface="in" name="V_NaCa"/>
    <variable units="flux" public_interface="in" name="V_uni"/>
    <variable units="second" public_interface="in" name="time"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply id="delta_psi_m_diff_eq">
        <eq/>
        <apply>
          <diff/>
          <bvar>
            <ci> time </ci>
          </bvar>
          <ci> delta_psi_m </ci>
        </apply>
        <apply>
          <divide/>
          <apply>
            <plus/>
            <ci> V_He </ci>
            <ci> V_He_F </ci>
            <apply>
              <minus/>
              <apply>
                <plus/>
                <ci> V_Hu </ci>
                <ci> V_ANT </ci>
                <ci> V_Hleak </ci>
                <ci> V_NaCa </ci>
                <apply>
                  <times/>
                  <cn cellml:units="dimensionless"> 2.0 </cn>
                  <ci> V_uni </ci>
                </apply>
              </apply>
            </apply>    
          </apply>
          <ci> C_mito </ci>
        </apply>
      </apply>
    </math>
  </component>
  
  <component name="V_CS">
    <variable units="flux" public_interface="out" name="V_CS"/>
    
    <variable units="millimolar" public_interface="in" name="OAA"/>
    <variable units="millimolar" public_interface="in" name="AcCoA"/>
    
    <variable units="millimolar" name="Km_AcCoA" initial_value="1.26E-2"/>
    <variable units="millimolar" name="Km_OAA" initial_value="6.4E-4"/>
    <variable units="first_order_rate_constant" name="Kcat_CS" initial_value="3.2"/>
    <variable units="millimolar" name="ET_CS" initial_value="0.4"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply id="V_CS_calculation">
        <eq/>
        <ci> V_CS </ci>
        <apply>
          <divide/>
          <apply>
            <times/>
            <ci> Kcat_CS </ci>
            <ci> ET_CS </ci>
          </apply>
          <apply>
            <plus/>
            <cn cellml:units="dimensionless"> 1.0 </cn>
            <apply>
              <divide/>
              <ci> Km_AcCoA </ci>
              <ci> AcCoA </ci>
            </apply>
            <apply>
              <divide/>
              <ci> Km_OAA </ci>
              <ci> OAA </ci>
            </apply>
            <apply>
              <times/>
              <apply>
                <divide/>
                <ci> Km_AcCoA </ci>
                <ci> AcCoA </ci>
              </apply>
              <apply>
                <divide/>
                <ci> Km_OAA </ci>
                <ci> OAA </ci>
              </apply>
            </apply>
          </apply>
        </apply>
      </apply>
    </math>
  </component>
  
  <component name="V_ACO">
    <variable units="flux" public_interface="out" name="V_ACO"/>
    
    <variable units="millimolar" public_interface="in" name="CIT"/>
    <variable units="millimolar" public_interface="in" name="ISOC"/>
    
    <variable units="first_order_rate_constant" name="Kf_ACO" initial_value="12.5"/>
    <variable units="dimensionless" name="KE_ACO" initial_value="2.22"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply id="V_ACO_calculation">
        <eq/>
        <ci> V_ACO </ci>
        <apply>
          <times/>
          <ci> Kf_ACO </ci>
          <apply>
            <minus/>
            <ci> CIT </ci>
            <apply>
              <divide/>
              <ci> ISOC </ci>
              <ci> KE_ACO </ci>
            </apply>
          </apply>
        </apply>
      </apply>
    </math>
  </component>
  
  <component name="V_IDH">
    <variable units="flux" public_interface="out" name="V_IDH"/>
    
    <variable units="millimolar" public_interface="in" name="NAD"/>
    <variable units="millimolar" public_interface="in" name="NADH"/>
    <variable units="millimolar" public_interface="in" name="ADP_m"/>
    <variable units="micromolar" public_interface="in" name="Ca_m"/>
    <variable units="millimolar" public_interface="in" name="H"/>
    <variable units="millimolar" public_interface="in" name="ISOC"/>
    
    <variable units="millimolar" name="Kh_1" initial_value="8.1E-5"/>
    <variable units="millimolar" name="Kh_2" initial_value="5.98E-5"/>
    <variable units="millimolar" name="Km_ISOC" initial_value="1.52"/>
    <variable units="millimolar" name="Ka_ADP" initial_value="6.2E-2"/>
    <variable units="micromolar" name="Ka_Ca" initial_value="1.41"/>
    <variable units="millimolar" name="Km_NAD" initial_value="0.923"/>
    <variable units="millimolar" name="Ki_NADH" initial_value="0.19"/>
    <variable units="first_order_rate_constant" name="Kcat_IDH" initial_value="1.94"/>
    <variable units="millimolar" name="ET_IDH" initial_value="0.109"/>
    <variable units="dimensionless" name="ni" initial_value="1"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply id="V_IDH_calculation">
        <eq/>
        <ci> V_IDH </ci>
        <apply>
          <divide/>
          <apply>
            <times/>
            <ci> Kcat_IDH </ci>
            <ci> ET_IDH </ci>
          </apply>
          <apply>
            <plus/>
            <cn cellml:units="dimensionless"> 1.0 </cn>
            <apply>
              <divide/>
              <ci> H </ci>
              <ci> Kh_1 </ci>
            </apply>
            <apply>
              <divide/>
              <ci> Kh_2 </ci>
              <ci> H </ci>
            </apply>
            <apply>
              <divide/>
              <apply>
                <power/>
                <apply>
                  <divide/>
                  <ci> Km_ISOC </ci>
                  <ci> ISOC </ci>
                </apply>
                <ci> ni </ci>
              </apply>
              <apply>
                <times/>
                <apply>
                  <plus/>
                  <cn cellml:units="dimensionless"> 1.0 </cn>
                  <apply>
                    <divide/>
                    <ci> ADP_m </ci>
                    <ci> Ka_ADP </ci>
                  </apply>
                </apply>
                <apply>
                  <plus/>
                  <cn cellml:units="dimensionless"> 1.0 </cn>
                  <apply>
                    <divide/>
                    <ci> Ca_m </ci>
                    <ci> Ka_Ca </ci>
                  </apply>
                </apply>
              </apply>
            </apply>
            <apply>
              <times/>
              <apply>
                <divide/>
                <ci> Km_NAD </ci>
                <ci> NAD </ci>
              </apply>
              <apply>
                <plus/>
                <cn cellml:units="dimensionless"> 1.0 </cn>
                <apply>
                  <divide/>
                  <ci> NADH </ci>
                  <ci> Ki_NADH </ci>
                </apply>
              </apply>
            </apply>
            <apply>
              <divide/>
              <apply>
                <times/>
                <apply>
                  <power/>
                  <apply>
                    <divide/>
                    <ci> Km_ISOC </ci>
                    <ci> ISOC </ci>
                  </apply>
                  <ci> ni </ci>
                </apply>
                <apply>
                  <divide/>
                  <ci> Km_NAD </ci>
                  <ci> NAD </ci>
                </apply>
                <apply>
                  <plus/>
                  <cn cellml:units="dimensionless"> 1.0 </cn>
                  <apply>
                    <divide/>
                    <ci> NADH </ci>
                    <ci> Ki_NADH </ci>
                  </apply>
                </apply>
              </apply>
              <apply>
                <times/>
                <apply>
                  <plus/>
                  <cn cellml:units="dimensionless"> 1.0 </cn>
                  <apply>
                    <divide/>
                    <ci> ADP_m </ci>
                    <ci> Ka_ADP </ci>
                  </apply>
                </apply>
                <apply>
                  <plus/>
                  <cn cellml:units="dimensionless"> 1.0 </cn>
                  <apply>
                    <divide/>
                    <ci> Ca_m </ci>
                    <ci> Ka_Ca </ci>
                  </apply>
                </apply>
              </apply>
            </apply>
          </apply>
        </apply>
      </apply>
    </math>
  </component>
  
  <component name="V_KGDH">
    <variable units="flux" public_interface="out" name="V_KGDH"/>
    
    <variable units="millimolar" public_interface="in" name="Mg"/>
    <variable units="micromolar" public_interface="in" name="Ca_m"/>
    <variable units="millimolar" public_interface="in" name="NAD"/>
    <variable units="millimolar" public_interface="in" name="alpha_KG"/>
    
    <variable units="millimolar" name="Km_alpha_KG" initial_value="1.94"/>
    <variable units="first_order_rate_constant" name="Kcat_KGDH" initial_value="0.15"/>
    <variable units="millimolar" name="ET_KGDH" initial_value="0.5"/>
    <variable units="millimolar" name="Kd_Mg" initial_value="0.0308"/>
    <variable units="micromolar" name="Kd_Ca" initial_value="1.27"/>
    <variable units="dimensionless" name="n_alpha_KG" initial_value="1.2"/>
    <variable units="millimolar" name="Km_NAD" initial_value="38.7"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply id="V_KGDH_calculation">
        <eq/>
        <ci> V_KGDH </ci>
        <apply>
          <divide/>
          <apply>
            <times/>
            <ci> Kcat_KGDH </ci>
            <ci> ET_KGDH </ci>
          </apply>
          <apply>
            <plus/>
            <cn cellml:units="dimensionless"> 1.0 </cn>
            <apply>
              <divide/>
              <apply>
                <power/>
                <apply>
                  <divide/>
                  <ci> Km_alpha_KG </ci>
                  <ci> alpha_KG </ci>
                </apply>
                <ci> n_alpha_KG </ci>
              </apply>
              <apply>
                <times/>
                <apply>
                  <plus/>
                  <cn cellml:units="dimensionless"> 1.0 </cn>
                  <apply>
                    <divide/>
                    <ci> Mg </ci>
                    <ci> Kd_Mg </ci>
                  </apply>
                </apply>
                <apply>
                  <plus/>
                  <cn cellml:units="dimensionless"> 1.0 </cn>
                  <apply>
                    <divide/>
                    <ci> Ca_m </ci>
                    <ci> Kd_Ca </ci>
                  </apply>
                </apply>
              </apply>
            </apply>
            <apply>
              <divide/>
              <apply>
                <divide/>
                <ci> Km_NAD </ci>
                <ci> NAD </ci>
              </apply>
              <apply>
                <times/>
                <apply>
                  <plus/>
                  <cn cellml:units="dimensionless"> 1.0 </cn>
                  <apply>
                    <divide/>
                    <ci> Mg </ci>
                    <ci> Kd_Mg </ci>
                  </apply>
                </apply>
                <apply>
                  <plus/>
                  <cn cellml:units="dimensionless"> 1.0 </cn>
                  <apply>
                    <divide/>
                    <ci> Ca_m </ci>
                    <ci> Kd_Ca </ci>
                  </apply>
                </apply>
              </apply>
            </apply>
          </apply>
        </apply>
      </apply>
    </math>
  </component>
  
  <component name="V_SL">
    <variable units="flux" public_interface="out" name="V_SL"/>
    
    <variable units="millimolar" public_interface="in" name="SCoA"/>
    <variable units="millimolar" public_interface="in" name="ADP_m"/>
    <variable units="millimolar" public_interface="in" name="Suc"/>
    <variable units="millimolar" public_interface="in" name="ATP_m"/>
    <variable units="millimolar" public_interface="in" name="CoA"/>
    
    <variable units="second_order_rate_constant" name="kf_SL" initial_value="0.127"/>
    <variable units="millimolar" name="Ke_SL" initial_value="3.115"/>
  
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply id="V_SL_calculation">
        <eq/>
        <ci> V_SL </ci>
        <apply>
          <times/>
          <ci> kf_SL </ci>
          <apply>
            <minus/>
            <apply>
              <times/>
              <ci> SCoA </ci>
              <ci> ADP_m </ci>
            </apply>
            <apply>
              <divide/>
              <apply>
                <times/>
                <ci> Suc </ci>
                <ci> ATP_m </ci>
                <ci> CoA </ci>
              </apply>
              <ci> Ke_SL </ci>
            </apply>     
          </apply>
        </apply>
      </apply>
    </math>
  </component>
  
  <component name="V_SDH">
    <variable units="flux" public_interface="out" name="V_SDH"/>
    
    <variable units="millimolar" public_interface="in" name="Suc"/>
    <variable units="millimolar" public_interface="in" name="FUM"/>
    <variable units="millimolar" public_interface="in" name="OAA"/>
    
    <variable units="millimolar" name="Kisdh_OAA" initial_value="0.15"/>
    <variable units="first_order_rate_constant" name="Kcat_SDH" initial_value="1.0"/>
    <variable units="millimolar" name="ET_SDH" initial_value="0.5"/>
    <variable units="millimolar" name="Km_Suc" initial_value="3.0E-2"/>
    <variable units="millimolar" name="Ki_FUM" initial_value="1.3"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply id="V_SDH_calculation">
        <eq/>
        <ci> V_SDH </ci>
        <apply>
          <divide/>
          <apply>
            <times/>
            <ci> Kcat_SDH </ci>
            <ci> ET_SDH </ci>
          </apply>
          <apply>
            <plus/>
            <cn cellml:units="dimensionless"> 1.0 </cn>
            <apply>
              <times/>
              <apply>
                <divide/>
                <ci> Km_Suc </ci>
                <ci> Suc </ci>
              </apply>
              <apply>
                <plus/>
                <cn cellml:units="dimensionless"> 1.0 </cn>
                <apply>
                  <divide/>
                  <ci> OAA </ci>
                  <ci> Kisdh_OAA </ci>
                </apply>
              </apply>
              <apply>
                <plus/>
                <cn cellml:units="dimensionless"> 1.0 </cn>
                <apply>
                  <divide/>
                  <ci> FUM </ci>
                  <ci> Ki_FUM </ci>
                </apply>
              </apply>
            </apply>
          </apply>
        </apply>
      </apply>
    </math>
  </component> 
  
  <component name="V_MDH">
    <variable units="flux" public_interface="out" name="V_MDH"/>
    
    <variable units="millimolar" public_interface="in" name="MAL"/>
    <variable units="millimolar" public_interface="in" name="OAA"/>
    <variable units="millimolar" public_interface="in" name="NAD"/>
    <variable units="millimolar" public_interface="in" name="H"/>
    
    <variable units="millimolar" name="Km_MAL" initial_value="1.493"/>
    <variable units="first_order_rate_constant" name="Kcat_MDH" initial_value="2.775E1"/>
    <variable units="millimolar" name="ET_MDH" initial_value="0.154"/>
    <variable units="millimolar" name="Ki_OAA" initial_value="3.1E-3"/>
    <variable units="dimensionless" name="fh_a"/>
    <variable units="dimensionless" name="fh_i"/>
    <variable units="millimolar" name="Km_NAD" initial_value="0.2244"/>
    <variable units="millimolar" name="kh1" initial_value="1.13E-5"/>
    <variable units="millimolar" name="kh2" initial_value="26.7"/>
    <variable units="millimolar" name="kh3" initial_value="6.68E-9"/>
    <variable units="millimolar" name="kh4" initial_value="5.62E-6"/>
    <variable units="dimensionless" name="k_offset" initial_value="3.99E-2"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply id="V_MDH_calculation">
        <eq/>
        <ci> V_MDH </ci>
        <apply>
          <divide/>
          <apply>
            <times/>
            <ci> Kcat_MDH </ci>
            <ci> ET_MDH </ci>
            <ci> fh_a </ci>
            <ci> fh_i </ci>
          </apply>
          <apply>
            <plus/>
            <cn cellml:units="dimensionless"> 1.0 </cn>
            <apply>
              <times/>
              <apply>
                <divide/>
                <ci> Km_MAL </ci>
                <ci> MAL </ci>
              </apply>
              <apply>
                <plus/>
                <cn cellml:units="dimensionless"> 1.0 </cn>
                <apply>
                  <divide/>
                  <ci> OAA </ci>
                  <ci> Ki_OAA </ci>
                </apply>
              </apply>
            </apply>
            <apply>
              <divide/>
              <ci> Km_NAD </ci>
              <ci> NAD </ci>
            </apply>
            <apply>
              <times/>
              <apply>
                <divide/>
                <ci> Km_MAL </ci>
                <ci> MAL </ci>
              </apply>
              <apply>
                <plus/>
                <cn cellml:units="dimensionless"> 1.0 </cn>
                <apply>
                  <divide/>
                  <ci> OAA </ci>
                  <ci> Ki_OAA </ci>
                </apply>
              </apply>
              <apply>
                <divide/>
                <ci> Km_NAD </ci>
                <ci> NAD </ci>
              </apply>
            </apply>
          </apply>
        </apply>
      </apply>
      
      <apply id="fh_a_calculation">
        <eq/>
        <ci> fh_a </ci>
        <apply>
          <plus/>
          <apply>
            <divide/>
            <cn cellml:units="dimensionless"> 1.0 </cn>
            <apply>
              <plus/>
              <cn cellml:units="dimensionless"> 1.0 </cn>
              <apply>
                <divide/>
                <ci> H </ci>
                <ci> kh1 </ci>
              </apply>
              <apply>
                <divide/>
                <apply>
                  <power/>
                  <ci> H </ci>
                  <cn cellml:units="dimensionless"> 2.0 </cn>
                </apply>
                <apply>
                  <times/>
                  <ci> kh1 </ci>
                  <ci> kh2 </ci> 
                </apply>
              </apply>
            </apply>
          </apply>
          <ci> k_offset </ci>
        </apply>
      </apply> 
      
      <apply id="fh_i_calculation">
        <eq/>
        <ci> fh_i </ci>
        <apply>
          <power/>
          <apply>
            <divide/>
            <cn cellml:units="dimensionless"> 1.0 </cn>
            <apply>
              <plus/>
              <cn cellml:units="dimensionless"> 1.0 </cn>
              <apply>
                <divide/>
                <ci> kh3 </ci>
                <ci> H </ci>
              </apply>
              <apply>
                <divide/>
                <apply>
                  <times/>
                  <ci> kh3 </ci>
                  <ci> kh4 </ci> 
                </apply>
                <apply>
                  <power/>
                  <ci> H </ci>
                  <cn cellml:units="dimensionless"> 2.0 </cn>
                </apply>
              </apply>
            </apply>
          </apply>
          <cn cellml:units="dimensionless"> 2.0 </cn>
        </apply>
      </apply> 
    </math>
  </component>
  
  <component name="V_FH">
    <variable units="flux" public_interface="out" name="V_FH"/>
    
    <variable units="millimolar" public_interface="in" name="MAL"/>
    <variable units="millimolar" public_interface="in" name="FUM"/>
    
    <variable units="dimensionless" name="Ke_FH" initial_value="1.0"/>
    <variable units="first_order_rate_constant" name="kf_FH" initial_value="0.83"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply id="V_FH_calculation">
        <eq/>
        <ci> V_FH </ci>
        <apply>
          <times/>
          <ci> kf_FH </ci>
          <apply>
            <minus/>
            <ci> FUM </ci>
            <apply>
              <divide/>
              <ci> MAL </ci>
              <ci> Ke_FH </ci>
            </apply>
          </apply>
        </apply>
      </apply>
    </math>
  </component> 
  
  <component name="V_AAT">
    <variable units="flux" public_interface="out" name="V_AAT"/>
    
    <variable units="millimolar" public_interface="in" name="OAA"/>
    <variable units="millimolar" public_interface="in" name="GLU"/>
    <variable units="millimolar" public_interface="in" name="ASP"/>
    <variable units="millimolar" public_interface="in" name="alpha_KG"/>
    
    <variable units="dimensionless" name="Ke_AAT" initial_value="6.6"/>
    <variable units="second_order_rate_constant" name="kf_AAT" initial_value="0.644"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply id="V_AAT_calculation">
        <eq/>
        <ci> V_AAT </ci>
        <apply>
          <times/>
          <ci> kf_AAT </ci>
          <apply>
            <minus/>
            <apply>
              <times/>
              <ci> OAA </ci>
              <ci> GLU </ci>
            </apply>
            <apply>
              <divide/>
              <apply>
                <times/>
                <ci> alpha_KG </ci>
                <ci> ASP </ci>
              </apply>
              <ci> Ke_AAT </ci>
            </apply>
          </apply>
        </apply>
      </apply>
    </math>
  </component>
  
  <component name="V_C_ASP">
    <variable units="flux" public_interface="out" name="V_C_ASP"/>
    
    <variable units="millimolar" public_interface="in" name="ASP"/>
    
    <variable units="first_order_rate_constant" name="k_C_ASP" initial_value="0.01"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply id="V_C_ASP_calculation">
        <eq/>
        <ci> V_C_ASP </ci>
        <apply>
          <times/>
          <ci> k_C_ASP </ci>
          <ci> ASP </ci>
        </apply>
      </apply>
    </math>
  </component>  
  
  <component name="oxidative_phosphorylation">
    <variable units="flux" public_interface="out" name="V_O2"/>
    <variable units="flux" public_interface="out" name="V_He"/>
    <variable units="flux" public_interface="out" name="V_He_F"/>
    <variable units="flux" public_interface="out" name="V_ATPase"/>
    <variable units="flux" public_interface="out" name="V_Hu"/>
    <variable units="flux" public_interface="out" name="V_Hleak"/>
    
	<variable units="volt_coulomb_per_mole_kelvin" public_interface="in" name="R"/>
    <variable units="kelvin" public_interface="in" name="T"/>
    <variable units="coulomb_per_mole" public_interface="in" name="F"/>
    <variable units="millimolar" public_interface="in" name="NAD"/>
    <variable units="millimolar" public_interface="in" name="NADH"/>
    <variable units="millimolar" public_interface="in" name="FAD"/>
    <variable units="millimolar" public_interface="in" name="FADH2"/>
    <variable units="millimolar" public_interface="in" name="ADP_m"/>
    <variable units="millimolar" public_interface="in" name="ATP_m"/>
    <variable units="millimolar" public_interface="in" name="Pi"/>
    <variable units="volt" public_interface="in" name="delta_psi_m"/>
    
	<variable units="millimolar" name="rho_res" initial_value="0.0006"/>
    <variable units="millimolar" name="rho_res_F" initial_value="0.0045"/>
    <variable units="first_order_rate_constant" name="ra" initial_value="6.394E-10"/>
    <variable units="first_order_rate_constant" name="rc1" initial_value="2.656E-19"/>
    <variable units="volt" name="Ares"/>
    <variable units="volt" name="Ares_F"/>
    <variable units="dimensionless" name="r1" initial_value="2.077E-18"/>
    <variable units="dimensionless" name="r2" initial_value="1.728E-9"/>
    <variable units="dimensionless" name="r3" initial_value="1.059E-26"/>
    <variable units="first_order_rate_constant" name="rb" initial_value="1.762E-13"/>
    <variable units="first_order_rate_constant" name="rc2" initial_value="8.632E-27"/>
    <variable units="dimensionless" name="Kres" initial_value="1.35E18"/>
    <variable units="dimensionless" name="Kres_F" initial_value="5.765E13"/>
    <variable units="millimolar_per_second_volt" name="gH" initial_value="0.01"/>
    <variable units="volt" name="delta_psi_B" initial_value="0.05"/>
    <variable units="dimensionless" name="g" initial_value="0.85"/>
    <variable units="volt" name="delta_mu_H"/>
    <variable units="dimensionless" name="delta_pH" initial_value="-0.6"/>
    <variable units="millimolar" name="rho_F1" initial_value="0.06"/>
    <variable units="first_order_rate_constant" name="pa" initial_value="1.656E-5"/>
    <variable units="first_order_rate_constant" name="pc1" initial_value="9.651E-14"/>
    <variable units="volt" name="AF1"/>
    <variable units="dimensionless" name="p1" initial_value="1.346E-8"/>
    <variable units="dimensionless" name="p2" initial_value="7.739E-7"/>
    <variable units="dimensionless" name="p3" initial_value="6.65E-15"/>
    <variable units="first_order_rate_constant" name="pb" initial_value="3.373E-7"/>
    <variable units="first_order_rate_constant" name="pc2" initial_value="4.585E-14"/>
    <variable units="millimolar" name="KF1" initial_value="1.71E6"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply id="V_O2_calculation">
        <eq/>
        <ci> V_O2 </ci>
        <apply>
          <times/>
          <cn cellml:units="dimensionless"> 0.5 </cn>
          <ci> rho_res </ci>
          <apply>
            <divide/>
            <apply>
              <plus/>
              <apply>
                <minus/>
                <apply>
                  <times/>
                  <apply>
                    <plus/>
                    <ci> ra </ci>
                    <apply>
                      <times/>
                      <ci> rc1 </ci>
                      <apply>
                        <exp/>
                        <apply>
                          <divide/>
                          <apply>
                            <times/>
                            <cn cellml:units="dimensionless"> 6.0 </cn>
                            <ci> F </ci>
                            <ci> delta_psi_B </ci>
                          </apply>
                          <apply>
                            <times/>
                            <ci> R </ci>
                            <ci> T </ci>
                          </apply>
                        </apply>
                      </apply>
                    </apply>
                  </apply>
                  <apply>
                    <exp/>
                    <apply>
                      <divide/>
                      <apply>
                        <times/>
                        <ci> Ares </ci>
                        <ci> F </ci>
                      </apply>
                      <apply>
                        <times/>
                        <ci> R </ci>
                        <ci> T </ci>
                      </apply>
                    </apply>
                  </apply>
                </apply>
                <apply>
                  <times/>
                  <ci> ra </ci>
                  <apply>
                    <exp/>
                    <apply>
                      <divide/>
                      <apply>
                        <times/>
                        <ci> g </ci>
                        <cn cellml:units="dimensionless"> 6.0 </cn>
                        <ci> F </ci>
                        <ci> delta_mu_H </ci>
                      </apply>
                      <apply>
                        <times/>
                        <ci> R </ci>
                        <ci> T </ci>
                      </apply>
                    </apply>
                  </apply>
                </apply>
              </apply>
              <apply>
                <times/>
                <ci> rc2 </ci>
                <apply>
                  <exp/>
                  <apply>
                    <divide/>
                    <apply>
                      <times/>
                      <ci> Ares </ci>
                      <ci> F </ci>
                    </apply>
                    <apply>
                      <times/>
                      <ci> R </ci>
                      <ci> T </ci>
                    </apply>
                  </apply>
                </apply>
                <apply>
                  <exp/>
                  <apply>
                    <divide/>
                    <apply>
                      <times/>
                      <ci> g </ci>
                      <cn cellml:units="dimensionless"> 6.0 </cn>
                      <ci> F </ci>
                      <ci> delta_mu_H </ci>
                    </apply>
                    <apply>
                      <times/>
                      <ci> R </ci>
                      <ci> T </ci>
                    </apply>
                  </apply>
                </apply>
              </apply>
            </apply>
            <apply>
              <plus/>
              <apply>
                <times/>
                <apply>
                  <plus/>
                  <cn cellml:units="dimensionless"> 1.0 </cn>
                  <apply>
                    <times/>
                    <ci> r1 </ci>
                    <apply>
                      <exp/>
                      <apply>
                        <divide/>
                        <apply>
                          <times/>
                          <ci> F </ci>
                          <ci> Ares </ci>
                        </apply>
                        <apply>
                          <times/>
                          <ci> R </ci>
                          <ci> T </ci>
                        </apply>
                      </apply>
                    </apply>
                  </apply>
                </apply>
                <apply>
                  <exp/>
                  <apply>
                    <divide/>
                    <apply>
                      <times/>
                      <cn cellml:units="dimensionless"> 6.0 </cn>
                      <ci> F </ci>
                      <ci> delta_psi_B </ci>
                    </apply>
                    <apply>
                      <times/>
                      <ci> R </ci>
                      <ci> T </ci>
                    </apply>
                  </apply>
                </apply>
              </apply>
              <apply>
                <times/>
                <apply>
                  <plus/>
                  <ci> r2 </ci>
                  <apply>
                    <times/>
                    <ci> r3 </ci>
                    <apply>
                      <exp/>
                      <apply>
                        <divide/>
                        <apply>
                          <times/>
                          <ci> F </ci>
                          <ci> Ares </ci>
                        </apply>
                        <apply>
                          <times/>
                          <ci> R </ci>
                          <ci> T </ci>
                        </apply>
                      </apply>
                    </apply>
                  </apply>
                </apply>
                <apply>
                  <exp/>
                  <apply>
                    <divide/>
                    <apply>
                      <times/>
                      <ci> g </ci>
                      <cn cellml:units="dimensionless"> 6.0 </cn>
                      <ci> F </ci>
                      <ci> delta_mu_H </ci>
                    </apply>
                    <apply>
                      <times/>
                      <ci> R </ci>
                      <ci> T </ci>
                    </apply>
                  </apply>
                </apply>
              </apply>
            </apply>
          </apply>
        </apply>
      </apply>
      
      <apply id="V_He_calculation">
        <eq/>
        <ci> V_He </ci>
        <apply>
          <times/>
          <cn cellml:units="dimensionless"> 6.0 </cn>
          <ci> rho_res </ci>
          <apply>
            <divide/>
            <apply>
              <minus/>
              <apply>
                <times/>
                <ci> ra </ci>
                <apply>
                  <exp/>
                  <apply>
                    <divide/>
                    <apply>
                      <times/>
                      <ci> F </ci>
                      <ci> Ares </ci>
                    </apply>
                    <apply>
                      <times/>
                      <ci> R </ci>
                      <ci> T </ci>
                    </apply>
                  </apply>
                </apply>
              </apply>
              <apply>
                <times/>
                <apply>
                  <plus/>
                  <ci> ra </ci>
                  <ci> rb </ci>
                </apply>
                <apply>
                  <exp/>
                  <apply>
                    <divide/>
                    <apply>
                      <times/>
                      <ci> g </ci>
                      <cn cellml:units="dimensionless"> 6.0 </cn>
                      <ci> F </ci>
                      <ci> delta_mu_H </ci>
                    </apply>
                    <apply>
                      <times/>
                      <ci> R </ci>
                      <ci> T </ci>
                    </apply>
                  </apply>
                </apply>
              </apply>
            </apply>
            <apply>
              <plus/>
              <apply>
                <times/>
                <apply>
                  <plus/>
                  <cn cellml:units="dimensionless"> 1.0 </cn>
                  <apply>
                    <times/>
                    <ci> r1 </ci>
                    <apply>
                      <exp/>
                      <apply>
                        <divide/>
                        <apply>
                          <times/>
                          <ci> F </ci>
                          <ci> Ares </ci>
                        </apply>
                        <apply>
                          <times/>
                          <ci> R </ci>
                          <ci> T </ci>
                        </apply>
                      </apply>
                    </apply>
                  </apply>
                </apply>
                <apply>
                  <exp/>
                  <apply>
                    <divide/>
                    <apply>
                      <times/>
                      <cn cellml:units="dimensionless"> 6.0 </cn>
                      <ci> F </ci>
                      <ci> delta_psi_B </ci>
                    </apply>
                    <apply>
                      <times/>
                      <ci> R </ci>
                      <ci> T </ci>
                    </apply>
                  </apply>
                </apply>
              </apply>
              <apply>
                <times/>
                <apply>
                  <plus/>
                  <ci> r2 </ci>
                  <apply>
                    <times/>
                    <ci> r3 </ci>
                    <apply>
                      <exp/>
                      <apply>
                        <divide/>
                        <apply>
                          <times/>
                          <ci> F </ci>
                          <ci> Ares </ci>
                        </apply>
                        <apply>
                          <times/>
                          <ci> R </ci>
                          <ci> T </ci>
                        </apply>
                      </apply>
                    </apply>
                  </apply>
                </apply>
                <apply>
                  <exp/>
                  <apply>
                    <divide/>
                    <apply>
                      <times/>
                      <ci> g </ci>
                      <cn cellml:units="dimensionless"> 6.0 </cn>
                      <ci> F </ci>
                      <ci> delta_mu_H </ci>
                    </apply>
                    <apply>
                      <times/>
                      <ci> R </ci>
                      <ci> T </ci>
                    </apply>
                  </apply>
                </apply>
              </apply>
            </apply>
          </apply>
        </apply>
      </apply>
      
      <apply id="Ares_calculation">
        <eq/>
        <ci> Ares </ci>
        <apply>
          <times/>
          <apply>
            <divide/>
            <apply>
              <times/>
              <ci> R </ci>
              <ci> T </ci>
            </apply>
            <ci> F </ci>
          </apply>
          <apply>
            <ln/>
            <apply>
              <times/>
              <ci> Kres </ci>
              <apply>
                <power/>
                <apply>
                  <divide/>
                  <ci> NADH </ci>
                  <ci> NAD </ci>
                </apply>
                <cn cellml:units="dimensionless"> 0.5 </cn>
              </apply>
            </apply>
          </apply>
        </apply>
      </apply> 
      
      <apply id="V_He_F_calculation">
        <eq/>
        <ci> V_He_F </ci>
        <apply>
          <times/>
          <cn cellml:units="dimensionless"> 6.0 </cn>
          <ci> rho_res_F </ci>
          <apply>
            <divide/>
            <apply>
              <minus/>
              <apply>
                <times/>
                <ci> ra </ci>
                <apply>
                  <exp/>
                  <apply>
                    <divide/>
                    <apply>
                      <times/>
                      <ci> F </ci>
                      <ci> Ares_F </ci>
                    </apply>
                    <apply>
                      <times/>
                      <ci> R </ci>
                      <ci> T </ci>
                    </apply>
                  </apply>
                </apply>
              </apply>
              <apply>
                <times/>
                <apply>
                  <plus/>
                  <ci> ra </ci>
                  <ci> rb </ci>
                </apply>
                <apply>
                  <exp/>
                  <apply>
                    <divide/>
                    <apply>
                      <times/>
                      <ci> g </ci>
                      <cn cellml:units="dimensionless"> 6.0 </cn>
                      <ci> F </ci>
                      <ci> delta_mu_H </ci>
                    </apply>
                    <apply>
                      <times/>
                      <ci> R </ci>
                      <ci> T </ci>
                    </apply>
                  </apply>
                </apply>
              </apply>
            </apply>
            <apply>
              <plus/>
              <apply>
                <times/>
                <apply>
                  <plus/>
                  <cn cellml:units="dimensionless"> 1.0 </cn>
                  <apply>
                    <times/>
                    <ci> r1 </ci>
                    <apply>
                      <exp/>
                      <apply>
                        <divide/>
                        <apply>
                          <times/>
                          <ci> F </ci>
                          <ci> Ares_F </ci>
                        </apply>
                        <apply>
                          <times/>
                          <ci> R </ci>
                          <ci> T </ci>
                        </apply>
                      </apply>
                    </apply>
                  </apply>
                </apply>
                <apply>
                  <exp/>
                  <apply>
                    <divide/>
                    <apply>
                      <times/>
                      <cn cellml:units="dimensionless"> 6.0 </cn>
                      <ci> F </ci>
                      <ci> delta_psi_B </ci>
                    </apply>
                    <apply>
                      <times/>
                      <ci> R </ci>
                      <ci> T </ci>
                    </apply>
                  </apply>
                </apply>
              </apply>
              <apply>
                <times/>
                <apply>
                  <plus/>
                  <ci> r2 </ci>
                  <apply>
                    <times/>
                    <ci> r3 </ci>
                    <apply>
                      <exp/>
                      <apply>
                        <divide/>
                        <apply>
                          <times/>
                          <ci> F </ci>
                          <ci> Ares_F </ci>
                        </apply>
                        <apply>
                          <times/>
                          <ci> R </ci>
                          <ci> T </ci>
                        </apply>
                      </apply>
                    </apply>
                  </apply>
                </apply>
                <apply>
                  <exp/>
                  <apply>
                    <divide/>
                    <apply>
                      <times/>
                      <ci> g </ci>
                      <cn cellml:units="dimensionless"> 6.0 </cn>
                      <ci> F </ci>
                      <ci> delta_mu_H </ci>
                    </apply>
                    <apply>
                      <times/>
                      <ci> R </ci>
                      <ci> T </ci>
                    </apply>
                  </apply>
                </apply>
              </apply>
            </apply>
          </apply>
        </apply>
      </apply>
      
      <apply id="Ares_F_calculation">
        <eq/>
        <ci> Ares_F </ci>
        <apply>
          <times/>
          <apply>
            <divide/>
            <apply>
              <times/>
              <ci> R </ci>
              <ci> T </ci>
            </apply>
            <ci> F </ci>
          </apply>
          <apply>
            <ln/>
            <apply>
              <times/>
              <ci> Kres_F </ci>
              <apply>
                <power/>
                <apply>
                  <divide/>
                  <ci> FADH2 </ci>
                  <ci> FAD </ci>
                </apply>
                <cn cellml:units="dimensionless"> 0.5 </cn>
              </apply>
            </apply>
          </apply>
        </apply>
      </apply>
      
      <apply id="V_Hleak_calculation">
        <eq/>
        <ci> V_Hleak </ci>
        <apply>
          <times/>
          <ci> gH </ci>
          <ci> delta_mu_H </ci>
        </apply>
      </apply>
      
      <apply id="delta_mu_H_calculation">
        <eq/>
        <ci> delta_mu_H </ci>
        <apply>
          <plus/>
          <apply>
            <times/>
            <apply>
              <divide/>
              <apply>
                <times/>
                <ci> R </ci>
                <ci> T </ci>
              </apply>
              <ci> F </ci>
            </apply>
            <ci> delta_pH </ci>
          </apply>
          <ci> delta_psi_m </ci>
        </apply>
      </apply>
    
      <apply id="V_ATPase_calculation">
        <eq/>
        <ci> V_ATPase </ci>
        <apply>
          <times/>
          <apply>
            <minus/>
            <ci> rho_F1 </ci>
          </apply>
          <apply>
            <divide/>
            <apply>
              <minus/>
              <apply>
                <times/>
                <apply>
                  <plus/>
                  <apply>
                    <times/>
                    <cn cellml:units="dimensionless"> 100.0 </cn>
                    <ci> pa </ci>
                  </apply>
                  <apply>
                    <times/>
                    <ci> pc1 </ci>
                    <apply>
                      <exp/>
                      <apply>
                        <divide/>
                        <apply>
                          <times/>
                          <cn cellml:units="dimensionless"> 3.0 </cn>
                          <ci> F </ci>
                          <ci> delta_psi_B </ci>
                        </apply>
                        <apply>
                          <times/>
                          <ci> R </ci>
                          <ci> T </ci>
                        </apply>
                      </apply>
                    </apply>
                  </apply>
                </apply>
                <apply>
                  <exp/>
                  <apply>
                    <divide/>
                    <apply>
                      <times/>
                      <ci> AF1 </ci>
                      <ci> F </ci>
                    </apply>
                    <apply>
                      <times/>
                      <ci> R </ci>
                      <ci> T </ci>
                    </apply>
                  </apply>
                </apply>
              </apply>
              <apply>
                <plus/>
                <apply>
                  <times/>
                  <ci> pa </ci>
                  <apply>
                    <exp/>
                    <apply>
                      <divide/>
                      <apply>
                        <times/>
                        <cn cellml:units="dimensionless"> 3.0 </cn>
                        <ci> F </ci>
                        <ci> delta_mu_H </ci>
                      </apply>
                      <apply>
                        <times/>
                        <ci> R </ci>
                        <ci> T </ci>
                      </apply>
                    </apply>
                  </apply>
                </apply>
                <apply>
                  <times/>
                  <ci> pc2 </ci>
                  <apply>
                    <exp/>
                    <apply>
                      <divide/>
                      <apply>
                        <times/>
                        <ci> AF1 </ci>
                        <ci> F </ci>
                      </apply>
                      <apply>
                        <times/>
                        <ci> R </ci>
                        <ci> T </ci>
                      </apply>
                    </apply>
                  </apply>
                  <apply>
                    <exp/>
                    <apply>
                      <divide/>
                      <apply>
                        <times/>
                        <cn cellml:units="dimensionless"> 3.0 </cn>
                        <ci> F </ci>
                        <ci> delta_mu_H </ci>
                      </apply>
                      <apply>
                        <times/>
                        <ci> R </ci>
                        <ci> T </ci>
                      </apply>
                    </apply>
                  </apply>
                </apply>
              </apply>
            </apply>
            <apply>
              <plus/>
              <apply>
                <times/>
                <apply>
                  <plus/>
                  <cn cellml:units="dimensionless"> 1.0 </cn>
                  <apply>
                    <times/>
                    <ci> p1 </ci>
                    <apply>
                      <exp/>
                      <apply>
                        <divide/>
                        <apply>
                          <times/>
                          <ci> F </ci>
                          <ci> AF1 </ci>
                        </apply>
                        <apply>
                          <times/>
                          <ci> R </ci>
                          <ci> T </ci>
                        </apply>
                      </apply>
                    </apply>
                  </apply>
                </apply>
                <apply>
                  <exp/>
                  <apply>
                    <divide/>
                    <apply>
                      <times/>
                      <cn cellml:units="dimensionless"> 3.0 </cn>
                      <ci> F </ci>
                      <ci> delta_psi_B </ci>
                    </apply>
                    <apply>
                      <times/>
                      <ci> R </ci>
                      <ci> T </ci>
                    </apply>
                  </apply>
                </apply>
              </apply>
              <apply>
                <times/>
                <apply>
                  <plus/>
                  <ci> p2 </ci>
                  <apply>
                    <times/>
                    <ci> p3 </ci>
                    <apply>
                      <exp/>
                      <apply>
                        <divide/>
                        <apply>
                          <times/>
                          <ci> F </ci>
                          <ci> AF1 </ci>
                        </apply>
                        <apply>
                          <times/>
                          <ci> R </ci>
                          <ci> T </ci>
                        </apply>
                      </apply>
                    </apply>
                  </apply>
                </apply>
                <apply>
                  <exp/>
                  <apply>
                    <divide/>
                    <apply>
                      <times/>
                      <cn cellml:units="dimensionless"> 3.0 </cn>
                      <ci> F </ci>
                      <ci> delta_mu_H </ci>
                    </apply>
                    <apply>
                      <times/>
                      <ci> R </ci>
                      <ci> T </ci>
                    </apply>
                  </apply>
                </apply>
              </apply>
            </apply>
          </apply>
        </apply>
      </apply>
      
      <apply id="V_Hu_calculation">
        <eq/>
        <ci> V_Hu </ci>
        <apply>
          <times/>
          <cn cellml:units="dimensionless"> -3.0 </cn>
          <ci> rho_F1 </ci>
          <apply>
            <divide/>
            <apply>
              <minus/>
              <apply>
                <times/>
                <cn cellml:units="dimensionless"> 100.0 </cn>
                <ci> pa </ci>
                <apply>
                  <plus/>
                  <cn cellml:units="dimensionless"> 1.0 </cn>
                  <apply>
                    <exp/>
                    <apply>
                      <divide/>
                      <apply>
                        <times/>
                        <ci> F </ci>
                        <ci> AF1 </ci>
                      </apply>
                      <apply>
                        <times/>
                        <ci> R </ci>
                        <ci> T </ci>
                      </apply>
                    </apply>
                  </apply>
                </apply>
              </apply>
              <apply>
                <times/>
                <apply>
                  <plus/>
                  <ci> pa </ci>
                  <ci> pb </ci>
                </apply>
                <apply>
                  <exp/>
                  <apply>
                    <divide/>
                    <apply>
                      <times/>
                      <cn cellml:units="dimensionless"> 3.0 </cn>
                      <ci> F </ci>
                      <ci> delta_mu_H </ci>
                    </apply>
                    <apply>
                      <times/>
                      <ci> R </ci>
                      <ci> T </ci>
                    </apply>
                  </apply>
                </apply>
              </apply>
            </apply>
            <apply>
              <plus/>
              <apply>
                <times/>
                <apply>
                  <plus/>
                  <cn cellml:units="dimensionless"> 1.0 </cn>
                  <apply>
                    <times/>
                    <ci> p1 </ci>
                    <apply>
                      <exp/>
                      <apply>
                        <divide/>
                        <apply>
                          <times/>
                          <ci> F </ci>
                          <ci> AF1 </ci>
                        </apply>
                        <apply>
                          <times/>
                          <ci> R </ci>
                          <ci> T </ci>
                        </apply>
                      </apply>
                    </apply>
                  </apply>
                </apply>
                <apply>
                  <exp/>
                  <apply>
                    <divide/>
                    <apply>
                      <times/>
                      <cn cellml:units="dimensionless"> 3.0 </cn>
                      <ci> F </ci>
                      <ci> delta_psi_B </ci>
                    </apply>
                    <apply>
                      <times/>
                      <ci> R </ci>
                      <ci> T </ci>
                    </apply>
                  </apply>
                </apply>
              </apply>
              <apply>
                <times/>
                <apply>
                  <plus/>
                  <ci> p2 </ci>
                  <apply>
                    <times/>
                    <ci> p3 </ci>
                    <apply>
                      <exp/>
                      <apply>
                        <divide/>
                        <apply>
                          <times/>
                          <ci> F </ci>
                          <ci> AF1 </ci>
                        </apply>
                        <apply>
                          <times/>
                          <ci> R </ci>
                          <ci> T </ci>
                        </apply>
                      </apply>
                    </apply>
                  </apply>
                </apply>
                <apply>
                  <exp/>
                  <apply>
                    <divide/>
                    <apply>
                      <times/>
                      <cn cellml:units="dimensionless"> 3.0 </cn>
                      <ci> F </ci>
                      <ci> delta_mu_H </ci>
                    </apply>
                    <apply>
                      <times/>
                      <ci> R </ci>
                      <ci> T </ci>
                    </apply>
                  </apply>
                </apply>
              </apply>
            </apply>
          </apply>
        </apply>
      </apply>
      
      <apply id="AF1_calculation">
        <eq/>
        <ci> AF1 </ci>
        <apply>
          <times/>
          <apply>
            <divide/>
            <apply>
              <times/>
              <ci> R </ci>
              <ci> T </ci>
            </apply>
            <ci> F </ci>
          </apply>
          <apply>
            <ln/>
            <apply>
              <times/>
              <ci> KF1 </ci>
              <apply>
                <divide/>
                <ci> ATP_m </ci>
                <apply>
                  <times/>
                  <ci> ADP_m </ci>
                  <ci> Pi </ci>
                </apply>
              </apply>
            </apply>
          </apply>
        </apply>
      </apply>
    </math>
  </component>
  
  <component name="calcium_dynamics">
    <variable units="flux" public_interface="out" name="V_ANT"/>
    <variable units="flux" public_interface="out" name="V_uni"/>
    <variable units="flux" public_interface="out" name="V_NaCa"/>
    
    <variable units="millimolar" public_interface="in" name="ADP_i"/>
    <variable units="millimolar" public_interface="in" name="ATP_i"/>
    <variable units="millimolar" public_interface="in" name="ADP_m"/>
    <variable units="millimolar" public_interface="in" name="ATP_m"/>
    <variable units="micromolar" public_interface="in" name="Ca_i"/>
    <variable units="micromolar" public_interface="in" name="Ca_m"/>
    <variable units="millimolar" public_interface="in" name="Na_i"/>
    <variable units="volt_coulomb_per_mole_kelvin" public_interface="in" name="R"/>
    <variable units="kelvin" public_interface="in" name="T"/>
    <variable units="coulomb_per_mole" public_interface="in" name="F"/>
    <variable units="volt" public_interface="in" name="delta_psi_m"/>
    
    <variable units="dimensionless" name="h" initial_value="0.5"/>
    <variable units="volt" name="delta_psi_0" initial_value="0.091"/>
    <variable units="flux" name="Vmax_ANT" initial_value="0.05"/>
    <variable units="dimensionless" name="L" initial_value="110.0"/> 
    <variable units="dimensionless" name="na" initial_value="2.8"/>
    <variable units="flux" name="Vmax_uni" initial_value="0.000625"/>
    <variable units="micromolar" name="K_act" initial_value="0.38"/>
    <variable units="micromolar" name="K_trans" initial_value="19.0"/>
    <variable units="dimensionless" name="n" initial_value="3.0"/>
    <variable units="flux" name="Vmax_NaCa" initial_value="0.005"/>
    <variable units="millimolar" name="KNa" initial_value="9.4"/>
    <variable units="micromolar" name="KCa" initial_value="3.75E-1"/>
    <variable units="dimensionless" name="b" initial_value="0.5"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply id="V_ANT_calculation">
        <eq/>
        <ci> V_ANT </ci>
        <apply>
          <times/>
          <ci> Vmax_ANT </ci>
          <apply>
            <divide/>
            <apply>
              <minus/>
              <cn cellml:units="dimensionless"> 1.0 </cn>
              <apply>
                <divide/>
                <apply>
                  <times/>
                  <cn cellml:units="dimensionless"> 0.05 </cn>
                  <ci> ATP_i </ci>
                  <cn cellml:units="dimensionless"> 0.45 </cn>
                  <cn cellml:units="dimensionless"> 0.8 </cn>
                  <ci> ADP_m </ci>
                </apply>
                <apply>
                  <times/>
                  <cn cellml:units="dimensionless"> 0.45 </cn>
                  <ci> ADP_i </ci>
                  <cn cellml:units="dimensionless"> 0.05 </cn>
                  <ci> ATP_m </ci>
                </apply>
              </apply>
            </apply>
            <apply>
              <times/>
              <apply>
                <plus/>
                <cn cellml:units="dimensionless"> 1.0 </cn>
                <apply>
                  <times/>
                  <apply>
                    <divide/>
                    <apply>
                      <times/>
                      <cn cellml:units="dimensionless"> 0.05 </cn>
                      <ci> ATP_i </ci>
                    </apply>
                    <apply>
                      <times/>
                      <cn cellml:units="dimensionless"> 0.45 </cn>
                      <ci> ADP_i </ci>
                    </apply>
                  </apply>
                  <apply>
                    <exp/>
                    <apply>
                      <divide/>
                      <apply>
                        <times/>
                        <apply>
                          <minus/>
                          <ci> h </ci>
                        </apply>
                        <ci> F </ci>
                        <ci> delta_psi_0 </ci>
                      </apply>
                      <apply>
                        <times/>
                        <ci> R </ci>
                        <ci> T </ci>
                      </apply>
                    </apply>
                  </apply>
                </apply>
              </apply>
              <apply>
                <plus/>
                <cn cellml:units="dimensionless"> 1.0 </cn>
                <apply>
                  <divide/>
                  <apply>
                    <times/>
                    <cn cellml:units="dimensionless"> 0.45 </cn>
                    <cn cellml:units="dimensionless"> 0.8 </cn>
                    <ci> ADP_m </ci>
                  </apply>
                  <apply>
                    <times/>
                    <cn cellml:units="dimensionless"> 0.05 </cn>
                    <ci> ATP_m </ci>
                  </apply>
                </apply>
              </apply>
            </apply>
          </apply>
        </apply>
      </apply>
    
      <apply id="V_uni_calculation">
        <eq/>
        <ci> V_uni </ci>
        <apply>
          <times/>
          <ci> Vmax_uni </ci>
          <apply>
            <divide/>
            <apply>
              <times/>
              <apply>
                <divide/>
                <ci> Ca_i </ci>
                <ci> K_trans </ci>
              </apply>
			  <apply>
                <power/>
                <apply>
                  <plus/>
                  <cn cellml:units="dimensionless"> 1.0 </cn>
                  <apply>
                    <divide/>
                    <ci> Ca_i </ci>
                    <ci> K_trans </ci>
                  </apply>
				</apply>
				<cn cellml:units="dimensionless"> 3.0 </cn>
              </apply>
              <apply>
                <divide/>
                <apply>
                  <times/>
                  <cn cellml:units="dimensionless"> 2.0 </cn>
                  <ci> F </ci>
                  <apply>
                    <minus/>
                    <ci> delta_psi_m </ci>
                    <ci> delta_psi_0 </ci>
                  </apply>
                </apply>
                <apply>
                  <times/>
                  <ci> R </ci>
                  <ci> T </ci>
                </apply>
              </apply>
            </apply>
            <apply>
              <plus/>
              <apply>
                <power/>
                <apply>
                  <plus/>
                  <cn cellml:units="dimensionless"> 1.0 </cn>
                  <apply>
                    <divide/>
                    <ci> Ca_i </ci>
                    <ci> K_trans </ci>
                  </apply>
                </apply>
                <cn cellml:units="dimensionless"> 4.0 </cn>
              </apply>
              <apply>
                <times/>
                <apply>
                  <divide/>
                  <ci> L </ci>
                  <apply>
                    <power/>
                    <apply>
                      <plus/>
                      <cn cellml:units="dimensionless"> 1.0 </cn>
                      <apply>
                        <divide/>
                        <ci> Ca_i </ci>
                        <ci> K_act </ci>
                      </apply>
                    </apply>
                    <ci> na </ci>
                  </apply>
                </apply>
                <apply>
                  <minus/>
                  <cn cellml:units="dimensionless"> 1.0 </cn>
                  <apply>
                    <exp/>
                    <apply>
                      <divide/>
                      <apply>
                        <times/>
                        <cn cellml:units="dimensionless"> -2.0 </cn>
                        <ci> F </ci>
                        <apply>
                          <minus/>
                          <ci> delta_psi_m </ci>
                          <ci> delta_psi_0 </ci>
                        </apply>
                      </apply>
                      <apply>
                        <times/>
                        <ci> R </ci>
                        <ci> T </ci>
                      </apply>
                    </apply>
                  </apply>
                </apply>
              </apply>
            </apply>
          </apply>
        </apply>
      </apply>
    
      <apply id="V_NaCa_calculation">
        <eq/>
        <ci> V_NaCa </ci>
        <apply>
          <times/>
          <ci> Vmax_NaCa </ci>
          <apply>
            <divide/>
            <apply>
              <times/>
              <apply>
                <exp/>
                <apply>
                  <divide/>
                  <apply>
                    <times/>
                    <ci> b </ci>
                    <ci> F </ci>
                    <apply>
                      <minus/>
                      <ci> delta_psi_m </ci>
                      <ci> delta_psi_0 </ci>
                    </apply>
                  </apply>
                  <apply>
                    <times/>
                    <ci> R </ci>
                    <ci> T </ci>
                  </apply>
                </apply>
              </apply>
              <apply>
                <exp/>
                <apply>
                  <ln/>
                  <apply>
                    <divide/>
                    <ci> Ca_i </ci>
                    <ci> Ca_m </ci>
                  </apply>
                </apply>
              </apply>
            </apply>
            <apply>
              <times/>
              <apply>
                <power/>
                <apply>
                  <plus/>
                  <cn cellml:units="dimensionless"> 1.0 </cn>
                  <apply>
                    <divide/>
                    <ci> KNa </ci>
                    <ci> Na_i </ci>
                  </apply>
                </apply>
                <ci> n </ci>
              </apply>
              <apply>
                <plus/>
                <cn cellml:units="dimensionless"> 1.0 </cn>
                <apply>
                  <divide/>
                  <ci> KCa </ci>
                  <ci> Ca_m </ci>
                </apply>
              </apply>
            </apply>
          </apply>
        </apply>
      </apply>
    </math>
  </component>
  
  <connection>
    <map_components component_2="oxidative_phosphorylation" component_1="ADP_m"/>
    <map_variables variable_2="ADP_m" variable_1="ADP_m"/>
    <map_variables variable_2="V_ATPase" variable_1="V_ATPase"/>
  </connection>
  
  <connection>
    <map_components component_2="calcium_dynamics" component_1="ADP_m"/>
    <map_variables variable_2="ADP_m" variable_1="ADP_m"/>
    <map_variables variable_2="V_ANT" variable_1="V_ANT"/>
  </connection>
  
  <connection>
    <map_components component_2="V_SL" component_1="ADP_m"/>
    <map_variables variable_2="ADP_m" variable_1="ADP_m"/>
    <map_variables variable_2="V_SL" variable_1="V_SL"/>
  </connection>
  
  <connection>
    <map_components component_2="oxidative_phosphorylation" component_1="NADH"/>
    <map_variables variable_2="NADH" variable_1="NADH"/>
    <map_variables variable_2="V_O2" variable_1="V_O2"/>
  </connection>
  
  <connection>
    <map_components component_2="V_IDH" component_1="NADH"/>
    <map_variables variable_2="NADH" variable_1="NADH"/>
    <map_variables variable_2="V_IDH" variable_1="V_IDH"/>
  </connection>
  
  <connection>
    <map_components component_2="V_KGDH" component_1="NADH"/>
    <map_variables variable_2="V_KGDH" variable_1="V_KGDH"/>
  </connection>
  
  <connection>
    <map_components component_2="V_MDH" component_1="NADH"/>
    <map_variables variable_2="V_MDH" variable_1="V_MDH"/>
  </connection>
  
  <connection>
    <map_components component_2="V_ACO" component_1="ISOC"/>
    <map_variables variable_2="ISOC" variable_1="ISOC"/>
    <map_variables variable_2="V_ACO" variable_1="V_ACO"/>
  </connection>
  
  <connection>
    <map_components component_2="V_IDH" component_1="ISOC"/>
    <map_variables variable_2="ISOC" variable_1="ISOC"/>
    <map_variables variable_2="V_IDH" variable_1="V_IDH"/>
  </connection>
  
  <connection>
    <map_components component_2="V_IDH" component_1="alpha_KG"/>
    <map_variables variable_2="V_IDH" variable_1="V_IDH"/>
  </connection>
  
  <connection>
    <map_components component_2="V_KGDH" component_1="alpha_KG"/>
    <map_variables variable_2="alpha_KG" variable_1="alpha_KG"/>
    <map_variables variable_2="V_KGDH" variable_1="V_KGDH"/>
  </connection>
  
  <connection>
    <map_components component_2="V_AAT" component_1="alpha_KG"/>
    <map_variables variable_2="alpha_KG" variable_1="alpha_KG"/>
    <map_variables variable_2="V_AAT" variable_1="V_AAT"/>
  </connection>
  
  <connection>
    <map_components component_2="V_KGDH" component_1="SCoA"/>
    <map_variables variable_2="V_KGDH" variable_1="V_KGDH"/>
  </connection>
  
  <connection>
    <map_components component_2="V_SL" component_1="SCoA"/>
    <map_variables variable_2="SCoA" variable_1="SCoA"/>
    <map_variables variable_2="V_SL" variable_1="V_SL"/>
  </connection>
  
  <connection>
    <map_components component_2="V_SL" component_1="Suc"/>
    <map_variables variable_2="Suc" variable_1="Suc"/>
    <map_variables variable_2="V_SL" variable_1="V_SL"/>
  </connection>
  
  <connection>
    <map_components component_2="V_SDH" component_1="Suc"/>
    <map_variables variable_2="Suc" variable_1="Suc"/>
    <map_variables variable_2="V_SDH" variable_1="V_SDH"/>
  </connection>
  
  <connection>
    <map_components component_2="V_SDH" component_1="FUM"/>
    <map_variables variable_2="FUM" variable_1="FUM"/>
    <map_variables variable_2="V_SDH" variable_1="V_SDH"/>
  </connection>
  
  <connection>
    <map_components component_2="V_FH" component_1="FUM"/>
    <map_variables variable_2="FUM" variable_1="FUM"/>
    <map_variables variable_2="V_FH" variable_1="V_FH"/>
  </connection>
  
  <connection>
    <map_components component_2="V_FH" component_1="MAL"/>
    <map_variables variable_2="MAL" variable_1="MAL"/>
    <map_variables variable_2="V_FH" variable_1="V_FH"/>
  </connection>
  
  <connection>
    <map_components component_2="V_MDH" component_1="MAL"/>
    <map_variables variable_2="MAL" variable_1="MAL"/>
    <map_variables variable_2="V_MDH" variable_1="V_MDH"/>
  </connection>
  
  <connection>
    <map_components component_2="V_MDH" component_1="OAA"/>
    <map_variables variable_2="OAA" variable_1="OAA"/>
    <map_variables variable_2="V_MDH" variable_1="V_MDH"/>
  </connection>
  
  <connection>
    <map_components component_2="V_CS" component_1="OAA"/>
    <map_variables variable_2="OAA" variable_1="OAA"/>
    <map_variables variable_2="V_CS" variable_1="V_CS"/>
  </connection>
  
  <connection>
    <map_components component_2="V_AAT" component_1="OAA"/>
    <map_variables variable_2="OAA" variable_1="OAA"/>
    <map_variables variable_2="V_AAT" variable_1="V_AAT"/>
  </connection>
  
  <connection>
    <map_components component_2="V_AAT" component_1="ASP"/>
    <map_variables variable_2="ASP" variable_1="ASP"/>
    <map_variables variable_2="V_AAT" variable_1="V_AAT"/>
  </connection>
  
  <connection>
    <map_components component_2="V_C_ASP" component_1="ASP"/>
    <map_variables variable_2="ASP" variable_1="ASP"/>
    <map_variables variable_2="V_C_ASP" variable_1="V_C_ASP"/>
  </connection>
  
  <connection>
    <map_components component_2="calcium_dynamics" component_1="Ca_m"/>
    <map_variables variable_2="Ca_m" variable_1="Ca_m"/>
    <map_variables variable_2="V_uni" variable_1="V_uni"/>
    <map_variables variable_2="V_NaCa" variable_1="V_NaCa"/>
  </connection>
  
  <connection>
    <map_components component_2="V_CS" component_1="AcCoA"/>
    <map_variables variable_2="AcCoA" variable_1="AcCoA"/>
  </connection>
  
  <connection>
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