Rendering of the source text

<?xml version='1.0' encoding='utf-8'?>
<!--  FILE :  mitochondria_and_Ca_signaling_2001.xml

CREATED :  14th January 2002

LAST MODIFIED : 12th August 2003

AUTHOR :  Catherine Lloyd
          Department of Engineering Science
          The University of Auckland
          
MODEL STATUS :  This model conforms to the CellML 1.0 Specification released on
10th August 2001, and the 16/01/2002 CellML Metadata 1.0 Specification.

DESCRIPTION :  This file contains a CellML description of Fall and Keizer's
2001 model of mitochondrial modulation of intracellular Ca2+ signaling.

CHANGES:  
  21/01/2002 - AAC - Updated metadata to conform to the 16/1/02 CellML Metadata
                     1.0 Specification.
  26/02/2002 - CML - Corrected several equations.
  01/03/2002 - CML - Corrected units.
  22/07/2002 - CML - Added more metadata.
  09/04/2003 - AAC - Added publication date information. 
  12/08/2003 - CML - Corrected equations. 
--><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="fall_keizer_2001_version01" name="fall_keizer_2001_version01">
<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
  <articleinfo>
  <title>Mitochondria And Ca2+ Signalling</title>
  <author>
    <firstname>Catherine</firstname>
          <surname>Lloyd</surname>
    <affiliation>
      <shortaffil>Bioengineering Institute, University of Auckland</shortaffil>
    </affiliation>
  </author>
</articleinfo>
  <section id="sec_status">
    <title>Model Status</title>
    <para>
            This is the original unchecked version of the model imported from the previous
            CellML model repository, 24-Jan-2006.
          </para>
  </section>
  <sect1 id="sec_structure">
<title>Model Structure</title>

<para>
In 2001 Christopher Fall and Joel Keizer published a detailed mathematical model to describe mitochondrial function and mitochondrial Ca<superscript>2+</superscript> handling coupled to endoplasmic reticulum (ER) based IP3-dependent Ca<superscript>2+</superscript> release.  Their aim was to create a biologically realistic model of the influence of mitochondria on IP3-mediated Ca<superscript>2+</superscript> signaling.  They aimed to integrate the separate <ulink url="${HTML_EXMPL_IP3_CA2+_MODEL}">IP3 receptor/channel (DeYoung-Keizer 1992)</ulink> and <ulink url="${HTML_EXMPL_MITOCHONDRIAL_CA_HANDLING}">mitochondrial Ca<superscript>2+</superscript> handling (Magnus-Keizer 1997, 1998)</ulink> models into a single, common framework (see <xref linkend="fig_cell_diagram"/> below).
</para>

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

<para>
<ulink url="http://www.sciencedirect.com/science?_ob=ArticleURL&amp;_udi=B6WMD-457VD48-2X&amp;_user=140507&amp;_coverDate=05%2F21%2F2001&amp;_alid=187119092&amp;_rdoc=1&amp;_fmt=summary&amp;_orig=search&amp;_qd=1&amp;_cdi=6932&amp;_sort=d&amp;_docanchor=&amp;view=c&amp;_acct=C000011498&amp;_version=1&amp;_urlVersion=0&amp;_userid=140507&amp;md5=c1b4b6377cc0e91c539a5f2046bd18e0">Mitochondrial Modulation of Intracellular Ca<superscript>2+</superscript> Signaling</ulink>, Christopher P. Fall and Joel E. Keizer, 2001, <ulink url="http://www.sciencedirect.com/science?_ob=JournalURL&amp;_cdi=6932&amp;_auth=y&amp;_acct=C000011498&amp;_version=1&amp;_urlVersion=0&amp;_userid=140507&amp;md5=c8e64d20ff203cda2255f4b6b7affe4f">
            <emphasis>J. theor. Biol.</emphasis>
          </ulink>, 210, 151-165.  (A <ulink url="http://www.sciencedirect.com/science?_ob=ArticleURL&amp;_udi=B6WMD-457VD48-2X&amp;_coverDate=05%2F21%2F2001&amp;_alid=187119092&amp;_rdoc=1&amp;_fmt=&amp;_orig=search&amp;_qd=1&amp;_cdi=6932&amp;_sort=d&amp;view=c&amp;_acct=C000011498&amp;_version=1&amp;_urlVersion=0&amp;_userid=140507&amp;md5=c6160e53309599f9017868cecfd56646">full text (html) </ulink> and PDF versions of the article are available to subscribers on the Science Direct website.)  <ulink url="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&amp;db=PubMed&amp;list_uids=11371172&amp;dopt=Abstract">PubMed ID: 11371172</ulink>
</para>

<para>
The raw CellML description of the mitochondria and Ca<superscript>2+</superscript> signaling model can be downloaded in various formats as described in <xref linkend="sec_download_this_model"/>.  For an example of a more complete documentation for an electrophysiological model, see <ulink url="${HTML_EXMPL_HHSA_INTRO}">The Hodgkin-Huxley Squid Axon Model, 1952</ulink>. 
</para>

<informalfigure float="0" id="fig_cell_diagram">
<mediaobject>
  <imageobject>
    <objectinfo>
      <title>diagram of the mitochondria and Ca2+ signaling model</title>
    </objectinfo>
    <imagedata fileref="fall_2001.png"/>
  </imageobject>
</mediaobject>
<caption>Key components of the IP3-mediated intracellular Ca<superscript>2+</superscript> signaling diagram shows endoplasmic reticulum based Ca<superscript>2+</superscript> release and uptake mechanisms, mitochondrial Ca<superscript>2+</superscript> release and uptake mechanisms, in addition to other components which are not included in the mathematical model.</caption>
</informalfigure>

<informalfigure float="0" id="fig_cellml_rendering">
<mediaobject>
  <imageobject>
    <objectinfo>
      <title>the cellml rendering of the mitochondria and Ca2+ signaling model</title>
    </objectinfo>
    <imagedata fileref="cellml_rendering.gif"/>
  </imageobject>
</mediaobject>
<caption>The network defined in the CellML description of the mitochondria and Ca<superscript>2+</superscript> signaling model.</caption>
</informalfigure>

</sect1>
</article>
</documentation>
  
  
  <!--
    Below, we define some additional units for association with variables and
    constants within the model. The identifiers are fairly self-explanatory.
  -->
  
  <units name="minute">
    <unit units="second" multiplier="60.0"/>
  </units>
  
  <units name="per_second">
    <unit units="second" exponent="-1"/>
  </units>
  
  <units name="millivolt">
    <unit units="volt" prefix="milli"/>
  </units>
  
  <units name="millimolar">
    <unit units="mole" prefix="milli"/>
    <unit units="litre" exponent="-1"/>
  </units>
  
  <units name="per_millimolar">
    <unit units="millimolar" exponent="-1"/>
  </units>
  
  <units name="micromolar">
    <unit units="mole" prefix="micro"/>
    <unit units="litre" exponent="-1"/>
  </units>
  
  <units name="nanomolar">
    <unit units="mole" prefix="nano"/>
    <unit units="litre" exponent="-1"/>
  </units>
  
  <units name="nanomole_per_mg">
    <unit units="mole" prefix="nano"/>
    <unit units="gram" prefix="milli" exponent="-1"/>
  </units>
  
  <units name="nanomole_per_minute_per_mg">
    <unit units="mole" prefix="nano"/>
    <unit units="minute" exponent="-1"/>
    <unit units="gram" prefix="milli" exponent="-1"/>
  </units>
  
  <units name="nanomole_per_minute_per_millimolar">
    <unit units="mole" prefix="nano"/>
    <unit units="minute" exponent="-1"/>
    <unit units="millimolar" exponent="-1"/>
  </units>
  
  <units name="milligram">
    <unit units="gram" prefix="milli"/>
  </units>
  
  <units name="millilitre">
    <unit units="litre" prefix="milli"/>
  </units>
  
  <units name="capacitance_units">
    <unit units="mole" prefix="nano"/>
    <unit units="millivolt" exponent="-1"/>
    <unit units="gram" prefix="milli" exponent="-1"/>
  </units>
  
  <units name="conductance_units">
    <unit units="mole" prefix="nano"/>
    <unit units="minute" exponent="-1"/>
    <unit units="millivolt" exponent="-1"/>
    <unit units="gram" prefix="milli" exponent="-1"/>
  </units>
  
  <units name="millijoule_per_mole_kelvin">
    <unit units="joule" prefix="milli"/>
    <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>
  
  <!--
    The "environment" component is used to declare variables that are used by
    all or most of the other components, in this case just "time".
  -->
  <component name="environment">
    <variable units="minute" public_interface="out" name="time"/>
  </component>
  
  <!--
    The "membrane" component is really the `root' node of our model.
  -->
  <component name="membrane">
    <variable units="millivolt" public_interface="out" name="V"/>
    <variable units="millivolt" public_interface="out" name="V_B" initial_value="50.0"/>
    <variable units="millijoule_per_mole_kelvin" public_interface="out" name="R" initial_value="8314.0"/>
    <variable units="kelvin" public_interface="out" name="T" initial_value="310.0"/>
    <variable units="coulomb_per_mole" public_interface="out" name="F" initial_value="96845.0"/>
    <variable units="dimensionless" public_interface="out" name="delta_pH" initial_value="-0.4"/>
    <variable units="nanomole_per_minute_per_mg" public_interface="out" name="proton_motive_force"/>
    <variable units="conductance_units" public_interface="out" name="g_H" initial_value="0.2"/>
    
    <variable units="capacitance_units" name="C" initial_value="0.00145"/>
    <variable units="dimensionless" name="pH_i"/>
    <variable units="dimensionless" name="pH_m"/>
    
    <variable units="nanomole_per_minute_per_mg" public_interface="in" name="JH_res"/>
    <variable units="nanomole_per_minute_per_mg" public_interface="in" name="JH_leak"/>
    <variable units="nanomole_per_minute_per_mg" public_interface="in" name="JH_F1"/>
    <variable units="nanomole_per_minute_per_mg" public_interface="in" name="J_ant"/>
    <variable units="nanomole_per_minute_per_mg" public_interface="in" name="J_uni"/>
    <variable units="minute" public_interface="in" name="time"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML">
    
    <apply id="membrane_voltage_diff_eq">
        <eq/>
        <apply>
          <diff/>
          <bvar>
            <ci> time </ci>
          </bvar>
          <ci> V </ci>
        </apply>
        <apply>
          <times/>
          <apply>
            <divide/>
            <cn cellml:units="dimensionless"> -1.0 </cn>
            <ci> C </ci>
          </apply>
          <apply>
            <minus/>
            <apply>
              <plus/>
              <ci> JH_F1 </ci>
              <ci> J_ant </ci>
              <ci> JH_leak </ci>
              <apply>
                <times/>
                <ci> J_uni </ci>
                <cn cellml:units="dimensionless"> 2.0 </cn>
              </apply>
            </apply>
            <ci> JH_res </ci>
          </apply>
        </apply>
      </apply>
      
      <apply id="delta_pH_calculation">
        <eq/>
        <ci> delta_pH </ci>
        <apply>
          <minus/>
          <ci> pH_i </ci>
          <ci> pH_m </ci>
        </apply>
      </apply>
      
      <apply id="proton_motive_force_calculation">
        <eq/>
        <ci> proton_motive_force </ci>
        <apply>
          <minus/>
          <ci> V </ci>
          <apply>
            <times/>
            <apply>
              <divide/>
              <apply>
                <times/>
                <cn cellml:units="dimensionless"> 2.303 </cn>
                <ci> R </ci>
                <ci> T </ci>
              </apply>
              <ci> F </ci>
            </apply>
            <ci> delta_pH </ci>
          </apply>
        </apply>
      </apply>
    </math>
  </component>
  
  <!--  Mitochondrial Ca2+ handling components. -->
  
  <component name="Ca_uniporter">
    <variable units="nanomole_per_minute_per_mg" public_interface="out" name="J_uni"/>
    <variable units="millivolt" public_interface="out" name="V_offset" initial_value="91.0"/>
    
    <variable units="nanomole_per_minute_per_mg" name="Jmax_uni" initial_value="300.0"/>
    <variable units="micromolar" name="K_trans" initial_value="19.0"/>
    <variable units="micromolar" name="K_act" initial_value="0.38"/>
    <variable units="dimensionless" name="L" initial_value="110.0"/>
    <variable units="dimensionless" name="na" initial_value="2.8"/>
    
    <variable units="nanomolar" public_interface="in" name="Ca_i"/>
    <variable units="millijoule_per_mole_kelvin" public_interface="in" name="R"/>
    <variable units="coulomb_per_mole" public_interface="in" name="F"/>
    <variable units="kelvin" public_interface="in" name="T"/>
    <variable units="millivolt" public_interface="in" name="V"/>
    <variable units="minute" public_interface="in" name="time"/>      
  
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply id="J_uni_calculation">
        <eq/>
        <ci> J_uni </ci>
        <apply>
          <times/>
          <ci> Jmax_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>
            <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>
                <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>
          </apply>
          <apply>
            <divide/>
            <apply>
              <divide/>
              <apply>
                <times/>
                <cn cellml:units="dimensionless"> 2.0 </cn>
                <ci> F </ci>
                <apply>
                  <minus/>
                  <ci> V </ci>
                  <ci> V_offset </ci>
                </apply>
              </apply>
              <apply>
                <times/>
                <ci> R </ci>
                <ci> T </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> V </ci>
                      <ci> V_offset </ci>
                    </apply>
                  </apply>
                  <apply>
                    <times/>
                    <ci> R </ci>
                    <ci> T </ci>
                  </apply>
                </apply>
              </apply>
            </apply>
          </apply>
        </apply>
      </apply>
    </math>
  </component>
  
  <component name="Na_Ca_exchanger">
    <variable units="nanomole_per_mg" public_interface="out" name="K_Ca" initial_value="0.003"/>
    <variable units="nanomole_per_minute_per_mg" public_interface="out" name="J_Na_Ca"/>
    
    <variable units="nanomole_per_minute_per_mg" name="Jmax_Na_Ca" initial_value="25.0"/>
    <variable units="millimolar" name="Na_i" initial_value="30.0"/>
    <variable units="millimolar" name="K_Na" initial_value="9.4"/>
    <variable units="dimensionless" name="b" initial_value="0.0"/>
    <variable units="dimensionless" name="n" initial_value="2.0"/>
    
    <variable units="nanomolar" public_interface="in" name="Ca_m"/>
    <variable units="millivolt" public_interface="in" name="V_offset"/>
    <variable units="millijoule_per_mole_kelvin" public_interface="in" name="R"/>
    <variable units="coulomb_per_mole" public_interface="in" name="F"/>
    <variable units="kelvin" public_interface="in" name="T"/>
    <variable units="millivolt" public_interface="in" name="V"/>
    <variable units="minute" public_interface="in" name="time"/>      
  
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply id="J_Na_Ca_calculation">
        <eq/>
        <ci> J_Na_Ca </ci>
        <apply>
          <times/>
          <ci> Jmax_Na_Ca </ci>
          <apply>
            <divide/>
            <apply>
              <exp/>
              <apply>
                <divide/>
                <apply>
                  <times/>
                  <ci> b </ci>
                  <ci> F </ci>
                  <apply>
                    <minus/>
                    <ci> V </ci>
                    <ci> V_offset </ci>
                  </apply>
                </apply>
                <apply>
                  <times/>
                  <ci> R </ci>
                  <ci> T </ci>
                </apply>
              </apply>
            </apply>
            <apply>
              <times/>
              <apply>
                <power/>
                <apply>
                  <plus/>
                  <cn cellml:units="dimensionless"> 1.0 </cn>
                  <apply>
                    <divide/>
                    <ci> K_Na </ci>
                    <ci> Na_i </ci>
                  </apply>
                </apply>
                <ci> n </ci>
              </apply>
              <apply>
                <plus/>
                <cn cellml:units="dimensionless"> 1.0 </cn>
                <apply>
                  <divide/>
                  <ci> K_Ca </ci>
                  <ci> Ca_m </ci>
                </apply>
              </apply>
            </apply>
          </apply>
        </apply>
      </apply>
    </math>
  </component>
  
  <!--  Mitochondrial components that do not transport Ca2+. -->
  
  <component name="proton_pump">
    <variable units="nanomole_per_minute_per_mg" public_interface="out" name="JH_res"/>
    <variable units="nanomole_per_minute_per_mg" public_interface="out" name="Jo"/>
    
    <variable units="dimensionless" name="A_res"/>
    <variable units="millimolar" name="K_res" initial_value="13500000000000000.0"/>
    <variable units="nanomole_per_mg" name="rho_res" initial_value="0.4"/>
    <variable units="dimensionless" name="r1" initial_value="0.000000000000000002077"/>
    <variable units="dimensionless" name="r2" initial_value="0.000000001728"/>
    <variable units="dimensionless" name="r3" initial_value="0.00000000000000000000000001059"/>
    <variable units="per_second" name="ra" initial_value="0.0000000006394"/>
    <variable units="per_second" name="rb" initial_value="0.0000000000001762"/>
    <variable units="per_second" name="rc1" initial_value="0.0000000000000000002656"/>
    <variable units="per_second" name="rc2" initial_value="0.000000000000000000000000008632"/>
    <variable units="dimensionless" name="g" initial_value="0.85"/>
    
    <variable units="dimensionless" public_interface="in" name="delta_pH"/>
    <variable units="nanomolar" public_interface="in" name="NAD_m"/>
    <variable units="nanomolar" public_interface="in" name="NADH_m"/>
    <variable units="millijoule_per_mole_kelvin" public_interface="in" name="R"/>
    <variable units="coulomb_per_mole" public_interface="in" name="F"/>
    <variable units="kelvin" public_interface="in" name="T"/>
    <variable units="millivolt" public_interface="in" name="V"/>
    <variable units="millivolt" public_interface="in" name="V_B"/>
    <variable units="minute" public_interface="in" name="time"/>  
    
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply id="JH_res_calculation">
        <eq/>
        <ci> JH_res </ci>
        <apply>
          <times/>
          <cn cellml:units="dimensionless"> 360.0 </cn>
          <ci> rho_res </ci>
          <apply>
            <divide/>
            <apply>
              <minus/>
              <apply>
                <plus/>
                <apply>
                  <times/>
                  <ci> ra </ci>
                  <apply>
                    <power/>
                    <cn cellml:units="dimensionless"> 10.0 </cn>
                    <apply>
                      <times/>
                      <cn cellml:units="dimensionless"> 6.0 </cn>
                      <ci> delta_pH </ci>
                    </apply>
                  </apply>
                  <apply>
                    <exp/>
                    <apply>
                      <divide/>
                      <apply>
                        <times/>
                        <ci> F </ci>
                        <ci> A_res </ci>
                      </apply>
                      <apply>
                        <times/>
                        <ci> R </ci>
                        <ci> T </ci>
                      </apply>
                    </apply>
                  </apply>
                </apply>
                <apply>
                  <times/>
                  <ci> rb </ci>
                  <apply>
                    <power/>
                    <cn cellml:units="dimensionless"> 10.0 </cn>
                    <apply>
                      <times/>
                      <cn cellml:units="dimensionless"> 6.0 </cn>
                      <ci> delta_pH </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> V </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> A_res </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> V_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> A_res </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> V </ci>
                    </apply>
                    <apply>
                      <times/>
                      <ci> R </ci>
                      <ci> T </ci>
                    </apply>
                  </apply>
                </apply>
              </apply>
            </apply>
          </apply>
        </apply>
      </apply>
      
      <apply id="Jo_calculation">
        <eq/>
        <ci> Jo </ci>
        <apply>
          <times/>
          <cn cellml:units="dimensionless"> 30.0 </cn>
          <ci> rho_res </ci>
          <apply>
            <divide/>
            <apply>
              <plus/>
              <apply>
                <minus/>
                <apply>
                  <times/>
                  <apply>
                    <plus/>
                    <apply>
                      <times/>
                      <ci> ra </ci>
                      <apply>
                        <power/>
                        <cn cellml:units="dimensionless"> 10.0 </cn>
                        <apply>
                          <times/>
                          <cn cellml:units="dimensionless"> 6.0 </cn>
                          <ci> delta_pH </ci>
                        </apply>
                      </apply>
                    </apply>
                    <apply>
                      <times/>
                      <ci> rc1 </ci>
                      <apply>
                        <exp/>
                        <apply>
                          <divide/>
                          <apply>
                            <times/>
                            <cn cellml:units="dimensionless"> 6.0 </cn>
                            <ci> F </ci>
                            <ci> V_B </ci>
                          </apply>
                          <apply>
                            <times/>
                            <ci> R </ci>
                            <ci> T </ci>
                          </apply>
                        </apply>
                      </apply>
                    </apply>
                  </apply>
                  <apply>
                    <exp/>
                    <apply>
                      <divide/>
                      <apply>
                        <times/>
                        <ci> F </ci>
                        <ci> A_res </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> V </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> F </ci>
                      <ci> A_res </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> V </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> A_res </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> V_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> A_res </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> V </ci>
                    </apply>
                    <apply>
                      <times/>
                      <ci> R </ci>
                      <ci> T </ci>
                    </apply>
                  </apply>
                </apply>
              </apply>
            </apply>
          </apply>
        </apply>
      </apply>        
     
      <apply id="A_res_calculation">
        <eq/>
        <ci> A_res </ci>
        <apply>
          <times/>
          <apply>
            <divide/>
            <apply>
              <times/>
              <ci> R </ci>
              <ci> T </ci>
            </apply>
            <ci> F </ci>
          </apply>
          <apply>
            <ln/>
            <apply>
              <divide/>
              <apply>
                <times/>
                <ci> K_res </ci>
                <apply>
                  <root/>
                  <ci> NADH_m </ci>
                </apply>
              </apply>
              <apply>
                <root/>
                <ci> NAD_m </ci>
              </apply>
            </apply>
          </apply>
        </apply>
      </apply>
    </math>
  </component>
  
  <component name="proton_leak">
    <variable units="nanomole_per_minute_per_mg" public_interface="out" name="JH_leak"/>
    
    <variable units="conductance_units" public_interface="in" name="g_H"/>
    <variable units="nanomole_per_minute_per_mg" public_interface="in" name="proton_motive_force"/>
    <variable units="minute" public_interface="in" name="time"/>  
    
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply id="JH_leak_calculation">
        <eq/>
        <ci> JH_leak </ci>   
        <apply>
          <times/>
          <ci> g_H </ci>
          <ci> proton_motive_force </ci>
        </apply>
      </apply>
    </math>
  </component>  
  
  <component name="F0_F1_ATPase">
    <variable units="nanomole_per_minute_per_mg" public_interface="out" name="JH_F1"/>
    <variable units="nanomole_per_minute_per_mg" public_interface="out" name="Jp_F1"/>
    
    <variable units="nanomole_per_mg" name="rho_F1" initial_value="0.7"/>
    <variable units="millimolar" name="K_F1" initial_value="1710000.0"/>
    <variable units="dimensionless" name="A_F1"/>
    <variable units="nanomolar" name="ADP_m_free"/>
    <variable units="millimolar" name="Pi_m" initial_value="20.0"/>
    <variable units="dimensionless" name="p1" initial_value="0.00000001346"/>
    <variable units="dimensionless" name="p2" initial_value="0.0000007739"/>
    <variable units="dimensionless" name="p3" initial_value="0.00000000000000665"/>
    <variable units="per_second" name="pa" initial_value="0.00001656"/>
    <variable units="per_second" name="pb" initial_value="0.0000003373"/>
    <variable units="per_second" name="pc1" initial_value="0.00000000000009651"/>
    <variable units="per_second" name="pc2" initial_value="0.0000000000000000004845"/>
    
    <variable units="nanomolar" public_interface="in" name="ATP_m"/>
    <variable units="nanomolar" public_interface="in" name="ADP_m"/> 
    <variable units="dimensionless" public_interface="in" name="delta_pH"/>    
    <variable units="millijoule_per_mole_kelvin" public_interface="in" name="R"/>
    <variable units="coulomb_per_mole" public_interface="in" name="F"/>
    <variable units="kelvin" public_interface="in" name="T"/>
    <variable units="millivolt" public_interface="in" name="V"/>
    <variable units="millivolt" public_interface="in" name="V_B"/>
    <variable units="minute" public_interface="in" name="time"/>     
    
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply id="JH_F1_calculation">
        <eq/>
        <ci> JH_F1 </ci>
        <apply>
          <times/>
          <cn cellml:units="dimensionless"> -180.0 </cn>
          <ci> rho_F1 </ci>
          <apply>
            <divide/>
            <apply>
              <minus/>
              <apply>
                <plus/>
                <apply>
                  <times/>
                  <ci> pa </ci>
                  <apply>
                    <power/>
                    <cn cellml:units="dimensionless"> 10.0 </cn>
                    <apply>
                      <times/>
                      <cn cellml:units="dimensionless"> 3.0 </cn>
                      <ci> delta_pH </ci>
                    </apply>
                  </apply>
                  <apply>
                    <exp/>
                    <apply>
                      <divide/>
                      <apply>
                        <times/>
                        <ci> F </ci>
                        <ci> A_F1 </ci>
                      </apply>
                      <apply>
                        <times/>
                        <ci> R </ci>
                        <ci> T </ci>
                      </apply>
                    </apply>
                  </apply>
                </apply>
                <apply>
                  <times/>
                  <ci> pb </ci>
                  <apply>
                    <power/>
                    <cn cellml:units="dimensionless"> 10.0 </cn>
                    <apply>
                      <times/>
                      <cn cellml:units="dimensionless"> 3.0 </cn>
                      <ci> delta_pH </ci>
                    </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> V </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> A_F1 </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> V_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> A_F1 </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> V </ci>
                    </apply>
                    <apply>
                      <times/>
                      <ci> R </ci>
                      <ci> T </ci>
                    </apply>
                  </apply>
                </apply>
              </apply>
            </apply>
          </apply>
        </apply>
      </apply>
      
      <apply id="Jp_F1_calculation">
        <eq/>
        <ci> Jp_F1 </ci>
        <apply>
          <times/>
          <cn cellml:units="dimensionless"> -60.0 </cn>
          <ci> rho_F1 </ci>
          <apply>
            <divide/>
            <apply>
              <plus/>
              <apply>
                <minus/>
                <apply>
                  <times/>
                  <apply>
                    <plus/>
                    <apply>
                      <times/>
                      <ci> pa </ci>
                      <apply>
                        <power/>
                        <cn cellml:units="dimensionless"> 10.0 </cn>
                        <apply>
                          <times/>
                          <cn cellml:units="dimensionless"> 3.0 </cn>
                          <ci> delta_pH </ci>
                        </apply>
                      </apply>
                    </apply>
                    <apply>
                      <times/>
                      <ci> pc1 </ci>
                      <apply>
                        <exp/>
                        <apply>
                          <divide/>
                          <apply>
                            <times/>
                            <cn cellml:units="dimensionless"> 3.0 </cn>
                            <ci> F </ci>
                            <ci> V_B </ci>
                          </apply>
                          <apply>
                            <times/>
                            <ci> R </ci>
                            <ci> T </ci>
                          </apply>
                        </apply>
                      </apply>
                    </apply>
                  </apply>
                  <apply>
                    <exp/>
                    <apply>
                      <divide/>
                      <apply>
                        <times/>
                        <ci> F </ci>
                        <ci> A_F1 </ci>
                      </apply>
                      <apply>
                        <times/>
                        <ci> R </ci>
                        <ci> T </ci>
                      </apply>
                    </apply>
                  </apply>
                </apply>
                <apply>
                  <times/>
                  <ci> pa </ci>
                  <apply>
                    <exp/>
                    <apply>
                      <divide/>
                      <apply>
                        <times/>
                        <cn cellml:units="dimensionless"> 3.0 </cn>
                        <ci> F </ci>
                        <ci> V </ci>
                      </apply>
                      <apply>
                        <times/>
                        <ci> R </ci>
                        <ci> T </ci>
                      </apply>
                    </apply>
                  </apply>
                </apply>
              </apply>
              <apply>
                <times/>
                <ci> pc2 </ci>          
                <apply>
                  <exp/>
                  <apply>
                    <divide/>
                    <apply>
                      <times/>
                      <ci> F </ci>
                      <ci> A_F1 </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> V </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> A_F1 </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> V_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> A_F1 </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> V </ci>
                    </apply>
                    <apply>
                      <times/>
                      <ci> R </ci>
                      <ci> T </ci>
                    </apply>
                  </apply>
                </apply>
              </apply>
            </apply>
          </apply>
        </apply>
      </apply>        
      
      <apply id="A_F1_calculation">
        <eq/>
        <ci> A_F1 </ci>
        <apply>
          <times/>
          <apply>
            <divide/>
            <apply>
              <times/>
              <ci> R </ci>
              <ci> T </ci>
            </apply>
            <ci> F </ci>
          </apply>
          <apply>
            <ln/>
            <apply>
              <divide/>
              <apply>
                <times/>
                <ci> K_F1 </ci>
                <ci> ATP_m </ci>
              </apply>
              <apply>
                <times/>
                <ci> ADP_m_free </ci>
                <ci> Pi_m </ci>
              </apply>
            </apply>
          </apply>
        </apply>
      </apply>
      
      <apply id="ADP_m_free_calculation">
        <eq/>
        <ci> ADP_m_free </ci>
        <apply>
          <times/>
          <cn cellml:units="dimensionless"> 0.8 </cn>
          <ci> ADP_m </ci>
        </apply>
      </apply>
    </math>
  </component>
  
  <component name="ATP_ADP_exchange">
    <variable units="nanomole_per_minute_per_mg" public_interface="out" name="J_ant"/>
    
    <variable units="nanomole_per_minute_per_mg" name="Jmax_ant" initial_value="1000.0"/>
    <variable units="dimensionless" name="f" initial_value="0.5"/>
    
    <variable units="nanomolar" public_interface="in" name="ADP_i"/>
    <variable units="nanomolar" public_interface="in" name="ADP_m"/>
    <variable units="nanomolar" public_interface="in" name="ATP_i"/>
    <variable units="nanomolar" public_interface="in" name="ATP_m"/>
    <variable units="nanomole_per_minute_per_mg" public_interface="in" name="Jp_F1"/>
    <variable units="millijoule_per_mole_kelvin" public_interface="in" name="R"/>
    <variable units="coulomb_per_mole" public_interface="in" name="F"/>
    <variable units="kelvin" public_interface="in" name="T"/>
    <variable units="millivolt" public_interface="in" name="V"/>
    <variable units="minute" public_interface="in" name="time"/>  
    
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply id="J_ant_calculation">
        <eq/>
        <ci> J_ant </ci>
        <apply>
          <times/>
          <ci> Jmax_ant </ci>
          <apply>
            <divide/>
            <apply>
              <minus/>
              <cn cellml:units="dimensionless"> 1.0 </cn>
              <apply>
                <times/>
                <apply>
                  <divide/>
                  <apply>
                    <times/>
                    <ci> ATP_i </ci>
                    <ci> ADP_m </ci>
                  </apply>
                  <apply>
                    <times/>
                    <ci> ADP_i </ci>
                    <ci> ATP_m </ci>
                  </apply>
                </apply>
                <apply>
                  <exp/>
                  <apply>
                    <divide/>
                    <apply>
                      <times/>
                      <apply>
                        <minus/>
                        <ci> F </ci>
                      </apply>
                      <ci> V </ci>
                    </apply>
                    <apply>
                      <times/>
                      <ci> R </ci>
                      <ci> T </ci>
                    </apply>
                  </apply>
                </apply>
              </apply>
            </apply>
            <apply>
              <times/>
              <apply>
                <plus/>
                <cn cellml:units="dimensionless"> 1.0 </cn>
                <apply>
                  <times/>
                  <apply>
                    <divide/>
                    <ci> ATP_i </ci>
                    <ci> ADP_i </ci>
                  </apply>
                  <apply>
                    <exp/>
                    <apply>
                      <divide/>
                      <apply>
                        <times/>
                        <apply>
                          <minus/>
                          <ci> f </ci>
                        </apply>
                        <ci> F </ci>
                        <ci> V </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/>
                  <ci> ADP_m </ci>
                  <ci> ATP_m </ci>
                </apply>
              </apply>
            </apply>
          </apply>
        </apply>
      </apply>    
    </math>
  </component>
  
  <component name="NAD_reduction">
    <variable units="nanomole_per_minute_per_mg" public_interface="out" name="J_red"/>
    <variable units="nanomole_per_minute_per_mg" public_interface="out" name="J_red_basal" initial_value="20.0"/>
    <variable units="dimensionless" public_interface="out" name="f_PDHa"/>
    
    <variable units="dimensionless" name="u1" initial_value="15.0"/>
    <variable units="dimensionless" name="u2" initial_value="1.1"/>
    
    <variable units="nanomole_per_minute_per_mg" public_interface="in" name="J_gly_tot"/>
    <variable units="nanomole_per_mg" public_interface="in" name="K_Ca"/>
    <variable units="nanomolar" public_interface="in" name="Ca_m"/>
    <variable units="minute" public_interface="in" name="time"/>  
    
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply id="f_PDHa_calculation">
        <eq/>
        <ci> f_PDHa </ci>
        <apply>
          <divide/>
          <cn cellml:units="dimensionless"> 1.0 </cn>
          <apply>
            <plus/>
            <cn cellml:units="dimensionless"> 1.0 </cn>
            <apply>
              <times/>
              <ci> u2 </ci>
              <apply>
                <plus/>
                <cn cellml:units="dimensionless"> 1.0 </cn>
                <apply>
                  <times/>
                  <ci> u1 </ci>
                  <apply>
                    <power/>
                    <apply>
                      <plus/>
                      <cn cellml:units="dimensionless"> 1.0 </cn>
                      <apply>
                        <divide/>
                        <ci> Ca_m </ci>
                        <ci> K_Ca </ci>
                      </apply>
                    </apply>
                    <cn cellml:units="dimensionless"> -2.0 </cn>
                  </apply>
                </apply>
              </apply>
            </apply>
          </apply>
        </apply>
      </apply>
      
      <apply id="J_red_calculation">
        <eq/>
        <ci> J_red </ci>
        <apply>
          <plus/>
          <ci> J_red_basal </ci>
          <apply>
            <times/>
            <cn cellml:units="dimensionless"> 7.36 </cn>
            <ci> f_PDHa </ci>
            <ci> J_gly_tot </ci>
          </apply>
        </apply>
      </apply>
    </math>
  </component>
  
  <component name="TCA_cycle_ADP_phosphorylation">
    <variable units="nanomole_per_minute_per_mg" public_interface="out" name="J_ptca"/>
    
    <variable units="dimensionless" public_interface="in" name="f_PDHa"/>
    <variable units="nanomole_per_minute_per_mg" public_interface="in" name="J_red_basal"/>
    <variable units="nanomole_per_minute_per_mg" public_interface="in" name="J_gly_tot"/>
    <variable units="minute" public_interface="in" name="time"/>  
    
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply id="J_ptca_calculation">
        <eq/>
        <ci> J_ptca </ci>
        <apply>
          <plus/>
          <apply>
            <divide/>
            <ci> J_red_basal </ci>
            <cn cellml:units="dimensionless"> 3.0 </cn>
          </apply>
          <apply>
            <times/>
            <cn cellml:units="dimensionless"> 0.84 </cn>
            <ci> f_PDHa </ci>
            <ci> J_gly_tot </ci>
          </apply>
        </apply>
      </apply>
    </math>
  </component>
  
  <!--  Cytosolic componets. -->
  
  <component name="glycolytic_phosphorylation_of_ADP">
    <variable units="nanomole_per_minute_per_mg" public_interface="out" name="J_gly_tot"/>
    <variable units="nanomolar" public_interface="out" name="Glc" initial_value="25.0"/>
    
    <variable units="nanomole_per_minute_per_millimolar" name="beta_max" initial_value="126.0"/>
    <variable units="per_millimolar" name="beta_1" initial_value="1.66"/>
    <variable units="per_millimolar" name="beta_3" initial_value="4.0"/>
    <variable units="per_millimolar" name="beta_4" initial_value="2.83"/>
    <variable units="per_millimolar" name="beta_5" initial_value="1.3"/>
    <variable units="per_millimolar" name="beta_6" initial_value="2.66"/>
    <variable units="per_millimolar" name="beta_7" initial_value="0.16"/>
    
    <variable units="nanomolar" public_interface="in" name="ATP_i"/>
    <variable units="minute" public_interface="in" name="time"/>  
    
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply id="J_gly_tot_calculation">
        <eq/>
        <ci> J_gly_tot </ci>
        <apply>
          <times/>
          <apply>
            <divide/>
            <apply>
              <times/>
              <ci> beta_max </ci>
              <apply>
                <plus/>
                <cn cellml:units="dimensionless"> 1.0 </cn>
                <apply>
                  <times/>
                  <ci> beta_1 </ci>
                  <ci> Glc </ci>
                </apply>
              </apply>
              <ci> Glc </ci>
              <ci> ATP_i </ci>
            </apply>
            <apply>
              <plus/>
              <cn cellml:units="dimensionless"> 1.0 </cn>
              <apply>
                <times/>
                <ci> beta_3 </ci>
                <ci> ATP_i </ci>
              </apply>
              <apply>
                <plus/>
                <cn cellml:units="dimensionless"> 1.0 </cn>
                <apply>
                  <times/>
                  <ci> beta_4 </ci>
                  <ci> ATP_i </ci>
                </apply>
              </apply>
            </apply>
          </apply>
          <apply>
            <plus/>
            <apply>
              <times/>
              <ci> beta_5 </ci>
              <ci> Glc </ci>
            </apply>
            <apply>
              <plus/>
              <cn cellml:units="dimensionless"> 1.0 </cn>
              <apply>
                <times/>
                <ci> beta_6 </ci>
                <ci> ATP_i </ci>
              </apply>
            </apply>
            <apply>
              <times/>
              <ci> beta_7 </ci>
              <apply>
                <power/>
                <ci> Glc </ci>
                <cn cellml:units="dimensionless"> 2.0 </cn>
              </apply>
            </apply>
          </apply>
        </apply>
      </apply>
    </math>
  </component>
    
  <component name="hydrolysis_of_ATP">
    <variable units="nanomole_per_minute_per_mg" public_interface="out" name="J_hyd"/>
    
    <variable units="nanomole_per_minute_per_mg" name="J_hyd_ss"/>
    <variable units="nanomole_per_minute_per_mg" name="Jmax_hyd" initial_value="30.1"/>
    <variable units="per_millimolar" name="k_hyd"/>
    <variable units="millimolar" name="K_Glc" initial_value="8.7"/>
    <variable units="dimensionless" name="n_hyd" initial_value="2.7"/>
     
    <variable units="nanomolar" public_interface="in" name="Glc"/>
    <variable units="nanomolar" public_interface="in" name="ATP_i"/>
    <variable units="minute" public_interface="in" name="time"/>  
    
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply id="J_hyd_calculation">
        <eq/>
        <ci> J_hyd </ci>
        <apply>
          <plus/>
          <apply>
            <times/>
            <ci> k_hyd </ci>
            <ci> ATP_i </ci>
          </apply>
          <ci> J_hyd_ss </ci>
        </apply>
      </apply>
      
      <apply id="J_hyd_ss_calculation">
        <eq/>
        <ci> J_hyd_ss </ci>
        <apply>
          <divide/>
          <ci> Jmax_hyd </ci>
          <apply>
            <plus/>
            <cn cellml:units="dimensionless"> 1.0 </cn>
            <apply>
              <power/>
              <apply>
                <divide/>
                <ci> K_Glc </ci>
                <ci> Glc </ci>
              </apply>
              <ci> n_hyd </ci>
            </apply>
          </apply>
        </apply>
      </apply>
    </math>
  </component>
  
  <!--  ER Ca2+ handling components. -->
  
  <component name="Ca_release_from_the_ER">
    <variable units="nanomole_per_minute_per_mg" public_interface="out" name="J_erout"/>
    
    <variable units="nanomole_per_minute_per_mg" name="Jmax_IP3" initial_value="3000.0"/>
    <variable units="micromolar" name="d_IP3" initial_value="0.25"/>
    <variable units="micromolar" name="d_ACT" initial_value="1.0"/>
    <variable units="nanomolar" name="IP3"/>
    
    <variable units="dimensionless" public_interface="in" name="h"/>
    <variable units="nanomole_per_minute_per_mg" public_interface="in" name="JH_leak"/> 
    <variable units="nanomolar" public_interface="in" name="Ca_i"/>
    <variable units="nanomolar" public_interface="in" name="Ca_ER"/>
    <variable units="minute" public_interface="in" name="time"/>  
    
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply id="J_erout_calculation">
        <eq/>
        <ci> J_erout </ci>
        <apply>
          <times/>
          <apply>
            <plus/>
            <apply>
              <times/>
              <ci> Jmax_IP3 </ci>
              <apply>
                <power/>
                <apply>
                  <divide/>
                  <ci> IP3 </ci>
                  <apply>
                    <plus/>
                    <ci> IP3 </ci>
                    <ci> d_IP3 </ci>
                  </apply>
                </apply>
                <cn cellml:units="dimensionless"> 3.0 </cn>
              </apply>
              <apply>
                <power/>
                <apply>
                  <divide/>
                  <ci> Ca_i </ci>
                  <apply>
                    <plus/>
                    <ci> Ca_i </ci>
                    <ci> d_ACT </ci>
                  </apply>
                </apply>
                <cn cellml:units="dimensionless"> 3.0 </cn>
              </apply>
              <apply>
                <power/>
                <ci> h </ci>
                <cn cellml:units="dimensionless"> 3.0 </cn>
              </apply>
            </apply>
            <ci> JH_leak </ci>
          </apply>
          <apply>
            <minus/>
            <ci> Ca_ER </ci>
            <ci> Ca_i </ci>
          </apply>
        </apply>
      </apply>
    </math>
  </component>
  
  <component name="pumping_Ca_into_the_ER">
    <variable units="nanomole_per_minute_per_mg" public_interface="out" name="J_serca"/>
    
    <variable units="nanomole_per_minute_per_mg" name="Jmax_serca" initial_value="110.0"/>
    <variable units="micromolar" name="k_serca" initial_value="0.4"/>
    
    <variable units="nanomolar" public_interface="in" name="Ca_i"/>
    <variable units="minute" public_interface="in" name="time"/>  
    
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply id="J_serca_calculation">
        <eq/>
        <ci> J_serca </ci>
        <apply>
          <times/>
          <ci> Jmax_serca </ci>
          <apply>
            <divide/>
            <apply>
              <power/>
              <ci> Ca_i </ci>
              <cn cellml:units="dimensionless"> 2.0 </cn>
            </apply>
            <apply>
              <plus/>
              <apply>
                <power/>
                <ci> k_serca </ci>
                <cn cellml:units="dimensionless"> 2.0 </cn>
              </apply>
              <apply>
                <power/>
                <ci> Ca_i </ci>
                <cn cellml:units="dimensionless"> 2.0 </cn>
              </apply>
            </apply>
          </apply>
        </apply>
      </apply>
    </math>
  </component>
  
  <component name="differential_equations">
    <variable units="nanomolar" public_interface="out" name="NADH_m"/>
    <variable units="nanomolar" public_interface="out" name="NAD_m"/>
    <variable units="nanomolar" public_interface="out" name="ADP_m"/>
    <variable units="nanomolar" public_interface="out" name="ATP_m"/>
    <variable units="nanomolar" public_interface="out" name="ADP_i"/>
    <variable units="nanomolar" public_interface="out" name="ATP_i"/>
    <variable units="nanomolar" public_interface="out" name="Ca_m"/>
    <variable units="nanomolar" public_interface="out" name="Ca_ER"/>
    <variable units="nanomolar" public_interface="out" name="Ca_i"/>
    <variable units="dimensionless" public_interface="out" name="h"/>
   
    <variable units="nanomolar" name="total_mitochondrial_adenosine_phosphate" initial_value="12.0"/> 
    <variable units="nanomolar" name="total_NAD_m" initial_value="8.0"/>
    <variable units="milligram" name="C" initial_value="37.5"/>
    <variable units="milligram" name="M" initial_value="50.0"/>
    <variable units="milligram" name="E" initial_value="100.0"/>
    <variable units="millilitre" name="Vc" initial_value="0.5"/>
    <variable units="millilitre" name="Vm" initial_value="0.05"/>
    <variable units="millilitre" name="Ve" initial_value="0.1"/>
    <variable units="dimensionless" name="fc" initial_value="0.01"/>
    <variable units="dimensionless" name="fm" initial_value="0.0003"/>
    <variable units="dimensionless" name="fe" initial_value="0.01"/>
    <variable units="micromolar" name="d_INH" initial_value="1.4"/>
    <variable units="second" name="tau" initial_value="4.0"/>      
    
    <variable units="nanomole_per_minute_per_mg" public_interface="in" name="J_red"/>
    <variable units="nanomole_per_minute_per_mg" public_interface="in" name="Jo"/>
    <variable units="nanomole_per_minute_per_mg" public_interface="in" name="J_ant"/>
    <variable units="nanomole_per_minute_per_mg" public_interface="in" name="J_ptca"/>
    <variable units="nanomole_per_minute_per_mg" public_interface="in" name="Jp_F1"/>
    <variable units="nanomole_per_minute_per_mg" public_interface="in" name="J_hyd"/>
    <variable units="nanomole_per_minute_per_mg" public_interface="in" name="J_gly_tot"/>
    <variable units="nanomole_per_minute_per_mg" public_interface="in" name="JH_res"/>
    <variable units="nanomole_per_minute_per_mg" public_interface="in" name="JH_F1"/>
    <variable units="nanomole_per_minute_per_mg" public_interface="in" name="JH_leak"/>
    <variable units="nanomole_per_minute_per_mg" public_interface="in" name="J_uni"/>
    <variable units="nanomole_per_minute_per_mg" public_interface="in" name="J_Na_Ca"/>
    <variable units="nanomole_per_minute_per_mg" public_interface="in" name="J_serca"/>
    <variable units="nanomole_per_minute_per_mg" public_interface="in" name="J_erout"/>
    <variable units="minute" public_interface="in" name="time"/>
            
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply id="NADH_m_diff_eq">
        <eq/>
        <apply>
          <diff/>
          <bvar>
            <ci> time </ci>
          </bvar>
          <ci> NADH_m </ci>
        </apply>
        <apply>
          <divide/>
          <apply>
            <times/>
            <ci> M </ci>
            <apply>
              <minus/>
              <ci> J_red </ci>
              <ci> Jo </ci>
            </apply>
          </apply>
          <ci> Vm </ci>
        </apply>
      </apply>
        
      <apply id="total_NAD_m_calculation">
        <eq/>
        <ci> total_NAD_m </ci>
        <apply>
          <plus/>
          <ci> NADH_m </ci>
          <ci> NAD_m </ci>
        </apply>
      </apply>
      
      <apply id="NAD_m_calculation">
        <eq/>
        <ci> NAD_m </ci>
        <apply>
          <minus/>
          <ci> total_NAD_m </ci>
          <ci> NADH_m </ci>
        </apply>
      </apply>
      
      <apply id="ADP_m_diff_eq">
        <eq/>
        <apply>
          <diff/>
          <bvar>
            <ci> time </ci>
          </bvar>
          <ci> ADP_m </ci>
        </apply>
        <apply>
          <divide/>
          <apply>
            <times/>
            <ci> M </ci>
            <apply>
              <minus/>
              <ci> J_ant </ci>
              <apply>
                <plus/>
                <ci> J_ptca </ci>
                <ci> Jp_F1 </ci>
              </apply>
            </apply>
          </apply>
          <ci> Vm </ci>
        </apply>
      </apply>
      
      <apply id="total_mitochondrial_adenosine_phosphate_calculation">
        <eq/>
        <ci> total_mitochondrial_adenosine_phosphate </ci>
        <apply>
          <plus/>
          <ci> ATP_m </ci>
          <ci> ADP_m </ci>
        </apply>
      </apply>
      
      <apply id="ATP_m_calculation">
        <eq/>
        <ci> ATP_m </ci>
        <apply>
          <minus/>
          <ci> total_mitochondrial_adenosine_phosphate </ci>
          <ci> ADP_m </ci>
        </apply>
      </apply>
      
      <apply id="ADP_i_diff_eq">
        <eq/>
        <apply>
          <diff/>
          <bvar>
            <ci> time </ci>
          </bvar>
          <ci> ADP_i </ci>
        </apply>
        <apply>
          <divide/>
          <apply>
            <plus/>
            <apply>
              <times/>
              <apply>
                <minus/>
                <ci> M </ci>
              </apply>
              <ci> J_ant </ci>
            </apply>
            <apply>
              <times/>
              <ci> C </ci>
              <apply>
                <minus/>
                <ci> J_hyd </ci>
                <ci> J_gly_tot </ci>
              </apply>
            </apply>
          </apply>
          <ci> Vc </ci>
        </apply>
      </apply>
      
      <apply id="ATP_i_calculation">
        <eq/>
        <ci> ATP_i </ci>
        <apply>
          <minus/>
          <cn cellml:units="millimolar"> 2.0 </cn>
          <ci> ADP_i </ci>
        </apply>
      </apply>
      
      <apply id="Ca_m_diff_eq">
        <eq/>
        <apply>
          <diff/>
          <bvar>
            <ci> time </ci>
          </bvar>
          <ci> Ca_m </ci>
        </apply>
        <apply>
          <divide/>
          <apply>
            <times/>
            <ci> fm </ci>
            <ci> M </ci>
            <apply>
              <minus/>
              <ci> J_uni </ci>
              <ci> J_Na_Ca </ci>
            </apply>
          </apply>
          <ci> Vm </ci>
        </apply>
      </apply>
      
      <apply id="Ca_ER_diff_eq">
        <eq/>
        <apply>
          <diff/>
          <bvar>
            <ci> time </ci>
          </bvar>
          <ci> Ca_ER </ci>
        </apply>
        <apply>
          <divide/>
          <apply>
            <times/>
            <ci> fe </ci>
            <ci> E </ci>
            <apply>
              <minus/>
              <ci> J_serca </ci>
              <ci> J_erout </ci>
            </apply>
          </apply>
          <ci> Ve </ci>
        </apply>
      </apply>
      
      <apply id="Ca_i_diff_eq">
        <eq/>
        <apply>
          <diff/>
          <bvar>
            <ci> time </ci>
          </bvar>
          <ci> Ca_i </ci>
        </apply>
        <apply>
          <divide/>
          <apply>
            <times/>
            <ci> fc </ci>
            <apply>
              <minus/>
              <apply>
                <times/>
                <ci> M </ci>
                <apply>
                  <minus/>
                  <ci> J_Na_Ca </ci>
                  <ci> J_uni </ci>
                </apply>
              </apply>
              <apply>
                <times/>
                <ci> E </ci>
                <apply>
                  <minus/>
                  <ci> J_serca </ci>
                  <ci> J_erout </ci>
                </apply>
              </apply>
            </apply>
          </apply>
          <ci> Vc </ci>
        </apply>
      </apply>
      
      <apply id="h_diff_eq">
        <eq/>
        <apply>
          <diff/>
          <bvar>
            <ci> time </ci>
          </bvar>
          <ci> h </ci>
        </apply>
        <apply>
          <divide/>
          <apply>
            <minus/>
            <ci> d_INH </ci>
            <apply>
              <times/>
              <apply>
                <plus/>
                <ci> Ca_i </ci>
                <ci> d_INH </ci>
              </apply>
              <ci> h </ci>
            </apply>
          </apply>
          <ci> tau </ci>
        </apply>
      </apply>
    </math>
  </component>
  
  <group>
    <relationship_ref relationship="containment"/>
    <component_ref component="membrane">
      <component_ref component="proton_pump"/>
      <component_ref component="proton_leak"/>
      <component_ref component="F0_F1_ATPase"/>
      <component_ref component="ATP_ADP_exchange"/>
      <component_ref component="Ca_uniporter"/>
      <component_ref component="Na_Ca_exchanger"/>
      <component_ref component="NAD_reduction"/>
      <component_ref component="TCA_cycle_ADP_phosphorylation"/>               
      <component_ref component="glycolytic_phosphorylation_of_ADP"/>
      <component_ref component="hydrolysis_of_ATP"/>
      <component_ref component="Ca_release_from_the_ER"/>
      <component_ref component="pumping_Ca_into_the_ER"/>
      <component_ref component="differential_equations"/>
    </component_ref>
  </group>
  
  <!--
    "Time" is passed from the "environment" component into all other components.
  -->
  
  <connection>
    <map_components component_2="environment" component_1="membrane"/>
    <map_variables variable_2="time" variable_1="time"/>
  </connection>
  
  <connection>
    <map_components component_2="proton_pump" component_1="environment"/>
    <map_variables variable_2="time" variable_1="time"/>
  </connection>
  
  <connection>
    <map_components component_2="proton_leak" component_1="environment"/>
    <map_variables variable_2="time" variable_1="time"/>
  </connection> 
  
  <connection>
    <map_components component_2="F0_F1_ATPase" component_1="environment"/>
    <map_variables variable_2="time" variable_1="time"/>
  </connection>
  
  <connection>
    <map_components component_2="ATP_ADP_exchange" component_1="environment"/>
    <map_variables variable_2="time" variable_1="time"/>
  </connection>
  
  <connection>
    <map_components component_2="Ca_uniporter" component_1="environment"/>
    <map_variables variable_2="time" variable_1="time"/>
  </connection>
  
  <connection>
    <map_components component_2="Na_Ca_exchanger" component_1="environment"/>
    <map_variables variable_2="time" variable_1="time"/>
  </connection>
  
  <connection>
    <map_components component_2="NAD_reduction" component_1="environment"/>
    <map_variables variable_2="time" variable_1="time"/>
  </connection>
  
  <connection>
    <map_components component_2="TCA_cycle_ADP_phosphorylation" component_1="environment"/>
    <map_variables variable_2="time" variable_1="time"/>
  </connection>
  
  <connection>
    <map_components component_2="glycolytic_phosphorylation_of_ADP" component_1="environment"/>
    <map_variables variable_2="time" variable_1="time"/>
  </connection>
  
  <connection>
    <map_components component_2="hydrolysis_of_ATP" component_1="environment"/>
    <map_variables variable_2="time" variable_1="time"/>
  </connection>
  
  <connection>
    <map_components component_2="Ca_release_from_the_ER" component_1="environment"/>
    <map_variables variable_2="time" variable_1="time"/>
  </connection>
  
  <connection>
    <map_components component_2="pumping_Ca_into_the_ER" component_1="environment"/>
    <map_variables variable_2="time" variable_1="time"/>
  </connection>
  
  <connection>
    <map_components component_2="differential_equations" component_1="environment"/>
    <map_variables variable_2="time" variable_1="time"/>
  </connection>
  
  <!--
    Several variables are passed between the "membrane" and its sub-components.
  -->
  
  <connection>
    <map_components component_2="proton_pump" component_1="membrane"/>
    <map_variables variable_2="JH_res" variable_1="JH_res"/>
    <map_variables variable_2="delta_pH" variable_1="delta_pH"/>
    <map_variables variable_2="V" variable_1="V"/>
    <map_variables variable_2="V_B" variable_1="V_B"/>
    <map_variables variable_2="R" variable_1="R"/>
    <map_variables variable_2="T" variable_1="T"/>
    <map_variables variable_2="F" variable_1="F"/>
  </connection>    
  
  <connection>
    <map_components component_2="proton_leak" component_1="membrane"/>
    <map_variables variable_2="JH_leak" variable_1="JH_leak"/>
    <map_variables variable_2="g_H" variable_1="g_H"/>
    <map_variables variable_2="proton_motive_force" variable_1="proton_motive_force"/>
  </connection>
  
  <connection>
    <map_components component_2="F0_F1_ATPase" component_1="membrane"/>
    <map_variables variable_2="JH_F1" variable_1="JH_F1"/>
    <map_variables variable_2="delta_pH" variable_1="delta_pH"/>
    <map_variables variable_2="V" variable_1="V"/>
    <map_variables variable_2="V_B" variable_1="V_B"/>
    <map_variables variable_2="R" variable_1="R"/>
    <map_variables variable_2="T" variable_1="T"/>
    <map_variables variable_2="F" variable_1="F"/>
  </connection> 
  
  <connection>
    <map_components component_2="ATP_ADP_exchange" component_1="membrane"/>
    <map_variables variable_2="J_ant" variable_1="J_ant"/>
    <map_variables variable_2="V" variable_1="V"/>
    <map_variables variable_2="R" variable_1="R"/>
    <map_variables variable_2="T" variable_1="T"/>
    <map_variables variable_2="F" variable_1="F"/>
  </connection> 
  
  <connection>
    <map_components component_2="Ca_uniporter" component_1="membrane"/>
    <map_variables variable_2="J_uni" variable_1="J_uni"/>
    <map_variables variable_2="V" variable_1="V"/>
    <map_variables variable_2="R" variable_1="R"/>
    <map_variables variable_2="T" variable_1="T"/>
    <map_variables variable_2="F" variable_1="F"/>
  </connection> 
  
  <connection>
    <map_components component_2="Na_Ca_exchanger" component_1="membrane"/>
    <map_variables variable_2="V" variable_1="V"/>
    <map_variables variable_2="R" variable_1="R"/>
    <map_variables variable_2="T" variable_1="T"/>
    <map_variables variable_2="F" variable_1="F"/>
  </connection>
  
  <!--  A few variables are passed between the sibling components. --> 
  
  <connection>
    <map_components component_2="Na_Ca_exchanger" component_1="Ca_uniporter"/>
    <map_variables variable_2="V_offset" variable_1="V_offset"/>
  </connection>
  
  <connection>
    <map_components component_2="differential_equations" component_1="Ca_uniporter"/>
    <map_variables variable_2="J_uni" variable_1="J_uni"/>
    <map_variables variable_2="Ca_i" variable_1="Ca_i"/>
  </connection>
  
  <connection>
    <map_components component_2="NAD_reduction" component_1="Na_Ca_exchanger"/>
    <map_variables variable_2="K_Ca" variable_1="K_Ca"/>
  </connection>
  
  <connection>
    <map_components component_2="differential_equations" component_1="Na_Ca_exchanger"/>
    <map_variables variable_2="J_Na_Ca" variable_1="J_Na_Ca"/>
    <map_variables variable_2="Ca_m" variable_1="Ca_m"/>
  </connection>
  
  <connection>
    <map_components component_2="differential_equations" component_1="proton_pump"/>
    <map_variables variable_2="JH_res" variable_1="JH_res"/>
    <map_variables variable_2="Jo" variable_1="Jo"/>
    <map_variables variable_2="NAD_m" variable_1="NAD_m"/>
    <map_variables variable_2="NADH_m" variable_1="NADH_m"/>
  </connection> 
  
  <connection>
    <map_components component_2="Ca_release_from_the_ER" component_1="proton_leak"/>
    <map_variables variable_2="JH_leak" variable_1="JH_leak"/>
  </connection>
  
  <connection>
    <map_components component_2="differential_equations" component_1="proton_leak"/>
    <map_variables variable_2="JH_leak" variable_1="JH_leak"/>
  </connection>
  
  <connection>
    <map_components component_2="differential_equations" component_1="F0_F1_ATPase"/>
    <map_variables variable_2="JH_F1" variable_1="JH_F1"/>
    <map_variables variable_2="Jp_F1" variable_1="Jp_F1"/>
    <map_variables variable_2="ADP_m" variable_1="ADP_m"/>
    <map_variables variable_2="ATP_m" variable_1="ATP_m"/>
  </connection>
  
  <connection>
    <map_components component_2="ATP_ADP_exchange" component_1="F0_F1_ATPase"/>
    <map_variables variable_2="Jp_F1" variable_1="Jp_F1"/>
  </connection>
  
  <connection>
    <map_components component_2="differential_equations" component_1="ATP_ADP_exchange"/>
    <map_variables variable_2="J_ant" variable_1="J_ant"/>
    <map_variables variable_2="ADP_m" variable_1="ADP_m"/>
    <map_variables variable_2="ATP_m" variable_1="ATP_m"/>
    <map_variables variable_2="ADP_i" variable_1="ADP_i"/>
    <map_variables variable_2="ATP_i" variable_1="ATP_i"/>
  </connection>
  
  <connection>
    <map_components component_2="differential_equations" component_1="NAD_reduction"/>
    <map_variables variable_2="J_red" variable_1="J_red"/>
    <map_variables variable_2="Ca_m" variable_1="Ca_m"/>
  </connection> 
  
  <connection>
    <map_components component_2="TCA_cycle_ADP_phosphorylation" component_1="NAD_reduction"/>
    <map_variables variable_2="J_red_basal" variable_1="J_red_basal"/>
    <map_variables variable_2="f_PDHa" variable_1="f_PDHa"/>
  </connection>
  
  <connection>
    <map_components component_2="glycolytic_phosphorylation_of_ADP" component_1="NAD_reduction"/>
    <map_variables variable_2="J_gly_tot" variable_1="J_gly_tot"/>
  </connection>
  
  <connection>
    <map_components component_2="differential_equations" component_1="TCA_cycle_ADP_phosphorylation"/>
    <map_variables variable_2="J_ptca" variable_1="J_ptca"/>
  </connection>
  
  <connection>
    <map_components component_2="glycolytic_phosphorylation_of_ADP" component_1="TCA_cycle_ADP_phosphorylation"/>
    <map_variables variable_2="J_gly_tot" variable_1="J_gly_tot"/>
  </connection>   
  
  <connection>
    <map_components component_2="differential_equations" component_1="glycolytic_phosphorylation_of_ADP"/>
    <map_variables variable_2="J_gly_tot" variable_1="J_gly_tot"/>
    <map_variables variable_2="ATP_i" variable_1="ATP_i"/>
  </connection> 
  
  <connection>
    <map_components component_2="hydrolysis_of_ATP" component_1="glycolytic_phosphorylation_of_ADP"/>
    <map_variables variable_2="Glc" variable_1="Glc"/>
  </connection>
  
  <connection>
    <map_components component_2="differential_equations" component_1="hydrolysis_of_ATP"/>
    <map_variables variable_2="J_hyd" variable_1="J_hyd"/>
    <map_variables variable_2="ATP_i" variable_1="ATP_i"/>
  </connection>  
  
  <connection>
    <map_components component_2="differential_equations" component_1="Ca_release_from_the_ER"/>
    <map_variables variable_2="J_erout" variable_1="J_erout"/>
    <map_variables variable_2="Ca_i" variable_1="Ca_i"/>
    <map_variables variable_2="Ca_ER" variable_1="Ca_ER"/>
    <map_variables variable_2="h" variable_1="h"/>
  </connection> 
  
  <connection>
    <map_components component_2="differential_equations" component_1="pumping_Ca_into_the_ER"/>
    <map_variables variable_2="J_serca" variable_1="J_serca"/>
    <map_variables variable_2="Ca_i" variable_1="Ca_i"/>
  </connection> 

<rdf:RDF>
  <rdf:Bag rdf:about="rdf:#c29bfb3e-8fd4-4f49-a193-c2b1498ee192">
    <rdf:li>mitochondria</rdf:li>
    <rdf:li>IP3</rdf:li>
    <rdf:li>signal transduction</rdf:li>
    <rdf:li>Pancreatic Beta-Cell</rdf:li>
    <rdf:li>calcium dynamics</rdf:li>
    <rdf:li>ip3</rdf:li>
    <rdf:li>electrophysiology</rdf:li>
    <rdf:li>beta cell</rdf:li>
  </rdf:Bag>
  <rdf:Seq rdf:about="rdf:#b3a3f2ac-46d2-4035-a6ec-447bf35a492d">
    <rdf:li rdf:resource="rdf:#9f13475f-fa73-4ef0-a865-7b63688525bb"/>
    <rdf:li rdf:resource="rdf:#2f12347e-cb2c-423a-a866-1a15238b32d5"/>
  </rdf:Seq>
  <rdf:Description rdf:about="rdf:#f3aec6c6-63ad-40a3-a0b0-94733361757d">
    <dcterms:W3CDTF>2002-03-01</dcterms:W3CDTF>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#8e43118f-6181-4020-a06e-168048d50965">
    <vCard:Given>Joel</vCard:Given>
    <vCard:Family>Keizer</vCard:Family>
    <vCard:Other>E</vCard:Other>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#88523781-7db3-4140-a982-17738d82d621">
    <vCard:N rdf:resource="rdf:#8ffd332f-8a0d-470f-9d64-a6e890c156e9"/>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#c1e21d13-af28-472c-8c65-a59a753d4393">
    <dcterms:W3CDTF>2003-08-12</dcterms:W3CDTF>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#44818b64-e445-4bb7-8cd0-e164c66ccb2e">
    <dcterms:W3CDTF>2002-02-26</dcterms:W3CDTF>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#aa96aebb-0ca4-4814-947e-fd16a2a25ea6">
    <vCard:N rdf:resource="rdf:#687c8001-1f94-4907-9eea-895868719876"/>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#034afd19-e9e9-477f-a1f8-df9682763cb0">
    <vCard:Orgname>The University of Auckland</vCard:Orgname>
    <vCard:Orgunit>The Bioengineering Research Group</vCard:Orgunit>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#046c83c6-30ec-4cbb-a560-2e9b4d67d0cb">
    <dc:title>Journal of theoretical Biology</dc:title>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#6abfe49a-24d8-4887-a0c1-9dde65c81472">
    <rdf:type rdf:resource="http://imc.org/vCard/3.0#internet"/>
    <rdf:value>c.lloyd@auckland.ac.nz</rdf:value>
  </rdf:Description>
  <rdf:Description rdf:about="#fall_keizer_2001_version01">
    <dc:title>
        Mitochondrial modulation of intracellular Ca2+ signaling
      </dc:title>
    <cmeta:bio_entity>Pancreatic Beta-cell</cmeta:bio_entity>
    <cmeta:comment rdf:resource="rdf:#0b4f9e85-26ae-4b3e-8770-2a06498b6414"/>
    <bqs:reference rdf:resource="rdf:#2eceb112-4036-49a6-9855-a58da4604aa3"/>
    <bqs:reference rdf:resource="rdf:#8daa00b1-ed3f-41f4-8ac0-7c38bb5db385"/>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#c039a9e6-c2e7-442c-ba1c-221f522ae4a6">
    <vCard:N rdf:resource="rdf:#e403397e-8b2f-4ee3-afc9-e9cca3d9043a"/>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#9f13475f-fa73-4ef0-a865-7b63688525bb">
    <rdf:type rdf:resource="http://www.cellml.org/bqs/1.0#Person"/>
    <vCard:N rdf:resource="rdf:#b9c91063-a861-4d97-8e95-152aed7a132a"/>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#1b363482-4f12-4984-adff-fa61fa8ef68f">
    <dcterms:modified rdf:resource="rdf:#c1e21d13-af28-472c-8c65-a59a753d4393"/>
    <rdf:value>
          Corrected equations: J_uni in Ca_uniporter component, JH_F1 in 
          F0_F1_ATPase component.
        </rdf:value>
    <cmeta:modifier rdf:resource="rdf:#aa96aebb-0ca4-4814-947e-fd16a2a25ea6"/>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#687c8001-1f94-4907-9eea-895868719876">
    <vCard:Given>Catherine</vCard:Given>
    <vCard:Family>Lloyd</vCard:Family>
    <vCard:Other>May</vCard:Other>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#27d5d643-6f55-4f6a-a9e5-c8b768f8a9e1">
    <vCard:N rdf:resource="rdf:#19adecdb-a83a-49a4-a2ee-f31d78e3dea5"/>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#6f349668-29d6-4db3-bf08-542ebb0aa5dd">
    <dc:creator rdf:resource="rdf:#b3a3f2ac-46d2-4035-a6ec-447bf35a492d"/>
    <dc:title>
            Mitochondrial Modulation of Intracellular Ca2+ Signalling
          </dc:title>
    <bqs:volume>210</bqs:volume>
    <bqs:first_page>151</bqs:first_page>
    <bqs:Journal rdf:resource="rdf:#046c83c6-30ec-4cbb-a560-2e9b4d67d0cb"/>
    <dcterms:issued rdf:resource="rdf:#cd3a0dbc-060e-4af8-b98a-faee25415bdc"/>
    <bqs:last_page>165</bqs:last_page>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#40df5899-4546-46bc-984c-99d2a85a91ee">
    <dcterms:modified rdf:resource="rdf:#3a2998d6-195e-4b6c-b63d-dd5488409e52"/>
    <rdf:value>
          Added more metadata.
        </rdf:value>
    <cmeta:modifier rdf:resource="rdf:#c039a9e6-c2e7-442c-ba1c-221f522ae4a6"/>
  </rdf:Description>
  <rdf:Description rdf:about="">
    <dc:publisher>
        The University of Auckland, Bioengineering Research Group
      </dc:publisher>
    <cmeta:modification rdf:resource="rdf:#00d9061e-2166-49f0-a4d4-ff78a4837cf4"/>
    <cmeta:modification rdf:resource="rdf:#183d5ee4-fb20-4087-a320-f25105af9505"/>
    <cmeta:modification rdf:resource="rdf:#1b363482-4f12-4984-adff-fa61fa8ef68f"/>
    <cmeta:modification rdf:resource="rdf:#40df5899-4546-46bc-984c-99d2a85a91ee"/>
    <cmeta:modification rdf:resource="rdf:#92b81c18-380b-4c2d-8e50-07277cbb5ec2"/>
    <cmeta:modification rdf:resource="rdf:#b6cce368-6692-4f45-a545-59ad4e298ec2"/>
    <dcterms:created rdf:resource="rdf:#fc2642a9-3b8f-4554-802b-a2193fdc8a5f"/>
    <dc:creator rdf:resource="rdf:#44be58dc-deab-4b01-9b9a-1c5b2da26146"/>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#e7b007ff-dbd6-4abf-b053-c394d93b9a09">
    <dcterms:W3CDTF>2002-01-21</dcterms:W3CDTF>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#8ffd332f-8a0d-470f-9d64-a6e890c156e9">
    <vCard:Given>Autumn</vCard:Given>
    <vCard:Family>Cuellar</vCard:Family>
    <vCard:Other>A</vCard:Other>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#0d33e716-c3b6-463c-ad19-7563cb2290ad">
    <dcterms:W3CDTF>2003-04-09</dcterms:W3CDTF>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#6f3b9982-e3d5-40d4-8b67-15bc03fad9f4">
    <bqs:subject_type>keyword</bqs:subject_type>
    <rdf:value rdf:resource="rdf:#c29bfb3e-8fd4-4f49-a193-c2b1498ee192"/>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#b6cce368-6692-4f45-a545-59ad4e298ec2">
    <dcterms:modified rdf:resource="rdf:#f3aec6c6-63ad-40a3-a0b0-94733361757d"/>
    <rdf:value>
          Corrected units.
        </rdf:value>
    <cmeta:modifier rdf:resource="rdf:#27d5d643-6f55-4f6a-a9e5-c8b768f8a9e1"/>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#8daa00b1-ed3f-41f4-8ac0-7c38bb5db385">
    <dc:subject rdf:resource="rdf:#6f3b9982-e3d5-40d4-8b67-15bc03fad9f4"/>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#2eceb112-4036-49a6-9855-a58da4604aa3">
    <bqs:Pubmed_id>11371172</bqs:Pubmed_id>
    <bqs:JournalArticle rdf:resource="rdf:#6f349668-29d6-4db3-bf08-542ebb0aa5dd"/>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#fc2642a9-3b8f-4554-802b-a2193fdc8a5f">
    <dcterms:W3CDTF>2002-01-14</dcterms:W3CDTF>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#2f12347e-cb2c-423a-a866-1a15238b32d5">
    <rdf:type rdf:resource="http://www.cellml.org/bqs/1.0#Person"/>
    <vCard:N rdf:resource="rdf:#8e43118f-6181-4020-a06e-168048d50965"/>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#e403397e-8b2f-4ee3-afc9-e9cca3d9043a">
    <vCard:Given>Catherine</vCard:Given>
    <vCard:Family>Lloyd</vCard:Family>
    <vCard:Other>May</vCard:Other>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#36735397-f7fd-441a-ba31-2cc159e41a4f">
    <vCard:Given>Catherine</vCard:Given>
    <vCard:Family>Lloyd</vCard:Family>
    <vCard:Other>May</vCard:Other>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#183d5ee4-fb20-4087-a320-f25105af9505">
    <dcterms:modified rdf:resource="rdf:#0d33e716-c3b6-463c-ad19-7563cb2290ad"/>
    <rdf:value>
          Added publication date information.
        </rdf:value>
    <cmeta:modifier rdf:resource="rdf:#88523781-7db3-4140-a982-17738d82d621"/>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#56f74f1d-ed1e-42e3-a343-d1fbfb7ecfab">
    <vCard:N rdf:resource="rdf:#440bb8bd-66b2-43ee-81f3-564fa549d4fb"/>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#650be6bc-08a6-4860-b9d8-0c26c6a2def5">
    <vCard:Given>Catherine</vCard:Given>
    <vCard:Family>Lloyd</vCard:Family>
    <vCard:Other>May</vCard:Other>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#0b4f9e85-26ae-4b3e-8770-2a06498b6414">
    <dc:creator rdf:resource="rdf:#7e1636a2-c45a-44d7-af73-383964a49718"/>
    <rdf:value>
          This is the CellML description of Christopher Fall and Joel Keizer's 
          2001 model of mitochondrial modulation of Ca2+ signaling.  They 
          combine the previously separate models of mitochondrial Ca2+ handling 
          and IP3-dependent Ca2+ release from the ER into a single, 
          comprehensive model. 
        </rdf:value>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#44be58dc-deab-4b01-9b9a-1c5b2da26146">
    <vCard:ORG rdf:resource="rdf:#034afd19-e9e9-477f-a1f8-df9682763cb0"/>
    <vCard:EMAIL rdf:resource="rdf:#6abfe49a-24d8-4887-a0c1-9dde65c81472"/>
    <vCard:N rdf:resource="rdf:#650be6bc-08a6-4860-b9d8-0c26c6a2def5"/>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#7e1636a2-c45a-44d7-af73-383964a49718">
    <vCard:FN>Catherine Lloyd</vCard:FN>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#92b81c18-380b-4c2d-8e50-07277cbb5ec2">
    <dcterms:modified rdf:resource="rdf:#44818b64-e445-4bb7-8cd0-e164c66ccb2e"/>
    <rdf:value>
          Corrected several equations.
        </rdf:value>
    <cmeta:modifier rdf:resource="rdf:#74378c80-ca82-4c1b-88a0-149b9baf90c3"/>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#19adecdb-a83a-49a4-a2ee-f31d78e3dea5">
    <vCard:Given>Catherine</vCard:Given>
    <vCard:Family>Lloyd</vCard:Family>
    <vCard:Other>May</vCard:Other>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#3a2998d6-195e-4b6c-b63d-dd5488409e52">
    <dcterms:W3CDTF>2002-07-22</dcterms:W3CDTF>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#440bb8bd-66b2-43ee-81f3-564fa549d4fb">
    <vCard:Given>Autumn</vCard:Given>
    <vCard:Family>Cuellar</vCard:Family>
    <vCard:Other>A.</vCard:Other>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#cd3a0dbc-060e-4af8-b98a-faee25415bdc">
    <dcterms:W3CDTF>2001-05-21</dcterms:W3CDTF>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#74378c80-ca82-4c1b-88a0-149b9baf90c3">
    <vCard:N rdf:resource="rdf:#36735397-f7fd-441a-ba31-2cc159e41a4f"/>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#b9c91063-a861-4d97-8e95-152aed7a132a">
    <vCard:Given>Christopher</vCard:Given>
    <vCard:Family>Fall</vCard:Family>
    <vCard:Other>P</vCard:Other>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#00d9061e-2166-49f0-a4d4-ff78a4837cf4">
    <dcterms:modified rdf:resource="rdf:#e7b007ff-dbd6-4abf-b053-c394d93b9a09"/>
    <rdf:value>
          Updated metadata to conform to the 16/1/02 CellML Metadata 1.0 
          Specification.
        </rdf:value>
    <cmeta:modifier rdf:resource="rdf:#56f74f1d-ed1e-42e3-a343-d1fbfb7ecfab"/>
  </rdf:Description>
</rdf:RDF>
</model>