Location: Calcium Dynamics Annotations @ 110f9ba31e34 / magnus_keizer_1997 / model / magnus_keizer_1997.cellml

Author:
neilstephen2001 <npar276@aucklanduni.ac.nz>
Date:
2021-01-24 21:37:35+13:00
Desc:
adding OMEX archives to workspace
Permanent Source URI:
http://models.cellml.org/workspace/7f1/rawfile/110f9ba31e34b7499c8d02e13a6b9984351c0e8f/magnus_keizer_1997/model/magnus_keizer_1997.cellml

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  <documentation xmlns="http://cellml.org/tmp-documentation">
    <article>
      <articleinfo>
        <title>Mitochondrial Ca2+ Handling</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 1997 Gerhard Magnus and Joel Keizer published a minimal mathematical model to describe Ca
          <superscript>2+</superscript>
          handling by mitochondria in the pancreatic beta-cell.  Their kinetic model includes six transport mechanisms in the inner mitochondrial membrane, including proton pumping via respiration and proton pumping by the F0F1-ATPase, a proton leak, adenine nucleotide exchange, the Ca
          <superscript>2+</superscript>
          uniporter and Na
          <superscript>+</superscript>
          /Ca
          <superscript>2+</superscript>
          exchange (see
          <xref linkend="fig_cell_diagram" />
          below).
        </para>
        <para>The complete original paper reference is cited below:</para>
        <para>
          Minimal model of beta-cell mitochondrial Ca
          <superscript>2+</superscript>
          handling, Gerhard Magnus and Joel Keizer, 1997,
          <ulink url="http://ajpcell.physiology.org/">
            <emphasis>American Journal of Physiology</emphasis>
          </ulink>
          , 273, C717-C733.
          <ulink url="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&amp;db=PubMed&amp;list_uids=9277370&amp;dopt=Abstract">PubMed ID: 9277370</ulink>
        </para>
        <para>
          The raw CellML description of the mitochondrial Ca
          <superscript>2+</superscript>
          handling 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 mitochondrial Ca2+ handling model showing ionic currents across the mitochondrial membrane</title>
              </objectinfo>
              <imagedata fileref="magnus_1997.png" />
            </imageobject>
          </mediaobject>
          <caption>A schematic representation of the ion fluxes through the mitochondrial inner membrane that are included in the Magnus-Keizer minimal model.</caption>
        </informalfigure>
        <informalfigure float="0" id="fig_cellml_rendering">
          <mediaobject>
            <imageobject>
              <objectinfo>
                <title>the cellml rendering of the mitochondrial Ca2+ handling model</title>
              </objectinfo>
              <imagedata fileref="cellml_rendering.gif" />
            </imageobject>
          </mediaobject>
          <caption>
            The network defined in the CellML description of the mitochondrial Ca
            <superscript>2+</superscript>
            handling model.
          </caption>
        </informalfigure>
      </sect1>
    </article>
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                <ci>NAD_m</ci>
              </apply>
            </apply>
          </apply>
        </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>
    </math>
  </component>
  <component name="proton_leak">
    <variable cmeta:id="proton_leak.JH_leak" name="JH_leak" public_interface="out" units="nanomole_per_minute_per_mg" />
    <variable cmeta:id="proton_leak.g_H" name="g_H" public_interface="in" units="conductance_units" />
    <variable cmeta:id="proton_leak.proton_motive_force" name="proton_motive_force" public_interface="in" units="nanomole_per_minute_per_mg" />
    <variable cmeta:id="proton_leak.time" name="time" public_interface="in" units="minute" />
    <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 cmeta:id="F0_F1_ATPase.JH_F1" name="JH_F1" public_interface="out" units="nanomole_per_minute_per_mg" />
    <variable cmeta:id="F0_F1_ATPase.Jp_F1" name="Jp_F1" public_interface="out" units="nanomole_per_minute_per_mg" />
    <variable cmeta:id="F0_F1_ATPase.rho_F1" initial_value="0.7" name="rho_F1" units="nanomole_per_mg" />
    <variable cmeta:id="F0_F1_ATPase.K_F1" initial_value="1710000.0" name="K_F1" units="millimolar" />
    <variable cmeta:id="F0_F1_ATPase.A_F1" name="A_F1" units="dimensionless" />
    <variable cmeta:id="F0_F1_ATPase.total_mitochondrial_adenosine_phosphate" initial_value="12.0" name="total_mitochondrial_adenosine_phosphate" units="nanomolar" />
    <variable cmeta:id="F0_F1_ATPase.ATP_m" name="ATP_m" units="nanomolar" />
    <variable cmeta:id="F0_F1_ATPase.ADP_m_free" name="ADP_m_free" units="nanomolar" />
    <variable cmeta:id="F0_F1_ATPase.Pi_m" initial_value="20.0" name="Pi_m" units="millimolar" />
    <variable cmeta:id="F0_F1_ATPase.p1" initial_value="0.00000001346" name="p1" units="dimensionless" />
    <variable cmeta:id="F0_F1_ATPase.p2" initial_value="0.0000007739" name="p2" units="dimensionless" />
    <variable cmeta:id="F0_F1_ATPase.p3" initial_value="0.00000000000000665" name="p3" units="dimensionless" />
    <variable cmeta:id="F0_F1_ATPase.pa" initial_value="0.00001656" name="pa" units="per_second" />
    <variable cmeta:id="F0_F1_ATPase.pb" initial_value="0.0000003373" name="pb" units="per_second" />
    <variable cmeta:id="F0_F1_ATPase.pc1" initial_value="0.00000000000009651" name="pc1" units="per_second" />
    <variable cmeta:id="F0_F1_ATPase.pc2" initial_value="0.0000000000000000004845" name="pc2" units="per_second" />
    <variable cmeta:id="F0_F1_ATPase.ADP_m" name="ADP_m" public_interface="in" units="nanomolar" />
    <variable cmeta:id="F0_F1_ATPase.delta_pH" name="delta_pH" public_interface="in" units="dimensionless" />
    <variable cmeta:id="F0_F1_ATPase.R" name="R" public_interface="in" units="millijoule_per_mole_kelvin" />
    <variable cmeta:id="F0_F1_ATPase.F" name="F" public_interface="in" units="coulomb_per_mole" />
    <variable cmeta:id="F0_F1_ATPase.T" name="T" public_interface="in" units="kelvin" />
    <variable cmeta:id="F0_F1_ATPase.V" name="V" public_interface="in" units="millivolt" />
    <variable cmeta:id="F0_F1_ATPase.V_B" name="V_B" public_interface="in" units="millivolt" />
    <variable cmeta:id="F0_F1_ATPase.time" name="time" public_interface="in" units="minute" />
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply id="JH_F1_calculation">
        <eq />
        <ci>JH_F1</ci>
        <apply>
          <times />
          <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">-180.0</cn>
          <ci>rho_F1</ci>
          <apply>
            <divide />
            <apply>
              <minus />
              <apply>
                <plus />
                <apply>
                  <times />
                  <ci>pa</ci>
                  <apply>
                    <power />
                    <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">10.0</cn>
                    <apply>
                      <times />
                      <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" 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 xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">10.0</cn>
                    <apply>
                      <times />
                      <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" 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 xmlns:cellml="http://www.cellml.org/cellml/1.0#" 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 xmlns:cellml="http://www.cellml.org/cellml/1.0#" 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 xmlns:cellml="http://www.cellml.org/cellml/1.0#" 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 xmlns:cellml="http://www.cellml.org/cellml/1.0#" 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 xmlns:cellml="http://www.cellml.org/cellml/1.0#" 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 xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">10.0</cn>
                        <apply>
                          <times />
                          <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" 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 xmlns:cellml="http://www.cellml.org/cellml/1.0#" 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 xmlns:cellml="http://www.cellml.org/cellml/1.0#" 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 xmlns:cellml="http://www.cellml.org/cellml/1.0#" 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 xmlns:cellml="http://www.cellml.org/cellml/1.0#" 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 xmlns:cellml="http://www.cellml.org/cellml/1.0#" 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 xmlns:cellml="http://www.cellml.org/cellml/1.0#" 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="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="ADP_m_free_calculation">
        <eq />
        <ci>ADP_m_free</ci>
        <apply>
          <times />
          <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">0.8</cn>
          <ci>ADP_m</ci>
        </apply>
      </apply>
    </math>
  </component>
  <component name="ATP_ADP_exchange">
    <variable cmeta:id="ATP_ADP_exchange.J_ant" name="J_ant" public_interface="out" units="nanomole_per_minute_per_mg" />
    <variable cmeta:id="ATP_ADP_exchange.ADP_m" name="ADP_m" public_interface="out" units="nanomolar" />
    <variable cmeta:id="ATP_ADP_exchange.Jmax_ant" initial_value="1000.0" name="Jmax_ant" units="nanomole_per_minute_per_mg" />
    <variable cmeta:id="ATP_ADP_exchange.ATP_i" name="ATP_i" units="nanomolar" />
    <variable cmeta:id="ATP_ADP_exchange.ATP_m" name="ATP_m" units="nanomolar" />
    <variable cmeta:id="ATP_ADP_exchange.ADP_i" name="ADP_i" units="nanomolar" />
    <variable cmeta:id="ATP_ADP_exchange.ATP4_i" name="ATP4_i" units="nanomolar" />
    <variable cmeta:id="ATP_ADP_exchange.ATP4_m" name="ATP4_m" units="nanomolar" />
    <variable cmeta:id="ATP_ADP_exchange.ADP3_i" name="ADP3_i" units="nanomolar" />
    <variable cmeta:id="ATP_ADP_exchange.ADP3_m" name="ADP3_m" units="nanomolar" />
    <variable cmeta:id="ATP_ADP_exchange.f" initial_value="0.5" name="f" units="dimensionless" />
    <variable cmeta:id="ATP_ADP_exchange.Jp_F1" name="Jp_F1" public_interface="in" units="nanomole_per_minute_per_mg" />
    <variable cmeta:id="ATP_ADP_exchange.R" name="R" public_interface="in" units="millijoule_per_mole_kelvin" />
    <variable cmeta:id="ATP_ADP_exchange.F" name="F" public_interface="in" units="coulomb_per_mole" />
    <variable cmeta:id="ATP_ADP_exchange.T" name="T" public_interface="in" units="kelvin" />
    <variable cmeta:id="ATP_ADP_exchange.V" name="V" public_interface="in" units="millivolt" />
    <variable cmeta:id="ATP_ADP_exchange.time" name="time" public_interface="in" units="minute" />
    <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 xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1.0</cn>
              <apply>
                <times />
                <apply>
                  <divide />
                  <apply>
                    <times />
                    <ci>ATP4_i</ci>
                    <ci>ADP3_m</ci>
                  </apply>
                  <apply>
                    <times />
                    <ci>ADP3_i</ci>
                    <ci>ATP4_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 xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1.0</cn>
                <apply>
                  <times />
                  <apply>
                    <divide />
                    <ci>ATP4_i</ci>
                    <ci>ADP3_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 xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1.0</cn>
                <apply>
                  <divide />
                  <ci>ADP3_m</ci>
                  <ci>ATP4_m</ci>
                </apply>
              </apply>
            </apply>
          </apply>
        </apply>
      </apply>
      <apply id="ADP_m_diff_eq">
        <eq />
        <apply>
          <diff />
          <bvar>
            <ci>time</ci>
          </bvar>
          <ci>ADP_m</ci>
        </apply>
        <apply>
          <minus />
          <ci>J_ant</ci>
          <ci>Jp_F1</ci>
        </apply>
      </apply>
      <apply id="ADP3_m_calculation">
        <eq />
        <ci>ADP3_m</ci>
        <apply>
          <times />
          <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">0.45</cn>
          <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">0.8</cn>
          <ci>ADP_m</ci>
        </apply>
      </apply>
      <apply id="ADP3_i_calculation">
        <eq />
        <ci>ADP3_i</ci>
        <apply>
          <times />
          <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">0.45</cn>
          <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1.0</cn>
          <ci>ADP_i</ci>
        </apply>
      </apply>
      <apply id="ATP4_m_calculation">
        <eq />
        <ci>ATP4_m</ci>
        <apply>
          <times />
          <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">0.05</cn>
          <ci>ATP_m</ci>
        </apply>
      </apply>
      <apply id="ATP4_i_calculation">
        <eq />
        <ci>ATP4_i</ci>
        <apply>
          <times />
          <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">0.05</cn>
          <ci>ATP_i</ci>
        </apply>
      </apply>
    </math>
  </component>
  <component name="Ca_uniporter">
    <variable cmeta:id="Ca_uniporter.J_uni" name="J_uni" public_interface="out" units="nanomole_per_minute_per_mg" />
    <variable cmeta:id="Ca_uniporter.V_offset" initial_value="91.0" name="V_offset" public_interface="out" units="millivolt" />
    <variable cmeta:id="Ca_uniporter.Jmax_uni" initial_value="300.0" name="Jmax_uni" units="nanomole_per_minute_per_mg" />
    <variable cmeta:id="Ca_uniporter.Ca_i" name="Ca_i" units="nanomolar" />
    <variable cmeta:id="Ca_uniporter.K_trans" initial_value="19.0" name="K_trans" units="micromolar" />
    <variable cmeta:id="Ca_uniporter.K_act" initial_value="0.38" name="K_act" units="micromolar" />
    <variable cmeta:id="Ca_uniporter.L" initial_value="110.0" name="L" units="dimensionless" />
    <variable cmeta:id="Ca_uniporter.na" initial_value="2.8" name="na" units="dimensionless" />
    <variable cmeta:id="Ca_uniporter.R" name="R" public_interface="in" units="millijoule_per_mole_kelvin" />
    <variable cmeta:id="Ca_uniporter.F" name="F" public_interface="in" units="coulomb_per_mole" />
    <variable cmeta:id="Ca_uniporter.T" name="T" public_interface="in" units="kelvin" />
    <variable cmeta:id="Ca_uniporter.V" name="V" public_interface="in" units="millivolt" />
    <variable cmeta:id="Ca_uniporter.time" name="time" public_interface="in" units="minute" />
    <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 xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1.0</cn>
                  <apply>
                    <divide />
                    <ci>Ca_i</ci>
                    <ci>K_trans</ci>
                  </apply>
                </apply>
                <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">3.0</cn>
              </apply>
            </apply>
            <apply>
              <plus />
              <apply>
                <power />
                <apply>
                  <plus />
                  <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1.0</cn>
                  <apply>
                    <divide />
                    <ci>Ca_i</ci>
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                  </apply>
                </apply>
                <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">4.0</cn>
              </apply>
              <apply>
                <divide />
                <ci>L</ci>
                <apply>
                  <power />
                  <apply>
                    <plus />
                    <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" 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 xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2.0</cn>
                <ci>F</ci>
                <apply>
                  <minus />
                  <ci>V</ci>
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                </apply>
              </apply>
              <apply>
                <times />
                <ci>R</ci>
                <ci>T</ci>
              </apply>
            </apply>
            <apply>
              <minus />
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                <exp />
                <apply>
                  <divide />
                  <apply>
                    <times />
                    <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">-2.0</cn>
                    <ci>F</ci>
                    <apply>
                      <minus />
                      <ci>V</ci>
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                    </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 cmeta:id="Na_Ca_exchanger.J_Na_Ca" name="J_Na_Ca" units="nanomole_per_minute_per_mg" />
    <variable cmeta:id="Na_Ca_exchanger.Jmax_Na_Ca" initial_value="25.0" name="Jmax_Na_Ca" units="nanomole_per_minute_per_mg" />
    <variable cmeta:id="Na_Ca_exchanger.Ca_m" name="Ca_m" units="nanomolar" />
    <variable cmeta:id="Na_Ca_exchanger.Na_i" initial_value="30.0" name="Na_i" units="millimolar" />
    <variable cmeta:id="Na_Ca_exchanger.K_Na" initial_value="9.4" name="K_Na" units="millimolar" />
    <variable cmeta:id="Na_Ca_exchanger.K_Ca" initial_value="0.003" name="K_Ca" units="nanomole_per_mg" />
    <variable cmeta:id="Na_Ca_exchanger.b" initial_value="0.0" name="b" units="dimensionless" />
    <variable cmeta:id="Na_Ca_exchanger.n" initial_value="2.0" name="n" units="dimensionless" />
    <variable cmeta:id="Na_Ca_exchanger.fm" initial_value="0.0003" name="fm" units="dimensionless" />
    <variable cmeta:id="Na_Ca_exchanger.J_uni" name="J_uni" public_interface="in" units="nanomole_per_minute_per_mg" />
    <variable cmeta:id="Na_Ca_exchanger.V_offset" name="V_offset" public_interface="in" units="millivolt" />
    <variable cmeta:id="Na_Ca_exchanger.R" name="R" public_interface="in" units="millijoule_per_mole_kelvin" />
    <variable cmeta:id="Na_Ca_exchanger.F" name="F" public_interface="in" units="coulomb_per_mole" />
    <variable cmeta:id="Na_Ca_exchanger.T" name="T" public_interface="in" units="kelvin" />
    <variable cmeta:id="Na_Ca_exchanger.V" name="V" public_interface="in" units="millivolt" />
    <variable cmeta:id="Na_Ca_exchanger.time" name="time" public_interface="in" units="minute" />
    <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>
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                  <apply>
                    <minus />
                    <ci>V</ci>
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                  </apply>
                </apply>
                <apply>
                  <times />
                  <ci>R</ci>
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                </apply>
              </apply>
            </apply>
            <apply>
              <times />
              <apply>
                <power />
                <apply>
                  <plus />
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                  <apply>
                    <divide />
                    <ci>K_Na</ci>
                    <ci>Na_i</ci>
                  </apply>
                </apply>
                <ci>n</ci>
              </apply>
              <apply>
                <plus />
                <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1.0</cn>
                <apply>
                  <divide />
                  <ci>K_Ca</ci>
                  <ci>Ca_m</ci>
                </apply>
              </apply>
            </apply>
          </apply>
        </apply>
      </apply>
      <apply id="Ca_m_diff_eq">
        <eq />
        <apply>
          <diff />
          <bvar>
            <ci>time</ci>
          </bvar>
          <ci>Ca_m</ci>
        </apply>
        <apply>
          <times />
          <ci>fm</ci>
          <apply>
            <minus />
            <ci>J_uni</ci>
            <ci>J_Na_Ca</ci>
          </apply>
        </apply>
      </apply>
    </math>
  </component>
  <group>
    <relationship_ref relationship="containment" />
    <component_ref component="membrane">
      <component_ref component="proton_leak" />
      <component_ref component="Ca_uniporter" />
      <component_ref component="ATP_ADP_exchange" />
      <component_ref component="proton_pump" />
      <component_ref component="Na_Ca_exchanger" />
      <component_ref component="F0_F1_ATPase" />
    </component_ref>
  </group>
  <connection>
    <map_components component_1="proton_pump" component_2="membrane" />
    <map_variables variable_1="JH_res" variable_2="JH_res" />
  </connection>
  <connection>
    <map_components component_1="environment" component_2="proton_pump" />
    <map_variables variable_1="time" variable_2="time" />
  </connection>
  <connection>
    <map_components component_1="Ca_uniporter" component_2="Na_Ca_exchanger" />
    <map_variables variable_1="J_uni" variable_2="J_uni" />
    <map_variables variable_1="V_offset" variable_2="V_offset" />
  </connection>
  <connection>
    <map_components component_1="membrane" component_2="Na_Ca_exchanger" />
    <map_variables variable_1="V" variable_2="V" />
    <map_variables variable_1="F" variable_2="F" />
    <map_variables variable_1="T" variable_2="T" />
    <map_variables variable_1="R" variable_2="R" />
  </connection>
  <connection>
    <map_components component_1="ATP_ADP_exchange" component_2="F0_F1_ATPase" />
    <map_variables variable_1="ADP_m" variable_2="ADP_m" />
  </connection>
  <connection>
    <map_components component_1="membrane" component_2="ATP_ADP_exchange" />
    <map_variables variable_1="V" variable_2="V" />
    <map_variables variable_1="F" variable_2="F" />
    <map_variables variable_1="T" variable_2="T" />
    <map_variables variable_1="R" variable_2="R" />
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  <connection>
    <map_components component_1="Ca_uniporter" component_2="membrane" />
    <map_variables variable_1="J_uni" variable_2="J_uni" />
  </connection>
  <connection>
    <map_components component_1="environment" component_2="F0_F1_ATPase" />
    <map_variables variable_1="time" variable_2="time" />
  </connection>
  <connection>
    <map_components component_1="ATP_ADP_exchange" component_2="membrane" />
    <map_variables variable_1="J_ant" variable_2="J_ant" />
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  <connection>
    <map_components component_1="environment" component_2="ATP_ADP_exchange" />
    <map_variables variable_1="time" variable_2="time" />
  </connection>
  <connection>
    <map_components component_1="membrane" component_2="Ca_uniporter" />
    <map_variables variable_1="V" variable_2="V" />
    <map_variables variable_1="F" variable_2="F" />
    <map_variables variable_1="T" variable_2="T" />
    <map_variables variable_1="R" variable_2="R" />
  </connection>
  <connection>
    <map_components component_1="environment" component_2="proton_leak" />
    <map_variables variable_1="time" variable_2="time" />
  </connection>
  <connection>
    <map_components component_1="F0_F1_ATPase" component_2="membrane" />
    <map_variables variable_1="JH_F1" variable_2="JH_F1" />
  </connection>
  <connection>
    <map_components component_1="membrane" component_2="proton_pump" />
    <map_variables variable_1="V" variable_2="V" />
    <map_variables variable_1="F" variable_2="F" />
    <map_variables variable_1="V_B" variable_2="V_B" />
    <map_variables variable_1="T" variable_2="T" />
    <map_variables variable_1="delta_pH" variable_2="delta_pH" />
    <map_variables variable_1="R" variable_2="R" />
  </connection>
  <connection>
    <map_components component_1="proton_leak" component_2="membrane" />
    <map_variables variable_1="JH_leak" variable_2="JH_leak" />
  </connection>
  <connection>
    <map_components component_1="environment" component_2="Na_Ca_exchanger" />
    <map_variables variable_1="time" variable_2="time" />
  </connection>
  <connection>
    <map_components component_1="environment" component_2="Ca_uniporter" />
    <map_variables variable_1="time" variable_2="time" />
  </connection>
  <connection>
    <map_components component_1="membrane" component_2="F0_F1_ATPase" />
    <map_variables variable_1="V" variable_2="V" />
    <map_variables variable_1="F" variable_2="F" />
    <map_variables variable_1="V_B" variable_2="V_B" />
    <map_variables variable_1="T" variable_2="T" />
    <map_variables variable_1="delta_pH" variable_2="delta_pH" />
    <map_variables variable_1="R" variable_2="R" />
  </connection>
  <connection>
    <map_components component_1="membrane" component_2="proton_leak" />
    <map_variables variable_1="g_H" variable_2="g_H" />
    <map_variables variable_1="proton_motive_force" variable_2="proton_motive_force" />
  </connection>
  <connection>
    <map_components component_1="environment" component_2="membrane" />
    <map_variables variable_1="time" variable_2="time" />
  </connection>
  <connection>
    <map_components component_1="F0_F1_ATPase" component_2="ATP_ADP_exchange" />
    <map_variables variable_1="Jp_F1" variable_2="Jp_F1" />
  </connection>
  <rdf:RDF xmlns:bqmodel="http://biomodels.net/model-qualifiers/" xmlns:bqbiol="http://biomodels.net/biology-qualifiers/" xmlns:ro="http://www.obofoundry.org/ro/ro.owl#" xmlns:opb="http://bhi.washington.edu/OPB#">
    <rdf:Description rdf:about="#Na_Ca_exchanger.Na_i">
      <semsim:isComputationalComponentFor>
        <rdf:Description rdf:about="#property_42">
          <semsim:physicalPropertyOf>
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              <ro:part_of>
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        </rdf:Description>
      </semsim:isComputationalComponentFor>
      <dcterms:description>concentration of intracellular sodium</dcterms:description>
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    <rdf:Description rdf:about="magnus_keizer_1997.cellml#ATP_ADP_exchange.Jmax_ant">
      <dcterms:description>maximum adenine nucleotide translocator flux</dcterms:description>
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    <rdf:Description rdf:about="#Ca_uniporter.V_offset">
      <dcterms:description>calcium uniporter voltage offset for calcium transport</dcterms:description>
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    <rdf:Description rdf:about="magnus_keizer_1997.cellml#proton_pump.total_NAD_m">
      <bqbiol:isPropertyOf>
        <rdf:Description rdf:about="magnus_keizer_1997.cellml#entity_2">
          <bqbiol:is rdf:resource="https://identifiers.org/chebi/CHEBI:13389" />
        </rdf:Description>
      </bqbiol:isPropertyOf>
      <dcterms:description>concentration of total mitochondrial NAD</dcterms:description>
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      <bqbiol:isPropertyOf>
        <rdf:Description rdf:about="magnus_keizer_1997.cellml#entity_0">
          <bqbiol:is rdf:resource="https://identifiers.org/chebi/CHEBI:29108" />
        </rdf:Description>
      </bqbiol:isPropertyOf>
      <dcterms:description>calcium equilibrium constant of F1F0-ATPase</dcterms:description>
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      <bqbiol:is rdf:resource="https://identifiers.org/opb/OPB_00410" />
    </rdf:Description>
    <rdf:Description rdf:about="magnus_keizer_1997.cellml#proton_pump.V_B">
      <dcterms:description>total phase boundary potential</dcterms:description>
    </rdf:Description>
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      <bqbiol:isPropertyOf>
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          <bqbiol:is rdf:resource="https://identifiers.org/chebi/CHEBI:22256" />
        </rdf:Description>
      </bqbiol:isPropertyOf>
      <dcterms:description>concentration of total mitochondrial adenosine phosphate</dcterms:description>
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      <bqbiol:is rdf:resource="https://identifiers.org/opb/OPB_01023" />
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      <bqbiol:is rdf:resource="https://identifiers.org/opb/OPB_01296" />
      <dcterms:description>sum of respiration driven proton pump products</dcterms:description>
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      <bqbiol:isPropertyOf>
        <rdf:Description rdf:about="magnus_keizer_1997.cellml#entity_17">
          <bqbiol:is rdf:resource="https://identifiers.org/chebi/CHEBI:29101" />
        </rdf:Description>
      </bqbiol:isPropertyOf>
      <dcterms:description>concentration of intracellular sodium</dcterms:description>
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      <semsim:isComputationalComponentFor>
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      </semsim:isComputationalComponentFor>
      <dcterms:description>sodium-calcium exchanger flux</dcterms:description>
    </rdf:Description>
    <rdf:Description rdf:about="#membrane.V">
      <semsim:isComputationalComponentFor>
        <rdf:Description rdf:about="#property_0">
          <semsim:hasPhysicalDefinition rdf:resource="https://identifiers.org/opb/OPB_00506" />
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      </semsim:isComputationalComponentFor>
      <dcterms:description>membrane potential</dcterms:description>
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      <bqbiol:is rdf:resource="https://identifiers.org/opb/OPB_00089" />
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    <rdf:Description rdf:about="#ATP_ADP_exchange.Jp_F1">
      <semsim:isComputationalComponentFor>
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          <semsim:hasPhysicalDefinition rdf:resource="https://identifiers.org/opb/OPB_00592" />
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      </semsim:isComputationalComponentFor>
      <dcterms:description>phosphate flux through F1F0-ATPase driven proton pumps</dcterms:description>
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    <rdf:Description rdf:about="magnus_keizer_1997.cellml#ATP_ADP_exchange.Jp_F1">
      <dcterms:description>phosphate flux through F1F0-ATPase driven proton pumps</dcterms:description>
    </rdf:Description>
    <rdf:Description rdf:about="magnus_keizer_1997.cellml#proton_leak.proton_motive_force">
      <dcterms:description>proton motive force</dcterms:description>
    </rdf:Description>
    <rdf:Description rdf:about="#membrane.Cmito">
      <dcterms:description>inner mitochondrial membrane capacitance</dcterms:description>
    </rdf:Description>
    <rdf:Description rdf:about="#ATP_ADP_exchange.ATP_i">
      <semsim:isComputationalComponentFor>
        <rdf:Description rdf:about="#property_26">
          <semsim:physicalPropertyOf>
            <rdf:Description rdf:about="#entity_10">
              <ro:part_of rdf:resource="#entity_1" />
              <semsim:hasPhysicalDefinition rdf:resource="https://identifiers.org/chebi/CHEBI:15422" />
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          </semsim:physicalPropertyOf>
          <semsim:hasPhysicalDefinition rdf:resource="https://identifiers.org/opb/OPB_00340" />
        </rdf:Description>
      </semsim:isComputationalComponentFor>
      <dcterms:description>concentration of cytosolic ATP</dcterms:description>
    </rdf:Description>
    <rdf:Description rdf:about="#F0_F1_ATPase.JH_F1">
      <semsim:isComputationalComponentFor>
        <rdf:Description rdf:about="#property_15">
          <semsim:hasPhysicalDefinition rdf:resource="https://identifiers.org/opb/OPB_00592" />
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      </semsim:isComputationalComponentFor>
      <dcterms:description>proton flux through F1F0-ATPase driven proton pumps</dcterms:description>
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    <rdf:Description rdf:about="magnus_keizer_1997.cellml#F0_F1_ATPase.Pi_m">
      <bqbiol:isPropertyOf>
        <rdf:Description rdf:about="magnus_keizer_1997.cellml#entity_9">
          <bqbiol:is rdf:resource="https://identifiers.org/chebi/CHEBI:24838" />
        </rdf:Description>
      </bqbiol:isPropertyOf>
      <dcterms:description>concentration of mitochondrial inorganic phosphate</dcterms:description>
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    <rdf:Description rdf:about="#membrane.F">
      <bqbiol:is rdf:resource="https://identifiers.org/opb/OPB_00089" />
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      <bqbiol:is rdf:resource="https://identifiers.org/opb/OPB_01296" />
      <dcterms:description>sum of respiration driven proton pump products</dcterms:description>
    </rdf:Description>
    <rdf:Description rdf:about="#proton_pump.R">
      <bqbiol:is rdf:resource="https://identifiers.org/opb/OPB_00410" />
    </rdf:Description>
    <rdf:Description rdf:about="magnus_keizer_1997.cellml#Na_Ca_exchanger.V">
      <dcterms:description>membrane potential</dcterms:description>
    </rdf:Description>
    <rdf:Description rdf:about="#Ca_uniporter.Ca_i">
      <semsim:isComputationalComponentFor>
        <rdf:Description rdf:about="#property_36">
          <semsim:physicalPropertyOf>
            <rdf:Description rdf:about="#entity_0">
              <ro:part_of rdf:resource="#entity_1" />
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            </rdf:Description>
          </semsim:physicalPropertyOf>
          <semsim:hasPhysicalDefinition rdf:resource="https://identifiers.org/opb/OPB_00340" />
        </rdf:Description>
      </semsim:isComputationalComponentFor>
      <dcterms:description>concentration of intracellular calcium</dcterms:description>
    </rdf:Description>
    <rdf:Description rdf:about="#Ca_uniporter.time">
      <bqbiol:is rdf:resource="https://identifiers.org/opb/OPB_01023" />
    </rdf:Description>
    <rdf:Description rdf:about="magnus_keizer_1997.cellml#proton_pump.K_res">
      <bqbiol:isPropertyOf rdf:resource="magnus_keizer_1997.cellml#entity_0" />
      <dcterms:description>calcium equilibrium constant of respiration driven proton pump</dcterms:description>
    </rdf:Description>
    <rdf:Description rdf:about="#ATP_ADP_exchange.T">
      <dcterms:description>absolute temperature</dcterms:description>
    </rdf:Description>
    <rdf:Description rdf:about="magnus_keizer_1997.cellml#ATP_ADP_exchange.ADP3_i">
      <bqbiol:isPropertyOf>
        <rdf:Description rdf:about="magnus_keizer_1997.cellml#entity_14">
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      <dcterms:description>concentration of cytosolic ADP(3-)</dcterms:description>
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    <rdf:Description rdf:about="magnus_keizer_1997.cellml#Ca_uniporter.L">
      <dcterms:description>equilibrium constant for calcium uniporter conformations</dcterms:description>
    </rdf:Description>
    <rdf:Description rdf:about="#Ca_uniporter.na">
      <dcterms:description>calcium uniporter activation cooperativity</dcterms:description>
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    <rdf:Description rdf:about="magnus_keizer_1997.cellml#ATP_ADP_exchange.T">
      <dcterms:description>absolute temperature</dcterms:description>
    </rdf:Description>
    <rdf:Description rdf:about="magnus_keizer_1997.cellml#proton_pump.rho_res">
      <dcterms:description>proton pump density</dcterms:description>
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    <rdf:Description rdf:about="magnus_keizer_1997.cellml#membrane.g_H">
      <dcterms:description>proton leakage conductance</dcterms:description>
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      <bqbiol:isPropertyOf rdf:resource="magnus_keizer_1997.cellml#entity_17" />
      <dcterms:description>sodium half-saturation constant of sodium-calcium exchanger</dcterms:description>
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    <rdf:Description rdf:about="magnus_keizer_1997.cellml#membrane.R">
      <bqbiol:is rdf:resource="https://identifiers.org/opb/OPB_00410" />
    </rdf:Description>
    <rdf:Description rdf:about="#membrane.pH_m">
      <dcterms:description>pH of mitochondrial matrix</dcterms:description>
    </rdf:Description>
    <rdf:Description rdf:about="#F0_F1_ATPase.V_B">
      <dcterms:description>total phase boundary potential</dcterms:description>
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    <rdf:Description rdf:about="magnus_keizer_1997.cellml#F0_F1_ATPase.pa">
      <bqbiol:is rdf:resource="https://identifiers.org/opb/OPB_01296" />
      <dcterms:description>sum of F1F0-ATPase products</dcterms:description>
    </rdf:Description>
    <rdf:Description rdf:about="#proton_pump.ra">
      <bqbiol:is rdf:resource="https://identifiers.org/opb/OPB_01296" />
      <dcterms:description>sum of respiration driven proton pump products</dcterms:description>
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    <rdf:Description rdf:about="magnus_keizer_1997.cellml#membrane.pH_i">
      <dcterms:description>pH of cytosol</dcterms:description>
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      <bqbiol:is rdf:resource="https://identifiers.org/opb/OPB_01023" />
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    <rdf:Description rdf:about="#proton_pump.JH_res">
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        <rdf:Description rdf:about="#property_7">
          <semsim:hasPhysicalDefinition rdf:resource="https://identifiers.org/opb/OPB_00592" />
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      </semsim:isComputationalComponentFor>
      <dcterms:description>proton flux via respiration driven proton pumps</dcterms:description>
    </rdf:Description>
    <rdf:Description rdf:about="#membrane.T">
      <dcterms:description>absolute temperature</dcterms:description>
    </rdf:Description>
    <rdf:Description rdf:about="#proton_leak.time">
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    <rdf:Description rdf:about="magnus_keizer_1997.cellml#F0_F1_ATPase.ADP_m">
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        <rdf:Description rdf:about="magnus_keizer_1997.cellml#entity_8">
          <bqbiol:is rdf:resource="https://identifiers.org/chebi/CHEBI:16761" />
        </rdf:Description>
      </bqbiol:isPropertyOf>
      <dcterms:description>concentration of mitochondrial ADP</dcterms:description>
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    <rdf:Description rdf:about="#F0_F1_ATPase.Jp_F1">
      <semsim:isComputationalComponentFor>
        <rdf:Description rdf:about="#property_16">
          <semsim:hasPhysicalDefinition rdf:resource="https://identifiers.org/opb/OPB_00592" />
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      </semsim:isComputationalComponentFor>
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      <dcterms:description>sum of F1F0-ATPase products</dcterms:description>
    </rdf:Description>
    <rdf:Description rdf:about="#proton_pump.r1">
      <dcterms:description>sum of respiration driven proton pump products</dcterms:description>
    </rdf:Description>
    <rdf:Description rdf:about="magnus_keizer_1997.cellml#F0_F1_ATPase.time">
      <bqbiol:is rdf:resource="https://identifiers.org/opb/OPB_01023" />
    </rdf:Description>
    <rdf:Description rdf:about="#proton_pump.V_B">
      <dcterms:description>total phase boundary potential</dcterms:description>
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    <rdf:Description rdf:about="#ATP_ADP_exchange.ATP4_m">
      <semsim:isComputationalComponentFor>
        <rdf:Description rdf:about="#property_30">
          <semsim:physicalPropertyOf>
            <rdf:Description rdf:about="#entity_13">
              <ro:part_of>
                <rdf:Description rdf:about="#entity_3">
                  <semsim:hasPhysicalDefinition rdf:resource="http://identifiers.org/fma/FMA:66864" />
                </rdf:Description>
              </ro:part_of>
              <semsim:hasPhysicalDefinition rdf:resource="https://identifiers.org/chebi/CHEBI:30616" />
            </rdf:Description>
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          <semsim:hasPhysicalDefinition rdf:resource="https://identifiers.org/opb/OPB_00340" />
        </rdf:Description>
      </semsim:isComputationalComponentFor>
      <dcterms:description>concentration of mitochondrial ATP(4-)</dcterms:description>
    </rdf:Description>
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      <dcterms:description>phosphate flux through F1F0-ATPase driven proton pumps</dcterms:description>
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      <dcterms:description>proton flux via respiration driven proton pumps</dcterms:description>
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    <rdf:Description rdf:about="#Ca_uniporter.V">
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        <rdf:Description rdf:about="#property_39">
          <semsim:hasPhysicalDefinition rdf:resource="https://identifiers.org/opb/OPB_00506" />
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      </semsim:isComputationalComponentFor>
      <dcterms:description>membrane potential</dcterms:description>
    </rdf:Description>
    <rdf:Description rdf:about="#ATP_ADP_exchange.R">
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    </rdf:Description>
    <rdf:Description rdf:about="magnus_keizer_1997.cellml#F0_F1_ATPase.pb">
      <bqbiol:is rdf:resource="https://identifiers.org/opb/OPB_01296" />
      <dcterms:description>sum of F1F0-ATPase products</dcterms:description>
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    <rdf:Description rdf:about="#F0_F1_ATPase.ADP_m">
      <semsim:isComputationalComponentFor>
        <rdf:Description rdf:about="#property_22">
          <semsim:physicalPropertyOf>
            <rdf:Description rdf:about="#entity_8">
              <ro:part_of rdf:resource="#entity_3" />
              <semsim:hasPhysicalDefinition rdf:resource="https://identifiers.org/chebi/CHEBI:16761" />
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          </semsim:physicalPropertyOf>
          <semsim:hasPhysicalDefinition rdf:resource="https://identifiers.org/opb/OPB_00340" />
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      </semsim:isComputationalComponentFor>
      <dcterms:description>concentration of mitochondrial ADP</dcterms:description>
    </rdf:Description>
    <rdf:Description rdf:about="#proton_pump.rb">
      <bqbiol:is rdf:resource="https://identifiers.org/opb/OPB_01296" />
      <dcterms:description>sum of respiration driven proton pump products</dcterms:description>
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    <rdf:Description rdf:about="magnus_keizer_1997.cellml#F0_F1_ATPase.pc1">
      <bqbiol:is rdf:resource="https://identifiers.org/opb/OPB_01296" />
      <dcterms:description>sum of F1F0-ATPase products</dcterms:description>
    </rdf:Description>
    <rdf:Description rdf:about="#proton_pump.g">
      <dcterms:description>voltage fitting factor for respiratory driven proton pump</dcterms:description>
    </rdf:Description>
    <rdf:Description rdf:about="#proton_pump.F">
      <bqbiol:is rdf:resource="https://identifiers.org/opb/OPB_00089" />
    </rdf:Description>
    <rdf:Description rdf:about="magnus_keizer_1997.cellml#F0_F1_ATPase.p2">
      <dcterms:description>sum of F1F0-ATPase products</dcterms:description>
    </rdf:Description>
    <rdf:Description rdf:about="magnus_keizer_1997.cellml#ATP_ADP_exchange.J_ant">
      <dcterms:description>adenine nucleotide translocator flux</dcterms:description>
    </rdf:Description>
    <rdf:Description rdf:about="magnus_keizer_1997.cellml#F0_F1_ATPase.A_F1">
      <dcterms:description>driving reaction affinity of F1F0-ATPase</dcterms:description>
    </rdf:Description>
    <rdf:Description rdf:about="#Ca_uniporter.L">
      <dcterms:description>equilibrium constant for calcium uniporter conformations</dcterms:description>
    </rdf:Description>
    <rdf:Description rdf:about="magnus_keizer_1997.cellml#ATP_ADP_exchange.V">
      <dcterms:description>membrane potential</dcterms:description>
    </rdf:Description>
    <rdf:Description rdf:about="magnus_keizer_1997.cellml#F0_F1_ATPase.rho_F1">
      <dcterms:description>F1F0-ATPase pump concentration</dcterms:description>
    </rdf:Description>
    <rdf:Description rdf:about="#proton_pump.r2">
      <dcterms:description>sum of respiration driven proton pump products</dcterms:description>
    </rdf:Description>
    <rdf:Description rdf:about="magnus_keizer_1997.cellml#ATP_ADP_exchange.ATP4_m">
      <bqbiol:isPropertyOf>
        <rdf:Description rdf:about="magnus_keizer_1997.cellml#entity_13">
          <bqbiol:is rdf:resource="https://identifiers.org/chebi/CHEBI:30616" />
        </rdf:Description>
      </bqbiol:isPropertyOf>
      <dcterms:description>concentration of mitochondrial ATP(4-)</dcterms:description>
    </rdf:Description>
    <rdf:Description rdf:about="magnus_keizer_1997.cellml#Na_Ca_exchanger.Jmax_Na_Ca">
      <dcterms:description>maximum sodium-calcium exchanger current</dcterms:description>
    </rdf:Description>
    <rdf:Description rdf:about="magnus_keizer_1997.cellml#ATP_ADP_exchange.f">
      <dcterms:description>fraction of effective voltage difference</dcterms:description>
    </rdf:Description>
    <rdf:Description rdf:about="magnus_keizer_1997.cellml#membrane.JH_F1">
      <dcterms:description>proton flux through F1F0-ATPase driven proton pumps</dcterms:description>
    </rdf:Description>
    <rdf:Description rdf:about="magnus_keizer_1997.cellml#ATP_ADP_exchange.ATP_i">
      <bqbiol:isPropertyOf>
        <rdf:Description rdf:about="magnus_keizer_1997.cellml#entity_10">
          <bqbiol:is rdf:resource="https://identifiers.org/chebi/CHEBI:15422" />
        </rdf:Description>
      </bqbiol:isPropertyOf>
      <dcterms:description>concentration of cytosolic ATP</dcterms:description>
    </rdf:Description>
    <rdf:Description rdf:about="magnus_keizer_1997.cellml#Na_Ca_exchanger.V_offset">
      <dcterms:description>calcium uniporter voltage offset for calcium transport</dcterms:description>
    </rdf:Description>
    <rdf:Description rdf:about="#Ca_uniporter.K_trans">
      <semsim:isComputationalComponentFor>
        <rdf:Description rdf:about="#property_37">
          <semsim:physicalPropertyOf rdf:resource="#entity_0" />
          <semsim:hasPhysicalDefinition rdf:resource="https://identifiers.org/opb/OPB_00340" />
        </rdf:Description>
      </semsim:isComputationalComponentFor>
      <dcterms:description>calcium dissociation constant of uniporter transportation</dcterms:description>
    </rdf:Description>
    <rdf:Description rdf:about="#Ca_uniporter.K_act">
      <semsim:isComputationalComponentFor>
        <rdf:Description rdf:about="#property_38">
          <semsim:physicalPropertyOf rdf:resource="#entity_0" />
          <semsim:hasPhysicalDefinition rdf:resource="https://identifiers.org/opb/OPB_00340" />
        </rdf:Description>
      </semsim:isComputationalComponentFor>
      <dcterms:description>calcium dissociation constant of uniporter activation</dcterms:description>
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    <rdf:Description rdf:about="#proton_pump.K_res">
      <semsim:isComputationalComponentFor>
        <rdf:Description rdf:about="#property_8">
          <semsim:physicalPropertyOf rdf:resource="#entity_0" />
          <semsim:hasPhysicalDefinition rdf:resource="https://identifiers.org/opb/OPB_00340" />
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      </semsim:isComputationalComponentFor>
      <dcterms:description>calcium equilibrium constant of respiration driven proton pump</dcterms:description>
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    </rdf:Description>
    <rdf:Description rdf:about="magnus_keizer_1997.cellml#F0_F1_ATPase.p3">
      <dcterms:description>sum of F1F0-ATPase products</dcterms:description>
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      <bqbiol:is rdf:resource="https://identifiers.org/opb/OPB_01023" />
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    <rdf:Description rdf:about="magnus_keizer_1997.cellml#entity_3">
      <bqbiol:is rdf:resource="http://identifiers.org/fma/FMA:66864" />
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    <rdf:Description rdf:about="magnus_keizer_1997.cellml#Ca_uniporter.K_act">
      <bqbiol:isPropertyOf rdf:resource="magnus_keizer_1997.cellml#entity_0" />
      <dcterms:description>calcium dissociation constant of uniporter activation</dcterms:description>
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    <rdf:Description rdf:about="#proton_pump.r3">
      <dcterms:description>sum of respiration driven proton pump products</dcterms:description>
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    <rdf:Description rdf:about="magnus_keizer_1997.cellml#ATP_ADP_exchange.ADP3_m">
      <bqbiol:isPropertyOf>
        <rdf:Description rdf:about="magnus_keizer_1997.cellml#entity_15">
          <bqbiol:is rdf:resource="https://identifiers.org/chebi/CHEBI:456216" />
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      </bqbiol:isPropertyOf>
      <dcterms:description>concentration of mitochondrial ADP(3-)</dcterms:description>
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        <rdf:Description rdf:about="#property_12">
          <semsim:hasPhysicalDefinition rdf:resource="https://identifiers.org/opb/OPB_00506" />
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      <semsim:isComputationalComponentFor>
        <rdf:Description rdf:about="#property_45">
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      <dcterms:description>maximum sodium-calcium exchanger current</dcterms:description>
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    <rdf:Description rdf:about="#environment.time">
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      <dcterms:description>proton motive force</dcterms:description>
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      <semsim:isComputationalComponentFor>
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        <rdf:Description rdf:about="#property_34">
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      <dcterms:description>sum of respiration driven proton pump products</dcterms:description>
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      <dcterms:description>sum of F1F0-ATPase products</dcterms:description>
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      <dcterms:description>calcium flux into mitochondrial matrix through uniporter</dcterms:description>
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      <dcterms:description>sum of F1F0-ATPase products</dcterms:description>
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      <dcterms:description>concentration of cytosolic ATP(4-)</dcterms:description>
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      <dcterms:description>pH difference between cytosol and mitochondrial matrix</dcterms:description>
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        <rdf:Description rdf:about="#property_13">
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    <rdf:Description rdf:about="magnus_keizer_1997.cellml#membrane.J_ant">
      <dcterms:description>adenine nucleotide translocator flux</dcterms:description>
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      <semsim:isComputationalComponentFor>
        <rdf:Description rdf:about="#property_27">
          <semsim:physicalPropertyOf rdf:resource="#entity_7" />
          <semsim:hasPhysicalDefinition rdf:resource="https://identifiers.org/opb/OPB_00340" />
        </rdf:Description>
      </semsim:isComputationalComponentFor>
      <dcterms:description>concentration of mitochondrial ATP</dcterms:description>
    </rdf:Description>
    <rdf:Description rdf:about="#proton_leak.proton_motive_force">
      <dcterms:description>proton motive force</dcterms:description>
    </rdf:Description>
    <rdf:Description rdf:about="magnus_keizer_1997.cellml#membrane.Cmito">
      <dcterms:description>inner mitochondrial membrane capacitance</dcterms:description>
    </rdf:Description>
    <rdf:Description rdf:about="#Ca_uniporter.T">
      <dcterms:description>absolute temperature</dcterms:description>
    </rdf:Description>
    <rdf:Description rdf:about="magnus_keizer_1997.cellml#Ca_uniporter.na">
      <dcterms:description>calcium uniporter activation cooperativity</dcterms:description>
    </rdf:Description>
    <rdf:Description rdf:about="magnus_keizer_1997.cellml#proton_pump.NADH_m">
      <bqbiol:isPropertyOf>
        <rdf:Description rdf:about="magnus_keizer_1997.cellml#entity_5">
          <bqbiol:is rdf:resource="https://identifiers.org/chebi/CHEBI:16908" />
        </rdf:Description>
      </bqbiol:isPropertyOf>
      <dcterms:description>concentration of mitochondrial NADH</dcterms:description>
    </rdf:Description>
    <rdf:Description rdf:about="#F0_F1_ATPase.Pi_m">
      <semsim:isComputationalComponentFor>
        <rdf:Description rdf:about="#property_21">
          <semsim:physicalPropertyOf>
            <rdf:Description rdf:about="#entity_9">
              <ro:part_of rdf:resource="#entity_3" />
              <semsim:hasPhysicalDefinition rdf:resource="https://identifiers.org/chebi/CHEBI:24838" />
            </rdf:Description>
          </semsim:physicalPropertyOf>
          <semsim:hasPhysicalDefinition rdf:resource="https://identifiers.org/opb/OPB_00340" />
        </rdf:Description>
      </semsim:isComputationalComponentFor>
      <dcterms:description>concentration of mitochondrial inorganic phosphate</dcterms:description>
    </rdf:Description>
    <rdf:Description rdf:about="magnus_keizer_1997.cellml#F0_F1_ATPase.V">
      <dcterms:description>membrane potential</dcterms:description>
    </rdf:Description>
    <rdf:Description rdf:about="#Ca_uniporter.Jmax_uni">
      <dcterms:description>maximum calcium flux through uniporter</dcterms:description>
    </rdf:Description>
    <rdf:Description rdf:about="#proton_pump.NADH_m">
      <semsim:isComputationalComponentFor>
        <rdf:Description rdf:about="#property_11">
          <semsim:physicalPropertyOf>
            <rdf:Description rdf:about="#entity_5">
              <ro:part_of rdf:resource="#entity_3" />
              <semsim:hasPhysicalDefinition rdf:resource="https://identifiers.org/chebi/CHEBI:16908" />
            </rdf:Description>
          </semsim:physicalPropertyOf>
          <semsim:hasPhysicalDefinition rdf:resource="https://identifiers.org/opb/OPB_00340" />
        </rdf:Description>
      </semsim:isComputationalComponentFor>
      <dcterms:description>concentration of mitochondrial NADH</dcterms:description>
    </rdf:Description>
    <rdf:Description rdf:about="magnus_keizer_1997.cellml#membrane.pH_m">
      <dcterms:description>pH of mitochondrial matrix</dcterms:description>
    </rdf:Description>
    <rdf:Description rdf:about="#ATP_ADP_exchange.J_ant">
      <semsim:isComputationalComponentFor>
        <rdf:Description rdf:about="#property_24">
          <semsim:hasPhysicalDefinition rdf:resource="https://identifiers.org/opb/OPB_00592" />
        </rdf:Description>
      </semsim:isComputationalComponentFor>
      <dcterms:description>adenine nucleotide translocator flux</dcterms:description>
    </rdf:Description>
    <rdf:Description rdf:about="magnus_keizer_1997.cellml#proton_pump.r2">
      <dcterms:description>sum of respiration driven proton pump products</dcterms:description>
    </rdf:Description>
    <rdf:Description rdf:about="#Na_Ca_exchanger.V_offset">
      <dcterms:description>calcium uniporter voltage offset for calcium transport</dcterms:description>
    </rdf:Description>
    <rdf:Description rdf:about="#F0_F1_ATPase.time">
      <bqbiol:is rdf:resource="https://identifiers.org/opb/OPB_01023" />
    </rdf:Description>
    <rdf:Description rdf:about="magnus_keizer_1997.cellml#ATP_ADP_exchange.ADP_m">
      <bqbiol:isPropertyOf rdf:resource="magnus_keizer_1997.cellml#entity_8" />
      <dcterms:description>concentration of mitochondrial ADP</dcterms:description>
    </rdf:Description>
    <rdf:Description rdf:about="#membrane.pH_i">
      <dcterms:description>pH of cytosol</dcterms:description>
    </rdf:Description>
    <rdf:Description rdf:about="magnus_keizer_1997.cellml#Ca_uniporter.K_trans">
      <bqbiol:isPropertyOf rdf:resource="magnus_keizer_1997.cellml#entity_0" />
      <dcterms:description>calcium dissociation constant of uniporter transportation</dcterms:description>
    </rdf:Description>
    <rdf:Description rdf:about="#proton_pump.Jo">
      <dcterms:description>half proton flux via respiration driven proton pumps</dcterms:description>
    </rdf:Description>
    <rdf:Description rdf:about="#membrane.JH_leak">
      <semsim:isComputationalComponentFor>
        <rdf:Description rdf:about="#property_3">
          <semsim:hasPhysicalDefinition rdf:resource="https://identifiers.org/opb/OPB_00592" />
        </rdf:Description>
      </semsim:isComputationalComponentFor>
      <dcterms:description>proton leakage flux</dcterms:description>
    </rdf:Description>
    <rdf:Description rdf:about="magnus_keizer_1997.cellml#membrane.V">
      <dcterms:description>membrane potential</dcterms:description>
    </rdf:Description>
    <rdf:Description rdf:about="magnus_keizer_1997.cellml#Na_Ca_exchanger.J_uni">
      <dcterms:description>calcium flux into mitochondrial matrix through uniporter</dcterms:description>
    </rdf:Description>
    <rdf:Description rdf:about="#proton_pump.A_res">
      <dcterms:description>driving reaction affinity of respiratory driven proton pump</dcterms:description>
    </rdf:Description>
    <rdf:Description rdf:about="magnus_keizer_1997.cellml#proton_pump.r1">
      <dcterms:description>sum of respiration driven proton pump products</dcterms:description>
    </rdf:Description>
    <rdf:Description rdf:about="magnus_keizer_1997.cellml#F0_F1_ATPase.ADP_m_free">
      <bqbiol:isPropertyOf rdf:resource="magnus_keizer_1997.cellml#entity_8" />
      <dcterms:description>concentration of free mitochondrial matrix ADP</dcterms:description>
    </rdf:Description>
    <rdf:Description rdf:about="magnus_keizer_1997.cellml#ATP_ADP_exchange.time">
      <bqbiol:is rdf:resource="https://identifiers.org/opb/OPB_01023" />
    </rdf:Description>
    <rdf:Description rdf:about="#ATP_ADP_exchange.Jmax_ant">
      <dcterms:description>maximum adenine nucleotide translocator flux</dcterms:description>
    </rdf:Description>
    <rdf:Description rdf:about="magnus_keizer_1997.cellml#proton_leak.g_H">
      <dcterms:description>proton leakage conductance</dcterms:description>
    </rdf:Description>
    <rdf:Description rdf:about="#F0_F1_ATPase.delta_pH">
      <dcterms:description>pH difference between cytosol and mitochondrial matrix</dcterms:description>
    </rdf:Description>
    <rdf:Description rdf:about="magnus_keizer_1997.cellml#Na_Ca_exchanger.time">
      <bqbiol:is rdf:resource="https://identifiers.org/opb/OPB_01023" />
    </rdf:Description>
    <rdf:Description rdf:about="magnus_keizer_1997.cellml#F0_F1_ATPase.T">
      <dcterms:description>absolute temperature</dcterms:description>
    </rdf:Description>
    <rdf:Description rdf:about="#membrane.delta_pH">
      <dcterms:description>pH difference between cytosol and mitochondrial matrix</dcterms:description>
    </rdf:Description>
    <rdf:Description rdf:about="#proton_leak.g_H">
      <semsim:isComputationalComponentFor>
        <rdf:Description rdf:about="#property_14">
          <semsim:hasPhysicalDefinition rdf:resource="https://identifiers.org/opb/OPB_00041" />
        </rdf:Description>
      </semsim:isComputationalComponentFor>
      <dcterms:description>proton leakage conductance</dcterms:description>
    </rdf:Description>
    <rdf:Description rdf:about="#Ca_uniporter.R">
      <bqbiol:is rdf:resource="https://identifiers.org/opb/OPB_00410" />
    </rdf:Description>
    <rdf:Description rdf:about="#ATP_ADP_exchange.ATP4_i">
      <semsim:isComputationalComponentFor>
        <rdf:Description rdf:about="#property_29">
          <semsim:physicalPropertyOf>
            <rdf:Description rdf:about="#entity_12">
              <ro:part_of rdf:resource="#entity_1" />
              <semsim:hasPhysicalDefinition rdf:resource="https://identifiers.org/chebi/CHEBI:30616" />
            </rdf:Description>
          </semsim:physicalPropertyOf>
          <semsim:hasPhysicalDefinition rdf:resource="https://identifiers.org/opb/OPB_00340" />
        </rdf:Description>
      </semsim:isComputationalComponentFor>
      <dcterms:description>concentration of cytosolic ATP(4-)</dcterms:description>
    </rdf:Description>
    <rdf:Description rdf:about="magnus_keizer_1997.cellml#membrane.time">
      <bqbiol:is rdf:resource="https://identifiers.org/opb/OPB_01023" />
    </rdf:Description>
    <rdf:Description rdf:about="#F0_F1_ATPase.A_F1">
      <dcterms:description>driving reaction affinity of F1F0-ATPase</dcterms:description>
    </rdf:Description>
  </rdf:RDF>
</model>