Rendering of the source text

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This CellML file was generated on 17/09/2007 at 12:19:39 using:

COR (0.9.31.769)
Copyright 2002-2007 Dr Alan Garny
http://COR.physiol.ox.ac.uk/ - COR@physiol.ox.ac.uk

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http://www.CellML.org/
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<article>
  <articleinfo>
  <title>Noble-Noble Model Of Sino-Atrial Node Electrical Activity, 1984</title>
  <author>
    <firstname>Catherine</firstname>
          <surname>Lloyd</surname>
    <affiliation>
      <shortaffil>Auckland Bioengineering Institute, The University of Auckland</shortaffil>
    </affiliation>
  </author>
</articleinfo>
  <section id="sec_status">
    <title>Model Status</title>
    <para>
            This model has been curated by Penny Noble of Oxford University and is known to run in PCEnv and COR and reproduce the results published in the paper it is based on.
          </para>
  </section>
  <sect1 id="sec_structure">
<title>Model Structure</title>

<para>
In 1984 D. Noble and S.J. Noble published a mathematical model which describes electrical activity in the sino-atrial node.  Their model is based on the Purkinje fibre model developed by D. DiFrancesco and D. Noble (please see the CellML version of the DiFrancesco-Noble Purkinje Fibre Model, 1985).  Most of the equations of this cardiac cell model remain unchanged.  However, based on the results of experimental work, where necessary, certain parameters have been modified in order to make the model appropriate to a sino-atrial node.
</para>

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

<para>
A Model of Sino-Atrial Node Electrical Activity Based on a Modification of the DiFrancesco-Noble (1984) Equations, D. Noble and S.J. Noble,<emphasis>Proceedings of the Royal Society of London. Series B, Biological Sciences</emphasis>, 222, 295-304.  <ulink url="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&amp;db=PubMed&amp;list_uids=6149553&amp;dopt=Abstract">PubMed ID: 6149553</ulink>
</para>

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<caption>A schematic diagram describing the current flows across the cell membrane that are captured in the NN SAN model.</caption>
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</sect1>
</article>
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            <eq/>
            <ci>E_Ca</ci>
            <apply>
               <times/>
               <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">0.5</cn>
               <ci>RTONF</ci>
               <apply>
                  <ln/>
                  <apply>
                     <divide/>
                     <ci>Cao</ci>
                     <ci>Cai</ci>
                  </apply>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>i_Ca_b</ci>
            <apply>
               <times/>
               <ci>g_Cab</ci>
               <apply>
                  <minus/>
                  <ci>V</ci>
                  <ci>E_Ca</ci>
               </apply>
            </apply>
         </apply>
      </math>
   </component>
   <component name="sodium_potassium_pump">
      <variable cmeta:id="sodium_potassium_pump_i_p" name="i_p" public_interface="out" units="nanoA"/>
      <variable initial_value="50" name="I_p" units="nanoA"/>
      <variable initial_value="1" name="K_mK" units="millimolar"/>
      <variable initial_value="40" name="K_mNa" units="millimolar"/>
      <variable name="time" public_interface="in" units="second"/>
      <variable name="V" public_interface="in" units="millivolt"/>
      <variable name="Nai" public_interface="in" units="millimolar"/>
      <variable name="Kc" public_interface="in" units="millimolar"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <ci>i_p</ci>
            <apply>
               <divide/>
               <apply>
                  <times/>
                  <apply>
                     <divide/>
                     <apply>
                        <times/>
                        <ci>I_p</ci>
                        <ci>Kc</ci>
                     </apply>
                     <apply>
                        <plus/>
                        <ci>K_mK</ci>
                        <ci>Kc</ci>
                     </apply>
                  </apply>
                  <ci>Nai</ci>
               </apply>
               <apply>
                  <plus/>
                  <ci>K_mNa</ci>
                  <ci>Nai</ci>
               </apply>
            </apply>
         </apply>
      </math>
   </component>
   <component name="Na_Ca_exchanger">
      <variable cmeta:id="Na_Ca_exchanger_i_NaCa" name="i_NaCa" public_interface="out" units="nanoA"/>
      <variable initial_value="3" name="n_NaCa" public_interface="out" units="dimensionless"/>
      <variable initial_value="0.002" name="K_NaCa" units="nanoA"/>
      <variable initial_value="0.0001" name="d_NaCa" units="dimensionless"/>
      <variable initial_value="0.5" name="gamma" units="dimensionless"/>
      <variable name="time" public_interface="in" units="second"/>
      <variable name="V" public_interface="in" units="millivolt"/>
      <variable name="RTONF" public_interface="in" units="millivolt"/>
      <variable name="Cao" public_interface="in" units="millimolar"/>
      <variable name="Cai" public_interface="in" units="millimolar"/>
      <variable name="Nai" public_interface="in" units="millimolar"/>
      <variable name="Nao" public_interface="in" units="millimolar"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <ci>i_NaCa</ci>
            <apply>
               <divide/>
               <apply>
                  <times/>
                  <ci>K_NaCa</ci>
                  <apply>
                     <minus/>
                     <apply>
                        <times/>
                        <apply>
                           <exp/>
                           <apply>
                              <divide/>
                              <apply>
                                 <times/>
                                 <ci>gamma</ci>
                                 <apply>
                                    <minus/>
                                    <ci>n_NaCa</ci>
                                    <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
                                 </apply>
                                 <ci>V</ci>
                              </apply>
                              <ci>RTONF</ci>
                           </apply>
                        </apply>
                        <apply>
                           <power/>
                           <ci>Nai</ci>
                           <ci>n_NaCa</ci>
                        </apply>
                        <ci>Cao</ci>
                     </apply>
                     <apply>
                        <times/>
                        <apply>
                           <exp/>
                           <apply>
                              <divide/>
                              <apply>
                                 <times/>
                                 <apply>
                                    <minus/>
                                    <ci>gamma</ci>
                                    <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
                                 </apply>
                                 <apply>
                                    <minus/>
                                    <ci>n_NaCa</ci>
                                    <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
                                 </apply>
                                 <ci>V</ci>
                              </apply>
                              <ci>RTONF</ci>
                           </apply>
                        </apply>
                        <apply>
                           <power/>
                           <ci>Nao</ci>
                           <ci>n_NaCa</ci>
                        </apply>
                        <ci>Cai</ci>
                     </apply>
                  </apply>
               </apply>
               <apply>
                  <times/>
                  <apply>
                     <plus/>
                     <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millimolar4">1</cn>
                     <apply>
                        <times/>
                        <ci>d_NaCa</ci>
                        <apply>
                           <plus/>
                           <apply>
                              <times/>
                              <ci>Cai</ci>
                              <apply>
                                 <power/>
                                 <ci>Nao</ci>
                                 <ci>n_NaCa</ci>
                              </apply>
                           </apply>
                           <apply>
                              <times/>
                              <ci>Cao</ci>
                              <apply>
                                 <power/>
                                 <ci>Nai</ci>
                                 <ci>n_NaCa</ci>
                              </apply>
                           </apply>
                        </apply>
                     </apply>
                  </apply>
                  <apply>
                     <plus/>
                     <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
                     <apply>
                        <divide/>
                        <ci>Cai</ci>
                        <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millimolar">0.0069</cn>
                     </apply>
                  </apply>
               </apply>
            </apply>
         </apply>
      </math>
   </component>
   <component name="fast_sodium_current">
      <variable cmeta:id="fast_sodium_current_i_Na" name="i_Na" public_interface="out" units="nanoA"/>
      <variable initial_value="1.25" name="g_Na" units="microS"/>
      <variable name="E_mh" units="millivolt"/>
      <variable name="time" private_interface="out" public_interface="in" units="second"/>
      <variable name="V" private_interface="out" public_interface="in" units="millivolt"/>
      <variable name="RTONF" public_interface="in" units="millivolt"/>
      <variable name="Nao" public_interface="in" units="millimolar"/>
      <variable name="Nai" public_interface="in" units="millimolar"/>
      <variable name="Kc" public_interface="in" units="millimolar"/>
      <variable name="Ki" public_interface="in" units="millimolar"/>
      <variable name="m" private_interface="in" units="dimensionless"/>
      <variable name="h" private_interface="in" units="dimensionless"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <ci>E_mh</ci>
            <apply>
               <times/>
               <ci>RTONF</ci>
               <apply>
                  <ln/>
                  <apply>
                     <divide/>
                     <apply>
                        <plus/>
                        <ci>Nao</ci>
                        <apply>
                           <times/>
                           <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">0.12</cn>
                           <ci>Kc</ci>
                        </apply>
                     </apply>
                     <apply>
                        <plus/>
                        <ci>Nai</ci>
                        <apply>
                           <times/>
                           <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">0.12</cn>
                           <ci>Ki</ci>
                        </apply>
                     </apply>
                  </apply>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>i_Na</ci>
            <apply>
               <times/>
               <ci>g_Na</ci>
               <apply>
                  <power/>
                  <ci>m</ci>
                  <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">3</cn>
               </apply>
               <ci>h</ci>
               <apply>
                  <minus/>
                  <ci>V</ci>
                  <ci>E_mh</ci>
               </apply>
            </apply>
         </apply>
      </math>
   </component>
   <component name="fast_sodium_current_m_gate">
      <variable initial_value="0.076" name="m" public_interface="out" units="dimensionless"/>
      <variable name="alpha_m" units="per_second"/>
      <variable name="beta_m" units="per_second"/>
      <variable name="V" public_interface="in" units="millivolt"/>
      <variable name="time" public_interface="in" units="second"/>
      <variable initial_value="1e-5" name="delta_m" units="millivolt"/>
      <variable name="E0_m" units="millivolt"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <ci>E0_m</ci>
            <apply>
               <plus/>
               <ci>V</ci>
               <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">41</cn>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>alpha_m</ci>
            <piecewise>
               <piece>
                  <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_second">2000</cn>
                  <apply>
                     <lt/>
                     <apply>
                        <abs/>
                        <ci>E0_m</ci>
                     </apply>
                     <ci>delta_m</ci>
                  </apply>
               </piece>
               <otherwise>
                  <apply>
                     <divide/>
                     <apply>
                        <times/>
                        <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_millivolt_second">200</cn>
                        <ci>E0_m</ci>
                     </apply>
                     <apply>
                        <minus/>
                        <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
                        <apply>
                           <exp/>
                           <apply>
                              <times/>
                              <apply>
                                 <minus/>
                                 <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_millivolt">0.1</cn>
                              </apply>
                              <ci>E0_m</ci>
                           </apply>
                        </apply>
                     </apply>
                  </apply>
               </otherwise>
            </piecewise>
         </apply>
         <apply>
            <eq/>
            <ci>beta_m</ci>
            <apply>
               <times/>
               <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_second">8000</cn>
               <apply>
                  <exp/>
                  <apply>
                     <times/>
                     <apply>
                        <minus/>
                        <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_millivolt">0.056</cn>
                     </apply>
                     <apply>
                        <plus/>
                        <ci>V</ci>
                        <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">66</cn>
                     </apply>
                  </apply>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <apply>
               <diff/>
               <bvar>
                  <ci>time</ci>
               </bvar>
               <ci>m</ci>
            </apply>
            <apply>
               <minus/>
               <apply>
                  <times/>
                  <ci>alpha_m</ci>
                  <apply>
                     <minus/>
                     <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
                     <ci>m</ci>
                  </apply>
               </apply>
               <apply>
                  <times/>
                  <ci>beta_m</ci>
                  <ci>m</ci>
               </apply>
            </apply>
         </apply>
      </math>
   </component>
   <component name="fast_sodium_current_h_gate">
      <variable initial_value="0.015" name="h" public_interface="out" units="dimensionless"/>
      <variable name="alpha_h" units="per_second"/>
      <variable name="beta_h" units="per_second"/>
      <variable name="V" public_interface="in" units="millivolt"/>
      <variable name="time" public_interface="in" units="second"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <ci>alpha_h</ci>
            <apply>
               <times/>
               <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_second">20</cn>
               <apply>
                  <exp/>
                  <apply>
                     <times/>
                     <apply>
                        <minus/>
                        <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_millivolt">0.125</cn>
                     </apply>
                     <apply>
                        <plus/>
                        <ci>V</ci>
                        <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">75</cn>
                     </apply>
                  </apply>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>beta_h</ci>
            <apply>
               <divide/>
               <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_second">2000</cn>
               <apply>
                  <plus/>
                  <apply>
                     <times/>
                     <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">320</cn>
                     <apply>
                        <exp/>
                        <apply>
                           <times/>
                           <apply>
                              <minus/>
                              <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_millivolt">0.1</cn>
                           </apply>
                           <apply>
                              <plus/>
                              <ci>V</ci>
                              <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">75</cn>
                           </apply>
                        </apply>
                     </apply>
                  </apply>
                  <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <apply>
               <diff/>
               <bvar>
                  <ci>time</ci>
               </bvar>
               <ci>h</ci>
            </apply>
            <apply>
               <minus/>
               <apply>
                  <times/>
                  <ci>alpha_h</ci>
                  <apply>
                     <minus/>
                     <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
                     <ci>h</ci>
                  </apply>
               </apply>
               <apply>
                  <times/>
                  <ci>beta_h</ci>
                  <ci>h</ci>
               </apply>
            </apply>
         </apply>
      </math>
   </component>
   <component name="second_inward_current">
      <variable cmeta:id="second_inward_current_i_si" name="i_si" public_interface="out" units="nanoA"/>
      <variable name="i_siCa" public_interface="out" units="nanoA"/>
      <variable name="i_siK" public_interface="out" units="nanoA"/>
      <variable name="i_siNa" public_interface="out" units="nanoA"/>
      <variable initial_value="7.5" name="P_si" units="nanoA_per_millimolar"/>
      <variable name="time" private_interface="out" public_interface="in" units="second"/>
      <variable name="V" private_interface="out" public_interface="in" units="millivolt"/>
      <variable name="RTONF" public_interface="in" units="millivolt"/>
      <variable name="Nao" public_interface="in" units="millimolar"/>
      <variable name="Nai" public_interface="in" units="millimolar"/>
      <variable name="Kc" public_interface="in" units="millimolar"/>
      <variable name="Ki" public_interface="in" units="millimolar"/>
      <variable name="Cao" public_interface="in" units="millimolar"/>
      <variable name="Cai" private_interface="out" public_interface="in" units="millimolar"/>
      <variable name="d" private_interface="in" units="dimensionless"/>
      <variable name="f" private_interface="in" units="dimensionless"/>
      <variable name="f2" private_interface="in" units="dimensionless"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <ci>i_siCa</ci>
            <apply>
               <times/>
               <apply>
                  <divide/>
                  <apply>
                     <times/>
                     <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">4</cn>
                     <ci>P_si</ci>
                     <apply>
                        <minus/>
                        <ci>V</ci>
                        <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">50</cn>
                     </apply>
                  </apply>
                  <apply>
                     <times/>
                     <ci>RTONF</ci>
                     <apply>
                        <minus/>
                        <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
                        <apply>
                           <exp/>
                           <apply>
                              <divide/>
                              <apply>
                                 <times/>
                                 <apply>
                                    <minus/>
                                    <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
                                 </apply>
                                 <apply>
                                    <minus/>
                                    <ci>V</ci>
                                    <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">50</cn>
                                 </apply>
                                 <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
                              </apply>
                              <ci>RTONF</ci>
                           </apply>
                        </apply>
                     </apply>
                  </apply>
               </apply>
               <apply>
                  <minus/>
                  <apply>
                     <times/>
                     <ci>Cai</ci>
                     <apply>
                        <exp/>
                        <apply>
                           <divide/>
                           <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">100</cn>
                           <ci>RTONF</ci>
                        </apply>
                     </apply>
                  </apply>
                  <apply>
                     <times/>
                     <ci>Cao</ci>
                     <apply>
                        <exp/>
                        <apply>
                           <divide/>
                           <apply>
                              <times/>
                              <apply>
                                 <minus/>
                                 <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
                              </apply>
                              <apply>
                                 <minus/>
                                 <ci>V</ci>
                                 <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">50</cn>
                              </apply>
                           </apply>
                           <ci>RTONF</ci>
                        </apply>
                     </apply>
                  </apply>
               </apply>
               <ci>d</ci>
               <ci>f</ci>
               <ci>f2</ci>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>i_siK</ci>
            <apply>
               <times/>
               <apply>
                  <divide/>
                  <apply>
                     <times/>
                     <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">0.01</cn>
                     <ci>P_si</ci>
                     <apply>
                        <minus/>
                        <ci>V</ci>
                        <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">50</cn>
                     </apply>
                  </apply>
                  <apply>
                     <times/>
                     <ci>RTONF</ci>
                     <apply>
                        <minus/>
                        <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
                        <apply>
                           <exp/>
                           <apply>
                              <divide/>
                              <apply>
                                 <times/>
                                 <apply>
                                    <minus/>
                                    <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
                                 </apply>
                                 <apply>
                                    <minus/>
                                    <ci>V</ci>
                                    <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">50</cn>
                                 </apply>
                              </apply>
                              <ci>RTONF</ci>
                           </apply>
                        </apply>
                     </apply>
                  </apply>
               </apply>
               <apply>
                  <minus/>
                  <apply>
                     <times/>
                     <ci>Ki</ci>
                     <apply>
                        <exp/>
                        <apply>
                           <divide/>
                           <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">50</cn>
                           <ci>RTONF</ci>
                        </apply>
                     </apply>
                  </apply>
                  <apply>
                     <times/>
                     <ci>Kc</ci>
                     <apply>
                        <exp/>
                        <apply>
                           <divide/>
                           <apply>
                              <times/>
                              <apply>
                                 <minus/>
                                 <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
                              </apply>
                              <apply>
                                 <minus/>
                                 <ci>V</ci>
                                 <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">50</cn>
                              </apply>
                           </apply>
                           <ci>RTONF</ci>
                        </apply>
                     </apply>
                  </apply>
               </apply>
               <ci>d</ci>
               <ci>f</ci>
               <ci>f2</ci>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>i_siNa</ci>
            <apply>
               <times/>
               <apply>
                  <divide/>
                  <apply>
                     <times/>
                     <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">0.01</cn>
                     <ci>P_si</ci>
                     <apply>
                        <minus/>
                        <ci>V</ci>
                        <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">50</cn>
                     </apply>
                  </apply>
                  <apply>
                     <times/>
                     <ci>RTONF</ci>
                     <apply>
                        <minus/>
                        <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
                        <apply>
                           <exp/>
                           <apply>
                              <divide/>
                              <apply>
                                 <times/>
                                 <apply>
                                    <minus/>
                                    <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
                                 </apply>
                                 <apply>
                                    <minus/>
                                    <ci>V</ci>
                                    <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">50</cn>
                                 </apply>
                              </apply>
                              <ci>RTONF</ci>
                           </apply>
                        </apply>
                     </apply>
                  </apply>
               </apply>
               <apply>
                  <minus/>
                  <apply>
                     <times/>
                     <ci>Nai</ci>
                     <apply>
                        <exp/>
                        <apply>
                           <divide/>
                           <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">50</cn>
                           <ci>RTONF</ci>
                        </apply>
                     </apply>
                  </apply>
                  <apply>
                     <times/>
                     <ci>Nao</ci>
                     <apply>
                        <exp/>
                        <apply>
                           <divide/>
                           <apply>
                              <times/>
                              <apply>
                                 <minus/>
                                 <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
                              </apply>
                              <apply>
                                 <minus/>
                                 <ci>V</ci>
                                 <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">50</cn>
                              </apply>
                           </apply>
                           <ci>RTONF</ci>
                        </apply>
                     </apply>
                  </apply>
               </apply>
               <ci>d</ci>
               <ci>f</ci>
               <ci>f2</ci>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>i_si</ci>
            <apply>
               <plus/>
               <ci>i_siCa</ci>
               <ci>i_siK</ci>
               <ci>i_siNa</ci>
            </apply>
         </apply>
      </math>
   </component>
   <component name="second_inward_current_d_gate">
      <variable initial_value="0.0011" name="d" public_interface="out" units="dimensionless"/>
      <variable name="alpha_d" units="per_second"/>
      <variable name="beta_d" units="per_second"/>
      <variable name="V" public_interface="in" units="millivolt"/>
      <variable name="time" public_interface="in" units="second"/>
      <variable initial_value="0.0001" name="delta_d" units="millivolt"/>
      <variable name="E0_d" units="millivolt"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <ci>E0_d</ci>
            <apply>
               <minus/>
               <apply>
                  <plus/>
                  <ci>V</ci>
                  <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">24</cn>
               </apply>
               <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">5</cn>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>alpha_d</ci>
            <piecewise>
               <piece>
                  <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_second">120</cn>
                  <apply>
                     <lt/>
                     <apply>
                        <abs/>
                        <ci>E0_d</ci>
                     </apply>
                     <ci>delta_d</ci>
                  </apply>
               </piece>
               <otherwise>
                  <apply>
                     <divide/>
                     <apply>
                        <times/>
                        <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_millivolt_second">30</cn>
                        <ci>E0_d</ci>
                     </apply>
                     <apply>
                        <minus/>
                        <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
                        <apply>
                           <exp/>
                           <apply>
                              <divide/>
                              <apply>
                                 <times/>
                                 <apply>
                                    <minus/>
                                    <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
                                 </apply>
                                 <ci>E0_d</ci>
                              </apply>
                              <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">4</cn>
                           </apply>
                        </apply>
                     </apply>
                  </apply>
               </otherwise>
            </piecewise>
         </apply>
         <apply>
            <eq/>
            <ci>beta_d</ci>
            <piecewise>
               <piece>
                  <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_second">120</cn>
                  <apply>
                     <lt/>
                     <apply>
                        <abs/>
                        <ci>E0_d</ci>
                     </apply>
                     <ci>delta_d</ci>
                  </apply>
               </piece>
               <otherwise>
                  <apply>
                     <divide/>
                     <apply>
                        <times/>
                        <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_millivolt_second">12</cn>
                        <ci>E0_d</ci>
                     </apply>
                     <apply>
                        <minus/>
                        <apply>
                           <exp/>
                           <apply>
                              <divide/>
                              <ci>E0_d</ci>
                              <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">10</cn>
                           </apply>
                        </apply>
                        <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
                     </apply>
                  </apply>
               </otherwise>
            </piecewise>
         </apply>
         <apply>
            <eq/>
            <apply>
               <diff/>
               <bvar>
                  <ci>time</ci>
               </bvar>
               <ci>d</ci>
            </apply>
            <apply>
               <minus/>
               <apply>
                  <times/>
                  <ci>alpha_d</ci>
                  <apply>
                     <minus/>
                     <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
                     <ci>d</ci>
                  </apply>
               </apply>
               <apply>
                  <times/>
                  <ci>beta_d</ci>
                  <ci>d</ci>
               </apply>
            </apply>
         </apply>
      </math>
   </component>
   <component name="second_inward_current_f_gate">
      <variable initial_value="0.785" name="f" public_interface="out" units="dimensionless"/>
      <variable name="alpha_f" units="per_second"/>
      <variable name="beta_f" units="per_second"/>
      <variable name="V" public_interface="in" units="millivolt"/>
      <variable name="time" public_interface="in" units="second"/>
      <variable initial_value="0.0001" name="delta_f" units="millivolt"/>
      <variable name="E0_f" units="millivolt"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <ci>E0_f</ci>
            <apply>
               <plus/>
               <ci>V</ci>
               <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">34</cn>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>alpha_f</ci>
            <piecewise>
               <piece>
                  <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_second">25</cn>
                  <apply>
                     <lt/>
                     <apply>
                        <abs/>
                        <ci>E0_f</ci>
                     </apply>
                     <ci>delta_f</ci>
                  </apply>
               </piece>
               <otherwise>
                  <apply>
                     <divide/>
                     <apply>
                        <times/>
                        <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_millivolt_second">6.25</cn>
                        <ci>E0_f</ci>
                     </apply>
                     <apply>
                        <minus/>
                        <apply>
                           <exp/>
                           <apply>
                              <divide/>
                              <ci>E0_f</ci>
                              <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">4</cn>
                           </apply>
                        </apply>
                        <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
                     </apply>
                  </apply>
               </otherwise>
            </piecewise>
         </apply>
         <apply>
            <eq/>
            <ci>beta_f</ci>
            <apply>
               <divide/>
               <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_second">50</cn>
               <apply>
                  <plus/>
                  <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
                  <apply>
                     <exp/>
                     <apply>
                        <divide/>
                        <apply>
                           <times/>
                           <apply>
                              <minus/>
                              <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
                           </apply>
                           <apply>
                              <plus/>
                              <ci>V</ci>
                              <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">34</cn>
                           </apply>
                        </apply>
                        <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">4</cn>
                     </apply>
                  </apply>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <apply>
               <diff/>
               <bvar>
                  <ci>time</ci>
               </bvar>
               <ci>f</ci>
            </apply>
            <apply>
               <minus/>
               <apply>
                  <times/>
                  <ci>alpha_f</ci>
                  <apply>
                     <minus/>
                     <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
                     <ci>f</ci>
                  </apply>
               </apply>
               <apply>
                  <times/>
                  <ci>beta_f</ci>
                  <ci>f</ci>
               </apply>
            </apply>
         </apply>
      </math>
   </component>
   <component name="second_inward_current_f2_gate">
      <variable initial_value="0.785" name="f2" public_interface="out" units="dimensionless"/>
      <variable initial_value="10" name="alpha_f2" units="per_second"/>
      <variable name="beta_f2" units="per_second"/>
      <variable initial_value="0.0005" name="K_mf2" units="millimolar"/>
      <variable name="V" public_interface="in" units="millivolt"/>
      <variable name="time" public_interface="in" units="second"/>
      <variable name="Cai" public_interface="in" units="millimolar"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <ci>beta_f2</ci>
            <apply>
               <divide/>
               <apply>
                  <times/>
                  <ci>Cai</ci>
                  <ci>alpha_f2</ci>
               </apply>
               <ci>K_mf2</ci>
            </apply>
         </apply>
         <apply>
            <eq/>
            <apply>
               <diff/>
               <bvar>
                  <ci>time</ci>
               </bvar>
               <ci>f2</ci>
            </apply>
            <apply>
               <minus/>
               <ci>alpha_f2</ci>
               <apply>
                  <times/>
                  <ci>f2</ci>
                  <apply>
                     <plus/>
                     <ci>alpha_f2</ci>
                     <ci>beta_f2</ci>
                  </apply>
               </apply>
            </apply>
         </apply>
      </math>
   </component>
   <component name="extracellular_sodium_concentration">
      <variable initial_value="140" name="Nao" public_interface="out" units="millimolar"/>
   </component>
   <component name="intracellular_sodium_concentration">
      <variable initial_value="7.5" name="Nai" public_interface="out" units="millimolar"/>
      <variable initial_value="0.08" name="radius" units="micrometre"/>
      <variable initial_value="0.08" name="length" units="micrometre"/>
      <variable initial_value="0.1" name="V_e_ratio" units="dimensionless"/>
      <variable name="V_Cell" units="micrometre3"/>
      <variable name="Vi" public_interface="out" units="micrometre3"/>
      <variable name="time" public_interface="in" units="second"/>
      <variable name="F" public_interface="in" units="coulomb_per_mole"/>
      <variable name="i_Na" public_interface="in" units="nanoA"/>
      <variable name="i_Na_b" public_interface="in" units="nanoA"/>
      <variable name="i_siNa" public_interface="in" units="nanoA"/>
      <variable name="i_p" public_interface="in" units="nanoA"/>
      <variable name="i_fNa" public_interface="in" units="nanoA"/>
      <variable name="i_NaCa" public_interface="in" units="nanoA"/>
      <variable name="n_NaCa" public_interface="in" units="dimensionless"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <ci>V_Cell</ci>
            <apply>
               <times/>
               <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">3.141592654</cn>
               <apply>
                  <power/>
                  <ci>radius</ci>
                  <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
               </apply>
               <ci>length</ci>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>Vi</ci>
            <apply>
               <times/>
               <ci>V_Cell</ci>
               <apply>
                  <minus/>
                  <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
                  <ci>V_e_ratio</ci>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <apply>
               <diff/>
               <bvar>
                  <ci>time</ci>
               </bvar>
               <ci>Nai</ci>
            </apply>
            <apply>
               <divide/>
               <apply>
                  <times/>
                  <apply>
                     <minus/>
                     <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="mA_nA">1</cn>
                  </apply>
                  <apply>
                     <plus/>
                     <ci>i_Na</ci>
                     <ci>i_Na_b</ci>
                     <ci>i_fNa</ci>
                     <ci>i_siNa</ci>
                     <apply>
                        <times/>
                        <ci>i_p</ci>
                        <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">3</cn>
                     </apply>
                     <apply>
                        <divide/>
                        <apply>
                           <times/>
                           <ci>i_NaCa</ci>
                           <ci>n_NaCa</ci>
                        </apply>
                        <apply>
                           <minus/>
                           <ci>n_NaCa</ci>
                           <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
                        </apply>
                     </apply>
                  </apply>
               </apply>
               <apply>
                  <times/>
                  <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="litre_micrometre3">1</cn>
                  <ci>Vi</ci>
                  <ci>F</ci>
               </apply>
            </apply>
         </apply>
      </math>
   </component>
   <component name="extracellular_calcium_concentration">
      <variable initial_value="2" name="Cao" public_interface="out" units="millimolar"/>
   </component>
   <component name="intracellular_calcium_concentration">
      <variable initial_value="5.8e-5" name="Cai" public_interface="out" units="millimolar"/>
      <variable name="V_up" units="micrometre3"/>
      <variable name="V_rel" units="micrometre3"/>
      <variable name="Vi" public_interface="in" units="micrometre3"/>
      <variable name="i_up" units="nanoA"/>
      <variable name="i_tr" units="nanoA"/>
      <variable name="i_rel" units="nanoA"/>
      <variable initial_value="1.98" name="Ca_up" units="millimolar"/>
      <variable initial_value="0.55" name="Ca_rel" units="millimolar"/>
      <variable initial_value="5" name="Ca_up_max" units="millimolar"/>
      <variable initial_value="0.002" name="K_mCa" units="millimolar"/>
      <variable initial_value="0.785" name="p" units="dimensionless"/>
      <variable name="alpha_p" units="per_second"/>
      <variable name="beta_p" units="per_second"/>
      <variable name="E0_p" units="millivolt"/>
      <variable initial_value="0.005" name="tau_up" units="second"/>
      <variable initial_value="0.2" name="tau_rep" units="second"/>
      <variable initial_value="0.01" name="tau_rel" units="second"/>
      <variable initial_value="2" name="rCa" units="dimensionless"/>
      <variable name="time" public_interface="in" units="second"/>
      <variable name="V" public_interface="in" units="millivolt"/>
      <variable name="F" public_interface="in" units="coulomb_per_mole"/>
      <variable name="i_Ca_b" public_interface="in" units="nanoA"/>
      <variable name="i_siCa" public_interface="in" units="nanoA"/>
      <variable name="i_NaCa" public_interface="in" units="nanoA"/>
      <variable name="n_NaCa" public_interface="in" units="dimensionless"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <ci>i_up</ci>
            <apply>
               <times/>
               <apply>
                  <divide/>
                  <apply>
                     <times/>
                     <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
                     <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="litre_micrometre3">1</cn>
                     <ci>Vi</ci>
                     <ci>F</ci>
                  </apply>
                  <apply>
                     <times/>
                     <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="mA_nA">1</cn>
                     <ci>tau_up</ci>
                     <ci>Ca_up_max</ci>
                  </apply>
               </apply>
               <ci>Cai</ci>
               <apply>
                  <minus/>
                  <ci>Ca_up_max</ci>
                  <ci>Ca_up</ci>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>i_tr</ci>
            <apply>
               <times/>
               <apply>
                  <divide/>
                  <apply>
                     <times/>
                     <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
                     <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="litre_micrometre3">1</cn>
                     <ci>V_rel</ci>
                     <ci>F</ci>
                  </apply>
                  <apply>
                     <times/>
                     <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="mA_nA">1</cn>
                     <ci>tau_rep</ci>
                  </apply>
               </apply>
               <ci>p</ci>
               <apply>
                  <minus/>
                  <ci>Ca_up</ci>
                  <ci>Ca_rel</ci>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>E0_p</ci>
            <apply>
               <minus/>
               <apply>
                  <plus/>
                  <ci>V</ci>
                  <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">34</cn>
               </apply>
               <apply>
                  <minus/>
                  <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">30</cn>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>alpha_p</ci>
            <apply>
               <divide/>
               <apply>
                  <times/>
                  <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_millivolt_second">0.625</cn>
                  <ci>E0_p</ci>
               </apply>
               <apply>
                  <minus/>
                  <apply>
                     <exp/>
                     <apply>
                        <divide/>
                        <ci>E0_p</ci>
                        <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">4</cn>
                     </apply>
                  </apply>
                  <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>beta_p</ci>
            <apply>
               <divide/>
               <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_second">5</cn>
               <apply>
                  <plus/>
                  <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
                  <apply>
                     <exp/>
                     <apply>
                        <divide/>
                        <apply>
                           <times/>
                           <apply>
                              <minus/>
                              <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
                           </apply>
                           <ci>E0_p</ci>
                        </apply>
                        <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">4</cn>
                     </apply>
                  </apply>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>i_rel</ci>
            <apply>
               <divide/>
               <apply>
                  <times/>
                  <apply>
                     <divide/>
                     <apply>
                        <times/>
                        <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
                        <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="litre_micrometre3">1</cn>
                        <ci>V_rel</ci>
                        <ci>F</ci>
                     </apply>
                     <apply>
                        <times/>
                        <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="mA_nA">1</cn>
                        <ci>tau_rel</ci>
                     </apply>
                  </apply>
                  <ci>Ca_rel</ci>
                  <apply>
                     <power/>
                     <ci>Cai</ci>
                     <ci>rCa</ci>
                  </apply>
               </apply>
               <apply>
                  <plus/>
                  <apply>
                     <power/>
                     <ci>Cai</ci>
                     <ci>rCa</ci>
                  </apply>
                  <apply>
                     <power/>
                     <ci>K_mCa</ci>
                     <ci>rCa</ci>
                  </apply>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <apply>
               <diff/>
               <bvar>
                  <ci>time</ci>
               </bvar>
               <ci>p</ci>
            </apply>
            <apply>
               <minus/>
               <apply>
                  <times/>
                  <ci>alpha_p</ci>
                  <apply>
                     <minus/>
                     <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
                     <ci>p</ci>
                  </apply>
               </apply>
               <apply>
                  <times/>
                  <ci>beta_p</ci>
                  <ci>p</ci>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <apply>
               <diff/>
               <bvar>
                  <ci>time</ci>
               </bvar>
               <ci>Ca_up</ci>
            </apply>
            <apply>
               <divide/>
               <apply>
                  <times/>
                  <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="mA_nA">1</cn>
                  <apply>
                     <minus/>
                     <ci>i_up</ci>
                     <ci>i_tr</ci>
                  </apply>
               </apply>
               <apply>
                  <times/>
                  <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
                  <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="litre_micrometre3">1</cn>
                  <ci>V_up</ci>
                  <ci>F</ci>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>V_up</ci>
            <apply>
               <times/>
               <ci>Vi</ci>
               <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">0.05</cn>
            </apply>
         </apply>
         <apply>
            <eq/>
            <apply>
               <diff/>
               <bvar>
                  <ci>time</ci>
               </bvar>
               <ci>Ca_rel</ci>
            </apply>
            <apply>
               <divide/>
               <apply>
                  <times/>
                  <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="mA_nA">1</cn>
                  <apply>
                     <minus/>
                     <ci>i_tr</ci>
                     <ci>i_rel</ci>
                  </apply>
               </apply>
               <apply>
                  <times/>
                  <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
                  <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="litre_micrometre3">1</cn>
                  <ci>V_rel</ci>
                  <ci>F</ci>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>V_rel</ci>
            <apply>
               <times/>
               <ci>Vi</ci>
               <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">0.02</cn>
            </apply>
         </apply>
         <apply>
            <eq/>
            <apply>
               <diff/>
               <bvar>
                  <ci>time</ci>
               </bvar>
               <ci>Cai</ci>
            </apply>
            <apply>
               <divide/>
               <apply>
                  <times/>
                  <apply>
                     <minus/>
                     <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="mA_nA">1</cn>
                  </apply>
                  <apply>
                     <plus/>
                     <apply>
                        <minus/>
                        <apply>
                           <minus/>
                           <apply>
                              <plus/>
                              <ci>i_siCa</ci>
                              <ci>i_Ca_b</ci>
                           </apply>
                           <apply>
                              <divide/>
                              <apply>
                                 <times/>
                                 <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
                                 <ci>i_NaCa</ci>
                              </apply>
                              <apply>
                                 <minus/>
                                 <ci>n_NaCa</ci>
                                 <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
                              </apply>
                           </apply>
                        </apply>
                        <ci>i_rel</ci>
                     </apply>
                     <ci>i_up</ci>
                  </apply>
               </apply>
               <apply>
                  <times/>
                  <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
                  <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="litre_micrometre3">1</cn>
                  <ci>Vi</ci>
                  <ci>F</ci>
               </apply>
            </apply>
         </apply>
      </math>
   </component>
   <component name="extracellular_potassium_concentration">
      <variable initial_value="3" name="Kc" public_interface="out" units="millimolar"/>
      <variable initial_value="0.00016077" name="V_e" units="micrometre3"/>
      <variable initial_value="3" name="Kb" units="millimolar"/>
      <variable name="i_mK" public_interface="out" units="nanoA"/>
      <variable initial_value="1" name="pf" units="per_second"/>
      <variable name="time" public_interface="in" units="second"/>
      <variable name="F" public_interface="in" units="coulomb_per_mole"/>
      <variable name="i_K1" public_interface="in" units="nanoA"/>
      <variable name="i_K" public_interface="in" units="nanoA"/>
      <variable name="i_fK" public_interface="in" units="nanoA"/>
      <variable name="i_siK" public_interface="in" units="nanoA"/>
      <variable name="i_p" public_interface="in" units="nanoA"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <ci>i_mK</ci>
            <apply>
               <minus/>
               <apply>
                  <plus/>
                  <ci>i_K1</ci>
                  <ci>i_K</ci>
                  <ci>i_fK</ci>
                  <ci>i_siK</ci>
               </apply>
               <apply>
                  <times/>
                  <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
                  <ci>i_p</ci>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <apply>
               <diff/>
               <bvar>
                  <ci>time</ci>
               </bvar>
               <ci>Kc</ci>
            </apply>
            <apply>
               <plus/>
               <apply>
                  <times/>
                  <apply>
                     <minus/>
                     <ci>pf</ci>
                  </apply>
                  <apply>
                     <minus/>
                     <ci>Kc</ci>
                     <ci>Kb</ci>
                  </apply>
               </apply>
               <apply>
                  <divide/>
                  <apply>
                     <times/>
                     <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="mA_nA">1</cn>
                     <ci>i_mK</ci>
                  </apply>
                  <apply>
                     <times/>
                     <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="litre_micrometre3">1</cn>
                     <ci>V_e</ci>
                     <ci>F</ci>
                  </apply>
               </apply>
            </apply>
         </apply>
      </math>
   </component>
   <component name="intracellular_potassium_concentration">
      <variable initial_value="140" name="Ki" public_interface="out" units="millimolar"/>
      <variable name="Vi" public_interface="in" units="micrometre3"/>
      <variable name="i_mK" public_interface="in" units="nanoA"/>
      <variable name="time" public_interface="in" units="second"/>
      <variable name="F" public_interface="in" units="coulomb_per_mole"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <apply>
               <diff/>
               <bvar>
                  <ci>time</ci>
               </bvar>
               <ci>Ki</ci>
            </apply>
            <apply>
               <divide/>
               <apply>
                  <times/>
                  <apply>
                     <minus/>
                     <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="mA_nA">1</cn>
                  </apply>
                  <ci>i_mK</ci>
               </apply>
               <apply>
                  <times/>
                  <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="litre_micrometre3">1</cn>
                  <ci>Vi</ci>
                  <ci>F</ci>
               </apply>
            </apply>
         </apply>
      </math>
   </component>
   <group>
      <relationship_ref relationship="containment"/>
      <component_ref component="membrane">
         <component_ref component="hyperpolarising_activated_current">
            <component_ref component="hyperpolarising_activated_current_y_gate"/>
         </component_ref>
         <component_ref component="time_dependent_potassium_current">
            <component_ref component="time_dependent_potassium_current_x_gate"/>
         </component_ref>
         <component_ref component="time_independent_potassium_current"/>
         <component_ref component="sodium_background_current"/>
         <component_ref component="calcium_background_current"/>
         <component_ref component="sodium_potassium_pump"/>
         <component_ref component="Na_Ca_exchanger"/>
         <component_ref component="fast_sodium_current">
            <component_ref component="fast_sodium_current_m_gate"/>
            <component_ref component="fast_sodium_current_h_gate"/>
         </component_ref>
         <component_ref component="second_inward_current">
            <component_ref component="second_inward_current_d_gate"/>
            <component_ref component="second_inward_current_f_gate"/>
            <component_ref component="second_inward_current_f2_gate"/>
         </component_ref>
         <component_ref component="intracellular_sodium_concentration"/>
         <component_ref component="extracellular_sodium_concentration"/>
         <component_ref component="intracellular_calcium_concentration"/>
         <component_ref component="extracellular_calcium_concentration"/>
         <component_ref component="extracellular_potassium_concentration"/>
         <component_ref component="intracellular_potassium_concentration"/>
      </component_ref>
   </group>
   <group>
      <relationship_ref relationship="encapsulation"/>
      <component_ref component="hyperpolarising_activated_current">
         <component_ref component="hyperpolarising_activated_current_y_gate"/>
      </component_ref>
      <component_ref component="time_dependent_potassium_current">
         <component_ref component="time_dependent_potassium_current_x_gate"/>
      </component_ref>
      <component_ref component="fast_sodium_current">
         <component_ref component="fast_sodium_current_m_gate"/>
         <component_ref component="fast_sodium_current_h_gate"/>
      </component_ref>
      <component_ref component="second_inward_current">
         <component_ref component="second_inward_current_d_gate"/>
         <component_ref component="second_inward_current_f_gate"/>
         <component_ref component="second_inward_current_f2_gate"/>
      </component_ref>
   </group>
   <connection>
      <map_components component_1="membrane" component_2="environment"/>
      <map_variables variable_1="time" variable_2="time"/>
   </connection>
   <connection>
      <map_components component_1="hyperpolarising_activated_current" component_2="environment"/>
      <map_variables variable_1="time" variable_2="time"/>
   </connection>
   <connection>
      <map_components component_1="time_dependent_potassium_current" component_2="environment"/>
      <map_variables variable_1="time" variable_2="time"/>
   </connection>
   <connection>
      <map_components component_1="time_independent_potassium_current" component_2="environment"/>
      <map_variables variable_1="time" variable_2="time"/>
   </connection>
   <connection>
      <map_components component_1="sodium_background_current" component_2="environment"/>
      <map_variables variable_1="time" variable_2="time"/>
   </connection>
   <connection>
      <map_components component_1="calcium_background_current" component_2="environment"/>
      <map_variables variable_1="time" variable_2="time"/>
   </connection>
   <connection>
      <map_components component_1="sodium_potassium_pump" component_2="environment"/>
      <map_variables variable_1="time" variable_2="time"/>
   </connection>
   <connection>
      <map_components component_1="Na_Ca_exchanger" component_2="environment"/>
      <map_variables variable_1="time" variable_2="time"/>
   </connection>
   <connection>
      <map_components component_1="fast_sodium_current" component_2="environment"/>
      <map_variables variable_1="time" variable_2="time"/>
   </connection>
   <connection>
      <map_components component_1="second_inward_current" component_2="environment"/>
      <map_variables variable_1="time" variable_2="time"/>
   </connection>
   <connection>
      <map_components component_1="intracellular_sodium_concentration" component_2="environment"/>
      <map_variables variable_1="time" variable_2="time"/>
   </connection>
   <connection>
      <map_components component_1="intracellular_calcium_concentration" component_2="environment"/>
      <map_variables variable_1="time" variable_2="time"/>
   </connection>
   <connection>
      <map_components component_1="extracellular_potassium_concentration" component_2="environment"/>
      <map_variables variable_1="time" variable_2="time"/>
   </connection>
   <connection>
      <map_components component_1="intracellular_potassium_concentration" component_2="environment"/>
      <map_variables variable_1="time" variable_2="time"/>
   </connection>
   <connection>
      <map_components component_1="hyperpolarising_activated_current" component_2="membrane"/>
      <map_variables variable_1="V" variable_2="V"/>
      <map_variables variable_1="RTONF" variable_2="RTONF"/>
      <map_variables variable_1="i_f" variable_2="i_f"/>
   </connection>
   <connection>
      <map_components component_1="time_dependent_potassium_current" component_2="membrane"/>
      <map_variables variable_1="V" variable_2="V"/>
      <map_variables variable_1="i_K" variable_2="i_K"/>
      <map_variables variable_1="RTONF" variable_2="RTONF"/>
   </connection>
   <connection>
      <map_components component_1="time_independent_potassium_current" component_2="membrane"/>
      <map_variables variable_1="V" variable_2="V"/>
      <map_variables variable_1="RTONF" variable_2="RTONF"/>
      <map_variables variable_1="i_K1" variable_2="i_K1"/>
   </connection>
   <connection>
      <map_components component_1="sodium_background_current" component_2="membrane"/>
      <map_variables variable_1="V" variable_2="V"/>
      <map_variables variable_1="i_Na_b" variable_2="i_Na_b"/>
   </connection>
   <connection>
      <map_components component_1="calcium_background_current" component_2="membrane"/>
      <map_variables variable_1="V" variable_2="V"/>
      <map_variables variable_1="RTONF" variable_2="RTONF"/>
      <map_variables variable_1="i_Ca_b" variable_2="i_Ca_b"/>
   </connection>
   <connection>
      <map_components component_1="sodium_potassium_pump" component_2="membrane"/>
      <map_variables variable_1="V" variable_2="V"/>
      <map_variables variable_1="i_p" variable_2="i_p"/>
   </connection>
   <connection>
      <map_components component_1="Na_Ca_exchanger" component_2="membrane"/>
      <map_variables variable_1="V" variable_2="V"/>
      <map_variables variable_1="i_NaCa" variable_2="i_NaCa"/>
      <map_variables variable_1="RTONF" variable_2="RTONF"/>
   </connection>
   <connection>
      <map_components component_1="fast_sodium_current" component_2="membrane"/>
      <map_variables variable_1="V" variable_2="V"/>
      <map_variables variable_1="i_Na" variable_2="i_Na"/>
      <map_variables variable_1="RTONF" variable_2="RTONF"/>
   </connection>
   <connection>
      <map_components component_1="second_inward_current" component_2="membrane"/>
      <map_variables variable_1="V" variable_2="V"/>
      <map_variables variable_1="i_si" variable_2="i_si"/>
      <map_variables variable_1="RTONF" variable_2="RTONF"/>
   </connection>
   <connection>
      <map_components component_1="intracellular_sodium_concentration" component_2="membrane"/>
      <map_variables variable_1="F" variable_2="F"/>
   </connection>
   <connection>
      <map_components component_1="intracellular_calcium_concentration" component_2="membrane"/>
      <map_variables variable_1="V" variable_2="V"/>
      <map_variables variable_1="F" variable_2="F"/>
   </connection>
   <connection>
      <map_components component_1="extracellular_potassium_concentration" component_2="membrane"/>
      <map_variables variable_1="F" variable_2="F"/>
   </connection>
   <connection>
      <map_components component_1="intracellular_potassium_concentration" component_2="membrane"/>
      <map_variables variable_1="F" variable_2="F"/>
   </connection>
   <connection>
      <map_components component_1="hyperpolarising_activated_current" component_2="extracellular_potassium_concentration"/>
      <map_variables variable_1="Kc" variable_2="Kc"/>
      <map_variables variable_1="i_fK" variable_2="i_fK"/>
   </connection>
   <connection>
      <map_components component_1="hyperpolarising_activated_current" component_2="intracellular_potassium_concentration"/>
      <map_variables variable_1="Ki" variable_2="Ki"/>
   </connection>
   <connection>
      <map_components component_1="hyperpolarising_activated_current" component_2="time_independent_potassium_current"/>
      <map_variables variable_1="E_K" variable_2="E_K"/>
   </connection>
   <connection>
      <map_components component_1="hyperpolarising_activated_current" component_2="sodium_background_current"/>
      <map_variables variable_1="E_Na" variable_2="E_Na"/>
   </connection>
   <connection>
      <map_components component_1="hyperpolarising_activated_current" component_2="intracellular_sodium_concentration"/>
      <map_variables variable_1="i_fNa" variable_2="i_fNa"/>
      <map_variables variable_1="Nai" variable_2="Nai"/>
   </connection>
   <connection>
      <map_components component_1="hyperpolarising_activated_current" component_2="extracellular_sodium_concentration"/>
      <map_variables variable_1="Nao" variable_2="Nao"/>
   </connection>
   <connection>
      <map_components component_1="calcium_background_current" component_2="extracellular_calcium_concentration"/>
      <map_variables variable_1="Cao" variable_2="Cao"/>
   </connection>
   <connection>
      <map_components component_1="time_dependent_potassium_current" component_2="extracellular_potassium_concentration"/>
      <map_variables variable_1="Kc" variable_2="Kc"/>
      <map_variables variable_1="i_K" variable_2="i_K"/>
   </connection>
   <connection>
      <map_components component_1="time_dependent_potassium_current" component_2="intracellular_potassium_concentration"/>
      <map_variables variable_1="Ki" variable_2="Ki"/>
   </connection>
   <connection>
      <map_components component_1="time_independent_potassium_current" component_2="extracellular_potassium_concentration"/>
      <map_variables variable_1="Kc" variable_2="Kc"/>
      <map_variables variable_1="i_K1" variable_2="i_K1"/>
   </connection>
   <connection>
      <map_components component_1="sodium_background_current" component_2="intracellular_sodium_concentration"/>
      <map_variables variable_1="i_Na_b" variable_2="i_Na_b"/>
   </connection>
   <connection>
      <map_components component_1="calcium_background_current" component_2="intracellular_calcium_concentration"/>
      <map_variables variable_1="i_Ca_b" variable_2="i_Ca_b"/>
      <map_variables variable_1="Cai" variable_2="Cai"/>
   </connection>
   <connection>
      <map_components component_1="sodium_potassium_pump" component_2="extracellular_potassium_concentration"/>
      <map_variables variable_1="i_p" variable_2="i_p"/>
      <map_variables variable_1="Kc" variable_2="Kc"/>
   </connection>
   <connection>
      <map_components component_1="sodium_potassium_pump" component_2="intracellular_sodium_concentration"/>
      <map_variables variable_1="i_p" variable_2="i_p"/>
      <map_variables variable_1="Nai" variable_2="Nai"/>
   </connection>
   <connection>
      <map_components component_1="Na_Ca_exchanger" component_2="extracellular_sodium_concentration"/>
      <map_variables variable_1="Nao" variable_2="Nao"/>
   </connection>
   <connection>
      <map_components component_1="Na_Ca_exchanger" component_2="extracellular_calcium_concentration"/>
      <map_variables variable_1="Cao" variable_2="Cao"/>
   </connection>
   <connection>
      <map_components component_1="Na_Ca_exchanger" component_2="intracellular_sodium_concentration"/>
      <map_variables variable_1="n_NaCa" variable_2="n_NaCa"/>
      <map_variables variable_1="i_NaCa" variable_2="i_NaCa"/>
      <map_variables variable_1="Nai" variable_2="Nai"/>
   </connection>
   <connection>
      <map_components component_1="Na_Ca_exchanger" component_2="intracellular_calcium_concentration"/>
      <map_variables variable_1="n_NaCa" variable_2="n_NaCa"/>
      <map_variables variable_1="i_NaCa" variable_2="i_NaCa"/>
      <map_variables variable_1="Cai" variable_2="Cai"/>
   </connection>
   <connection>
      <map_components component_1="fast_sodium_current" component_2="intracellular_sodium_concentration"/>
      <map_variables variable_1="i_Na" variable_2="i_Na"/>
      <map_variables variable_1="Nai" variable_2="Nai"/>
   </connection>
   <connection>
      <map_components component_1="fast_sodium_current" component_2="intracellular_potassium_concentration"/>
      <map_variables variable_1="Ki" variable_2="Ki"/>
   </connection>
   <connection>
      <map_components component_1="fast_sodium_current" component_2="extracellular_potassium_concentration"/>
      <map_variables variable_1="Kc" variable_2="Kc"/>
   </connection>
   <connection>
      <map_components component_1="fast_sodium_current" component_2="extracellular_sodium_concentration"/>
      <map_variables variable_1="Nao" variable_2="Nao"/>
   </connection>
   <connection>
      <map_components component_1="second_inward_current" component_2="intracellular_calcium_concentration"/>
      <map_variables variable_1="i_siCa" variable_2="i_siCa"/>
      <map_variables variable_1="Cai" variable_2="Cai"/>
   </connection>
   <connection>
      <map_components component_1="second_inward_current" component_2="extracellular_calcium_concentration"/>
      <map_variables variable_1="Cao" variable_2="Cao"/>
   </connection>
   <connection>
      <map_components component_1="second_inward_current" component_2="extracellular_sodium_concentration"/>
      <map_variables variable_1="Nao" variable_2="Nao"/>
   </connection>
   <connection>
      <map_components component_1="second_inward_current" component_2="extracellular_potassium_concentration"/>
      <map_variables variable_1="i_siK" variable_2="i_siK"/>
      <map_variables variable_1="Kc" variable_2="Kc"/>
   </connection>
   <connection>
      <map_components component_1="second_inward_current" component_2="intracellular_sodium_concentration"/>
      <map_variables variable_1="i_siNa" variable_2="i_siNa"/>
      <map_variables variable_1="Nai" variable_2="Nai"/>
   </connection>
   <connection>
      <map_components component_1="second_inward_current" component_2="intracellular_potassium_concentration"/>
      <map_variables variable_1="Ki" variable_2="Ki"/>
   </connection>
   <connection>
      <map_components component_1="hyperpolarising_activated_current" component_2="hyperpolarising_activated_current_y_gate"/>
      <map_variables variable_1="y" variable_2="y"/>
      <map_variables variable_1="time" variable_2="time"/>
      <map_variables variable_1="V" variable_2="V"/>
   </connection>
   <connection>
      <map_components component_1="time_dependent_potassium_current" component_2="time_dependent_potassium_current_x_gate"/>
      <map_variables variable_1="x" variable_2="x"/>
      <map_variables variable_1="time" variable_2="time"/>
      <map_variables variable_1="V" variable_2="V"/>
   </connection>
   <connection>
      <map_components component_1="fast_sodium_current" component_2="fast_sodium_current_m_gate"/>
      <map_variables variable_1="m" variable_2="m"/>
      <map_variables variable_1="time" variable_2="time"/>
      <map_variables variable_1="V" variable_2="V"/>
   </connection>
   <connection>
      <map_components component_1="fast_sodium_current" component_2="fast_sodium_current_h_gate"/>
      <map_variables variable_1="h" variable_2="h"/>
      <map_variables variable_1="time" variable_2="time"/>
      <map_variables variable_1="V" variable_2="V"/>
   </connection>
   <connection>
      <map_components component_1="second_inward_current" component_2="second_inward_current_d_gate"/>
      <map_variables variable_1="d" variable_2="d"/>
      <map_variables variable_1="time" variable_2="time"/>
      <map_variables variable_1="V" variable_2="V"/>
   </connection>
   <connection>
      <map_components component_1="second_inward_current" component_2="second_inward_current_f_gate"/>
      <map_variables variable_1="f" variable_2="f"/>
      <map_variables variable_1="time" variable_2="time"/>
      <map_variables variable_1="V" variable_2="V"/>
   </connection>
   <connection>
      <map_components component_1="second_inward_current" component_2="second_inward_current_f2_gate"/>
      <map_variables variable_1="f2" variable_2="f2"/>
      <map_variables variable_1="time" variable_2="time"/>
      <map_variables variable_1="V" variable_2="V"/>
      <map_variables variable_1="Cai" variable_2="Cai"/>
   </connection>
   <connection>
      <map_components component_1="intracellular_sodium_concentration" component_2="intracellular_calcium_concentration"/>
      <map_variables variable_1="Vi" variable_2="Vi"/>
   </connection>
   <connection>
      <map_components component_1="intracellular_sodium_concentration" component_2="intracellular_potassium_concentration"/>
      <map_variables variable_1="Vi" variable_2="Vi"/>
   </connection>
   <connection>
      <map_components component_1="extracellular_potassium_concentration" component_2="intracellular_potassium_concentration"/>
      <map_variables variable_1="i_mK" variable_2="i_mK"/>
   </connection>
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