Location: Noble, Difrancesco, Denyer, 1989 @ a444a916bd71 / noble_difrancesco_denyer_1989.cellml

Author:
pmr2.import <nobody@models.cellml.org>
Date:
2006-09-14 23:48:18+12:00
Desc:
committing version01 of noble_difrancesco_denyer_1989
Permanent Source URI:
http://models.cellml.org/workspace/noble_difrancesco_denyer_1989/rawfile/a444a916bd71f4173ab71983df17ace586c26f4a/noble_difrancesco_denyer_1989.cellml

<?xml version='1.0' encoding='utf-8'?>
<!--
This CellML file was generated on 05/07/2005 at 16:04:08 using:

COR (0.9.31.77)
Copyright 2002-2005 Oxford Cardiac Electrophysiology Group
http://COR.physiol.ox.ac.uk/ - COR@physiol.ox.ac.uk

CellML 1.0 was used to generate this cellular model
http://www.CellML.org/
--><model xmlns="http://www.cellml.org/cellml/1.0#" xmlns:cmeta="http://www.cellml.org/metadata/1.0#" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:bqs="http://www.cellml.org/bqs/1.0#" xmlns:cellml="http://www.cellml.org/cellml/1.0#" xmlns:dcterms="http://purl.org/dc/terms/" xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" cmeta:id="noble_difrancesco_denyer_1989_version01" name="noble_difrancesco_denyer_1989_version01">
   
    <documentation xmlns="http://cellml.org/tmp-documentation">
<article>

  <section id="sec_status">
    <title>Model Status</title>
    <para>
Version 01 is the original model imported from the old repository. Version 01 has been verified to run in PCEnv.
          </para>
  </section>
  <sect1 id="sec_structure">
<title>Model Structure</title>

<para>
<informalfigure float="0" id="fig_reaction_diagram">
<mediaobject>
  <imageobject>
    <objectinfo>
      <title>model diagram</title>
    </objectinfo>
    <imagedata fileref="noble_1989.png"/>
  </imageobject>
</mediaobject>
<caption>Schematic diagram of the Noble et al 1989 model.</caption>
</informalfigure>
</para>

<para>
This model was based on the article:
</para>
<para>
"Ionic Mechanisms in Normal and Abnormal Cardiac Pacemaker Activity"
</para>
<para>
This article can be found in the book "Neuronal and Cellular Oscillators"
</para>
<para>
pp. 59-85
</para>
<para>
Edited by Jon W. Jacklet
</para>
<para>
Part of the "Cellular Clocks" series, published by Marcel Dekker Inc.
</para> 
<para>
Further documentation is pending a summary of this article.
</para>
</sect1>
</article>
</documentation>   


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                              <divide/>
                              <apply>
                                 <times/>
                                 <ci>gamma</ci>
                                 <apply>
                                    <minus/>
                                    <ci>n_NaCa</ci>
                                    <cn cellml:units="dimensionless">2</cn>
                                 </apply>
                                 <ci>V</ci>
                                 <ci>F</ci>
                              </apply>
                              <apply>
                                 <times/>
                                 <ci>R</ci>
                                 <ci>T</ci>
                              </apply>
                           </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 cellml:units="dimensionless">1</cn>
                                 </apply>
                                 <apply>
                                    <minus/>
                                    <ci>n_NaCa</ci>
                                    <cn cellml:units="dimensionless">2</cn>
                                 </apply>
                                 <ci>V</ci>
                                 <ci>F</ci>
                              </apply>
                              <apply>
                                 <times/>
                                 <ci>R</ci>
                                 <ci>T</ci>
                              </apply>
                           </apply>
                        </apply>
                        <apply>
                           <power/>
                           <ci>Nao</ci>
                           <ci>n_NaCa</ci>
                        </apply>
                        <ci>Cai</ci>
                     </apply>
                  </apply>
               </apply>
               <apply>
                  <times/>
                  <apply>
                     <plus/>
                     <cn cellml:units="dimensionless">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 cellml:units="dimensionless">1</cn>
                     <apply>
                        <divide/>
                        <ci>Cai</ci>
                        <cn cellml:units="concentration_units">0.0069</cn>
                     </apply>
                  </apply>
               </apply>
            </apply>
         </apply>
      </math>
   </component>
   <component name="fast_sodium_current">
      <variable units="nanoamp" public_interface="out" name="i_Na"/>
      <variable units="microS" name="g_Na" initial_value="0.0125"/>
      <variable units="millivolt" name="E_mh"/>
      <variable units="second" public_interface="in" private_interface="out" name="time"/>
      <variable units="millivolt" public_interface="in" private_interface="out" name="V"/>
      <variable units="millijoule_per_mole_kelvin" public_interface="in" name="R"/>
      <variable units="kelvin" public_interface="in" name="T"/>
      <variable units="coulomb_per_mole" public_interface="in" name="F"/>
      <variable units="concentration_units" public_interface="in" name="Nao"/>
      <variable units="concentration_units" public_interface="in" name="Nai"/>
      <variable units="concentration_units" public_interface="in" name="Kc"/>
      <variable units="concentration_units" public_interface="in" name="Ki"/>
      <variable units="dimensionless" private_interface="in" name="m"/>
      <variable units="dimensionless" private_interface="in" name="h"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <ci>E_mh</ci>
            <apply>
               <times/>
               <apply>
                  <divide/>
                  <apply>
                     <times/>
                     <ci>R</ci>
                     <ci>T</ci>
                  </apply>
                  <ci>F</ci>
               </apply>
               <apply>
                  <ln/>
                  <apply>
                     <divide/>
                     <apply>
                        <plus/>
                        <ci>Nao</ci>
                        <apply>
                           <times/>
                           <cn cellml:units="dimensionless">0.12</cn>
                           <ci>Kc</ci>
                        </apply>
                     </apply>
                     <apply>
                        <plus/>
                        <ci>Nai</ci>
                        <apply>
                           <times/>
                           <cn 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 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 units="dimensionless" public_interface="out" name="m" initial_value="0.0365"/>
      <variable units="per_second" name="alpha_m"/>
      <variable units="per_second" name="beta_m"/>
      <variable units="millivolt" public_interface="in" name="V"/>
      <variable units="second" public_interface="in" name="time"/>
      <variable units="dimensionless" name="delta_m" initial_value="1e-5"/>
      <variable units="millivolt" name="E0_m"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <ci>E0_m</ci>
            <apply>
               <plus/>
               <ci>V</ci>
               <cn cellml:units="millivolt">41</cn>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>alpha_m</ci>
            <piecewise>
               <piece>
                  <cn 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 cellml:units="per_millivolt_second">200</cn>
                        <ci>E0_m</ci>
                     </apply>
                     <apply>
                        <minus/>
                        <cn cellml:units="dimensionless">1</cn>
                        <apply>
                           <exp/>
                           <apply>
                              <times/>
                              <apply>
                                 <minus/>
                                 <cn cellml:units="dimensionless">0.1</cn>
                              </apply>
                              <ci>E0_m</ci>
                           </apply>
                        </apply>
                     </apply>
                  </apply>
               </otherwise>
            </piecewise>
         </apply>
         <apply>
            <eq/>
            <ci>beta_m</ci>
            <apply>
               <times/>
               <cn cellml:units="per_second">8000</cn>
               <apply>
                  <exp/>
                  <apply>
                     <times/>
                     <apply>
                        <minus/>
                        <cn cellml:units="dimensionless">0.056</cn>
                     </apply>
                     <apply>
                        <plus/>
                        <ci>V</ci>
                        <cn 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 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 units="dimensionless" public_interface="out" name="h" initial_value="0.1969"/>
      <variable units="per_second" name="alpha_h"/>
      <variable units="per_second" name="beta_h"/>
      <variable units="millivolt" public_interface="in" name="V"/>
      <variable units="second" public_interface="in" name="time"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <ci>alpha_h</ci>
            <apply>
               <times/>
               <cn cellml:units="per_second">20</cn>
               <apply>
                  <exp/>
                  <apply>
                     <times/>
                     <apply>
                        <minus/>
                        <cn cellml:units="dimensionless">0.125</cn>
                     </apply>
                     <apply>
                        <plus/>
                        <ci>V</ci>
                        <cn cellml:units="millivolt">75</cn>
                     </apply>
                  </apply>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>beta_h</ci>
            <apply>
               <divide/>
               <cn cellml:units="per_second">2000</cn>
               <apply>
                  <plus/>
                  <apply>
                     <times/>
                     <cn cellml:units="dimensionless">320</cn>
                     <apply>
                        <exp/>
                        <apply>
                           <times/>
                           <apply>
                              <minus/>
                              <cn cellml:units="dimensionless">0.1</cn>
                           </apply>
                           <apply>
                              <plus/>
                              <ci>V</ci>
                              <cn cellml:units="millivolt">75</cn>
                           </apply>
                        </apply>
                     </apply>
                  </apply>
                  <cn 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 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 units="nanoamp" public_interface="out" name="i_si"/>
      <variable units="nanoamp" public_interface="out" name="i_siCa"/>
      <variable units="nanoamp" public_interface="out" name="i_siK"/>
      <variable units="nanoamp" public_interface="out" name="i_siNa"/>
      <variable units="dimensionless" name="P_si" initial_value="0.12"/>
      <variable units="second" public_interface="in" private_interface="out" name="time"/>
      <variable units="millivolt" public_interface="in" private_interface="out" name="V"/>
      <variable units="millijoule_per_mole_kelvin" public_interface="in" name="R"/>
      <variable units="kelvin" public_interface="in" name="T"/>
      <variable units="coulomb_per_mole" public_interface="in" name="F"/>
      <variable units="concentration_units" public_interface="in" name="Nao"/>
      <variable units="concentration_units" public_interface="in" name="Nai"/>
      <variable units="concentration_units" public_interface="in" name="Kc"/>
      <variable units="concentration_units" public_interface="in" name="Ki"/>
      <variable units="concentration_units" public_interface="in" name="Cao"/>
      <variable units="concentration_units" public_interface="in" private_interface="out" name="Cai"/>
      <variable units="dimensionless" private_interface="in" name="d"/>
      <variable units="dimensionless" private_interface="in" name="f"/>
      <variable units="dimensionless" private_interface="in" name="f2"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <ci>i_siCa</ci>
            <apply>
               <times/>
               <apply>
                  <divide/>
                  <apply>
                     <times/>
                     <cn cellml:units="dimensionless">4</cn>
                     <ci>P_si</ci>
                     <apply>
                        <minus/>
                        <ci>V</ci>
                        <cn cellml:units="millivolt">50</cn>
                     </apply>
                     <ci>F</ci>
                  </apply>
                  <apply>
                     <times/>
                     <ci>R</ci>
                     <ci>T</ci>
                     <apply>
                        <minus/>
                        <cn cellml:units="dimensionless">1</cn>
                        <apply>
                           <exp/>
                           <apply>
                              <divide/>
                              <apply>
                                 <times/>
                                 <apply>
                                    <minus/>
                                    <cn cellml:units="dimensionless">1</cn>
                                 </apply>
                                 <apply>
                                    <minus/>
                                    <ci>V</ci>
                                    <cn cellml:units="millivolt">50</cn>
                                 </apply>
                                 <ci>F</ci>
                                 <cn cellml:units="dimensionless">2</cn>
                              </apply>
                              <apply>
                                 <times/>
                                 <ci>R</ci>
                                 <ci>T</ci>
                              </apply>
                           </apply>
                        </apply>
                     </apply>
                  </apply>
               </apply>
               <apply>
                  <minus/>
                  <apply>
                     <times/>
                     <ci>Cai</ci>
                     <apply>
                        <exp/>
                        <apply>
                           <divide/>
                           <apply>
                              <times/>
                              <cn cellml:units="dimensionless">100</cn>
                              <ci>F</ci>
                           </apply>
                           <apply>
                              <times/>
                              <ci>R</ci>
                              <ci>T</ci>
                           </apply>
                        </apply>
                     </apply>
                  </apply>
                  <apply>
                     <times/>
                     <ci>Cao</ci>
                     <apply>
                        <exp/>
                        <apply>
                           <divide/>
                           <apply>
                              <times/>
                              <apply>
                                 <minus/>
                                 <cn cellml:units="dimensionless">2</cn>
                              </apply>
                              <apply>
                                 <minus/>
                                 <ci>V</ci>
                                 <cn cellml:units="millivolt">50</cn>
                              </apply>
                              <ci>F</ci>
                           </apply>
                           <apply>
                              <times/>
                              <ci>R</ci>
                              <ci>T</ci>
                           </apply>
                        </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 cellml:units="dimensionless">0.01</cn>
                     <ci>P_si</ci>
                     <apply>
                        <minus/>
                        <ci>V</ci>
                        <cn cellml:units="millivolt">50</cn>
                     </apply>
                     <ci>F</ci>
                  </apply>
                  <apply>
                     <times/>
                     <ci>R</ci>
                     <ci>T</ci>
                     <apply>
                        <minus/>
                        <cn cellml:units="dimensionless">1</cn>
                        <apply>
                           <exp/>
                           <apply>
                              <divide/>
                              <apply>
                                 <times/>
                                 <apply>
                                    <minus/>
                                    <cn cellml:units="dimensionless">1</cn>
                                 </apply>
                                 <apply>
                                    <minus/>
                                    <ci>V</ci>
                                    <cn cellml:units="millivolt">50</cn>
                                 </apply>
                                 <ci>F</ci>
                              </apply>
                              <apply>
                                 <times/>
                                 <ci>R</ci>
                                 <ci>T</ci>
                              </apply>
                           </apply>
                        </apply>
                     </apply>
                  </apply>
               </apply>
               <apply>
                  <minus/>
                  <apply>
                     <times/>
                     <ci>Ki</ci>
                     <apply>
                        <exp/>
                        <apply>
                           <divide/>
                           <apply>
                              <times/>
                              <cn cellml:units="dimensionless">50</cn>
                              <ci>F</ci>
                           </apply>
                           <apply>
                              <times/>
                              <ci>R</ci>
                              <ci>T</ci>
                           </apply>
                        </apply>
                     </apply>
                  </apply>
                  <apply>
                     <times/>
                     <ci>Kc</ci>
                     <apply>
                        <exp/>
                        <apply>
                           <divide/>
                           <apply>
                              <times/>
                              <apply>
                                 <minus/>
                                 <cn cellml:units="dimensionless">1</cn>
                              </apply>
                              <apply>
                                 <minus/>
                                 <ci>V</ci>
                                 <cn cellml:units="millivolt">50</cn>
                              </apply>
                              <ci>F</ci>
                           </apply>
                           <apply>
                              <times/>
                              <ci>R</ci>
                              <ci>T</ci>
                           </apply>
                        </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 cellml:units="dimensionless">0.01</cn>
                     <ci>P_si</ci>
                     <apply>
                        <minus/>
                        <ci>V</ci>
                        <cn cellml:units="millivolt">50</cn>
                     </apply>
                     <ci>F</ci>
                  </apply>
                  <apply>
                     <times/>
                     <ci>R</ci>
                     <ci>T</ci>
                     <apply>
                        <minus/>
                        <cn cellml:units="dimensionless">1</cn>
                        <apply>
                           <exp/>
                           <apply>
                              <divide/>
                              <apply>
                                 <times/>
                                 <apply>
                                    <minus/>
                                    <cn cellml:units="dimensionless">1</cn>
                                 </apply>
                                 <apply>
                                    <minus/>
                                    <ci>V</ci>
                                    <cn cellml:units="millivolt">50</cn>
                                 </apply>
                                 <ci>F</ci>
                              </apply>
                              <apply>
                                 <times/>
                                 <ci>R</ci>
                                 <ci>T</ci>
                              </apply>
                           </apply>
                        </apply>
                     </apply>
                  </apply>
               </apply>
               <apply>
                  <minus/>
                  <apply>
                     <times/>
                     <ci>Nai</ci>
                     <apply>
                        <exp/>
                        <apply>
                           <divide/>
                           <apply>
                              <times/>
                              <cn cellml:units="dimensionless">50</cn>
                              <ci>F</ci>
                           </apply>
                           <apply>
                              <times/>
                              <ci>R</ci>
                              <ci>T</ci>
                           </apply>
                        </apply>
                     </apply>
                  </apply>
                  <apply>
                     <times/>
                     <ci>Nao</ci>
                     <apply>
                        <exp/>
                        <apply>
                           <divide/>
                           <apply>
                              <times/>
                              <apply>
                                 <minus/>
                                 <cn cellml:units="dimensionless">1</cn>
                              </apply>
                              <apply>
                                 <minus/>
                                 <ci>V</ci>
                                 <cn cellml:units="millivolt">50</cn>
                              </apply>
                              <ci>F</ci>
                           </apply>
                           <apply>
                              <times/>
                              <ci>R</ci>
                              <ci>T</ci>
                           </apply>
                        </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 units="dimensionless" public_interface="out" name="d" initial_value="0"/>
      <variable units="per_second" name="alpha_d"/>
      <variable units="per_second" name="beta_d"/>
      <variable units="millivolt" public_interface="in" name="V"/>
      <variable units="second" public_interface="in" name="time"/>
      <variable units="dimensionless" name="delta_d" initial_value="0.0001"/>
      <variable units="millivolt" name="E0_d"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <ci>E0_d</ci>
            <apply>
               <minus/>
               <apply>
                  <plus/>
                  <ci>V</ci>
                  <cn cellml:units="millivolt">24</cn>
               </apply>
               <cn cellml:units="millivolt">5</cn>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>alpha_d</ci>
            <piecewise>
               <piece>
                  <cn 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 cellml:units="per_millivolt_second">30</cn>
                        <ci>E0_d</ci>
                     </apply>
                     <apply>
                        <minus/>
                        <cn cellml:units="dimensionless">1</cn>
                        <apply>
                           <exp/>
                           <apply>
                              <divide/>
                              <apply>
                                 <times/>
                                 <apply>
                                    <minus/>
                                    <cn cellml:units="dimensionless">1</cn>
                                 </apply>
                                 <ci>E0_d</ci>
                              </apply>
                              <cn cellml:units="millivolt">4</cn>
                           </apply>
                        </apply>
                     </apply>
                  </apply>
               </otherwise>
            </piecewise>
         </apply>
         <apply>
            <eq/>
            <ci>beta_d</ci>
            <piecewise>
               <piece>
                  <cn 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 cellml:units="per_millivolt_second">12</cn>
                        <ci>E0_d</ci>
                     </apply>
                     <apply>
                        <minus/>
                        <apply>
                           <exp/>
                           <apply>
                              <divide/>
                              <ci>E0_d</ci>
                              <cn cellml:units="millivolt">10</cn>
                           </apply>
                        </apply>
                        <cn 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 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 units="dimensionless" public_interface="out" name="f" initial_value="0.9997"/>
      <variable units="per_second" name="alpha_f"/>
      <variable units="per_second" name="beta_f"/>
      <variable units="millivolt" public_interface="in" name="V"/>
      <variable units="second" public_interface="in" name="time"/>
      <variable units="dimensionless" name="delta_f" initial_value="0.0001"/>
      <variable units="millivolt" name="E0_f"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <ci>E0_f</ci>
            <apply>
               <plus/>
               <ci>V</ci>
               <cn cellml:units="millivolt">34</cn>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>alpha_f</ci>
            <piecewise>
               <piece>
                  <cn 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 cellml:units="per_millivolt_second">6.25</cn>
                        <ci>E0_f</ci>
                     </apply>
                     <apply>
                        <minus/>
                        <apply>
                           <exp/>
                           <apply>
                              <divide/>
                              <ci>E0_f</ci>
                              <cn cellml:units="millivolt">4</cn>
                           </apply>
                        </apply>
                        <cn cellml:units="dimensionless">1</cn>
                     </apply>
                  </apply>
               </otherwise>
            </piecewise>
         </apply>
         <apply>
            <eq/>
            <ci>beta_f</ci>
            <apply>
               <divide/>
               <cn cellml:units="per_second">50</cn>
               <apply>
                  <plus/>
                  <cn cellml:units="dimensionless">1</cn>
                  <apply>
                     <exp/>
                     <apply>
                        <divide/>
                        <apply>
                           <times/>
                           <apply>
                              <minus/>
                              <cn cellml:units="dimensionless">1</cn>
                           </apply>
                           <apply>
                              <plus/>
                              <ci>V</ci>
                              <cn cellml:units="millivolt">34</cn>
                           </apply>
                        </apply>
                        <cn 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 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 units="dimensionless" public_interface="out" name="f2" initial_value="0.5765"/>
      <variable units="per_second" name="alpha_f2" initial_value="10"/>
      <variable units="per_second" name="beta_f2"/>
      <variable units="concentration_units" name="K_mf2" initial_value="0.0005"/>
      <variable units="millivolt" public_interface="in" name="V"/>
      <variable units="second" public_interface="in" name="time"/>
      <variable units="concentration_units" public_interface="in" name="Cai"/>
      <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 units="concentration_units" public_interface="out" name="Nao" initial_value="140"/>
   </component>
   <component name="intracellular_sodium_concentration">
      <variable units="concentration_units" public_interface="out" name="Nai" initial_value="7.5"/>
      <variable units="micrometre" name="radius" initial_value="10"/>
      <variable units="micrometre" name="length" initial_value="28"/>
      <variable units="dimensionless" name="V_e_ratio" initial_value="0.1"/>
      <variable units="microlitre" name="V_Cell"/>
      <variable units="microlitre" public_interface="out" name="Vi"/>
      <variable units="second" public_interface="in" name="time"/>
      <variable units="coulomb_per_mole" public_interface="in" name="F"/>
      <variable units="nanoamp" public_interface="in" name="i_Na"/>
      <variable units="nanoamp" public_interface="in" name="i_Na_b"/>
      <variable units="nanoamp" public_interface="in" name="i_siNa"/>
      <variable units="nanoamp" public_interface="in" name="i_p"/>
      <variable units="nanoamp" public_interface="in" name="i_fNa"/>
      <variable units="nanoamp" public_interface="in" name="i_NaCa"/>
      <variable units="dimensionless" public_interface="in" name="n_NaCa"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <ci>V_Cell</ci>
            <apply>
               <divide/>
               <apply>
                  <times/>
                  <cn cellml:units="dimensionless">3.141592654</cn>
                  <apply>
                     <power/>
                     <apply>
                        <divide/>
                        <ci>radius</ci>
                        <cn cellml:units="dimensionless">1000</cn>
                     </apply>
                     <cn cellml:units="dimensionless">2</cn>
                  </apply>
                  <ci>length</ci>
               </apply>
               <cn cellml:units="dimensionless">1000</cn>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>Vi</ci>
            <apply>
               <times/>
               <ci>V_Cell</ci>
               <apply>
                  <minus/>
                  <cn 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>
                  <minus/>
                  <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 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 cellml:units="dimensionless">2</cn>
                        </apply>
                     </apply>
                  </apply>
               </apply>
               <apply>
                  <times/>
                  <ci>Vi</ci>
                  <ci>F</ci>
               </apply>
            </apply>
         </apply>
      </math>
   </component>
   <component name="extracellular_calcium_concentration">
      <variable units="concentration_units" public_interface="out" name="Cao" initial_value="2"/>
   </component>
   <component name="intracellular_calcium_concentration">
      <variable units="concentration_units" public_interface="out" name="Cai" initial_value="5.6e-5"/>
      <variable units="microlitre" name="V_up"/>
      <variable units="microlitre" name="V_rel"/>
      <variable units="microlitre" public_interface="in" name="Vi"/>
      <variable units="nanoamp" name="i_up"/>
      <variable units="nanoamp" name="i_tr"/>
      <variable units="nanoamp" name="i_rel"/>
      <variable units="per_second" name="alpha_up"/>
      <variable units="per_second" name="alpha_tr"/>
      <variable units="per_second" name="alpha_rel"/>
      <variable units="concentration_units" name="Ca_up" initial_value="2.3909"/>
      <variable units="concentration_units" name="Ca_rel" initial_value="0.2207"/>
      <variable units="concentration_units" name="Ca_up_max" initial_value="5"/>
      <variable units="concentration_units" name="K_mCa" initial_value="0.002"/>
      <variable units="dimensionless" name="p" initial_value="0.237"/>
      <variable units="per_second" name="alpha_p"/>
      <variable units="per_second" name="beta_p"/>
      <variable units="millivolt" name="E0_p"/>
      <variable units="second" name="tau_up" initial_value="0.005"/>
      <variable units="second" name="tau_rep" initial_value="0.2"/>
      <variable units="second" name="tau_rel" initial_value="0.01"/>
      <variable units="dimensionless" name="rCa" initial_value="2"/>
      <variable units="second" public_interface="in" name="time"/>
      <variable units="millivolt" public_interface="in" name="V"/>
      <variable units="coulomb_per_mole" public_interface="in" name="F"/>
      <variable units="nanoamp" public_interface="in" name="i_Ca_b"/>
      <variable units="nanoamp" public_interface="in" name="i_siCa"/>
      <variable units="nanoamp" public_interface="in" name="i_NaCa"/>
      <variable units="dimensionless" public_interface="in" name="n_NaCa"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <ci>i_up</ci>
            <apply>
               <times/>
               <ci>alpha_up</ci>
               <ci>Cai</ci>
               <apply>
                  <minus/>
                  <ci>Ca_up_max</ci>
                  <ci>Ca_up</ci>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>alpha_up</ci>
            <apply>
               <divide/>
               <apply>
                  <times/>
                  <cn cellml:units="dimensionless">2</cn>
                  <ci>Vi</ci>
                  <ci>F</ci>
               </apply>
               <apply>
                  <times/>
                  <ci>tau_up</ci>
                  <ci>Ca_up_max</ci>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>i_tr</ci>
            <apply>
               <times/>
               <ci>alpha_tr</ci>
               <ci>p</ci>
               <apply>
                  <minus/>
                  <ci>Ca_up</ci>
                  <ci>Ca_rel</ci>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>alpha_tr</ci>
            <apply>
               <divide/>
               <apply>
                  <times/>
                  <cn cellml:units="dimensionless">2</cn>
                  <ci>V_rel</ci>
                  <ci>F</ci>
               </apply>
               <ci>tau_rep</ci>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>E0_p</ci>
            <apply>
               <minus/>
               <apply>
                  <plus/>
                  <ci>V</ci>
                  <cn cellml:units="millivolt">34</cn>
               </apply>
               <apply>
                  <minus/>
                  <cn cellml:units="millivolt">30</cn>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>alpha_p</ci>
            <apply>
               <divide/>
               <apply>
                  <times/>
                  <cn cellml:units="per_millivolt_second">0.625</cn>
                  <ci>E0_p</ci>
               </apply>
               <apply>
                  <minus/>
                  <apply>
                     <exp/>
                     <apply>
                        <divide/>
                        <ci>E0_p</ci>
                        <cn cellml:units="millivolt">4</cn>
                     </apply>
                  </apply>
                  <cn cellml:units="dimensionless">1</cn>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>beta_p</ci>
            <apply>
               <divide/>
               <cn cellml:units="per_second">5</cn>
               <apply>
                  <plus/>
                  <cn cellml:units="dimensionless">1</cn>
                  <apply>
                     <exp/>
                     <apply>
                        <divide/>
                        <apply>
                           <times/>
                           <apply>
                              <minus/>
                              <cn cellml:units="dimensionless">1</cn>
                           </apply>
                           <ci>E0_p</ci>
                        </apply>
                        <cn cellml:units="millivolt">4</cn>
                     </apply>
                  </apply>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>i_rel</ci>
            <apply>
               <divide/>
               <apply>
                  <times/>
                  <ci>alpha_rel</ci>
                  <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/>
            <ci>alpha_rel</ci>
            <apply>
               <divide/>
               <apply>
                  <times/>
                  <cn cellml:units="dimensionless">2</cn>
                  <ci>V_rel</ci>
                  <ci>F</ci>
               </apply>
               <ci>tau_rel</ci>
            </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 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>
                  <minus/>
                  <ci>i_up</ci>
                  <ci>i_tr</ci>
               </apply>
               <apply>
                  <times/>
                  <cn cellml:units="dimensionless">2</cn>
                  <ci>V_up</ci>
                  <ci>F</ci>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>V_up</ci>
            <apply>
               <times/>
               <ci>Vi</ci>
               <cn 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>
                  <minus/>
                  <ci>i_tr</ci>
                  <ci>i_rel</ci>
               </apply>
               <apply>
                  <times/>
                  <cn cellml:units="dimensionless">2</cn>
                  <ci>V_rel</ci>
                  <ci>F</ci>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>V_rel</ci>
            <apply>
               <times/>
               <ci>Vi</ci>
               <cn cellml:units="dimensionless">0.02</cn>
            </apply>
         </apply>
         <apply>
            <eq/>
            <apply>
               <diff/>
               <bvar>
                  <ci>time</ci>
               </bvar>
               <ci>Cai</ci>
            </apply>
            <apply>
               <divide/>
               <apply>
                  <minus/>
                  <apply>
                     <plus/>
                     <apply>
                        <minus/>
                        <apply>
                           <minus/>
                           <apply>
                              <plus/>
                              <ci>i_siCa</ci>
                              <ci>i_Ca_b</ci>
                           </apply>
                           <apply>
                              <divide/>
                              <apply>
                                 <times/>
                                 <cn cellml:units="dimensionless">2</cn>
                                 <ci>i_NaCa</ci>
                              </apply>
                              <apply>
                                 <minus/>
                                 <ci>n_NaCa</ci>
                                 <cn cellml:units="dimensionless">2</cn>
                              </apply>
                           </apply>
                        </apply>
                        <ci>i_rel</ci>
                     </apply>
                     <ci>i_up</ci>
                  </apply>
               </apply>
               <apply>
                  <times/>
                  <cn cellml:units="dimensionless">2</cn>
                  <ci>Vi</ci>
                  <ci>F</ci>
               </apply>
            </apply>
         </apply>
      </math>
   </component>
   <component name="extracellular_potassium_concentration">
      <variable units="concentration_units" public_interface="out" name="Kc" initial_value="3"/>
   </component>
   <component name="intracellular_potassium_concentration">
      <variable units="concentration_units" public_interface="out" name="Ki" initial_value="140"/>
      <variable units="microlitre" public_interface="in" name="Vi"/>
      <variable units="nanoamp" public_interface="in" name="i_K1"/>
      <variable units="nanoamp" public_interface="in" name="i_K"/>
      <variable units="nanoamp" public_interface="in" name="i_fK"/>
      <variable units="nanoamp" public_interface="in" name="i_siK"/>
      <variable units="nanoamp" public_interface="in" name="i_p"/>
      <variable units="nanoamp" name="i_mK"/>
      <variable units="second" public_interface="in" name="time"/>
      <variable units="coulomb_per_mole" public_interface="in" name="F"/>
      <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 cellml:units="dimensionless">2</cn>
                  <ci>i_p</ci>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <apply>
               <diff/>
               <bvar>
                  <ci>time</ci>
               </bvar>
               <ci>Ki</ci>
            </apply>
            <apply>
               <divide/>
               <apply>
                  <minus/>
                  <ci>i_mK</ci>
               </apply>
               <apply>
                  <times/>
                  <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_2="environment" component_1="membrane"/>
      <map_variables variable_2="time" variable_1="time"/>
   </connection>
   <connection>
      <map_components component_2="environment" component_1="hyperpolarising_activated_current"/>
      <map_variables variable_2="time" variable_1="time"/>
   </connection>
   <connection>
      <map_components component_2="environment" component_1="time_dependent_potassium_current"/>
      <map_variables variable_2="time" variable_1="time"/>
   </connection>
   <connection>
      <map_components component_2="environment" component_1="time_independent_potassium_current"/>
      <map_variables variable_2="time" variable_1="time"/>
   </connection>
   <connection>
      <map_components component_2="environment" component_1="sodium_background_current"/>
      <map_variables variable_2="time" variable_1="time"/>
   </connection>
   <connection>
      <map_components component_2="environment" component_1="calcium_background_current"/>
      <map_variables variable_2="time" variable_1="time"/>
   </connection>
   <connection>
      <map_components component_2="environment" component_1="sodium_potassium_pump"/>
      <map_variables variable_2="time" variable_1="time"/>
   </connection>
   <connection>
      <map_components component_2="environment" component_1="Na_Ca_exchanger"/>
      <map_variables variable_2="time" variable_1="time"/>
   </connection>
   <connection>
      <map_components component_2="environment" component_1="fast_sodium_current"/>
      <map_variables variable_2="time" variable_1="time"/>
   </connection>
   <connection>
      <map_components component_2="environment" component_1="second_inward_current"/>
      <map_variables variable_2="time" variable_1="time"/>
   </connection>
   <connection>
      <map_components component_2="environment" component_1="intracellular_sodium_concentration"/>
      <map_variables variable_2="time" variable_1="time"/>
   </connection>
   <connection>
      <map_components component_2="environment" component_1="intracellular_calcium_concentration"/>
      <map_variables variable_2="time" variable_1="time"/>
   </connection>
   <connection>
      <map_components component_2="environment" component_1="intracellular_potassium_concentration"/>
      <map_variables variable_2="time" variable_1="time"/>
   </connection>
   <connection>
      <map_components component_2="membrane" component_1="hyperpolarising_activated_current"/>
      <map_variables variable_2="V" variable_1="V"/>
      <map_variables variable_2="R" variable_1="R"/>
      <map_variables variable_2="T" variable_1="T"/>
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