Location: Mcallister, Noble, Tsien, 1975 @ dfff9cd4dd91 / mcallister_noble_tsien_1975.cellml

Author:
pmr2.import <nobody@models.cellml.org>
Date:
2006-09-14 22:48:37+12:00
Desc:
committing version04 of mcallister_noble_tsien_1975
Permanent Source URI:
https://staging.physiomeproject.org/workspace/mcallister_noble_tsien_1975/rawfile/dfff9cd4dd9115bb55ad1e72cb40f06b4373678e/mcallister_noble_tsien_1975.cellml

<?xml version='1.0' encoding='utf-8'?>
<!--
This CellML file was generated on 21/02/2006 at 11:57:13 using:

COR (0.9.31.227)
Copyright 2002-2006 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/
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<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
  <articleinfo>
  <title>McAllister-Noble-Tsien Purkinje Fibre Model 1975</title>
  <author>
    <firstname>Catherine</firstname>
          <surname>Lloyd</surname>
    <affiliation>
      <shortaffil>Bioengineering Institute, University of Auckland</shortaffil>
    </affiliation>
  </author>
</articleinfo>
  <section id="sec_status">
    <title>Model Status</title>
    <para>
            This is the original unchecked version of the model imported from the previous
            CellML model repository, 24-Jan-2006.
          </para>
  </section>
  <sect1 id="sec_structure">
<title>Model Structure</title>

<para>
Following Denis Noble's 1962 model of cardiac action potentials in Purkinje fibres, the next significant development in cardiac membrane modelling occurred when R.E. McAllister, D. Noble and R.W. Tsien (1975) published a paper which formulated new ionic current equations based on new experimental data.  The description of the kinetics of the currents is still based on the Hodgkin-Huxley formalism, but the currents themselves incorporate some significant new changes, and the total ionic current is broken down into nine discrete, individual ionic fluxes (see the figure below). 
</para>

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

<para>
<ulink url="http://www.jphysiol.org/cgi/content/abstract/251/1/1b">Reconstruction of the Electrical Activity of Cardiac Purkinje Fibres</ulink>, McAllister, R.E. Noble, D. and Tsien, R.W. 1975, <ulink url="http://www.jphysiol.org/">
            <emphasis>Journal of Physiology</emphasis>
          </ulink>, 251, 1-59.  <ulink url="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&amp;db=PubMed&amp;list_uids=1185607&amp;dopt=Abstract">PubMed ID: 1185607</ulink>
</para>

<informalfigure float="0" id="fig_cell_diagram">
<mediaobject>
  <imageobject>
    <objectinfo>
      <title>cell diagram of the MNT model showing ionic currents across the sarcoplasmic reticulum</title>
    </objectinfo>
    <imagedata fileref="mcallister_noble_tsien_1975.png"/>
  </imageobject>
</mediaobject>
<caption>A schematic diagram describing the current flows across the cell membrane that are captured in the MNT model.</caption>
</informalfigure>

<informalfigure float="0" id="fig_cellml_rendering">
<mediaobject>
  <imageobject>
    <objectinfo>
      <title>the cellml rendering of the MNT model</title>
    </objectinfo>
    <imagedata fileref="cellml_rendering.gif"/>
  </imageobject>
</mediaobject>
<caption>The network defined in the CellML description of the McAllister-Noble-Tsien model. A key describing the significance of the shapes of the components and the colours of the connections between them is in the <ulink url="${HTML_EXMPL_GRAPHICAL_NOTATION}">notation guide</ulink>.  For simplicity, not all the variables are shown.</caption>
</informalfigure>

<para>
The membrane physically contains the currents as indicated by the blue arrows in <xref linkend="fig_cellml_rendering"/>. The currents act independently and are not connected to each other. Several of the channels encapsulate <emphasis>and</emphasis> contain further components which represent activation and inactivation gates. The addition of an encapsulation relationship informs modellers and processing software that the gates are important parts of the current model. It also prevents any other components that aren't also encapsulated by the parent component from connecting to its gates, effectively hiding them from the rest of the model.
</para>

<para>
The breakdown of the model into components and the definition of encapsulation and containment relationships between them is somewhat arbitrary. When considering how a model should be broken into components, modellers are encouraged to consider which parts of a model might be re-used and how the physiological elements of the system being modelled are naturally bounded. Containment relationships should be used to provide simple rendering information for processing software (ideally, this will correspond to the layout of the physical system), and encapsulation should be used to group sets of components into sub-models.
</para>

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


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                  </apply>
               </apply>
               <apply>
                  <minus/>
                  <cn cellml:units="dimensionless">1</cn>
                  <apply>
                     <exp/>
                     <apply>
                        <times/>
                        <apply>
                           <minus/>
                           <cn cellml:units="per_millivolt">0.2</cn>
                        </apply>
                        <apply>
                           <minus/>
                           <ci>V</ci>
                           <ci>E_s</ci>
                        </apply>
                     </apply>
                  </apply>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>beta_s</ci>
            <apply>
               <times/>
               <cn cellml:units="per_millisecond">0.00005</cn>
               <apply>
                  <exp/>
                  <apply>
                     <times/>
                     <apply>
                        <minus/>
                        <cn cellml:units="per_millivolt">0.067</cn>
                     </apply>
                     <apply>
                        <minus/>
                        <ci>V</ci>
                        <ci>E_s</ci>
                     </apply>
                  </apply>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <apply>
               <diff/>
               <bvar>
                  <ci>time</ci>
               </bvar>
               <ci>s</ci>
            </apply>
            <apply>
               <minus/>
               <apply>
                  <times/>
                  <ci>alpha_s</ci>
                  <apply>
                     <minus/>
                     <cn cellml:units="dimensionless">1</cn>
                     <ci>s</ci>
                  </apply>
               </apply>
               <apply>
                  <times/>
                  <ci>beta_s</ci>
                  <ci>s</ci>
               </apply>
            </apply>
         </apply>
      </math>
   </component>
   <component name="plateau_potassium_current1">
      <variable units="microA_per_cm2" public_interface="out" name="i_x1"/>
      <variable units="microA_per_cm2" name="I_x1"/>
      <variable units="millisecond" public_interface="in" private_interface="out" name="time"/>
      <variable units="millivolt" public_interface="in" private_interface="out" name="V"/>
      <variable units="dimensionless" private_interface="in" name="x1"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <ci>i_x1</ci>
            <apply>
               <times/>
               <ci>x1</ci>
               <ci>I_x1</ci>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>I_x1</ci>
            <apply>
               <divide/>
               <apply>
                  <times/>
                  <cn cellml:units="microA_per_cm2">1.2</cn>
                  <apply>
                     <minus/>
                     <apply>
                        <exp/>
                        <apply>
                           <divide/>
                           <apply>
                              <plus/>
                              <ci>V</ci>
                              <cn cellml:units="millivolt">95</cn>
                           </apply>
                           <cn cellml:units="millivolt">25</cn>
                        </apply>
                     </apply>
                     <cn cellml:units="dimensionless">1</cn>
                  </apply>
               </apply>
               <apply>
                  <exp/>
                  <apply>
                     <divide/>
                     <apply>
                        <plus/>
                        <ci>V</ci>
                        <cn cellml:units="millivolt">45</cn>
                     </apply>
                     <cn cellml:units="millivolt">25</cn>
                  </apply>
               </apply>
            </apply>
         </apply>
      </math>
   </component>
   <component name="plateau_potassium_current1_x1_gate">
      <variable units="dimensionless" public_interface="out" name="x1" initial_value="0.02030289"/>
      <variable units="per_millisecond" name="alpha_x1"/>
      <variable units="per_millisecond" name="beta_x1"/>
      <variable units="millivolt" public_interface="in" name="V"/>
      <variable units="millisecond" public_interface="in" name="time"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <ci>alpha_x1</ci>
            <apply>
               <divide/>
               <apply>
                  <times/>
                  <cn cellml:units="microA_per_cm2">5e-4</cn>
                  <apply>
                     <exp/>
                     <apply>
                        <divide/>
                        <apply>
                           <plus/>
                           <ci>V</ci>
                           <cn cellml:units="millivolt">50</cn>
                        </apply>
                        <cn cellml:units="millivolt">12.1</cn>
                     </apply>
                  </apply>
               </apply>
               <apply>
                  <plus/>
                  <cn cellml:units="dimensionless">1</cn>
                  <apply>
                     <exp/>
                     <apply>
                        <divide/>
                        <apply>
                           <plus/>
                           <ci>V</ci>
                           <cn cellml:units="millivolt">50</cn>
                        </apply>
                        <cn cellml:units="millivolt">17.5</cn>
                     </apply>
                  </apply>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>beta_x1</ci>
            <apply>
               <divide/>
               <apply>
                  <times/>
                  <cn cellml:units="microA_per_cm2">0.0013</cn>
                  <apply>
                     <exp/>
                     <apply>
                        <divide/>
                        <apply>
                           <minus/>
                           <apply>
                              <plus/>
                              <ci>V</ci>
                              <cn cellml:units="millivolt">20</cn>
                           </apply>
                        </apply>
                        <cn cellml:units="millivolt">16.67</cn>
                     </apply>
                  </apply>
               </apply>
               <apply>
                  <plus/>
                  <cn cellml:units="dimensionless">1</cn>
                  <apply>
                     <exp/>
                     <apply>
                        <divide/>
                        <apply>
                           <minus/>
                           <apply>
                              <plus/>
                              <ci>V</ci>
                              <cn cellml:units="millivolt">20</cn>
                           </apply>
                        </apply>
                        <cn cellml:units="millivolt">25</cn>
                     </apply>
                  </apply>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <apply>
               <diff/>
               <bvar>
                  <ci>time</ci>
               </bvar>
               <ci>x1</ci>
            </apply>
            <apply>
               <minus/>
               <apply>
                  <times/>
                  <ci>alpha_x1</ci>
                  <apply>
                     <minus/>
                     <cn cellml:units="dimensionless">1</cn>
                     <ci>x1</ci>
                  </apply>
               </apply>
               <apply>
                  <times/>
                  <ci>beta_x1</ci>
                  <ci>x1</ci>
               </apply>
            </apply>
         </apply>
      </math>
   </component>
   <component name="plateau_potassium_current2">
      <variable units="microA_per_cm2" public_interface="out" name="i_x2"/>
      <variable units="microA_per_cm2" name="I_x2"/>
      <variable units="millisecond" public_interface="in" private_interface="out" name="time"/>
      <variable units="millivolt" public_interface="in" private_interface="out" name="V"/>
      <variable units="dimensionless" private_interface="in" name="x2"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <ci>i_x2</ci>
            <apply>
               <times/>
               <ci>x2</ci>
               <ci>I_x2</ci>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>I_x2</ci>
            <apply>
               <plus/>
               <cn cellml:units="microA_per_cm2">25</cn>
               <apply>
                  <times/>
                  <cn cellml:units="per_millivolt">0.385</cn>
                  <ci>V</ci>
               </apply>
            </apply>
         </apply>
      </math>
   </component>
   <component name="plateau_potassium_current2_x2_gate">
      <variable units="dimensionless" public_interface="out" name="x2" initial_value="0.0176854"/>
      <variable units="per_millisecond" name="alpha_x2"/>
      <variable units="per_millisecond" name="beta_x2"/>
      <variable units="millivolt" public_interface="in" name="V"/>
      <variable units="millisecond" public_interface="in" name="time"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <ci>alpha_x2</ci>
            <apply>
               <divide/>
               <apply>
                  <times/>
                  <cn cellml:units="microA_per_cm2">0.000127</cn>
                  <cn cellml:units="dimensionless">1</cn>
               </apply>
               <apply>
                  <plus/>
                  <cn cellml:units="dimensionless">1</cn>
                  <apply>
                     <exp/>
                     <apply>
                        <divide/>
                        <apply>
                           <minus/>
                           <apply>
                              <plus/>
                              <ci>V</ci>
                              <cn cellml:units="millivolt">19</cn>
                           </apply>
                        </apply>
                        <cn cellml:units="millivolt">5</cn>
                     </apply>
                  </apply>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>beta_x2</ci>
            <apply>
               <divide/>
               <apply>
                  <times/>
                  <cn cellml:units="microA_per_cm2">0.0003</cn>
                  <apply>
                     <exp/>
                     <apply>
                        <divide/>
                        <apply>
                           <minus/>
                           <apply>
                              <plus/>
                              <ci>V</ci>
                              <cn cellml:units="millivolt">20</cn>
                           </apply>
                        </apply>
                        <cn cellml:units="millivolt">16.67</cn>
                     </apply>
                  </apply>
               </apply>
               <apply>
                  <plus/>
                  <cn cellml:units="dimensionless">1</cn>
                  <apply>
                     <exp/>
                     <apply>
                        <divide/>
                        <apply>
                           <minus/>
                           <apply>
                              <plus/>
                              <ci>V</ci>
                              <cn cellml:units="millivolt">20</cn>
                           </apply>
                        </apply>
                        <cn cellml:units="millivolt">25</cn>
                     </apply>
                  </apply>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <apply>
               <diff/>
               <bvar>
                  <ci>time</ci>
               </bvar>
               <ci>x2</ci>
            </apply>
            <apply>
               <minus/>
               <apply>
                  <times/>
                  <ci>alpha_x2</ci>
                  <apply>
                     <minus/>
                     <cn cellml:units="dimensionless">1</cn>
                     <ci>x2</ci>
                  </apply>
               </apply>
               <apply>
                  <times/>
                  <ci>beta_x2</ci>
                  <ci>x2</ci>
               </apply>
            </apply>
         </apply>
      </math>
   </component>
   <component name="transient_chloride_current">
      <variable units="microA_per_cm2" public_interface="out" name="i_qr"/>
      <variable units="millivolt" public_interface="out" name="E_Cl" initial_value="-70"/>
      <variable units="milliS_per_cm2" name="g_qr" initial_value="2.5"/>
      <variable units="millisecond" public_interface="in" private_interface="out" name="time"/>
      <variable units="millivolt" public_interface="in" private_interface="out" name="V"/>
      <variable units="dimensionless" private_interface="in" name="q"/>
      <variable units="dimensionless" private_interface="in" name="r"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <ci>i_qr</ci>
            <apply>
               <times/>
               <ci>g_qr</ci>
               <ci>q</ci>
               <ci>r</ci>
               <apply>
                  <minus/>
                  <ci>V</ci>
                  <ci>E_Cl</ci>
               </apply>
            </apply>
         </apply>
      </math>
   </component>
   <component name="transient_chloride_current_q_gate">
      <variable units="dimensionless" public_interface="out" name="q" initial_value="3.11285794"/>
      <variable units="per_millisecond" name="alpha_q"/>
      <variable units="per_millisecond" name="beta_q"/>
      <variable units="millivolt" public_interface="in" name="V"/>
      <variable units="millisecond" public_interface="in" name="time"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <ci>alpha_q</ci>
            <apply>
               <divide/>
               <apply>
                  <times/>
                  <cn cellml:units="per_millivolt_millisecond">0.008</cn>
                  <ci>V</ci>
               </apply>
               <apply>
                  <minus/>
                  <cn cellml:units="dimensionless">1</cn>
                  <apply>
                     <exp/>
                     <apply>
                        <times/>
                        <apply>
                           <minus/>
                           <cn cellml:units="per_millivolt">0.1</cn>
                        </apply>
                        <ci>V</ci>
                     </apply>
                  </apply>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>beta_q</ci>
            <apply>
               <times/>
               <cn cellml:units="per_millisecond">0.08</cn>
               <apply>
                  <exp/>
                  <apply>
                     <times/>
                     <apply>
                        <minus/>
                        <cn cellml:units="per_millivolt">0.0888</cn>
                     </apply>
                     <ci>V</ci>
                  </apply>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <apply>
               <diff/>
               <bvar>
                  <ci>time</ci>
               </bvar>
               <ci>q</ci>
            </apply>
            <apply>
               <minus/>
               <apply>
                  <times/>
                  <ci>alpha_q</ci>
                  <apply>
                     <minus/>
                     <cn cellml:units="dimensionless">1</cn>
                     <ci>q</ci>
                  </apply>
               </apply>
               <apply>
                  <times/>
                  <ci>beta_q</ci>
                  <ci>q</ci>
               </apply>
            </apply>
         </apply>
      </math>
   </component>
   <component name="transient_chloride_current_r_gate">
      <variable units="dimensionless" public_interface="out" name="r" initial_value="0.13500116"/>
      <variable units="per_millisecond" name="alpha_r"/>
      <variable units="per_millisecond" name="beta_r"/>
      <variable units="millivolt" public_interface="in" name="V"/>
      <variable units="millisecond" public_interface="in" name="time"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <ci>alpha_r</ci>
            <apply>
               <times/>
               <cn cellml:units="per_millisecond">0.000033</cn>
               <apply>
                  <exp/>
                  <apply>
                     <minus/>
                     <apply>
                        <divide/>
                        <ci>V</ci>
                        <cn cellml:units="millivolt">17</cn>
                     </apply>
                  </apply>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>beta_r</ci>
            <apply>
               <divide/>
               <cn cellml:units="per_millisecond">0.033</cn>
               <apply>
                  <plus/>
                  <apply>
                     <exp/>
                     <apply>
                        <divide/>
                        <apply>
                           <minus/>
                           <apply>
                              <plus/>
                              <ci>V</ci>
                              <cn cellml:units="millivolt">30</cn>
                           </apply>
                        </apply>
                        <cn cellml:units="millivolt">8</cn>
                     </apply>
                  </apply>
                  <cn cellml:units="dimensionless">1</cn>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <apply>
               <diff/>
               <bvar>
                  <ci>time</ci>
               </bvar>
               <ci>r</ci>
            </apply>
            <apply>
               <minus/>
               <apply>
                  <times/>
                  <ci>alpha_r</ci>
                  <apply>
                     <minus/>
                     <cn cellml:units="dimensionless">1</cn>
                     <ci>r</ci>
                  </apply>
               </apply>
               <apply>
                  <times/>
                  <ci>beta_r</ci>
                  <ci>r</ci>
               </apply>
            </apply>
         </apply>
      </math>
   </component>
   <component name="time_independent_outward_current">
      <variable units="microA_per_cm2" public_interface="out" name="i_K1"/>
      <variable units="millivolt" name="E_K1" initial_value="-30"/>
      <variable units="millisecond" public_interface="in" name="time"/>
      <variable units="millivolt" public_interface="in" name="V"/>
      <variable units="microA_per_cm2" public_interface="in" name="I_K2"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <ci>i_K1</ci>
            <apply>
               <plus/>
               <apply>
                  <divide/>
                  <ci>I_K2</ci>
                  <cn cellml:units="dimensionless">2.8</cn>
               </apply>
               <apply>
                  <divide/>
                  <apply>
                     <times/>
                     <cn cellml:units="dimensionless">0.2</cn>
                     <apply>
                        <minus/>
                        <ci>V</ci>
                        <ci>E_K1</ci>
                     </apply>
                  </apply>
                  <apply>
                     <minus/>
                     <cn cellml:units="dimensionless">1</cn>
                     <apply>
                        <exp/>
                        <apply>
                           <divide/>
                           <apply>
                              <minus/>
                              <apply>
                                 <minus/>
                                 <ci>V</ci>
                                 <ci>E_K1</ci>
                              </apply>
                           </apply>
                           <cn cellml:units="millivolt">25</cn>
                        </apply>
                     </apply>
                  </apply>
               </apply>
            </apply>
         </apply>
      </math>
   </component>
   <component name="sodium_background_current">
      <variable units="microA_per_cm2" public_interface="out" name="i_Na_b"/>
      <variable units="milliS_per_cm2" name="g_Nab" initial_value="0.105"/>
      <variable units="millisecond" public_interface="in" name="time"/>
      <variable units="millivolt" public_interface="in" name="V"/>
      <variable units="millivolt" public_interface="in" name="E_Na"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <ci>i_Na_b</ci>
            <apply>
               <times/>
               <ci>g_Nab</ci>
               <apply>
                  <minus/>
                  <ci>V</ci>
                  <ci>E_Na</ci>
               </apply>
            </apply>
         </apply>
      </math>
   </component>
   <component name="chloride_background_current">
      <variable units="microA_per_cm2" public_interface="out" name="i_Cl_b"/>
      <variable units="milliS_per_cm2" name="g_Clb" initial_value="0.01"/>
      <variable units="millisecond" public_interface="in" name="time"/>
      <variable units="millivolt" public_interface="in" name="V"/>
      <variable units="millivolt" public_interface="in" name="E_Cl"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <ci>i_Cl_b</ci>
            <apply>
               <times/>
               <ci>g_Clb</ci>
               <apply>
                  <minus/>
                  <ci>V</ci>
                  <ci>E_Cl</ci>
               </apply>
            </apply>
         </apply>
      </math>
   </component>
   <group>
      <relationship_ref relationship="containment"/>
      <component_ref component="membrane">
         <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="secondary_inward_current">
            <component_ref component="secondary_inward_current_d_gate"/>
            <component_ref component="secondary_inward_current_f_gate"/>
            <component_ref component="secondary_inward_current_d1_gate"/>
         </component_ref>
         <component_ref component="pacemaker_potassium_current">
            <component_ref component="pacemaker_potassium_current_s_gate"/>
         </component_ref>
         <component_ref component="plateau_potassium_current1">
            <component_ref component="plateau_potassium_current1_x1_gate"/>
         </component_ref>
         <component_ref component="plateau_potassium_current2">
            <component_ref component="plateau_potassium_current2_x2_gate"/>
         </component_ref>
         <component_ref component="transient_chloride_current">
            <component_ref component="transient_chloride_current_q_gate"/>
            <component_ref component="transient_chloride_current_r_gate"/>
         </component_ref>
         <component_ref component="time_independent_outward_current"/>
         <component_ref component="sodium_background_current"/>
         <component_ref component="chloride_background_current"/>
      </component_ref>
   </group>
   <group>
      <relationship_ref relationship="encapsulation"/>
      <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="secondary_inward_current">
         <component_ref component="secondary_inward_current_d_gate"/>
         <component_ref component="secondary_inward_current_f_gate"/>
         <component_ref component="secondary_inward_current_d1_gate"/>
      </component_ref>
      <component_ref component="pacemaker_potassium_current">
         <component_ref component="pacemaker_potassium_current_s_gate"/>
      </component_ref>
      <component_ref component="transient_chloride_current">
         <component_ref component="transient_chloride_current_q_gate"/>
         <component_ref component="transient_chloride_current_r_gate"/>
      </component_ref>
      <component_ref component="plateau_potassium_current1">
         <component_ref component="plateau_potassium_current1_x1_gate"/>
      </component_ref>
      <component_ref component="plateau_potassium_current2">
         <component_ref component="plateau_potassium_current2_x2_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="fast_sodium_current"/>
      <map_variables variable_2="time" variable_1="time"/>
   </connection>
   <connection>
      <map_components component_2="environment" component_1="secondary_inward_current"/>
      <map_variables variable_2="time" variable_1="time"/>
   </connection>
   <connection>
      <map_components component_2="environment" component_1="pacemaker_potassium_current"/>
      <map_variables variable_2="time" variable_1="time"/>
   </connection>
   <connection>
      <map_components component_2="environment" component_1="plateau_potassium_current1"/>
      <map_variables variable_2="time" variable_1="time"/>
   </connection>
   <connection>
      <map_components component_2="environment" component_1="plateau_potassium_current2"/>
      <map_variables variable_2="time" variable_1="time"/>
   </connection>
   <connection>
      <map_components component_2="environment" component_1="transient_chloride_current"/>
      <map_variables variable_2="time" variable_1="time"/>
   </connection>
   <connection>
      <map_components component_2="environment" component_1="time_independent_outward_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="chloride_background_current"/>
      <map_variables variable_2="time" variable_1="time"/>
   </connection>
   <connection>
      <map_components component_2="fast_sodium_current" component_1="membrane"/>
      <map_variables variable_2="V" variable_1="V"/>
      <map_variables variable_2="i_Na" variable_1="i_Na"/>
   </connection>
   <connection>
      <map_components component_2="membrane" component_1="secondary_inward_current"/>
      <map_variables variable_2="V" variable_1="V"/>
      <map_variables variable_2="i_si" variable_1="i_si"/>
   </connection>
   <connection>
      <map_components component_2="membrane" component_1="pacemaker_potassium_current"/>
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