Rendering of the source text

<?xml version='1.0' encoding='utf-8'?>
<!-- FILE : ebihara_johnson_model_1980.xml

CREATED : 17th December 2001

LAST MODIFIED : 9th April 2003

AUTHOR : Catherine Lloyd
         Department of Engineering Science
         The University of Auckland
         
MODEL STATUS : This model conforms to the CellML 1.0 Specification released on
10th August 2001, and the 16/1/2002 CellML Metadata 1.0 Specification.

DESCRIPTION : This file contains a CellML description of the fast sodium current
in cardiac muscle, based on the Ebihara-johnson model, 1980. 

CHANGES:  
  04/01/2002 - CML - Added the components of the Beeler-Reuter Model.
  21/01/2002 - AAC - Updated metadata to conform with the 16/1/02 CellML 
                     Metadata 1.0 Specification.
  25/02/2002 - CML - Corrected several equations.
  28/02/2002 - CML - Corrected the membrane voltage differential equation.
  19/07/2002 - CML - Added more metadata.                   
  09/04/2003 - AAC - Added publication date information.  
--><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="ebihara_johnson_1980_version02" name="ebihara_johnson_1980_version02">

<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
  <articleinfo>
  <title>The Ebihara-Johnson Sodium Current Model (1980)</title>
  <author>
    <firstname>Catherine</firstname>
          <surname>Lloyd</surname>

    <affiliation>
      <shortaffil>Bioengineering Institute, University of Auckland</shortaffil>
    </affiliation>
  </author>
</articleinfo>
  <section id="sec_status">
    <title>Model Status</title>
    <para>

            This is the original unchecked version of the model imported from the previous
            CellML model repository, 24-Jan-2006.
          </para>
  </section>
  <sect1 id="sec_structure">
<title>Model Structure</title>

<para>
In 1980, Lisa Ebihara and Edward A. Johnson published the first electrophysiological model to specifically target a single ion channel and attempt to quantify its parameters.  They used the <ulink url="${HTML_EXMPL_HHSA_INTRO}">Hodgkin-Huxley formulation</ulink> to revise the parameters of the fast sodium current in cardiac muscle.  This model exhibits a faster sodium current than the <ulink url="${HTML_EXMPL_BR_MODEL}">Beeler-Reuter model</ulink>, and when the two models are coupled, the Ebihara-Johnson can be used as a direct replacement of the sodium kinetics of the Beeler-Reuter. 

</para>

<para>
<informalfigure float="0" id="fig_reaction_diagram">
<mediaobject>
  <imageobject>
    <objectinfo>
      <title>model diagram</title>
    </objectinfo>
    <imagedata fileref="ebihara_1980.png"/>
  </imageobject>
</mediaobject>
<caption>Schematic diagram of the Ebihara and Johnson model.</caption>
</informalfigure>
</para>

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

<para>
<ulink url="http://www.biophysj.org/cgi/content/abstract/32/2/779">Fast Sodium Current In Cardiac Muscle</ulink>, Lisa Ebihara and Edward A. Johnson, 1980, <ulink url="http://www.biophysj.org/">
            <emphasis>Biophys. J.</emphasis>
          </ulink> 32, 779-790.  <ulink url="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&amp;db=PubMed&amp;list_uids=7260301&amp;dopt=Abstract">PubMed ID: 7260301</ulink>

</para>

<para>
The raw CellML description of the Ebihara-Johnson model can be downloaded in various formats as described in <xref linkend="sec_download_this_model"/>.  For an example of a more complete documentation for an electrophysiological model, see <ulink url="${HTML_EXMPL_HHSA_INTRO}">The Hodgkin-Huxley Squid Axon Model, 1952</ulink>. 
</para>
</sect1>
</article>
</documentation>
    
  
  <!--
    Below, we define some additional units for association with variables and
    constants within the model. The identifiers are fairly self-explanatory.
  -->
  <units name="ms">
    <unit units="second" prefix="milli"/>
  </units>
  
  <units name="per_ms">
    <unit units="second" prefix="milli" exponent="-1"/>
  </units>

  <units name="mV">
    <unit units="volt" prefix="milli"/>
  </units>

  <units name="per_mV">
    <unit units="volt" prefix="milli" exponent="-1"/>
  </units>
  
  <units name="per_mV_ms">
    <unit units="mV" exponent="-1"/>
    <unit units="ms" exponent="-1"/>
  </units>
  
  <units name="mS_per_mm2">
    <unit units="siemens" prefix="milli"/>
    <unit units="metre" prefix="milli" exponent="-2"/>
  </units>

  <units name="uF_per_mm2">
    <unit units="farad" prefix="micro"/>
    <unit units="metre" prefix="milli" exponent="-2"/>
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  <units name="uA_per_mm2">
    <unit units="ampere" prefix="micro"/>
    <unit units="metre" prefix="milli" exponent="-2"/>
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  <units name="concentration_units">
    <unit units="mole" prefix="nano"/>
    <unit units="metre" prefix="milli" exponent="-3"/>
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  <units name="per_concentration_units">
    <unit units="concentration_units" exponent="-1"/>
  </units>
   
  <!--
    The "environment" component is used to declare variables that are used by
    all or most of the other components, in this case just "time".
  -->
  <component cmeta:id="environment" name="environment">
    <variable units="ms" public_interface="out" name="time"/>
  </component>
  
  <component cmeta:id="membrane" name="membrane">
    
    <variable units="mV" public_interface="out" name="V" initial_value="-87.0"/>
    
    <variable units="uF_per_mm2" name="C" initial_value="0.013"/>
    
    <variable units="ms" public_interface="in" name="time"/>
    <variable units="uA_per_mm2" public_interface="in" name="i_Na"/>
    <variable units="uA_per_mm2" public_interface="in" name="i_s"/>
    <variable units="uA_per_mm2" public_interface="in" name="i_x1"/>
    <variable units="uA_per_mm2" public_interface="in" name="i_K1"/>
    <variable units="uA_per_mm2" name="Istim"/>
    
    
    <math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="membrane_voltage_diff_eq">
      <apply id="membrane_voltage_diff_eq">
        <eq/>
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          <diff/>
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            <ci> time </ci>
          </bvar>
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            <minus/>
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              <ci> i_K1 </ci>
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    <variable units="uA_per_mm2" public_interface="out" name="IStimC"/>
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    </math>
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    <variable units="uA_per_mm2" public_interface="out" name="i_Na"/>
    <variable units="mS_per_mm2" name="g_Na" initial_value="23.0e-2"/>
    <variable units="mV" name="E_Na" initial_value="29.0"/>
    <variable units="dimensionless" private_interface="in" name="m"/>
    <variable units="dimensionless" private_interface="in" name="h"/>
    <variable units="ms" public_interface="in" private_interface="out" name="time"/>
    <variable units="mV" public_interface="in" private_interface="out" name="V"/>

    
    <math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="i_Na_calculation_eq">
      <apply id="i_Na_calculation">
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        <ci> i_Na </ci>
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          <times/>
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        </apply>
      </apply>
    </math>
  </component> 
  
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    <variable units="per_ms" name="beta_m"/>
    <variable units="mV" public_interface="in" name="V"/>
    <variable units="ms" public_interface="in" name="time"/>
    
    
    <math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="alpha_m_calculation_eq">
      <apply id="alpha_m_calculation">
        <eq/>
        <ci> alpha_m </ci>
        <apply>
          <divide/>
          <apply>
            <times/>
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            <apply>
              <plus/>
              <cn cellml:units="mV"> 47.13 </cn>
              <ci> V </ci>
            </apply>
          </apply>
          <apply>
            <minus/>
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            <apply>
              <exp/>
              <apply>
                <minus/>
                <apply>
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                </apply>
                <cn cellml:units="mV"> 47.13 </cn>
              </apply>
            </apply>
          </apply>
        </apply>
      </apply>
    </math>
    
    
    <math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="beta_m_calculation_eq">
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          <apply>
            <exp/>
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    </math>
    
    
    <math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="dm_dt_eq">
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          <diff/>
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            <ci> time </ci>
          </bvar>
          <ci> m </ci>
        </apply>
        <apply>
          <minus/>
          <apply>
            <times/>
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            <apply>
              <minus/>
              <cn cellml:units="per_mV"> 1.0 </cn>
              <ci> m </ci>
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          <apply>
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            <ci> beta_m </ci>
            <ci> m </ci>
          </apply>
        </apply>
      </apply>
    </math>
  </component>
    
  <component cmeta:id="fast_sodium_current_h_gate" name="fast_sodium_current_h_gate">
    

    <variable units="dimensionless" public_interface="out" name="h" initial_value="0.18"/>
    <variable units="per_ms" name="alpha_h"/>
    <variable units="per_ms" name="beta_h"/>
    <variable units="mV" public_interface="in" name="V"/>
    <variable units="ms" public_interface="in" name="time"/>
    
    
    <math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="alpha_h_calculation_eq">
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            <apply>
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              <apply>
                <exp/>
                <apply>
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                  <cn cellml:units="mV"> 6.8 </cn>
                </apply>
              </apply>
            </apply>
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              <lt/>
              <ci> V </ci> 
              <cn cellml:units="mV"> -40.0 </cn>
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          <otherwise>
            <cn cellml:units="per_ms"> 0.0 </cn>
          </otherwise>
        </piecewise>
      </apply>
    </math>
      
    
    <math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="beta_h_calculation_eq">
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        <ci> beta_h </ci>
        <piecewise>
          <piece>
            <apply>
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                <cn cellml:units="per_ms"> 3.56 </cn>
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    <math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="dh_dt_eq">
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  </component>
  
  <component cmeta:id="slow_inward_current" name="slow_inward_current">
    

    <variable units="uA_per_mm2" public_interface="out" name="i_s"/>
 
    <variable units="mS_per_mm2" name="g_s" initial_value="9.0e-4"/>
    <variable units="mV" name="E_s"/>
    <variable units="concentration_units" name="Cai" initial_value="0.000000177"/>
    
    <variable units="ms" public_interface="in" private_interface="out" name="time"/>
    <variable units="mV" public_interface="in" private_interface="out" name="V"/>
    
    <variable units="dimensionless" private_interface="in" name="d"/>
    <variable units="dimensionless" private_interface="in" name="f"/>
    
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          <ci> f </ci>
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  <component cmeta:id="slow_inward_current_d_gate" name="slow_inward_current_d_gate">
    

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    <variable units="per_ms" name="alpha_d"/>
    <variable units="per_ms" name="beta_d"/>
    
    <variable units="mV" public_interface="in" name="V"/>
    <variable units="ms" public_interface="in" name="time"/>

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          <apply>
            <times/>
            <ci> beta_f </ci>
            <ci> f </ci>
          </apply>
        </apply>
      </apply>
    </math>
  </component>
    
  
  <component cmeta:id="time_dependent_outward_current" name="time_dependent_outward_current">
    

    <variable units="uA_per_mm2" public_interface="out" name="i_x1"/>
    
    <variable units="per_ms" name="alpha_x1"/>
    <variable units="per_ms" name="beta_x1"/>
    
    <variable units="ms" public_interface="in" private_interface="out" name="time"/>
    <variable units="mV" 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 id="i_x1_calculation">
        <eq/>
        <ci> i_x1 </ci>
        <apply>
          <times/>
          <ci> x1 </ci>
          <cn cellml:units="dimensionless"> 8.0e-3 </cn>
          <apply>
            <divide/>
            <apply>
              <minus/>
              <apply>
                <exp/>
                <apply>
                  <times/>
                  <cn cellml:units="per_mV"> 0.04 </cn>
                  <apply>
                    <plus/>
                    <ci> V </ci>
                    <cn cellml:units="mV"> 77.0 </cn>
                  </apply>
                </apply>
              </apply>
              <cn cellml:units="dimensionless"> 1.0 </cn>
            </apply>
            <apply>
              <exp/>
              <apply>
                <times/>
                <cn cellml:units="per_mV"> 0.04 </cn>
                <apply>
                  <plus/> 
                  <ci> V </ci>
                  <cn cellml:units="mV"> 35.0 </cn>
                </apply>
              </apply>
            </apply>
          </apply>
        </apply>
      </apply>
    </math>
  </component>
  
  <component cmeta:id="time_dependent_outward_current_x1_gate" name="time_dependent_outward_current_x1_gate">
    

    <variable units="dimensionless" public_interface="out" name="x1"/>
    <variable units="per_ms" name="alpha_x1"/>
    <variable units="per_ms" name="beta_x1"/>
    <variable units="mV" public_interface="in" name="V"/>
    <variable units="ms" public_interface="in" name="time"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML">        
      <apply id="alpha_x1_calculation">
        <eq/>
        <ci> alpha_x1 </ci>
        <apply>
          <times/>
          <cn cellml:units="per_ms"> 0.0005 </cn>
          <apply>
            <divide/>
            <apply>
              <exp/>
              <apply>
                <divide/>
                <apply>
                  <plus/>
                  <ci> V </ci>
                  <cn cellml:units="mV"> 50.0 </cn>                      
                </apply>
                <cn cellml:units="mV"> 12.1 </cn>
              </apply>
            </apply>
            <apply>
              <plus/>
              <cn cellml:units="dimensionless"> 1.0 </cn>
              <apply>
                <exp/>
                <apply>
                  <divide/>
                  <apply>
                    <plus/>
                    <ci> V </ci>
                    <cn cellml:units="mV"> 50.0 </cn>
                  </apply>
                  <cn cellml:units="mV"> 17.5 </cn>
                </apply>
              </apply>
            </apply>
          </apply>
        </apply>
      </apply>
         
      <apply id="beta_x1_calculation">
        <eq/>
        <ci> beta_x1 </ci>
        <apply>
          <times/>
          <cn cellml:units="per_ms"> 0.0013 </cn>
          <apply>
            <divide/>
            <apply>
              <exp/>
              <apply>
                <minus/>
                <apply>
                  <divide/>
                  <apply>
                    <plus/>
                    <ci> V </ci>                                                
                    <cn cellml:units="mV"> 20.0 </cn>
                  </apply>
                  <cn cellml:units="mV"> 16.67 </cn>
                </apply>
              </apply>
            </apply>
            <apply>
              <plus/>
              <cn cellml:units="dimensionless"> 1.0 </cn>
              <apply>
                <exp/>
                <apply>
                  <minus/>
                  <apply>
                    <divide/>
                    <apply>
                      <plus/>
                      <ci> V </ci>
                      <cn cellml:units="mV"> 20.0 </cn>
                    </apply>
                    <cn cellml:units="mV"> 25.0 </cn>
                  </apply> 
                </apply>
              </apply>
            </apply>
          </apply>
        </apply>
      </apply>
      
      <apply id="dx1_dt">
        <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"> 1.0 </cn>
              <ci> x1 </ci>
            </apply>
          </apply>
          <apply>
            <times/>
            <ci> beta_x1 </ci>
            <ci> x1 </ci>
          </apply>
        </apply>
      </apply>
    </math>
  </component>
     
  
  <component cmeta:id="time_independent_outward_current" name="time_independent_outward_current">
    

    <variable units="uA_per_mm2" public_interface="out" name="i_K1"/>
    
    <variable units="ms" public_interface="in" name="time"/>
    <variable units="mV" public_interface="in" name="V"/>
        
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply id="i_K1_calculation">
        <eq/>
        <ci> i_K1 </ci>
        <apply>
          <times/>
          <cn cellml:units="dimensionless"> 0.0035 </cn>
          <apply>
            <plus/>
            <apply>
              <times/>
              <cn cellml:units="per_ms"> 4.0 </cn>
              <apply>
                <divide/>
                <apply>
                  <minus/>
                  <apply>
                    <exp/>
                    <apply>
                      <times/>
                      <cn cellml:units="per_mV"> 0.04 </cn>
                      <apply>
                        <plus/>
                        <ci> V </ci>
                        <cn cellml:units="mV"> 85.0 </cn>
                      </apply>
                    </apply>                   
                  </apply>
                  <cn cellml:units="dimensionless"> 1.0 </cn>
                </apply>
                <apply>
                  <plus/>
                  <apply>
                    <exp/>
                    <apply>
                      <times/>
                      <cn cellml:units="per_mV"> 0.08 </cn>
                      <apply>
                        <plus/>
                        <ci> V </ci>
                        <cn cellml:units="mV"> 53 </cn>
                      </apply>
                    </apply>
                  </apply>
                  <apply>
                    <exp/>
                    <apply>
                      <times/> 
                      <cn cellml:units="per_mV"> 0.04 </cn>
                      <apply>
                        <plus/>
                        <ci> V </ci>
                        <cn cellml:units="mV"> 53.0 </cn>
                      </apply>
                    </apply>          
                  </apply>
                </apply>
              </apply>
            </apply>
            <apply>
              <times/>
              <cn cellml:units="per_ms"> 0.2 </cn>
              <apply>
                <divide/>
                <apply>
                  <plus/>
                  <ci> V </ci>
                  <cn cellml:units="mV"> 23.0 </cn>
                </apply>
                <apply>
                  <minus/>
                  <cn cellml:units="dimensionless"> 1.0 </cn>
                  <apply>
                    <exp/>
                    <apply>
                      <times/>
                      <cn cellml:units="per_mV"> -0.04 </cn>
                      <apply>
                        <plus/>
                        <ci> V </ci>
                        <cn cellml:units="mV"> 23.0 </cn>
                      </apply>
                    </apply>
                  </apply>
                </apply>
              </apply>
            </apply>
          </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="slow_inward_current">
        <component_ref component="slow_inward_current_d_gate"/>
        <component_ref component="slow_inward_current_f_gate"/>
      </component_ref>
      <component_ref component="time_dependent_outward_current">
        <component_ref component="time_dependent_outward_current_x1_gate"/>
      </component_ref>
      <component_ref component="time_independent_outward_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="slow_inward_current">
      <component_ref component="slow_inward_current_d_gate"/>
      <component_ref component="slow_inward_current_f_gate"/>
    </component_ref>
    <component_ref component="time_dependent_outward_current">
      <component_ref component="time_dependent_outward_current_x1_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="slow_inward_current"/>
    <map_variables variable_2="time" variable_1="time"/>
  </connection>

  <connection>
    <map_components component_2="environment" component_1="time_dependent_outward_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="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="slow_inward_current" component_1="membrane"/>
    <map_variables variable_2="V" variable_1="V"/>
    <map_variables variable_2="i_s" variable_1="i_s"/>
  </connection>

  <connection>
    <map_components component_2="time_dependent_outward_current" component_1="membrane"/>
    <map_variables variable_2="V" variable_1="V"/>
    <map_variables variable_2="i_x1" variable_1="i_x1"/>
  </connection>
  
  <connection>
    <map_components component_2="time_independent_outward_current" component_1="membrane"/>
    <map_variables variable_2="V" variable_1="V"/>
    <map_variables variable_2="i_K1" variable_1="i_K1"/>
  </connection>
  
  <connection>
    <map_components component_2="fast_sodium_current_m_gate" component_1="fast_sodium_current"/>
    <map_variables variable_2="m" variable_1="m"/>
    <map_variables variable_2="time" variable_1="time"/>
    <map_variables variable_2="V" variable_1="V"/>
  </connection>

  <connection>
    <map_components component_2="fast_sodium_current_h_gate" component_1="fast_sodium_current"/>
    <map_variables variable_2="h" variable_1="h"/>
    <map_variables variable_2="time" variable_1="time"/>
    <map_variables variable_2="V" variable_1="V"/>
  </connection>
  
  <connection>
    <map_components component_2="time_dependent_outward_current_x1_gate" component_1="time_dependent_outward_current"/>
    <map_variables variable_2="x1" variable_1="x1"/>
    <map_variables variable_2="time" variable_1="time"/>
    <map_variables variable_2="V" variable_1="V"/>
  </connection>
  
  <connection>
    <map_components component_2="slow_inward_current_d_gate" component_1="slow_inward_current"/>
    <map_variables variable_2="d" variable_1="d"/>
    <map_variables variable_2="time" variable_1="time"/>
    <map_variables variable_2="V" variable_1="V"/>
  </connection>
  
  <connection>
    <map_components component_2="slow_inward_current_f_gate" component_1="slow_inward_current"/>
    <map_variables variable_2="f" variable_1="f"/>
    <map_variables variable_2="time" variable_1="time"/>
    <map_variables variable_2="V" variable_1="V"/>
  </connection>







<rdf:RDF>
  <rdf:Seq rdf:about="rdf:#citationAuthorsSeq">
    <rdf:li rdf:resource="rdf:#author1Vcard"/>
    <rdf:li rdf:resource="rdf:#author2Vcard"/>
  </rdf:Seq>
  <rdf:Description rdf:about="#membrane_voltage_diff_eq">
    <cmeta:comment rdf:resource="rdf:#01ce2bc3-4b1b-4cd8-8132-ea8fd74bec04"/>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#ee288d2a-834d-438d-8313-056b4becbacf">
    <rdf:value>
            Calculation of the fast sodium current.
          </rdf:value>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#5cc27f0d-03e6-429a-a6e7-50150cc3ade6">
    <rdf:value>
            In their 1980 paper, Ebihara and Johnson do not include all the 
            ionic fluxes across the membrane of the cardiac muscle cell, they 
            only describe the fast sodium current.  The Ebihara-Johnson model 
            can be coupled to the Beeler-Reuter model (1977) as a direct 
            replacement for the sodium current.  The other ionic currents were 
            very similar to those found using the Beeler-Reuter model. I have 
            included these equations from the Beeler-Reuter 1977 model in this 
            CellML description. 
          </rdf:value>
  </rdf:Description>
  <rdf:Description rdf:about="#beta_m_calculation_eq">
    <cmeta:comment rdf:resource="rdf:#eadb1115-8ade-4316-bdbd-febac44f269c"/>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#fb2e8466-2340-493d-8a08-0bd2cff3fc73">
    <rdf:value>
            The standard Beeler Reuter (1977) activation gate for the slow
            inward current.
          </rdf:value>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#1ac263c4-d516-4882-8c09-b73a88f548ce">
    <bqs:Pubmed_id>7260301</bqs:Pubmed_id>
    <bqs:JournalArticle rdf:resource="rdf:#4f33c5f6-83d3-4ce9-acb0-9ab1053087c9"/>
  </rdf:Description>
  <rdf:Description rdf:about="#slow_inward_current_d_gate">
    <cmeta:comment rdf:resource="rdf:#fb2e8466-2340-493d-8a08-0bd2cff3fc73"/>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#d3d82ce2-4c1a-4677-96dd-9c8156c31c4c">
    <dcterms:modified rdf:resource="rdf:#97c6b53f-6075-4322-9f74-ded798ea53d1"/>
    <rdf:value>
          Corrected the membrane voltage differential equation.
        </rdf:value>
    <cmeta:modifier rdf:resource="rdf:#31e76dd7-4d24-47f5-b195-91fba99deea0"/>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#6a4b539d-ac99-4f56-afd3-bac27c6552f1">
    <dcterms:modified rdf:resource="rdf:#abe4ceea-c7b8-4182-b46d-253956884630"/>
    <rdf:value>
          Corrected several equations.
        </rdf:value>
    <cmeta:modifier rdf:resource="rdf:#3261da5c-a39f-4b31-8bea-5bcfcc0a4a6f"/>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#fb27e1b0-f505-4b81-8c51-1468542ddae5">
    <dcterms:modified rdf:resource="rdf:#957a00b0-2398-4ae3-995a-a6d007429847"/>
    <rdf:value>
          Added the components of the Beeler-Reuter Model.
        </rdf:value>
    <cmeta:modifier rdf:resource="rdf:#8983930a-6651-463f-b4ae-a726a382ec54"/>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#030183f5-43aa-4f81-aa00-5a9058891496">
    <dcterms:W3CDTF>2003-07-22</dcterms:W3CDTF>
  </rdf:Description>
  <rdf:Description rdf:about="#slow_inward_current">
    <cmeta:comment rdf:resource="rdf:#a6c51603-7a67-4a8e-8b43-650cabc68bab"/>
  </rdf:Description>
  <rdf:Description rdf:about="#dm_dt_eq">
    <cmeta:comment rdf:resource="rdf:#576f3fda-98a7-477d-a519-d9c6984b2c37"/>
  </rdf:Description>
  <rdf:Description rdf:about="#alpha_h_calculation_eq">
    <cmeta:comment rdf:resource="rdf:#84728cc5-836c-4cb1-933a-1e59f62d488c"/>
  </rdf:Description>
  <rdf:Description rdf:about="#ebihara_johnson_1980_version02">
    <dc:title>
        The Ebihara-Johnson Model of the Fast Sodium Current in Cardiac Muscle,
        1980
      </dc:title>
    <cmeta:bio_entity>Cardiac Myocyte</cmeta:bio_entity>
    <cmeta:comment rdf:resource="rdf:#b08fb71e-7d93-43a9-957e-dfcb7212674b"/>
    <bqs:reference rdf:resource="rdf:#1ac263c4-d516-4882-8c09-b73a88f548ce"/>
<bqs:reference rdf:parseType="Resource">
  <dc:subject rdf:parseType="Resource">
    <bqs:subject_type>keyword</bqs:subject_type>
    <rdf:value>
      <rdf:Bag>
        <rdf:li>cardiac</rdf:li>
        <rdf:li>electrophysiology</rdf:li>
        <rdf:li>channel kinetics</rdf:li>
        <rdf:li>fast sodium current</rdf:li>
      </rdf:Bag>
    </rdf:value>
  </dc:subject>
</bqs:reference>
    <cmeta:species>Mammalia</cmeta:species>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#590f631b-df75-4e74-aed8-ed3781d3d805">
    <dcterms:W3CDTF>2003-04-09</dcterms:W3CDTF>
  </rdf:Description>
  <rdf:Description rdf:about="#fast_sodium_current">
    <cmeta:comment rdf:resource="rdf:#db57f440-4dde-4241-a41b-72f02b7daf21"/>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#3261da5c-a39f-4b31-8bea-5bcfcc0a4a6f">
    <vCard:N rdf:resource="rdf:#c905db44-62db-44e3-b99b-afc71f0d5a65"/>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#576f3fda-98a7-477d-a519-d9c6984b2c37">
    <rdf:value>
            The gating kinetics of the m gate.
          </rdf:value>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#eadb1115-8ade-4316-bdbd-febac44f269c">
    <rdf:value>
            The closing rate for the m gate.
          </rdf:value>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#3d6ff7fe-7d60-463b-8474-f1182b075ec0">
    <vCard:ORG rdf:resource="rdf:#64aca2e0-9474-4df4-ab17-5d5d84b20622"/>
    <vCard:EMAIL rdf:resource="rdf:#f6de55fb-72b1-43fe-98ff-cff13ee5a3ec"/>
    <vCard:N rdf:resource="rdf:#0976283e-c5b6-4c35-aef0-c65178e85297"/>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#c905db44-62db-44e3-b99b-afc71f0d5a65">
    <vCard:Given>Catherine</vCard:Given>
    <vCard:Family>Lloyd</vCard:Family>
    <vCard:Other>May</vCard:Other>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#999fe272-8af9-43bc-937e-35b8703cd376">
    <dcterms:W3CDTF>2002-07-19</dcterms:W3CDTF>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#4fc75d49-fdec-4c58-970a-2f4c306512b6">
    <vCard:N rdf:resource="rdf:#e4e609cb-a650-429c-be6e-84c34512c499"/>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#1775ef0f-301e-4bf4-8865-2941d72b7ee9">
    <rdf:value>
            This is a dummy equation that we simply use to make grabbing the
            value in CMISS much easier.
          </rdf:value>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#abe4ceea-c7b8-4182-b46d-253956884630">
    <dcterms:W3CDTF>2002-02-25</dcterms:W3CDTF>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#f6de55fb-72b1-43fe-98ff-cff13ee5a3ec">
    <rdf:type rdf:resource="http://imc.org/vCard/3.0#internet"/>
    <rdf:value>c.lloyd@auckland.ac.nz</rdf:value>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#6f854acd-c72d-431b-9b98-6982e23c5233">
    <dcterms:W3CDTF>1980-01-01</dcterms:W3CDTF>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#97c6b53f-6075-4322-9f74-ded798ea53d1">
    <rdf:type rdf:resource="http://purl.org/dc/terms/W3CDTF"/>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#9b82fa5c-edb2-49d8-8237-a2438bdf0a38">
    <rdf:type rdf:resource="http://purl.org/dc/terms/W3CDTF"/>
  </rdf:Description>
  <rdf:Description rdf:about="#time_independent_outward_current">
    <cmeta:comment rdf:resource="rdf:#c7b9f342-a9db-4929-9f02-69c6900f0e87"/>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#ee7d7e8a-2227-40e3-8655-a9abc47c4c20">
    <vCard:N rdf:resource="rdf:#18ee33d0-2964-4744-9f1f-21a9762aa174"/>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#0976283e-c5b6-4c35-aef0-c65178e85297">
    <vCard:Given>Catherine</vCard:Given>
    <vCard:Family>Lloyd</vCard:Family>
    <vCard:Other>May</vCard:Other>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#7cd6a17f-b952-4d6a-8caa-e3296cf19f34">
    <vCard:N rdf:resource="rdf:#92222b87-8be0-463b-9d5d-1ca4192bde54"/>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#e4e609cb-a650-429c-be6e-84c34512c499">
    <vCard:Given>David</vCard:Given>
    <vCard:Family>Nickerson</vCard:Family>
    <vCard:Other>P</vCard:Other>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#c2dd38ca-3802-429a-a960-89f055f705c7">
    <vCard:FN>Catherine Lloyd</vCard:FN>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#3bf76602-b671-47f0-9947-fec3bed0f386">
    <rdf:type rdf:resource="http://www.w3.org/2001/vcard-rdf/3.0#N"/>
    <vCard:Given>Autumn</vCard:Given>
    <vCard:Family>Cuellar</vCard:Family>
    <vCard:Other>A.</vCard:Other>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#db57f440-4dde-4241-a41b-72f02b7daf21">
    <rdf:value>
            In the calculation of the fast sodium current there is no variable 
            corresponding to the j gate used in the Beeler-Reuter model because 
            the experimental results showed no need to include a second 
            deactivation variable.
          </rdf:value>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#8983930a-6651-463f-b4ae-a726a382ec54">
    <rdf:type rdf:resource="http://www.w3.org/2001/vcard-rdf/3.0#N"/>
    <vCard:Given>Catherine</vCard:Given>
    <vCard:Family>Lloyd</vCard:Family>
    <vCard:Other>May</vCard:Other>
  </rdf:Description>
  <rdf:Description rdf:about="#time_dependent_outward_current">
    <cmeta:comment rdf:resource="rdf:#60cef239-b78f-4f1a-bffe-436e77c9c5c0"/>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#7cdc05ad-9b3c-4f5a-96c1-ed3e5043f5e0">
    <rdf:value>
            The voltage-dependent inactivation gate of the fast sodium channel -
            the h gate.
          </rdf:value>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#author2VcardN">
    <vCard:Given>E</vCard:Given>
    <vCard:Family>Johnson</vCard:Family>
    <vCard:Other>A</vCard:Other>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#957a00b0-2398-4ae3-995a-a6d007429847">
    <rdf:type rdf:resource="http://purl.org/dc/terms/W3CDTF"/>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#aa7cb718-9eb0-4a51-a313-e36082d71045">
    <dcterms:modified rdf:resource="rdf:#9b82fa5c-edb2-49d8-8237-a2438bdf0a38"/>
    <rdf:value>
          Updated metadata to conform to the 16/1/02 CellML Metadata 1.0 
          Specification.
        </rdf:value>
    <cmeta:modifier rdf:resource="rdf:#3bf76602-b671-47f0-9947-fec3bed0f386"/>
  </rdf:Description>
  <rdf:Description rdf:about="#beta_h_calculation_eq">
    <cmeta:comment rdf:resource="rdf:#5e910089-77bc-441b-b41e-33be9a0d4f03"/>
  </rdf:Description>
  <rdf:Description rdf:about="#dh_dt_eq">
    <cmeta:comment rdf:resource="rdf:#810d2e14-ca70-47f5-aea8-cc6bf21c9546"/>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#4f33c5f6-83d3-4ce9-acb0-9ab1053087c9">
    <dc:creator rdf:resource="rdf:#citationAuthorsSeq"/>
    <dc:title>Fast sodium current in cardiac muscle: A quantitative description</dc:title>
    <bqs:volume>32</bqs:volume>
    <bqs:first_page>779</bqs:first_page>
    <bqs:Journal rdf:resource="rdf:#cd6555f2-87e2-43d7-9aac-aae4892f5712"/>
    <dcterms:issued rdf:resource="rdf:#6f854acd-c72d-431b-9b98-6982e23c5233"/>
    <bqs:last_page>790</bqs:last_page>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#bb615aad-5fac-47b3-b3be-dc17081713ca">
    <dcterms:modified rdf:resource="rdf:#030183f5-43aa-4f81-aa00-5a9058891496"/>
    <rdf:value>
          Modifying units and adding a stimulus current.
        </rdf:value>
    <cmeta:modifier rdf:resource="rdf:#4fc75d49-fdec-4c58-970a-2f4c306512b6"/>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#a6c51603-7a67-4a8e-8b43-650cabc68bab">
    <rdf:value>
            The standard Beeler Reuter (1977) slow inward (calcium) current
            formulation.
          </rdf:value>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#31e76dd7-4d24-47f5-b195-91fba99deea0">
    <rdf:type rdf:resource="http://www.w3.org/2001/vcard-rdf/3.0#N"/>
    <vCard:Given>Catherine</vCard:Given>
    <vCard:Family>Lloyd</vCard:Family>
    <vCard:Other>May</vCard:Other>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#b08fb71e-7d93-43a9-957e-dfcb7212674b">
    <dc:creator rdf:resource="rdf:#c2dd38ca-3802-429a-a960-89f055f705c7"/>
    <rdf:value>This is the CellML description of Ebihara and Johnson's mathematical model of the fast sodium current in cardiac muscle (1980). It describes the ionic current with Hodgkin-Huxley formalism. This model was the first to specifically target a single channel and attempt to quantify its parameters.</rdf:value>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#84728cc5-836c-4cb1-933a-1e59f62d488c">
    <rdf:value>
            The opening rate of the h gate.
          </rdf:value>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#be03ca7a-50b4-414b-b329-3123c3b93114">
    <rdf:value>
            The standard Beeler Reuter (1977) inactivation gate for the slow
            inward current.
          </rdf:value>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#author2Vcard">
    <rdf:type rdf:resource="http://www.cellml.org/bqs/1.0#Person"/>
    <vCard:N rdf:resource="rdf:#author2VcardN"/>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#810d2e14-ca70-47f5-aea8-cc6bf21c9546">
    <rdf:value>
            The kinetics of the h gate.
          </rdf:value>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#c7b9f342-a9db-4929-9f02-69c6900f0e87">
    <rdf:value>
            The standard Beeler Reuter (1977) time-independent outward
            (potassium) current.
          </rdf:value>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#cd6555f2-87e2-43d7-9aac-aae4892f5712">
    <dc:title>Biophysical Journal</dc:title>
  </rdf:Description>
  <rdf:Description rdf:about="">
    <dc:publisher>
        The University of Auckland, Bioengineering Research Group
      </dc:publisher>
    <cmeta:modification rdf:resource="rdf:#5402da3f-dcfc-469e-ba89-7b436382f5d0"/>
    <cmeta:modification rdf:resource="rdf:#6a4b539d-ac99-4f56-afd3-bac27c6552f1"/>
    <cmeta:modification rdf:resource="rdf:#aa7cb718-9eb0-4a51-a313-e36082d71045"/>
    <cmeta:modification rdf:resource="rdf:#b0705a4b-f5de-4b90-a39b-b48af2595019"/>
    <cmeta:modification rdf:resource="rdf:#bb615aad-5fac-47b3-b3be-dc17081713ca"/>
    <cmeta:modification rdf:resource="rdf:#d3d82ce2-4c1a-4677-96dd-9c8156c31c4c"/>
    <cmeta:modification rdf:resource="rdf:#fb27e1b0-f505-4b81-8c51-1468542ddae5"/>
    <dcterms:created rdf:resource="rdf:#97bb2ebc-f171-45c7-8986-a4ca1332b713"/>
    <dc:creator rdf:resource="rdf:#3d6ff7fe-7d60-463b-8474-f1182b075ec0"/>
  </rdf:Description>
  <rdf:Description rdf:about="#slow_inward_current_f_gate">
    <cmeta:comment rdf:resource="rdf:#be03ca7a-50b4-414b-b329-3123c3b93114"/>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#92222b87-8be0-463b-9d5d-1ca4192bde54">
    <vCard:Given>Catherine</vCard:Given>
    <vCard:Family>Lloyd</vCard:Family>
    <vCard:Other>May</vCard:Other>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#18ee33d0-2964-4744-9f1f-21a9762aa174">
    <vCard:Given>Autumn</vCard:Given>
    <vCard:Family>Cuellar</vCard:Family>
    <vCard:Other>A</vCard:Other>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#5402da3f-dcfc-469e-ba89-7b436382f5d0">
    <dcterms:modified rdf:resource="rdf:#999fe272-8af9-43bc-937e-35b8703cd376"/>
    <rdf:value>
          Added more metadata.
        </rdf:value>
    <cmeta:modifier rdf:resource="rdf:#7cd6a17f-b952-4d6a-8caa-e3296cf19f34"/>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#ef13ffa5-1608-4b48-9da5-dba5f8875869">
    <rdf:value>
            The voltage-dependent activation gate for the fast sodium channel -
            the m gate.
          </rdf:value>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#ed6daded-7ab4-4c3a-aa18-37b92c670be2">
    <rdf:value>
            The opening rate for the m gate. The equation for alpha-m was
            incorrectly stated in the original 1980 paper, but it appears as
            shown below in Spach and Heidlage (1993), who cite a later paper by
            Johnson as their source (Johnson, 1983).
          </rdf:value>
  </rdf:Description>
  <rdf:Description rdf:about="#fast_sodium_current_h_gate">
    <cmeta:comment rdf:resource="rdf:#7cdc05ad-9b3c-4f5a-96c1-ed3e5043f5e0"/>
  </rdf:Description>
  <rdf:Description rdf:about="#IStim_for_cmiss_eq">
    <cmeta:comment rdf:resource="rdf:#1775ef0f-301e-4bf4-8865-2941d72b7ee9"/>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#author1Vcard">
    <rdf:type rdf:resource="http://www.cellml.org/bqs/1.0#Person"/>
    <vCard:N rdf:resource="rdf:#author1VcardN"/>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#4f5fc73d-6169-46d0-9b6e-3d8b2f870dcf">
    <rdf:value>
            The standard Beeler Reuter (1977) gating variable for the
            time-dependent outward potassium current.
          </rdf:value>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#author1VcardN">
    <vCard:Given>L</vCard:Given>
    <vCard:Family>Ebihara</vCard:Family>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#5e910089-77bc-441b-b41e-33be9a0d4f03">
    <rdf:value>
            The closing rate of the h gate.
          </rdf:value>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#97bb2ebc-f171-45c7-8986-a4ca1332b713">
    <dcterms:W3CDTF>2001-12-17</dcterms:W3CDTF>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#01ce2bc3-4b1b-4cd8-8132-ea8fd74bec04">
    <rdf:value>
            The main differential equation for the model specifying the rate of
            change of the transmembrane potential as the sum of the ionic
            currents and an applied stimulus current.
          </rdf:value>
  </rdf:Description>
  <rdf:Description rdf:about="#alpha_m_calculation_eq">
    <cmeta:comment rdf:resource="rdf:#ed6daded-7ab4-4c3a-aa18-37b92c670be2"/>
  </rdf:Description>
  <rdf:Description rdf:about="#membrane">
    <cmeta:comment rdf:resource="rdf:#5cc27f0d-03e6-429a-a6e7-50150cc3ade6"/>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#60cef239-b78f-4f1a-bffe-436e77c9c5c0">
    <rdf:value>
            The standard Beeler Reuter (1977) time-dependent outward (potassium)
            current.
          </rdf:value>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#b0705a4b-f5de-4b90-a39b-b48af2595019">
    <dcterms:modified rdf:resource="rdf:#590f631b-df75-4e74-aed8-ed3781d3d805"/>
    <rdf:value>
          Added publication date information.
        </rdf:value>
    <cmeta:modifier rdf:resource="rdf:#ee7d7e8a-2227-40e3-8655-a9abc47c4c20"/>
  </rdf:Description>
  <rdf:Description rdf:about="#i_Na_calculation_eq">
    <cmeta:comment rdf:resource="rdf:#ee288d2a-834d-438d-8313-056b4becbacf"/>
  </rdf:Description>
  <rdf:Description rdf:about="#fast_sodium_current_m_gate">
    <cmeta:comment rdf:resource="rdf:#ef13ffa5-1608-4b48-9da5-dba5f8875869"/>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#64aca2e0-9474-4df4-ab17-5d5d84b20622">
    <vCard:Orgname>The University of Auckland</vCard:Orgname>
    <vCard:Orgunit>The Bioengineering Research Group</vCard:Orgunit>
  </rdf:Description>
  <rdf:Description rdf:about="#time_dependent_outward_current_x1_gate">
    <cmeta:comment rdf:resource="rdf:#4f5fc73d-6169-46d0-9b6e-3d8b2f870dcf"/>
  </rdf:Description>
</rdf:RDF>
</model>