Location: Fridlyand, Tamarina, Philipson, 2003 @ c0bc0382dc05 / fridlyand_tamarina_philipson_2003.cellml

Author:
rcai987 <devnull@localhost>
Date:
2015-02-02 13:03:56+13:00
Desc:
Added annotations to fridyland_tamarina_philipson_2003.cellml model
Permanent Source URI:
https://models.physiomeproject.org/workspace/fridlyand_tamarina_philipson_2003/rawfile/c0bc0382dc05eca7b252df50d363445468825c26/fridlyand_tamarina_philipson_2003.cellml

<?xml version="1.0"?>
<!--  FILE :  fridlyand_model_2003.xml

CREATED :  14th November 2002

LAST MODIFIED : 14th November 2003

AUTHOR :  Catherine Lloyd
          The Bioengineering Institute
          The University of Auckland
          
MODEL STATUS :  This model conforms to the CellML 1.0 Specification released on
10th August 2001, and the CellML Metadata 1.0 Specification released on 16th
January, 2002.

DESCRIPTION :  This file contains a CellML description of Fridlyand et al's 2003 mathematical model of Ca2+ fluxes in pancreatic beta-cells.

CHANGES: 
   
--><model xmlns="http://www.cellml.org/cellml/1.0#" xmlns:bqs="http://www.cellml.org/bqs/1.0#" xmlns:cellml="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:dcterms="http://purl.org/dc/terms/" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" xml:base="file:///H:/fridlyand_tamarina_philipson_2003/fridlyand_tamarina_philipson_2003.cellml" cmeta:id="fridlyand_tamarina_philipson_2003_version01" name="fridlyand_tamarina_philipson_2003_version01">
<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
  <articleinfo>
  <title>Modelling Ca2+ Flux in Pancreatic Beta-cells</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>
An increase in the concentration of intracellular free calcium ([Ca<superscript>2+</superscript>]<subscript>i</subscript>) is an essential signal for the initiation of insulin secretion in pancreatic beta-cells.  This increase is primarily due to the opening of Ca<superscript>2+</superscript> channels in the plasma membrane in response to glucose.  Glucose metabolism leads to an increase in the cytosolic ATP:ADP ratio, which in turn causes the ATP-sensitive potassium channels to close.  The beta-cell membrane becomes depolarised, Ca<superscript>2+</superscript> channels open, and Ca<superscript>2+</superscript> enters the cell.  These events underlie the glucose-induced electrical activity, which in pancreatic islets, consists of Ca<superscript>2+</superscript>-dependent action potentials.
</para> 

<para>
There is an abundance of literature that describes beta-cell electrical activity and its relationship to [Ca<superscript>2+</superscript>]<subscript>i</subscript>.  Complex and cyclic spike-burst activity, and corresponding [Ca<superscript>2+</superscript>]<subscript>i</subscript> oscillations in pancreatic islets and beta-cell clusters are induced in response to a rise in extracellular glucose concentration.  Intermediate glucose concentrations induce both fast and slow oscillations.  The authors of this current study: Fridlyand, Tamarina and Philipson, have previously studied slow and fast [Ca<superscript>2+</superscript>]<subscript>i</subscript> oscillations in islets in response to a variety of conditions.  However, the experimental results were complex, and precise understanding was limited by the large number of channels and pumps in the beta-cell plasma membrane that were simultaneously working.
</para>  

<para>
In order to better understand the molecular mechanisms underlying this behaviour, in this publication Fridlyand <emphasis>et al.</emphasis> have developed a mathematical model of the Ca<superscript>2+</superscript> fluxes in pancreatic beta-cells.  Several other mathematical models of glucose-induced insulin secretion, with corresponding descriptions of glucose transport, metabolism and ion regulation, have been published.  These include:
</para>
<itemizedlist>
  <listitem>
            <para>
              <ulink url="${HTML_EXMPL_CHAY_MODEL97}">Extracellular and Intracellular Calcium Effects on Pancreatic Beta Cells, Chay, 1997</ulink>;</para>
          </listitem>
  <listitem>
            <para>
              <ulink url="${HTML_EXMPL_GALL_MODEL}">Na<superscript>+</superscript>/Ca<superscript>2+</superscript> Exchange in Models for Pancreatic Beta-Cells, Gall and Susa, 1999</ulink>; and</para>
          </listitem>
  <listitem>
            <para>
              <ulink url="${HTML_EXMPL_BERTRAM_MODEL}">The Phantom Burster Model for Pancreatic Beta-Cells, Bertram <emphasis>et al.</emphasis>, 2000</ulink>.</para>
          </listitem>
</itemizedlist>
<para>
However, most of these models are focused on describing one specific phenomenon. They only include a very limited set of channels and pumps, and therefore it is difficult to apply them to a another situation.  In addition, since their publication, new experimental data has become available, and these new findings should be included in a theoretical model.  For this reason Fridlyand <emphasis>et al.</emphasis> have developed the new mathematical model described here (see the raw CellML description of the Fridlyand <emphasis>et al.</emphasis> 2003 model in <xref linkend="sec_download_this_model"/>).  They have adopted the more complex style of modelling that has previously been used successfully to describe the electrophysiology of cardiac myocytes and other cell types (for example in <ulink url="${HTML_EXMPL_NYGREN_ATRIAL_MODEL}">Human Atrial Cell Model, Nygren <emphasis>et al.</emphasis> 1998</ulink> and in <ulink url="${HTML_EXMPL_RICE_MODEL2}">Modelling Interval-Force Relations in Cardiac Muscle, Rice <emphasis>et al.</emphasis>, 2000</ulink>).    </para>

<para>
Their new model includes a wider range of channels and pumps, as well as endoplasmic reticulum (ER) Ca<superscript>2+</superscript> sequestration mechanisms (see <xref linkend="fig_cell_diagram"/> below).  Using this model they were able to simulate whole cell electrical activity and [Ca<superscript>2+</superscript>]<subscript>i</subscript>, free calcium in the ER ([Ca<superscript>2+</superscript>]<subscript>ER</subscript>), intracellular Na<superscript> +</superscript> ([Na<superscript>+</superscript>]<subscript>i</subscript>), cytosolic ATP ([ATP]<subscript>i</subscript>), and inositol triphosphate ([IP<subscript>3</subscript>]<subscript>i</subscript>) concentrations.  However, they acknowledge that this model does not consider metabolic processes or insulin secretion.
</para>

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

<para>
<ulink url="http://ajpendo.physiology.org/cgi/content/abstract/285/1/E138">Modeling of Ca<superscript>2+</superscript> flux in pancreatic beta-cells: role of the plasma membrane and intracellular stores</ulink>, Leonid E. Fridlyand, Natalia Tamarina, and Louis H. Philipson, 2003, <ulink url="http://ajpendo.physiology.org/">
            <emphasis>American Journal of Physiology</emphasis>
          </ulink>, 285, E138-E154.  (<ulink url="http://ajpendo.physiology.org/cgi/content/full/285/1/E138">Full text (HTML)</ulink> and <ulink url="http://ajpendo.physiology.org/cgi/reprint/285/1/E138.pdf">PDF</ulink> versions of the article are available on the <emphasis>American Jounal of Physiology</emphasis> website.)  <ulink url="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&amp;db=PubMed&amp;list_uids=12644446&amp;dopt=Abstract">PubMed ID: 12644446</ulink>
</para>

<informalfigure float="0" id="fig_cell_diagram">
<mediaobject>
  <imageobject>
    <objectinfo>
      <title>cell diagram</title>
    </objectinfo>
    <imagedata fileref="fridlyand_2003.png"/>
  </imageobject>
</mediaobject>
<caption>Schematic representation of currents and ion fluxes, through the plasma membrane and the endoplasmic reticulum membrane, which have been included in the whole beta-cell mathematical model.</caption>
</informalfigure>

</sect1>
</article>
</documentation>
  
  
  
  <units name="millisecond">
    <unit prefix="milli" units="second"/>
  </units>
  
  <units name="first_order_rate_constant">
    <unit exponent="-1" units="millisecond"/>
  </units>
  
  <units name="second_order_rate_constant">
    <unit exponent="-1" units="micromolar"/>
    <unit exponent="-1" units="millisecond"/>
  </units>
  
  <units name="third_order_rate_constant">
    <unit exponent="-2" units="micromolar"/>
    <unit exponent="-1" units="millisecond"/>
  </units>
  
  <units name="forth_order_rate_constant">
    <unit exponent="-3" units="micromolar"/>
    <unit exponent="-1" units="millisecond"/>
  </units>
  
  <units name="flux">
    <unit units="micromolar"/>
    <unit exponent="-1" units="millisecond"/>
  </units>

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

  <units name="picoS_per_millivolt">
    <unit units="picoS"/>
    <unit exponent="-1" units="millivolt"/>
  </units>
  
  <units name="per_millivolt_millisecond">
    <unit exponent="-1" units="millivolt"/>
    <unit exponent="-1" units="millisecond"/>
  </units>
  
  <units name="picoS">
    <unit prefix="pico" units="siemens"/>
  </units>
  
  <units name="picol">
    <unit prefix="pico" units="litre"/>
  </units>
  
  <units name="picol_per_ms">
    <unit units="picol"/>
    <unit exponent="-1" units="millisecond"/>
  </units>

  <units name="femtoA">
    <unit prefix="femto" units="ampere"/>
  </units>
  
  <units name="femtoF">
    <unit prefix="femto" units="farad"/>
  </units>
  
  <units name="millimolar">
    <unit prefix="micro" units="mole"/>
    <unit exponent="-1" units="litre"/>
  </units>
  
  <units name="micromolar">
    <unit prefix="micro" units="mole"/>
    <unit exponent="-1" units="litre"/>
  </units>
  
  <units name="joule_per_kilomole_kelvin">
    <unit units="joule"/>
    <unit exponent="-1" prefix="kilo" units="mole"/>
    <unit exponent="-1" units="kelvin"/>
  </units>
  
  <units name="coulomb_per_mole">
    <unit units="coulomb"/>
    <unit exponent="-1" units="mole"/>
  </units>
  
  
  <component name="environment">
    <variable name="time" public_interface="out" units="millisecond"/>
  </component>
  
  <component cmeta:id="id_00001" name="membrane">
    <variable initial_value="-84.624" name="V" public_interface="out" units="millivolt"/>
    
    <variable initial_value="6158.0" name="Cm" units="femtoF"/>
    
    <variable name="time" public_interface="in" units="millisecond"/>
    <variable cmeta:id="id_00001" name="i_VCa" public_interface="in" units="femtoA"/>
    <variable cmeta:id="id_00022" name="i_Ca_pump" public_interface="in" units="femtoA"/>
    <variable cmeta:id="id_00028" name="i_NaCa" public_interface="in" units="femtoA"/>
    <variable cmeta:id="id_00002" name="i_CRAN" public_interface="in" units="femtoA"/>
    <variable cmeta:id="id_00035" name="i_Na" public_interface="in" units="femtoA"/>
    <variable cmeta:id="id_00045" name="i_NaK" public_interface="in" units="femtoA"/>
    <variable cmeta:id="id_00051" name="i_KDr" public_interface="in" units="femtoA"/>
    <variable cmeta:id="id_00068" name="i_KCa" public_interface="in" units="femtoA"/>
    <variable cmeta:id="id_00076" name="i_KATP" public_interface="in" units="femtoA"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply id="membrane_voltage_diff_eq">
        <eq/>
        <apply>
          <diff/>
          <bvar>
            <ci> time </ci>
          </bvar>
          <ci> V </ci>
        </apply>
        <apply>
          <divide/>
          <apply>
            <plus/>
            <ci> i_VCa </ci>
            <ci> i_Ca_pump </ci>
            <ci> i_NaCa </ci>
            <ci> i_CRAN </ci>
            <ci> i_Na </ci>
            <ci> i_NaK </ci>
            <ci> i_KDr </ci>
            <ci> i_KCa </ci>
            <ci> i_KATP </ci>
          </apply>
          <apply>
            <minus/>
            <ci> Cm </ci>
          </apply>
        </apply>
      </apply>
    </math>
  </component>
  
  <component cmeta:id="id_00012" name="whole_cell_calcium_current">
    <variable cmeta:id="id_00013" name="i_VCa" public_interface="out" units="femtoA"/>
    
    <variable cmeta:id="id_00014" name="V_Ca" units="millivolt"/>
    <variable cmeta:id="id_00015" initial_value="770.0" name="gm_VCa" units="picoS"/>
    
    <variable name="V" private_interface="out" public_interface="in" units="millivolt"/>
    <variable name="R" public_interface="in" units="joule_per_kilomole_kelvin"/>
    <variable name="F" public_interface="in" units="coulomb_per_mole"/>
    <variable name="T" public_interface="in" units="kelvin"/>
    <variable name="Cai" public_interface="in" units="micromolar"/>
    <variable name="Cao" public_interface="in" units="micromolar"/>
   
    <variable cmeta:id="id_00016" name="p_VCa" private_interface="in" units="dimensionless"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply id="i_VCa_calculation">
        <eq/>
        <ci> i_VCa </ci>
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            <minus/>
            <ci> V </ci>
            <ci> V_Ca </ci>
          </apply>
        </apply>
      </apply>
      
      <apply id="V_Ca_calculation">
        <eq/>
        <ci> V_Ca </ci>
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          <apply>
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              <times/>
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              <cn cellml:units="dimensionless"> 2.0 </cn>
              <ci> F </ci>
            </apply>
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          <apply>
            <ln/>                
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            </apply>
          </apply>
        </apply>
      </apply> 
    </math>
  </component>
  
  <component cmeta:id="id_00017" name="whole_cell_calcium_current_p_VCa_gate">
    <variable cmeta:id="id_00018" name="p_VCa" public_interface="out" units="dimensionless"/>
        
    <variable cmeta:id="id_00019" initial_value="-19.0" name="V_Cah" units="millivolt"/>
    <variable cmeta:id="id_00020" initial_value="9.5" name="K_Cah" units="millivolt"/>

    <variable name="V" public_interface="in" units="millivolt"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply id="p_VCa_calculation">
        <eq/>
        <ci> p_VCa </ci>
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          <cn cellml:units="dimensionless"> 1.0 </cn>
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            <cn cellml:units="dimensionless"> 1.0 </cn>
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                </apply>
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              </apply>
            </apply>
          </apply>
        </apply>
      </apply>
    </math>
  </component>
  
  <component cmeta:id="id_00023" name="PM_calcium_pumps">
    <variable cmeta:id="id_00024" name="i_Ca_pump" public_interface="out" units="femtoA"/>
    
    <variable cmeta:id="id_00025" initial_value="2000.0" name="Pm_Cap" units="femtoA"/>
    <variable cmeta:id="id_00026" initial_value="0.1" name="K_Cap" units="micromolar"/>
    
    <variable name="Cai" public_interface="in" units="micromolar"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply id="i_Ca_pump_calculation">
        <eq/>
        <ci> i_Ca_pump </ci>
        <apply>
          <times/>
          <ci> Pm_Cap </ci>
          <apply>
            <divide/>
            <apply>
              <power/>
              <ci> Cai </ci>
              <cn cellml:units="dimensionless"> 2.0 </cn>
            </apply>
            <apply>
              <plus/>
              <apply>
                <power/>
                <ci> K_Cap </ci>
                <cn cellml:units="dimensionless"> 2.0 </cn>
              </apply>
              <apply>
                <power/>
                <ci> Cai </ci>
                <cn cellml:units="dimensionless"> 2.0 </cn>
              </apply>
            </apply>
          </apply>
        </apply>
      </apply>
    </math>
  </component>
  
  <component cmeta:id="id_00029" name="sodium_calcium_exchanger">
    <variable cmeta:id="id_00030" name="i_NaCa" public_interface="out" units="femtoA"/>
    
    <variable cmeta:id="id_00031" name="V_NaCa" units="millivolt"/>
    <variable cmeta:id="id_00032" initial_value="271.0" name="g_NaCa" units="picoS"/>
    <variable cmeta:id="id_00033" initial_value="0.75" name="K_NaCa" units="micromolar"/>
    
    <variable name="V" public_interface="in" units="millivolt"/>
    <variable name="R" public_interface="in" units="joule_per_kilomole_kelvin"/>
    <variable name="F" public_interface="in" units="coulomb_per_mole"/>
    <variable name="T" public_interface="in" units="kelvin"/>
    <variable name="Cai" public_interface="in" units="micromolar"/>
    <variable name="Cao" public_interface="in" units="micromolar"/>
    <variable name="Nai" public_interface="in" units="micromolar"/>
    <variable name="Nao" public_interface="in" units="micromolar"/>
   
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply id="i_NaCa_calculation">
        <eq/>
        <ci> i_NaCa </ci>
        <apply>
          <times/>
          <ci> g_NaCa </ci>
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            <divide/>
            <apply>
              <power/>
              <ci> Cai </ci>
              <cn cellml:units="dimensionless"> 5.0 </cn>
            </apply>
            <apply>
              <plus/>
              <apply>
                <power/>
                <ci> Cai </ci>
                <cn cellml:units="dimensionless"> 5.0 </cn>
              </apply>
              <apply>
                <power/>
                <ci> K_NaCa </ci>
                <cn cellml:units="dimensionless"> 5.0 </cn>
              </apply>
            </apply>
          </apply>
          <apply>
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            <ci> V </ci>
            <ci> V_NaCa </ci>
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        </apply>
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      <apply id="V_NaCa_calculation">
        <eq/>
        <ci> V_NaCa </ci>
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          <times/>
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            <divide/>
            <apply>
              <times/>
              <ci> R </ci>
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            <ci> F </ci>
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          <apply>
            <minus/>
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              <times/>
              <cn cellml:units="dimensionless"> 3.0 </cn>
              <apply>
                <ln/>                
                <apply>
                  <divide/>
                  <ci> Nao </ci>
                  <ci> Nai </ci>
                </apply>
              </apply>
            </apply>
            <apply>
              <ln/>                
              <apply>
                <divide/>
                <ci> Cao </ci>
                <ci> Cai </ci>
              </apply>
            </apply>
          </apply>
        </apply>
      </apply> 
    </math>
  </component>
  
  <component cmeta:id="id_00003" name="nonselective_cation_current">
    <variable cmeta:id="id_00004" name="i_CRAN" public_interface="out" units="femtoA"/>
    
    <variable cmeta:id="id_00005" initial_value="0.0" name="V_CRAN" units="millivolt"/>
    <variable cmeta:id="id_00006" initial_value="0.7" name="gm_CRAN" units="picoS_per_millivolt"/>
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    <variable cmeta:id="id_00008" name="f_CRAN" units="dimensionless"/>
    <variable cmeta:id="id_00009" name="P_CRAN" units="millivolt"/>
    
    <variable name="V" public_interface="in" units="millivolt"/>
    <variable name="V_Na" public_interface="in" units="millivolt"/>
    <variable name="CaER" public_interface="in" units="micromolar"/>
   
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply id="i_CRAN_calculation">
        <eq/>
        <ci> i_CRAN </ci>
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          <times/>
          <ci> f_CRAN </ci>
          <ci> P_CRAN </ci>
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            <minus/>
            <ci> V </ci>
            <ci> V_Na </ci>
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      <apply id="f_CRAN_calculation">
        <eq/>
        <ci> f_CRAN </ci>
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          <divide/>
          <apply>
            <minus/>
            <ci> gm_CRAN </ci>
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            <plus/>
            <cn cellml:units="dimensionless"> 1.0 </cn>
            <apply>
              <exp/>
              <apply>
                <divide/>
                <apply>
                  <minus/>
                  <ci> CaER </ci>
                  <ci> K_Car </ci>
                </apply>
                <cn cellml:units="dimensionless"> 3.0 </cn>
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      <apply id="P_CRAN_calculation">
        <eq/>
        <ci> P_CRAN </ci>
        <apply>
          <minus/>
          <ci> V </ci>
          <ci> V_CRAN </ci>
        </apply>
      </apply> 
    </math>
  </component>
  
  <component cmeta:id="id_00036" name="sodium_current">
    <variable cmeta:id="id_00037" name="i_Na" public_interface="out" units="femtoA"/>
    <variable cmeta:id="id_00038" name="V_Na" public_interface="out" units="millivolt"/>
    
    <variable cmeta:id="id_00039" initial_value="1200.0" name="gm_Na" units="picoS"/>
    
    <variable name="V" private_interface="out" public_interface="in" units="millivolt"/>
    <variable name="R" public_interface="in" units="joule_per_kilomole_kelvin"/>
    <variable name="F" public_interface="in" units="coulomb_per_mole"/>
    <variable name="T" public_interface="in" units="kelvin"/>
    <variable name="Nai" public_interface="in" units="micromolar"/>
    <variable name="Nao" public_interface="in" units="micromolar"/>
   
    <variable cmeta:id="id_00040" name="p_Na" private_interface="in" units="dimensionless"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply id="i_Na_calculation">
        <eq/>
        <ci> i_Na </ci>
        <apply>
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          <ci> gm_Na </ci>
          <ci> p_Na </ci>
          <apply>
            <minus/>
            <ci> V </ci>
            <ci> V_Na </ci>
          </apply>
        </apply>
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      <apply id="V_Na_calculation">
        <eq/>
        <ci> V_Na </ci>
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            <divide/>
            <apply>
              <times/>
              <ci> R </ci>
              <ci> T </ci>
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            <ci> F </ci>
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          <apply>
            <ln/>                
            <apply>
              <divide/>
              <ci> Nao </ci>
              <ci> Nai </ci>
            </apply>
          </apply>
        </apply>
      </apply> 
    </math>
  </component>
  
  <component cmeta:id="id_00041" name="sodium_current_p_Na_gate">
    <variable cmeta:id="id_00042" name="p_Na" public_interface="out" units="dimensionless"/>
        
    <variable name="V" public_interface="in" units="millivolt"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply id="p_Na_calculation">
        <eq/>
        <ci> p_Na </ci>
        <apply>
          <divide/>
          <cn cellml:units="dimensionless"> 1.0 </cn>
          <apply>
            <plus/>
            <cn cellml:units="dimensionless"> 1.0 </cn>
            <apply>
              <exp/>
              <apply>
                <divide/>
                <apply>
                  <plus/>
                  <cn cellml:units="millivolt"> 104.0 </cn>
                  <ci> V </ci>
                </apply>
                <cn cellml:units="millivolt"> 8.0 </cn>
              </apply>
            </apply>
          </apply>
        </apply>
      </apply>
    </math>
  </component>
  
  <component cmeta:id="id_00046" name="sodium_potassium_active_transport">
    <variable cmeta:id="id_00047" name="i_NaK" public_interface="out" units="femtoA"/>
    
    <variable cmeta:id="id_00048" initial_value="600.0" name="P_NaK" units="femtoA"/>
    <variable initial_value="4950.0" name="P" units="micromolar"/>
    <variable name="K_supi" units="micromolar"/>
    <variable name="F1" units="first_order_rate_constant"/>
    <variable name="F4" units="first_order_rate_constant"/>
    <variable name="F5" units="first_order_rate_constant"/>
    <variable initial_value="2.5E-10" name="f1" units="forth_order_rate_constant"/>
    <variable initial_value="10.0" name="f2" units="first_order_rate_constant"/>
    <variable initial_value="0.172" name="f3" units="first_order_rate_constant"/>
    <variable initial_value="1.5E-8" name="f4" units="third_order_rate_constant"/>
    <variable initial_value="0.002" name="f5_" units="second_order_rate_constant"/>
    <variable name="f5" units="second_order_rate_constant"/>
    <variable initial_value="11.5" name="f6" units="first_order_rate_constant"/>
    <variable initial_value="100.0" name="b1" units="first_order_rate_constant"/>
    <variable initial_value="0.0001" name="b2" units="second_order_rate_constant"/>
    <variable initial_value="1.72E-17" name="b3" units="forth_order_rate_constant"/>
    <variable initial_value="0.0002" name="b4" units="second_order_rate_constant"/>
    <variable initial_value="0.03" name="b5_" units="first_order_rate_constant"/>
    <variable name="b5" units="first_order_rate_constant"/>
    <variable initial_value="6.0E-7" name="b6" units="second_order_rate_constant"/>
    <variable name="B2" units="first_order_rate_constant"/>
    <variable name="B3" units="first_order_rate_constant"/>
    <variable name="B4" units="first_order_rate_constant"/>
    <variable name="B6" units="first_order_rate_constant"/>
    <variable name="D" units="dimensionless"/>
    
    <variable name="V" public_interface="in" units="millivolt"/>
    <variable name="R" public_interface="in" units="joule_per_kilomole_kelvin"/>
    <variable name="F" public_interface="in" units="coulomb_per_mole"/>
    <variable name="T" public_interface="in" units="kelvin"/>
    <variable name="Nai" public_interface="in" units="micromolar"/>
    <variable name="Nao" public_interface="in" units="micromolar"/>
    <variable name="ATPi" public_interface="in" units="micromolar"/>
    <variable name="ADPi" public_interface="in" units="micromolar"/>
    <variable name="Ko" public_interface="in" units="micromolar"/>
   
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply id="i_NaK_calculation">
        <eq/>
        <ci> i_NaK </ci>
        <apply>
          <times/>
          <ci> P_NaK </ci>
          <apply>
            <divide/>
            <apply>
              <minus/>
              <apply>
                <times/>
                <ci> F1 </ci>
                <ci> f2 </ci>
                <ci> f3 </ci>
                <ci> F4 </ci>
                <ci> F5 </ci>
                <ci> f6 </ci>
              </apply>
              <apply>
                <times/>
                <ci> b1 </ci>
                <ci> B2 </ci>
                <ci> B3 </ci>
                <ci> B4 </ci>
                <ci> b5 </ci>
                <ci> B6 </ci>
              </apply>
            </apply>
            <ci> D </ci>
          </apply>
        </apply>
      </apply>
      
      <apply id="D_calculation">
        <eq/>
        <ci> D </ci>
        <apply>
          <plus/>
          <apply>
            <times/>
            <ci> f2 </ci>
            <ci> f3 </ci>
            <ci> F4 </ci>
            <ci> F5 </ci>
            <ci> f6 </ci>
          </apply>
          <apply>
            <times/>
            <ci> b1 </ci>
            <ci> f3 </ci>
            <ci> F4 </ci>
            <ci> F5 </ci>
            <ci> f6 </ci>
          </apply>
          <apply>
            <times/>
            <ci> b1 </ci>
            <ci> B2 </ci>
            <ci> F4 </ci>
            <ci> F5 </ci>
            <ci> f6 </ci>
          </apply>
          <apply>
            <times/>
            <ci> b1 </ci>
            <ci> B2 </ci>
            <ci> B3 </ci>
            <ci> F5 </ci>
            <ci> f6 </ci>
          </apply>
          <apply>
            <times/>
            <ci> b1 </ci>
            <ci> B2 </ci>
            <ci> B3 </ci>
            <ci> B4 </ci>
            <ci> f6 </ci>
          </apply>
          <apply>
            <times/>
            <ci> b1 </ci>
            <ci> B2 </ci>
            <ci> B3 </ci>
            <ci> B4 </ci>
            <ci> b5 </ci>
          </apply>
        </apply>
      </apply>
      
      <apply id="F1_calculation">
        <eq/>
        <ci> F1 </ci>
        <apply>
          <times/>
          <ci> f1 </ci>
          <apply>
            <power/>
            <ci> Nai </ci>
            <cn cellml:units="dimensionless"> 3.0 </cn>
          </apply>
        </apply>
      </apply>
      
      <apply id="F4_calculation">
        <eq/>
        <ci> F4 </ci>
        <apply>
          <times/>
          <ci> f4 </ci>
          <apply>
            <power/>
            <ci> Ko </ci>
            <cn cellml:units="dimensionless"> 2.0 </cn>
          </apply>
        </apply>
      </apply>
      
      <apply id="F5_calculation">
        <eq/>
        <ci> F5 </ci>
        <apply>
          <times/>
          <ci> f5 </ci>
          <ci> ATPi </ci>
        </apply>
      </apply>
      
      <apply id="f5_calculation">
        <eq/>
        <ci> f5 </ci>
        <apply>
          <times/>
          <ci> f5_ </ci>
          <apply>
            <exp/>
            <apply>
              <divide/>
              <apply>
                <times/>
                <ci> V </ci>
                <ci> F </ci>
              </apply>
              <apply>
                <times/>
                <cn cellml:units="dimensionless"> 2.0 </cn>
                <ci> R </ci>
                <ci> T </ci>
              </apply>
            </apply>
          </apply>
        </apply>
      </apply>
      
      <apply id="B2_calculation">
        <eq/>
        <ci> B2 </ci>
        <apply>
          <times/>
          <ci> b2 </ci>
          <ci> ATPi </ci>
        </apply>
      </apply>
      
      <apply id="B3_calculation">
        <eq/>
        <ci> B3 </ci>
        <apply>
          <times/>
          <ci> b3 </ci>
          <apply>
            <power/>
            <ci> Nai </ci>
            <cn cellml:units="dimensionless"> 3.0 </cn>
          </apply>
        </apply>
      </apply>
      
      <apply id="B4_calculation">
        <eq/>
        <ci> B4 </ci>
        <apply>
          <times/>
          <ci> b4 </ci>
          <ci> P </ci>
        </apply>
      </apply>
      
      <apply id="B6_calculation">
        <eq/>
        <ci> B6 </ci>
        <apply>
          <times/>
          <ci> b6 </ci>
          <apply>
            <power/>
            <ci> K_supi </ci>
            <cn cellml:units="dimensionless"> 2.0 </cn>
          </apply>
        </apply>
      </apply>
      
      <apply id="b5_calculation">
        <eq/>
        <ci> b5 </ci>
        <apply>
          <times/>
          <ci> b5_ </ci>
          <apply>
            <exp/>
            <apply>
              <divide/>
              <apply>
                <minus/>
                <apply>
                  <times/>
                  <ci> V </ci>
                  <ci> F </ci>
                </apply>
              </apply>
              <apply>
                <times/>
                <cn cellml:units="dimensionless"> 2.0 </cn>
                <ci> R </ci>
                <ci> T </ci>
              </apply>
            </apply>
          </apply>
        </apply>
      </apply>
    </math>
  </component>
  
  <component cmeta:id="id_00052" name="voltage_dependent_potassium_current">
    <variable cmeta:id="id_00053" name="i_KDr" public_interface="out" units="femtoA"/>
    <variable cmeta:id="id_00054" name="V_K" public_interface="out" units="millivolt"/>
    
    <variable cmeta:id="id_00055" initial_value="3000.0" name="gm_KDr" units="picoS"/>
    
    <variable name="time" private_interface="out" public_interface="in" units="millisecond"/>
    <variable name="V" private_interface="out" public_interface="in" units="millivolt"/>
    <variable name="R" public_interface="in" units="joule_per_kilomole_kelvin"/>
    <variable name="F" public_interface="in" units="coulomb_per_mole"/>
    <variable name="T" public_interface="in" units="kelvin"/>
    <variable name="Ki" public_interface="in" units="micromolar"/>
    <variable name="Ko" public_interface="in" units="micromolar"/>
   
    <variable name="n" private_interface="in" units="dimensionless"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply id="i_KDr_calculation">
        <eq/>
        <ci> i_KDr </ci>
        <apply>
          <times/>
          <ci> gm_KDr </ci>
          <ci> n </ci>
          <apply>
            <minus/>
            <ci> V </ci>
            <ci> V_K </ci>
          </apply>
        </apply>
      </apply>
      
      <apply id="V_K_calculation">
        <eq/>
        <ci> V_K </ci>
        <apply>
          <times/>
          <apply>
            <divide/>
            <apply>
              <times/>
              <ci> R </ci>
              <ci> T </ci>
            </apply>
            <ci> F </ci>
          </apply>
          <apply>
            <ln/>                
            <apply>
              <divide/>
              <ci> Ko </ci>
              <ci> Ki </ci>
            </apply>
          </apply>
        </apply>
      </apply> 
    </math>
  </component>
  
  <component cmeta:id="id_00056" name="voltage_dependent_potassium_current_n_gate">
    <variable cmeta:id="id_00057" initial_value="0.00123" name="n" public_interface="out" units="dimensionless"/>
    
    <variable cmeta:id="id_00058" name="tau_n" units="dimensionless"/>
    <variable cmeta:id="id_00059" name="n_infinity" units="dimensionless"/>
    <variable cmeta:id="id_00060" initial_value="-14.0" name="Vn" units="millivolt"/>
    <variable cmeta:id="id_00061" initial_value="-75.0" name="Vtau" units="millivolt"/>
    <variable cmeta:id="id_00062" initial_value="7.0" name="Sn" units="millivolt"/>
    <variable initial_value="65.0" name="a" units="millivolt"/>
    <variable initial_value="20.0" name="b" units="millivolt"/>
    <variable initial_value="20.0" name="c" units="millisecond"/>
    
    <variable name="V" public_interface="in" units="millivolt"/>
    <variable name="time" public_interface="in" units="millisecond"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML">
       <apply id="n_diff_eq">
        <eq/>
        <apply>
          <diff/>
          <bvar>
            <ci> time </ci>
          </bvar>
          <ci> n </ci>
        </apply>
        <apply>
          <divide/>
          <apply>
            <minus/>
            <ci> n_infinity </ci>
            <ci> n </ci>
          </apply>
          <ci> tau_n </ci>
        </apply>
      </apply>
                
      <apply id="n_infinity_calculation">
        <eq/>
        <ci> n_infinity </ci>
        <apply>
          <divide/>
          <cn cellml:units="dimensionless"> 1.0 </cn>
          <apply>
            <plus/>
            <cn cellml:units="dimensionless"> 1.0 </cn>
            <apply>
              <exp/>
              <apply>
                <divide/>
                <apply>
                  <minus/>
                  <ci> Vn </ci>
                  <ci> V </ci>
                </apply>
                <ci> Sn </ci>
              </apply>
            </apply>
          </apply>
        </apply>
      </apply>
      
      <apply id="tau_n_calculation">
        <eq/>
        <ci> tau_n </ci>
        <apply>
          <divide/>
          <ci> c </ci>
          <apply>
            <plus/>
            <apply>
              <exp/>
              <apply>
                <divide/>
                <apply>
                  <minus/>
                  <ci> V </ci>
                  <ci> Vtau </ci>
                </apply>
                <ci> a </ci>
              </apply>
            </apply>
            <apply>
              <exp/>
              <apply>
                <divide/>
                <apply>
                  <minus/>
                  <ci> Vtau </ci>
                  <ci> V </ci>
                </apply>
                <ci> b </ci>
              </apply>
            </apply>
          </apply>
        </apply>
      </apply>
    </math>
  </component>
  
  <component cmeta:id="id_00069" name="calcium_dependent_potassium_current">
    <variable cmeta:id="id_00070" name="i_KCa" public_interface="out" units="femtoA"/>
    
    <variable cmeta:id="id_00071" initial_value="130.0" name="gm_KCa" units="picoS"/>
    
    <variable cmeta:id="id_00072" name="V_K" public_interface="in" units="millivolt"/>
    <variable name="V" public_interface="in" units="millivolt"/>
    <variable name="Cai" private_interface="out" public_interface="in" units="micromolar"/>
    
    <variable name="fCa" private_interface="in" units="dimensionless"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply id="i_KCa_calculation">
        <eq/>
        <ci> i_KCa </ci>
        <apply>
          <times/>
          <ci> gm_KCa </ci>
          <ci> fCa </ci>
          <apply>
            <minus/>
            <ci> V </ci>
            <ci> V_K </ci>
          </apply>
        </apply>
      </apply>
    </math>
  </component>
  
  <component cmeta:id="id_00073" name="calcium_dependent_potassium_current_fCa_gate">
    <variable cmeta:id="id_00074" name="fCa" public_interface="out" units="dimensionless"/>
    
    <variable cmeta:id="id_00075" initial_value="0.1" name="K_KCa" units="micromolar"/>
    
    <variable name="Cai" public_interface="in" units="micromolar"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply id="fCa_calculation">
        <eq/>
        <ci> fCa </ci>
        <apply>
          <divide/>
          <apply>
            <power/>
            <ci> Cai </ci>
            <cn cellml:units="dimensionless"> 4.0 </cn>
          </apply>
          <apply>
            <plus/>
            <apply>
              <power/>
              <ci> Cai </ci>
              <cn cellml:units="dimensionless"> 4.0 </cn>
            </apply>
            <apply>
              <power/>
              <ci> K_KCa </ci>
              <cn cellml:units="dimensionless"> 4.0 </cn>
            </apply>
          </apply>
        </apply>
      </apply>
    </math>
  </component>
  
  <component cmeta:id="id_00063" name="ATP_dependent_potassium_current">
    <variable cmeta:id="id_00064" name="i_KATP" public_interface="out" units="femtoA"/>
    
    <variable cmeta:id="id_00065" initial_value="24000.0" name="gm_KATP" units="picoS"/>
    <variable cmeta:id="id_00066" name="O_KATP" units="dimensionless"/>
    <variable initial_value="17.0" name="Kdd" units="micromolar"/>
    <variable initial_value="26.0" name="Ktd" units="micromolar"/>
    <variable initial_value="1.0" name="Ktt" units="micromolar"/>
    
    <variable name="V" public_interface="in" units="millivolt"/>
    <variable name="V_K" public_interface="in" units="millivolt"/>
    <variable name="ADPi" public_interface="in" units="micromolar"/>
    <variable name="ATPi" public_interface="in" units="micromolar"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply id="i_KATP_calculation">
        <eq/>
        <ci> i_KATP </ci>
        <apply>
          <times/>
          <ci> gm_KATP </ci>
          <ci> O_KATP </ci>
          <apply>
            <minus/>
            <ci> V </ci>
            <ci> V_K </ci>
          </apply>
        </apply>
      </apply>
      
      <apply id="O_KATP_calculation">
        <eq/>
        <ci> O_KATP </ci>
        <apply>
          <divide/>
          <apply>
            <plus/>
            <apply>
              <times/>
              <cn cellml:units="dimensionless"> 0.08 </cn>
              <apply>
                <plus/>
                <cn cellml:units="dimensionless"> 1.0 </cn>
                <apply>
                  <divide/>
                  <apply>
                    <times/>
                    <cn cellml:units="dimensionless"> 0.33 </cn>
                    <ci> ADPi </ci>
                  </apply>
                  <ci> Kdd </ci>
                </apply>
              </apply>
            </apply>
            <apply>
              <times/>
              <cn cellml:units="dimensionless"> 0.89 </cn>
              <apply>
                <power/>
                <apply>
                  <plus/>
                  <cn cellml:units="dimensionless"> 0.165 </cn>
                  <apply>
                    <divide/>
                    <ci> ADPi </ci>
                    <ci> Kdd </ci>
                  </apply>
                </apply>
                <cn cellml:units="dimensionless"> 2.0 </cn>
              </apply>
            </apply>
          </apply>
          <apply>
            <times/>
            <apply>
              <power/>
              <apply>
                <plus/>
                <cn cellml:units="dimensionless"> 0.165 </cn>
                <apply>
                  <divide/>
                  <ci> ADPi </ci>
                  <ci> Kdd </ci>
                </apply>
              </apply>
              <cn cellml:units="dimensionless"> 2.0 </cn>
            </apply>
            <apply>
              <plus/>
              <cn cellml:units="dimensionless"> 1.0 </cn>
              <apply>
                <divide/>
                <apply>
                  <times/>
                  <cn cellml:units="dimensionless"> 0.135 </cn>
                  <ci> ADPi </ci>
                </apply>
                <ci> Ktd </ci>
              </apply>
              <apply>
                <divide/>
                <apply>
                  <times/>
                  <cn cellml:units="dimensionless"> 0.05 </cn>
                  <ci> ATPi </ci>
                </apply>
                <ci> Ktt </ci>
              </apply>
            </apply>
          </apply>
        </apply>
      </apply>
    </math>
  </component>
 
  <component cmeta:id="id_00077" name="SERCA_pump">
    <variable cmeta:id="id_00078" name="Jer_p" public_interface="out" units="flux"/>
    
    <variable cmeta:id="id_00079" initial_value="0.105" name="P_CaER" units="flux"/>
    <variable cmeta:id="id_00080" initial_value="0.5" name="K_Carp" units="micromolar"/>
    
    <variable name="Cai" public_interface="in" units="micromolar"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply id="Jer_p_calculation">
        <eq/>
        <ci> Jer_p </ci>
        <apply>
          <times/>
          <ci> P_CaER </ci>
          <apply>
            <divide/>
            <apply>
              <power/>
              <ci> Cai </ci>
              <cn cellml:units="dimensionless"> 2.0 </cn>
            </apply>
            <apply>
              <plus/>
              <apply>
                <power/>
                <ci> Cai </ci>
                <cn cellml:units="dimensionless"> 2.0 </cn>
              </apply>
              <apply>
                <power/>
                <ci> K_Carp </ci>
                <cn cellml:units="dimensionless"> 2.0 </cn>
              </apply>
            </apply>
          </apply>
        </apply>
      </apply>
    </math>
  </component>
  
  <component cmeta:id="id_00081" name="IP3_metabolism">
    <variable cmeta:id="id_00082" initial_value="0.33" name="IP3i" public_interface="out" units="micromolar"/>
    
    <variable initial_value="0.0003" name="kIP" units="flux"/>
    <variable initial_value="0.00004" name="kdIP" units="first_order_rate_constant"/>
    <variable cmeta:id="id_00083" initial_value="0.4" name="K_IPCa" units="micromolar"/>
    
    <variable name="Cai" public_interface="in" units="micromolar"/>
    <variable name="time" public_interface="in" units="millisecond"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply id="IP3_diff_eq">
        <eq/>
        <apply>
          <diff/>
          <bvar>
            <ci> time </ci>
          </bvar>
          <ci> IP3i </ci>
        </apply>
        <apply>
          <minus/>
          <apply>
            <times/>
            <ci> kIP </ci>
            <apply>
              <divide/>
              <apply>
                <power/>
                <ci> Cai </ci>
                <cn cellml:units="dimensionless"> 2.0 </cn>
              </apply>
              <apply>
                <plus/>
                <apply>
                  <power/>
                  <ci> Cai </ci>
                  <cn cellml:units="dimensionless"> 2.0 </cn>
                </apply>
                <apply>
                  <power/>
                  <ci> K_IPCa </ci>
                  <cn cellml:units="dimensionless"> 2.0 </cn>
                </apply>
              </apply>
            </apply>
          </apply>
          <apply>
            <times/>
            <ci> kdIP </ci>
            <ci> IP3i </ci>
          </apply>
        </apply>
      </apply>
    </math>
  </component>
  
  <component name="CaER_mobilisation">
    <variable name="J_out" public_interface="out" units="flux"/>
    
    <variable cmeta:id="id_00087" initial_value="0.0001" name="P_leak" units="picol_per_ms"/>
    <variable cmeta:id="id_00086" initial_value="0.0012" name="P_IP3" units="picol_per_ms"/>
    <variable name="O_infinity" units="dimensionless"/>
    <variable initial_value="3.2" name="K_RCa" units="micromolar"/>
    <variable cmeta:id="id_00084" initial_value="0.077" name="K_IP3" units="micromolar"/>
    
    <variable cmeta:id="id_00085" name="IP3i" public_interface="in" units="micromolar"/>
    <variable name="Cai" public_interface="in" units="micromolar"/>
    <variable name="CaER" public_interface="in" units="micromolar"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply>
        <eq/>
        <ci> J_out </ci>
        <apply>
          <times/>
          <apply>
            <plus/>
            <ci> P_leak </ci>
            <apply>
              <times/>
              <ci> P_IP3 </ci>
              <ci> O_infinity </ci>
            </apply>
          </apply>
          <apply>
            <minus/>
            <ci> CaER </ci>
            <ci> Cai </ci>
          </apply>
        </apply>
      </apply>
      
      <apply>
        <eq/>
        <ci> O_infinity </ci>
        <apply>
          <times/>
          <apply>
            <divide/>
            <ci> Cai </ci>
            <apply>
              <plus/>
              <ci> Cai </ci>
              <ci> K_RCa </ci>
            </apply>
          </apply>
          <apply>
            <divide/>
            <apply>
              <power/>
              <ci> IP3i </ci>
              <cn cellml:units="dimensionless"> 3.0 </cn>
            </apply>
            <apply>
              <plus/>
              <apply>
                <power/>
                <ci> IP3i </ci>
                <cn cellml:units="dimensionless"> 3.0 </cn>
              </apply>
              <apply>
                <power/>
                <ci> K_IP3 </ci>
                <cn cellml:units="dimensionless"> 3.0 </cn>
              </apply>
            </apply>
          </apply>
        </apply>
      </apply>
    </math>
  </component>
  
  <component cmeta:id="id_00044" name="calcium_and_sodium_dynamics">
    <variable initial_value="0.085" name="Cai" public_interface="out" units="micromolar"/>
    <variable initial_value="22.8" name="CaER" public_interface="out" units="micromolar"/>
    <variable initial_value="9858.0" name="Nai" public_interface="out" units="micromolar"/>
    
    <variable initial_value="0.01" name="fi" units="dimensionless"/>
    <variable initial_value="0.03" name="fer" units="dimensionless"/>
    <variable initial_value="0.0001" name="ksg" units="first_order_rate_constant"/>
    <variable initial_value="0.280" name="Ver" units="picol"/>
    
    <variable name="Vi" public_interface="in" units="picol"/>
    <variable cmeta:id="id_00021" name="i_VCa" public_interface="in" units="femtoA"/>
    <variable cmeta:id="id_00034" name="i_NaCa" public_interface="in" units="femtoA"/>
    <variable name="i_Ca_pump" public_interface="in" units="femtoA"/>
    <variable cmeta:id="id_00049" name="i_NaK" public_interface="in" units="femtoA"/>
    <variable cmeta:id="id_00043" name="i_Na" public_interface="in" units="femtoA"/>
    <variable cmeta:id="id_00011" name="i_CRAN" public_interface="in" units="femtoA"/>
    <variable name="F" public_interface="in" units="coulomb_per_mole"/>
    <variable name="J_out" public_interface="in" units="flux"/>
    <variable name="Jer_p" public_interface="in" units="flux"/>
    <variable name="time" public_interface="in" units="millisecond"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply id="Cai_diff_eq">
        <eq/>
        <apply>
          <diff/>
          <bvar>
            <ci> time </ci>
          </bvar>
          <ci> Cai </ci>
        </apply>
        <apply>
          <minus/>
          <apply>
            <times/>
            <ci> fi </ci>
            <apply>
              <plus/>
              <apply>
                <minus/>
                <apply>
                  <divide/>
                  <apply>
                    <minus/>
                    <apply>
                      <plus/>
                      <apply>
                        <minus/>
                        <ci> i_VCa </ci>
                      </apply>
                      <apply>
                        <times/>
                        <ci> i_NaCa </ci>
                        <cn cellml:units="dimensionless"> 2.0 </cn>
                      </apply>
                    </apply>
                    <apply>
                      <times/>
                      <ci> i_Ca_pump </ci>
                      <cn cellml:units="dimensionless"> 2.0 </cn>
                    </apply>
                  </apply>
                  <apply>
                    <times/>
                    <cn cellml:units="dimensionless"> 2.0 </cn>
                    <ci> F </ci>
                    <ci> Vi </ci>
                  </apply>
                </apply>
                <ci> Jer_p </ci>
              </apply>
              <apply>
                <divide/>
                <ci> J_out </ci>
                <ci> Vi </ci>
              </apply>
            </apply>
          </apply>
          <apply>
            <times/>
            <ci> ksg </ci>
            <ci> Cai </ci>
          </apply>
        </apply>
      </apply>
      
      <apply id="CaER_diff_eq">
        <eq/>
        <apply>
          <diff/>
          <bvar>
            <ci> time </ci>
          </bvar>
          <ci> CaER </ci>
        </apply>
        <apply>
          <times/>
          <apply>
            <divide/>
            <ci> fer </ci>
            <ci> Ver </ci>
          </apply>
          <apply>
            <minus/>
            <apply>
              <times/>
              <ci> Jer_p </ci>
              <ci> Vi </ci>
            </apply>
            <ci> J_out </ci>
          </apply>
        </apply>
      </apply>
      
      <apply id="Nai_diff_eq">
        <eq/>
        <apply>
          <diff/>
          <bvar>
            <ci> time </ci>
          </bvar>
          <ci> Nai </ci>
        </apply>
        <apply>
          <divide/>
          <apply>
            <minus/>
            <apply>
              <plus/>
              <apply>
                <times/>
                <cn cellml:units="dimensionless"> 3.0 </cn>
                <ci> i_NaCa </ci>
              </apply>
              <apply>
                <times/>
                <cn cellml:units="dimensionless"> 3.0 </cn>
                <ci> i_NaK </ci>
              </apply>
              <ci> i_Na </ci>   
              <ci> i_CRAN </ci>
            </apply> 
          </apply>
          <apply>
            <times/>
            <ci> Vi </ci>
            <ci> F </ci>
          </apply>
        </apply> 
      </apply>      
    </math>
  </component>
  
  <component cmeta:id="id_00090" name="ATP_homeostasis">
    <variable cmeta:id="id_00088" initial_value="932.1" name="ATPi" public_interface="out" units="micromolar"/>
    <variable cmeta:id="id_00091" name="ADPi" public_interface="out" units="millimolar"/>
    
    <variable cmeta:id="id_00092" name="k_ADP" units="first_order_rate_constant"/>
    <variable cmeta:id="id_00067" initial_value="0.00005" name="k_ATP" units="first_order_rate_constant"/>
    <variable cmeta:id="id_00089" initial_value="0.00005" name="k_ATP_Ca" units="second_order_rate_constant"/>
    <variable initial_value="4000.0" name="Ao" units="micromolar"/>
    
    <variable name="Vi" public_interface="in" units="picol"/>
    <variable name="Cai" public_interface="in" units="micromolar"/>
    <variable cmeta:id="id_00027" name="i_Ca_pump" public_interface="in" units="femtoA"/>
    <variable cmeta:id="id_00010" name="i_CRAN" public_interface="in" units="femtoA"/>
    <variable cmeta:id="id_00050" name="i_NaK" public_interface="in" units="femtoA"/>
    <variable name="F" public_interface="in" units="coulomb_per_mole"/>
    <variable name="Jer_p" public_interface="in" units="flux"/>
    <variable name="time" public_interface="in" units="millisecond"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply id="ATPi_diff_eq">
        <eq/>
        <apply>
          <diff/>
          <bvar>
            <ci> time </ci>
          </bvar>
          <ci> ATPi </ci>
        </apply>
        <apply>
          <minus/>
          <apply>
            <times/>
            <ci> k_ADP </ci>
            <ci> ADPi </ci>
          </apply>
          <apply>
            <plus/>
            <apply>
              <divide/>
              <apply>
                <plus/>
                <ci> i_NaK </ci>
                <ci> i_CRAN </ci>
              </apply>
              <apply>
                <times/>
                <ci> Vi </ci>
                <ci> F </ci>
              </apply>
            </apply>
            <apply>
              <divide/>
              <ci> Jer_p </ci>
              <cn cellml:units="dimensionless"> 2.0 </cn>
            </apply>
            <apply>
              <times/>
              <apply>
                <plus/>
                <apply>
                  <times/>
                  <ci> k_ATP_Ca </ci>
                  <ci> Cai </ci>
                </apply>
                <ci> k_ATP </ci>
              </apply>
              <ci> ATPi </ci>
            </apply>
          </apply>         
        </apply>
      </apply>
      
      <apply>
        <eq/>
        <ci> ADPi </ci>
        <apply>
          <minus/>
          <ci> Ao </ci>
          <ci> ATPi </ci>
        </apply>
      </apply>      
    </math>
  </component>
  
  <component cmeta:id="id_00093" name="cell_and_external_parameters">
    <variable initial_value="2.6" name="Cao" public_interface="out" units="millimolar"/>
    <variable initial_value="140.0" name="Nao" public_interface="out" units="millimolar"/>
    <variable initial_value="8.0" name="Ko" public_interface="out" units="millimolar"/>
    <variable initial_value="132.4" name="Ki" public_interface="out" units="millimolar"/>
    <variable initial_value="8314.0" name="R" public_interface="out" units="joule_per_kilomole_kelvin"/>
    <variable initial_value="310.0" name="T" public_interface="out" units="kelvin"/>
    <variable initial_value="96500.0" name="F" public_interface="out" units="coulomb_per_mole"/>
    <variable initial_value="0.764" name="Vi" public_interface="out" units="picol"/>
  </component>
  
  <group>
    <relationship_ref relationship="containment"/>
    <component_ref component="membrane">
      <component_ref component="whole_cell_calcium_current">
        <component_ref component="whole_cell_calcium_current_p_VCa_gate"/>
      </component_ref>
      <component_ref component="PM_calcium_pumps"/>
      <component_ref component="sodium_calcium_exchanger"/>
      <component_ref component="nonselective_cation_current"/>
      <component_ref component="sodium_current">
        <component_ref component="sodium_current_p_Na_gate"/>
      </component_ref>
      <component_ref component="voltage_dependent_potassium_current">
        <component_ref component="voltage_dependent_potassium_current_n_gate"/>
      </component_ref>
      <component_ref component="calcium_dependent_potassium_current">
       <component_ref component="calcium_dependent_potassium_current_fCa_gate"/>
      </component_ref>
      <component_ref component="sodium_potassium_active_transport"/>
      <component_ref component="ATP_dependent_potassium_current"/>
      <component_ref component="SERCA_pump"/>
      <component_ref component="IP3_metabolism"/>
      <component_ref component="CaER_mobilisation"/>
      <component_ref component="calcium_and_sodium_dynamics"/>
      <component_ref component="ATP_homeostasis"/>
      <component_ref component="cell_and_external_parameters"/>
    </component_ref>
  </group>
  
  <group>
    <relationship_ref relationship="encapsulation"/>
    <component_ref component="whole_cell_calcium_current">
      <component_ref component="whole_cell_calcium_current_p_VCa_gate"/>
    </component_ref>
    <component_ref component="sodium_current">
      <component_ref component="sodium_current_p_Na_gate"/>
    </component_ref>
    <component_ref component="voltage_dependent_potassium_current">
      <component_ref component="voltage_dependent_potassium_current_n_gate"/>
    </component_ref>
    <component_ref component="calcium_dependent_potassium_current">
      <component_ref component="calcium_dependent_potassium_current_fCa_gate"/>
    </component_ref>
  </group>
  
  
  <connection>
    <map_components component_1="membrane" component_2="environment"/>
    <map_variables variable_1="time" variable_2="time"/>
  </connection>
  
  <connection>
    <map_components component_1="IP3_metabolism" component_2="environment"/>
    <map_variables variable_1="time" variable_2="time"/>
  </connection>
  
  <connection>
    <map_components component_1="calcium_and_sodium_dynamics" component_2="environment"/>
    <map_variables variable_1="time" variable_2="time"/>
  </connection>
  
  <connection>
    <map_components component_1="ATP_homeostasis" component_2="environment"/>
    <map_variables variable_1="time" variable_2="time"/>
  </connection>
  
  <connection>
    <map_components component_1="voltage_dependent_potassium_current" component_2="environment"/>
    <map_variables variable_1="time" variable_2="time"/>
  </connection>
  
  <connection>
    <map_components component_1="membrane" component_2="whole_cell_calcium_current"/>
    <map_variables variable_1="i_VCa" variable_2="i_VCa"/>
    <map_variables variable_1="V" variable_2="V"/>
  </connection>
  
  <connection>
    <map_components component_1="membrane" component_2="PM_calcium_pumps"/>
    <map_variables variable_1="i_Ca_pump" variable_2="i_Ca_pump"/>
  </connection>
  
  <connection>
    <map_components component_1="membrane" component_2="sodium_calcium_exchanger"/>
    <map_variables variable_1="i_NaCa" variable_2="i_NaCa"/>
    <map_variables variable_1="V" variable_2="V"/>
  </connection>
  
  <connection>
    <map_components component_1="membrane" component_2="sodium_potassium_active_transport"/>
    <map_variables variable_1="i_NaK" variable_2="i_NaK"/>
    <map_variables variable_1="V" variable_2="V"/>
  </connection>
  
  <connection>
    <map_components component_1="membrane" component_2="nonselective_cation_current"/>
    <map_variables variable_1="i_CRAN" variable_2="i_CRAN"/>
    <map_variables variable_1="V" variable_2="V"/>
  </connection>
  
  <connection>
    <map_components component_1="membrane" component_2="sodium_current"/>
    <map_variables variable_1="i_Na" variable_2="i_Na"/>
    <map_variables variable_1="V" variable_2="V"/>
  </connection>
  
  <connection>
    <map_components component_1="membrane" component_2="voltage_dependent_potassium_current"/>
    <map_variables variable_1="i_KDr" variable_2="i_KDr"/>
    <map_variables variable_1="V" variable_2="V"/>
  </connection>
  
  <connection>
    <map_components component_1="membrane" component_2="calcium_dependent_potassium_current"/>
    <map_variables variable_1="i_KCa" variable_2="i_KCa"/>
    <map_variables variable_1="V" variable_2="V"/>
  </connection>
  
  <connection>
    <map_components component_1="membrane" component_2="ATP_dependent_potassium_current"/>
    <map_variables variable_1="i_KATP" variable_2="i_KATP"/>
    <map_variables variable_1="V" variable_2="V"/>
  </connection>
  
  <connection>
    <map_components component_1="calcium_and_sodium_dynamics" component_2="whole_cell_calcium_current"/>
    <map_variables variable_1="Cai" variable_2="Cai"/>
    <map_variables variable_1="i_VCa" variable_2="i_VCa"/>
  </connection>
  
  <connection>
    <map_components component_1="calcium_and_sodium_dynamics" component_2="PM_calcium_pumps"/>
    <map_variables variable_1="Cai" variable_2="Cai"/>
    <map_variables variable_1="i_Ca_pump" variable_2="i_Ca_pump"/>
  </connection>
  
  <connection>
    <map_components component_1="calcium_and_sodium_dynamics" component_2="sodium_calcium_exchanger"/>
    <map_variables variable_1="Cai" variable_2="Cai"/>
    <map_variables variable_1="Nai" variable_2="Nai"/>
    <map_variables variable_1="i_NaCa" variable_2="i_NaCa"/>
  </connection>
  
  <connection>
    <map_components component_1="calcium_and_sodium_dynamics" component_2="sodium_potassium_active_transport"/>
    <map_variables variable_1="Nai" variable_2="Nai"/>
    <map_variables variable_1="i_NaK" variable_2="i_NaK"/>
  </connection>
  
  <connection>
    <map_components component_1="calcium_and_sodium_dynamics" component_2="nonselective_cation_current"/>
    <map_variables variable_1="CaER" variable_2="CaER"/>
    <map_variables variable_1="i_CRAN" variable_2="i_CRAN"/>
  </connection>
  
  <connection>
    <map_components component_1="calcium_and_sodium_dynamics" component_2="sodium_current"/>
    <map_variables variable_1="Nai" variable_2="Nai"/>
    <map_variables variable_1="i_Na" variable_2="i_Na"/>
  </connection>
  
  <connection>
    <map_components component_1="calcium_and_sodium_dynamics" component_2="calcium_dependent_potassium_current"/>
    <map_variables variable_1="Cai" variable_2="Cai"/>
  </connection>
  
  <connection>
    <map_components component_1="calcium_and_sodium_dynamics" component_2="SERCA_pump"/>
    <map_variables variable_1="Cai" variable_2="Cai"/>
    <map_variables variable_1="Jer_p" variable_2="Jer_p"/>
  </connection>
  
  <connection>
    <map_components component_1="calcium_and_sodium_dynamics" component_2="IP3_metabolism"/>
    <map_variables variable_1="Cai" variable_2="Cai"/>
  </connection>
  
  <connection>
    <map_components component_1="calcium_and_sodium_dynamics" component_2="CaER_mobilisation"/>
    <map_variables variable_1="CaER" variable_2="CaER"/>
    <map_variables variable_1="Cai" variable_2="Cai"/>
    <map_variables variable_1="J_out" variable_2="J_out"/>
  </connection>
  
  <connection>
    <map_components component_1="calcium_and_sodium_dynamics" component_2="ATP_homeostasis"/>
    <map_variables variable_1="Cai" variable_2="Cai"/>
  </connection>
  
  <connection>
    <map_components component_1="cell_and_external_parameters" component_2="whole_cell_calcium_current"/>
    <map_variables variable_1="Cao" variable_2="Cao"/>
    <map_variables variable_1="R" variable_2="R"/>
    <map_variables variable_1="T" variable_2="T"/>
    <map_variables variable_1="F" variable_2="F"/>
  </connection>
  
  <connection>
    <map_components component_1="cell_and_external_parameters" component_2="sodium_calcium_exchanger"/>
    <map_variables variable_1="Cao" variable_2="Cao"/>
    <map_variables variable_1="Nao" variable_2="Nao"/>
    <map_variables variable_1="R" variable_2="R"/>
    <map_variables variable_1="T" variable_2="T"/>
    <map_variables variable_1="F" variable_2="F"/>
  </connection>
  
  <connection>
    <map_components component_1="cell_and_external_parameters" component_2="sodium_potassium_active_transport"/>
    <map_variables variable_1="Ko" variable_2="Ko"/>
    <map_variables variable_1="Nao" variable_2="Nao"/>
    <map_variables variable_1="R" variable_2="R"/>
    <map_variables variable_1="T" variable_2="T"/>
    <map_variables variable_1="F" variable_2="F"/>
  </connection>
  
  <connection>
    <map_components component_1="cell_and_external_parameters" component_2="sodium_current"/>
    <map_variables variable_1="Nao" variable_2="Nao"/>
    <map_variables variable_1="R" variable_2="R"/>
    <map_variables variable_1="T" variable_2="T"/>
    <map_variables variable_1="F" variable_2="F"/>
  </connection>
  
  <connection>
    <map_components component_1="cell_and_external_parameters" component_2="voltage_dependent_potassium_current"/>
    <map_variables variable_1="Ko" variable_2="Ko"/>
    <map_variables variable_1="Ki" variable_2="Ki"/>
    <map_variables variable_1="R" variable_2="R"/>
    <map_variables variable_1="T" variable_2="T"/>
    <map_variables variable_1="F" variable_2="F"/>
  </connection>
  
  <connection>
    <map_components component_1="cell_and_external_parameters" component_2="calcium_and_sodium_dynamics"/>
    <map_variables variable_1="F" variable_2="F"/>
    <map_variables variable_1="Vi" variable_2="Vi"/>
  </connection>
  
  <connection>
    <map_components component_1="cell_and_external_parameters" component_2="ATP_homeostasis"/>
    <map_variables variable_1="F" variable_2="F"/>
    <map_variables variable_1="Vi" variable_2="Vi"/>
  </connection>
  
  <connection>
    <map_components component_1="nonselective_cation_current" component_2="sodium_current"/>
    <map_variables variable_1="V_Na" variable_2="V_Na"/>
  </connection>
  
  <connection>
    <map_components component_1="voltage_dependent_potassium_current" component_2="calcium_dependent_potassium_current"/>
    <map_variables variable_1="V_K" variable_2="V_K"/>
  </connection>
  
  <connection>
    <map_components component_1="voltage_dependent_potassium_current" component_2="ATP_dependent_potassium_current"/>
    <map_variables variable_1="V_K" variable_2="V_K"/>
  </connection>
  
  <connection>
    <map_components component_1="IP3_metabolism" component_2="CaER_mobilisation"/>
    <map_variables variable_1="IP3i" variable_2="IP3i"/>
  </connection>
  
  <connection>
    <map_components component_1="ATP_homeostasis" component_2="PM_calcium_pumps"/>
    <map_variables variable_1="i_Ca_pump" variable_2="i_Ca_pump"/>
  </connection>
  
  <connection>
    <map_components component_1="ATP_homeostasis" component_2="sodium_potassium_active_transport"/>
    <map_variables variable_1="i_NaK" variable_2="i_NaK"/>
    <map_variables variable_1="ATPi" variable_2="ATPi"/>
    <map_variables variable_1="ADPi" variable_2="ADPi"/>
  </connection>
  
  <connection>
    <map_components component_1="ATP_homeostasis" component_2="SERCA_pump"/>
    <map_variables variable_1="Jer_p" variable_2="Jer_p"/>
  </connection>
  
  <connection>
    <map_components component_1="ATP_homeostasis" component_2="ATP_dependent_potassium_current"/>
    <map_variables variable_1="ATPi" variable_2="ATPi"/>
    <map_variables variable_1="ADPi" variable_2="ADPi"/>
  </connection>
  
  <connection>
    <map_components component_1="ATP_homeostasis" component_2="nonselective_cation_current"/>
    <map_variables variable_1="i_CRAN" variable_2="i_CRAN"/>
  </connection>
  
  <connection>
    <map_components component_1="whole_cell_calcium_current" component_2="whole_cell_calcium_current_p_VCa_gate"/>
    <map_variables variable_1="p_VCa" variable_2="p_VCa"/>
    <map_variables variable_1="V" variable_2="V"/>
  </connection>
  
  <connection>
    <map_components component_1="sodium_current" component_2="sodium_current_p_Na_gate"/>
    <map_variables variable_1="p_Na" variable_2="p_Na"/>
    <map_variables variable_1="V" variable_2="V"/>
  </connection>
  
  <connection>
    <map_components component_1="voltage_dependent_potassium_current" component_2="voltage_dependent_potassium_current_n_gate"/>
    <map_variables variable_1="n" variable_2="n"/>
    <map_variables variable_1="time" variable_2="time"/>
    <map_variables variable_1="V" variable_2="V"/>
  </connection>
  
  <connection>
    <map_components component_1="calcium_dependent_potassium_current" component_2="calcium_dependent_potassium_current_fCa_gate"/>
    <map_variables variable_1="fCa" variable_2="fCa"/>
    <map_variables variable_1="Cai" variable_2="Cai"/>
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