Rendering of the source text

<?xml version='1.0' encoding='utf-8'?>
<!--  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: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="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>
  
  
  
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    <variable units="millivolt" public_interface="in" name="V"/>
    
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    <variable units="second_order_rate_constant" name="f5"/>
    <variable units="first_order_rate_constant" name="f6" initial_value="11.5"/>
    <variable units="first_order_rate_constant" name="b1" initial_value="100.0"/>
    <variable units="second_order_rate_constant" name="b2" initial_value="0.0001"/>
    <variable units="forth_order_rate_constant" name="b3" initial_value="1.72E-17"/>
    <variable units="second_order_rate_constant" name="b4" initial_value="0.0002"/>
    <variable units="first_order_rate_constant" name="b5_" initial_value="0.03"/>
    <variable units="first_order_rate_constant" name="b5"/>
    <variable units="second_order_rate_constant" name="b6" initial_value="6.0E-7"/>
    <variable units="first_order_rate_constant" name="B2"/>
    <variable units="first_order_rate_constant" name="B3"/>
    <variable units="first_order_rate_constant" name="B4"/>
    <variable units="first_order_rate_constant" name="B6"/>
    <variable units="dimensionless" name="D"/>
    
    <variable units="millivolt" public_interface="in" name="V"/>
    <variable units="joule_per_kilomole_kelvin" public_interface="in" name="R"/>
    <variable units="coulomb_per_mole" public_interface="in" name="F"/>
    <variable units="kelvin" public_interface="in" name="T"/>
    <variable units="micromolar" public_interface="in" name="Nai"/>
    <variable units="micromolar" public_interface="in" name="Nao"/>
    <variable units="micromolar" public_interface="in" name="ATPi"/>
    <variable units="micromolar" public_interface="in" name="ADPi"/>
    <variable units="micromolar" public_interface="in" name="Ko"/>
   
    <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 name="voltage_dependent_potassium_current">
    <variable units="femtoA" public_interface="out" name="i_KDr"/>
    <variable units="millivolt" public_interface="out" name="V_K"/>
    
    <variable units="picoS" name="gm_KDr" initial_value="3000.0"/>
    
    <variable units="millisecond" public_interface="in" private_interface="out" name="time"/>
    <variable units="millivolt" public_interface="in" private_interface="out" name="V"/>
    <variable units="joule_per_kilomole_kelvin" public_interface="in" name="R"/>
    <variable units="coulomb_per_mole" public_interface="in" name="F"/>
    <variable units="kelvin" public_interface="in" name="T"/>
    <variable units="micromolar" public_interface="in" name="Ki"/>
    <variable units="micromolar" public_interface="in" name="Ko"/>
   
    <variable units="dimensionless" private_interface="in" name="n"/>
    
    <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 name="voltage_dependent_potassium_current_n_gate">
    <variable units="dimensionless" public_interface="out" name="n" initial_value="0.00123"/>
    
    <variable units="dimensionless" name="tau_n"/>
    <variable units="dimensionless" name="n_infinity"/>
    <variable units="millivolt" name="Vn" initial_value="-14.0"/>
    <variable units="millivolt" name="Vtau" initial_value="-75.0"/>
    <variable units="millivolt" name="Sn" initial_value="7.0"/>
    <variable units="millivolt" name="a" initial_value="65.0"/>
    <variable units="millivolt" name="b" initial_value="20.0"/>
    <variable units="millisecond" name="c" initial_value="20.0"/>
    
    <variable units="millivolt" public_interface="in" name="V"/>
    <variable units="millisecond" public_interface="in" name="time"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML">
       <apply 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 name="calcium_dependent_potassium_current">
    <variable units="femtoA" public_interface="out" name="i_KCa"/>
    
    <variable units="picoS" name="gm_KCa" initial_value="130.0"/>
    
    <variable units="millivolt" public_interface="in" name="V_K"/>
    <variable units="millivolt" public_interface="in" name="V"/>
    <variable units="micromolar" public_interface="in" private_interface="out" name="Cai"/>
    
    <variable units="dimensionless" private_interface="in" name="fCa"/>
    
    <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 name="calcium_dependent_potassium_current_fCa_gate">
    <variable units="dimensionless" public_interface="out" name="fCa"/>
    
    <variable units="micromolar" name="K_KCa" initial_value="0.1"/>
    
    <variable units="micromolar" public_interface="in" name="Cai"/>
    
    <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 name="ATP_dependent_potassium_current">
    <variable units="femtoA" public_interface="out" name="i_KATP"/>
    
    <variable units="picoS" name="gm_KATP" initial_value="24000.0"/>
    <variable units="dimensionless" name="O_KATP"/>
    <variable units="micromolar" name="Kdd" initial_value="17.0"/>
    <variable units="micromolar" name="Ktd" initial_value="26.0"/>
    <variable units="micromolar" name="Ktt" initial_value="1.0"/>
    
    <variable units="millivolt" public_interface="in" name="V"/>
    <variable units="millivolt" public_interface="in" name="V_K"/>
    <variable units="micromolar" public_interface="in" name="ADPi"/>
    <variable units="micromolar" public_interface="in" name="ATPi"/>
    
    <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 name="SERCA_pump">
    <variable units="flux" public_interface="out" name="Jer_p"/>
    
    <variable units="flux" name="P_CaER" initial_value="0.105"/>
    <variable units="micromolar" name="K_Carp" initial_value="0.5"/>
    
    <variable units="micromolar" public_interface="in" name="Cai"/>
    
    <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 name="IP3_metabolism">
    <variable units="micromolar" public_interface="out" name="IP3i" initial_value="0.33"/>
    
    <variable units="flux" name="kIP" initial_value="0.0003"/>
    <variable units="first_order_rate_constant" name="kdIP" initial_value="0.00004"/>
    <variable units="micromolar" name="K_IPCa" initial_value="0.4"/>
    
    <variable units="micromolar" public_interface="in" name="Cai"/>
    <variable units="millisecond" public_interface="in" name="time"/>
    
    <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 units="flux" public_interface="out" name="J_out"/>
    
    <variable units="picol_per_ms" name="P_leak" initial_value="0.0001"/>
    <variable units="picol_per_ms" name="P_IP3" initial_value="0.0012"/>
    <variable units="dimensionless" name="O_infinity"/>
    <variable units="micromolar" name="K_RCa" initial_value="3.2"/>
    <variable units="micromolar" name="K_IP3" initial_value="0.077"/>
    
    <variable units="micromolar" public_interface="in" name="IP3i"/>
    <variable units="micromolar" public_interface="in" name="Cai"/>
    <variable units="micromolar" public_interface="in" name="CaER"/>
    
    <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 name="calcium_and_sodium_dynamics">
    <variable units="micromolar" public_interface="out" name="Cai" initial_value="0.085"/>
    <variable units="micromolar" public_interface="out" name="CaER" initial_value="22.8"/>
    <variable units="micromolar" public_interface="out" name="Nai" initial_value="9858.0"/>
    
    <variable units="dimensionless" name="fi" initial_value="0.01"/>
    <variable units="dimensionless" name="fer" initial_value="0.03"/>
    <variable units="first_order_rate_constant" name="ksg" initial_value="0.0001"/>
    <variable units="picol" name="Ver" initial_value="0.280"/>
    
    <variable units="picol" public_interface="in" name="Vi"/>
    <variable units="femtoA" public_interface="in" name="i_VCa"/>
    <variable units="femtoA" public_interface="in" name="i_NaCa"/>
    <variable units="femtoA" public_interface="in" name="i_Ca_pump"/>
    <variable units="femtoA" public_interface="in" name="i_NaK"/>
    <variable units="femtoA" public_interface="in" name="i_Na"/>
    <variable units="femtoA" public_interface="in" name="i_CRAN"/>
    <variable units="coulomb_per_mole" public_interface="in" name="F"/>
    <variable units="flux" public_interface="in" name="J_out"/>
    <variable units="flux" public_interface="in" name="Jer_p"/>
    <variable units="millisecond" public_interface="in" name="time"/>
    
    <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/>
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    <variable units="millimolar" public_interface="out" name="ADPi"/>
    
    <variable units="first_order_rate_constant" name="k_ADP"/>
    <variable units="first_order_rate_constant" name="k_ATP" initial_value="0.00005"/>
    <variable units="second_order_rate_constant" name="k_ATP_Ca" initial_value="0.00005"/>
    <variable units="micromolar" name="Ao" initial_value="4000.0"/>
    
    <variable units="picol" public_interface="in" name="Vi"/>
    <variable units="micromolar" public_interface="in" name="Cai"/>
    <variable units="femtoA" public_interface="in" name="i_Ca_pump"/>
    <variable units="femtoA" public_interface="in" name="i_CRAN"/>
    <variable units="femtoA" public_interface="in" name="i_NaK"/>
    <variable units="coulomb_per_mole" public_interface="in" name="F"/>
    <variable units="flux" public_interface="in" name="Jer_p"/>
    <variable units="millisecond" public_interface="in" name="time"/>
    
    <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/>
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            <ci> ADPi </ci>
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          <apply>
            <plus/>
            <apply>
              <divide/>
              <apply>
                <plus/>
                <ci> i_NaK </ci>
                <ci> i_CRAN </ci>
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              <apply>
                <times/>
                <ci> Vi </ci>
                <ci> F </ci>
              </apply>
            </apply>
            <apply>
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              <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 name="cell_and_external_parameters">
    <variable units="millimolar" public_interface="out" name="Cao" initial_value="2.6"/>
    <variable units="millimolar" public_interface="out" name="Nao" initial_value="140.0"/>
    <variable units="millimolar" public_interface="out" name="Ko" initial_value="8.0"/>
    <variable units="millimolar" public_interface="out" name="Ki" initial_value="132.4"/>
    <variable units="joule_per_kilomole_kelvin" public_interface="out" name="R" initial_value="8314.0"/>
    <variable units="kelvin" public_interface="out" name="T" initial_value="310.0"/>
    <variable units="coulomb_per_mole" public_interface="out" name="F" initial_value="96500.0"/>
    <variable units="picol" public_interface="out" name="Vi" initial_value="0.764"/>
  </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>
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      <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_2="environment" component_1="membrane"/>
    <map_variables variable_2="time" variable_1="time"/>
  </connection>
  
  <connection>
    <map_components component_2="environment" component_1="IP3_metabolism"/>
    <map_variables variable_2="time" variable_1="time"/>
  </connection>
  
  <connection>
    <map_components component_2="environment" component_1="calcium_and_sodium_dynamics"/>
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  </connection>
  
  <connection>
    <map_components component_2="environment" component_1="ATP_homeostasis"/>
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  </connection>
  
  <connection>
    <map_components component_2="environment" component_1="voltage_dependent_potassium_current"/>
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  </connection>
  
  <connection>
    <map_components component_2="whole_cell_calcium_current" component_1="membrane"/>
    <map_variables variable_2="i_VCa" variable_1="i_VCa"/>
    <map_variables variable_2="V" variable_1="V"/>
  </connection>
  
  <connection>
    <map_components component_2="PM_calcium_pumps" component_1="membrane"/>
    <map_variables variable_2="i_Ca_pump" variable_1="i_Ca_pump"/>
  </connection>
  
  <connection>
    <map_components component_2="sodium_calcium_exchanger" component_1="membrane"/>
    <map_variables variable_2="i_NaCa" variable_1="i_NaCa"/>
    <map_variables variable_2="V" variable_1="V"/>
  </connection>
  
  <connection>
    <map_components component_2="sodium_potassium_active_transport" component_1="membrane"/>
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    <map_variables variable_2="V" variable_1="V"/>
  </connection>
  
  <connection>
    <map_components component_2="nonselective_cation_current" component_1="membrane"/>
    <map_variables variable_2="i_CRAN" variable_1="i_CRAN"/>
    <map_variables variable_2="V" variable_1="V"/>
  </connection>
  
  <connection>
    <map_components component_2="sodium_current" component_1="membrane"/>
    <map_variables variable_2="i_Na" variable_1="i_Na"/>
    <map_variables variable_2="V" variable_1="V"/>
  </connection>
  
  <connection>
    <map_components component_2="voltage_dependent_potassium_current" component_1="membrane"/>
    <map_variables variable_2="i_KDr" variable_1="i_KDr"/>
    <map_variables variable_2="V" variable_1="V"/>
  </connection>
  
  <connection>
    <map_components component_2="calcium_dependent_potassium_current" component_1="membrane"/>
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    <map_variables variable_2="V" variable_1="V"/>
  </connection>
  
  <connection>
    <map_components component_2="ATP_dependent_potassium_current" component_1="membrane"/>
    <map_variables variable_2="i_KATP" variable_1="i_KATP"/>
    <map_variables variable_2="V" variable_1="V"/>
  </connection>
  
  <connection>
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    <map_variables variable_2="Cai" variable_1="Cai"/>
    <map_variables variable_2="i_VCa" variable_1="i_VCa"/>
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  <connection>
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    <map_variables variable_2="i_Ca_pump" variable_1="i_Ca_pump"/>
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  <connection>
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    <map_variables variable_2="Cai" variable_1="Cai"/>
    <map_variables variable_2="Nai" variable_1="Nai"/>
    <map_variables variable_2="i_NaCa" variable_1="i_NaCa"/>
  </connection>
  
  <connection>
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    <map_variables variable_2="i_NaK" variable_1="i_NaK"/>
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  <connection>
    <map_components component_2="nonselective_cation_current" component_1="calcium_and_sodium_dynamics"/>
    <map_variables variable_2="CaER" variable_1="CaER"/>
    <map_variables variable_2="i_CRAN" variable_1="i_CRAN"/>
  </connection>
  
  <connection>
    <map_components component_2="sodium_current" component_1="calcium_and_sodium_dynamics"/>
    <map_variables variable_2="Nai" variable_1="Nai"/>
    <map_variables variable_2="i_Na" variable_1="i_Na"/>
  </connection>
  
  <connection>
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  <connection>
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    <map_variables variable_2="Cai" variable_1="Cai"/>
    <map_variables variable_2="Jer_p" variable_1="Jer_p"/>
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  <connection>
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  </connection>
  
  <connection>
    <map_components component_2="CaER_mobilisation" component_1="calcium_and_sodium_dynamics"/>
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    <map_variables variable_2="J_out" variable_1="J_out"/>
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  <connection>
    <map_components component_2="ATP_homeostasis" component_1="calcium_and_sodium_dynamics"/>
    <map_variables variable_2="Cai" variable_1="Cai"/>
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  <connection>
    <map_components component_2="whole_cell_calcium_current" component_1="cell_and_external_parameters"/>
    <map_variables variable_2="Cao" variable_1="Cao"/>
    <map_variables variable_2="R" variable_1="R"/>
    <map_variables variable_2="T" variable_1="T"/>
    <map_variables variable_2="F" variable_1="F"/>
  </connection>
  
  <connection>
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    <map_variables variable_2="Nao" variable_1="Nao"/>
    <map_variables variable_2="R" variable_1="R"/>
    <map_variables variable_2="T" variable_1="T"/>
    <map_variables variable_2="F" variable_1="F"/>
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  <connection>
    <map_components component_2="sodium_potassium_active_transport" component_1="cell_and_external_parameters"/>
    <map_variables variable_2="Ko" variable_1="Ko"/>
    <map_variables variable_2="Nao" variable_1="Nao"/>
    <map_variables variable_2="R" variable_1="R"/>
    <map_variables variable_2="T" variable_1="T"/>
    <map_variables variable_2="F" variable_1="F"/>
  </connection>
  
  <connection>
    <map_components component_2="sodium_current" component_1="cell_and_external_parameters"/>
    <map_variables variable_2="Nao" variable_1="Nao"/>
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    <map_variables variable_2="T" variable_1="T"/>
    <map_variables variable_2="F" variable_1="F"/>
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  <connection>
    <map_components component_2="voltage_dependent_potassium_current" component_1="cell_and_external_parameters"/>
    <map_variables variable_2="Ko" variable_1="Ko"/>
    <map_variables variable_2="Ki" variable_1="Ki"/>
    <map_variables variable_2="R" variable_1="R"/>
    <map_variables variable_2="T" variable_1="T"/>
    <map_variables variable_2="F" variable_1="F"/>
  </connection>
  
  <connection>
    <map_components component_2="calcium_and_sodium_dynamics" component_1="cell_and_external_parameters"/>
    <map_variables variable_2="F" variable_1="F"/>
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  </connection>
  
  <connection>
    <map_components component_2="ATP_homeostasis" component_1="cell_and_external_parameters"/>
    <map_variables variable_2="F" variable_1="F"/>
    <map_variables variable_2="Vi" variable_1="Vi"/>
  </connection>
  
  <connection>
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    <map_variables variable_2="V_Na" variable_1="V_Na"/>
  </connection>
  
  <connection>
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  </connection>
  
  <connection>
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    <map_variables variable_2="V_K" variable_1="V_K"/>
  </connection>
  
  <connection>
    <map_components component_2="CaER_mobilisation" component_1="IP3_metabolism"/>
    <map_variables variable_2="IP3i" variable_1="IP3i"/>
  </connection>
  
  <connection>
    <map_components component_2="PM_calcium_pumps" component_1="ATP_homeostasis"/>
    <map_variables variable_2="i_Ca_pump" variable_1="i_Ca_pump"/>
  </connection>
  
  <connection>
    <map_components component_2="sodium_potassium_active_transport" component_1="ATP_homeostasis"/>
    <map_variables variable_2="i_NaK" variable_1="i_NaK"/>
    <map_variables variable_2="ATPi" variable_1="ATPi"/>
    <map_variables variable_2="ADPi" variable_1="ADPi"/>
  </connection>
  
  <connection>
    <map_components component_2="SERCA_pump" component_1="ATP_homeostasis"/>
    <map_variables variable_2="Jer_p" variable_1="Jer_p"/>
  </connection>
  
  <connection>
    <map_components component_2="ATP_dependent_potassium_current" component_1="ATP_homeostasis"/>
    <map_variables variable_2="ATPi" variable_1="ATPi"/>
    <map_variables variable_2="ADPi" variable_1="ADPi"/>
  </connection>
  
  <connection>
    <map_components component_2="nonselective_cation_current" component_1="ATP_homeostasis"/>
    <map_variables variable_2="i_CRAN" variable_1="i_CRAN"/>
  </connection>
  
  <connection>
    <map_components component_2="whole_cell_calcium_current_p_VCa_gate" component_1="whole_cell_calcium_current"/>
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    <map_variables variable_2="V" variable_1="V"/>
  </connection>
  
  <connection>
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  </connection>
  
  <connection>
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    <map_variables variable_2="V" variable_1="V"/>
  </connection>
  
  <connection>
    <map_components component_2="calcium_dependent_potassium_current_fCa_gate" component_1="calcium_dependent_potassium_current"/>
    <map_variables variable_2="fCa" variable_1="fCa"/>
    <map_variables variable_2="Cai" variable_1="Cai"/>
  </connection>


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    <rdf:li>calcium dynamics</rdf:li>
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    <rdf:value>c.lloyd@auckland.ac.nz</rdf:value>
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    <vCard:Given>Leonid</vCard:Given>
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    <vCard:FN>Catherine Lloyd</vCard:FN>
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            Modeling of Ca2+ flux in pancreatic beta-cells: role of the plasma 
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    <vCard:Given>Louis</vCard:Given>
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Model Curation
  • Curation Status c0
  • JSim c0
  • COR c0
  • OpenCell c0
Source
Derived from workspace Fridlyand, Tamarina, Philipson, 2003 at changeset 78a543ec8519.
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License

This work is licensed under a Creative Commons Attribution 3.0 Unported License.