Location: Chay, 1997 @ fd536f4617e3 / chay_1997.cellml

Author:
pmr2.import <nobody@models.cellml.org>
Date:
2007-04-11 23:51:37+12:00
Desc:
committing version02 of chay_1997
Permanent Source URI:
https://models.cellml.org/workspace/chay_1997/rawfile/fd536f4617e3256bd804c2b20d75f99cca00d320/chay_1997.cellml

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COR (0.9.31.397)
Copyright 2002-2006 Oxford Cardiac Electrophysiology Group
http://COR.physiol.ox.ac.uk/ - COR@physiol.ox.ac.uk

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http://www.CellML.org/
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<article>
  <articleinfo>
  <title>Extracellular And Intracellular Calcium Effects On Pancreatic Beta-Cells</title>
  <author>
    <firstname>Catherine</firstname>
          <surname>Lloyd</surname>
    <affiliation>
      <shortaffil>Oxford University</shortaffil>
    </affiliation>
  </author>
</articleinfo>
  <section id="sec_status">
    <title>Model Status</title>
    <para>
            This model was corrected by Penny Noble, Oxford University.
          </para>
  </section>
  <sect1 id="sec_structure">
<title>Model Structure</title>

<para>
When exposed to a threshold concentration of glucose, pancreatic beta-cells exhibit a complicated pattern of electrical activity.  Bursts of action potential spikes (the "active" phase) are observed, separated by a "silent" phase of membrane repolarisation.  At even higher glucose concentrations, continuous action potentials are seen.  This electrical activity is influenced by the extracellular calcium concentration ([Ca<superscript>2+</superscript>]<subscript>o</subscript>).  Specifically, in a mouse pancreatic beta-cell in a medium containing a moderate amount of glucose, an increase in [Ca<superscript>2+</superscript>]<subscript>o</subscript> lowers the repolarisation potential, raises the plateau potential and shortens the spike and plateau durations.  The mechanisms underlying these affects are not well understood.
</para>

<para>  
In her 1997 paper, Teresa Chay elucidates the role of extracellular calcium concentration in influencing electrical activity, intracellular calcium concentration, and the luminal calcium concentration in the intracellular calcium store of pancreatic beta-cells.  She studies the extracellular calcium effect using a mathematical model which includes seven currents across the plasma membrane and two calcium fluxes across the membrane of the endoplasmic reticulum (ER) (see <xref linkend="fig_cell_diagram"/> below).
</para>

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

<para>
<ulink url="http://www.biophysj.org/cgi/content/abstract/73/3/1673">Effects of extracellular Calcium on Electrical Bursting and Intracellular  and Luminal Calcium Oscillations in Insulin Secreting Pancreatic Beta-Cells</ulink>, Teresa Ree Chay, 1997, <ulink url="http://www.biophysj.org/">
            <emphasis>Biophysical Journal</emphasis>
          </ulink>, 73, 1673-1688.  <ulink url="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&amp;db=PubMed&amp;list_uids=9284334&amp;dopt=Abstract">PubMed ID: 9284334</ulink>  
</para>

<para>
The raw CellML description of the model can be downloaded in various formats as described in <xref linkend="sec_download_this_model"/>
</para>

<informalfigure float="0" id="fig_cell_diagram">
<mediaobject>
  <imageobject>
    <objectinfo>
      <title>diagram of the mitochondrial Ca2+ handling model</title>
    </objectinfo>
    <imagedata fileref="cell_diagram.gif"/>
  </imageobject>
</mediaobject>
<caption>A schematic representation of the current and fluxes captured by the Chay 1997 pancreatic beta-cell model.  This diagram shows the plasma membrane currents associated with burst and spike oscillations: the fast current, I<subscript>fast</subscript>; the calcium current, I <subscript>Ca<superscript>2+</superscript>
            </subscript>; the cationic nonselective inward current, I<subscript>NS</subscript>; the delayed-rectifying K<superscript>+</superscript> current, I<subscript>K(dr)</subscript>, the calcium-sensitive K<superscript>+</superscript> current, I<subscript>K(Ca)</subscript>; the ATP-sensitive K<superscript>+</superscript> current, I<subscript>K(ATP)</subscript>; and the Na<superscript>+</superscript> leak current, I<subscript>Na(L)</subscript>.  The ER intracellular Ca<superscript>2+</superscript> store is also shown with its associated transmembrane calcium fluxes: calcium release, J<subscript>rel</subscript>; and calcium uptake by the Ca<superscript>2+</superscript>-ATPase, J<subscript>pump</subscript>.</caption>
</informalfigure>

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

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                           <apply>
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                              <ci>Vn</ci>
                              <ci>V</ci>
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                              <cn cellml:units="dimensionless">2</cn>
                              <ci>Sn</ci>
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                        </apply>
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                     <apply>
                        <exp/>
                        <apply>
                           <divide/>
                           <apply>
                              <minus/>
                              <ci>V</ci>
                              <ci>Vn</ci>
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                              <ci>Sn</ci>
                           </apply>
                        </apply>
                     </apply>
                  </apply>
               </apply>
            </apply>
         </apply>
      </math>
   </component>
   <component name="Ca_sensitive_K_current">
      <variable units="nanoA_per_cm2" public_interface="out" name="i_K_Ca"/>
      <variable units="microS_per_cm2" name="g_K_Ca" initial_value="5"/>
      <variable units="micromolar" public_interface="in" name="K_Ca"/>
      <variable units="second" public_interface="in" name="time"/>
      <variable units="millivolt" public_interface="in" name="V"/>
      <variable units="millivolt" public_interface="in" name="V_K"/>
      <variable units="micromolar" public_interface="in" name="Ca_i"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <ci>i_K_Ca</ci>
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               <times/>
               <apply>
                  <divide/>
                  <apply>
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                        <power/>
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                     <plus/>
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                        <ci>K_Ca</ci>
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                     <apply>
                        <power/>
                        <ci>Ca_i</ci>
                        <cn cellml:units="dimensionless">3</cn>
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               <apply>
                  <minus/>
                  <ci>V</ci>
                  <ci>V_K</ci>
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            </apply>
         </apply>
      </math>
   </component>
   <component name="ATP_sensitive_K_current">
      <variable units="nanoA_per_cm2" public_interface="out" name="i_K_ATP"/>
      <variable units="microS_per_cm2" name="g_K_ATP" initial_value="2"/>
      <variable units="second" public_interface="in" name="time"/>
      <variable units="millivolt" public_interface="in" name="V"/>
      <variable units="millivolt" public_interface="in" name="V_K"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
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               <ci>g_K_ATP</ci>
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                  <minus/>
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                  <ci>V_K</ci>
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            </apply>
         </apply>
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   <component name="Na_leak_current">
      <variable units="nanoA_per_cm2" public_interface="out" name="i_NaL"/>
      <variable units="microS_per_cm2" name="g_NaL" initial_value="0.3"/>
      <variable units="millivolt" name="V_Na" initial_value="80"/>
      <variable units="second" public_interface="in" name="time"/>
      <variable units="millivolt" public_interface="in" name="V"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
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               <times/>
               <ci>g_NaL</ci>
               <apply>
                  <minus/>
                  <ci>V</ci>
                  <ci>V_Na</ci>
               </apply>
            </apply>
         </apply>
      </math>
   </component>
   <component name="cytosolic_calcium">
      <variable units="micromolar" public_interface="out" name="Ca_i" initial_value="0.6959466"/>
      <variable units="micromolar" public_interface="out" name="Ca_lum" initial_value="102.686"/>
      <variable units="per_second" name="k_rel" initial_value="0.2"/>
      <variable units="per_second" name="k_Ca" initial_value="7"/>
      <variable units="per_second" name="k_pump" initial_value="30"/>
      <variable units="dimensionless" name="omega" initial_value="0.2"/>
      <variable units="nanoA_per_cm2" public_interface="in" name="i_Ca"/>
      <variable units="second" public_interface="in" name="time"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <apply>
               <diff/>
               <bvar>
                  <ci>time</ci>
               </bvar>
               <ci>Ca_i</ci>
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            <apply>
               <minus/>
               <apply>
                  <times/>
                  <ci>k_rel</ci>
                  <apply>
                     <minus/>
                     <ci>Ca_lum</ci>
                     <ci>Ca_i</ci>
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               <apply>
                  <plus/>
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                     <ci>omega</ci>
                     <ci>i_Ca</ci>
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                  <apply>
                     <times/>
                     <ci>k_Ca</ci>
                     <ci>Ca_i</ci>
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                  <apply>
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            </apply>
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         <apply>
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               <ci>Ca_lum</ci>
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            <apply>
               <plus/>
               <apply>
                  <times/>
                  <apply>
                     <minus/>
                     <ci>k_rel</ci>
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                  <apply>
                     <minus/>
                     <ci>Ca_lum</ci>
                     <ci>Ca_i</ci>
                  </apply>
               </apply>
               <apply>
                  <times/>
                  <ci>k_pump</ci>
                  <ci>Ca_i</ci>
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            </apply>
         </apply>
      </math>
   </component>
   <group>
      <relationship_ref relationship="containment"/>
      <component_ref component="membrane">
         <component_ref component="fast_current">
            <component_ref component="fast_current_m_gate"/>
            <component_ref component="fast_current_h_gate"/>
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         <component_ref component="calcium_current">
            <component_ref component="calcium_current_d_gate"/>
            <component_ref component="calcium_current_f_gate"/>
         </component_ref>
         <component_ref component="cationic_nonselective_inward_current"/>
         <component_ref component="delayed_rectifier_K_channel_current">
            <component_ref component="delayed_rectifier_K_channel_current_n_gate"/>
         </component_ref>
         <component_ref component="Ca_sensitive_K_current"/>
         <component_ref component="ATP_sensitive_K_current"/>
         <component_ref component="Na_leak_current"/>
         <component_ref component="cytosolic_calcium"/>
      </component_ref>
   </group>
   <group>
      <relationship_ref relationship="encapsulation"/>
      <component_ref component="fast_current">
         <component_ref component="fast_current_m_gate"/>
         <component_ref component="fast_current_h_gate"/>
      </component_ref>
      <component_ref component="calcium_current">
         <component_ref component="calcium_current_d_gate"/>
         <component_ref component="calcium_current_f_gate"/>
      </component_ref>
      <component_ref component="delayed_rectifier_K_channel_current">
         <component_ref component="delayed_rectifier_K_channel_current_n_gate"/>
      </component_ref>
   </group>
   <connection>
      <map_components component_2="environment" component_1="membrane"/>
      <map_variables variable_2="time" variable_1="time"/>
   </connection>
   <connection>
      <map_components component_2="environment" component_1="fast_current"/>
      <map_variables variable_2="time" variable_1="time"/>
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   <connection>
      <map_components component_2="environment" component_1="calcium_current"/>
      <map_variables variable_2="time" variable_1="time"/>
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   <connection>
      <map_components component_2="environment" component_1="cationic_nonselective_inward_current"/>
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   <connection>
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   <connection>
      <map_components component_2="environment" component_1="Ca_sensitive_K_current"/>
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   <connection>
      <map_components component_2="environment" component_1="ATP_sensitive_K_current"/>
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   <connection>
      <map_components component_2="environment" component_1="Na_leak_current"/>
      <map_variables variable_2="time" variable_1="time"/>
   </connection>
   <connection>
      <map_components component_2="environment" component_1="cytosolic_calcium"/>
      <map_variables variable_2="time" variable_1="time"/>
   </connection>
   <connection>
      <map_components component_2="membrane" component_1="fast_current"/>
      <map_variables variable_2="V" variable_1="V"/>
      <map_variables variable_2="i_fast" variable_1="i_fast"/>
   </connection>
   <connection>
      <map_components component_2="membrane" component_1="calcium_current"/>
      <map_variables variable_2="V" variable_1="V"/>
      <map_variables variable_2="i_Ca" variable_1="i_Ca"/>
      <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="membrane" component_1="cationic_nonselective_inward_current"/>
      <map_variables variable_2="V" variable_1="V"/>
      <map_variables variable_2="i_NS" variable_1="i_NS"/>
   </connection>
   <connection>
      <map_components component_2="membrane" component_1="delayed_rectifier_K_channel_current"/>
      <map_variables variable_2="V" variable_1="V"/>
      <map_variables variable_2="i_K_dr" variable_1="i_K_dr"/>
   </connection>
   <connection>
      <map_components component_2="membrane" component_1="Ca_sensitive_K_current"/>
      <map_variables variable_2="V" variable_1="V"/>
      <map_variables variable_2="i_K_Ca" variable_1="i_K_Ca"/>
   </connection>
   <connection>
      <map_components component_2="membrane" component_1="ATP_sensitive_K_current"/>
      <map_variables variable_2="V" variable_1="V"/>
      <map_variables variable_2="i_K_ATP" variable_1="i_K_ATP"/>
   </connection>
   <connection>
      <map_components component_2="membrane" component_1="Na_leak_current"/>
      <map_variables variable_2="V" variable_1="V"/>
      <map_variables variable_2="i_NaL" variable_1="i_NaL"/>
   </connection>
   <connection>
      <map_components component_2="cytosolic_calcium" component_1="calcium_current"/>
      <map_variables variable_2="i_Ca" variable_1="i_Ca"/>
      <map_variables variable_2="Ca_i" variable_1="Ca_i"/>
   </connection>
   <connection>
      <map_components component_2="cytosolic_calcium" component_1="Ca_sensitive_K_current"/>
      <map_variables variable_2="Ca_i" variable_1="Ca_i"/>
   </connection>
   <connection>
      <map_components component_2="Ca_sensitive_K_current" component_1="calcium_current"/>
      <map_variables variable_2="K_Ca" variable_1="K_Ca"/>
   </connection>
   <connection>
      <map_components component_2="ATP_sensitive_K_current" component_1="delayed_rectifier_K_channel_current"/>
      <map_variables variable_2="V_K" variable_1="V_K"/>
   </connection>
   <connection>
      <map_components component_2="Ca_sensitive_K_current" component_1="delayed_rectifier_K_channel_current"/>
      <map_variables variable_2="V_K" variable_1="V_K"/>
   </connection>
   <connection>
      <map_components component_2="cytosolic_calcium" component_1="cationic_nonselective_inward_current"/>
      <map_variables variable_2="Ca_lum" variable_1="Ca_lum"/>
   </connection>
   <connection>
      <map_components component_2="fast_current_m_gate" component_1="fast_current"/>
      <map_variables variable_2="m_infinity" variable_1="m_infinity"/>
      <map_variables variable_2="time" variable_1="time"/>
      <map_variables variable_2="V" variable_1="V"/>
   </connection>
   <connection>
      <map_components component_2="fast_current_h_gate" component_1="fast_current"/>
      <map_variables variable_2="h" variable_1="h"/>
      <map_variables variable_2="time" variable_1="time"/>
      <map_variables variable_2="V" variable_1="V"/>
   </connection>
   <connection>
      <map_components component_2="calcium_current_f_gate" component_1="calcium_current"/>
      <map_variables variable_2="f_infinity" variable_1="f_infinity"/>
      <map_variables variable_2="Ca_i" variable_1="Ca_i"/>
      <map_variables variable_2="K_Ca" variable_1="K_Ca"/>
   </connection>
   <connection>
      <map_components component_2="calcium_current_d_gate" component_1="calcium_current"/>
      <map_variables variable_2="d" variable_1="d"/>
      <map_variables variable_2="time" variable_1="time"/>
      <map_variables variable_2="V" variable_1="V"/>
   </connection>
   <connection>
      <map_components component_2="delayed_rectifier_K_channel_current_n_gate" component_1="delayed_rectifier_K_channel_current"/>
      <map_variables variable_2="n" variable_1="n"/>
      <map_variables variable_2="time" variable_1="time"/>
      <map_variables variable_2="V" variable_1="V"/>
   </connection>


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        The Chay et al 1997 mathematical model of the effects of extracellular 
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           Effects of extracellular calcium on electrical bursting and                      intracellular and luminal calcium oscillations in insulin secreting              pancreatic beta-cells
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