Location: Chay, 1997 @ d802e054fe42 / chay_1997.cellml

Author:
rcai987 <devnull@localhost>
Date:
2015-01-16 12:39:31+13:00
Desc:
Added annotations to chay_1997 model
Permanent Source URI:
https://models.cellml.org/workspace/chay_1997/rawfile/d802e054fe420d488fa7bc73f32c103269d20fff/chay_1997.cellml

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<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
  <articleinfo>
  <title>Extracellular And Intracellular Calcium Effects On Pancreatic Beta-Cells</title>
  <author>
    <firstname>Catherine</firstname>
          <surname>Lloyd</surname>
    <affiliation>
      <shortaffil>Auckland Bioengineering Institute, The university of Auckland</shortaffil>
    </affiliation>
  </author>
</articleinfo>
  <section id="sec_status">
    <title>Model Status</title>
    <para>
           This CellML model runs in both OpenCell and COR to reproduce the published results. The value for the variable 'Ca_o' in the component 'calcium_current' can be altered to 0, 2.5, 5 or 7.5 mM to reproduce figures 5 a,b,c,d, respectively.
          </para>
  </section>
  <sect1 id="sec_structure">
<title>Model Structure</title>

<para>
ABSTRACT: The extracellular calcium concentration has interesting effects on bursting of pancreatic beta-cells. The mechanism underlying the extracellular Ca2+ effect is not well understood. By incorporating a low-threshold transient inward current to the store-operated bursting model of Chay, this paper elucidates the role of the extracellular Ca2+ concentration in influencing electrical activity, intracellular Ca2+ concentration, and the luminal Ca2+ concentration in the intracellular Ca2+ store. The possibility that this inward current is a carbachol-sensitive and TTX-insensitive Na+ current discovered by others is discussed. In addition, this paper explains how these three variables respond when various pharmacological agents are applied to the store-operated model.
</para>

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

<para>
Effects of extracellular Calcium on Electrical Bursting and Intracellular and Luminal Calcium Oscillations in Insulin Secreting Pancreatic Beta-Cells, Teresa Ree Chay, 1997, 
            <emphasis>Biophysical Journal</emphasis>
          , 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>



<informalfigure float="0" id="fig_cell_diagram">
<mediaobject>
  <imageobject>
    <objectinfo>
      <title>diagram of the mitochondrial Ca2+ handling model</title>
    </objectinfo>
    <imagedata fileref="chay_1997.png"/>
  </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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      <variable cmeta:id="id_00026" initial_value="12.5" name="lamda_n" units="per_second"/>
      <variable cmeta:id="id_00027" initial_value="-18" name="Vn" units="millivolt"/>
      <variable cmeta:id="id_00028" initial_value="14" name="Sn" units="millivolt"/>
      <variable cmeta:id="id_00029" name="n_infinity" units="dimensionless"/>
      <variable cmeta:id="id_00030" name="tau_n" units="second"/>
      <variable name="V" public_interface="in" units="millivolt"/>
      <variable name="time" public_interface="in" units="second"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <apply>
               <diff/>
               <bvar>
                  <ci>time</ci>
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            <apply>
               <divide/>
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                  <minus/>
                  <ci>n_infinity</ci>
                  <ci>n</ci>
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         </apply>
         <apply>
            <eq/>
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               <divide/>
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                  <apply>
                     <exp/>
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                        <divide/>
                        <apply>
                           <minus/>
                           <ci>Vn</ci>
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                        <ci>Sn</ci>
                     </apply>
                  </apply>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>tau_n</ci>
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               <divide/>
               <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
               <apply>
                  <times/>
                  <ci>lamda_n</ci>
                  <apply>
                     <plus/>
                     <apply>
                        <exp/>
                        <apply>
                           <divide/>
                           <apply>
                              <minus/>
                              <ci>Vn</ci>
                              <ci>V</ci>
                           </apply>
                           <apply>
                              <times/>
                              <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
                              <ci>Sn</ci>
                           </apply>
                        </apply>
                     </apply>
                     <apply>
                        <exp/>
                        <apply>
                           <divide/>
                           <apply>
                              <minus/>
                              <ci>V</ci>
                              <ci>Vn</ci>
                           </apply>
                           <apply>
                              <times/>
                              <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
                              <ci>Sn</ci>
                           </apply>
                        </apply>
                     </apply>
                  </apply>
               </apply>
            </apply>
         </apply>
      </math>
   </component>
   <component cmeta:id="id_00031" name="Ca_sensitive_K_current">
      <variable cmeta:id="Ca_sensitive_K_current_i_K_Ca" name="i_K_Ca" public_interface="out" units="nanoA_per_cm2"/>
      <variable cmeta:id="id_00032" initial_value="5" name="g_K_Ca" units="microS_per_cm2"/>
      <variable cmeta:id="id_00033" name="K_Ca" public_interface="in" units="micromolar"/>
      <variable name="time" public_interface="in" units="second"/>
      <variable name="V" public_interface="in" units="millivolt"/>
      <variable cmeta:id="id_00035" name="V_K" public_interface="in" units="millivolt"/>
      <variable cmeta:id="id_00034" name="Ca_i" public_interface="in" units="micromolar"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <ci>i_K_Ca</ci>
            <apply>
               <times/>
               <apply>
                  <divide/>
                  <apply>
                     <times/>
                     <ci>g_K_Ca</ci>
                     <apply>
                        <power/>
                        <ci>Ca_i</ci>
                        <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">3</cn>
                     </apply>
                  </apply>
                  <apply>
                     <plus/>
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                        <power/>
                        <ci>K_Ca</ci>
                        <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">3</cn>
                     </apply>
                     <apply>
                        <power/>
                        <ci>Ca_i</ci>
                        <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">3</cn>
                     </apply>
                  </apply>
               </apply>
               <apply>
                  <minus/>
                  <ci>V</ci>
                  <ci>V_K</ci>
               </apply>
            </apply>
         </apply>
      </math>
   </component>
   <component cmeta:id="id_00036" name="ATP_sensitive_K_current">
      <variable cmeta:id="ATP_sensitive_K_current_i_K_ATP" name="i_K_ATP" public_interface="out" units="nanoA_per_cm2"/>
      <variable cmeta:id="id_00037" initial_value="2" name="g_K_ATP" units="microS_per_cm2"/>
      <variable name="time" public_interface="in" units="second"/>
      <variable name="V" public_interface="in" units="millivolt"/>
      <variable name="V_K" public_interface="in" units="millivolt"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <ci>i_K_ATP</ci>
            <apply>
               <times/>
               <ci>g_K_ATP</ci>
               <apply>
                  <minus/>
                  <ci>V</ci>
                  <ci>V_K</ci>
               </apply>
            </apply>
         </apply>
      </math>
   </component>
   <component cmeta:id="id_00038" name="Na_leak_current">
      <variable cmeta:id="Na_leak_current_i_NaL" name="i_NaL" public_interface="out" units="nanoA_per_cm2"/>
      <variable cmeta:id="id_00039" initial_value="0.3" name="g_NaL" units="microS_per_cm2"/>
      <variable cmeta:id="id_00040" initial_value="80" name="V_Na" units="millivolt"/>
      <variable name="time" public_interface="in" units="second"/>
      <variable name="V" public_interface="in" units="millivolt"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <ci>i_NaL</ci>
            <apply>
               <times/>
               <ci>g_NaL</ci>
               <apply>
                  <minus/>
                  <ci>V</ci>
                  <ci>V_Na</ci>
               </apply>
            </apply>
         </apply>
      </math>
   </component>
   <component cmeta:id="id_00041" name="cytosolic_calcium">
      <variable cmeta:id="cytosolic_calcium_Ca_i" initial_value="0.6959466" name="Ca_i" public_interface="out" units="micromolar"/>
      <variable cmeta:id="cytosolic_calcium_Ca_lum" initial_value="102.686" name="Ca_lum" public_interface="out" units="micromolar"/>
      <variable cmeta:id="id_00042" initial_value="0.2" name="k_rel" units="per_second"/>
      <variable cmeta:id="id_00043" initial_value="7" name="k_Ca" units="per_second"/>
      <variable cmeta:id="id_00044" initial_value="30" name="k_pump" units="per_second"/>
      <variable cmeta:id="id_00046" initial_value="0.2" name="omega" units="micromolar_cm2_per_nanoA_per_second"/>
      <variable cmeta:id="id_00045" name="i_Ca" public_interface="in" units="nanoA_per_cm2"/>
      <variable name="time" public_interface="in" units="second"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <apply>
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               <bvar>
                  <ci>time</ci>
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               <ci>Ca_i</ci>
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            <apply>
               <minus/>
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                  <ci>k_rel</ci>
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               </apply>
               <apply>
                  <plus/>
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                     <ci>omega</ci>
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                  <apply>
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                     <ci>k_Ca</ci>
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                  <apply>
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         <apply>
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            <apply>
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               <bvar>
                  <ci>time</ci>
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               <plus/>
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                  <apply>
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                     <ci>k_rel</ci>
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                  <apply>
                     <minus/>
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               <apply>
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                  <ci>k_pump</ci>
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      </math>
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   <group>
      <relationship_ref relationship="encapsulation"/>
      <component_ref component="fast_current">
         <component_ref component="fast_current_m_gate"/>
         <component_ref component="fast_current_h_gate"/>
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      <map_components component_1="cationic_nonselective_inward_current" component_2="environment"/>
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   <connection>
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   <connection>
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   <connection>
      <map_components component_1="calcium_current" component_2="membrane"/>
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   <connection>
      <map_components component_1="cationic_nonselective_inward_current" component_2="membrane"/>
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      <map_variables variable_1="i_NS" variable_2="i_NS"/>
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   <connection>
      <map_components component_1="delayed_rectifier_K_channel_current" component_2="membrane"/>
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      <map_components component_1="Ca_sensitive_K_current" component_2="membrane"/>
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   <connection>
      <map_components component_1="Na_leak_current" component_2="membrane"/>
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   <connection>
      <map_components component_1="calcium_current" component_2="cytosolic_calcium"/>
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   <connection>
      <map_components component_1="Ca_sensitive_K_current" component_2="cytosolic_calcium"/>
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   <connection>
      <map_components component_1="calcium_current" component_2="Ca_sensitive_K_current"/>
      <map_variables variable_1="K_Ca" variable_2="K_Ca"/>
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   <connection>
      <map_components component_1="delayed_rectifier_K_channel_current" component_2="ATP_sensitive_K_current"/>
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   <connection>
      <map_components component_1="cationic_nonselective_inward_current" component_2="cytosolic_calcium"/>
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   <connection>
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   <connection>
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   <connection>
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      <map_variables variable_1="Ca_i" variable_2="Ca_i"/>
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   <connection>
      <map_components component_1="calcium_current" component_2="calcium_current_d_gate"/>
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   <connection>
      <map_components component_1="delayed_rectifier_K_channel_current" component_2="delayed_rectifier_K_channel_current_n_gate"/>
      <map_variables variable_1="n" variable_2="n"/>
      <map_variables variable_1="time" variable_2="time"/>
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