Location: Bertram, Previte, Sherman, Kinard, Satin, 2000 @ 97c9fcf27025 / bertram_previte_sherman_kinard_satin_2000.cellml

Author:
pmr2.import <nobody@models.cellml.org>
Date:
2006-07-09 08:02:32+12:00
Desc:
committing version01 of bertram_previte_sherman_kinard_satin_2000
Permanent Source URI:
https://models.cellml.org/workspace/2e0/rawfile/97c9fcf2702501d9812a705d768e9bd21e352b90/bertram_previte_sherman_kinard_satin_2000.cellml

<?xml version='1.0' encoding='utf-8'?>
<!--  FILE :  bertram_model_2000.xml

CREATED :  10th April 2002

LAST MODIFIED : 9th April 2003

AUTHOR :  Catherine Lloyd
          Bioengineering Institute
          The University of Auckland
          
MODEL STATUS :  This model conforms to the CellML 1.0 Specification released on
10th August 2001, and the 16/01/2002 CellML Metadata 1.0 Specification.

DESCRIPTION :  This file contains a CellML description of Bertram et al's
2000 phantom burster model for pancreatic beta-cells.

CHANGES:  
  18/07/2002 - CML - Added more metadata.
  09/04/2003 - AAC - Added publication date information.  
--><model xmlns="http://www.cellml.org/cellml/1.0#" xmlns:cmeta="http://www.cellml.org/metadata/1.0#" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:bqs="http://www.cellml.org/bqs/1.0#" xmlns:cellml="http://www.cellml.org/cellml/1.0#" xmlns:dcterms="http://purl.org/dc/terms/" xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" cmeta:id="bertram_previte_sherman_kinard_satin_2000_version01" name="bertram_previte_sherman_kinard_satin_2000_version01">
<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
  <articleinfo>
  <title>The Phantom Burster Model For 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>
Pancreatic beta-cells have been the subject of both experimental and theoretical studies for several decades.  One reason for this interest has been the essential role beta-cells play in glucose homeostasis - they are the only source of insulin that most cells require in order to take up and metabolise glucose, and impairment of beta-cell function contributes to diabetes.  A major focus of theoretical work has been beta-cell dynamics, especially in the form of bursting electrical activity.  The bursts consist of active phases of Ca<superscript>2+</superscript>-carrying action potentials alternating with silent phases of repolarisation and are accompanied by oscillations in cytosolic Ca<superscript>2+</superscript>, which drive pulses of insulin secretion.  
</para>

<para>
Experimentally, electrical activity in beta-cells is studied in two distinct preparations: islets of Langerhans, which are microorgans containing thousands of endocrine cells, and isolated cells.  Pancreatic beta-cells exhibit bursting oscillations with a wide range of periods.  Whereas periods in isolated cells are generally either a few seconds or a few minutes, in intact islets of Langerhans they are intermediate (10-60 seconds).  In their 2000 publication, Richard Bertram, Joseph Previte, Arthur Sherman, Tracie A. Kinard and Leslie S. Satin develop a mathematical model for beta-cell electrical activity capable of generating this wide range of bursting oscillations.  Unlike previously published models, bursting is driven by the interaction of two slow processes (I<subscript>s1</subscript> and I<subscript>s2</subscript> in <xref linkend="fig_cell_diagram"/> below), one with a relatively small time constant (1-5 seconds) and the other with a much larger time constant (1-2 minutes).  Bursting on the intermediate time scale is generated without the need for a slow process having an intermediate time constant, hence phantom bursting.  This mathematical model has been translated into a CellML description which can be downloaded in various formats as described in <xref linkend="sec_download_this_model"/>.
</para>

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

<para>
<ulink url="http://www.biophysj.org/cgi/content/abstract/79/6/2880">The Phantom Burster Model for Pancreatic beta-Cells</ulink>, Richard Bertram, Joseph Previte, Arthur Sherman, Tracie A. Kinard and Leslie S. Satin, 2000, <ulink url="http://www.biophysj.org/">
            <emphasis>Biophysical Journal</emphasis>
          </ulink>, 79, 2880-2892.  (<ulink url="http://www.biophysj.org/cgi/content/full/79/6/2880">Full text</ulink> and <ulink url="http://www.biophysj.org/cgi/reprint/79/6/2880.pdf">PDF</ulink> versions of the article are available for Journal Members on the Biophysical Journal website.)  <ulink url="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&amp;db=PubMed&amp;list_uids=11106596&amp;dopt=Abstract">PubMed ID: 11106596</ulink>  
</para>


<informalfigure float="0" id="fig_cell_diagram">
<mediaobject>
  <imageobject>
    <objectinfo>
      <title>cell schematic for the model</title>
    </objectinfo>
    <imagedata fileref="cell_diagram.gif"/>
  </imageobject>
</mediaobject>
<caption>Schematic diagram of the pancreatic beta-cell plasma membrane showing the ionic currents captured by the phantom burster model.</caption>
</informalfigure>

</sect1>
</article>
</documentation>
  
  
  <!--
    Below, we define some additional units for association with variables and
    constants within the model. The identifiers are fairly self-explanatory.
  -->
  
  <units name="minute">
    <unit units="second" multiplier="60.0"/>
  </units>
  
  <units name="picoA">
    <unit units="ampere" prefix="pico"/>
  </units>
  
  <units name="femtoF">
    <unit units="farad" prefix="femto"/>
  </units>
  
  <units name="millivolt">
    <unit units="volt" prefix="milli"/>
  </units>
  
  <units name="picoS">
    <unit units="siemens" prefix="pico"/>
  </units>
  
  <!--
    The "environment" component is used to declare variables that are used by
    all or most of the other components, in this case just "time".
  -->
  <component name="environment">
    <variable units="second" public_interface="out" name="time"/>
  </component>
  
  <component name="membrane">
    <variable units="millivolt" public_interface="out" name="V"/>
    
    <variable units="femtoF" name="Cm" initial_value="4524.0"/>
    
    <variable units="second" public_interface="in" name="time"/>
    <variable units="picoA" public_interface="in" name="i_Ca"/>
    <variable units="picoA" public_interface="in" name="i_K"/>
    <variable units="picoA" public_interface="in" name="i_s1"/>
    <variable units="picoA" public_interface="in" name="i_s2"/>
    <variable units="picoA" public_interface="in" name="i_L"/>
    
    <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>
            <minus/>
            <apply>
              <plus/>
              <ci> i_Ca </ci>
              <ci> i_K </ci>
              <ci> i_s1 </ci>
              <ci> i_s2 </ci>
              <ci> i_L </ci>
            </apply>
          </apply>
          <ci> Cm </ci>
        </apply>
      </apply>
    </math>
  </component>
  
  <component name="calcium_current">
    <variable units="picoA" public_interface="out" name="i_Ca"/>
    
    <variable units="millivolt" name="V_Ca" initial_value="100.0"/>
    <variable units="picoS" name="g_Ca" initial_value="280.0"/>   
   
    <variable units="second" public_interface="in" private_interface="out" name="time"/>
    <variable units="millivolt" public_interface="in" private_interface="out" name="V"/>
    
    <variable units="dimensionless" private_interface="in" name="m_infinity"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply id="i_Ca_calculation">
        <eq/>
        <ci> i_Ca </ci>
        <apply>
          <times/>
          <ci> g_Ca </ci>
          <ci> m_infinity </ci>
          <apply>
            <minus/>
            <ci> V </ci>
            <ci> V_Ca </ci>
          </apply>
        </apply>
      </apply>
    </math>
  </component> 
  
  <component name="calcium_current_m_gate">
    <variable units="dimensionless" public_interface="out" name="m_infinity"/>
    
    <variable units="millivolt" public_interface="in" name="V"/>
    <variable units="second" public_interface="in" name="time"/>
   
    <math xmlns="http://www.w3.org/1998/Math/MathML">
     <apply id="m_infinity_calculation">
        <eq/>
        <ci> m_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/>
                  <cn cellml:units="millivolt"> -22.0 </cn>
                  <ci> V </ci>
                </apply>
                <cn cellml:units="millivolt"> 7.5 </cn>
              </apply>
            </apply>    
          </apply>
        </apply>
      </apply>
    </math>
  </component>   
  
  <component name="rapidly_activating_K_current">
    <variable units="picoA" public_interface="out" name="i_K"/>
    <variable units="millivolt" public_interface="out" name="V_K" initial_value="-80.0"/>
   
    <variable units="picoS" name="g_K" initial_value="1300.0"/>   
   
    <variable units="second" public_interface="in" private_interface="out" name="time"/>
    <variable units="millivolt" public_interface="in" private_interface="out" name="V"/>
    
    <variable units="dimensionless" private_interface="in" name="n"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply id="i_K_calculation">
        <eq/>
        <ci> i_K </ci>
        <apply>
          <times/>
          <ci> g_K </ci>
          <ci> n </ci>
          <apply>
            <minus/>
            <ci> V </ci>
            <ci> V_K </ci>
          </apply>
        </apply>
      </apply>
    </math>
  </component> 
  
  <component name="rapidly_activating_K_current_n_gate">
    <variable units="dimensionless" public_interface="out" name="n"/>
    
    <variable units="dimensionless" name="n_infinity"/>
    <variable units="second" name="tau_n"/>
    
    <variable units="millivolt" public_interface="in" name="V"/>
    <variable units="second" 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/>
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            <minus/>
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            <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/>
                  <cn cellml:units="millivolt"> -9.0 </cn>
                  <ci> V </ci>
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                <cn cellml:units="millivolt"> 10.0 </cn>
              </apply>
            </apply>    
          </apply>
        </apply>
      </apply>
      
      <apply id="tau_n_calculation">
        <eq/>
        <ci> tau_n </ci>
        <apply>
          <divide/>
          <cn cellml:units="second"> 8.3 </cn>
          <apply>
            <plus/>
            <cn cellml:units="dimensionless"> 1.0 </cn>
            <apply>
              <exp/>
              <apply>
                <divide/>
                <apply>
                  <plus/>
                  <ci> V </ci>
                  <cn cellml:units="millivolt"> 9.0 </cn>
                </apply>
                <cn cellml:units="millivolt"> 10.0 </cn>
              </apply>
            </apply>    
          </apply>
        </apply>
      </apply>
    </math>
  </component>   
          
  <component name="slow_K_current">
    <variable units="picoA" public_interface="out" name="i_s1"/>
    
    <variable units="picoS" name="g_s1" initial_value="3.0"/>   
    
    <variable units="millivolt" public_interface="in" name="V_K"/>
    <variable units="second" public_interface="in" private_interface="out" name="time"/>
    <variable units="millivolt" public_interface="in" private_interface="out" name="V"/>
    
    <variable units="dimensionless" private_interface="in" name="s1"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply id="i_s1_calculation">
        <eq/>
        <ci> i_s1 </ci>
        <apply>
          <times/>
          <ci> g_s1 </ci>
          <ci> s1 </ci>
          <apply>
            <minus/>
            <ci> V </ci>
            <ci> V_K </ci>
          </apply>
        </apply>
      </apply>
    </math>
  </component> 
  
  <component name="slow_K_current_s1_gate">
    <variable units="dimensionless" public_interface="out" name="s1"/>
    
    <variable units="dimensionless" name="s1_infinity"/>
    <variable units="second" name="tau_s1" initial_value="1.0"/>
    
    <variable units="millivolt" public_interface="in" name="V"/>
    <variable units="second" public_interface="in" name="time"/>
   
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply id="s1_diff_eq">
        <eq/>
        <apply>
          <diff/>
          <bvar>
            <ci> time </ci>
          </bvar>
          <ci> s1 </ci>
        </apply>
        <apply>
          <divide/>
          <apply>
            <minus/>
            <ci> s1_infinity </ci>
            <ci> s1 </ci>
          </apply>
          <ci> tau_s1 </ci>
        </apply>
      </apply>
      
      <apply id="s1_infinity_calculation">
        <eq/>
        <ci> s1_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/>
                  <cn cellml:units="millivolt"> -40.0 </cn>
                  <ci> V </ci>
                </apply>
                <cn cellml:units="millivolt"> 0.5 </cn>
              </apply>
            </apply>    
          </apply>
        </apply>
      </apply>
    </math>
  </component>   
  
  <component name="very_slow_K_current">
    <variable units="picoA" public_interface="out" name="i_s2"/>
    
    <variable units="picoS" name="g_s2" initial_value="32.0"/>   
    
    <variable units="millivolt" public_interface="in" name="V_K"/>
    <variable units="second" public_interface="in" private_interface="out" name="time"/>
    <variable units="millivolt" public_interface="in" private_interface="out" name="V"/>
    
    <variable units="dimensionless" private_interface="in" name="s2"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply id="i_s2_calculation">
        <eq/>
        <ci> i_s2 </ci>
        <apply>
          <times/>
          <ci> g_s2 </ci>
          <ci> s2 </ci>
          <apply>
            <minus/>
            <ci> V </ci>
            <ci> V_K </ci>
          </apply>
        </apply>
      </apply>
    </math>
  </component> 
  
  <component name="very_slow_K_current_s2_gate">
    <variable units="dimensionless" public_interface="out" name="s2"/>
    
    <variable units="dimensionless" name="s2_infinity"/>
    <variable units="minute" name="tau_s2" initial_value="2.0"/>
    
    <variable units="millivolt" public_interface="in" name="V"/>
    <variable units="second" public_interface="in" name="time"/>
   
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply id="s2_diff_eq">
        <eq/>
        <apply>
          <diff/>
          <bvar>
            <ci> time </ci>
          </bvar>
          <ci> s2 </ci>
        </apply>
        <apply>
          <divide/>
          <apply>
            <minus/>
            <ci> s2_infinity </ci>
            <ci> s2 </ci>
          </apply>
          <ci> tau_s2 </ci>
        </apply>
      </apply>
      
      <apply id="s2_infinity_calculation">
        <eq/>
        <ci> s2_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/>
                  <cn cellml:units="millivolt"> -42.0 </cn>
                  <ci> V </ci>
                </apply>
                <cn cellml:units="millivolt"> 0.4 </cn>
              </apply>
            </apply>    
          </apply>
        </apply>
      </apply>
    </math>
  </component>
  
  <component name="leak_current">
    <variable units="picoA" public_interface="out" name="i_L"/>
    
    <variable units="picoS" name="g_L" initial_value="25.0"/>   
    <variable units="millivolt" name="V_L" initial_value="-40.0"/>
   
    <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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        <eq/>
        <ci> i_L </ci>
        <apply>
          <times/>
          <ci> g_L </ci>
          <apply>
            <minus/>
            <ci> V </ci>
            <ci> V_L </ci>
          </apply>
        </apply>
      </apply>
    </math>
  </component>
  
  <group>
    <relationship_ref relationship="containment"/>
    <component_ref component="membrane">
      <component_ref component="calcium_current">
        <component_ref component="calcium_current_m_gate"/>
      </component_ref>
      <component_ref component="rapidly_activating_K_current">
        <component_ref component="rapidly_activating_K_current_n_gate"/>
      </component_ref>
      <component_ref component="slow_K_current">
        <component_ref component="slow_K_current_s1_gate"/>
      </component_ref>
      <component_ref component="very_slow_K_current">
        <component_ref component="very_slow_K_current_s2_gate"/>
      </component_ref>
      <component_ref component="leak_current"/>
    </component_ref>
  </group>
  
  <group>
    <relationship_ref relationship="encapsulation"/>
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      <component_ref component="calcium_current_m_gate"/>
    </component_ref>
    <component_ref component="rapidly_activating_K_current">
      <component_ref component="rapidly_activating_K_current_n_gate"/>
    </component_ref>
    <component_ref component="slow_K_current">
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    </component_ref>
    <component_ref component="very_slow_K_current">
      <component_ref component="very_slow_K_current_s2_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="calcium_current"/>
    <map_variables variable_2="time" variable_1="time"/>
  </connection>
  
  <connection>
    <map_components component_2="environment" component_1="rapidly_activating_K_current"/>
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  <connection>
    <map_components component_2="environment" component_1="slow_K_current"/>
    <map_variables variable_2="time" variable_1="time"/>
  </connection>
  
  <connection>
    <map_components component_2="environment" component_1="very_slow_K_current"/>
    <map_variables variable_2="time" variable_1="time"/>
  </connection>
  
  <connection>
    <map_components component_2="environment" component_1="leak_current"/>
    <map_variables variable_2="time" variable_1="time"/>
  </connection>
  
  <connection>
    <map_components component_2="calcium_current" component_1="membrane"/>
    <map_variables variable_2="V" variable_1="V"/>
    <map_variables variable_2="i_Ca" variable_1="i_Ca"/>
  </connection> 
  
  <connection>
    <map_components component_2="rapidly_activating_K_current" component_1="membrane"/>
    <map_variables variable_2="V" variable_1="V"/>
    <map_variables variable_2="i_K" variable_1="i_K"/>
  </connection>
  
  <connection>
    <map_components component_2="slow_K_current" component_1="membrane"/>
    <map_variables variable_2="V" variable_1="V"/>
    <map_variables variable_2="i_s1" variable_1="i_s1"/>
  </connection> 
  
  <connection>
    <map_components component_2="very_slow_K_current" component_1="membrane"/>
    <map_variables variable_2="V" variable_1="V"/>
    <map_variables variable_2="i_s2" variable_1="i_s2"/>
  </connection>
  
  <connection>
    <map_components component_2="leak_current" component_1="membrane"/>
    <map_variables variable_2="V" variable_1="V"/>
    <map_variables variable_2="i_L" variable_1="i_L"/>
  </connection>
  
  <connection>
    <map_components component_2="slow_K_current" component_1="rapidly_activating_K_current"/>
    <map_variables variable_2="V_K" variable_1="V_K"/>
  </connection> 
  
  <connection>
    <map_components component_2="very_slow_K_current" component_1="rapidly_activating_K_current"/>
    <map_variables variable_2="V_K" variable_1="V_K"/>
  </connection>
  
  <connection>
    <map_components component_2="calcium_current_m_gate" component_1="calcium_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="rapidly_activating_K_current_n_gate" component_1="rapidly_activating_K_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> 
  
  <connection>
    <map_components component_2="slow_K_current_s1_gate" component_1="slow_K_current"/>
    <map_variables variable_2="s1" variable_1="s1"/>
    <map_variables variable_2="time" variable_1="time"/>
    <map_variables variable_2="V" variable_1="V"/>
  </connection>
  
  <connection>
    <map_components component_2="very_slow_K_current_s2_gate" component_1="very_slow_K_current"/>
    <map_variables variable_2="s2" variable_1="s2"/>
    <map_variables variable_2="time" variable_1="time"/>
    <map_variables variable_2="V" variable_1="V"/>
  </connection>


<rdf:RDF>
  <rdf:Seq rdf:about="rdf:#d8f19ca0-76df-41ee-b343-51ad337ab4bc">
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