Location: Bertram, Sherman, 2004 @ a13aeb48b605 / bertram_sherman_2004.cellml

Author:

rcai987 <devnull@localhost>

Date:

2015-01-07 16:14:44+13:00

Desc:

Added annotations to bertram_sherman_2004 model

Permanent Source URI:

https://models.physiomeproject.org/workspace/bertram_sherman_2004/rawfile/a13aeb48b6051fe9df4c13eea72b90319113fb14/bertram_sherman_2004.cellml

<?xml version="1.0"?>
<!--  FILE :  bertram_model_2004.xml

CREATED :  2nd September 2004

LAST MODIFIED : 2nd September 2004

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 and Sherman's
calcium-based phantom bursting model for pancreatic islets. 

CHANGES:  
   
--><model xmlns="http://www.cellml.org/cellml/1.0#" xmlns:bqs="http://www.cellml.org/bqs/1.0#" xmlns:cellml="http://www.cellml.org/cellml/1.0#" xmlns:cmeta="http://www.cellml.org/metadata/1.0#" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:dcterms="http://purl.org/dc/terms/" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" xml:base="file:///H:/bertram_sherman_2004/bertram_sherman_2004.cellml" cmeta:id="bertram_sherman_2004_version01" name="bertram_sherman_2004_version01">
<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
  <articleinfo>
  <title>A Calcium-based Phantom Bursting Model for Pancreatic Islets</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 model is has consistent units and has been verified as valid CellML by ValidateCellML. It is currently unsuitably constrained and can not be solved.
          </para>
  </section>
  <sect1 id="sec_structure">
<title>Model Structure</title>

<para>
Pancreatic beta-cells are located in clusters within the pancreas called the islets of Langerhans.  Beta-cells secrete the hormone insulin in response to elevated blood glucose levels, and in doing so, they play an essential role in glucose homeostasis.  When beta-cells fail to function properly, this can lead to pathologies such as type II diabetes.
</para> 

<para>
Insulin secretion is oscillatory, and it is in-phase with oscillations in the free cytosolic calcium concentration ([Ca<superscript>2+</superscript>]<subscript>i</subscript>), and theses Ca<superscript>2+</superscript> oscillations reflect a bursting pattern in the beta-cell electrical activity.  Electrical bursting consists of periodic active phases of cell firing (excitation) followed by silent phases of hyperpolarisation (rest).  These oscillations can be divided into three categories:
</para>
<itemizedlist>
  <listitem>
            <para>
              <emphasis>Fast bursting</emphasis>, which has a period between 2 and 5 seconds and which often occurs in single cells and in islets where acetylcholine is present;</para>
          </listitem>
  <listitem>
            <para>
              <emphasis>Medium bursting</emphasis>, which has a period of 10 to 60 seconds and which occurs in islets where there is a stimulatory glucose concentration; and</para>
          </listitem>
  <listitem>
            <para>
              <emphasis>Slow bursting</emphasis>, which has a period of 2 to 4 minutes and which occurs in single cells and in islets.</para>
          </listitem>
</itemizedlist>

<para>
The first mathematical models of beta-cells were developed to describe medium bursting, and the first models to address the variability in beta-cell oscillations were developed by Chay in 1995 and 1997 (see <ulink url="${HTML_EXMPL_CHAY_MODEL97}">Extracellular and Intracellular Calcium Effects on Pancreatic Beta Cells, Chay, 1997</ulink> for more details).  In these models the main mechanism for oscillations was variation in the Ca<superscript>2+</superscript> concentration in the ER, which directly or indirectly modulates one or more Ca<superscript>2+</superscript>-dependent channels.  In the Bertram and Sherman model described here the authors analyse in detail how the ER exerts its affects using a phantom bursting model (see <xref linkend="fig_cell_diagram"/> below). 
</para>

<para>
The phantom bursting model is a general paradigm for temporal plasticity in bursting in beta-cells in which bursting is driven by the interaction of two slow variables with disparate time constants (see <ulink url="${HTML_EXMPL_BERTRAM_MODEL}">The Phantom Burster Model for Pancreatic Beta-Cells, 2000</ulink> for more details).  There are three potential slow variables which could drive the phantom bursting <emphasis>in vivo</emphasis>:
</para>
<itemizedlist>
  <listitem>
            <para>cytosolic Ca<superscript>2+</superscript> concentration;</para>
          </listitem>
  <listitem>
            <para>ER Ca<superscript>2+</superscript> concentration;</para>
          </listitem>
  <listitem>
            <para>and the ADP to ATP ratio.</para>
          </listitem>
</itemizedlist>

<para>
The model has been described here in CellML (the raw CellML description of the Bertram and Sherman 2004 model 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.sciencedirect.com/science?_ob=ArticleURL&amp;_udi=B6WC7-4BS4GC2-1&amp;_user=140507&amp;_coverDate=09%2F30%2F2004&amp;_alid=197872630&amp;_rdoc=1&amp;_fmt=summary&amp;_orig=search&amp;_qd=1&amp;_cdi=6731&amp;_sort=d&amp;_docanchor=&amp;view=c&amp;_acct=C000011498&amp;_version=1&amp;_urlVersion=0&amp;_userid=140507&amp;md5=e1fdd19a27b1c7938c1d568e59a560e0">A Calcium-based Phantom Bursting Model for Pancreatic Islets</ulink>, Richard Bertram and Arthur Sherman, 2004, <ulink url="http://www.molbiolcell.org/">
            <emphasis>Bulletin of Mathematical Biology</emphasis>
          </ulink>, 66, 1313-1344.  (<ulink url="http://www.sciencedirect.com/science?_ob=ArticleURL&amp;_udi=B6WC7-4BS4GC2-1&amp;_coverDate=09%2F30%2F2004&amp;_alid=197872630&amp;_rdoc=1&amp;_fmt=&amp;_orig=search&amp;_qd=1&amp;_cdi=6731&amp;_sort=d&amp;view=c&amp;_acct=C000011498&amp;_version=1&amp;_urlVersion=0&amp;_userid=140507&amp;md5=b34962c344ab1a8911383073cd53016f">Full text (HTML)</ulink> and <ulink url="http://www.sciencedirect.com/science?_ob=MImg&amp;_imagekey=B6WC7-4BS4GC2-1-3Y&amp;_cdi=6731&amp;_orig=search&amp;_coverDate=09%2F30%2F2004&amp;_qd=1&amp;_sk=999339994&amp;view=c&amp;wchp=dGLbVzz-zSkWz&amp;_acct=C000011498&amp;_version=1&amp;_userid=140507&amp;md5=4f701b4338556df3136f0c4815596563&amp;ie=f.pdf">PDF</ulink> versions of the article are available to subscribers on the <emphasis>Bulletin of Mathematical Biology</emphasis> website.)  <ulink url="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&amp;db=PubMed&amp;list_uids=15294427&amp;dopt=Abstract">PubMed ID: 15294427</ulink>
</para>

<informalfigure float="0" id="fig_cell_diagram">
<mediaobject>
  <imageobject>
    <objectinfo>
      <title>cell diagram</title>
    </objectinfo>
    <imagedata fileref="bertram_2004.png"/>
  </imageobject>
</mediaobject>
<caption>A schematic diagram of the ionic currents and fluxes across the ER and the cell surface membranes, which are described by the mathematical model.</caption>
</informalfigure>

</sect1>
</article>
</documentation>
  
  
  
  <units name="millisecond">
    <unit prefix="milli" units="second"/>
  </units>
  
  <units name="millivolt">
    <unit prefix="milli" units="volt"/>
  </units>
  
  <units name="micromolar">
    <unit prefix="micro" units="mole"/>
    <unit exponent="-1" units="litre"/>
  </units>
  
  <units name="picoS">
    <unit prefix="pico" units="siemens"/>
  </units>
  
  <units name="femtoF">
    <unit prefix="femto" units="farad"/>
  </units>
  
  <units name="femtoA">
    <unit prefix="femto" units="ampere"/>
  </units>
  
  <units name="first_order_rate_constant">
    <unit exponent="-1" units="millisecond"/>
  </units>
  
  <units name="micromolar_per_femtoA_millisecond">
    <unit units="micromolar"/>
    <unit exponent="-1" units="femtoA"/>
    <unit exponent="-1" units="millisecond"/>
  </units>
  
  <units name="flux">
    <unit units="micromolar"/>
    <unit exponent="-1" units="millisecond"/>
  </units>
  
  <component name="environment">
    <variable name="time" public_interface="out" units="millisecond"/>
  </component>
  
  <component name="membrane">
    <variable name="V" public_interface="out" units="millivolt"/>
             
    <variable initial_value="5300.0" name="Cm" units="femtoF"/>
  
    <variable name="time" public_interface="in" units="millisecond"/>
    <variable name="i_Ca" public_interface="in" units="femtoA"/>
    <variable name="i_K" public_interface="in" units="femtoA"/>
    <variable name="i_K_Ca" public_interface="in" units="femtoA"/>
    <variable name="i_K_ATP" public_interface="in" units="femtoA"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply id="membrane_voltage_diff_eq">
        <eq/>
        <apply>
          <diff/>
          <bvar>
            <ci> time </ci>
          </bvar>
          <ci> V </ci>
        </apply>
        <apply>
          <divide/>
          <apply>
            <minus/>
            <apply>
              <plus/>
              <ci> i_Ca </ci>
              <ci> i_K </ci>
              <ci> i_K_Ca </ci>
              <ci> i_K_ATP </ci>
            </apply>
          </apply>
          <ci> Cm </ci>
        </apply>
      </apply>
    </math>
  </component>
  
  <component cmeta:id="id_00001" name="calcium_current">
    <variable cmeta:id="id_00002" name="i_Ca" public_interface="out" units="femtoA"/>
    
    <variable cmeta:id="id_00003" initial_value="1200.0" name="g_Ca" units="picoS"/>
    <variable cmeta:id="id_00004" initial_value="25.0" name="V_Ca" units="millivolt"/>
   
    <variable name="V" private_interface="out" public_interface="in" units="millivolt"/>
    <variable name="time" private_interface="out" public_interface="in" units="millisecond"/>
    
    <variable name="m_infinity" private_interface="in" units="dimensionless"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply id="i_Ca_calculation">
        <eq/>
        <ci> i_Ca </ci>
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          <times/>
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            <minus/>
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            <ci> V_Ca </ci>
          </apply>
        </apply>
      </apply>
    </math>
  </component>
  
  <component cmeta:id="id_00005" name="calcium_current_m_gate">
    <variable name="m_infinity" public_interface="out" units="dimensionless"/>
    
    <variable initial_value="-20.0" name="vm" units="millivolt"/>
    <variable initial_value="12.0" name="sm" units="millivolt"/>
  
    <variable name="V" public_interface="in" units="millivolt"/>
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    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply id="m_infinity_calculation">
        <eq/>
        <ci> m_infinity </ci>
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            <plus/>
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        </apply>
      </apply>
    </math>
  </component>
  
  <component cmeta:id="id_00006" name="delayed_rectifier_potassium_current">
    <variable cmeta:id="id_00008" name="i_K" public_interface="out" units="femtoA"/>
    <variable cmeta:id="id_00009" initial_value="-75.0" name="V_K" public_interface="out" units="millivolt"/>
    
    <variable cmeta:id="id_00010" initial_value="3000.0" name="g_K" units="picoS"/>
    
    <variable name="V" private_interface="out" public_interface="in" units="millivolt"/>
    <variable name="time" private_interface="out" public_interface="in" units="millisecond"/>
    
    <variable name="n" private_interface="in" units="dimensionless"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply id="i_K_calculation">
        <eq/>
        <ci> i_K </ci>
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            <minus/>
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          </apply>
        </apply>
      </apply>
    </math>
  </component>
  
  <component cmeta:id="id_00007" name="delayed_rectifier_potassium_current_n_gate">
    <variable name="n" public_interface="out" units="dimensionless"/>
    
    <variable initial_value="16.0" name="tau_n" units="millisecond"/>
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      </apply>
      
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        <eq/>
        <ci> n_infinity </ci>
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        </apply>
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    </math>
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  <component cmeta:id="id_00011" name="calcium_dependent_potassium_current">
    <variable cmeta:id="id_00012" name="i_K_Ca" public_interface="out" units="femtoA"/>
    
    <variable cmeta:id="id_00013" initial_value="300.0" name="g_K_Ca" units="picoS"/>
    
    <variable cmeta:id="id_00015" name="V_K" public_interface="in" units="millivolt"/>
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    <variable name="time" public_interface="in" units="millisecond"/>
    
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    <math xmlns="http://www.w3.org/1998/Math/MathML">
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          </apply>
        </apply>
      </apply>
    </math>
  </component>
  
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    <variable name="omega" public_interface="out" units="dimensionless"/>
    
    <variable initial_value="0.3" name="kD" units="micromolar"/>
    
    <variable name="c" public_interface="in" units="micromolar"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML">
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  <component cmeta:id="id_00023" name="calcium_influx_into_the_ER">
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    <variable initial_value="0.0005" name="pleak" units="first_order_rate_constant"/>
    
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    <variable name="c_er" public_interface="in" units="micromolar"/>
    
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          <apply>
            <minus/>
            <ci> c_er </ci>
            <ci> c </ci>
          </apply>
        </apply>
      </apply>
    </math>
  </component>
  
  <component cmeta:id="id_00025" name="calcium_efflux_through_the_IP3R">
    <variable cmeta:id="id_00027" name="JIP3" public_interface="out" units="flux"/>
    
    <variable name="O_infinity" units="first_order_rate_constant"/>
    <variable initial_value="0.35" name="d_act" units="micromolar"/>
    <variable initial_value="0.5" name="d_IP3" units="micromolar"/>
    <variable initial_value="0.4" name="d_inact" units="micromolar"/>
    <variable cmeta:id="id_00028" name="IP3" units="micromolar"/>
    
    <variable name="c" public_interface="in" units="micromolar"/>
    <variable name="c_er" public_interface="in" units="micromolar"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply id="JIP3_eq">
        <eq/>
        <ci> JIP3 </ci>
        <apply>
          <times/>
          <ci> O_infinity </ci>
          <apply>
            <minus/>
            <ci> c_er </ci>
            <ci> c </ci>
          </apply>
        </apply>
      </apply>
      
      <apply id="O_infinity_eq">
        <eq/>
        <ci>O_infinity</ci>
        <apply>
          <times/>
          <apply>
            <power/>
            <apply>
              <divide/>
              <ci>c</ci>
              <apply>
                <plus/>
                <ci>d_act</ci>
                <ci>c</ci>
              </apply>
            </apply>
            <cn cellml:units="dimensionless">3</cn>
          </apply>
          <apply>
            <power/>
            <apply>
              <divide/>
              <ci>IP3</ci>
              <apply>
                <plus/>
                <ci>d_IP3</ci>
                <ci>IP3</ci>
              </apply>
            </apply>
            <cn cellml:units="dimensionless">3</cn>
          </apply>
          <apply>
            <power/>
            <apply>
              <divide/>
              <ci>c</ci>
              <apply>
                <plus/>
                <ci>d_inact</ci>
                <ci>c</ci>
              </apply>
            </apply>
            <cn cellml:units="dimensionless">3</cn>
          </apply>
          <cn cellml:units="first_order_rate_constant">1</cn>
        </apply>
      </apply>
    </math>
  </component>
  
  <component cmeta:id="id_00026" name="net_calcium_efflux_out_of_the_ER">
    <variable name="Jer" public_interface="out" units="flux"/>
    
    <variable name="Jleak" public_interface="in" units="flux"/>
    <variable cmeta:id="id_00029" name="JIP3" public_interface="in" units="flux"/>
    <variable name="J_SERCA" public_interface="in" units="flux"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply id="Jer_eq">
        <eq/>
        <ci> Jer </ci>
        <apply>
          <minus/>
          <apply>
            <plus/>
            <ci> Jleak </ci>
            <ci> JIP3 </ci>
          </apply>
          <ci> J_SERCA </ci>
        </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="delayed_rectifier_potassium_current">
        <component_ref component="delayed_rectifier_potassium_current_n_gate"/>
      </component_ref>
      <component_ref component="calcium_dependent_potassium_current">
    <component_ref component="calcium_dependent_potassium_current_omega_gate"/>
      </component_ref>
      <component_ref component="nucleotide_sensitive_potassium_current">
    <component_ref component="nucleotide_sensitive_potassium_current_a_gate"/>
      </component_ref>
      <component_ref component="cytosolic_free_calcium_concentration"/>
      <component_ref component="calcium_flux_through_the_membrane"/>
      <component_ref component="calcium_influx_into_the_ER"/>
      <component_ref component="calcium_leak_out_of_the_ER"/>
      <component_ref component="calcium_efflux_through_the_IP3R"/>
      <component_ref component="net_calcium_efflux_out_of_the_ER"/>
      <component_ref component="ER_calcium_concentration"/>
    </component_ref>
  </group>
  
  <group>
    <relationship_ref relationship="encapsulation"/>
    <component_ref component="calcium_current">
      <component_ref component="calcium_current_m_gate"/>
    </component_ref>
    <component_ref component="delayed_rectifier_potassium_current">
      <component_ref component="delayed_rectifier_potassium_current_n_gate"/>
    </component_ref>
    <component_ref component="calcium_dependent_potassium_current">
    <component_ref component="calcium_dependent_potassium_current_omega_gate"/>
    </component_ref>
    <component_ref component="nucleotide_sensitive_potassium_current">
     <component_ref component="nucleotide_sensitive_potassium_current_a_gate"/>
    </component_ref>
  </group>
  
  
  <connection>
    <map_components component_1="membrane" component_2="environment"/>
    <map_variables variable_1="time" variable_2="time"/>
  </connection>
  
  <connection>
    <map_components component_1="calcium_current" component_2="environment"/>
    <map_variables variable_1="time" variable_2="time"/>
  </connection>
 
  <connection>
    <map_components component_1="ER_calcium_concentration" component_2="environment"/>
    <map_variables variable_1="time" variable_2="time"/>
  </connection>
  
  <connection>
    <map_components component_1="delayed_rectifier_potassium_current" component_2="environment"/>
    <map_variables variable_1="time" variable_2="time"/>
  </connection>
  
  <connection>
    <map_components component_1="nucleotide_sensitive_potassium_current" component_2="environment"/>
    <map_variables variable_1="time" variable_2="time"/>
  </connection>
  
  <connection>
    <map_components component_1="calcium_dependent_potassium_current" component_2="environment"/>
    <map_variables variable_1="time" variable_2="time"/>
  </connection>
  
  <connection>
    <map_components component_1="cytosolic_free_calcium_concentration" component_2="environment"/>
    <map_variables variable_1="time" variable_2="time"/>
  </connection>
  
  <connection>
    <map_components component_1="delayed_rectifier_potassium_current" component_2="membrane"/>
    <map_variables variable_1="V" variable_2="V"/>
    <map_variables variable_1="i_K" variable_2="i_K"/>
  </connection>
  
  <connection>
    <map_components component_1="calcium_current" component_2="membrane"/>
    <map_variables variable_1="V" variable_2="V"/>
    <map_variables variable_1="i_Ca" variable_2="i_Ca"/>
  </connection>
  
  <connection>
    <map_components component_1="calcium_dependent_potassium_current" component_2="membrane"/>
    <map_variables variable_1="V" variable_2="V"/>
    <map_variables variable_1="i_K_Ca" variable_2="i_K_Ca"/>
  </connection>
  
  <connection>
    <map_components component_1="nucleotide_sensitive_potassium_current" component_2="membrane"/>
    <map_variables variable_1="V" variable_2="V"/>
    <map_variables variable_1="i_K_ATP" variable_2="i_K_ATP"/>
  </connection>
  
  <connection>
    <map_components component_1="cytosolic_free_calcium_concentration" component_2="calcium_flux_through_the_membrane"/>
    <map_variables variable_1="c" variable_2="c"/>
    <map_variables variable_1="Jmem" variable_2="Jmem"/>
  </connection>
  
  <connection>
    <map_components component_1="cytosolic_free_calcium_concentration" component_2="nucleotide_sensitive_potassium_current"/>
    <map_variables variable_1="c" variable_2="c"/>
  </connection>
  
  <connection>
    <map_components component_1="cytosolic_free_calcium_concentration" component_2="calcium_dependent_potassium_current"/>
    <map_variables variable_1="c" variable_2="c"/>
  </connection>
  
  <connection>
    <map_components component_1="cytosolic_free_calcium_concentration" component_2="calcium_leak_out_of_the_ER"/>
    <map_variables variable_1="c" variable_2="c"/>
  </connection>
  
  <connection>
    <map_components component_1="cytosolic_free_calcium_concentration" component_2="calcium_influx_into_the_ER"/>
    <map_variables variable_1="c" variable_2="c"/>
  </connection>
  
  <connection>
    <map_components component_1="cytosolic_free_calcium_concentration" component_2="calcium_efflux_through_the_IP3R"/>
    <map_variables variable_1="c" variable_2="c"/>
  </connection>
  
  <connection>
    <map_components component_1="ER_calcium_concentration" component_2="calcium_leak_out_of_the_ER"/>
    <map_variables variable_1="c_er" variable_2="c_er"/>
  </connection>
  
  <connection>
    <map_components component_1="ER_calcium_concentration" component_2="calcium_efflux_through_the_IP3R"/>
    <map_variables variable_1="c_er" variable_2="c_er"/>
  </connection>
  
  <connection>
    <map_components component_1="net_calcium_efflux_out_of_the_ER" component_2="calcium_influx_into_the_ER"/>
    <map_variables variable_1="J_SERCA" variable_2="J_SERCA"/>
  </connection>
  
  <connection>
    <map_components component_1="net_calcium_efflux_out_of_the_ER" component_2="calcium_efflux_through_the_IP3R"/>
    <map_variables variable_1="JIP3" variable_2="JIP3"/>
  </connection>
  
  <connection>
    <map_components component_1="net_calcium_efflux_out_of_the_ER" component_2="calcium_leak_out_of_the_ER"/>
    <map_variables variable_1="Jleak" variable_2="Jleak"/>
  </connection>
  
  <connection>
    <map_components component_1="net_calcium_efflux_out_of_the_ER" component_2="cytosolic_free_calcium_concentration"/>
    <map_variables variable_1="Jer" variable_2="Jer"/>
  </connection>
  
  <connection>
    <map_components component_1="net_calcium_efflux_out_of_the_ER" component_2="ER_calcium_concentration"/>
    <map_variables variable_1="Jer" variable_2="Jer"/>
  </connection>
  
  <connection>
    <map_components component_1="calcium_current" component_2="calcium_flux_through_the_membrane"/>
    <map_variables variable_1="i_Ca" variable_2="i_Ca"/>
  </connection>
  
  <connection>
    <map_components component_1="delayed_rectifier_potassium_current" component_2="calcium_dependent_potassium_current"/>
    <map_variables variable_1="V_K" variable_2="V_K"/>
  </connection>
  
  <connection>
    <map_components component_1="delayed_rectifier_potassium_current" component_2="nucleotide_sensitive_potassium_current"/>
    <map_variables variable_1="V_K" variable_2="V_K"/>
  </connection>
  
  <connection>
    <map_components component_1="calcium_current" component_2="calcium_current_m_gate"/>
    <map_variables variable_1="m_infinity" variable_2="m_infinity"/>
    <map_variables variable_1="time" variable_2="time"/>
    <map_variables variable_1="V" variable_2="V"/>
  </connection>
  
  <connection>
    <map_components component_1="delayed_rectifier_potassium_current" component_2="delayed_rectifier_potassium_current_n_gate"/>
    <map_variables variable_1="n" variable_2="n"/>
    <map_variables variable_1="time" variable_2="time"/>
    <map_variables variable_1="V" variable_2="V"/>
  </connection>
  
  <connection>
    <map_components component_1="nucleotide_sensitive_potassium_current" component_2="nucleotide_sensitive_potassium_current_a_gate"/>
    <map_variables variable_1="a" variable_2="a"/>
    <map_variables variable_1="time" variable_2="time"/>
    <map_variables variable_1="c" variable_2="c"/>
  </connection>
  
  <connection>
    <map_components component_1="calcium_dependent_potassium_current" component_2="calcium_dependent_potassium_current_omega_gate"/>
    <map_variables variable_1="omega" variable_2="omega"/>
    <map_variables variable_1="c" variable_2="c"/>
  </connection>
  



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