Location: Devries, Sherman, 2000 @ 3ba0eafdb008 / devries_sherman_2000.cellml

Author:

rcai987 <devnull@localhost>

Date:

2015-01-20 11:34:31+13:00

Desc:

Added annotations to devries_sherman_2000 model

Permanent Source URI:

http://models.cellml.org/workspace/devries_sherman_2000/rawfile/3ba0eafdb0081a6e80664f37a3e496fb6d2debf8/devries_sherman_2000.cellml

<?xml version='1.0'?>
<!--  FILE :  devries_model_2000.xml

CREATED :  9th May 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 De Vries and Sherman's
2000 mathematical model of channel sharing in pancreatic beta cells.

CHANGES:  
  18/07/2002 - CML - Added more metadata.
  09/04/2003 - AAC - Added publication date information.  
-->
<model name="devries_2000" 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#">
    <documentation xmlns="http://cellml.org/tmp-documentation">
        <article>
            <articleinfo>
                <title>Enhancement Of Emergent Bursting In 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 model has been validated and is known to run in OpenCell and COR to recreate the published results (figure 1). The paper by Devries and Sherman describes several different parameter sets including single cell and two cell sets, and also describes a deterministic and a stochastic model. This CellML model uses equations 1-3 and the parameters given in table 1 for the single cell deterministic model. For this particular model lambda = 0.9.  Note there is a unit inconsistency in the equation for V, but our attempts to balance the units for this equation resulted in a model which no longer worked.
          </para>
            </section>
            <sect1 id="sec_structure">
                <title>Model Structure</title>
                <para>
ABSTRACT: Secretion of insulin by electrically coupled populations of pancreatic beta -cells is governed by bursting electrical activity. Isolated beta -cells, however, exhibit atypical bursting or continuous spike activity. We study bursting as an emergent property of the population, focussing on interactions among the subclass of spiking cells. These are modelled by equipping the fast subsystem with a saddle-node-loop bifurcation, which makes it monostable. Such cells can only spike tonically or remain silent when isolated, but can be induced to burst with weak diffusive coupling. With stronger coupling, the cells revert to tonic spiking. We demonstrate that the addition of noise dramatically increases, via a phenomenon like stochastic resonance, the coupling range over which bursting is seen.
</para>
                <para>
The original paper reference is cited below:
</para>
                <para>
Channel Sharing in Pancreatic Beta-Cells Revisited: Enhancement of Emergent Bursting by Noise, Gerda De Vries and Arthur Sherman, 2000,
            <emphasis>The Journal Of Theoretical Biology</emphasis>
          , 207, 513-530. <ulink url="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&amp;db=PubMed&amp;list_uids=11093836&amp;dopt=Abstract">PubMed ID: 11093836</ulink>
                </para>
                <informalfigure float="0" id="fig_cell_diagram">
                    <mediaobject>
                        <imageobject>
                            <objectinfo>
                                <title>diagram of the model</title>
                            </objectinfo>
                            <imagedata fileref="devries_2000.png"/>
                        </imageobject>
                    </mediaobject>
                    <caption>A schematic representation of the four transmembrane currents captured by the De Vries and Sherman 2000 pancreatic beta-cell 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="nanoS">
        <unit prefix="nano" units="siemens"/>
    </units>
    <units name="picoA">
        <unit prefix="pico" units="ampere"/>
    </units>
    <component name="environment">
        <variable name="time" public_interface="out" units="millisecond"/>
    </component>
    <component cmeta:id="id_000000001" name="membrane">
        <variable initial_value="-64.0" name="V" public_interface="out" units="millivolt"/>
        <variable initial_value="20.0" name="tau" public_interface="out" units="millisecond"/>
        <variable name="time" public_interface="in" units="millisecond"/>
        <variable cmeta:id="id_000000002" name="i_K" public_interface="in" units="picoA"/>
        <variable cmeta:id="id_000000003" name="i_K_ATP" public_interface="in" units="picoA"/>
        <variable cmeta:id="id_000000015" name="i_Ca" public_interface="in" units="picoA"/>
        <variable name="i_s" public_interface="in" units="picoA"/>
        <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_ATP </ci>
                            <ci> i_s </ci>
                        </apply>
                    </apply>
                    <ci> tau </ci>
                </apply>
            </apply>
        </math>
    </component>
    <component cmeta:id="id_000000016" name="calcium_current">
        <variable name="i_Ca" public_interface="out" units="picoA"/>
        <variable initial_value="3.6" name="g_Ca" units="nanoS"/>
        <variable initial_value="25.0" name="V_Ca" units="millivolt"/>
        <variable name="time" public_interface="in" units="millisecond"/>
        <variable name="V" private_interface="out" public_interface="in" units="millivolt"/>
        <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>
                <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 cmeta:id="id_000000017" name="calcium_current_m_gate">
        <variable cmeta:id="id_000000018" name="m_infinity" public_interface="out" units="dimensionless"/>
        <variable cmeta:id="id_000000019" initial_value="-20.0" name="V_m" units="millivolt"/>
        <variable cmeta:id="id_000000020" initial_value="12.0" name="theta_m" units="millivolt"/>
        <variable cmeta:id="id_000000021" name="V" public_interface="in" units="millivolt"/>
        <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" xmlns:cellml="http://www.cellml.org/cellml/1.0#"> 1.0 </cn>
                    <apply>
                        <plus/>
                        <cn cellml:units="dimensionless" xmlns:cellml="http://www.cellml.org/cellml/1.0#"> 1.0 </cn>
                        <apply>
                            <exp/>
                            <apply>
                                <divide/>
                                <apply>
                                    <minus/>
                                    <ci> V_m </ci>
                                    <ci> V </ci>
                                </apply>
                                <ci> theta_m </ci>
                            </apply>
                        </apply>
                    </apply>
                </apply>
            </apply>
        </math>
    </component>
    <component cmeta:id="id_000000004" name="potassium_current">
        <variable cmeta:id="potassium_current_i_K" name="i_K" public_interface="out" units="picoA"/>
        <variable cmeta:id="id_000000005" initial_value="-75.0" name="V_K" public_interface="out" units="millivolt"/>
        <variable cmeta:id="id_000000006" initial_value="10.0" name="g_K" units="nanoS"/>
        <variable name="time" private_interface="out" public_interface="in" units="millisecond"/>
        <variable name="V" private_interface="out" public_interface="in" units="millivolt"/>
        <variable name="tau" 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>
                <apply>
                    <times/>
                    <ci> g_K </ci>
                    <ci> n </ci>
                    <apply>
                        <minus/>
                        <ci> V </ci>
                        <ci> V_K </ci>
                    </apply>
                </apply>
            </apply>
        </math>
    </component>
    <component cmeta:id="id_000000007" name="potassium_current_n_gate">
        <variable cmeta:id="id_000000008" initial_value="0.01" name="n" public_interface="out" units="dimensionless"/>
        <variable cmeta:id="id_000000009" name="n_infinity" units="dimensionless"/>
        <variable cmeta:id="id_000000010" initial_value="-17.0" name="V_n" units="millivolt"/>
        <variable cmeta:id="id_000000011" initial_value="5.6" name="theta_n" units="millivolt"/>
        <variable initial_value="0.9" name="lambda" units="dimensionless"/>
        <variable name="V" public_interface="in" units="millivolt"/>
        <variable name="tau" public_interface="in" units="millisecond"/>
        <variable name="time" public_interface="in" units="millisecond"/>
        <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>
                        <times/>
                        <ci> lambda </ci>
                        <apply>
                            <minus/>
                            <ci> n_infinity </ci>
                            <ci> n </ci>
                        </apply>
                    </apply>
                    <ci> tau </ci>
                </apply>
            </apply>
            <apply id="n_infinity_calculation">
                <eq/>
                <ci> n_infinity </ci>
                <apply>
                    <divide/>
                    <cn cellml:units="dimensionless" xmlns:cellml="http://www.cellml.org/cellml/1.0#"> 1.0 </cn>
                    <apply>
                        <plus/>
                        <cn cellml:units="dimensionless" xmlns:cellml="http://www.cellml.org/cellml/1.0#"> 1.0 </cn>
                        <apply>
                            <exp/>
                            <apply>
                                <divide/>
                                <apply>
                                    <minus/>
                                    <ci> V_n </ci>
                                    <ci> V </ci>
                                </apply>
                                <ci> theta_n </ci>
                            </apply>
                        </apply>
                    </apply>
                </apply>
            </apply>
        </math>
    </component>
    <component name="slow_current">
        <variable name="i_s" public_interface="out" units="picoA"/>
        <variable initial_value="4.0" name="g_s" units="nanoS"/>
        <variable name="time" private_interface="out" public_interface="in" units="millisecond"/>
        <variable name="V" private_interface="out" public_interface="in" units="millivolt"/>
        <variable name="V_K" public_interface="in" units="millivolt"/>
        <variable name="s" private_interface="in" units="dimensionless"/>
        <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply id="i_s_calculation">
                <eq/>
                <ci> i_s </ci>
                <apply>
                    <times/>
                    <ci> g_s </ci>
                    <ci> s </ci>
                    <apply>
                        <minus/>
                        <ci> V </ci>
                        <ci> V_K </ci>
                    </apply>
                </apply>
            </apply>
        </math>
    </component>
    <component name="slow_current_s_gate">
        <variable initial_value="0.01" name="s" public_interface="out" units="dimensionless"/>
        <variable name="s_infinity" units="dimensionless"/>
        <variable initial_value="-22.0" name="V_s" units="millivolt"/>
        <variable initial_value="8.0" name="theta_s" units="millivolt"/>
        <variable initial_value="20000.0" name="tau_s" units="millisecond"/>
        <variable name="V" public_interface="in" units="millivolt"/>
        <variable name="time" public_interface="in" units="millisecond"/>
        <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply id="s_diff_eq">
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci> time </ci>
                    </bvar>
                    <ci> s </ci>
                </apply>
                <apply>
                    <divide/>
                    <apply>
                        <minus/>
                        <ci> s_infinity </ci>
                        <ci> s </ci>
                    </apply>
                    <ci> tau_s </ci>
                </apply>
            </apply>
            <apply id="s_infinity_calculation">
                <eq/>
                <ci> s_infinity </ci>
                <apply>
                    <divide/>
                    <cn cellml:units="dimensionless" xmlns:cellml="http://www.cellml.org/cellml/1.0#"> 1.0 </cn>
                    <apply>
                        <plus/>
                        <cn cellml:units="dimensionless" xmlns:cellml="http://www.cellml.org/cellml/1.0#"> 1.0 </cn>
                        <apply>
                            <exp/>
                            <apply>
                                <divide/>
                                <apply>
                                    <minus/>
                                    <ci> V_s </ci>
                                    <ci> V </ci>
                                </apply>
                                <ci> theta_s </ci>
                            </apply>
                        </apply>
                    </apply>
                </apply>
            </apply>
        </math>
    </component>
    <component cmeta:id="id_000000012" name="ATP_sensitive_potassium_current">
        <variable cmeta:id="ATP_sensitive_potassium_current_i_K_ATP" name="i_K_ATP" public_interface="out" units="picoA"/>
        <variable cmeta:id="id_000000013" initial_value="1.2" name="g_K_ATP" units="nanoS"/>
        <variable initial_value="0.5" name="p" units="dimensionless"/>
        <variable name="time" public_interface="in" units="millisecond"/>
        <variable name="V" public_interface="in" units="millivolt"/>
        <variable cmeta:id="id_000000014" name="V_K" public_interface="in" units="millivolt"/>
        <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply id="i_K_ATP_calculation">
                <eq/>
                <ci> i_K_ATP </ci>
                <apply>
                    <times/>
                    <ci> g_K_ATP </ci>
                    <ci> p </ci>
                    <apply>
                        <minus/>
                        <ci> V </ci>
                        <ci> V_K </ci>
                    </apply>
                </apply>
            </apply>
        </math>
    </component>
    <group>
        <relationship_ref relationship="encapsulation"/>
        <component_ref component="calcium_current">
            <component_ref component="calcium_current_m_gate"/>
        </component_ref>
        <component_ref component="potassium_current">
            <component_ref component="potassium_current_n_gate"/>
        </component_ref>
        <component_ref component="slow_current">
            <component_ref component="slow_current_s_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="potassium_current" component_2="environment"/>
        <map_variables variable_1="time" variable_2="time"/>
    </connection>
    <connection>
        <map_components component_1="slow_current" component_2="environment"/>
        <map_variables variable_1="time" variable_2="time"/>
    </connection>
    <connection>
        <map_components component_1="ATP_sensitive_potassium_current" component_2="environment"/>
        <map_variables variable_1="time" variable_2="time"/>
    </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="potassium_current" component_2="membrane"/>
        <map_variables variable_1="V" variable_2="V"/>
        <map_variables variable_1="i_K" variable_2="i_K"/>
        <map_variables variable_1="tau" variable_2="tau"/>
    </connection>
    <connection>
        <map_components component_1="slow_current" component_2="membrane"/>
        <map_variables variable_1="V" variable_2="V"/>
        <map_variables variable_1="i_s" variable_2="i_s"/>
    </connection>
    <connection>
        <map_components component_1="ATP_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="potassium_current" component_2="slow_current"/>
        <map_variables variable_1="V_K" variable_2="V_K"/>
    </connection>
    <connection>
        <map_components component_1="potassium_current" component_2="ATP_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="V" variable_2="V"/>
    </connection>
    <connection>
        <map_components component_1="potassium_current" component_2="potassium_current_n_gate"/>
        <map_variables variable_1="n" variable_2="n"/>
        <map_variables variable_1="V" variable_2="V"/>
        <map_variables variable_1="time" variable_2="time"/>
        <map_variables variable_1="tau" variable_2="tau"/>
    </connection>
    <connection>
        <map_components component_1="slow_current" component_2="slow_current_s_gate"/>
        <map_variables variable_1="s" variable_2="s"/>
        <map_variables variable_1="V" variable_2="V"/>
        <map_variables variable_1="time" variable_2="time"/>
    </connection>
    <rdf:RDF>
        <rdf:Description rdf:about="#id_000000001">
            <isVersionOf xmlns="http://biomodels.net/biology-qualifiers/">
                <rdf:Description rdf:about="http://identifiers.org/go/GO:0045837"/>
            </isVersionOf>
            <isVersionOf xmlns="http://biomodels.net/biology-qualifiers/">
                <rdf:Description rdf:about="http://identifiers.org/go/GO:0060075"/>
            </isVersionOf>
            <isVersionOf xmlns="http://biomodels.net/biology-qualifiers/">
                <rdf:Description rdf:about="http://identifiers.org/go/GO:0030322"/>
            </isVersionOf>
        </rdf:Description>
        <rdf:Description rdf:about="#id_000000002">
            <isVersionOf xmlns="http://biomodels.net/biology-qualifiers/">
                <rdf:Description rdf:about="http://identifiers.org/go/GO:0005267"/>
            </isVersionOf>
            <isVersionOf xmlns="http://biomodels.net/biology-qualifiers/">
                <rdf:Description rdf:about="http://identifiers.org/go/GO:0034705"/>
            </isVersionOf>
            <isVersionOf xmlns="http://biomodels.net/biology-qualifiers/">
                <rdf:Description rdf:about="http://identifiers.org/go/GO:0005249"/>
            </isVersionOf>
            <isVersionOf xmlns="http://biomodels.net/biology-qualifiers/">
                <rdf:Description rdf:about="http://identifiers.org/go/GO:0008076"/>
            </isVersionOf>
        </rdf:Description>
        <rdf:Description rdf:about="#id_000000003">
            <isVersionOf xmlns="http://biomodels.net/biology-qualifiers/">
                <rdf:Description rdf:about="http://identifiers.org/go/GO:0005267"/>
            </isVersionOf>
            <isVersionOf xmlns="http://biomodels.net/biology-qualifiers/">
                <rdf:Description rdf:about="http://identifiers.org/go/GO:0034705"/>
            </isVersionOf>
            <isVersionOf xmlns="http://biomodels.net/biology-qualifiers/">
                <rdf:Description rdf:about="http://identifiers.org/go/GO:0005249"/>
            </isVersionOf>
            <isVersionOf xmlns="http://biomodels.net/biology-qualifiers/">
                <rdf:Description rdf:about="http://identifiers.org/go/GO:0008076"/>
            </isVersionOf>
            <isVersionOf xmlns="http://biomodels.net/biology-qualifiers/">
                <rdf:Description rdf:about="http://identifiers.org/go/GO:0008282"/>
            </isVersionOf>
        </rdf:Description>
        <rdf:Description rdf:about="#id_000000004">
            <isVersionOf xmlns="http://biomodels.net/biology-qualifiers/">
                <rdf:Description rdf:about="http://identifiers.org/go/GO:0005267"/>
            </isVersionOf>
            <isVersionOf xmlns="http://biomodels.net/biology-qualifiers/">
                <rdf:Description rdf:about="http://identifiers.org/go/GO:0034705"/>
            </isVersionOf>
            <isVersionOf xmlns="http://biomodels.net/biology-qualifiers/">
                <rdf:Description rdf:about="http://identifiers.org/go/GO:0005249"/>
            </isVersionOf>
            <isVersionOf xmlns="http://biomodels.net/biology-qualifiers/">
                <rdf:Description rdf:about="http://identifiers.org/go/GO:0008076"/>
            </isVersionOf>
        </rdf:Description>
        <rdf:Description rdf:about="#potassium_current_i_K">
            <isVersionOf xmlns="http://biomodels.net/biology-qualifiers/">
                <rdf:Description rdf:about="http://identifiers.org/go/GO:0005267"/>
            </isVersionOf>
            <isVersionOf xmlns="http://biomodels.net/biology-qualifiers/">
                <rdf:Description rdf:about="http://identifiers.org/go/GO:0034705"/>
            </isVersionOf>
            <isVersionOf xmlns="http://biomodels.net/biology-qualifiers/">
                <rdf:Description rdf:about="http://identifiers.org/go/GO:0005249"/>
            </isVersionOf>
            <isVersionOf xmlns="http://biomodels.net/biology-qualifiers/">
                <rdf:Description rdf:about="http://identifiers.org/go/GO:0008076"/>
            </isVersionOf>
        </rdf:Description>
        <rdf:Description rdf:about="#id_000000005">
            <isVersionOf xmlns="http://biomodels.net/biology-qualifiers/">
                <rdf:Description rdf:about="http://identifiers.org/go/GO:0005267"/>
            </isVersionOf>
            <isVersionOf xmlns="http://biomodels.net/biology-qualifiers/">
                <rdf:Description rdf:about="http://identifiers.org/go/GO:0034705"/>
            </isVersionOf>
            <isVersionOf xmlns="http://biomodels.net/biology-qualifiers/">
                <rdf:Description rdf:about="http://identifiers.org/go/GO:0005249"/>
            </isVersionOf>
            <isVersionOf xmlns="http://biomodels.net/biology-qualifiers/">
                <rdf:Description rdf:about="http://identifiers.org/go/GO:0008076"/>
            </isVersionOf>
        </rdf:Description>
        <rdf:Description rdf:about="#id_000000006">
            <isVersionOf xmlns="http://biomodels.net/biology-qualifiers/">
                <rdf:Description rdf:about="http://identifiers.org/go/GO:0005267"/>
            </isVersionOf>
            <isVersionOf xmlns="http://biomodels.net/biology-qualifiers/">
                <rdf:Description rdf:about="http://identifiers.org/go/GO:0034705"/>
            </isVersionOf>
            <isVersionOf xmlns="http://biomodels.net/biology-qualifiers/">
                <rdf:Description rdf:about="http://identifiers.org/go/GO:0005249"/>
            </isVersionOf>
            <isVersionOf xmlns="http://biomodels.net/biology-qualifiers/">
                <rdf:Description rdf:about="http://identifiers.org/go/GO:0008076"/>
            </isVersionOf>
        </rdf:Description>
        <rdf:Description rdf:about="#id_000000007">
            <isVersionOf xmlns="http://biomodels.net/biology-qualifiers/">
                <rdf:Description rdf:about="http://identifiers.org/go/GO:0005267"/>
            </isVersionOf>
            <isVersionOf xmlns="http://biomodels.net/biology-qualifiers/">
                <rdf:Description rdf:about="http://identifiers.org/go/GO:0034705"/>
            </isVersionOf>
            <isVersionOf xmlns="http://biomodels.net/biology-qualifiers/">
                <rdf:Description rdf:about="http://identifiers.org/go/GO:0005249"/>
            </isVersionOf>
            <isVersionOf xmlns="http://biomodels.net/biology-qualifiers/">
                <rdf:Description rdf:about="http://identifiers.org/go/GO:0008076"/>
            </isVersionOf>
        </rdf:Description>
        <rdf:Description rdf:about="#id_000000008">
            <isVersionOf xmlns="http://biomodels.net/biology-qualifiers/">
                <rdf:Description rdf:about="http://identifiers.org/go/GO:0005267"/>
            </isVersionOf>
            <isVersionOf xmlns="http://biomodels.net/biology-qualifiers/">
                <rdf:Description rdf:about="http://identifiers.org/go/GO:0034705"/>
            </isVersionOf>
            <isVersionOf xmlns="http://biomodels.net/biology-qualifiers/">
                <rdf:Description rdf:about="http://identifiers.org/go/GO:0005249"/>
            </isVersionOf>
            <isVersionOf xmlns="http://biomodels.net/biology-qualifiers/">
                <rdf:Description rdf:about="http://identifiers.org/go/GO:0008076"/>
            </isVersionOf>
        </rdf:Description>
        <rdf:Description rdf:about="#id_000000009">
            <isVersionOf xmlns="http://biomodels.net/biology-qualifiers/">
                <rdf:Description rdf:about="http://identifiers.org/go/GO:0005267"/>
            </isVersionOf>
            <isVersionOf xmlns="http://biomodels.net/biology-qualifiers/">
                <rdf:Description rdf:about="http://identifiers.org/go/GO:0034705"/>
            </isVersionOf>
            <isVersionOf xmlns="http://biomodels.net/biology-qualifiers/">
                <rdf:Description rdf:about="http://identifiers.org/go/GO:0005249"/>
            </isVersionOf>
            <isVersionOf xmlns="http://biomodels.net/biology-qualifiers/">
                <rdf:Description rdf:about="http://identifiers.org/go/GO:0008076"/>
            </isVersionOf>
        </rdf:Description>
        <rdf:Description rdf:about="#id_000000010">
            <isVersionOf xmlns="http://biomodels.net/biology-qualifiers/">
                <rdf:Description rdf:about="http://identifiers.org/go/GO:0005267"/>
            </isVersionOf>
            <isVersionOf xmlns="http://biomodels.net/biology-qualifiers/">
                <rdf:Description rdf:about="http://identifiers.org/go/GO:0034705"/>
            </isVersionOf>
            <isVersionOf xmlns="http://biomodels.net/biology-qualifiers/">
                <rdf:Description rdf:about="http://identifiers.org/go/GO:0005249"/>
            </isVersionOf>
            <isVersionOf xmlns="http://biomodels.net/biology-qualifiers/">
                <rdf:Description rdf:about="http://identifiers.org/go/GO:0008076"/>
            </isVersionOf>
        </rdf:Description>
        <rdf:Description rdf:about="#id_000000011">
            <isVersionOf xmlns="http://biomodels.net/biology-qualifiers/">
                <rdf:Description rdf:about="http://identifiers.org/go/GO:0005267"/>
            </isVersionOf>
            <isVersionOf xmlns="http://biomodels.net/biology-qualifiers/">
                <rdf:Description rdf:about="http://identifiers.org/go/GO:0034705"/>
            </isVersionOf>
            <isVersionOf xmlns="http://biomodels.net/biology-qualifiers/">
                <rdf:Description rdf:about="http://identifiers.org/go/GO:0005249"/>
            </isVersionOf>
            <isVersionOf xmlns="http://biomodels.net/biology-qualifiers/">
                <rdf:Description rdf:about="http://identifiers.org/go/GO:0008076"/>
            </isVersionOf>
        </rdf:Description>
        <rdf:Description rdf:about="#id_000000012">
            <isVersionOf xmlns="http://biomodels.net/biology-qualifiers/">
                <rdf:Description rdf:about="http://identifiers.org/go/GO:0005267"/>
            </isVersionOf>
            <isVersionOf xmlns="http://biomodels.net/biology-qualifiers/">
                <rdf:Description rdf:about="http://identifiers.org/go/GO:0034705"/>
            </isVersionOf>
            <isVersionOf xmlns="http://biomodels.net/biology-qualifiers/">
                <rdf:Description rdf:about="http://identifiers.org/go/GO:0005249"/>
            </isVersionOf>
            <isVersionOf xmlns="http://biomodels.net/biology-qualifiers/">
                <rdf:Description rdf:about="http://identifiers.org/go/GO:0008076"/>
            </isVersionOf>
            <isVersionOf xmlns="http://biomodels.net/biology-qualifiers/">
                <rdf:Description rdf:about="http://identifiers.org/go/GO:0008282"/>
            </isVersionOf>
        </rdf:Description>
        <rdf:Description rdf:about="#ATP_sensitive_potassium_current_i_K_ATP">
            <isVersionOf xmlns="http://biomodels.net/biology-qualifiers/">
                <rdf:Description rdf:about="http://identifiers.org/go/GO:0005267"/>
            </isVersionOf>
            <isVersionOf xmlns="http://biomodels.net/biology-qualifiers/">
                <rdf:Description rdf:about="http://identifiers.org/go/GO:0034705"/>
            </isVersionOf>
            <isVersionOf xmlns="http://biomodels.net/biology-qualifiers/">
                <rdf:Description rdf:about="http://identifiers.org/go/GO:0005249"/>
            </isVersionOf>
            <isVersionOf xmlns="http://biomodels.net/biology-qualifiers/">
                <rdf:Description rdf:about="http://identifiers.org/go/GO:0008076"/>
            </isVersionOf>
            <isVersionOf xmlns="http://biomodels.net/biology-qualifiers/">
                <rdf:Description rdf:about="http://identifiers.org/go/GO:0008282"/>
            </isVersionOf>
        </rdf:Description>
        <rdf:Description rdf:about="#id_000000013">
            <isVersionOf xmlns="http://biomodels.net/biology-qualifiers/">
                <rdf:Description rdf:about="http://identifiers.org/go/GO:0005267"/>
            </isVersionOf>
            <isVersionOf xmlns="http://biomodels.net/biology-qualifiers/">
                <rdf:Description rdf:about="http://identifiers.org/go/GO:0034705"/>
            </isVersionOf>
            <isVersionOf xmlns="http://biomodels.net/biology-qualifiers/">
                <rdf:Description rdf:about="http://identifiers.org/go/GO:0005249"/>
            </isVersionOf>
            <isVersionOf xmlns="http://biomodels.net/biology-qualifiers/">
                <rdf:Description rdf:about="http://identifiers.org/go/GO:0008076"/>
            </isVersionOf>
            <isVersionOf xmlns="http://biomodels.net/biology-qualifiers/">
                <rdf:Description rdf:about="http://identifiers.org/go/GO:0008282"/>
            </isVersionOf>
        </rdf:Description>
        <rdf:Description rdf:about="#id_000000014">
            <isVersionOf xmlns="http://biomodels.net/biology-qualifiers/">
                <rdf:Description rdf:about="http://identifiers.org/go/GO:0005267"/>
            </isVersionOf>
            <isVersionOf xmlns="http://biomodels.net/biology-qualifiers/">
                <rdf:Description rdf:about="http://identifiers.org/go/GO:0034705"/>
            </isVersionOf>
            <isVersionOf xmlns="http://biomodels.net/biology-qualifiers/">
                <rdf:Description rdf:about="http://identifiers.org/go/GO:0005249"/>
            </isVersionOf>
            <isVersionOf xmlns="http://biomodels.net/biology-qualifiers/">
                <rdf:Description rdf:about="http://identifiers.org/go/GO:0008076"/>
            </isVersionOf>
        </rdf:Description>
        <rdf:Description rdf:about="#id_000000015">
            <isVersionOf xmlns="http://biomodels.net/biology-qualifiers/">
                <rdf:Description rdf:about="http://identifiers.org/go/GO:0005262"/>
            </isVersionOf>
            <isVersionOf xmlns="http://biomodels.net/biology-qualifiers/">
                <rdf:Description rdf:about="http://identifiers.org/go/GO:0034704"/>
            </isVersionOf>
            <isVersionOf xmlns="http://biomodels.net/biology-qualifiers/">
                <rdf:Description rdf:about="http://identifiers.org/go/GO:0005245"/>
            </isVersionOf>
            <isVersionOf xmlns="http://biomodels.net/biology-qualifiers/">
                <rdf:Description rdf:about="http://identifiers.org/go/GO:0005891"/>
            </isVersionOf>
        </rdf:Description>
        <rdf:Description rdf:about="#id_000000016">
            <isVersionOf xmlns="http://biomodels.net/biology-qualifiers/">
                <rdf:Description rdf:about="http://identifiers.org/go/GO:0005262"/>
            </isVersionOf>
            <isVersionOf xmlns="http://biomodels.net/biology-qualifiers/">
                <rdf:Description rdf:about="http://identifiers.org/go/GO:0034704"/>
            </isVersionOf>
            <isVersionOf xmlns="http://biomodels.net/biology-qualifiers/">
                <rdf:Description rdf:about="http://identifiers.org/go/GO:0005245"/>
            </isVersionOf>
            <isVersionOf xmlns="http://biomodels.net/biology-qualifiers/">
                <rdf:Description rdf:about="http://identifiers.org/go/GO:0005891"/>
            </isVersionOf>
        </rdf:Description>
        <rdf:Description rdf:about="#id_000000017">
            <isVersionOf xmlns="http://biomodels.net/biology-qualifiers/">
                <rdf:Description rdf:about="http://identifiers.org/go/GO:0005262"/>
            </isVersionOf>
            <isVersionOf xmlns="http://biomodels.net/biology-qualifiers/">
                <rdf:Description rdf:about="http://identifiers.org/go/GO:0034704"/>
            </isVersionOf>
            <isVersionOf xmlns="http://biomodels.net/biology-qualifiers/">
                <rdf:Description rdf:about="http://identifiers.org/go/GO:0005245"/>
            </isVersionOf>
            <isVersionOf xmlns="http://biomodels.net/biology-qualifiers/">
                <rdf:Description rdf:about="http://identifiers.org/go/GO:0005891"/>
            </isVersionOf>
        </rdf:Description>
        <rdf:Description rdf:about="#id_000000018">
            <isVersionOf xmlns="http://biomodels.net/biology-qualifiers/">
                <rdf:Description rdf:about="http://identifiers.org/go/GO:0005262"/>
            </isVersionOf>
            <isVersionOf xmlns="http://biomodels.net/biology-qualifiers/">
                <rdf:Description rdf:about="http://identifiers.org/go/GO:0034704"/>
            </isVersionOf>
            <isVersionOf xmlns="http://biomodels.net/biology-qualifiers/">
                <rdf:Description rdf:about="http://identifiers.org/go/GO:0005245"/>
            </isVersionOf>
            <isVersionOf xmlns="http://biomodels.net/biology-qualifiers/">
                <rdf:Description rdf:about="http://identifiers.org/go/GO:0005891"/>
            </isVersionOf>
        </rdf:Description>
        <rdf:Description rdf:about="#id_000000019">
            <isVersionOf xmlns="http://biomodels.net/biology-qualifiers/">
                <rdf:Description rdf:about="http://identifiers.org/go/GO:0005262"/>
            </isVersionOf>
            <isVersionOf xmlns="http://biomodels.net/biology-qualifiers/">
                <rdf:Description rdf:about="http://identifiers.org/go/GO:0034704"/>
            </isVersionOf>
            <isVersionOf xmlns="http://biomodels.net/biology-qualifiers/">
                <rdf:Description rdf:about="http://identifiers.org/go/GO:0005245"/>
            </isVersionOf>
            <isVersionOf xmlns="http://biomodels.net/biology-qualifiers/">
                <rdf:Description rdf:about="http://identifiers.org/go/GO:0005891"/>
            </isVersionOf>
        </rdf:Description>
        <rdf:Description rdf:about="#id_000000020">
            <isVersionOf xmlns="http://biomodels.net/biology-qualifiers/">
                <rdf:Description rdf:about="http://identifiers.org/go/GO:0005262"/>
            </isVersionOf>
            <isVersionOf xmlns="http://biomodels.net/biology-qualifiers/">
                <rdf:Description rdf:about="http://identifiers.org/go/GO:0034704"/>
            </isVersionOf>
            <isVersionOf xmlns="http://biomodels.net/biology-qualifiers/">
                <rdf:Description rdf:about="http://identifiers.org/go/GO:0005245"/>
            </isVersionOf>
            <isVersionOf xmlns="http://biomodels.net/biology-qualifiers/">
                <rdf:Description rdf:about="http://identifiers.org/go/GO:0005891"/>
            </isVersionOf>
        </rdf:Description>
        <rdf:Description rdf:about="#id_000000021">
            <isVersionOf xmlns="http://biomodels.net/biology-qualifiers/">
                <rdf:Description rdf:about="http://identifiers.org/go/GO:0005262"/>
            </isVersionOf>
            <isVersionOf xmlns="http://biomodels.net/biology-qualifiers/">
                <rdf:Description rdf:about="http://identifiers.org/go/GO:0034704"/>
            </isVersionOf>
            <isVersionOf xmlns="http://biomodels.net/biology-qualifiers/">
                <rdf:Description rdf:about="http://identifiers.org/go/GO:0005245"/>
            </isVersionOf>
            <isVersionOf xmlns="http://biomodels.net/biology-qualifiers/">
                <rdf:Description rdf:about="http://identifiers.org/go/GO:0005891"/>
            </isVersionOf>
        </rdf:Description>
    </rdf:RDF>
</model>