- Author:
- Catherine Lloyd <c.lloyd@auckland.ac.nz>
- Date:
- 2009-12-17 13:28:27+13:00
- Desc:
- Added model file to the workspace.
- Permanent Source URI:
- http://models.cellml.org/workspace/wierschem_bertram_2004/rawfile/45096dc84f15d30f672a8ef493b2e37361537316/wierschem_2004.cellml
<?xml version="1.0"?>
<!-- FILE : wierschem_2004.cellml
CREATED : 14th Dec 2009
LAST MODIFIED : 16th Dec 2009
AUTHOR : Ethan Choi
MODEL STATUS : This model conforms to the CellML 1.1 Specification. Runs in COR and PCEnv
DESCRIPTION : This file contains a CellML description of Wierschem and Bertram's 2004 mathematical model for complex bursting in pancreatic islets -->
<model name="wierschem_2004" cmeta:id="wierschem_2004" xmlns="http://www.cellml.org/cellml/1.0#" xmlns:cellml="http://www.cellml.org/cellml/1.0#" xmlns:cmeta="http://www.cellml.org/metadata/1.0#" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:dcterms="http://purl.org/dc/terms/" xmlns:bqs="http://www.cellml.org/bqs/1.0#" xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#">
<!-- documentation -->
<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
<articleinfo>
<title>Complex bursting in pancreatic islets: a potential glycolytic mechanism</title>
<author>
<firstname>Ethan</firstname>
<surname>Choi</surname>
<affiliation>
<shortaffil>Bioengineering Institute, University of Auckland</shortaffil>
</affiliation>
</author>
</articleinfo>
<section id="sec_status">
<title>Model Status</title>
<para>This model has been built with the differential expressions in Wierschem's 2004 paper and also the XPPAUT code from Richard Bertram. This file is known to run in PCEnv and COR, however the model works in milliseconds, and must be run for at least 600000 time units or more (to simulate 10 minutes) and could not be changed to portray minutes instead. Due to the large iterations, and large point density required to run the model, problems were found in PCEnv and COR where the model would crash or not display properly giving an memory exceded error. Current parameterization of the model replicates Figure 9 of the paper. The initial conditions for all variables were provided in the Bertram code (given as V=-66, n=0, c=0.17, ATP=2.4, ADP=0.05) however these figures still required a warmup period for the functions so they were changed by running the model to steady state then cloning to the output to better replicate the figures from the paper. </para>
</section>
<sect1 id="sec_structure">
<title>Model Structure</title>
<para>ABSTRACT: The electrical activity of insulin-secreting pancreatic islets of Langerhans is characterized by bursts of action potentials. Most often this bursting is periodic, but in some cases it is modulated by an underlying slower rhythm. We suggest that the modulatory rhythm for this complex bursting pattern is due to oscillations in glycolysis, while the bursting itself is generated by some other slow process. To demonstrate this hypothesis, we couple a minimal model of glycolytic oscillations to a minimal model for activity-dependent bursting in islets. We show that the combined model can reproduce several complex bursting patterns from mouse islets published in the literature, and we illustrate how these complex oscillations are produced through the use of a fast/slow analysis.</para>
<para>
Complex bursting in pancreatic islets: a potential glycolytic mechanism, Wierschem, Bertram, 2004, <emphasis>Journal of Theoretical Biology</emphasis>
, 228, 513-521. <ulink url="http://www.ncbi.nlm.nih.gov/pubmed/15178199">PubMed ID: 15178199</ulink>
</para>
<informalfigure>
<mediaobject>
<imageobject>
<objectinfo>
<title>Model Diagram</title>
</objectinfo>
<imagedata fileref="wierschem_2004.png"/>
</imageobject>
</mediaobject>
<caption>Schematic diagram of the composite model.</caption>
</informalfigure>
</sect1>
</article>
</documentation>
<!-- units -->
<units name="millisecond">
<unit prefix="milli" units="second"/>
</units>
<units name="per_millisecond">
<unit exponent="-1" units="millisecond"/>
</units>
<units name="millivolt">
<unit prefix="milli" units="volt"/>
</units>
<units name="picosiemens">
<unit prefix="pico" units="siemens"/>
</units>
<units name="per_litre">
<unit exponent="-1" units="litre"/>
</units>
<units name="micromolar">
<unit prefix="micro" units="mole"/>
<unit units="per_litre"/>
</units>
<units name="femtoampere">
<unit prefix="femto" units="ampere"/>
</units>
<units name="micromolar_per_fA_ms">
<unit units="micromolar"/>
<unit exponent="-1" units="femtoampere"/>
<unit exponent="-1" units="millisecond"/>
</units>
<units name="micromolar_per_ms">
<unit units="micromolar"/>
<unit exponent="-1" units="millisecond"/>
</units>
<units name="femtofarad">
<unit prefix="femto" units="farad"/>
</units>
<!-- components -->
<component name="environment">
<variable name="time" public_interface="out" units="millisecond"/>
</component>
<component name="nucleotides" cmeta:id="nucleotides">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#nucleotides">This component stores information related to the ATP and ADP model</rdf:Description>
<rdf:Description rdf:about="#ADP">adenosine diphosphate</rdf:Description>
<rdf:Description rdf:about="#ATP">adenosine triphosphate</rdf:Description>
</rdf:RDF>
<variable name="time" public_interface="in" units="millisecond"/>
<variable name="tau_c" initial_value="1200" units="second"/>
<variable name="eta" initial_value="185" units="dimensionless"/>
<variable name="v" initial_value="10" units="dimensionless"/>
<variable name="k" initial_value="20" units="dimensionless"/>
<variable name="phi" units="dimensionless"/>
<variable name="ADP" cmeta:id="ADP" initial_value="0.085817" units="dimensionless"/>
<variable name="ATP" cmeta:id="ATP" initial_value="2.1047" public_interface="out" units="dimensionless"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>phi</ci>
<apply>
<times/>
<ci>ATP</ci>
<apply>
<power/>
<apply>
<plus/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.1#" cellml:units="dimensionless">1</cn>
<apply>
<times/>
<ci>k</ci>
<ci>ADP</ci>
</apply>
</apply>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.1#" cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>ATP</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci>v</ci>
<ci>phi</ci>
</apply>
<apply>
<times/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.1#" cellml:units="dimensionless">1000</cn>
<ci>tau_c</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>ADP</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci>phi</ci>
<apply>
<times/>
<ci>eta</ci>
<ci>ADP</ci>
</apply>
</apply>
<apply>
<times/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.1#" cellml:units="dimensionless">1000</cn>
<ci>tau_c</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="membrane" cmeta:id="membrane">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#membrane">This component stores information related the equations for voltage</rdf:Description>
<rdf:Description rdf:about="#V">voltage</rdf:Description>
</rdf:RDF>
<variable name="time" public_interface="in" units="millisecond"/>
<variable name="C_m" initial_value="5300" units="femtofarad"/>
<variable name="I_Ca" public_interface="in" units="femtoampere"/>
<variable name="I_K" public_interface="in" units="femtoampere"/>
<variable name="I_KCa" public_interface="in" units="femtoampere"/>
<variable name="I_KATP" public_interface="in" units="femtoampere"/>
<variable name="V" cmeta:id="V" initial_value="-67.018" public_interface="out" units="millivolt"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<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_KCa</ci>
<ci>I_KATP</ci>
</apply>
</apply>
<ci>C_m</ci>
</apply>
</apply>
</math>
</component>
<component name="Ca_current" cmeta:id="Ca_current">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#Ca_current">This component stores information related to the Ca2+ current</rdf:Description>
<rdf:Description rdf:about="#m_infinity">steady state function</rdf:Description>
<rdf:Description rdf:about="#I_Ca">Ca2+ current</rdf:Description>
</rdf:RDF>
<variable name="g_Ca_" initial_value="1200" units="picosiemens"/>
<variable name="V_Ca" initial_value="25" units="millivolt"/>
<variable name="v_m" initial_value="-20" units="millivolt"/>
<variable name="s_m" initial_value="12" units="millivolt"/>
<variable name="V" public_interface="in" units="millivolt"/>
<variable name="m_infinity" cmeta:id="m_infinity" units="dimensionless"/>
<variable name="I_Ca" cmeta:id="I_Ca" public_interface="out" units="femtoampere"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<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>
<apply>
<eq/>
<ci>m_infinity</ci>
<apply>
<divide/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.1#" cellml:units="dimensionless">1</cn>
<apply>
<plus/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.1#" cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<ci>v_m</ci>
<ci>V</ci>
</apply>
<ci>s_m</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="K_current" cmeta:id="K_current">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#K_current">This component stores information related to the K+ current</rdf:Description>
<rdf:Description rdf:about="#I_K">K+ current</rdf:Description>
</rdf:RDF>
<variable name="time" private_interface="out" public_interface="in" units="millisecond"/>
<variable name="g_K_" initial_value="3000" units="picosiemens"/>
<variable name="V_K" initial_value="-75" public_interface="out" units="millivolt"/>
<variable name="n" private_interface="in" units="dimensionless"/>
<variable name="V" private_interface="out" public_interface="in" units="millivolt"/>
<variable name="I_K" cmeta:id="I_K" public_interface="out" units="femtoampere"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<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="Ca_activated_K_current" cmeta:id="Ca_activated_K_current">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#Ca_activated_K_current">This component stores information related to the Ca2+ -activated K+ current</rdf:Description>
<rdf:Description rdf:about="#omega">the Ca2+ dependent activation variable for I_KCa</rdf:Description>
<rdf:Description rdf:about="#I_KCa">Ca2+ activated K+ current</rdf:Description>
</rdf:RDF>
<variable name="g_KCa_" initial_value="300" units="picosiemens"/>
<variable name="k_D" initial_value="0.3" units="micromolar"/>
<variable name="V_K" public_interface="in" units="millivolt"/>
<variable name="c" public_interface="in" units="micromolar"/>
<variable name="V" public_interface="in" units="millivolt"/>
<variable name="omega" cmeta:id="omega" units="dimensionless"/>
<variable name="I_KCa" cmeta:id="I_KCa" public_interface="out" units="femtoampere"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>omega</ci>
<apply>
<divide/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.1#" cellml:units="dimensionless">1</cn>
<apply>
<plus/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.1#" cellml:units="dimensionless">1</cn>
<apply>
<divide/>
<ci>k_D</ci>
<ci>c</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>I_KCa</ci>
<apply>
<times/>
<ci>g_KCa_</ci>
<ci>omega</ci>
<apply>
<minus/>
<ci>V</ci>
<ci>V_K</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="ATP_sensitive_K_current" cmeta:id="ATP_sensitive_K_current">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#ATP_sensitive_K_current">This component stores information related to the ATP-sensitive K+ current</rdf:Description>
<rdf:Description rdf:about="#I_KATP">ATP-sensitive K+ current</rdf:Description>
</rdf:RDF>
<variable name="time" private_interface="out" public_interface="in" units="millisecond"/>
<variable name="V_K" public_interface="in" units="millivolt"/>
<variable name="ATP" private_interface="in" units="dimensionless"/>
<variable name="g_KATP_" initial_value="350" units="picosiemens"/>
<variable name="V" public_interface="in" units="millivolt"/>
<variable name="I_KATP" cmeta:id="I_KATP" public_interface="out" units="femtoampere"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>I_KATP</ci>
<apply>
<divide/>
<apply>
<times/>
<apply>
<minus/>
<ci>V</ci>
<ci>V_K</ci>
</apply>
<ci>g_KATP_</ci>
</apply>
<ci>ATP</ci>
</apply>
</apply>
</math>
</component>
<component name="K_channel_activation" cmeta:id="K_channel_activation">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#K_channel_activation">This component stores information related to the K+ channel activation (n)</rdf:Description>
<rdf:Description rdf:about="#n_infinity">steady-state function</rdf:Description>
<rdf:Description rdf:about="#n">K+ channel activation</rdf:Description>
</rdf:RDF>
<variable name="time" public_interface="in" units="millisecond"/>
<variable name="tau_n" initial_value="16" units="millisecond"/>
<variable name="v_n" initial_value="-16" units="millivolt"/>
<variable name="s_n" initial_value="5.6" units="millivolt"/>
<variable name="V" public_interface="in" units="millivolt"/>
<variable name="n_infinity" cmeta:id="n_infinity" units="dimensionless"/>
<variable name="n" cmeta:id="n" initial_value="0.00011" public_interface="out" units="dimensionless"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>n_infinity</ci>
<apply>
<divide/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.1#" cellml:units="dimensionless">1</cn>
<apply>
<plus/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.1#" cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<ci>v_n</ci>
<ci>V</ci>
</apply>
<ci>s_n</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>n</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci>n_infinity</ci>
<ci>n</ci>
</apply>
<ci>tau_n</ci>
</apply>
</apply>
</math>
</component>
<component name="cytosolic_Ca" cmeta:id="cytosolic_Ca">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#cytosolic_Ca">This component stores information related to the free cytosolic Ca2+ concentration</rdf:Description>
<rdf:Description rdf:about="#c">free cytosolic Ca2+ concentration</rdf:Description>
</rdf:RDF>
<variable name="time" public_interface="in" units="millisecond"/>
<variable name="J_mem" public_interface="in" units="micromolar_per_ms"/>
<variable name="c" cmeta:id="c" initial_value="0.15666" public_interface="out" units="micromolar"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>c</ci>
</apply>
<ci>J_mem</ci>
</apply>
</math>
</component>
<component name="Ca_influx" cmeta:id="Ca_influx">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#Ca_influx">This component stores information related to the Ca2+ influx through the membrane</rdf:Description>
<rdf:Description rdf:about="#J_mem">Ca2+ influx through the membrane</rdf:Description>
</rdf:RDF>
<variable name="f" initial_value="0.001" units="dimensionless"/>
<variable name="alpha" initial_value="0.00000225" units="micromolar_per_fA_ms"/>
<variable name="k_c" initial_value="0.1" units="per_millisecond"/>
<variable name="I_Ca" public_interface="in" units="femtoampere"/>
<variable name="c" public_interface="in" units="micromolar"/>
<variable name="J_mem" cmeta:id="J_mem" public_interface="out" units="micromolar_per_ms"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>J_mem</ci>
<apply>
<times/>
<apply>
<minus/>
<ci>f</ci>
</apply>
<apply>
<plus/>
<apply>
<times/>
<ci>alpha</ci>
<ci>I_Ca</ci>
</apply>
<apply>
<times/>
<ci>k_c</ci>
<ci>c</ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<!-- groups -->
<group>
<relationship_ref relationship="encapsulation"/>
<component_ref component="ATP_sensitive_K_current">
<component_ref component="nucleotides"/>
</component_ref>
<component_ref component="K_current">
<component_ref component="K_channel_activation"/>
</component_ref>
</group>
<!-- connections -->
<connection>
<map_components component_1="environment" component_2="membrane"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="environment" component_2="cytosolic_Ca"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="environment" component_2="K_current"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="environment" component_2="ATP_sensitive_K_current"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="ATP_sensitive_K_current" component_2="nucleotides"/>
<map_variables variable_1="ATP" variable_2="ATP"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="membrane" component_2="Ca_current"/>
<map_variables variable_1="V" variable_2="V"/>
<map_variables variable_1="I_Ca" variable_2="I_Ca"/>
</connection>
<connection>
<map_components component_1="membrane" component_2="K_current"/>
<map_variables variable_1="V" variable_2="V"/>
<map_variables variable_1="I_K" variable_2="I_K"/>
</connection>
<connection>
<map_components component_1="membrane" component_2="Ca_activated_K_current"/>
<map_variables variable_1="V" variable_2="V"/>
<map_variables variable_1="I_KCa" variable_2="I_KCa"/>
</connection>
<connection>
<map_components component_1="membrane" component_2="ATP_sensitive_K_current"/>
<map_variables variable_1="V" variable_2="V"/>
<map_variables variable_1="I_KATP" variable_2="I_KATP"/>
</connection>
<connection>
<map_components component_1="K_current" component_2="K_channel_activation"/>
<map_variables variable_1="V" variable_2="V"/>
<map_variables variable_1="n" variable_2="n"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="K_current" component_2="ATP_sensitive_K_current"/>
<map_variables variable_1="V_K" variable_2="V_K"/>
</connection>
<connection>
<map_components component_1="K_current" component_2="Ca_activated_K_current"/>
<map_variables variable_1="V_K" variable_2="V_K"/>
</connection>
<connection>
<map_components component_1="Ca_current" component_2="Ca_influx"/>
<map_variables variable_1="I_Ca" variable_2="I_Ca"/>
</connection>
<connection>
<map_components component_1="Ca_activated_K_current" component_2="cytosolic_Ca"/>
<map_variables variable_1="c" variable_2="c"/>
</connection>
<connection>
<map_components component_1="cytosolic_Ca" component_2="Ca_influx"/>
<map_variables variable_1="c" variable_2="c"/>
<map_variables variable_1="J_mem" variable_2="J_mem"/>
</connection>
<!-- metadata -->
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:bqs="http://www.cellml.org/bqs/1.0#" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:dcterms="http://purl.org/dc/terms/" xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#">
<rdf:Description rdf:about="">
<dc:creator xmlns:dc="http://purl.org/dc/elements/1.1/" rdf:parseType="Resource">
<vCard:N xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" rdf:parseType="Resource">
<vCard:Family>Choi</vCard:Family>
<vCard:Given>Ethan</vCard:Given>
</vCard:N>
<vCard:EMAIL xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" rdf:parseType="Resource">
<rdf:value>mcho099@aucklanduni.ac.nz</rdf:value>
<rdf:type rdf:resource="http://imc.org/vCard/3.0#internet"/>
</vCard:EMAIL>
<vCard:ORG xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" rdf:parseType="Resource">
<vCard:Orgname>The University of Auckland</vCard:Orgname>
<vCard:Orgunit>Auckland Bioengineering Institute</vCard:Orgunit>
</vCard:ORG>
</dc:creator>
<dcterms:created xmlns:dcterms="http://purl.org/dc/terms/" rdf:parseType="Resource">
<dcterms:W3CDTF>2009-12-16</dcterms:W3CDTF>
</dcterms:created>
<dcterms:created rdf:parseType="Resource">
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