- Author:
- Ethan Choi <mcho099@aucklanduni.ac.nz>
- Date:
- 2010-02-18 15:53:01+13:00
- Desc:
- Fixed model equations and components and now model can run. Cannot replicate figures however. Fixed RDF tags and removed links.
- Permanent Source URI:
- https://models.cellml.org/workspace/pedersen_bertram_sherman_2005/rawfile/86474d395066f9c5731f9ce6b268ce1d3b1f87ed/pedersen_bertram_sherman_2005.cellml
<?xml version="1.0" encoding="utf-8"?>
<!-- FILE : pedersen_bertram_sherman_2005.cellml
CREATED : 27th July 2007
LAST MODIFIED : 18th Feb 2010
AUTHOR : Catherine Lloyd
Bioengineering Institute
The University of Auckland
MODEL STATUS : This model conforms to the CellML 1.1 Specification.
DESCRIPTION : This file contains a CellML description of Pedersen, Bertram and Sherman's 2005 mathematical model of metabolically driven insulin secretion in pancreatic beta cells.
-->
<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="pedersen_model_2005" name="pedersen_bertram_sherman_model_2005_version01">
<!-- documentation -->
<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
<articleinfo>
<title>Intra- and inter-islet synchronization of metabolically driven insulin secretion</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 has been built with the differential expressions in Pedersen's 2005 paper. This file is known to run in PCEnv and COR, and the parameters have been set to table one. Currently the model cannot replicate the diagrams in the paper figures.</para>
</section>
<sect1 id="sec_structure">
<title>Model Structure</title>
<para>Insulin secretion from pancreatic beta-cells is known to be pulsatile, with a period of 5-10 milliseconds. It has been suggested that this pulsatile behaviour stems from oscillations in the glycolysis pathway, mediated by the enzyme phosphofructokinase (PFK). In turn, this rhythmical enzymatic behaviour induces periodic activity of ATP-dependent potassium channels (K(ATP)-channels) in the plasma membrane. Insulin pulsatility is impaired in diabetic patients, which are also relatively insulin insensitive. Target tissues, such as the liver, are more sensitive to pulsatile insulin than to constant levels, and therefore an improved understanding of the mechanisms underlying pulsatile insulin secretion is important in the search for a potential therapeutic treatment for diabetes.</para>
<para>The link between metabolism and calcium ion influx leading to insulin secretion is provided by the electrical activity of the beta-cells, which has a characteristic behaviour known as <emphasis>bursting</emphasis>. A burst consists of an active phase of spiking followed by a silent phase of membrane repolarisation. During the active burst calcium ions diffuse into the cell through voltage-gated calcium channels, and the subsequent rise in the cytosolic calcium concentration results in the secretion of insulin (see diagram below). </para>
<para>In the paper described here, Pedersen <emphasis>et al.</emphasis> present a mathematical model of metabolically driven insulin secretion. This model is based on one which has been published previously by Bertram <emphasis>et al.</emphasis> (2004), which has also been described in CellML and can be found in the model repository. Model simulation data indicate that electrical coupling is sufficient to synchronise electrical bursting activity and metabolic oscillations.</para>
<informalfigure float="0" id="fig_reaction_diagram">
<mediaobject>
<imageobject>
<objectinfo>
<title>model diagram</title>
</objectinfo>
<imagedata fileref="pedersen_2005.png"/>
</imageobject>
</mediaobject>
<caption>Schematic diagram of the pathways described by the mathematical model. Extracellular glucose (Ge) enters the pancreatic beta-cell through GLUT-2 transporters in the plasma membrane, and is subsequently broken down through a series of enzyme-catalysed reactions in the glycolysis pathway. The metabolic products of the glycolysis pathway feed into the mitchondria, the site of aerobic respiration, where they are used to produce ATP. ATP represents the common substrate, linking the metabolic (glycolysis) and electrical (membrane potential) components of the mathematical model by regulating the flow of potassium ions through the K(ATP)-channels in the plasma membrane. In turn, these control regulate the membrane potential and calcium ion flow leading to insulin secretion. Insulin acts to lower the plasma glucose concentration though the functions of the liver (represented by a dashed line).</caption>
</informalfigure>
<para>The complete original paper reference is cited below:</para>
<para>
Intra- and inter-islet synchronization of metabolically driven insulin secretion, Morten Gram Pedersen, Richard Bertram, and Arthur Sherman, 2005,<emphasis>Biophysical Journal</emphasis>
, 89, 107-119. <ulink url="http://www.ncbi.nlm.nih.gov/pubmed/15834002">PubMed ID: 15834002</ulink>
</para>
<para>
The authors highlight that the original model code can be downloaded <ulink url="http://mrb.niddk.nih.gov/sherman">here</ulink>
. The CellML translation of this model represents the core model and it will run in the PCEnv software. However the pulsatile behaviour of the model, as published in the original paper can not be recreated. To achieve these results I suspect several cell models have to be run simultaneously, generating many bursts which are clustered together into what is termed <emphasis>compound bursting</emphasis>
.</para>
</sect1>
</article>
</documentation>
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<cn cellml:units="dimensionless">1</cn>
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<cn cellml:units="dimensionless">1</cn>
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<cn cellml:units="dimensionless">1</cn>
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<cn cellml:units="dimensionless">1</cn>
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<variable name="Ca" units="micromolar" public_interface="in"/>
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<variable name="JGPDH" units="micromolar_millisecond" public_interface="in"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
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<eq/>
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<times/>
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<variable name="cm" units="femtofarad" initial_value="5300"/>
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<variable name="I_K" units="picoampere" public_interface="in"/>
<variable name="I_K_Ca" units="picoampere" public_interface="in"/>
<variable name="I_K_ATP" units="picoampere" public_interface="in"/>
<variable name="time" units="millisecond" public_interface="in"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
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<rdf:Description rdf:about="#I_K">
<dc:title xmlns:dc="http://purl.org/dc/elements/1.1/">I_K</dc:title>
<dcterms:alternative xmlns:dcterms="http://purl.org/dc/terms/">voltage-dependent potassium current</dcterms:alternative>
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<variable name="gK_" units="picosiemens" initial_value="2700"/>
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<variable name="vK" units="millivolt" public_interface="in"/>
<variable name="v" units="millivolt" public_interface="in" private_interface="out"/>
<variable name="n" units="dimensionless" private_interface="in"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
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<rdf:Description rdf:about="#n">
<dc:title xmlns:dc="http://purl.org/dc/elements/1.1/">n</dc:title>
<dcterms:alternative xmlns:dcterms="http://purl.org/dc/terms/">voltage-dependent potassium current n gate</dcterms:alternative>
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<variable name="n_infinity" units="dimensionless"/>
<variable name="tau_n" units="millisecond"/>
<variable name="time" units="millisecond" public_interface="in"/>
<variable name="v" units="millivolt" public_interface="in"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
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<eq/>
<apply>
<diff/>
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<apply>
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<eq/>
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<cosh/>
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<divide/>
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<plus/>
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<cn cellml:units="millivolt">22.4</cn>
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<eq/>
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<divide/>
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<cn cellml:units="dimensionless">1</cn>
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<divide/>
<apply>
<minus/>
<apply>
<plus/>
<ci>v</ci>
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<cn cellml:units="millivolt">5.6</cn>
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<rdf:Description rdf:about="#I_Ca">
<dc:title xmlns:dc="http://purl.org/dc/elements/1.1/">I_Ca</dc:title>
<dcterms:alternative xmlns:dcterms="http://purl.org/dc/terms/">voltage-dependent calcium current</dcterms:alternative>
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</rdf:RDF>
<variable name="I_Ca" units="picoampere" public_interface="out"/>
<variable name="gCa_" units="picosiemens" initial_value="1000"/>
<variable name="time" units="millisecond" public_interface="in"/>
<variable name="vCa" units="millivolt" public_interface="in"/>
<variable name="v" units="millivolt" public_interface="in" private_interface="out"/>
<variable name="m_infinity" units="dimensionless" private_interface="in"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>I_Ca</ci>
<apply>
<times/>
<ci>gCa_</ci>
<ci>m_infinity</ci>
<apply>
<minus/>
<ci>v</ci>
<ci>vCa</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component xmlns="http://www.cellml.org/cellml/1.0#" name="m" cmeta:id="m">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#m">
<dc:title xmlns:dc="http://purl.org/dc/elements/1.1/">m</dc:title>
<dcterms:alternative xmlns:dcterms="http://purl.org/dc/terms/">voltage-dependent calcium current m gate</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable name="m_infinity" units="dimensionless" public_interface="out"/>
<variable name="v" units="millivolt" public_interface="in"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>m_infinity</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<plus/>
<ci>v</ci>
<cn cellml:units="millivolt">20</cn>
</apply>
</apply>
<cn cellml:units="millivolt">12</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component xmlns="http://www.cellml.org/cellml/1.0#" name="I_K_Ca" cmeta:id="I_K_Ca">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#I_K_Ca">
<dc:title xmlns:dc="http://purl.org/dc/elements/1.1/">I_K_Ca</dc:title>
<dcterms:alternative xmlns:dcterms="http://purl.org/dc/terms/">calcium-activated potassium current</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable name="I_K_Ca" units="picoampere" public_interface="out"/>
<variable name="gkCa_" units="picosiemens" initial_value="400"/>
<variable name="gkCa" units="picosiemens"/>
<variable name="KD" units="micromolar" initial_value="0.5"/>
<variable name="time" units="millisecond" public_interface="in"/>
<variable name="vK" units="millivolt" public_interface="in"/>
<variable name="Ca" units="micromolar" public_interface="in"/>
<variable name="v" units="millivolt" public_interface="in"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>I_K_Ca</ci>
<apply>
<times/>
<ci>gkCa</ci>
<apply>
<minus/>
<ci>v</ci>
<ci>vK</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>gkCa</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>gkCa_</ci>
<apply>
<power/>
<ci>Ca</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
<apply>
<plus/>
<apply>
<power/>
<ci>KD</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<apply>
<power/>
<ci>Ca</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component xmlns="http://www.cellml.org/cellml/1.0#" name="I_K_ATP" cmeta:id="I_K_ATP">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#I_K_ATP">
<dc:title xmlns:dc="http://purl.org/dc/elements/1.1/">I_K_ATP</dc:title>
<dcterms:alternative xmlns:dcterms="http://purl.org/dc/terms/">ATP-sensitive potassium current</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable name="I_K_ATP" units="picoampere" public_interface="out"/>
<variable name="gkATP_" units="picosiemens" initial_value="40000"/>
<variable name="gkATP" units="picosiemens"/>
<variable name="o_infinity" units="dimensionless"/>
<variable name="MgADP" units="micromolar"/>
<variable name="ADP3_" units="micromolar"/>
<variable name="ATP4_" units="micromolar"/>
<variable name="time" units="millisecond" public_interface="in"/>
<variable name="vK" units="millivolt" public_interface="in"/>
<variable name="ATP" units="micromolar" public_interface="in"/>
<variable name="ADP" units="micromolar" public_interface="in"/>
<variable name="v" units="millivolt" public_interface="in"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>I_K_ATP</ci>
<apply>
<times/>
<ci>gkATP</ci>
<apply>
<minus/>
<ci>v</ci>
<ci>vK</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>gkATP</ci>
<apply>
<times/>
<ci>gkATP_</ci>
<ci>o_infinity</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>o_infinity</ci>
<apply>
<divide/>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="dimensionless">0.08</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<ci>MgADP</ci>
</apply>
<cn cellml:units="micromolar">17</cn>
</apply>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">0.89</cn>
<apply>
<power/>
<apply>
<divide/>
<ci>MgADP</ci>
<cn cellml:units="micromolar">17</cn>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
<apply>
<times/>
<apply>
<power/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless">1</cn>
<ci>MgADP</ci>
</apply>
<cn cellml:units="micromolar">17</cn>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<divide/>
<ci>ADP3_</ci>
<cn cellml:units="micromolar">26</cn>
</apply>
<apply>
<divide/>
<ci>ATP4_</ci>
<cn cellml:units="micromolar">1</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>MgADP</ci>
<apply>
<times/>
<cn cellml:units="dimensionless">0.165</cn>
<ci>ADP</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>ADP3_</ci>
<apply>
<times/>
<cn cellml:units="dimensionless">0.135</cn>
<ci>ADP</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>ATP4_</ci>
<apply>
<times/>
<cn cellml:units="dimensionless">0.005</cn>
<ci>ATP</ci>
</apply>
</apply>
</math>
</component>
<component xmlns="http://www.cellml.org/cellml/1.0#" name="Ca" cmeta:id="Ca">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#Ca">
<dc:title xmlns:dc="http://purl.org/dc/elements/1.1/">Ca</dc:title>
<dcterms:alternative xmlns:dcterms="http://purl.org/dc/terms/">calcium</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable name="Ca" units="micromolar" initial_value="0.1" public_interface="out"/>
<variable name="fcyt" units="dimensionless" initial_value="0.01"/>
<variable name="Jmem" units="micromolar_millisecond" public_interface="in"/>
<variable name="Jer" units="micromolar_millisecond" public_interface="in"/>
<variable name="time" units="millisecond" public_interface="in"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>Ca</ci>
</apply>
<apply>
<times/>
<ci>fcyt</ci>
<apply>
<plus/>
<ci>Jmem</ci>
<ci>Jer</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component xmlns="http://www.cellml.org/cellml/1.0#" name="Caer" cmeta:id="Caer">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#Caer">
<dc:title xmlns:dc="http://purl.org/dc/elements/1.1/">Caer</dc:title>
<dcterms:alternative xmlns:dcterms="http://purl.org/dc/terms/">calcium</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable name="Caer" units="micromolar" initial_value="185" public_interface="out"/>
<variable name="fer" units="dimensionless" initial_value="0.01"/>
<variable name="Vcyt_Ver" units="dimensionless" initial_value="31"/>
<variable name="Jer" units="micromolar_millisecond" public_interface="in"/>
<variable name="time" units="millisecond" public_interface="in"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>Caer</ci>
</apply>
<apply>
<times/>
<apply>
<minus/>
<ci>fer</ci>
</apply>
<ci>Vcyt_Ver</ci>
<ci>Jer</ci>
</apply>
</apply>
</math>
</component>
<component xmlns="http://www.cellml.org/cellml/1.0#" name="Jmem" cmeta:id="Jmem">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#Jmem">
<dc:title xmlns:dc="http://purl.org/dc/elements/1.1/">Jmem</dc:title>
<dcterms:alternative xmlns:dcterms="http://purl.org/dc/terms/">rate of calcium flux across the plasma membrane</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable name="Jmem" units="micromolar_millisecond" public_interface="out"/>
<variable name="kPMCA" units="first_order_rate_constant" initial_value="0.18"/>
<variable name="alpha" units="micromolar_millisecond" initial_value="4.5e-6"/>
<variable name="Ca" units="micromolar" public_interface="in"/>
<variable name="I_Ca" units="picoampere" public_interface="in"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>Jmem</ci>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<times/>
<ci>alpha</ci>
<ci>I_Ca</ci>
</apply>
<apply>
<times/>
<ci>kPMCA</ci>
<ci>Ca</ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component xmlns="http://www.cellml.org/cellml/1.0#" name="Jer" cmeta:id="Jer">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#Jer">
<dc:title xmlns:dc="http://purl.org/dc/elements/1.1/">Jer</dc:title>
<dcterms:alternative xmlns:dcterms="http://purl.org/dc/terms/">rate of calcium flux out of the endoplasmic reticulum</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable name="Jer" units="micromolar_millisecond" public_interface="out"/>
<variable name="Jleak" units="micromolar_millisecond" public_interface="in"/>
<variable name="JSERCA" units="micromolar_millisecond" public_interface="in"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>Jer</ci>
<apply>
<minus/>
<ci>Jleak</ci>
<ci>JSERCA</ci>
</apply>
</apply>
</math>
</component>
<component xmlns="http://www.cellml.org/cellml/1.0#" name="JSERCA" cmeta:id="JSERCA">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#JSERCA">
<dc:title xmlns:dc="http://purl.org/dc/elements/1.1/">JSERCA</dc:title>
<dcterms:alternative xmlns:dcterms="http://purl.org/dc/terms/">rate of calcium flux into the endoplasmic reticulum through the SERCA pumps</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable name="JSERCA" units="micromolar_millisecond" public_interface="out"/>
<variable name="kSERCA" units="first_order_rate_constant" initial_value="0.4"/>
<variable name="Ca" units="micromolar" public_interface="in"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>JSERCA</ci>
<apply>
<times/>
<ci>kSERCA</ci>
<ci>Ca</ci>
</apply>
</apply>
</math>
</component>
<component xmlns="http://www.cellml.org/cellml/1.0#" name="Jleak" cmeta:id="Jleak">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#Jleak">
<dc:title>Jleak</dc:title>
<dcterms:alternative>rate of calcium leakage out of the endoplasmic reticulum</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable name="Jleak" units="micromolar_millisecond" public_interface="out"/>
<variable name="pleak" units="first_order_rate_constant" initial_value="0.0002"/>
<variable name="Ca" units="micromolar" public_interface="in"/>
<variable name="Caer" units="micromolar" public_interface="in"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>Jleak</ci>
<apply>
<times/>
<ci>pleak</ci>
<apply>
<minus/>
<ci>Caer</ci>
<ci>Ca</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component xmlns="http://www.cellml.org/cellml/1.0#" name="I" cmeta:id="I">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#I">
<dc:title xmlns:dc="http://purl.org/dc/elements/1.1/">I</dc:title>
<dcterms:alternative xmlns:dcterms="http://purl.org/dc/terms/">insulin</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable name="I" units="dimensionless" initial_value="0" public_interface="out"/>
<variable name="I_infinity" units="dimensionless"/>
<variable name="tau_I" units="millisecond" initial_value="10000"/>
<variable name="I_slope" units="per_micromolar" initial_value="210"/>
<variable name="Canull" units="micromolar" initial_value="0.055"/>
<variable name="Ca" units="micromolar" public_interface="in"/>
<variable name="time" units="millisecond" public_interface="in"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>I</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci>I_infinity</ci>
<ci>I</ci>
</apply>
<ci>tau_I</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>I_infinity</ci>
<piecewise>
<piece>
<apply>
<times/>
<ci>I_slope</ci>
<apply>
<minus/>
<ci>Ca</ci>
<ci>Canull</ci>
</apply>
</apply>
<apply>
<geq/>
<ci>Ca</ci>
<ci>Canull</ci>
</apply>
</piece>
<piece>
<cn cellml:units="dimensionless">0</cn>
<apply>
<lt/>
<ci>Ca</ci>
<ci>Canull</ci>
</apply>
</piece>
</piecewise>
</apply>
</math>
</component>
<component xmlns="http://www.cellml.org/cellml/1.0#" name="model_parameters">
<variable name="kappa" units="dimensionless" initial_value="0.005" public_interface="out"/>
<variable name="vK" units="millivolt" initial_value="-75" public_interface="out"/>
<variable name="vCa" units="millivolt" initial_value="25" public_interface="out"/>
</component>
<!-- groups -->
<group xmlns="http://www.cellml.org/cellml/1.0#">
<relationship_ref relationship="containment"/>
<component_ref component="membrane">
<component_ref component="I_Ca">
<component_ref component="m"/>
</component_ref>
<component_ref component="I_K">
<component_ref component="n"/>
</component_ref>
<component_ref component="I_K_Ca"/>
<component_ref component="I_K_ATP"/>
</component_ref>
</group>
<group xmlns="http://www.cellml.org/cellml/1.0#">
<relationship_ref relationship="encapsulation"/>
<component_ref component="I_Ca">
<component_ref component="m"/>
</component_ref>
<component_ref component="I_K">
<component_ref component="n"/>
</component_ref>
</group>
<!-- connections -->
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="Gi" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="Ge" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="G6P" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="FBP" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="ADP" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="membrane" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="I_K" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="I_Ca" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="I_K_Ca" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="I_K_ATP" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="Ca" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="Caer" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="I" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="Gi" component_2="Jgk"/>
<map_variables variable_1="Gi" variable_2="Gi"/>
<map_variables variable_1="Jgk" variable_2="Jgk"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="Gi" component_2="Jglut"/>
<map_variables variable_1="Gi" variable_2="Gi"/>
<map_variables variable_1="Jglut" variable_2="Jglut"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="G6P" component_2="Jgk"/>
<map_variables variable_1="Jgk" variable_2="Jgk"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="G6P" component_2="JPFK"/>
<map_variables variable_1="JPFK" variable_2="JPFK"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="G6P" component_2="model_parameters"/>
<map_variables variable_1="kappa" variable_2="kappa"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="G6P" component_2="F6P"/>
<map_variables variable_1="G6P" variable_2="G6P"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="FBP" component_2="JGPDH"/>
<map_variables variable_1="FBP" variable_2="FBP"/>
<map_variables variable_1="JGPDH" variable_2="JGPDH"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="FBP" component_2="JPFK"/>
<map_variables variable_1="JPFK" variable_2="JPFK"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="FBP" component_2="model_parameters"/>
<map_variables variable_1="kappa" variable_2="kappa"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="Jglut" component_2="Ge"/>
<map_variables variable_1="Ge" variable_2="Ge"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="JPFK" component_2="w"/>
<map_variables variable_1="w0000" variable_2="w0000"/>
<map_variables variable_1="w0001" variable_2="w0001"/>
<map_variables variable_1="w0010" variable_2="w0010"/>
<map_variables variable_1="w0100" variable_2="w0100"/>
<map_variables variable_1="w0101" variable_2="w0101"/>
<map_variables variable_1="w0110" variable_2="w0110"/>
<map_variables variable_1="w0111" variable_2="w0111"/>
<map_variables variable_1="w1000" variable_2="w1000"/>
<map_variables variable_1="w1001" variable_2="w1001"/>
<map_variables variable_1="w1010" variable_2="w1010"/>
<map_variables variable_1="w1011" variable_2="w1011"/>
<map_variables variable_1="w1100" variable_2="w1100"/>
<map_variables variable_1="w1101" variable_2="w1101"/>
<map_variables variable_1="w1110" variable_2="w1110"/>
<map_variables variable_1="w1111" variable_2="w1111"/>
<map_variables variable_1="w0011" variable_2="w0011"/>
</connection>
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