<?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.
-->
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<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>Auckland Bioengineering Institute, The University of Auckland</shortaffil>
</affiliation>
</author>
</articleinfo>
<section id="sec_status">
<title>Model Status</title>
<para>This CellML model runs in OpenCell and COR but does not recreate the published results. The model is based on the authors original XPPAUT.ode file which can be found at www.math.fsu.edu/~bertram/software/islet/BJ_05. The units have been checked and they are consistent. We are unsure why the CellML model is not recreating the published results.</para>
</section>
<sect1 id="sec_structure">
<title>Model Structure</title>
<para>ABSTRACT: Insulin secretion from pancreatic beta-cells is pulsatile with a period of 5-10 min and is believed to be responsible for plasma insulin oscillations with similar frequency. To observe an overall oscillatory insulin profile it is necessary that the insulin secretion from individual beta-cells is synchronized within islets, and that the population of islets is also synchronized. We have recently developed a model in which pulsatile insulin secretion is produced as a result of calcium-driven electrical oscillations in combination with oscillations in glycolysis. We use this model to investigate possible mechanisms for intra-islet and inter-islet synchronization. We show that electrical coupling is sufficient to synchronize both electrical bursting activity and metabolic oscillations. We also demonstrate that islets can synchronize by mutually entraining each other by their effects on a simple model "liver," which responds to the level of insulin secretion by adjusting the blood glucose concentration in an appropriate way. Since all islets are exposed to the blood, the distributed islet-liver system can synchronize the individual islet insulin oscillations. Thus, we demonstrate how intra-islet and inter-islet synchronization of insulin oscillations may be achieved.</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 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>
</sect1>
</article>
</documentation>
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<power/>
<ci>ATP</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<apply>
<times/>
<cn cellml:units="millimolar">1</cn>
<ci>K4</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>topa2</ci>
<ci>topa1</ci>
</apply>
<apply>
<eq/>
<ci>bottom2</ci>
<apply>
<plus/>
<ci>bottom1</ci>
<ci>weight2</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>weight13</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>AMP</ci>
<ci>FBP</ci>
</apply>
<apply>
<times/>
<ci>K1</ci>
<ci>K2</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>topa13</ci>
<ci>topa12</ci>
</apply>
<apply>
<eq/>
<ci>bottom13</ci>
<apply>
<plus/>
<ci>bottom12</ci>
<ci>weight13</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>weight11</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>AMP</ci>
<apply>
<power/>
<ci>F6P</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="millimolar">1</cn>
<ci>K1</ci>
<ci>K3</ci>
<ci>famp</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>topa11</ci>
<apply>
<plus/>
<ci>topa10</ci>
<ci>weight11</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>bottom11</ci>
<apply>
<plus/>
<ci>bottom10</ci>
<ci>weight11</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>weight10</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>AMP</ci>
<apply>
<power/>
<ci>ATP</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="millimolar">1</cn>
<ci>K1</ci>
<ci>K4</ci>
<ci>fmt</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>topa10</ci>
<ci>topa9</ci>
</apply>
<apply>
<eq/>
<ci>bottom10</ci>
<apply>
<plus/>
<ci>bottom9</ci>
<ci>weight10</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>weight6</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>FBP</ci>
<apply>
<power/>
<ci>ATP</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="millimolar">1</cn>
<ci>K2</ci>
<ci>K4</ci>
<ci>fbt</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>topa6</ci>
<ci>topa5</ci>
</apply>
<apply>
<eq/>
<ci>bottom6</ci>
<apply>
<plus/>
<ci>bottom5</ci>
<ci>weight6</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>weight4</ci>
<apply>
<divide/>
<apply>
<power/>
<apply>
<times/>
<ci>F6P</ci>
<ci>ATP</ci>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
<apply>
<times/>
<cn cellml:units="millimolar2">1</cn>
<ci>fatp</ci>
<ci>K3</ci>
<ci>K4</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>topa4</ci>
<apply>
<plus/>
<ci>topa3</ci>
<ci>weight4</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>bottom4</ci>
<apply>
<plus/>
<ci>bottom3</ci>
<ci>weight4</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>weight7</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>FBP</ci>
<apply>
<power/>
<ci>F6P</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="millimolar">1</cn>
<ci>K2</ci>
<ci>K3</ci>
<ci>ffbp</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>topa7</ci>
<apply>
<plus/>
<ci>topa6</ci>
<ci>weight7</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>bottom7</ci>
<apply>
<plus/>
<ci>bottom6</ci>
<ci>weight7</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>weight15</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>AMP</ci>
<ci>FBP</ci>
<apply>
<power/>
<ci>F6P</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="millimolar">1</cn>
<ci>K1</ci>
<ci>K2</ci>
<ci>K3</ci>
<ci>ffbp</ci>
<ci>famp</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>topa15</ci>
<ci>topa14</ci>
</apply>
<apply>
<eq/>
<ci>topb</ci>
<ci>weight15</ci>
</apply>
<apply>
<eq/>
<ci>bottom15</ci>
<apply>
<plus/>
<ci>bottom14</ci>
<ci>weight15</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>weight8</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>FBP</ci>
<apply>
<power/>
<ci>F6P</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<apply>
<power/>
<ci>ATP</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="millimolar2">1</cn>
<ci>K2</ci>
<ci>K3</ci>
<ci>K4</ci>
<ci>ffbp</ci>
<ci>fbt</ci>
<ci>fatp</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>topa8</ci>
<apply>
<plus/>
<ci>topa7</ci>
<ci>weight8</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>bottom8</ci>
<apply>
<plus/>
<ci>bottom7</ci>
<ci>weight8</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>weight12</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>AMP</ci>
<apply>
<power/>
<ci>F6P</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<apply>
<power/>
<ci>ATP</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="millimolar2">1</cn>
<ci>K1</ci>
<ci>K3</ci>
<ci>K4</ci>
<ci>famp</ci>
<ci>fmt</ci>
<ci>fatp</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>topa12</ci>
<apply>
<plus/>
<ci>topa11</ci>
<ci>weight12</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>bottom12</ci>
<apply>
<plus/>
<ci>bottom11</ci>
<ci>weight12</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>weight14</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>AMP</ci>
<ci>FBP</ci>
<apply>
<power/>
<ci>ATP</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="millimolar">1</cn>
<ci>K1</ci>
<ci>K2</ci>
<ci>K4</ci>
<ci>fbt</ci>
<ci>fmt</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>topa14</ci>
<ci>topa13</ci>
</apply>
<apply>
<eq/>
<ci>bottom14</ci>
<apply>
<plus/>
<ci>bottom13</ci>
<ci>weight14</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>weight16</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>AMP</ci>
<ci>FBP</ci>
<apply>
<power/>
<ci>F6P</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<apply>
<power/>
<ci>ATP</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="millimolar2">1</cn>
<ci>K1</ci>
<ci>K2</ci>
<ci>K3</ci>
<ci>K4</ci>
<ci>ffbp</ci>
<ci>famp</ci>
<ci>fbt</ci>
<ci>fmt</ci>
<ci>fatp</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>topa16</ci>
<apply>
<plus/>
<ci>topa15</ci>
<ci>weight16</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>bottom16</ci>
<apply>
<plus/>
<ci>bottom15</ci>
<ci>weight16</ci>
</apply>
</apply>
</math>
</component>
<component name="ATP" cmeta:id="ATP">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#ATP">
<dc:title xmlns:dc="http://purl.org/dc/elements/1.1/">ATP</dc:title>
<dcterms:alternative xmlns:dcterms="http://purl.org/dc/terms/">adenosine triphosphate</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable name="ATP" units="micromolar" public_interface="out"/>
<variable name="Atot" units="micromolar" initial_value="3000"/>
<variable name="rad" units="micromolar"/>
<variable name="ADP" units="micromolar" public_interface="in"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>ATP</ci>
<apply>
<times/>
<cn cellml:units="dimensionless">0.5</cn>
<apply>
<minus/>
<apply>
<plus/>
<ci>Atot</ci>
<ci>rad</ci>
</apply>
<ci>ADP</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>rad</ci>
<apply>
<root/>
<apply>
<minus/>
<apply>
<power/>
<apply>
<minus/>
<ci>ADP</ci>
<ci>Atot</ci>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">4</cn>
<apply>
<power/>
<ci>ADP</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="AMP" cmeta:id="AMP">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#AMP">
<dc:title xmlns:dc="http://purl.org/dc/elements/1.1/">AMP</dc:title>
<dcterms:alternative xmlns:dcterms="http://purl.org/dc/terms/">adenosine monophosphate</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable name="AMP" units="micromolar" public_interface="out"/>
<variable name="ATP" units="micromolar" public_interface="in"/>
<variable name="ADP" units="micromolar" public_interface="in"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>AMP</ci>
<apply>
<divide/>
<apply>
<power/>
<ci>ADP</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>ATP</ci>
</apply>
</apply>
</math>
</component>
<component name="ADP" cmeta:id="ADP">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#ADP">
<dc:title xmlns:dc="http://purl.org/dc/elements/1.1/">ADP</dc:title>
<dcterms:alternative xmlns:dcterms="http://purl.org/dc/terms/">adenosine diphosphate</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable name="ADP" units="micromolar" initial_value="537.6" public_interface="out"/>
<variable name="y" units="dimensionless"/>
<variable name="tau_a" units="millisecond" initial_value="300000"/>
<variable name="r" units="dimensionless" initial_value="0.5"/>
<variable name="r1" units="micromolar" initial_value="0.35"/>
<variable name="autoadp" units="dimensionless" initial_value="1.0"/>
<variable name="adpknot" units="micromolar" initial_value="800.0"/>
<variable name="fback" units="dimensionless"/>
<variable name="ky" units="dimensionless" initial_value="2.2"/>
<variable name="kg" units="micromolar_per_millisecond" initial_value="0.1"/>
<variable name="JGPDH" units="micromolar_per_millisecond" public_interface="in"/>
<variable name="Ca" units="micromolar" public_interface="in"/>
<variable name="ATP" 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>ADP</ci>
</apply>
<apply>
<plus/>
<apply>
<times/>
<ci>autoadp</ci>
<apply>
<plus/>
<apply>
<divide/>
<apply>
<minus/>
<ci>ATP</ci>
<apply>
<times/>
<ci>ADP</ci>
<apply>
<exp/>
<apply>
<times/>
<ci>fback</ci>
<apply>
<divide/>
<apply>
<minus/>
<cn cellml:units="micromolar">1</cn>
<ci>Ca</ci>
</apply>
<ci>r1</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<ci>tau_a</ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="first_order_rate_constant">1</cn>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<ci>autoadp</ci>
</apply>
<apply>
<minus/>
<ci>adpknot</ci>
<ci>ADP</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>y</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>ky</ci>
<ci>JGPDH</ci>
</apply>
<apply>
<plus/>
<ci>kg</ci>
<ci>JGPDH</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>fback</ci>
<apply>
<plus/>
<ci>r</ci>
<ci>y</ci>
</apply>
</apply>
</math>
</component>
<component name="membrane" cmeta:id="membrane">
<variable name="v" units="millivolt" initial_value="-66.7" public_interface="out"/>
<variable name="cm" units="femtofarad" initial_value="5300"/>
<variable name="I_Ca" units="femtoampere" public_interface="in"/>
<variable name="I_K" units="femtoampere" public_interface="in"/>
<variable name="I_K_Ca" units="femtoampere" public_interface="in"/>
<variable name="I_K_ATP" units="femtoampere" 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>v</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<plus/>
<ci>I_K</ci>
<ci>I_Ca</ci>
<ci>I_K_Ca</ci>
<ci>I_K_ATP</ci>
</apply>
</apply>
<ci>cm</ci>
</apply>
</apply>
</math>
</component>
<component name="I_K" cmeta:id="I_K">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<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>
</rdf:Description>
</rdf:RDF>
<variable name="I_K" units="femtoampere" public_interface="out"/>
<variable name="gK" units="picosiemens" initial_value="2700"/>
<variable name="time" units="millisecond" public_interface="in" private_interface="out"/>
<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">
<apply>
<eq/>
<ci>I_K</ci>
<apply>
<times/>
<ci>gK</ci>
<ci>n</ci>
<apply>
<minus/>
<ci>v</ci>
<ci>vK</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="n" cmeta:id="n">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<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>
</rdf:Description>
</rdf:RDF>
<variable name="n" units="dimensionless" initial_value="0.00012" public_interface="out"/>
<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">
<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>
<apply>
<eq/>
<ci>tau_n</ci>
<apply>
<divide/>
<cn cellml:units="millisecond">1</cn>
<apply>
<times/>
<cn cellml:units="dimensionless">0.035</cn>
<apply>
<cosh/>
<apply>
<divide/>
<apply>
<minus/>
<ci>v</ci>
<cn cellml:units="millivolt">-16</cn>
</apply>
<cn cellml:units="millivolt">22.4</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>n_infinity</ci>
<apply>
<times/>
<cn cellml:units="dimensionless">0.5</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<tanh/>
<apply>
<divide/>
<apply>
<minus/>
<ci>v</ci>
<cn cellml:units="millivolt">-16</cn>
</apply>
<cn cellml:units="millivolt">11.2</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="I_Ca" cmeta:id="I_Ca">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<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>
</rdf:Description>
</rdf:RDF>
<variable name="I_Ca" units="femtoampere" 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 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>
<times/>
<cn cellml:units="dimensionless">0.5</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<tanh/>
<apply>
<divide/>
<apply>
<minus/>
<ci>v</ci>
<cn cellml:units="millivolt">-20</cn>
</apply>
<cn cellml:units="millivolt">24</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component 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="femtoampere" public_interface="out"/>
<variable name="gkCa" units="picosiemens" initial_value="400"/>
<variable name="KD" units="micromolar" initial_value="0.5"/>
<variable name="nh" units="dimensionless" initial_value="2.0"/>
<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/>
<apply>
<divide/>
<ci>gkCa</ci>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<power/>
<apply>
<divide/>
<ci>KD</ci>
<ci>Ca</ci>
</apply>
<ci>nh</ci>
</apply>
</apply>
</apply>
<apply>
<minus/>
<ci>v</ci>
<ci>vK</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component 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="femtoampere" public_interface="out"/>
<variable name="gkATP_bar" units="picosiemens" initial_value="2000"/>
<variable name="katpo" units="dimensionless"/>
<variable name="topo" units="dimensionless"/>
<variable name="bottomo" 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_bar</ci>
<ci>katpo</ci>
<apply>
<minus/>
<ci>v</ci>
<ci>vK</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>katpo</ci>
<apply>
<times/>
<cn cellml:units="dimensionless">20.0</cn>
<apply>
<divide/>
<ci>topo</ci>
<ci>bottomo</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>topo</ci>
<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>
<apply>
<eq/>
<ci>bottomo</ci>
<apply>
<times/>
<apply>
<power/>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<divide/>
<ci>MgADP</ci>
<cn cellml:units="micromolar">17</cn>
</apply>
</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>
<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">0.05</cn>
<ci>ATP</ci>
</apply>
</apply>
</math>
</component>
<component 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="0.05626" public_interface="out"/>
<variable name="fcyt" units="dimensionless" initial_value="0.01"/>
<variable name="Jmem" units="micromolar_per_millisecond" public_interface="in"/>
<variable name="Jer" units="micromolar_per_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 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="121.8" public_interface="out"/>
<variable name="fer" units="dimensionless" initial_value="0.01"/>
<variable name="sigmav" units="dimensionless" initial_value="31"/>
<variable name="Jer" units="micromolar_per_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>sigmav</ci>
<ci>Jer</ci>
</apply>
</apply>
</math>
</component>
<component 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_per_millisecond" public_interface="out"/>
<variable name="kPMCA" units="first_order_rate_constant" initial_value="0.18"/>
<variable name="alpha" units="micromolar_per_millisecond" initial_value="4.5e-6"/>
<variable name="Ca" units="micromolar" public_interface="in"/>
<variable name="I_Ca" units="femtoampere" 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>
<cn cellml:units="per_femtoampere">1</cn>
<ci>I_Ca</ci>
</apply>
<apply>
<times/>
<ci>kPMCA</ci>
<ci>Ca</ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component 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_per_millisecond" public_interface="out"/>
<variable name="Jleak" units="micromolar_per_millisecond" public_interface="in"/>
<variable name="JSERCA" units="micromolar_per_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 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_per_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 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_per_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 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="0.316" public_interface="out"/>
<variable name="I_infinity" units="dimensionless"/>
<variable name="tau_I" units="millisecond" initial_value="10000"/>
<variable name="I_max" units="dimensionless" initial_value="20"/>
<variable name="delta" units="dimensionless" initial_value="8.0"/>
<variable name="ki" units="micromolar" initial_value="0.1"/>
<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>
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<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>
<apply>
<times/>
<ci>I_max</ci>
<apply>
<divide/>
<apply>
<power/>
<ci>Ca</ci>
<ci>delta</ci>
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<apply>
<plus/>
<apply>
<power/>
<ci>ki</ci>
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</apply>
<apply>
<power/>
<ci>Ca</ci>
<ci>delta</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="model_parameters">
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<variable name="vK" units="millivolt" initial_value="-75" public_interface="out"/>
<variable name="vCa" units="millivolt" initial_value="25" public_interface="out"/>
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</group>
<connection>
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<connection>
<map_components component_1="Ge" component_2="environment"/>
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<connection>
<map_components component_1="G6P" component_2="environment"/>
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<connection>
<map_components component_1="FBP" component_2="environment"/>
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<connection>
<map_components component_1="ADP" component_2="environment"/>
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<connection>
<map_components component_1="membrane" component_2="environment"/>
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<connection>
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<connection>
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<connection>
<map_components component_1="I_K_Ca" component_2="environment"/>
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<connection>
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<connection>
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<connection>
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<connection>
<map_components component_1="I" component_2="environment"/>
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<connection>
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<map_variables variable_1="Jgk" variable_2="Jgk"/>
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<connection>
<map_components component_1="Gi" component_2="Jglut"/>
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<connection>
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<connection>
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<connection>
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<connection>
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<connection>
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<connection>
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<connection>
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<connection>
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<connection>
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<connection>
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<connection>
<map_components component_1="w" component_2="ATP"/>
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<connection>
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<connection>
<map_components component_1="w" component_2="FBP"/>
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<connection>
<map_components component_1="ATP" component_2="AMP"/>
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<connection>
<map_components component_1="ATP" component_2="ADP"/>
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<connection>
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<connection>
<map_components component_1="ADP" component_2="Ca"/>
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<connection>
<map_components component_1="membrane" component_2="I_Ca"/>
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<connection>
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<connection>
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<connection>
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<connection>
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<connection>
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<connection>
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<connection>
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<connection>
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<connection>
<map_components component_1="I_K_Ca" component_2="Ca"/>
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<connection>
<map_components component_1="I_K_ATP" component_2="model_parameters"/>
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<connection>
<map_components component_1="I_K_ATP" component_2="ATP"/>
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<connection>
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<connection>
<map_components component_1="ADP" component_2="JGPDH"/>
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<connection>
<map_components component_1="Ca" component_2="Jmem"/>
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<connection>
<map_components component_1="Ca" component_2="Jer"/>
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<connection>
<map_components component_1="Caer" component_2="Jer"/>
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<connection>
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<connection>
<map_components component_1="Jer" component_2="JSERCA"/>
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<connection>
<map_components component_1="Ca" component_2="JSERCA"/>
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<connection>
<map_components component_1="Ca" component_2="Jleak"/>
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<connection>
<map_components component_1="Caer" component_2="Jleak"/>
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<connection>
<map_components component_1="Ca" component_2="I"/>
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</connection>
<connection>
<map_components component_1="I_Ca" component_2="Jmem"/>
<map_variables variable_1="I_Ca" variable_2="I_Ca"/>
</connection>
<!-- metadata -->
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Bag rdf:about="rdf:#45ceff5c-0914-4676-a569-6b29103af117">
<rdf:li>endocrine</rdf:li>
<rdf:li>pancreatic beta cell</rdf:li>
<rdf:li>insulin</rdf:li>
<rdf:li>glycolysis</rdf:li>
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