- Author:
- pmr2.import <nobody@models.cellml.org>
- Date:
- 2009-06-17 12:33:06+12:00
- Desc:
- committing version02 of bertram_satin_zhang_smolen_sherman_2004
- Permanent Source URI:
- https://models.cellml.org/workspace/bertram_satin_zhang_smolen_sherman_2004/rawfile/3e7461aff0452f42c65f0166ffb57cee1d50b942/bertram_satin_zhang_smolen_sherman_2004_b.cellml
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<article>
<articleinfo>
<title>Modelling Multiple Bursting Models in Pancreatic Islets</title>
<author>
<firstname>James</firstname>
<surname>Lawson</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 rebuilt and coded by translating the authors original XPPAUT .ode file, which can be found at http://www.math.fsu.edu/~bertram/software/islet/BJ_04a.ode . This file runs in PCEnv and produces the output expected, however PCEnv is only able to produce one cycle of bursting. This is a pending issue.
</para>
</section>
<sect1 id="sec_structure">
<title>Model Structure</title>
<para>
Secretion of insulin from pancreatic islets is oscillatory and multimodal. These oscillations occur over a fairly broad range of time scales:
</para>
<itemizedlist>
<listitem>
<para>Fast oscillations have a period of tens of seconds and they are in phase with the intracellular free calcium concentration ([Ca<superscript>2+</superscript>]<subscript>i</subscript>) of beta-cells, the insulin-secreting cells of the islet.</para>
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<listitem>
<para>The second component of the oscillatory insulin signal has a period of 5-10 minutes and it is known to play some physiological role which is lost in patients with type II diabetes.</para>
</listitem>
<listitem>
<para>Even slower ultradian rhythms with a period of 2 hours, and circadian rhythms with a period of about 24 hours, have also been observed.</para>
</listitem>
</itemizedlist>
<para>
In mouse islets, Ca<superscript>2+</superscript> oscillations are driven by bursting electrical activity at stimulatory glucose levels. It is though that when Ca<superscript>2+</superscript> enters the cell during an action potential, the increase in [Ca<superscript>2+</superscript>]<subscript>i</subscript> provides negative feedg onto the membrane through the activation of K<superscript>+</superscript> channels, in turn leading to membrane hyperpolarisation and ending bursting electrical activity. After cytosolic Ca<superscript>2+</superscript> has been cleared by the action of ATP-drive calcium pumps (Ca<superscript>2+</superscript> ATPases) in the plasma membrane and in the ER membrane, an active spiking phase restarts. Thus Ca<superscript>2+</superscript> may act directly to activate Ca<superscript>2+</superscript>-activated K<superscript>+</superscript> channels, or indirectly by lowering the ratio of ATP to ADP (through the action of the Ca<superscript>2+</superscript> ATPases), which in turn activates ATP-sensitive K<superscript>+</superscript> channels. The interaction of these mechanisms is analysed in more detail in <ulink url="${HTML_EXMPL_BERTRAM_MODEL}">The Phantom Burster Model for Pancreatic Beta-Cells, Bertram <emphasis>et al.</emphasis>, 2000</ulink>, and <ulink url="${HTML_EXMPL_BERTRAM_MODEL04}">A Calcium-based Phantom Bursting Model for Pancreatic Islets, Bertram and Sherman, 2004</ulink>
</para>
<para>
An alternative theory is that electrical activity is exclusively driven by slow oscillations in glycolysis due to the allosteric enzyme phosphofructokinase (PFK). Glycolytic products serve as substrates for mitochondrial metabolism, so their rhythmical synthesis is likely to lead to oscillations in the ATP to ADP ratio which then drives bursting activity through their effects on beta-cell ATP-sensitive K<superscript>+</superscript> channels.
</para>
<para>
In this current study, Bertram <emphasis>et al.</emphasis> analyse these two mechanisms for insulin oscillations in pancreatic islets. They demonstrate via a mathematical model that they are not mutually exclusive but instead they can cooperate to produce rhythmical insulin secretion. The mathematical model (see <xref linkend="fig_cell_diagram"/> below) is based in part on an earlier model for Ca<superscript>2+</superscript>-dependent bursting (<ulink url="${HTML_EXMPL_BERTRAM_MODEL04}">Bertram and Sherman, 2004</ulink>), which has been extended to include glycolytic components.
</para>
<para>
The model has been described here in CellML (the raw CellML description of the Bertram <emphasis>et al.</emphasis> 2004 model can be downloaded in various formats as described in <xref linkend="sec_download_this_model"/>).
</para>
<para>
The article has bee published online adhead of print. To view this article as a PDF, please follow the link below:
</para>
<para>
<ulink url="http://www.biophysj.org/cgi/rapidpdf/biophysj.104.049262v1.pdf">Calcium and Glycolysis Mediate Multiple Bursting Modes in Pancreatic Islets</ulink>, Richard Bertram, Leslie Satin, Min Zhang, Paul Smolen, and Arthur Sherman, 2004, <ulink url="http://www.molbiolcell.org/">
<emphasis>Biophysical Journal</emphasis>
</ulink> <!--, 66, 1313-1344. (<ulink url="http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6WC7-4BS4GC2-1&_coverDate=09%2F30%2F2004&_alid=197872630&_rdoc=1&_fmt=&_orig=search&_qd=1&_cdi=6731&_sort=d&view=c&_acct=C000011498&_version=1&_urlVersion=0&_userid=140507&md5=b34962c344ab1a8911383073cd53016f">Full text (HTML)</ulink> and <ulink url="http://www.sciencedirect.com/science?_ob=MImg&_imagekey=B6WC7-4BS4GC2-1-3Y&_cdi=6731&_orig=search&_coverDate=09%2F30%2F2004&_qd=1&_sk=999339994&view=c&wchp=dGLbVzz-zSkWz&_acct=C000011498&_version=1&_userid=140507&md5=4f701b4338556df3136f0c4815596563&ie=f.pdf">PDF</ulink> versions of the article are available to subscribers on the <emphasis>Biophysical Journal</emphasis> website.) --> <ulink url="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&list_uids=15347584&dopt=Abstract">PubMed ID: 15347584</ulink>
</para>
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<title>cell diagram</title>
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<caption>A schematic diagram of the ionic currents and fluxes across the ER and the cell surface membranes which are described by the mathematical model.</caption>
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</sect1>
</article>
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<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/>
<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>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="0100">
<apply>
<eq/>
<ci>weight5</ci>
<apply>
<divide/>
<ci>fbp</ci>
<ci>k2</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>topa5</ci>
<ci>topa4</ci>
</apply>
<apply>
<eq/>
<ci>bottom5</ci>
<apply>
<plus/>
<ci>bottom4</ci>
<ci>weight5</ci>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="0101">
<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/>
<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>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="0110">
<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/>
<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>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="0111">
<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/>
<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>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="1000">
<apply>
<eq/>
<ci>weight9</ci>
<apply>
<divide/>
<ci>amp</ci>
<ci>k1</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>topa9</ci>
<ci>topa8</ci>
</apply>
<apply>
<eq/>
<ci>bottom9</ci>
<apply>
<plus/>
<ci>bottom8</ci>
<ci>weight9</ci>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="1001">
<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/>
<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>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="1010">
<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/>
<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>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="1011">
<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/>
<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>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="1100">
<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>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="1101">
<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/>
<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>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="1110">
<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/>
<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>bottom15</ci>
<apply>
<plus/>
<ci>bottom14</ci>
<ci>weight15</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>topb</ci>
<ci>weight15</ci>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="1111">
<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/>
<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>
<variable units="dimensionless" name="topb"/>
<variable units="micromolar" public_interface="in" name="fbp"/>
<variable units="micromolar" public_interface="in" name="amp"/>
</component>
<component name="KATP">
<variable units="millisecond" public_interface="in" name="time"/>
<variable units="micromolar" name="mgadp"/>
<variable units="micromolar" name="adp3m"/>
<variable units="micromolar" name="atp4m"/>
<variable units="dimensionless" name="topo"/>
<variable units="dimensionless" name="bottomo"/>
<variable units="dimensionless" name="katpo"/>
<variable units="femtoA" public_interface="out" name="IKATP"/>
<variable units="millivolt" public_interface="out" name="VK" initial_value="-75"/>
<variable units="picoS" name="gkatpbar" initial_value="25000"/>
<variable units="micromolar" public_interface="in" name="atp"/>
<variable units="micromolar" public_interface="in" name="adp" initial_value=""/>
<variable units="dimensionless" name="kdd" initial_value="17"/>
<variable units="dimensionless" name="ktd" initial_value="26"/>
<variable units="dimensionless" name="ktt" initial_value="1"/>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="mgadp">
<apply>
<eq/>
<ci>mgadp</ci>
<apply>
<times/>
<cn cellml:units="dimensionless">0.165</cn>
<ci>adp</ci>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="adp3m">
<apply>
<eq/>
<ci>adp3m</ci>
<apply>
<times/>
<cn cellml:units="dimensionless">0.135</cn>
<ci>adp</ci>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="atp4m">
<apply>
<eq/>
<ci>atp4m</ci>
<apply>
<times/>
<cn cellml:units="dimensionless">0.05</cn>
<ci>atp</ci>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="topo">
<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>
<ci>kdd</ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">0.89</cn>
<apply>
<power/>
<apply>
<divide/>
<ci>mgadp</ci>
<ci>kdd</ci>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="bottomo">
<apply>
<eq/>
<ci>bottomo</ci>
<apply>
<times/>
<apply>
<power/>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<divide/>
<ci>mgadp</ci>
<ci>kdd</ci>
</apply>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<divide/>
<ci>adp3m</ci>
<ci>ktd</ci>
</apply>
<apply>
<divide/>
<ci>atp4m</ci>
<ci>ktt</ci>
</apply>
</apply>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="katpo">
<apply>
<eq/>
<ci>katpo</ci>
<apply>
<divide/>
<ci>topo</ci>
<ci>bottomo</ci>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="ikatp">
<apply>
<eq/>
<ci>IKATP</ci>
<apply>
<times/>
<ci>gkatpbar</ci>
<ci>katpo</ci>
<apply>
<minus/>
<ci>V</ci>
<ci>VK</ci>
</apply>
</apply>
</apply>
</math>
<variable units="millivolt" public_interface="in" name="V"/>
</component>
<component name="nucleotides">
<variable units="millisecond" public_interface="in" name="time"/>
<variable units="micromolar" public_interface="out" name="atp"/>
<variable units="micromolar" public_interface="out" name="adp" initial_value="780"/>
<variable units="dimensionless" name="fback"/>
<variable units="dimensionless" name="taua" initial_value="300000"/>
<variable units="micromolar" name="r1" initial_value="0.35"/>
<variable units="micromolar" public_interface="in" name="c"/>
<variable units="dimensionless" name="r" initial_value="1"/>
<variable units="dimensionless" name="y"/>
<variable units="dimensionless" name="vg" initial_value="2.2"/>
<variable units="flux" public_interface="in" name="rgpdh"/>
<variable units="flux" name="kg" initial_value="10"/>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="delta/t adp">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>adp</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci>atp</ci>
<apply>
<times/>
<ci>adp</ci>
<apply>
<exp/>
<apply>
<times/>
<ci>fback</ci>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<divide/>
<ci>c</ci>
<ci>r1</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<ci>taua</ci>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="fback">
<apply>
<eq/>
<ci>fback</ci>
<apply>
<plus/>
<ci>r</ci>
<ci>y</ci>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="y">
<apply>
<eq/>
<ci>y</ci>
<apply>
<times/>
<ci>vg</ci>
<apply>
<divide/>
<ci>rgpdh</ci>
<apply>
<plus/>
<ci>kg</ci>
<ci>rgpdh</ci>
</apply>
</apply>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="atp">
<apply>
<eq/>
<ci>atp</ci>
<apply>
<times/>
<cn cellml:units="dimensionless">0.5</cn>
<apply>
<plus/>
<apply>
<minus/>
<ci>atot</ci>
<ci>adp</ci>
</apply>
<ci>rad</ci>
</apply>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="amp">
<apply>
<eq/>
<ci>amp</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>adp</ci>
<ci>adp</ci>
</apply>
<ci>atp</ci>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="ratio">
<apply>
<eq/>
<ci>ratio</ci>
<apply>
<divide/>
<ci>atp</ci>
<ci>adp</ci>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="rad">
<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>
<variable units="micromolar" public_interface="out" name="amp"/>
<variable units="dimensionless" name="rad"/>
<variable units="dimensionless" name="ratio"/>
<variable units="micromolar" public_interface="in" name="atot"/>
</component>
<connection>
<map_components component_2="membrane" component_1="environment"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="membrane" component_1="calcium_handling"/>
<map_variables variable_2="c" variable_1="c"/>
<map_variables variable_2="ICa" variable_1="ICa"/>
</connection>
<connection>
<map_components component_2="calcium_handling" component_1="environment"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="glycolysis" component_1="environment"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="pfk" component_1="environment"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="pfk" component_1="glycolysis"/>
<map_variables variable_2="pfkbas" variable_1="pfkbas"/>
<map_variables variable_2="f6p" variable_1="f6p"/>
<map_variables variable_2="fbp" variable_1="fbp"/>
<map_variables variable_2="pfk" variable_1="pfk"/>
</connection>
<connection>
<map_components component_2="pfk" component_1="nucleotides"/>
<map_variables variable_2="atp" variable_1="atp"/>
<map_variables variable_2="amp" variable_1="amp"/>
</connection>
<connection>
<map_components component_2="KATP" component_1="environment"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="KATP" component_1="nucleotides"/>
<map_variables variable_2="atp" variable_1="atp"/>
<map_variables variable_2="adp" variable_1="adp"/>
</connection>
<connection>
<map_components component_2="nucleotides" component_1="environment"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="nucleotides" component_1="calcium_handling"/>
<map_variables variable_2="c" variable_1="c"/>
</connection>
<connection>
<map_components component_2="nucleotides" component_1="glycolysis"/>
<map_variables variable_2="rgpdh" variable_1="rgpdh"/>
<map_variables variable_2="atot" variable_1="atot"/>
</connection>
<connection>
<map_components component_2="KATP" component_1="membrane"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="VK" variable_1="VK"/>
<map_variables variable_2="IKATP" variable_1="IKATP"/>
</connection>
<rdf:RDF>
<rdf:Bag rdf:about="rdf:#2a3e1a2b-3efe-41f2-8c13-bcdbf6801dac">
<rdf:li>calcium dynamics</rdf:li>
<rdf:li>insulin</rdf:li>
<rdf:li>glucose homeostasis</rdf:li>
<rdf:li>metabolism</rdf:li>
</rdf:Bag>
<rdf:Seq rdf:about="rdf:#2124e2ff-5d41-40b2-a651-67c3b6787e7c">
<rdf:li rdf:resource="rdf:#1ed204cd-f80d-4ea3-b59a-cffa82daf09f"/>
<rdf:li rdf:resource="rdf:#a8aed505-7b87-46ed-8b5d-884ca4ba0519"/>
<rdf:li rdf:resource="rdf:#f8f5c77e-f5c8-4c81-82ea-2b2edc761802"/>
<rdf:li rdf:resource="rdf:#a71e0f4f-d87f-4d0b-bed5-92fc2e3e6721"/>
<rdf:li rdf:resource="rdf:#53097ff0-df0c-405d-bc4a-e8445ed2ae27"/>
</rdf:Seq>
<rdf:Description rdf:about="rdf:#0dc39aa0-db10-4d97-8c6e-67589d7de059">
<dcterms:W3CDTF>2004-10-01T00:00:00+00:00</dcterms:W3CDTF>
</rdf:Description>
<rdf:Description rdf:about="rdf:#$PXk6c">
<ns7:endingValue>50000</ns7:endingValue>
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