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  <title>Calcium and Glycolysis Mediate Multiple Bursting Modes in Pancreatic Islets</title>
  <author>
    <firstname>Catherine</firstname>
          <surname>Lloyd</surname>
    <affiliation>
      <shortaffil>Auckland Bioengineering Institute, University of Auckland</shortaffil>
    </affiliation>
  </author>
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  <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 COR and is able to produce the expected output. This model has been parameterised for the 'compound bursting' model.  Some equations have inconsistent magnitudes due to the fact that time is defined in milliseconds, yet flux is defined in micromolar per second.
</para>

  </section>
  <sect1 id="sec_structure">
<title>Model Structure</title>

<para>
ABSTRACT: Pancreatic islets of Langerhans produce bursts of electrical activity when exposed to stimulatory glucose levels. These bursts often have a regular repeating pattern, with a period of 10-60 s. In some cases, however, the bursts are episodic, clustered into bursts of bursts, which we call compound bursting. Consistent with this are recordings of free Ca2+ concentration, oxygen consumption, mitochondrial membrane potential, and intraislet glucose levels that exhibit very slow oscillations, with faster oscillations superimposed. We describe a new mathematical model of the pancreatic beta-cell that can account for these multimodal patterns. The model includes the feedback of cytosolic Ca2+ onto ion channels that can account for bursting, and a metabolic subsystem that is capable of producing slow oscillations driven by oscillations in glycolysis. This slow rhythm is responsible for the slow mode of compound bursting in the model. We also show that it is possible for glycolytic oscillations alone to drive a very slow form of bursting, which we call "glycolytic bursting." Finally, the model predicts that there is bistability between stationary and oscillatory glycolysis for a range of parameter values. We provide experimental support for this model prediction. Overall, the model can account for a diversity of islet behaviors described in the literature over the past 20 years.
</para>

<para>
Calcium and Glycolysis Mediate Multiple Bursting Modes in Pancreatic Islets, Richard Bertram, Leslie Satin, Min Zhang, Paul Smolen, and Arthur Sherman, 2004,
            <emphasis>Biophysical Journal</emphasis>, 87, 3074-3087. <ulink url="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&amp;db=PubMed&amp;list_uids=15347584&amp;dopt=Abstract">PubMed ID: 15347584</ulink>
</para>

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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>
</informalfigure>
</sect1>
</article>
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            <math xmlns="http://www.w3.org/1998/Math/MathML" id="0011">
                  <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/>
                                    <ci>fatp</ci>
                                    <ci>k3</ci>
                                    <ci>k4</ci>
                                    <apply>
                                          <power/>
                                          <cn cellml:units="micromolar">1</cn>
                                          <cn cellml:units="dimensionless">2</cn>
                                    </apply>
                              </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>
                                    <cn cellml:units="micromolar">1</cn>
                              </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>
                                    <cn cellml:units="micromolar">1</cn>
                              </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>
                                          <power/>
                                          <cn cellml:units="micromolar">1</cn>
                                          <cn cellml:units="dimensionless">2</cn>
                                    </apply>
                              </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>
                                    <cn cellml:units="micromolar">1</cn>
                              </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>
                                    <cn cellml:units="micromolar">1</cn>
                              </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>
                                          <power/>
                                          <cn cellml:units="micromolar">1</cn>
                                          <cn cellml:units="dimensionless">2</cn>
                                    </apply>
                              </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>
                                    <cn cellml:units="micromolar">1</cn>
                              </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>
                                    <cn cellml:units="micromolar">1</cn>
                              </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>
                                          <power/>
                                          <cn cellml:units="micromolar">1</cn>
                                          <cn cellml:units="dimensionless">2</cn>
                                    </apply>
                              </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"/>
            <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>
                                                <apply>
                                                      <times/>
                                                      <ci>kdd</ci>
                                                      <cn cellml:units="micromolar">1</cn>
                                                </apply>
                                          </apply>
                                    </apply>
                              </apply>
                              <apply>
                                    <times/>
                                    <cn cellml:units="dimensionless">0.89</cn>
                                    <apply>
                                          <power/>
                                          <apply>
                                                <divide/>
                                                <ci>mgadp</ci>
                                                <apply>
                                                      <times/>
                                                      <ci>kdd</ci>
                                                      <cn cellml:units="micromolar">1</cn>
                                                </apply>
                                          </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>
                                                <apply>
                                                      <times/>
                                                      <ci>kdd</ci>
                                                      <cn cellml:units="micromolar">1</cn>
                                                </apply>
                                          </apply>
                                    </apply>
                                    <cn cellml:units="dimensionless">2</cn>
                              </apply>
                              <apply>
                                    <plus/>
                                    <cn cellml:units="dimensionless">1</cn>
                                    <apply>
                                          <divide/>
                                          <ci>adp3m</ci>
                                          <apply>
                                                <times/>
                                                <ci>ktd</ci>
                                                <cn cellml:units="micromolar">1</cn>
                                          </apply>
                                    </apply>
                                    <apply>
                                          <divide/>
                                          <ci>atp4m</ci>
                                          <apply>
                                                <times/>
                                                <ci>ktt</ci>
                                                <cn cellml:units="micromolar">1</cn>
                                          </apply>
                                    </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="d(adp)/d(time)">
                  <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>
                              <apply>
                                    <times/>
                                    <ci>taua</ci>
                                    <cn cellml:units="millisecond">1</cn>
                              </apply>
                        </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>
                                    <apply>
                                          <times/>
                                          <ci>rad</ci>
                                          <cn cellml:units="micromolar">1</cn>
                                    </apply>
                              </apply>
                        </apply>
                  </apply>
            </math>
            <math xmlns="http://www.w3.org/1998/Math/MathML" id="amp">
                  <apply>
                        <eq/>
                        <ci>amp</ci>
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                              <apply>
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                  </apply>
            </math>
            <math xmlns="http://www.w3.org/1998/Math/MathML" id="rad">
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                        <ci>rad</ci>
                        <apply>
                              <divide/>
                              <apply>
                                    <root/>
                                    <apply>
                                          <abs/>
                                          <apply>
                                                <minus/>
                                                <apply>
                                                      <power/>
                                                      <apply>
                                                            <minus/>
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                                                            <ci>atot</ci>
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                                                      <cn cellml:units="dimensionless">4</cn>
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                                                      </apply>
                                                </apply>
                                          </apply>
                                    </apply>
                              </apply>
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                        </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="KATP"/>
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            <map_variables variable_2="VK" variable_1="VK"/>
            <map_variables variable_2="V" variable_1="V"/>
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      <connection>
            <map_components component_2="calcium_handling" component_1="environment"/>
            <map_variables variable_2="time" variable_1="time"/>
      </connection>
      <connection>
            <map_components component_2="calcium_handling" component_1="membrane"/>
            <map_variables variable_2="ICa" variable_1="ICa"/>
            <map_variables variable_2="c" variable_1="c"/>
      </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"/>
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      <connection>
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      </connection>
      <connection>
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      <connection>
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      <connection>
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      </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"/>
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      <rdf:RDF>
            <rdf:Bag rdf:about="rdf:#2a3e1a2b-3efe-41f2-8c13-bcdbf6801dac">
                  <rdf:li>calcium dynamics</rdf:li>
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                  <vCard:FN>James Lawson</vCard:FN>
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                  <vCard:Given>James</vCard:Given>
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                  <dcterms:W3CDTF>2004-11-01 00:00</dcterms:W3CDTF>
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            <rdf:Description rdf:about="">
			      <dc:title>Calcium and Glycolysis Mediate Multiple Bursting Modes in Pancreatic Islets (compound bursting model)</dc:title>
                  <dc:publisher>The University of Auckland, Auckland Bioengineering Institute</dc:publisher>
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                  <dcterms:W3CDTF>2007-08-06T12:07:27+12:00</dcterms:W3CDTF>
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                  <ns7:endingValue>1000</ns7:endingValue>
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                  <ns7:nonstandard-algorithm>bdf15</ns7:nonstandard-algorithm>
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                  <dcterms:W3CDTF>2007-08-03T00:00:00+00:00</dcterms:W3CDTF>
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                  <vCard:Given>Arthur</vCard:Given>
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                  <vCard:Given>James</vCard:Given>
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                  <vCard:Other>Richard</vCard:Other>
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            <rdf:Description rdf:about="rdf:#054cda44-e70b-4b71-86be-db058391c283">
                  <bqs:Pubmed_id>15347584</bqs:Pubmed_id>
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                  <rdf:value>This is the CellML description of Bertram et al.'s 2004 mathematical model of calcium and glycolysis mediated bursting modes in pancreatic islets.</rdf:value>
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                  <vCard:FN>Catherine Lloyd</vCard:FN>
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                  <vCard:Given>James</vCard:Given>
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                  <dcterms:W3CDTF>2009-05-25T16:03:37+12:00</dcterms:W3CDTF>
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                  <dc:title>Calcium and Glycolysis Mediate Multiple Bursting Modes in Pancreatic Islets</dc:title>
                  <bqs:volume>87(5)</bqs:volume>
                  <bqs:first_page>3074</bqs:first_page>
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                  <bqs:last_page>3087</bqs:last_page>
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                  <vCard:Orgname>The University of Auckland</vCard:Orgname>
                  <vCard:Orgunit>Auckland Bioengineering Institute</vCard:Orgunit>
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            <rdf:Description rdf:about="rdf:#874dff13-d862-4051-9e0f-1e60388eca0a">
                  <vCard:Given>Leslie</vCard:Given>
                  <vCard:Family>Satin</vCard:Family>
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                  <rdf:value>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 is able to produce the expected output for a few cycles, after which the output degenerates. This model has been parameterised for the 'compound bursting' model.</rdf:value>
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                  <rdf:value>updated curation status</rdf:value>
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                  <dc:title>Biophysical Journal</dc:title>
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                  <vCard:Given>Min</vCard:Given>
                  <vCard:Family>Zhang</vCard:Family>
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                  <dc:title>Bertram et al.'s 2004 mathematical model of calcium and glycolysis mediated bursting modes in pancreatic islets.</dc:title>
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                  <vCard:Given>Richard</vCard:Given>
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                  <vCard:Given>Paul</vCard:Given>
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                  <rdf:value>The equation defining rgpdh has been changed from rgpdh = 0.2{units="dimensionless"} * root(fbp) to: rgpdh = 0.2{units="dimensionless"} * root(abs(fbp).  Since rgpdh was starting to approach zero near where the offending NaN was being produced in version 01 variant 01. This partially fixes the problem but the output is still not totally satisfactory.  The sqrt function in the equation defining rad also had an 'abs' function added: rad = root(abs(power(adp - atot, 2{units="dimensionless"}) - 4{units="dimensionless"} * power(adp, 2{units="dimensionless"}))</rdf:value>
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