Location: Calcium Dynamics Annotations @ 4d6408caaf3e / bertram_sherman_2004 / model / bertram_sherman_2004.cellml

Author:

neilstephen2001 <npar276@aucklanduni.ac.nz>

Date:

2021-01-26 14:35:03+13:00

Desc:

modifying rdf files

Permanent Source URI:

https://models.physiomeproject.org/workspace/7f1/rawfile/4d6408caaf3e7b1b86d33d53d26105360ef95347/bertram_sherman_2004/model/bertram_sherman_2004.cellml

<?xml version="1.0" encoding="UTF-8"?>
<model xmlns="http://www.cellml.org/cellml/1.1#" xmlns:cmeta="http://www.cellml.org/metadata/1.0#" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:bqs="http://www.cellml.org/bqs/1.0#" xmlns:semsim="http://www.bhi.washington.edu/SemSim#" xmlns:dcterms="http://purl.org/dc/terms/" xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" name="bertram_sherman_2004" cmeta:id="bertram_sherman_2004_version01">
  <documentation xmlns="http://cellml.org/tmp-documentation">
    <article>
      <articleinfo>
        <title>A Calcium-based Phantom Bursting Model for Pancreatic Islets</title>
        <author>
          <firstname>Catherine</firstname>
          <surname>Lloyd</surname>
          <affiliation>
            <shortaffil>Bioengineering Institute, University of Auckland</shortaffil>
          </affiliation>
        </author>
      </articleinfo>
      <section id="sec_status">
        <title>Model Status</title>
        <para>This model is has consistent units and has been verified as valid CellML by ValidateCellML. It is currently unsuitably constrained and can not be solved.</para>
      </section>
      <sect1 id="sec_structure">
        <title>Model Structure</title>
        <para>Pancreatic beta-cells are located in clusters within the pancreas called the islets of Langerhans.  Beta-cells secrete the hormone insulin in response to elevated blood glucose levels, and in doing so, they play an essential role in glucose homeostasis.  When beta-cells fail to function properly, this can lead to pathologies such as type II diabetes.</para>
        <para>
          Insulin secretion is oscillatory, and it is in-phase with oscillations in the free cytosolic calcium concentration ([Ca
          <superscript>2+</superscript>
          ]
          <subscript>i</subscript>
          ), and theses Ca
          <superscript>2+</superscript>
          oscillations reflect a bursting pattern in the beta-cell electrical activity.  Electrical bursting consists of periodic active phases of cell firing (excitation) followed by silent phases of hyperpolarisation (rest).  These oscillations can be divided into three categories:
        </para>
        <itemizedlist>
          <listitem>
            <para>
              <emphasis>Fast bursting</emphasis>
              , which has a period between 2 and 5 seconds and which often occurs in single cells and in islets where acetylcholine is present;
            </para>
          </listitem>
          <listitem>
            <para>
              <emphasis>Medium bursting</emphasis>
              , which has a period of 10 to 60 seconds and which occurs in islets where there is a stimulatory glucose concentration; and
            </para>
          </listitem>
          <listitem>
            <para>
              <emphasis>Slow bursting</emphasis>
              , which has a period of 2 to 4 minutes and which occurs in single cells and in islets.
            </para>
          </listitem>
        </itemizedlist>
        <para>
          The first mathematical models of beta-cells were developed to describe medium bursting, and the first models to address the variability in beta-cell oscillations were developed by Chay in 1995 and 1997 (see
          <ulink url="${HTML_EXMPL_CHAY_MODEL97}">Extracellular and Intracellular Calcium Effects on Pancreatic Beta Cells, Chay, 1997</ulink>
          for more details).  In these models the main mechanism for oscillations was variation in the Ca
          <superscript>2+</superscript>
          concentration in the ER, which directly or indirectly modulates one or more Ca
          <superscript>2+</superscript>
          -dependent channels.  In the Bertram and Sherman model described here the authors analyse in detail how the ER exerts its affects using a phantom bursting model (see
          <xref linkend="fig_cell_diagram" />
          below).
        </para>
        <para>
          The phantom bursting model is a general paradigm for temporal plasticity in bursting in beta-cells in which bursting is driven by the interaction of two slow variables with disparate time constants (see
          <ulink url="${HTML_EXMPL_BERTRAM_MODEL}">The Phantom Burster Model for Pancreatic Beta-Cells, 2000</ulink>
          for more details).  There are three potential slow variables which could drive the phantom bursting
          <emphasis>in vivo</emphasis>
          :
        </para>
        <itemizedlist>
          <listitem>
            <para>
              cytosolic Ca
              <superscript>2+</superscript>
              concentration;
            </para>
          </listitem>
          <listitem>
            <para>
              ER Ca
              <superscript>2+</superscript>
              concentration;
            </para>
          </listitem>
          <listitem>
            <para>and the ADP to ATP ratio.</para>
          </listitem>
        </itemizedlist>
        <para>
          The model has been described here in CellML (the raw CellML description of the Bertram and Sherman 2004 model can be downloaded in various formats as described in
          <xref linkend="sec_download_this_model" />
          ).
        </para>
        <para>The complete original paper reference is cited below:</para>
        <para>
          <ulink url="http://www.sciencedirect.com/science?_ob=ArticleURL&amp;_udi=B6WC7-4BS4GC2-1&amp;_user=140507&amp;_coverDate=09%2F30%2F2004&amp;_alid=197872630&amp;_rdoc=1&amp;_fmt=summary&amp;_orig=search&amp;_qd=1&amp;_cdi=6731&amp;_sort=d&amp;_docanchor=&amp;view=c&amp;_acct=C000011498&amp;_version=1&amp;_urlVersion=0&amp;_userid=140507&amp;md5=e1fdd19a27b1c7938c1d568e59a560e0">A Calcium-based Phantom Bursting Model for Pancreatic Islets</ulink>
          , Richard Bertram and Arthur Sherman, 2004,
          <ulink url="http://www.molbiolcell.org/">
            <emphasis>Bulletin of Mathematical Biology</emphasis>
          </ulink>
          , 66, 1313-1344.  (
          <ulink url="http://www.sciencedirect.com/science?_ob=ArticleURL&amp;_udi=B6WC7-4BS4GC2-1&amp;_coverDate=09%2F30%2F2004&amp;_alid=197872630&amp;_rdoc=1&amp;_fmt=&amp;_orig=search&amp;_qd=1&amp;_cdi=6731&amp;_sort=d&amp;view=c&amp;_acct=C000011498&amp;_version=1&amp;_urlVersion=0&amp;_userid=140507&amp;md5=b34962c344ab1a8911383073cd53016f">Full text (HTML)</ulink>
          and
          <ulink url="http://www.sciencedirect.com/science?_ob=MImg&amp;_imagekey=B6WC7-4BS4GC2-1-3Y&amp;_cdi=6731&amp;_orig=search&amp;_coverDate=09%2F30%2F2004&amp;_qd=1&amp;_sk=999339994&amp;view=c&amp;wchp=dGLbVzz-zSkWz&amp;_acct=C000011498&amp;_version=1&amp;_userid=140507&amp;md5=4f701b4338556df3136f0c4815596563&amp;ie=f.pdf">PDF</ulink>
          versions of the article are available to subscribers on the
          <emphasis>Bulletin of Mathematical Biology</emphasis>
          website.)
          <ulink url="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&amp;db=PubMed&amp;list_uids=15294427&amp;dopt=Abstract">PubMed ID: 15294427</ulink>
        </para>
        <informalfigure float="0" id="fig_cell_diagram">
          <mediaobject>
            <imageobject>
              <objectinfo>
                <title>cell diagram</title>
              </objectinfo>
              <imagedata fileref="bertram_2004.png" />
            </imageobject>
          </mediaobject>
          <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>
  </documentation>
  <units name="femtoA">
    <unit prefix="femto" units="ampere" />
  </units>
  <units name="millivolt">
    <unit prefix="milli" units="volt" />
  </units>
  <units name="picoS">
    <unit prefix="pico" units="siemens" />
  </units>
  <units name="millisecond">
    <unit prefix="milli" units="second" />
  </units>
  <units name="micromolar">
    <unit exponent="-1.0" units="litre" />
    <unit prefix="micro" units="mole" />
  </units>
  <units name="first_order_rate_constant">
    <unit exponent="-1.0" units="millisecond" />
  </units>
  <units name="femtoF">
    <unit prefix="femto" units="farad" />
  </units>
  <units name="flux">
    <unit exponent="-1.0" units="millisecond" />
    <unit units="micromolar" />
  </units>
  <units name="micromolar_per_femtoA_millisecond">
    <unit exponent="-1.0" units="millisecond" />
    <unit units="micromolar" />
    <unit exponent="-1.0" units="femtoA" />
  </units>
  <component name="environment">
    <variable cmeta:id="environment.time" name="time" public_interface="out" units="millisecond" />
  </component>
  <component name="membrane">
    <variable cmeta:id="membrane.V" name="V" public_interface="out" units="millivolt" />
    <variable cmeta:id="membrane.Cm" initial_value="5300.0" name="Cm" units="femtoF" />
    <variable cmeta:id="membrane.time" name="time" public_interface="in" units="millisecond" />
    <variable cmeta:id="membrane.i_Ca" name="i_Ca" public_interface="in" units="femtoA" />
    <variable cmeta:id="membrane.i_K" name="i_K" public_interface="in" units="femtoA" />
    <variable cmeta:id="membrane.i_K_Ca" name="i_K_Ca" public_interface="in" units="femtoA" />
    <variable cmeta:id="membrane.i_K_ATP" name="i_K_ATP" public_interface="in" units="femtoA" />
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply id="membrane_voltage_diff_eq">
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        </apply>
        <apply>
          <divide />
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            <minus />
            <apply>
              <plus />
              <ci>i_Ca</ci>
              <ci>i_K</ci>
              <ci>i_K_Ca</ci>
              <ci>i_K_ATP</ci>
            </apply>
          </apply>
          <ci>Cm</ci>
        </apply>
      </apply>
    </math>
  </component>
  <component name="calcium_current">
    <variable cmeta:id="calcium_current.i_Ca" name="i_Ca" public_interface="out" units="femtoA" />
    <variable cmeta:id="calcium_current.g_Ca" initial_value="1200.0" name="g_Ca" units="picoS" />
    <variable cmeta:id="calcium_current.V_Ca" initial_value="25.0" name="V_Ca" units="millivolt" />
    <variable cmeta:id="calcium_current.V" name="V" public_interface="in" private_interface="out" units="millivolt" />
    <variable cmeta:id="calcium_current.time" name="time" public_interface="in" private_interface="out" units="millisecond" />
    <variable cmeta:id="calcium_current.m_infinity" name="m_infinity" private_interface="in" units="dimensionless" />
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply id="i_Ca_calculation">
        <eq />
        <ci>i_Ca</ci>
        <apply>
          <times />
          <ci>g_Ca</ci>
          <ci>m_infinity</ci>
          <apply>
            <minus />
            <ci>V</ci>
            <ci>V_Ca</ci>
          </apply>
        </apply>
      </apply>
    </math>
  </component>
  <component name="calcium_current_m_gate">
    <variable cmeta:id="calcium_current_m_gate.m_infinity" name="m_infinity" public_interface="out" units="dimensionless" />
    <variable cmeta:id="calcium_current_m_gate.vm" initial_value="-20.0" name="vm" units="millivolt" />
    <variable cmeta:id="calcium_current_m_gate.sm" initial_value="12.0" name="sm" units="millivolt" />
    <variable cmeta:id="calcium_current_m_gate.V" name="V" public_interface="in" units="millivolt" />
    <variable cmeta:id="calcium_current_m_gate.time" name="time" public_interface="in" units="millisecond" />
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply id="m_infinity_calculation">
        <eq />
        <ci>m_infinity</ci>
        <apply>
          <power />
          <apply>
            <plus />
            <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1.0</cn>
            <apply>
              <exp />
              <apply>
                <divide />
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                <ci>sm</ci>
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            </apply>
          </apply>
          <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">-1.0</cn>
        </apply>
      </apply>
    </math>
  </component>
  <component name="delayed_rectifier_potassium_current">
    <variable cmeta:id="delayed_rectifier_potassium_current.i_K" name="i_K" public_interface="out" units="femtoA" />
    <variable cmeta:id="delayed_rectifier_potassium_current.V_K" initial_value="-75.0" name="V_K" public_interface="out" units="millivolt" />
    <variable cmeta:id="delayed_rectifier_potassium_current.g_K" initial_value="3000.0" name="g_K" units="picoS" />
    <variable cmeta:id="delayed_rectifier_potassium_current.V" name="V" public_interface="in" private_interface="out" units="millivolt" />
    <variable cmeta:id="delayed_rectifier_potassium_current.time" name="time" public_interface="in" private_interface="out" units="millisecond" />
    <variable cmeta:id="delayed_rectifier_potassium_current.n" name="n" private_interface="in" units="dimensionless" />
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply id="i_K_calculation">
        <eq />
        <ci>i_K</ci>
        <apply>
          <times />
          <ci>g_K</ci>
          <ci>n</ci>
          <apply>
            <minus />
            <ci>V</ci>
            <ci>V_K</ci>
          </apply>
        </apply>
      </apply>
    </math>
  </component>
  <component name="delayed_rectifier_potassium_current_n_gate">
    <variable cmeta:id="delayed_rectifier_potassium_current_n_gate.n" name="n" public_interface="out" units="dimensionless" />
    <variable cmeta:id="delayed_rectifier_potassium_current_n_gate.tau_n" initial_value="16.0" name="tau_n" units="millisecond" />
    <variable cmeta:id="delayed_rectifier_potassium_current_n_gate.n_infinity" name="n_infinity" units="dimensionless" />
    <variable cmeta:id="delayed_rectifier_potassium_current_n_gate.vn" initial_value="-16.0" name="vn" units="millivolt" />
    <variable cmeta:id="delayed_rectifier_potassium_current_n_gate.sn" initial_value="5.0" name="sn" units="millivolt" />
    <variable cmeta:id="delayed_rectifier_potassium_current_n_gate.V" name="V" public_interface="in" units="millivolt" />
    <variable cmeta:id="delayed_rectifier_potassium_current_n_gate.time" name="time" public_interface="in" units="millisecond" />
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply id="n_diff_eq">
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        <apply>
          <diff />
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        <apply>
          <divide />
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            <ci>n</ci>
          </apply>
          <ci>tau_n</ci>
        </apply>
      </apply>
      <apply id="n_infinity_calculation">
        <eq />
        <ci>n_infinity</ci>
        <apply>
          <power />
          <apply>
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            <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1.0</cn>
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          </apply>
          <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">-1.0</cn>
        </apply>
      </apply>
    </math>
  </component>
  <component name="calcium_dependent_potassium_current">
    <variable cmeta:id="calcium_dependent_potassium_current.i_K_Ca" name="i_K_Ca" public_interface="out" units="femtoA" />
    <variable cmeta:id="calcium_dependent_potassium_current.g_K_Ca" initial_value="300.0" name="g_K_Ca" units="picoS" />
    <variable cmeta:id="calcium_dependent_potassium_current.V_K" name="V_K" public_interface="in" units="millivolt" />
    <variable cmeta:id="calcium_dependent_potassium_current.V" name="V" public_interface="in" units="millivolt" />
    <variable cmeta:id="calcium_dependent_potassium_current.c" name="c" public_interface="in" private_interface="out" units="micromolar" />
    <variable cmeta:id="calcium_dependent_potassium_current.time" name="time" public_interface="in" units="millisecond" />
    <variable cmeta:id="calcium_dependent_potassium_current.omega" name="omega" private_interface="in" units="dimensionless" />
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply id="i_K_Ca_calculation">
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        <ci>i_K_Ca</ci>
        <apply>
          <times />
          <ci>g_K_Ca</ci>
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            <ci>V_K</ci>
          </apply>
        </apply>
      </apply>
    </math>
  </component>
  <component name="calcium_dependent_potassium_current_omega_gate">
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    <variable cmeta:id="calcium_dependent_potassium_current_omega_gate.kD" initial_value="0.3" name="kD" units="micromolar" />
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          </apply>
        </apply>
      </apply>
    </math>
  </component>
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            <ci>Jmem</ci>
            <ci>Jer</ci>
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    </math>
  </component>
  <component name="ER_calcium_concentration">
    <variable cmeta:id="ER_calcium_concentration.c_er" name="c_er" public_interface="out" units="micromolar" />
    <variable cmeta:id="ER_calcium_concentration.fer" initial_value="0.01" name="fer" units="dimensionless" />
    <variable cmeta:id="ER_calcium_concentration.Vcyt_Ver" initial_value="5.0" name="Vcyt_Ver" units="dimensionless" />
    <variable cmeta:id="ER_calcium_concentration.Jer" name="Jer" public_interface="in" units="flux" />
    <variable cmeta:id="ER_calcium_concentration.time" name="time" public_interface="in" units="millisecond" />
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply id="c_er_diff_eq">
        <eq />
        <apply>
          <diff />
          <bvar>
            <ci>time</ci>
          </bvar>
          <ci>c_er</ci>
        </apply>
        <apply>
          <times />
          <apply>
            <minus />
            <ci>fer</ci>
          </apply>
          <ci>Vcyt_Ver</ci>
          <ci>Jer</ci>
        </apply>
      </apply>
    </math>
  </component>
  <component name="calcium_flux_through_the_membrane">
    <variable cmeta:id="calcium_flux_through_the_membrane.Jmem" name="Jmem" public_interface="out" units="flux" />
    <variable cmeta:id="calcium_flux_through_the_membrane.alpha" initial_value="4.5E-6" name="alpha" units="micromolar_per_femtoA_millisecond" />
    <variable cmeta:id="calcium_flux_through_the_membrane.kPMCA" initial_value="0.2" name="kPMCA" units="first_order_rate_constant" />
    <variable cmeta:id="calcium_flux_through_the_membrane.c" name="c" public_interface="in" units="micromolar" />
    <variable cmeta:id="calcium_flux_through_the_membrane.i_Ca" name="i_Ca" public_interface="in" units="femtoA" />
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply id="Jmem_eq">
        <eq />
        <ci>Jmem</ci>
        <apply>
          <minus />
          <apply>
            <plus />
            <apply>
              <times />
              <ci>alpha</ci>
              <ci>i_Ca</ci>
            </apply>
            <apply>
              <times />
              <ci>kPMCA</ci>
              <ci>c</ci>
            </apply>
          </apply>
        </apply>
      </apply>
    </math>
  </component>
  <component name="calcium_influx_into_the_ER">
    <variable cmeta:id="calcium_influx_into_the_ER.J_SERCA" name="J_SERCA" public_interface="out" units="flux" />
    <variable cmeta:id="calcium_influx_into_the_ER.kSERCA" initial_value="0.4" name="kSERCA" units="first_order_rate_constant" />
    <variable cmeta:id="calcium_influx_into_the_ER.c" name="c" public_interface="in" units="micromolar" />
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply id="J_SERCA_eq">
        <eq />
        <ci>J_SERCA</ci>
        <apply>
          <times />
          <ci>kSERCA</ci>
          <ci>c</ci>
        </apply>
      </apply>
    </math>
  </component>
  <component name="calcium_leak_out_of_the_ER">
    <variable cmeta:id="calcium_leak_out_of_the_ER.Jleak" name="Jleak" public_interface="out" units="flux" />
    <variable cmeta:id="calcium_leak_out_of_the_ER.pleak" initial_value="0.0005" name="pleak" units="first_order_rate_constant" />
    <variable cmeta:id="calcium_leak_out_of_the_ER.c" name="c" public_interface="in" units="micromolar" />
    <variable cmeta:id="calcium_leak_out_of_the_ER.c_er" name="c_er" public_interface="in" units="micromolar" />
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply id="Jleak_eq">
        <eq />
        <ci>Jleak</ci>
        <apply>
          <times />
          <ci>pleak</ci>
          <apply>
            <minus />
            <ci>c_er</ci>
            <ci>c</ci>
          </apply>
        </apply>
      </apply>
    </math>
  </component>
  <component name="calcium_efflux_through_the_IP3R">
    <variable cmeta:id="calcium_efflux_through_the_IP3R.JIP3" name="JIP3" public_interface="out" units="flux" />
    <variable cmeta:id="calcium_efflux_through_the_IP3R.O_infinity" name="O_infinity" units="first_order_rate_constant" />
    <variable cmeta:id="calcium_efflux_through_the_IP3R.d_act" initial_value="0.35" name="d_act" units="micromolar" />
    <variable cmeta:id="calcium_efflux_through_the_IP3R.d_IP3" initial_value="0.5" name="d_IP3" units="micromolar" />
    <variable cmeta:id="calcium_efflux_through_the_IP3R.d_inact" initial_value="0.4" name="d_inact" units="micromolar" />
    <variable cmeta:id="calcium_efflux_through_the_IP3R.IP3" name="IP3" units="micromolar" />
    <variable cmeta:id="calcium_efflux_through_the_IP3R.c" name="c" public_interface="in" units="micromolar" />
    <variable cmeta:id="calcium_efflux_through_the_IP3R.c_er" name="c_er" public_interface="in" units="micromolar" />
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply id="JIP3_eq">
        <eq />
        <ci>JIP3</ci>
        <apply>
          <times />
          <ci>O_infinity</ci>
          <apply>
            <minus />
            <ci>c_er</ci>
            <ci>c</ci>
          </apply>
        </apply>
      </apply>
      <apply id="O_infinity_eq">
        <eq />
        <ci>O_infinity</ci>
        <apply>
          <times />
          <apply>
            <power />
            <apply>
              <divide />
              <ci>c</ci>
              <apply>
                <plus />
                <ci>d_act</ci>
                <ci>c</ci>
              </apply>
            </apply>
            <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">3</cn>
          </apply>
          <apply>
            <power />
            <apply>
              <divide />
              <ci>IP3</ci>
              <apply>
                <plus />
                <ci>d_IP3</ci>
                <ci>IP3</ci>
              </apply>
            </apply>
            <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">3</cn>
          </apply>
          <apply>
            <power />
            <apply>
              <divide />
              <ci>c</ci>
              <apply>
                <plus />
                <ci>d_inact</ci>
                <ci>c</ci>
              </apply>
            </apply>
            <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">3</cn>
          </apply>
          <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="first_order_rate_constant">1</cn>
        </apply>
      </apply>
    </math>
  </component>
  <component name="net_calcium_efflux_out_of_the_ER">
    <variable cmeta:id="net_calcium_efflux_out_of_the_ER.Jer" name="Jer" public_interface="out" units="flux" />
    <variable cmeta:id="net_calcium_efflux_out_of_the_ER.Jleak" name="Jleak" public_interface="in" units="flux" />
    <variable cmeta:id="net_calcium_efflux_out_of_the_ER.JIP3" name="JIP3" public_interface="in" units="flux" />
    <variable cmeta:id="net_calcium_efflux_out_of_the_ER.J_SERCA" name="J_SERCA" public_interface="in" units="flux" />
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply id="Jer_eq">
        <eq />
        <ci>Jer</ci>
        <apply>
          <minus />
          <apply>
            <plus />
            <ci>Jleak</ci>
            <ci>JIP3</ci>
          </apply>
          <ci>J_SERCA</ci>
        </apply>
      </apply>
    </math>
  </component>
  <group>
    <relationship_ref relationship="containment" />
    <component_ref component="membrane">
      <component_ref component="nucleotide_sensitive_potassium_current">
        <component_ref component="nucleotide_sensitive_potassium_current_a_gate" />
      </component_ref>
      <component_ref component="calcium_current">
        <component_ref component="calcium_current_m_gate" />
      </component_ref>
      <component_ref component="calcium_flux_through_the_membrane" />
      <component_ref component="ER_calcium_concentration" />
      <component_ref component="calcium_efflux_through_the_IP3R" />
      <component_ref component="calcium_leak_out_of_the_ER" />
      <component_ref component="net_calcium_efflux_out_of_the_ER" />
      <component_ref component="delayed_rectifier_potassium_current">
        <component_ref component="delayed_rectifier_potassium_current_n_gate" />
      </component_ref>
      <component_ref component="cytosolic_free_calcium_concentration" />
      <component_ref component="calcium_dependent_potassium_current">
        <component_ref component="calcium_dependent_potassium_current_omega_gate" />
      </component_ref>
      <component_ref component="calcium_influx_into_the_ER" />
    </component_ref>
  </group>
  <group>
    <relationship_ref relationship="encapsulation" />
    <component_ref component="nucleotide_sensitive_potassium_current">
      <component_ref component="nucleotide_sensitive_potassium_current_a_gate" />
    </component_ref>
    <component_ref component="calcium_current">
      <component_ref component="calcium_current_m_gate" />
    </component_ref>
    <component_ref component="delayed_rectifier_potassium_current">
      <component_ref component="delayed_rectifier_potassium_current_n_gate" />
    </component_ref>
    <component_ref component="calcium_dependent_potassium_current">
      <component_ref component="calcium_dependent_potassium_current_omega_gate" />
    </component_ref>
  </group>
  <connection>
    <map_components component_1="delayed_rectifier_potassium_current" component_2="calcium_dependent_potassium_current" />
    <map_variables variable_1="V_K" variable_2="V_K" />
  </connection>
  <connection>
    <map_components component_1="environment" component_2="calcium_dependent_potassium_current" />
    <map_variables variable_1="time" variable_2="time" />
  </connection>
  <connection>
    <map_components component_1="calcium_current" component_2="calcium_flux_through_the_membrane" />
    <map_variables variable_1="i_Ca" variable_2="i_Ca" />
  </connection>
  <connection>
    <map_components component_1="membrane" component_2="calcium_current" />
    <map_variables variable_1="V" variable_2="V" />
  </connection>
  <connection>
    <map_components component_1="calcium_leak_out_of_the_ER" component_2="net_calcium_efflux_out_of_the_ER" />
    <map_variables variable_1="Jleak" variable_2="Jleak" />
  </connection>
  <connection>
    <map_components component_1="membrane" component_2="calcium_dependent_potassium_current" />
    <map_variables variable_1="V" variable_2="V" />
  </connection>
  <connection>
    <map_components component_1="nucleotide_sensitive_potassium_current" component_2="nucleotide_sensitive_potassium_current_a_gate" />
    <map_variables variable_1="time" variable_2="time" />
    <map_variables variable_1="c" variable_2="c" />
  </connection>
  <connection>
    <map_components component_1="cytosolic_free_calcium_concentration" component_2="nucleotide_sensitive_potassium_current" />
    <map_variables variable_1="c" variable_2="c" />
  </connection>
  <connection>
    <map_components component_1="cytosolic_free_calcium_concentration" component_2="calcium_leak_out_of_the_ER" />
    <map_variables variable_1="c" variable_2="c" />
  </connection>
  <connection>
    <map_components component_1="calcium_dependent_potassium_current" component_2="calcium_dependent_potassium_current_omega_gate" />
    <map_variables variable_1="c" variable_2="c" />
  </connection>
  <connection>
    <map_components component_1="calcium_current_m_gate" component_2="calcium_current" />
    <map_variables variable_1="m_infinity" variable_2="m_infinity" />
  </connection>
  <connection>
    <map_components component_1="environment" component_2="delayed_rectifier_potassium_current" />
    <map_variables variable_1="time" variable_2="time" />
  </connection>
  <connection>
    <map_components component_1="cytosolic_free_calcium_concentration" component_2="calcium_influx_into_the_ER" />
    <map_variables variable_1="c" variable_2="c" />
  </connection>
  <connection>
    <map_components component_1="environment" component_2="ER_calcium_concentration" />
    <map_variables variable_1="time" variable_2="time" />
  </connection>
  <connection>
    <map_components component_1="calcium_current" component_2="membrane" />
    <map_variables variable_1="i_Ca" variable_2="i_Ca" />
  </connection>
  <connection>
    <map_components component_1="environment" component_2="nucleotide_sensitive_potassium_current" />
    <map_variables variable_1="time" variable_2="time" />
  </connection>
  <connection>
    <map_components component_1="cytosolic_free_calcium_concentration" component_2="calcium_dependent_potassium_current" />
    <map_variables variable_1="c" variable_2="c" />
  </connection>
  <connection>
    <map_components component_1="ER_calcium_concentration" component_2="calcium_efflux_through_the_IP3R" />
    <map_variables variable_1="c_er" variable_2="c_er" />
  </connection>
  <connection>
    <map_components component_1="calcium_flux_through_the_membrane" component_2="cytosolic_free_calcium_concentration" />
    <map_variables variable_1="Jmem" variable_2="Jmem" />
  </connection>
  <connection>
    <map_components component_1="net_calcium_efflux_out_of_the_ER" component_2="ER_calcium_concentration" />
    <map_variables variable_1="Jer" variable_2="Jer" />
  </connection>
  <connection>
    <map_components component_1="environment" component_2="membrane" />
    <map_variables variable_1="time" variable_2="time" />
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  <connection>
    <map_components component_1="calcium_dependent_potassium_current" component_2="membrane" />
    <map_variables variable_1="i_K_Ca" variable_2="i_K_Ca" />
  </connection>
  <connection>
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    <map_variables variable_1="c_er" variable_2="c_er" />
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  <connection>
    <map_components component_1="delayed_rectifier_potassium_current" component_2="membrane" />
    <map_variables variable_1="i_K" variable_2="i_K" />
  </connection>
  <connection>
    <map_components component_1="calcium_efflux_through_the_IP3R" component_2="net_calcium_efflux_out_of_the_ER" />
    <map_variables variable_1="JIP3" variable_2="JIP3" />
  </connection>
  <connection>
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  <connection>
    <map_components component_1="net_calcium_efflux_out_of_the_ER" component_2="cytosolic_free_calcium_concentration" />
    <map_variables variable_1="Jer" variable_2="Jer" />
  </connection>
  <connection>
    <map_components component_1="calcium_dependent_potassium_current_omega_gate" component_2="calcium_dependent_potassium_current" />
    <map_variables variable_1="omega" variable_2="omega" />
  </connection>
  <connection>
    <map_components component_1="cytosolic_free_calcium_concentration" component_2="calcium_efflux_through_the_IP3R" />
    <map_variables variable_1="c" variable_2="c" />
  </connection>
  <connection>
    <map_components component_1="nucleotide_sensitive_potassium_current_a_gate" component_2="nucleotide_sensitive_potassium_current" />
    <map_variables variable_1="a" variable_2="a" />
  </connection>
  <connection>
    <map_components component_1="calcium_influx_into_the_ER" component_2="net_calcium_efflux_out_of_the_ER" />
    <map_variables variable_1="J_SERCA" variable_2="J_SERCA" />
  </connection>
  <connection>
    <map_components component_1="environment" component_2="cytosolic_free_calcium_concentration" />
    <map_variables variable_1="time" variable_2="time" />
  </connection>
  <connection>
    <map_components component_1="calcium_current" component_2="calcium_current_m_gate" />
    <map_variables variable_1="V" variable_2="V" />
    <map_variables variable_1="time" variable_2="time" />
  </connection>
  <connection>
    <map_components component_1="delayed_rectifier_potassium_current" component_2="delayed_rectifier_potassium_current_n_gate" />
    <map_variables variable_1="V" variable_2="V" />
    <map_variables variable_1="time" variable_2="time" />
  </connection>
  <connection>
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  </connection>
  <connection>
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  <connection>
    <map_components component_1="delayed_rectifier_potassium_current_n_gate" component_2="delayed_rectifier_potassium_current" />
    <map_variables variable_1="n" variable_2="n" />
  </connection>
  <connection>
    <map_components component_1="membrane" component_2="delayed_rectifier_potassium_current" />
    <map_variables variable_1="V" variable_2="V" />
  </connection>
  <connection>
    <map_components component_1="environment" component_2="calcium_current" />
    <map_variables variable_1="time" variable_2="time" />
  </connection>
  <connection>
    <map_components component_1="nucleotide_sensitive_potassium_current" component_2="membrane" />
    <map_variables variable_1="i_K_ATP" variable_2="i_K_ATP" />
  </connection>
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      <dcterms:description>calcium-dependent potassium current</dcterms:description>
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      <dcterms:description>Michaelis-Menten constant of IP3 receptor activation by cytosolic calcium</dcterms:description>
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      <dcterms:description>potassium reversal potential</dcterms:description>
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      <dcterms:description>Michaelis-Menten constant of IP3 receptor activation by IP3</dcterms:description>
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      <dcterms:description>delayed rectifier activation variable</dcterms:description>
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      <dcterms:description>calcium leak flux out of endoplasmic reticulum</dcterms:description>
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      <bqbiol:isPropertyOf rdf:resource="bertram_sherman_2004.cellml#entity_0" />
      <dcterms:description>concentration of free cytosolic calcium</dcterms:description>
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      <dcterms:description>net calcium flux through the endoplasmic reticulum membrane</dcterms:description>
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      <dcterms:description>net calcium flux through the endoplasmic reticulum membrane</dcterms:description>
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      <dcterms:description>nucleotide ratio of ADP to ATP</dcterms:description>
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    <rdf:Description rdf:about="bertram_sherman_2004.cellml#calcium_current_m_gate.m_infinity">
      <dcterms:description>steady state function of calcium channel activation variable</dcterms:description>
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      <bqbiol:is rdf:resource="https://identifiers.org/opb/OPB_01023" />
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      <dcterms:description>membrane potential</dcterms:description>
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      <dcterms:description>net calcium flux through the endoplasmic reticulum membrane</dcterms:description>
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      <bqbiol:is rdf:resource="https://identifiers.org/opb/OPB_01296" />
      <dcterms:description>leak rate constant</dcterms:description>
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      <dcterms:description>activation potential of calcium current</dcterms:description>
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      <bqbiol:isPropertyOf rdf:resource="bertram_sherman_2004.cellml#entity_6" />
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      <semsim:modelName>bertram_sherman_2004</semsim:modelName>
    </rdf:Description>
    <rdf:Description rdf:about="bertram_sherman_2004.cellml#nucleotide_sensitive_potassium_current_a_gate.tau_a">
      <dcterms:description>time constant of nucleotide oscillations</dcterms:description>
    </rdf:Description>
    <rdf:Description rdf:about="#calcium_dependent_potassium_current.i_K_Ca">
      <semsim:isComputationalComponentFor>
        <rdf:Description rdf:about="#property_13">
          <semsim:hasPhysicalDefinition rdf:resource="https://identifiers.org/opb/OPB_00318" />
        </rdf:Description>
      </semsim:isComputationalComponentFor>
      <dcterms:description>calcium-dependent potassium current</dcterms:description>
    </rdf:Description>
    <rdf:Description rdf:about="#calcium_dependent_potassium_current.V">
      <semsim:isComputationalComponentFor>
        <rdf:Description rdf:about="#property_15">
          <semsim:hasPhysicalDefinition rdf:resource="https://identifiers.org/opb/OPB_00506" />
        </rdf:Description>
      </semsim:isComputationalComponentFor>
      <dcterms:description>membrane potential</dcterms:description>
    </rdf:Description>
    <rdf:Description rdf:about="bertram_sherman_2004.cellml#cytosolic_free_calcium_concentration.Jer">
      <dcterms:description>net calcium flux through the endoplasmic reticulum membrane</dcterms:description>
    </rdf:Description>
    <rdf:Description rdf:about="bertram_sherman_2004.cellml#entity_2">
      <bqbiol:is rdf:resource="http://identifiers.org/fma/FMA:85704" />
    </rdf:Description>
    <rdf:Description rdf:about="bertram_sherman_2004.cellml#membrane.i_Ca">
      <dcterms:description>calcium current</dcterms:description>
    </rdf:Description>
    <rdf:Description rdf:about="bertram_sherman_2004.cellml#nucleotide_sensitive_potassium_current.a">
      <dcterms:description>nucleotide ratio of ADP to ATP</dcterms:description>
    </rdf:Description>
    <rdf:Description rdf:about="#nucleotide_sensitive_potassium_current.V">
      <semsim:isComputationalComponentFor>
        <rdf:Description rdf:about="#property_21">
          <semsim:hasPhysicalDefinition rdf:resource="https://identifiers.org/opb/OPB_00506" />
        </rdf:Description>
      </semsim:isComputationalComponentFor>
      <dcterms:description>membrane potential</dcterms:description>
    </rdf:Description>
    <rdf:Description rdf:about="bertram_sherman_2004.cellml#nucleotide_sensitive_potassium_current.i_K_ATP">
      <dcterms:description>ATP-sensitive potassium current</dcterms:description>
    </rdf:Description>
    <rdf:Description rdf:about="#calcium_current_m_gate.vm">
      <dcterms:description>activation potential of calcium current</dcterms:description>
    </rdf:Description>
    <rdf:Description rdf:about="bertram_sherman_2004.cellml#nucleotide_sensitive_potassium_current_a_gate.a_infinity">
      <dcterms:description>equilibrium function of ADP to ATP nucleotide ratio</dcterms:description>
    </rdf:Description>
    <rdf:Description rdf:about="#delayed_rectifier_potassium_current_n_gate.V">
      <semsim:isComputationalComponentFor>
        <rdf:Description rdf:about="#property_12">
          <semsim:hasPhysicalDefinition rdf:resource="https://identifiers.org/opb/OPB_00506" />
        </rdf:Description>
      </semsim:isComputationalComponentFor>
      <dcterms:description>membrane potential</dcterms:description>
    </rdf:Description>
    <rdf:Description rdf:about="bertram_sherman_2004.cellml#membrane.i_K">
      <dcterms:description>delayed rectifier potassium current</dcterms:description>
    </rdf:Description>
  </rdf:RDF>
</model>