Location: semantic-annotation @ dcab0d9157ad / warren_2010.cellml

Author:

Dewan Sarwar <sarwarcse@gmail.com>

Date:

2019-03-11 12:09:49+13:00

Desc:

added blood capillary flux model

Permanent Source URI:

https://models.physiomeproject.org/workspace/584/rawfile/dcab0d9157ad4fb602c5084666c323fb3e30323a/warren_2010.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="warren_2010" cmeta:id="warren_2010">
  <documentation xmlns="http://cellml.org/tmp-documentation">
    <article>
      <articleinfo>
        <title>Mathematical modelling of calcium wave propagation in mammalian airway epithelium: evidence for regenerative ATP release</title>
        <author>
          <firstname>Catherine</firstname>
          <surname>Lloyd</surname>
          <affiliation>
            <shortaffil>Auckland Bioengineering Institute, The University of Auckland</shortaffil>
          </affiliation>
        </author>
      </articleinfo>
      <section id="sec_status">
        <title>Model Status</title>
        <para>This CellML model runs in both COR and OpenCell to replicate the results from the original published model.  The units have been checked and they balance.  We'd like to thank the original model author Nic Warren for taking the time to develop the CellML version of his model.</para>
      </section>
      <sect1 id="sec_structure">
        <title>Model Structure</title>
        <para>ABSTRACT: Airway epithelium has been shown to exhibit intracellular calcium waves after mechanical stimulation. Two classes of mechanism have been proposed to explain calcium wave propagation: diffusion through gap junctions of the intracellular messenger inositol 1,4,5-trisphosphate (IP3), and diffusion of paracrine extracellular messengers such as ATP. We have used single cell recordings of airway epithelium to parametreize a model of an airway epithelial cell. This was then incorporated into a spatial model of a cell culture where both mechanisms for calcium wave propagation are possible. It is shown that a decreasing return on the radius of Ca2+ wave propagation is achieved as the amount of ATP released from the stimulated cell increases. It is therefore shown that for a Ca2+ wave to propagate large distances, a significant fraction of the intracellular ATP pool would be required to be released. Further to this, the radial distribution of maximal calcium response from the stimulated cell does not produce the same flat profile of maximal calcium response seen in experiential studies. This suggests that an additional mechanism is important in Ca2+ wave propagation, such as regenerative release of ATP from cells downstream of the stimulated cell.</para>
        <para>The original paper reference is cited below:</para>
        <para>
          Mathematical modelling of calcium wave propagation in mammalian airway epithelium: evidence for regenerative ATP release, N.J. Warren, M.H. Tawhai and E.J. Crampin, 2010,
          <emphasis>Experimental Physiology</emphasis>
          95, 232-249.
          <ulink url="http://www.ncbi.nlm.nih.gov/pubmed/19700517">PubMed ID: 19700517</ulink>
        </para>
        <informalfigure float="0" id="diagram">
          <mediaobject>
            <imageobject>
              <objectinfo>
                <title>diagram</title>
              </objectinfo>
              <imagedata fileref="warren_2010.png" />
            </imageobject>
          </mediaobject>
          <caption>Schematic representation of model components and subsystems: Mechanical stimulation triggers the release of ATP from the stimulated cell as well as direct opening of plasma membrane Ca2+ channels (PMCCs). The release of ATP results in the production of IP3 after binding to cell-surface P2Y2 receptors. The IP3 can diffuse through the cytosol to initiate the release of Ca2+ from the ER or diffuse through gap junctions to initiate Ca2+ release from the ER of an adjacent cell.</caption>
        </informalfigure>
      </sect1>
    </article>
  </documentation>
  <units name="micromolar">
    <unit exponent="-1.0" units="litre" />
    <unit prefix="micro" units="mole" />
  </units>
  <units name="milliV">
    <unit prefix="milli" units="volt" />
  </units>
  <units name="flux">
    <unit units="microM" />
    <unit exponent="-1.0" units="second" />
  </units>
  <units name="Volumepersec">
    <unit units="volume" />
    <unit exponent="-1.0" units="second" />
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    <unit prefix="-21" units="ampere" />
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    <unit units="microM" />
    <unit exponent="-1.0" units="second" />
  </units>
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    <unit exponent="-1.0" units="mole" />
    <unit units="ampere" />
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  <units name="micron">
    <unit prefix="micro" units="meter" />
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  <units name="conductance">
    <unit prefix="-18" units="siemens" />
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  <units name="per_secmicroM">
    <unit exponent="-1.0" units="microM" />
    <unit exponent="-1.0" units="second" />
  </units>
  <units name="mMvolumepersec">
    <unit units="volume" />
    <unit units="mM" />
    <unit exponent="-1.0" units="second" />
  </units>
  <units name="millijoule_per_mole_kelvin">
    <unit exponent="-1.0" units="kelvin" />
    <unit prefix="milli" units="joule" />
    <unit exponent="-1.0" units="mole" />
  </units>
  <units name="per_sec">
    <unit exponent="-1.0" units="second" />
  </units>
  <units name="area">
    <unit exponent="2.0" units="micron" />
  </units>
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    <unit units="volume" />
    <unit exponent="-1.0" units="second" />
    <unit units="microM" />
  </units>
  <units name="capacitance">
    <unit prefix="pico" units="farad" />
    <unit exponent="-1.0" units="area" />
  </units>
  <units name="conductancesec2permicroM2volume">
    <unit exponent="-2.0" units="microM" />
    <unit exponent="-1.0" units="volume" />
    <unit exponent="2.0" units="second" />
    <unit units="conductance" />
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    <unit units="volume" />
    <unit units="mM" />
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    <unit exponent="-1.0" units="mmol" />
  </units>
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    <unit units="volume" />
    <unit units="microM" />
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    <unit exponent="-1.0" units="micromolar" />
    <unit exponent="-1.0" units="second" />
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    <unit exponent="3.0" units="micron" />
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  <units name="mM">
    <unit prefix="milli" units="mole" />
    <unit exponent="-1.0" units="litre" />
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    <unit units="conductance" />
    <unit exponent="-1.0" units="volume" />
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  <units name="mmol">
    <unit prefix="milli" units="mole" />
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    <unit exponent="-1.0" units="second" />
    <unit units="microM" />
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    <unit exponent="-1.0" units="litre" />
    <unit prefix="micro" units="mole" />
  </units>
  <units name="per_microM">
    <unit exponent="-1.0" units="microM" />
  </units>
  <component name="environment">
    <variable cmeta:id="environment_time" name="time" public_interface="out" units="second" />
  </component>
  <component name="volume_i">
    <variable cmeta:id="volume_i.volume_i0" initial_value="1450" name="volume_i0" public_interface="out" units="volume" />
    <variable cmeta:id="volume_i.volume_i" name="volume_i" public_interface="out" units="volume" />
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply>
        <eq />
        <ci>volume_i</ci>
        <ci>volume_i0</ci>
      </apply>
    </math>
  </component>
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    <variable cmeta:id="volume_er.gamma" initial_value="4.9" name="gamma" units="dimensionless" />
    <variable cmeta:id="volume_er.volume_i" name="volume_i" public_interface="in" units="volume" />
    <variable cmeta:id="volume_er.volume_er" name="volume_er" public_interface="out" units="volume" />
    <math xmlns="http://www.w3.org/1998/Math/MathML">
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        <eq />
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        </apply>
      </apply>
    </math>
  </component>
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    <variable cmeta:id="volumeCa_i.Jipt" name="Jipt" public_interface="in" units="microMvolumepersec" />
    <variable cmeta:id="volumeCa_i.Jryr" name="Jryr" public_interface="in" units="microMvolumepersec" />
    <variable cmeta:id="volumeCa_i.Jer" name="Jer" public_interface="in" units="microMvolumepersec" />
    <variable cmeta:id="volumeCa_i.Jserca" name="Jserca" public_interface="in" units="microMvolumepersec" />
    <variable cmeta:id="volumeCa_i.Jin" name="Jin" public_interface="in" units="microMvolumepersec" />
    <variable cmeta:id="volumeCa_i.Jpm" name="Jpm" public_interface="in" units="microMvolumepersec" />
    <variable cmeta:id="volumeCa_i.time" name="time" public_interface="in" units="second" />
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply>
        <eq />
        <apply>
          <diff />
          <bvar>
            <ci>time</ci>
          </bvar>
          <ci>volumeCa_i</ci>
        </apply>
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          </apply>
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            <ci>Jin</ci>
            <ci>Jpm</ci>
          </apply>
        </apply>
      </apply>
    </math>
  </component>
  <component name="Ca_i">
    <variable cmeta:id="Ca_i.Ca_i" name="Ca_i" public_interface="out" units="microM" />
    <variable cmeta:id="Ca_i.volume_i" name="volume_i" public_interface="in" units="volume" />
    <variable cmeta:id="Ca_i.volumeCa_i" name="volumeCa_i" public_interface="in" units="microMVolume" />
    <math xmlns="http://www.w3.org/1998/Math/MathML">
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    <variable cmeta:id="volumeCa_er.volume_er" name="volume_er" public_interface="in" units="volume" />
    <variable cmeta:id="volumeCa_er.Jipt" name="Jipt" public_interface="in" units="microMvolumepersec" />
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    <variable cmeta:id="volumeCa_er.Jer" name="Jer" public_interface="in" units="microMvolumepersec" />
    <variable cmeta:id="volumeCa_er.Jserca" name="Jserca" public_interface="in" units="microMvolumepersec" />
    <variable cmeta:id="volumeCa_er.time" name="time" public_interface="in" units="second" />
    <math xmlns="http://www.w3.org/1998/Math/MathML">
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          </bvar>
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        </apply>
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            <minus />
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              <plus />
              <ci>Jipt</ci>
              <ci>Jryr</ci>
              <ci>Jer</ci>
            </apply>
            <ci>Jserca</ci>
          </apply>
        </apply>
      </apply>
    </math>
  </component>
  <component name="Ca_er">
    <variable cmeta:id="Ca_er_Ca_er" name="Ca_er" public_interface="out" units="microM" />
    <variable cmeta:id="Ca_er.volume_er" name="volume_er" public_interface="in" units="volume" />
    <variable cmeta:id="Ca_er.volumeCa_er" name="volumeCa_er" public_interface="in" units="microMVolume" />
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply>
        <eq />
        <ci>Ca_er</ci>
        <apply>
          <divide />
          <ci>volumeCa_er</ci>
          <ci>volume_er</ci>
        </apply>
      </apply>
    </math>
  </component>
  <component name="volume_iIP3">
    <variable cmeta:id="volume_iIP3.volume_iIP3" initial_value="-3.28287434380887e-93" name="volume_iIP3" public_interface="out" units="microMVolume" />
    <variable cmeta:id="volume_iIP3.volume_i" name="volume_i" public_interface="in" units="volume" />
    <variable cmeta:id="volume_iIP3.J_ip3P" name="J_ip3P" public_interface="in" units="microMpersec" />
    <variable cmeta:id="volume_iIP3.J_ip3D" name="J_ip3D" public_interface="in" units="microMpersec" />
    <variable cmeta:id="volume_iIP3.time" name="time" public_interface="in" units="second" />
    <math xmlns="http://www.w3.org/1998/Math/MathML">
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          </bvar>
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        </apply>
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            <ci>J_ip3D</ci>
          </apply>
          <ci>volume_i</ci>
        </apply>
      </apply>
    </math>
  </component>
  <component name="IP3">
    <variable cmeta:id="IP3_IP3" name="IP3" public_interface="out" units="microM" />
    <variable cmeta:id="IP3.volume_i" name="volume_i" public_interface="in" units="volume" />
    <variable cmeta:id="IP3.volume_iIP3" name="volume_iIP3" public_interface="in" units="microMVolume" />
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply>
        <eq />
        <ci>IP3</ci>
        <apply>
          <divide />
          <ci>volume_iIP3</ci>
          <ci>volume_i</ci>
        </apply>
      </apply>
    </math>
  </component>
  <component name="PIP2">
    <variable cmeta:id="PIP2.PIP2" initial_value="1" name="PIP2" public_interface="out" units="dimensionless" />
    <variable cmeta:id="PIP2.PIP2_Total" initial_value="5" name="PIP2_Total" units="microM" />
    <variable cmeta:id="PIP2.J_ip3P" name="J_ip3P" public_interface="in" units="microMpersec" />
    <variable cmeta:id="PIP2.J_ip3R" name="J_ip3R" public_interface="in" units="per_sec" />
    <variable cmeta:id="PIP2.IPX" name="IPX" public_interface="in" units="dimensionless" />
    <variable cmeta:id="PIP2.time" name="time" public_interface="in" units="second" />
    <math xmlns="http://www.w3.org/1998/Math/MathML">
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            <ci>PIP2_Total</ci>
          </apply>
        </apply>
      </apply>
    </math>
  </component>
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    <variable cmeta:id="IPX.PIP2" name="PIP2" public_interface="in" units="dimensionless" />
    <variable cmeta:id="IPX.IP3" name="IP3" public_interface="in" units="microM" />
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            <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
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        <ci>J_ip3R0</ci>
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    <variable cmeta:id="receptor.time" name="time" public_interface="in" units="second" />
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    <variable cmeta:id="receptor.C_4" initial_value="10" name="C_4" public_interface="out" units="microM" />
    <variable cmeta:id="receptor.V_ATP" initial_value="0.001" name="V_ATP" units="microMpersec" />
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          <piece>
            <ci>V_mech0</ci>
            <apply>
              <and />
              <apply>
                <gt />
                <ci>time</ci>
                <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="second">10</cn>
              </apply>
              <apply>
                <lt />
                <ci>time</ci>
                <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="second">25</cn>
              </apply>
              <apply>
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                <ci>MechanicalStimulation</ci>
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              </apply>
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          </piece>
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              </apply>
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              </apply>
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                <power />
                <ci>ATP_e</ci>
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              </apply>
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            <apply>
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              <ci>V_ATP</ci>
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          <apply>
            <plus />
            <ci>K_ATP</ci>
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        </apply>
      </apply>
    </math>
  </component>
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        <eq />
        <ci>J_ip3P</ci>
        <apply>
          <times />
          <ci>V_IP3</ci>
          <ci>PIP2</ci>
        </apply>
      </apply>
    </math>
  </component>
  <component name="J_ip3D">
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    <variable cmeta:id="J_ip3D.IP3" name="IP3" public_interface="in" units="microM" />
    <variable cmeta:id="J_ip3D.volume_i0" name="volume_i0" public_interface="in" units="volume" />
    <variable cmeta:id="J_ip3D.Beta_1" initial_value="0" name="Beta_1" units="microMpersec" />
    <variable cmeta:id="J_ip3D.Beta_2" initial_value="36" name="Beta_2" units="microMpersec" />
    <variable cmeta:id="J_ip3D.Ca_i" name="Ca_i" public_interface="in" units="microM" />
    <variable cmeta:id="J_ip3D.F_Ca" name="F_Ca" units="dimensionless" />
    <variable cmeta:id="J_ip3D.K_rc" initial_value="0.3" name="K_rc" units="microM" />
    <variable cmeta:id="J_ip3D.K_IP3" initial_value="0.01" name="K_IP3" units="microM" />
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply>
        <eq />
        <ci>F_Ca</ci>
        <apply>
          <divide />
          <ci>Ca_i</ci>
          <apply>
            <plus />
            <ci>K_rc</ci>
            <ci>Ca_i</ci>
          </apply>
        </apply>
      </apply>
      <apply>
        <eq />
        <ci>J_ip3D</ci>
        <apply>
          <divide />
          <apply>
            <times />
            <apply>
              <plus />
              <ci>Beta_1</ci>
              <apply>
                <times />
                <ci>Beta_2</ci>
                <apply>
                  <power />
                  <ci>F_Ca</ci>
                  <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
                </apply>
              </apply>
            </apply>
            <ci>IP3</ci>
          </apply>
          <apply>
            <plus />
            <ci>K_IP3</ci>
            <ci>IP3</ci>
          </apply>
        </apply>
      </apply>
    </math>
  </component>
  <component name="Jipt">
    <variable cmeta:id="Jipt.Jipt" name="Jipt" public_interface="out" units="microMvolumepersec" />
    <variable cmeta:id="Jipt.Ca_i" name="Ca_i" public_interface="in" units="microM" />
    <variable cmeta:id="Jipt.Ca_er" name="Ca_er" public_interface="in" units="microM" />
    <variable cmeta:id="Jipt.Pipt" name="Pipt" units="dimensionless" />
    <variable cmeta:id="Jipt.O" name="O" public_interface="in" units="dimensionless" />
    <variable cmeta:id="Jipt.volume_i0" name="volume_i0" public_interface="in" units="volume" />
    <variable cmeta:id="Jipt.Jipt0" initial_value="28" name="Jipt0" units="per_sec" />
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply>
        <eq />
        <ci>Pipt</ci>
        <apply>
          <power />
          <ci>O</ci>
          <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">4</cn>
        </apply>
      </apply>
      <apply>
        <eq />
        <ci>Jipt</ci>
        <apply>
          <times />
          <ci>Jipt0</ci>
          <ci>volume_i0</ci>
          <ci>Pipt</ci>
          <apply>
            <minus />
            <ci>Ca_er</ci>
            <ci>Ca_i</ci>
          </apply>
        </apply>
      </apply>
    </math>
  </component>
  <component name="Jryr">
    <variable cmeta:id="Jryr.Ka" initial_value="0.3722419" name="Ka" units="microM" />
    <variable cmeta:id="Jryr.Kb" initial_value="0.636005" name="Kb" units="microM" />
    <variable cmeta:id="Jryr.Kc" initial_value="0.0571428" name="Kc" units="dimensionless" />
    <variable cmeta:id="Jryr.Ca_i" name="Ca_i" public_interface="in" units="microM" />
    <variable cmeta:id="Jryr.Ca_er" name="Ca_er" public_interface="in" units="microM" />
    <variable cmeta:id="Jryr.volume_i0" name="volume_i0" public_interface="in" units="volume" />
    <variable cmeta:id="Jryr_Jryr" name="Jryr" public_interface="out" units="microMvolumepersec" />
    <variable cmeta:id="Jryr.Jryr0" initial_value="0" name="Jryr0" units="per_sec" />
    <variable cmeta:id="Jryr.Pryr" name="Pryr" units="dimensionless" />
    <variable cmeta:id="Jryr.W_inf" name="W_inf" units="dimensionless" />
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply>
        <eq />
        <ci>W_inf</ci>
        <apply>
          <divide />
          <apply>
            <plus />
            <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
            <apply>
              <power />
              <apply>
                <divide />
                <ci>Ka</ci>
                <ci>Ca_i</ci>
              </apply>
              <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">4</cn>
            </apply>
            <apply>
              <power />
              <apply>
                <divide />
                <ci>Ca_i</ci>
                <ci>Kb</ci>
              </apply>
              <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">3</cn>
            </apply>
          </apply>
          <apply>
            <plus />
            <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
            <apply>
              <divide />
              <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
              <ci>Kc</ci>
            </apply>
            <apply>
              <power />
              <apply>
                <divide />
                <ci>Ca_i</ci>
                <ci>Kb</ci>
              </apply>
              <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">3</cn>
            </apply>
            <apply>
              <power />
              <apply>
                <divide />
                <ci>Ka</ci>
                <ci>Ca_i</ci>
              </apply>
              <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">4</cn>
            </apply>
          </apply>
        </apply>
      </apply>
      <apply>
        <eq />
        <ci>Pryr</ci>
        <apply>
          <divide />
          <apply>
            <times />
            <ci>W_inf</ci>
            <apply>
              <plus />
              <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
              <apply>
                <power />
                <apply>
                  <divide />
                  <ci>Ka</ci>
                  <ci>Ca_i</ci>
                </apply>
                <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">4</cn>
              </apply>
              <apply>
                <power />
                <apply>
                  <divide />
                  <ci>Ca_i</ci>
                  <ci>Kb</ci>
                </apply>
                <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">3</cn>
              </apply>
            </apply>
          </apply>
          <apply>
            <plus />
            <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
            <apply>
              <divide />
              <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
              <ci>Kc</ci>
            </apply>
            <apply>
              <power />
              <apply>
                <divide />
                <ci>Ca_i</ci>
                <ci>Kb</ci>
              </apply>
              <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">3</cn>
            </apply>
            <apply>
              <power />
              <apply>
                <divide />
                <ci>Ka</ci>
                <ci>Ca_i</ci>
              </apply>
              <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">4</cn>
            </apply>
          </apply>
        </apply>
      </apply>
      <apply>
        <eq />
        <ci>Jryr</ci>
        <apply>
          <times />
          <ci>Jryr0</ci>
          <ci>volume_i0</ci>
          <apply>
            <minus />
            <ci>Ca_er</ci>
            <ci>Ca_i</ci>
          </apply>
        </apply>
      </apply>
    </math>
  </component>
  <component name="Jer">
    <variable cmeta:id="Jer_Jer" name="Jer" public_interface="out" units="microMvolumepersec" />
    <variable cmeta:id="Jer.Ca_i" name="Ca_i" public_interface="in" units="microM" />
    <variable cmeta:id="Jer.Ca_er" name="Ca_er" public_interface="in" units="microM" />
    <variable cmeta:id="Jer.volume_i0" name="volume_i0" public_interface="in" units="volume" />
    <variable cmeta:id="Jer.Jer0" initial_value="0.0035" name="Jer0" units="per_sec" />
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply>
        <eq />
        <ci>Jer</ci>
        <apply>
          <times />
          <ci>Jer0</ci>
          <ci>volume_i0</ci>
          <apply>
            <minus />
            <ci>Ca_er</ci>
            <ci>Ca_i</ci>
          </apply>
        </apply>
      </apply>
    </math>
  </component>
  <component name="Jserca">
    <variable cmeta:id="Jserca_Jserca" name="Jserca" public_interface="out" units="microMvolumepersec" />
    <variable cmeta:id="Jserca.Ca_i" name="Ca_i" public_interface="in" units="microM" />
    <variable cmeta:id="Jserca.Ca_er" name="Ca_er" public_interface="in" units="microM" />
    <variable cmeta:id="Jserca.volume_i0" name="volume_i0" public_interface="in" units="volume" />
    <variable cmeta:id="Jserca.Vserca" initial_value="0.09" name="Vserca" units="microM2persec" />
    <variable cmeta:id="Jserca.Kserca" initial_value="0.04" name="Kserca" units="microM" />
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply>
        <eq />
        <ci>Jserca</ci>
        <apply>
          <divide />
          <apply>
            <times />
            <apply>
              <divide />
              <apply>
                <times />
                <ci>volume_i0</ci>
                <ci>Vserca</ci>
                <apply>
                  <power />
                  <ci>Ca_i</ci>
                  <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
                </apply>
              </apply>
              <apply>
                <plus />
                <apply>
                  <power />
                  <ci>Kserca</ci>
                  <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
                </apply>
                <apply>
                  <power />
                  <ci>Ca_i</ci>
                  <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
                </apply>
              </apply>
            </apply>
            <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
          </apply>
          <ci>Ca_er</ci>
        </apply>
      </apply>
    </math>
  </component>
  <component name="Jin">
    <variable cmeta:id="Jin.Jin" name="Jin" public_interface="out" units="microMvolumepersec" />
    <variable cmeta:id="Jin.Ca_i" name="Ca_i" public_interface="in" units="microM" />
    <variable cmeta:id="Jin.Ca_er" name="Ca_er" public_interface="in" units="microM" />
    <variable cmeta:id="Jin.Vm" initial_value="-39" name="Vm" units="milliV" />
    <variable cmeta:id="Jin.V_Ca" name="V_Ca" units="milliV" />
    <variable cmeta:id="Jin.R" initial_value="8314" name="R" units="millijoule_per_mole_kelvin" />
    <variable cmeta:id="Jin.T" initial_value="310" name="T" units="kelvin" />
    <variable cmeta:id="Jin.F" initial_value="96485" name="F" units="coulomb_per_mole" />
    <variable cmeta:id="Jin.z_Ca" initial_value="2" name="z_Ca" units="dimensionless" />
    <variable cmeta:id="Jin.Ca_ext" initial_value="1300" name="Ca_ext" units="microM" />
    <variable cmeta:id="Jin.P_pm_1" initial_value="0.6" name="P_pm_1" units="conductancepervolume" />
    <variable cmeta:id="Jin.P_pm_2" initial_value="28" name="P_pm_2" units="conductancepervolume" />
    <variable cmeta:id="Jin.Iin_1" name="Iin_1" units="current" />
    <variable cmeta:id="Jin.Iin_2" name="Iin_2" units="current" />
    <variable cmeta:id="Jin.Jin_1" name="Jin_1" units="microMvolumepersec" />
    <variable cmeta:id="Jin.Jin_2" name="Jin_2" units="microMvolumepersec" />
    <variable cmeta:id="Jin.volume_i0" name="volume_i0" public_interface="in" units="volume" />
    <variable cmeta:id="Jin.V_mech" name="V_mech" public_interface="in" units="dimensionless" />
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply>
        <eq />
        <ci>V_Ca</ci>
        <apply>
          <times />
          <apply>
            <divide />
            <apply>
              <times />
              <ci>R</ci>
              <ci>T</ci>
            </apply>
            <apply>
              <times />
              <ci>z_Ca</ci>
              <ci>F</ci>
            </apply>
          </apply>
          <apply>
            <ln />
            <apply>
              <divide />
              <ci>Ca_ext</ci>
              <ci>Ca_i</ci>
            </apply>
          </apply>
        </apply>
      </apply>
      <apply>
        <eq />
        <ci>Iin_1</ci>
        <apply>
          <times />
          <ci>volume_i0</ci>
          <ci>P_pm_1</ci>
          <apply>
            <minus />
            <ci>V_Ca</ci>
            <ci>Vm</ci>
          </apply>
        </apply>
      </apply>
      <apply>
        <eq />
        <ci>Iin_2</ci>
        <apply>
          <times />
          <ci>volume_i0</ci>
          <ci>P_pm_2</ci>
          <ci>V_mech</ci>
          <apply>
            <minus />
            <ci>V_Ca</ci>
            <ci>Vm</ci>
          </apply>
        </apply>
      </apply>
      <apply>
        <eq />
        <ci>Jin_1</ci>
        <apply>
          <divide />
          <ci>Iin_1</ci>
          <apply>
            <times />
            <ci>z_Ca</ci>
            <ci>F</ci>
          </apply>
        </apply>
      </apply>
      <apply>
        <eq />
        <ci>Jin_2</ci>
        <apply>
          <divide />
          <ci>Iin_2</ci>
          <apply>
            <times />
            <ci>z_Ca</ci>
            <ci>F</ci>
          </apply>
        </apply>
      </apply>
      <apply>
        <eq />
        <ci>Jin</ci>
        <apply>
          <plus />
          <ci>Jin_1</ci>
          <ci>Jin_2</ci>
        </apply>
      </apply>
    </math>
  </component>
  <component name="Jpm">
    <variable cmeta:id="Jpm_Jpm" name="Jpm" public_interface="out" units="microMvolumepersec" />
    <variable cmeta:id="Jpm.Ca_i" name="Ca_i" public_interface="in" units="microM" />
    <variable cmeta:id="Jpm.Vpm" initial_value="0.072" name="Vpm" units="microMpersec" />
    <variable cmeta:id="Jpm.Kpm" initial_value="0.6" name="Kpm" units="microM" />
    <variable cmeta:id="Jpm.volume_i0" name="volume_i0" public_interface="in" units="volume" />
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply>
        <eq />
        <ci>Jpm</ci>
        <apply>
          <divide />
          <apply>
            <times />
            <ci>Vpm</ci>
            <ci>volume_i0</ci>
            <apply>
              <power />
              <ci>Ca_i</ci>
              <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
            </apply>
          </apply>
          <apply>
            <plus />
            <apply>
              <power />
              <ci>Kpm</ci>
              <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
            </apply>
            <apply>
              <power />
              <ci>Ca_i</ci>
              <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
            </apply>
          </apply>
        </apply>
      </apply>
    </math>
  </component>
  <component name="O">
    <variable cmeta:id="O.O" initial_value="-2.42013500345263e-89" name="O" public_interface="out" units="dimensionless" />
    <variable cmeta:id="O.S" name="S" units="dimensionless" />
    <variable cmeta:id="O.I1" name="I1" public_interface="in" units="dimensionless" />
    <variable cmeta:id="O.I2" name="I2" public_interface="in" units="dimensionless" />
    <variable cmeta:id="O.IP3" name="IP3" public_interface="in" units="micromolar" />
    <variable cmeta:id="O.k1" name="k1" public_interface="in" units="per_secmicroM" />
    <variable cmeta:id="O.k1_" name="k1_" public_interface="in" units="first_order_rate_constant" />
    <variable cmeta:id="O.k2" name="k2" public_interface="in" units="first_order_rate_constant" />
    <variable cmeta:id="O.time" name="time" public_interface="in" units="second" />
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply>
        <eq />
        <apply>
          <diff />
          <bvar>
            <ci>time</ci>
          </bvar>
          <ci>O</ci>
        </apply>
        <apply>
          <minus />
          <apply>
            <times />
            <ci>k1</ci>
            <ci>IP3</ci>
            <ci>S</ci>
          </apply>
          <apply>
            <plus />
            <apply>
              <times />
              <ci>k1_</ci>
              <ci>O</ci>
            </apply>
            <apply>
              <times />
              <ci>k2</ci>
              <ci>O</ci>
            </apply>
          </apply>
        </apply>
      </apply>
      <apply>
        <eq />
        <ci>S</ci>
        <apply>
          <minus />
          <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
          <apply>
            <plus />
            <ci>O</ci>
            <ci>I1</ci>
            <ci>I2</ci>
          </apply>
        </apply>
      </apply>
    </math>
  </component>
  <component name="I1">
    <variable cmeta:id="I1.I1" initial_value="2.24343309680416e-81" name="I1" public_interface="out" units="dimensionless" />
    <variable cmeta:id="I1.O" name="O" public_interface="in" units="dimensionless" />
    <variable cmeta:id="I1.k2" name="k2" public_interface="in" units="first_order_rate_constant" />
    <variable cmeta:id="I1.k3" name="k3" public_interface="in" units="first_order_rate_constant" />
    <variable cmeta:id="I1.k4" name="k4" public_interface="in" units="first_order_rate_constant" />
    <variable cmeta:id="I1.time" name="time" public_interface="in" units="second" />
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply>
        <eq />
        <apply>
          <diff />
          <bvar>
            <ci>time</ci>
          </bvar>
          <ci>I1</ci>
        </apply>
        <apply>
          <minus />
          <apply>
            <times />
            <ci>k2</ci>
            <ci>O</ci>
          </apply>
          <apply>
            <times />
            <apply>
              <plus />
              <ci>k3</ci>
              <ci>k4</ci>
            </apply>
            <ci>I1</ci>
          </apply>
        </apply>
      </apply>
    </math>
  </component>
  <component name="I2">
    <variable cmeta:id="I2.I2" initial_value="1.01276768045278e-40" name="I2" public_interface="out" units="dimensionless" />
    <variable cmeta:id="I2.I1" name="I1" public_interface="in" units="dimensionless" />
    <variable cmeta:id="I2.k4" name="k4" public_interface="in" units="first_order_rate_constant" />
    <variable cmeta:id="I2.k5" name="k5" public_interface="in" units="first_order_rate_constant" />
    <variable cmeta:id="I2.time" name="time" public_interface="in" units="second" />
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply>
        <eq />
        <apply>
          <diff />
          <bvar>
            <ci>time</ci>
          </bvar>
          <ci>I2</ci>
        </apply>
        <apply>
          <minus />
          <apply>
            <times />
            <ci>k4</ci>
            <ci>I1</ci>
          </apply>
          <apply>
            <times />
            <ci>k5</ci>
            <ci>I2</ci>
          </apply>
        </apply>
      </apply>
    </math>
  </component>
  <component name="constants">
    <variable cmeta:id="constants.k1" name="k1" public_interface="out" units="per_secmicroM" />
    <variable cmeta:id="constants.k1_" initial_value="0.88" name="k1_" public_interface="out" units="first_order_rate_constant" />
    <variable cmeta:id="constants.k2" initial_value="0.5" name="k2" public_interface="out" units="first_order_rate_constant" />
    <variable cmeta:id="constants.k3" initial_value="0.5" name="k3" public_interface="out" units="first_order_rate_constant" />
    <variable cmeta:id="constants.k4" name="k4" public_interface="out" units="first_order_rate_constant" />
    <variable cmeta:id="constants.k5" initial_value="0.02" name="k5" public_interface="out" units="first_order_rate_constant" />
    <variable cmeta:id="constants.IP3" name="IP3" public_interface="in" units="microM" />
    <variable cmeta:id="constants.alpha_1" initial_value="40" name="alpha_1" units="per_secmicroM" />
    <variable cmeta:id="constants.beta_1" initial_value="0.8" name="beta_1" units="microM" />
    <variable cmeta:id="constants.alpha_4" initial_value="0.06" name="alpha_4" units="first_order_rate_constant" />
    <variable cmeta:id="constants.beta_4" initial_value="0.01" name="beta_4" units="microM" />
    <variable cmeta:id="constants.Ca_i" name="Ca_i" public_interface="in" units="microM" />
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply>
        <eq />
        <ci>k1</ci>
        <apply>
          <divide />
          <apply>
            <times />
            <ci>alpha_1</ci>
            <apply>
              <power />
              <ci>Ca_i</ci>
              <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">3</cn>
            </apply>
          </apply>
          <apply>
            <plus />
            <apply>
              <power />
              <ci>beta_1</ci>
              <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">3</cn>
            </apply>
            <apply>
              <power />
              <ci>Ca_i</ci>
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</model>