Location: Calcium Dynamics Annotations @ 110f9ba31e34 / albrecht_colegrove_friel_2002 / model / albrecht_colegrove_friel_2002.cellml

Author:
neilstephen2001 <npar276@aucklanduni.ac.nz>
Date:
2021-01-24 21:37:35+13:00
Desc:
adding OMEX archives to workspace
Permanent Source URI:
http://models.cellml.org/workspace/7f1/rawfile/110f9ba31e34b7499c8d02e13a6b9984351c0e8f/albrecht_colegrove_friel_2002/model/albrecht_colegrove_friel_2002.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="albrecht_colegrove_friel_2002" cmeta:id="albrecht_colegrove_friel_2002_version01">
  <documentation xmlns="http://cellml.org/tmp-documentation">
    <article>
      <articleinfo>
        <title>Differential Regulation of ER Ca2+ Uptake and Release Rates Accounts for Multiple Modes of Ca2+-induced Ca2+ Release</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 consistently represented within the CellML but contains sets of algebraic equations that prevent the model from being solved in currently available software - 03/08.</para>
        <para>ValidateCellML found unit inconsistencies in this model</para>
      </section>
      <sect1 id="sec_structure">
        <title>Model Structure</title>
        <para>
          Calcium is an important signalling ion, and changes in Ca
          <superscript>2+</superscript>
          concentration ([Ca
          <superscript>2+</superscript>
          ]) regulate diverse processes in many cellular compartments.  In excitable cells, depolarisation-induced Ca
          <superscript>2+</superscript>
          entry increases [Ca
          <superscript>2+</superscript>
          ]
          <subscript>i</subscript>
          , leading to secondary changes in [Ca
          <superscript>2+</superscript>
          ] within organelles such as mitochondria and ER that regulate specific Ca
          <superscript>2+</superscript>
          -sensitive targets within these organelles.  Although mitochondria accumulate Ca
          <superscript>2+</superscript>
          in response to depolarisation-evoked [Ca
          <superscript>2+</superscript>
          ]
          <subscript>i</subscript>
          elevations (see
          <ulink url="${HTML_EXMPL_COLEGROVE_MODEL}">
            The Colegrove
            <emphasis>et al</emphasis>
            Model Of Mitochondrial Ca
            <superscript>2+</superscript>
            Uptake And Release, 2000
          </ulink>
          ), the ER is also an important component in Ca
          <superscript>2+</superscript>
          signalling in virtually all non-muscle cells, and it has been described as either a Ca
          <superscript>2+</superscript>
          source or sink.  Different modes of net ER Ca
          <superscript>2+</superscript>
          transport are expected to have very different effects on cytoplasmic and intraluminal Ca
          <superscript>2+</superscript>
          signals and on the processes they regulate (see
          <ulink url="${HTML_EXMPL_ALBRECHT_MODEL1}">
            The Albrecht
            <emphasis>et al</emphasis>
            Model Of Multiple Modes of Ca
            <superscript>2+</superscript>
            -induced Ca
            <superscript>2+</superscript>
            Release in Sympathetic Neurons, 2001
          </ulink>
          ).
        </para>
        <para>
          In a follow up study to their 2001 paper, Meredith A. Albrecht, Stephen L. Colegrove and David D. Friel have examined how differential regulation of ER Ca
          <superscript>2+</superscript>
          uptake and release rates accounts for multiple modes of Ca
          <superscript>2+</superscript>
          -induced Ca
          <superscript>2+</superscript>
          release.  Three different macroscopic Ca
          <superscript>2+</superscript>
          fluxes were modelled: J
          <subscript>SERCA</subscript>
          , the rate of Ca
          <superscript>2+</superscript>
          uptake via SR Ca-ATPases; J
          <subscript>ICa</subscript>
          , the total cytoplasmic Ca
          <superscript>2+</superscript>
          flux when SR Ca-ATPases are inhibited; and J
          <subscript>pm</subscript>
          , the rate of Ca
          <superscript>2+</superscript>
          extrusion across the plasma membrane.  One additional flux J
          <subscript>release</subscript>
          was calculated from the difference between J
          <subscript>ICa</subscript>
          and J
          <subscript>pm</subscript>
          (see
          <xref linkend="fig_cell_diagram" />
          below).  This mathematical model has been translated into a CellML description which 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.jgp.org/cgi/content/abstract/119/3/211">
            Differential Regulation of ER Ca
            <superscript>2+</superscript>
            Uptake and Release Rates Accounts for Multiple Modes of Ca
            <superscript>2+</superscript>
            -induced Ca
            <superscript>2+</superscript>
            Release
          </ulink>
          , Meredith A. Albrecht, Stephen L. Colegrove and David D. Friel, 2002,
          <ulink url="http://www.jgp.org/">
            <emphasis>The Journal Of General Physiology</emphasis>
          </ulink>
          , 119, 211-233.  (
          <ulink url="http://www.jgp.org/cgi/content/full/119/3/211">Full text</ulink>
          and
          <ulink url="http://www.jgp.org/cgi/reprint/119/3/211.pdf">PDF</ulink>
          versions of the article are available for Journal Members on the JGP website.)
          <ulink url="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&amp;db=PubMed&amp;list_uids=11865019&amp;dopt=Abstract">PubMed ID: 11865019</ulink>
        </para>
        <informalfigure float="0" id="fig_cell_diagram">
          <mediaobject>
            <imageobject>
              <objectinfo>
                <title>cell schematic for the model</title>
              </objectinfo>
              <imagedata fileref="albrecht_2002.png" />
            </imageobject>
          </mediaobject>
          <caption>
            Schematic of the model indicating Ca
            <superscript>2+</superscript>
            compartmentation in the extracellular matrix, cytosol and the ER and pathways for Ca
            <superscript>2+</superscript>
            ion movement between the compartments.
          </caption>
        </informalfigure>
      </sect1>
    </article>
  </documentation>
  <units name="micromolar_per_second">
    <unit units="micromolar" />
    <unit exponent="-1.0" units="second" />
  </units>
  <units name="millimolar">
    <unit prefix="micro" units="mole" />
    <unit exponent="-1.0" units="litre" />
  </units>
  <units name="picoA">
    <unit prefix="pico" units="ampere" />
  </units>
  <units name="coulomb_per_millimole">
    <unit exponent="-1.0" prefix="milli" units="mole" />
    <unit units="coulomb" />
  </units>
  <units name="micro_litre">
    <unit prefix="micro" units="litre" />
  </units>
  <units name="nanomolar">
    <unit prefix="nano" units="mole" />
    <unit exponent="-1.0" units="litre" />
  </units>
  <units name="micromolar">
    <unit prefix="micro" units="mole" />
    <unit exponent="-1.0" units="litre" />
  </units>
  <units name="millivolt">
    <unit prefix="milli" units="volt" />
  </units>
  <units name="nanomolar_per_second">
    <unit exponent="-1.0" units="second" />
    <unit units="nanomolar" />
  </units>
  <units name="per_second">
    <unit exponent="-1.0" units="second" />
  </units>
  <component name="environment" cmeta:id="submodel_0">
    <variable cmeta:id="environment.time" name="time" public_interface="out" units="second" />
  </component>
  <component name="cytoplasmic_calcium" cmeta:id="submodel_1">
    <variable cmeta:id="cytoplasmic_calcium.Ca_i" name="Ca_i" public_interface="out" units="nanomolar" />
    <variable cmeta:id="cytoplasmic_calcium.J_i" name="J_i" units="nanomolar_per_second" />
    <variable cmeta:id="cytoplasmic_calcium.J_ER" name="J_ER" public_interface="in" units="nanomolar_per_second" />
    <variable cmeta:id="cytoplasmic_calcium.J_pm" name="J_pm" public_interface="in" units="nanomolar_per_second" />
    <variable cmeta:id="cytoplasmic_calcium.time" name="time" public_interface="in" units="second" />
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply id="Ca_i_diff_eq">
        <eq />
        <apply>
          <diff />
          <bvar>
            <ci>time</ci>
          </bvar>
          <ci>Ca_i</ci>
        </apply>
        <apply>
          <minus />
          <ci>J_i</ci>
        </apply>
      </apply>
      <apply id="J_i_calculation">
        <eq />
        <ci>J_i</ci>
        <apply>
          <plus />
          <ci>J_pm</ci>
          <ci>J_ER</ci>
        </apply>
      </apply>
    </math>
  </component>
  <component name="intraluminal_calcium" cmeta:id="submodel_2">
    <variable cmeta:id="intraluminal_calcium.Ca_ER" name="Ca_ER" public_interface="out" units="nanomolar" />
    <variable cmeta:id="intraluminal_calcium.v_ER" name="v_ER" units="micro_litre" />
    <variable cmeta:id="intraluminal_calcium.k_ER" name="k_ER" units="dimensionless" />
    <variable cmeta:id="intraluminal_calcium.Ca_ER_init" name="Ca_ER_init" units="nanomolar" />
    <variable cmeta:id="intraluminal_calcium.Ca_i" name="Ca_i" public_interface="in" units="nanomolar" />
    <variable cmeta:id="intraluminal_calcium.v_i" name="v_i" public_interface="in" units="micro_litre" />
    <variable cmeta:id="intraluminal_calcium.k_i" name="k_i" public_interface="in" units="dimensionless" />
    <variable cmeta:id="intraluminal_calcium.J_ER" name="J_ER" public_interface="in" units="nanomolar_per_second" />
    <variable cmeta:id="intraluminal_calcium.P_ER" name="P_ER" public_interface="in" units="per_second" />
    <variable cmeta:id="intraluminal_calcium.J_SERCA" name="J_SERCA" public_interface="in" units="nanomolar_per_second" />
    <variable cmeta:id="intraluminal_calcium.time" name="time" public_interface="in" units="second" />
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply id="Ca_ER_diff_eq">
        <eq />
        <apply>
          <diff />
          <bvar>
            <ci>time</ci>
          </bvar>
          <ci>Ca_ER</ci>
        </apply>
        <apply>
          <times />
          <ci>J_ER</ci>
          <apply>
            <divide />
            <apply>
              <times />
              <ci>v_i</ci>
              <ci>k_i</ci>
            </apply>
            <apply>
              <times />
              <ci>v_ER</ci>
              <ci>k_ER</ci>
            </apply>
          </apply>
        </apply>
      </apply>
      <apply id="Ca_ER_init_calculation">
        <eq />
        <ci>Ca_ER_init</ci>
        <apply>
          <plus />
          <ci>Ca_i</ci>
          <apply>
            <divide />
            <apply>
              <times />
              <ci>J_SERCA</ci>
              <ci>Ca_i</ci>
            </apply>
            <apply>
              <times />
              <ci>P_ER</ci>
              <apply>
                <divide />
                <ci>Ca_i</ci>
                <ci>v_i</ci>
              </apply>
            </apply>
          </apply>
        </apply>
      </apply>
    </math>
  </component>
  <component name="total_cytoplasmic_Ca_flux" cmeta:id="submodel_3">
    <variable cmeta:id="total_cytoplasmic_Ca_flux.J_ICa" name="J_ICa" public_interface="out" units="nanomolar_per_second" />
    <variable cmeta:id="total_cytoplasmic_Ca_flux.v_i" name="v_i" public_interface="out" units="micro_litre" />
    <variable cmeta:id="total_cytoplasmic_Ca_flux.k_i" name="k_i" public_interface="out" units="dimensionless" />
    <variable cmeta:id="total_cytoplasmic_Ca_flux.F" initial_value="96.5" name="F" units="coulomb_per_millimole" />
    <variable cmeta:id="total_cytoplasmic_Ca_flux.I_Ca" name="I_Ca" units="picoA" />
    <variable cmeta:id="total_cytoplasmic_Ca_flux.time" name="time" public_interface="in" units="second" />
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply id="J_ICa_calculation">
        <eq />
        <ci>J_ICa</ci>
        <apply>
          <divide />
          <ci>I_Ca</ci>
          <apply>
            <times />
            <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2.0</cn>
            <ci>F</ci>
            <ci>v_i</ci>
            <ci>k_i</ci>
          </apply>
        </apply>
      </apply>
    </math>
  </component>
  <component name="Ca_extrusion_across_the_plasma_membrane" cmeta:id="submodel_4">
    <variable cmeta:id="Ca_extrusion_across_the_plasma_membrane.J_pm" name="J_pm" public_interface="out" units="nanomolar_per_second" />
    <variable cmeta:id="Ca_extrusion_across_the_plasma_membrane.J_extru" name="J_extru" units="nanomolar_per_second" />
    <variable cmeta:id="Ca_extrusion_across_the_plasma_membrane.k_leak_pm" initial_value="0.00000015" name="k_leak_pm" units="per_second" />
    <variable cmeta:id="Ca_extrusion_across_the_plasma_membrane.Vmax_extru" initial_value="25.0" name="Vmax_extru" units="nanomolar_per_second" />
    <variable cmeta:id="Ca_extrusion_across_the_plasma_membrane.EC50_extru" initial_value="386.0" name="EC50_extru" units="nanomolar" />
    <variable cmeta:id="Ca_extrusion_across_the_plasma_membrane.n_extru" initial_value="2.4" name="n_extru" units="dimensionless" />
    <variable cmeta:id="Ca_extrusion_across_the_plasma_membrane.Ca_o" initial_value="2.0" name="Ca_o" units="millimolar" />
    <variable cmeta:id="Ca_extrusion_across_the_plasma_membrane.J_ICa" name="J_ICa" public_interface="in" units="nanomolar_per_second" />
    <variable cmeta:id="Ca_extrusion_across_the_plasma_membrane.k_i" name="k_i" public_interface="in" units="dimensionless" />
    <variable cmeta:id="Ca_extrusion_across_the_plasma_membrane.Ca_i" name="Ca_i" public_interface="in" units="nanomolar" />
    <variable cmeta:id="Ca_extrusion_across_the_plasma_membrane.time" name="time" public_interface="in" units="second" />
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply id="J_pm_calculation">
        <eq />
        <ci>J_pm</ci>
        <apply>
          <plus />
          <ci>J_extru</ci>
          <ci>J_ICa</ci>
        </apply>
      </apply>
      <apply id="J_extru_calculation">
        <eq />
        <ci>J_extru</ci>
        <apply>
          <times />
          <apply>
            <power />
            <ci>k_i</ci>
            <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">-1.0</cn>
          </apply>
          <apply>
            <plus />
            <apply>
              <times />
              <ci>k_leak_pm</ci>
              <apply>
                <minus />
                <ci>Ca_i</ci>
                <ci>Ca_o</ci>
              </apply>
            </apply>
            <apply>
              <divide />
              <ci>Vmax_extru</ci>
              <apply>
                <plus />
                <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1.0</cn>
                <apply>
                  <power />
                  <apply>
                    <divide />
                    <ci>EC50_extru</ci>
                    <ci>Ca_i</ci>
                  </apply>
                  <ci>n_extru</ci>
                </apply>
              </apply>
            </apply>
          </apply>
        </apply>
      </apply>
    </math>
  </component>
  <component name="Ca_uptake_by_SR_Ca_ATPase" cmeta:id="submodel_5">
    <variable cmeta:id="Ca_uptake_by_SR_Ca_ATPase.J_SERCA" name="J_SERCA" public_interface="out" units="nanomolar_per_second" />
    <variable cmeta:id="Ca_uptake_by_SR_Ca_ATPase.Vmax_SERCA" initial_value="2146.0" name="Vmax_SERCA" units="nanomolar_per_second" />
    <variable cmeta:id="Ca_uptake_by_SR_Ca_ATPase.EC50_SERCA" initial_value="30.3" name="EC50_SERCA" units="micromolar" />
    <variable cmeta:id="Ca_uptake_by_SR_Ca_ATPase.n_SERCA" initial_value="2.5" name="n_SERCA" units="dimensionless" />
    <variable cmeta:id="Ca_uptake_by_SR_Ca_ATPase.k_i" name="k_i" public_interface="in" units="dimensionless" />
    <variable cmeta:id="Ca_uptake_by_SR_Ca_ATPase.Ca_i" name="Ca_i" public_interface="in" units="nanomolar" />
    <variable cmeta:id="Ca_uptake_by_SR_Ca_ATPase.time" name="time" public_interface="in" units="second" />
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply id="J_SERCA_calculation">
        <eq />
        <ci>J_SERCA</ci>
        <apply>
          <divide />
          <ci>Vmax_SERCA</ci>
          <apply>
            <times />
            <ci>k_i</ci>
            <apply>
              <plus />
              <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1.0</cn>
              <apply>
                <power />
                <apply>
                  <divide />
                  <ci>EC50_SERCA</ci>
                  <ci>Ca_i</ci>
                </apply>
                <ci>n_SERCA</ci>
              </apply>
            </apply>
          </apply>
        </apply>
      </apply>
    </math>
  </component>
  <component name="ER_Ca_release" cmeta:id="submodel_6">
    <variable cmeta:id="ER_Ca_release.J_ER" name="J_ER" public_interface="out" units="nanomolar_per_second" />
    <variable cmeta:id="ER_Ca_release.P_ER" name="P_ER" public_interface="out" units="per_second" />
    <variable cmeta:id="ER_Ca_release.P_basal" initial_value="0.009" name="P_basal" units="per_second" />
    <variable cmeta:id="ER_Ca_release.Pmax_RyR" initial_value="0.05" name="Pmax_RyR" units="per_second" />
    <variable cmeta:id="ER_Ca_release.EC50_RyR" initial_value="2641.0" name="EC50_RyR" units="nanomolar" />
    <variable cmeta:id="ER_Ca_release.n_RyR" initial_value="0.96" name="n_RyR" units="dimensionless" />
    <variable cmeta:id="ER_Ca_release.J_release" name="J_release" units="nanomolar_per_second" />
    <variable cmeta:id="ER_Ca_release.J_SERCA" name="J_SERCA" public_interface="in" units="nanomolar_per_second" />
    <variable cmeta:id="ER_Ca_release.v_i" name="v_i" public_interface="in" units="micro_litre" />
    <variable cmeta:id="ER_Ca_release.k_i" name="k_i" public_interface="in" units="dimensionless" />
    <variable cmeta:id="ER_Ca_release.Ca_i" name="Ca_i" public_interface="in" units="nanomolar" />
    <variable cmeta:id="ER_Ca_release.Ca_ER" name="Ca_ER" public_interface="in" units="nanomolar" />
    <variable cmeta:id="ER_Ca_release.time" name="time" public_interface="in" units="second" />
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply id="J_release_calculation">
        <eq />
        <ci>J_release</ci>
        <apply>
          <divide />
          <apply>
            <times />
            <ci>P_ER</ci>
            <apply>
              <minus />
              <ci>Ca_i</ci>
              <ci>Ca_ER</ci>
            </apply>
          </apply>
          <apply>
            <times />
            <ci>v_i</ci>
            <ci>k_i</ci>
          </apply>
        </apply>
      </apply>
      <apply id="J_ER_calculation">
        <eq />
        <ci>J_ER</ci>
        <apply>
          <plus />
          <ci>J_SERCA</ci>
          <ci>J_release</ci>
        </apply>
      </apply>
      <apply id="P_ER_v_i_calculation">
        <eq />
        <ci>P_ER</ci>
        <apply>
          <times />
          <ci>v_i</ci>
          <apply>
            <plus />
            <ci>P_basal</ci>
            <apply>
              <divide />
              <ci>Pmax_RyR</ci>
              <apply>
                <plus />
                <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1.0</cn>
                <apply>
                  <power />
                  <apply>
                    <divide />
                    <ci>EC50_RyR</ci>
                    <ci>Ca_i</ci>
                  </apply>
                  <ci>n_RyR</ci>
                </apply>
              </apply>
            </apply>
          </apply>
        </apply>
      </apply>
    </math>
  </component>
  <connection>
    <map_components component_1="cytoplasmic_calcium" component_2="Ca_extrusion_across_the_plasma_membrane" />
    <map_variables variable_1="Ca_i" variable_2="Ca_i" />
  </connection>
  <connection>
    <map_components component_1="Ca_uptake_by_SR_Ca_ATPase" component_2="ER_Ca_release" />
    <map_variables variable_1="J_SERCA" variable_2="J_SERCA" />
  </connection>
  <connection>
    <map_components component_1="Ca_uptake_by_SR_Ca_ATPase" component_2="intraluminal_calcium" />
    <map_variables variable_1="J_SERCA" variable_2="J_SERCA" />
  </connection>
  <connection>
    <map_components component_1="cytoplasmic_calcium" component_2="Ca_uptake_by_SR_Ca_ATPase" />
    <map_variables variable_1="Ca_i" variable_2="Ca_i" />
  </connection>
  <connection>
    <map_components component_1="ER_Ca_release" component_2="intraluminal_calcium" />
    <map_variables variable_1="J_ER" variable_2="J_ER" />
    <map_variables variable_1="P_ER" variable_2="P_ER" />
  </connection>
  <connection>
    <map_components component_1="environment" component_2="Ca_extrusion_across_the_plasma_membrane" />
    <map_variables variable_1="time" variable_2="time" />
  </connection>
  <connection>
    <map_components component_1="environment" component_2="cytoplasmic_calcium" />
    <map_variables variable_1="time" variable_2="time" />
  </connection>
  <connection>
    <map_components component_1="Ca_extrusion_across_the_plasma_membrane" component_2="cytoplasmic_calcium" />
    <map_variables variable_1="J_pm" variable_2="J_pm" />
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