Location: Calcium Dynamics Annotations @ 110f9ba31e34 / colegrove_albrecht_friel_2000 / model / colegrove_albrecht_friel_2000.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/colegrove_albrecht_friel_2000/model/colegrove_albrecht_friel_2000.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="colegrove_albrecht_friel_2000" cmeta:id="colegrove_albrecht_friel_2000_version01">
  <documentation xmlns="http://cellml.org/tmp-documentation">
    <article>
      <articleinfo>
        <title>Quantitative Analysis Of Mitochondrial Ca2+ Uptake And Release Pathways In Sympathetic Neurons</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 can not be solved as it is unsuitably constrained.</para>
        <para>ValidateCellML verifies this model as valid CellML with consistent units.</para>
      </section>
      <sect1 id="sec_structure">
        <title>Model Structure</title>
        <para>
          One of the central goals in the study of calcium signalling is to understand the basis of [Ca
          <superscript>2+</superscript>
          ] dynamics.  This is complicated by the fact that Ca
          <superscript>2+</superscript>
          is present in several membrane-bound intracellular compartments, each of which uses a distinct Ca
          <superscript>2+</superscript>
          transport system and the rate of Ca
          <superscript>2+</superscript>
          transport between these compartments can exhibit a complex non-linear dependence on free [Ca
          <superscript>2+</superscript>
          ].
        </para>
        <para>
          In their 2000 model, Stephen L. Colegrove, Meredith A. Albrecht and David D. Friel have studied how mitochondrial Ca
          <superscript>2+</superscript>
          transport contributes to the redistribution of intracellular Ca
          <superscript>2+</superscript>
          during and after depolarisation-evoked Ca
          <superscript>2+</superscript>
          entry in sympathetic neurons.  The total Ca
          <superscript>2+</superscript>
          flux during the recovery phase following membrane depolarisation was divided into three components (see
          <xref linkend="fig_cell_diagram" />
          below): one representing net Ca
          <superscript>2+</superscript>
          extrusion across the plasma membrane (J
          <subscript>extru</subscript>
          ), one representing mitochondrial Ca
          <superscript>2+</superscript>
          uptake via the uniporter (J
          <subscript>uni</subscript>
          ) and one representing mitochondrial Ca
          <superscript>2+</superscript>
          release via the Na
          <superscript>+</superscript>
          /Ca
          <superscript>2+</superscript>
          exchanger (J
          <subscript>NaCa</subscript>
          ).  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>
          Quantitative Analysis of Mitochondrial Ca
          <superscript>2+</superscript>
          Uptake and Release Pathways in Sympathetic Neurons
          <emphasis>
            Reconstruction of the Recovery after Depolarisation-evoked [Ca
            <superscript>2+</superscript>
            ] Elevations
          </emphasis>
          , Stephen L. Colegrove, Meredith A. Albrecht and David D. Friel, 2000,
          <emphasis>The Journal Of General Physiology</emphasis>
          , 115, 371-388.
          <ulink url="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&amp;db=PubMed&amp;list_uids=10694264&amp;dopt=Abstract">PubMed ID: 10694264</ulink>
        </para>
        <informalfigure float="0" id="fig_cell_diagram">
          <mediaobject>
            <imageobject>
              <objectinfo>
                <title>cell schematic for the model</title>
              </objectinfo>
              <imagedata fileref="colegrove_2000.png" />
            </imageobject>
          </mediaobject>
          <caption>
            Schematic of the model indicating Ca
            <superscript>2+</superscript>
            compartmentalization in the extracellular matrix, cytosol and the mitochondrial matrix and pathways for Ca
            <superscript>2+</superscript>
            ion movement between the compartments.
          </caption>
        </informalfigure>
      </sect1>
    </article>
  </documentation>
  <units name="micro_litre">
    <unit prefix="micro" units="litre" />
  </units>
  <units name="nanomolar">
    <unit exponent="-1.0" units="litre" />
    <unit prefix="nano" units="mole" />
  </units>
  <units name="per_second">
    <unit exponent="-1.0" units="second" />
  </units>
  <units name="nanomolar_per_second">
    <unit exponent="-1.0" units="second" />
    <unit units="nanomolar" />
  </units>
  <units name="millivolt">
    <unit prefix="milli" units="volt" />
  </units>
  <units name="micromolar">
    <unit exponent="-1.0" units="litre" />
    <unit prefix="micro" units="mole" />
  </units>
  <units name="micromolar_per_second">
    <unit exponent="-1.0" units="second" />
    <unit units="micromolar" />
  </units>
  <component name="environment" cmeta:id="submodel_0">
    <variable cmeta:id="environment.time" name="time" public_interface="out" units="second" />
  </component>
  <component name="Ca_extrusion_across_the_plasma_membrane" cmeta:id="submodel_1">
    <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_leak" name="J_leak" 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" initial_value="0.00000037" name="k_leak" units="per_second" />
    <variable cmeta:id="Ca_extrusion_across_the_plasma_membrane.Vmax_extru" initial_value="28.3" name="Vmax_extru" units="nanomolar_per_second" />
    <variable cmeta:id="Ca_extrusion_across_the_plasma_membrane.EC50_extru" initial_value="378.8" name="EC50_extru" units="nanomolar" />
    <variable cmeta:id="Ca_extrusion_across_the_plasma_membrane.n_extru" initial_value="1.8" name="n_extru" units="dimensionless" />
    <variable cmeta:id="Ca_extrusion_across_the_plasma_membrane.Ca_o" initial_value="0.002" name="Ca_o" units="nanomolar" />
    <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_leak</ci>
          <ci>J_extru</ci>
        </apply>
      </apply>
      <apply id="J_leak_calculation">
        <eq />
        <ci>J_leak</ci>
        <apply>
          <times />
          <ci>k_leak</ci>
          <apply>
            <minus />
            <ci>Ca_i</ci>
            <ci>Ca_o</ci>
          </apply>
        </apply>
      </apply>
      <apply id="J_extru_calculation">
        <eq />
        <ci>J_extru</ci>
        <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>
    </math>
  </component>
  <component name="mitochondrial_Ca_uptake" cmeta:id="submodel_2">
    <variable cmeta:id="mitochondrial_Ca_uptake.J_uni" name="J_uni" public_interface="out" units="nanomolar_per_second" />
    <variable cmeta:id="mitochondrial_Ca_uptake.kuni_max" initial_value="75.9" name="kuni_max" units="per_second" />
    <variable cmeta:id="mitochondrial_Ca_uptake.EC50_uni" initial_value="10.0" name="EC50_uni" units="micromolar" />
    <variable cmeta:id="mitochondrial_Ca_uptake.n_uni" initial_value="2.0" name="n_uni" units="dimensionless" />
    <variable cmeta:id="mitochondrial_Ca_uptake.Ca_i" name="Ca_i" public_interface="in" units="nanomolar" />
    <variable cmeta:id="mitochondrial_Ca_uptake.time" name="time" public_interface="in" units="second" />
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply id="J_uni_calculation">
        <eq />
        <ci>J_uni</ci>
        <apply>
          <divide />
          <apply>
            <times />
            <ci>kuni_max</ci>
            <ci>Ca_i</ci>
          </apply>
          <apply>
            <plus />
            <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1.0</cn>
            <apply>
              <power />
              <apply>
                <divide />
                <ci>EC50_uni</ci>
                <ci>Ca_i</ci>
              </apply>
              <ci>n_uni</ci>
            </apply>
          </apply>
        </apply>
      </apply>
    </math>
  </component>
  <component name="mitochondrial_Ca_release" cmeta:id="submodel_3">
    <variable cmeta:id="mitochondrial_Ca_release.J_NaCa" name="J_NaCa" public_interface="out" units="nanomolar_per_second" />
    <variable cmeta:id="mitochondrial_Ca_release.Ca_inhibited_J_NaCa" name="Ca_inhibited_J_NaCa" public_interface="out" units="nanomolar_per_second" />
    <variable cmeta:id="mitochondrial_Ca_release.J_mito" name="J_mito" public_interface="out" units="nanomolar_per_second" />
    <variable cmeta:id="mitochondrial_Ca_release.Vmax_NaCa" initial_value="-35.0" name="Vmax_NaCa" units="nanomolar_per_second" />
    <variable cmeta:id="mitochondrial_Ca_release.EC50_NaCa" initial_value="307.0" name="EC50_NaCa" units="nanomolar" />
    <variable cmeta:id="mitochondrial_Ca_release.n_inhib" initial_value="6.0" name="n_inhib" units="dimensionless" />
    <variable cmeta:id="mitochondrial_Ca_release.k_inhib" initial_value="500.0" name="k_inhib" units="nanomolar" />
    <variable cmeta:id="mitochondrial_Ca_release.delta_Ca_i" name="delta_Ca_i" units="dimensionless" />
    <variable cmeta:id="mitochondrial_Ca_release.J_uni" name="J_uni" public_interface="in" units="nanomolar_per_second" />
    <variable cmeta:id="mitochondrial_Ca_release.Ca_i" name="Ca_i" public_interface="in" units="nanomolar" />
    <variable cmeta:id="mitochondrial_Ca_release.Ca_m" name="Ca_m" public_interface="in" units="nanomolar" />
    <variable cmeta:id="mitochondrial_Ca_release.time" name="time" public_interface="in" units="second" />
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply id="J_NaCa_calculation">
        <eq />
        <ci>J_NaCa</ci>
        <apply>
          <divide />
          <apply>
            <minus />
            <ci>Vmax_NaCa</ci>
          </apply>
          <apply>
            <plus />
            <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1.0</cn>
            <apply>
              <divide />
              <ci>EC50_NaCa</ci>
              <ci>Ca_m</ci>
            </apply>
          </apply>
        </apply>
      </apply>
      <apply id="Ca_inhibited_J_NaCa_calculation">
        <eq />
        <ci>Ca_inhibited_J_NaCa</ci>
        <apply>
          <divide />
          <apply>
            <minus />
            <apply>
              <times />
              <ci>delta_Ca_i</ci>
              <ci>Vmax_NaCa</ci>
            </apply>
          </apply>
          <apply>
            <plus />
            <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1.0</cn>
            <apply>
              <divide />
              <ci>EC50_NaCa</ci>
              <ci>Ca_i</ci>
            </apply>
          </apply>
        </apply>
      </apply>
      <apply id="delta_Ca_i_calculation">
        <eq />
        <ci>delta_Ca_i</ci>
        <apply>
          <minus />
          <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1.0</cn>
          <apply>
            <divide />
            <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1.0</cn>
            <apply>
              <minus />
              <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1.0</cn>
              <apply>
                <power />
                <apply>
                  <divide />
                  <ci>k_inhib</ci>
                  <ci>Ca_i</ci>
                </apply>
                <ci>n_inhib</ci>
              </apply>
            </apply>
          </apply>
        </apply>
      </apply>
      <apply id="J_mito_calculation">
        <eq />
        <ci>J_mito</ci>
        <apply>
          <plus />
          <ci>J_uni</ci>
          <ci>J_NaCa</ci>
        </apply>
      </apply>
    </math>
  </component>
  <component name="intracellular_calcium" cmeta:id="submodel_4">
    <variable cmeta:id="intracellular_calcium.Ca_i" name="Ca_i" public_interface="out" units="nanomolar" />
    <variable cmeta:id="intracellular_calcium.J_pm" name="J_pm" public_interface="in" units="nanomolar_per_second" />
    <variable cmeta:id="intracellular_calcium.J_mito" name="J_mito" public_interface="in" units="nanomolar_per_second" />
    <variable cmeta:id="intracellular_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 />
          <apply>
            <plus />
            <ci>J_pm</ci>
            <ci>J_mito</ci>
          </apply>
        </apply>
      </apply>
    </math>
  </component>
  <component name="mitochondrial_calcium" cmeta:id="submodel_5">
    <variable cmeta:id="mitochondrial_calcium.Ca_m" name="Ca_m" public_interface="out" units="nanomolar" />
    <variable cmeta:id="mitochondrial_calcium.gamma" initial_value="2.0" name="gamma" units="dimensionless" />
    <variable cmeta:id="mitochondrial_calcium.v_m" name="v_m" units="micro_litre" />
    <variable cmeta:id="mitochondrial_calcium.k_m" name="k_m" units="dimensionless" />
    <variable cmeta:id="mitochondrial_calcium.v_i" name="v_i" units="micro_litre" />
    <variable cmeta:id="mitochondrial_calcium.k_i" name="k_i" units="dimensionless" />
    <variable cmeta:id="mitochondrial_calcium.J_mito" name="J_mito" public_interface="in" units="nanomolar_per_second" />
    <variable cmeta:id="mitochondrial_calcium.time" name="time" public_interface="in" units="second" />
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply id="Ca_m_diff_eq">
        <eq />
        <apply>
          <diff />
          <bvar>
            <ci>time</ci>
          </bvar>
          <ci>Ca_m</ci>
        </apply>
        <apply>
          <divide />
          <ci>J_mito</ci>
          <ci>gamma</ci>
        </apply>
      </apply>
      <apply id="gamma_calculation">
        <eq />
        <ci>gamma</ci>
        <apply>
          <divide />
          <apply>
            <times />
            <ci>v_m</ci>
            <ci>k_m</ci>
          </apply>
          <apply>
            <times />
            <ci>v_i</ci>
            <ci>k_i</ci>
          </apply>
        </apply>
      </apply>
    </math>
  </component>
  <connection>
    <map_components component_1="mitochondrial_Ca_release" component_2="intracellular_calcium" />
    <map_variables variable_1="J_mito" variable_2="J_mito" />
  </connection>
  <connection>
    <map_components component_1="environment" component_2="mitochondrial_calcium" />
    <map_variables variable_1="time" variable_2="time" />
  </connection>
  <connection>
    <map_components component_1="mitochondrial_calcium" component_2="mitochondrial_Ca_release" />
    <map_variables variable_1="Ca_m" variable_2="Ca_m" />
  </connection>
  <connection>
    <map_components component_1="intracellular_calcium" component_2="mitochondrial_Ca_release" />
    <map_variables variable_1="Ca_i" variable_2="Ca_i" />
  </connection>
  <connection>
    <map_components component_1="Ca_extrusion_across_the_plasma_membrane" component_2="intracellular_calcium" />
    <map_variables variable_1="J_pm" variable_2="J_pm" />
  </connection>
  <connection>
    <map_components component_1="intracellular_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="environment" component_2="mitochondrial_Ca_release" />
    <map_variables variable_1="time" variable_2="time" />
  </connection>
  <connection>
    <map_components component_1="mitochondrial_Ca_release" component_2="mitochondrial_calcium" />
    <map_variables variable_1="J_mito" variable_2="J_mito" />
  </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="mitochondrial_Ca_uptake" component_2="mitochondrial_Ca_release" />
    <map_variables variable_1="J_uni" variable_2="J_uni" />
  </connection>
  <connection>
    <map_components component_1="environment" component_2="mitochondrial_Ca_uptake" />
    <map_variables variable_1="time" variable_2="time" />
  </connection>
  <connection>
    <map_components component_1="environment" component_2="intracellular_calcium" />
    <map_variables variable_1="time" variable_2="time" />
  </connection>
  <connection>
    <map_components component_1="intracellular_calcium" component_2="mitochondrial_Ca_uptake" />
    <map_variables variable_1="Ca_i" variable_2="Ca_i" />
  </connection>
</model>