Location: Intercellular calcium waves mediated by diffusion of inositol trisphosphate: a two-dimensional model. J. Sneyd, B.T. Wetton, A.C. Charles and M.J. Sanderson, 1995 @ 87c187f85354 / sneyd_1995.cellml

Author:
AnandR <a.rampadarath@auckland.ac.nz>
Date:
2019-09-16 15:53:16+12:00
Desc:
added omex file
Permanent Source URI:
https://models.physiomeproject.org/workspace/5b5/rawfile/87c187f853545b3cf5cea480c7e36916329eab7a/sneyd_1995.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="sneyd_1995" cmeta:id="sneyd_1995">
  <documentation xmlns="http://cellml.org/tmp-documentation">
    <article>
      <section id="sec_status">
        <title>Model Status</title>
        <para>This CellML model runs in both OpenCell and COR to reproduce the published results. The units have been checked and they are consistent.</para>
      </section>
      <sect1 id="sec_structure">
        <title>Model Structure</title>
        <para>ABSTRACT:  In response to mechanical stimulation of a single cell, airway epithelial cells in culture exhibit a wave of increased intracellular free Ca2+ concentration that spreads from cell to cell over a limited distance through the culture. We present a detailed analysis of the intercellular wave in a two-dimensional sheet of cells. The model is based on the hypothesis that the wave is the result of diffusion of inositol trisphosphate (IP3) from the stimulated cell. The two-dimensional model agrees well with experimental data and makes the following quantitative predictions: as the distance from the stimulated cells increases, 1) the intercellular delay increases exponentially, 2) the intracellular wave speed decreases exponentially, and 3) the arrival time increases exponentially. Furthermore, 4) a proportion of the cells at the periphery of the response will exhibit waves of decreased amplitude, 5) the intercellular membrane permeability to IP3 must be approximately 2 microns/s or greater, and 6) the ratio of the maximum concentration of IP3 in the stimulated cell to the Km of the IP3 receptor (with respect to IP3) must be approximately 300 or greater. These predictions constitute a rigorous test of the hypothesis that the intercellular Ca2+ waves are mediated by IP3 diffusion.</para>
        <para>The original paper is cited below:</para>
        <para>
          Intercellular calcium waves mediated by diffusion of inositol trisphosphate: a two-dimensional model. J. Sneyd, B.T. Wetton, A.C. Charles and M.J. Sanderson, 1995, American Journal of Physiology, 268, C1537-C1545.
          <ulink url="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=pubmed&amp;cmd=Retrieve&amp;dopt=AbstractPlus&amp;list_uids=7611375&amp;query_hl=1&amp;itool=pubmed_docsum">PubMed ID: 7611375</ulink>
        </para>
        <informalfigure float="0" id="fig_reaction_diagram">
          <mediaobject>
            <imageobject>
              <objectinfo>
                <title>Diagram of model</title>
              </objectinfo>
              <imagedata fileref="sneyd_1995.png" />
            </imageobject>
          </mediaobject>
          <caption>A schematic diagram of the pathway described by the mathematical model.</caption>
        </informalfigure>
      </sect1>
    </article>
  </documentation>
  <units name="flux">
    <unit units="micromolar" />
    <unit exponent="-1.0" units="second" />
  </units>
  <units name="micromolar">
    <unit exponent="-1.0" units="litre" />
    <unit prefix="micro" units="mole" />
  </units>
  <units name="per_second">
    <unit exponent="-1.0" units="second" />
  </units>
  <units name="per_sec_square">
    <unit exponent="-2.0" units="second" />
  </units>
  <units name="micromolar_per_second">
    <unit units="per_second" />
    <unit units="micromolar" />
  </units>
  <units name="micromolar_square_per_second">
    <unit units="per_second" />
    <unit exponent="2.0" units="micromolar" />
  </units>
  <component name="enviroment">
    <variable cmeta:id="enviroment_time" name="time" public_interface="out" units="second" />
  </component>
  <component name="P">
    <variable cmeta:id="P_P" initial_value="0" name="P" public_interface="out" units="micromolar" />
    <variable cmeta:id="P.V_p" initial_value="0.08" name="V_p" units="per_second" />
    <variable cmeta:id="P.k_p" initial_value="1" name="k_p" units="micromolar" />
    <variable cmeta:id="P.IPR_3_flux" initial_value="0.72" name="IPR_3_flux" units="flux" />
    <variable cmeta:id="P.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>P</ci>
        </apply>
        <piecewise>
          <piece>
            <apply>
              <minus />
              <ci>IPR_3_flux</ci>
              <apply>
                <divide />
                <apply>
                  <times />
                  <ci>V_p</ci>
                  <ci>P</ci>
                  <ci>k_p</ci>
                </apply>
                <apply>
                  <plus />
                  <ci>k_p</ci>
                  <ci>P</ci>
                </apply>
              </apply>
            </apply>
            <apply>
              <leq />
              <ci>time</ci>
              <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="second">15</cn>
            </apply>
          </piece>
          <otherwise>
            <apply>
              <divide />
              <apply>
                <times />
                <apply>
                  <minus />
                  <ci>V_p</ci>
                </apply>
                <ci>P</ci>
                <ci>k_p</ci>
              </apply>
              <apply>
                <plus />
                <ci>k_p</ci>
                <ci>P</ci>
              </apply>
            </apply>
          </otherwise>
        </piecewise>
      </apply>
    </math>
  </component>
  <component name="c">
    <variable cmeta:id="c_c" initial_value="0.3" name="c" public_interface="out" units="micromolar" />
    <variable cmeta:id="c.J_flux" name="J_flux" public_interface="in" units="flux" />
    <variable cmeta:id="c.J_pump" name="J_pump" public_interface="in" units="flux" />
    <variable cmeta:id="c.J_leak" name="J_leak" public_interface="in" units="flux" />
    <variable cmeta:id="c.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>c</ci>
        </apply>
        <apply>
          <plus />
          <apply>
            <minus />
            <ci>J_flux</ci>
            <ci>J_pump</ci>
          </apply>
          <ci>J_leak</ci>
        </apply>
      </apply>
    </math>
  </component>
  <component name="J_flux">
    <variable cmeta:id="J_flux_J_flux" name="J_flux" public_interface="out" units="flux" />
    <variable cmeta:id="J_flux.k_flux" initial_value="3" name="k_flux" units="micromolar_per_second" />
    <variable cmeta:id="J_flux.mu" name="mu" public_interface="in" units="dimensionless" />
    <variable cmeta:id="J_flux.h" name="h" public_interface="in" units="dimensionless" />
    <variable cmeta:id="J_flux.b" initial_value="0.11" name="b" units="dimensionless" />
    <variable cmeta:id="J_flux.c" name="c" public_interface="in" units="micromolar" />
    <variable cmeta:id="J_flux.k_1" initial_value="0.7" name="k_1" units="micromolar" />
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply>
        <eq />
        <ci>J_flux</ci>
        <apply>
          <times />
          <ci>k_flux</ci>
          <ci>mu</ci>
          <ci>h</ci>
          <apply>
            <plus />
            <ci>b</ci>
            <apply>
              <divide />
              <apply>
                <times />
                <apply>
                  <minus />
                  <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
                  <ci>b</ci>
                </apply>
                <ci>c</ci>
              </apply>
              <apply>
                <plus />
                <ci>k_1</ci>
                <ci>c</ci>
              </apply>
            </apply>
          </apply>
        </apply>
      </apply>
    </math>
  </component>
  <component name="J_pump">
    <variable cmeta:id="J_pump_J_pump" name="J_pump" public_interface="out" units="flux" />
    <variable cmeta:id="J_pump.c" name="c" public_interface="in" units="micromolar" />
    <variable cmeta:id="J_pump.gamma" initial_value="1" name="gamma" units="micromolar_per_second" />
    <variable cmeta:id="J_pump.k_gamma" initial_value="0.27" name="k_gamma" units="micromolar" />
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply>
        <eq />
        <ci>J_pump</ci>
        <apply>
          <divide />
          <apply>
            <times />
            <ci>gamma</ci>
            <apply>
              <power />
              <ci>c</ci>
              <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
            </apply>
          </apply>
          <apply>
            <plus />
            <apply>
              <power />
              <ci>k_gamma</ci>
              <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
            </apply>
            <apply>
              <power />
              <ci>c</ci>
              <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
            </apply>
          </apply>
        </apply>
      </apply>
    </math>
  </component>
  <component name="J_leak">
    <variable cmeta:id="J_leak_J_leak" name="J_leak" public_interface="out" units="flux" />
    <variable cmeta:id="J_leak.beta" initial_value="0.15" name="beta" units="flux" />
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply>
        <eq />
        <ci>J_leak</ci>
        <ci>beta</ci>
      </apply>
    </math>
  </component>
  <component name="mu">
    <variable cmeta:id="mu.mu" name="mu" public_interface="out" units="dimensionless" />
    <variable cmeta:id="mu.P" name="P" public_interface="in" units="micromolar" />
    <variable cmeta:id="mu.k_mu" initial_value="0.01" name="k_mu" units="micromolar" />
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply>
        <eq />
        <ci>mu</ci>
        <apply>
          <divide />
          <apply>
            <power />
            <ci>P</ci>
            <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">3</cn>
          </apply>
          <apply>
            <plus />
            <apply>
              <power />
              <ci>k_mu</ci>
              <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">3</cn>
            </apply>
            <apply>
              <power />
              <ci>P</ci>
              <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">3</cn>
            </apply>
          </apply>
        </apply>
      </apply>
    </math>
  </component>
  <component name="h">
    <variable cmeta:id="h.h" initial_value="1" name="h" public_interface="out" units="dimensionless" />
    <variable cmeta:id="h.c" name="c" public_interface="in" units="micromolar" />
    <variable cmeta:id="h.k_2" initial_value="0.7" name="k_2" units="micromolar" />
    <variable cmeta:id="h.tau_h" initial_value="0.2" name="tau_h" units="second" />
    <variable cmeta:id="h.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>h</ci>
        </apply>
        <apply>
          <divide />
          <apply>
            <minus />
            <apply>
              <divide />
              <apply>
                <power />
                <ci>k_2</ci>
                <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
              </apply>
              <apply>
                <plus />
                <apply>
                  <power />
                  <ci>k_2</ci>
                  <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
                </apply>
                <apply>
                  <power />
                  <ci>c</ci>
                  <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
                </apply>
              </apply>
            </apply>
            <ci>h</ci>
          </apply>
          <ci>tau_h</ci>
        </apply>
      </apply>
    </math>
  </component>
  <connection>
    <map_components component_1="c" component_2="J_pump" />
    <map_variables variable_1="c" variable_2="c" />
  </connection>
  <connection>
    <map_components component_1="c" component_2="J_flux" />
    <map_variables variable_1="c" variable_2="c" />
  </connection>
  <connection>
    <map_components component_1="c" component_2="h" />
    <map_variables variable_1="c" variable_2="c" />
  </connection>
  <connection>
    <map_components component_1="J_pump" component_2="c" />
    <map_variables variable_1="J_pump" variable_2="J_pump" />
  </connection>
  <connection>
    <map_components component_1="J_leak" component_2="c" />
    <map_variables variable_1="J_leak" variable_2="J_leak" />
  </connection>
  <connection>
    <map_components component_1="J_flux" component_2="c" />
    <map_variables variable_1="J_flux" variable_2="J_flux" />
  </connection>
  <connection>
    <map_components component_1="enviroment" component_2="c" />
    <map_variables variable_1="time" variable_2="time" />
  </connection>
  <connection>
    <map_components component_1="enviroment" component_2="h" />
    <map_variables variable_1="time" variable_2="time" />
  </connection>
  <connection>
    <map_components component_1="P" component_2="mu" />
    <map_variables variable_1="P" variable_2="P" />
  </connection>
  <connection>
    <map_components component_1="mu" component_2="J_flux" />
    <map_variables variable_1="mu" variable_2="mu" />
  </connection>
  <connection>
    <map_components component_1="h" component_2="J_flux" />
    <map_variables variable_1="h" variable_2="h" />
  </connection>
  <connection>
    <map_components component_1="enviroment" component_2="P" />
    <map_variables variable_1="time" variable_2="time" />
  </connection>
</model>