- Author:
- Hanne <Hanne@hanne-nielsens-macbook.local>
- Date:
- 2010-06-23 12:28:51+12:00
- Desc:
- added xul, session file will not overwrite with new version?
- Permanent Source URI:
- https://models.physiomeproject.org/workspace/warren_tawhai_crampin_2009/rawfile/b63b518834bb283b01ab18e86fa2f6edd908f935/warren_2009.cellml
<?xml version="1.0" encoding="utf-8"?>
<!--
This CellML file was generated on 10/12/2009 at 11:00:54 at a.m. using:
COR (0.9.31.1351)
Copyright 2002-2009 Dr Alan Garny
http://cor.physiol.ox.ac.uk/ - cor@physiol.ox.ac.uk
CellML 1.0 was used to generate this model
http://www.cellml.org/
-->
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<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
<articleinfo>
<title>Mathematical modelling of calcium wave propagation in airway epithelium: evidence for regenerative ATP release</title>
<author>
<firstname>Catherine</firstname>
<surname>Lloyd</surname>
<affiliation>
<shortaffil>Auckland Bioengineering Institute, University of Auckland</shortaffil>
</affiliation>
</author>
</articleinfo>
<section id="sec_status">
<title>Model Status</title>
<para>
This CellML model runs in both COR and PCEnv 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-triphosphate (IP(3)), and diffusion of paracrine extracellular messengers such as ATP. We have used single cell recordings of airway epithelium to parameterise 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 Ca(2+) wave propagation is achieved as the amount of ATP released from the stimulated cell increases. It is therefore shown that for a Ca(2+) 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 Ca(2+) wave propagation, such as regenerative release of ATP from cells down stream of the stimulated cell.
</para>
<para>
The original paper reference is cited below:
</para>
<para>Mathematical modelling of calcium wave propagation in airway epithelium: evidence for regenerative ATP release, N.J. Warren, M.H. Tawhai and E.J. Crampin, 2009,
<emphasis>Experimental Physiology</emphasis> (Epub ahead of print). <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_2009.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>
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<variable name="volume_i0" units="volume" public_interface="in"/>
<variable name="Jryr" units="microMvolumepersec" public_interface="out"/>
<variable name="Jryr0" units="per_sec" initial_value="0"/>
<variable name="Pryr" units="dimensionless"/>
<variable 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 cellml:units="dimensionless">1</cn>
<apply>
<power/>
<apply>
<divide/>
<ci>Ka</ci>
<ci>Ca_i</ci>
</apply>
<cn cellml:units="dimensionless">4</cn>
</apply>
<apply>
<power/>
<apply>
<divide/>
<ci>Ca_i</ci>
<ci>Kb</ci>
</apply>
<cn cellml:units="dimensionless">3</cn>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<ci>Kc</ci>
</apply>
<apply>
<power/>
<apply>
<divide/>
<ci>Ca_i</ci>
<ci>Kb</ci>
</apply>
<cn cellml:units="dimensionless">3</cn>
</apply>
<apply>
<power/>
<apply>
<divide/>
<ci>Ka</ci>
<ci>Ca_i</ci>
</apply>
<cn 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 cellml:units="dimensionless">1</cn>
<apply>
<power/>
<apply>
<divide/>
<ci>Ka</ci>
<ci>Ca_i</ci>
</apply>
<cn cellml:units="dimensionless">4</cn>
</apply>
<apply>
<power/>
<apply>
<divide/>
<ci>Ca_i</ci>
<ci>Kb</ci>
</apply>
<cn cellml:units="dimensionless">3</cn>
</apply>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<ci>Kc</ci>
</apply>
<apply>
<power/>
<apply>
<divide/>
<ci>Ca_i</ci>
<ci>Kb</ci>
</apply>
<cn cellml:units="dimensionless">3</cn>
</apply>
<apply>
<power/>
<apply>
<divide/>
<ci>Ka</ci>
<ci>Ca_i</ci>
</apply>
<cn 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 xmlns="http://www.cellml.org/cellml/1.0#" name="Jer">
<variable name="Jer" units="microMvolumepersec" public_interface="out"/>
<variable name="Ca_i" units="microM" public_interface="in"/>
<variable name="Ca_er" units="microM" public_interface="in"/>
<variable name="volume_i0" units="volume" public_interface="in"/>
<variable name="Jer0" units="per_sec" initial_value="0.0035"/>
<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 xmlns="http://www.cellml.org/cellml/1.0#" name="Jserca">
<variable name="Jserca" units="microMvolumepersec" public_interface="out"/>
<variable name="Ca_i" units="microM" public_interface="in"/>
<variable name="Ca_er" units="microM" public_interface="in"/>
<variable name="volume_i0" units="volume" public_interface="in"/>
<variable name="Vserca" units="microM2persec" initial_value="0.09"/>
<variable name="Kserca" units="microM" initial_value="0.04"/>
<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 cellml:units="dimensionless">2</cn>
</apply>
</apply>
<apply>
<plus/>
<apply>
<power/>
<ci>Kserca</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<apply>
<power/>
<ci>Ca_i</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
<cn cellml:units="dimensionless">1</cn>
</apply>
<ci>Ca_er</ci>
</apply>
</apply>
</math>
</component>
<component xmlns="http://www.cellml.org/cellml/1.0#" name="Jin">
<variable name="Jin" units="microMvolumepersec" public_interface="out"/>
<variable name="Ca_i" units="microM" public_interface="in"/>
<variable name="Ca_er" units="microM" public_interface="in"/>
<variable name="Vm" units="milliV" initial_value="-39"/>
<variable name="V_Ca" units="milliV"/>
<variable name="R" units="millijoule_per_mole_kelvin" initial_value="8314"/>
<variable name="T" units="kelvin" initial_value="310"/>
<variable name="F" units="coulomb_per_mole" initial_value="96485"/>
<variable name="z_Ca" units="dimensionless" initial_value="2"/>
<variable name="Ca_ext" units="microM" initial_value="1300"/>
<variable name="P_pm_1" units="conductancepervolume" initial_value="0.6"/>
<variable name="P_pm_2" units="conductancepervolume" initial_value="28"/>
<variable name="Iin_1" units="current"/>
<variable name="Iin_2" units="current"/>
<variable name="Jin_1" units="microMvolumepersec"/>
<variable name="Jin_2" units="microMvolumepersec"/>
<variable name="volume_i0" units="volume" public_interface="in"/>
<variable name="V_mech" units="dimensionless" public_interface="in"/>
<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 xmlns="http://www.cellml.org/cellml/1.0#" name="Jpm">
<variable name="Jpm" units="microMvolumepersec" public_interface="out"/>
<variable name="Ca_i" units="microM" public_interface="in"/>
<variable name="Vpm" units="microMpersec" initial_value="0.072"/>
<variable name="Kpm" units="microM" initial_value="0.6"/>
<variable name="volume_i0" units="volume" public_interface="in"/>
<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 cellml:units="dimensionless">2</cn>
</apply>
</apply>
<apply>
<plus/>
<apply>
<power/>
<ci>Kpm</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<apply>
<power/>
<ci>Ca_i</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component xmlns="http://www.cellml.org/cellml/1.0#" name="O">
<variable name="O" units="dimensionless" initial_value="-2.42013500345263e-89" public_interface="out"/>
<variable name="S" units="dimensionless"/>
<variable name="I1" units="dimensionless" public_interface="in"/>
<variable name="I2" units="dimensionless" public_interface="in"/>
<variable name="IP3" units="micromolar" public_interface="in"/>
<variable name="k1" units="per_secmicroM" public_interface="in"/>
<variable name="k1_" units="first_order_rate_constant" public_interface="in"/>
<variable name="k2" units="first_order_rate_constant" public_interface="in"/>
<variable name="time" units="second" public_interface="in"/>
<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 cellml:units="dimensionless">1</cn>
<apply>
<plus/>
<ci>O</ci>
<ci>I1</ci>
<ci>I2</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component xmlns="http://www.cellml.org/cellml/1.0#" name="I1">
<variable name="I1" units="dimensionless" initial_value="2.24343309680416e-81" public_interface="out"/>
<variable name="O" units="dimensionless" public_interface="in"/>
<variable name="k2" units="first_order_rate_constant" public_interface="in"/>
<variable name="k3" units="first_order_rate_constant" public_interface="in"/>
<variable name="k4" units="first_order_rate_constant" public_interface="in"/>
<variable name="time" units="second" public_interface="in"/>
<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 xmlns="http://www.cellml.org/cellml/1.0#" name="I2">
<variable name="I2" units="dimensionless" initial_value="1.01276768045278e-40" public_interface="out"/>
<variable name="I1" units="dimensionless" public_interface="in"/>
<variable name="k4" units="first_order_rate_constant" public_interface="in"/>
<variable name="k5" units="first_order_rate_constant" public_interface="in"/>
<variable name="time" units="second" public_interface="in"/>
<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 xmlns="http://www.cellml.org/cellml/1.0#" name="constants">
<variable name="k1" units="per_secmicroM" public_interface="out"/>
<variable name="k1_" units="first_order_rate_constant" initial_value="0.88" public_interface="out"/>
<variable name="k2" units="first_order_rate_constant" initial_value="0.5" public_interface="out"/>
<variable name="k3" units="first_order_rate_constant" initial_value="0.5" public_interface="out"/>
<variable name="k4" units="first_order_rate_constant" public_interface="out"/>
<variable name="k5" units="first_order_rate_constant" initial_value="0.02" public_interface="out"/>
<variable name="IP3" units="microM" public_interface="in"/>
<variable name="alpha_1" units="per_secmicroM" initial_value="40"/>
<variable name="beta_1" units="microM" initial_value="0.8"/>
<variable name="alpha_4" units="first_order_rate_constant" initial_value="0.06"/>
<variable name="beta_4" units="microM" initial_value="0.01"/>
<variable name="Ca_i" units="microM" public_interface="in"/>
<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 cellml:units="dimensionless">3</cn>
</apply>
</apply>
<apply>
<plus/>
<apply>
<power/>
<ci>beta_1</ci>
<cn cellml:units="dimensionless">3</cn>
</apply>
<apply>
<power/>
<ci>Ca_i</ci>
<cn cellml:units="dimensionless">3</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>k4</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>alpha_4</ci>
<ci>IP3</ci>
</apply>
<apply>
<plus/>
<ci>beta_4</ci>
<ci>IP3</ci>
</apply>
</apply>
</apply>
</math>
</component>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="receptor" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="receptor" component_2="J_ip3P"/>
<map_variables variable_1="V_IP3" variable_2="V_IP3"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="receptor" component_2="Jin"/>
<map_variables variable_1="V_mech" variable_2="V_mech"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="Jer" component_2="volume_i"/>
<map_variables variable_1="volume_i0" variable_2="volume_i0"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="Jserca" component_2="volume_i"/>
<map_variables variable_1="volume_i0" variable_2="volume_i0"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="Jipt" component_2="volume_i"/>
<map_variables variable_1="volume_i0" variable_2="volume_i0"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="Jipt" component_2="O"/>
<map_variables variable_1="O" variable_2="O"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="Jipt" component_2="Ca_i"/>
<map_variables variable_1="Ca_i" variable_2="Ca_i"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="Jipt" component_2="Ca_er"/>
<map_variables variable_1="Ca_er" variable_2="Ca_er"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="Jryr" component_2="volume_i"/>
<map_variables variable_1="volume_i0" variable_2="volume_i0"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="J_ip3D" component_2="volume_i"/>
<map_variables variable_1="volume_i0" variable_2="volume_i0"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="Jin" component_2="volume_i"/>
<map_variables variable_1="volume_i0" variable_2="volume_i0"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="Jpm" component_2="volume_i"/>
<map_variables variable_1="volume_i0" variable_2="volume_i0"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="IP3" component_2="O"/>
<map_variables variable_1="IP3" variable_2="IP3"/>
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<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="volumeCa_i" component_2="Jipt"/>
<map_variables variable_1="Jipt" variable_2="Jipt"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="volumeCa_i" component_2="Jryr"/>
<map_variables variable_1="Jryr" variable_2="Jryr"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="volumeCa_i" component_2="Jer"/>
<map_variables variable_1="Jer" variable_2="Jer"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="volumeCa_i" component_2="Jserca"/>
<map_variables variable_1="Jserca" variable_2="Jserca"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="volumeCa_i" component_2="Jpm"/>
<map_variables variable_1="Jpm" variable_2="Jpm"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="volumeCa_i" component_2="Jin"/>
<map_variables variable_1="Jin" variable_2="Jin"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="volumeCa_er" component_2="Jipt"/>
<map_variables variable_1="Jipt" variable_2="Jipt"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="volumeCa_er" component_2="Jryr"/>
<map_variables variable_1="Jryr" variable_2="Jryr"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="volumeCa_er" component_2="Jer"/>
<map_variables variable_1="Jer" variable_2="Jer"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="volumeCa_er" component_2="Jserca"/>
<map_variables variable_1="Jserca" variable_2="Jserca"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="volumeCa_i" component_2="volume_i"/>
<map_variables variable_1="volume_i" variable_2="volume_i"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="volumeCa_i" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="volumeCa_i" component_2="Ca_i"/>
<map_variables variable_1="volumeCa_i" variable_2="volumeCa_i"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="volume_i" component_2="Ca_i"/>
<map_variables variable_1="volume_i" variable_2="volume_i"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="volumeCa_er" component_2="volume_er"/>
<map_variables variable_1="volume_er" variable_2="volume_er"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="volumeCa_er" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="O" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="volumeCa_er" component_2="Ca_er"/>
<map_variables variable_1="volumeCa_er" variable_2="volumeCa_er"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="volume_er" component_2="Ca_er"/>
<map_variables variable_1="volume_er" variable_2="volume_er"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="volume_er" component_2="volume_i"/>
<map_variables variable_1="volume_i" variable_2="volume_i"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="volume_iIP3" component_2="J_ip3P"/>
<map_variables variable_1="J_ip3P" variable_2="J_ip3P"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="volume_iIP3" component_2="J_ip3D"/>
<map_variables variable_1="J_ip3D" variable_2="J_ip3D"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="volume_iIP3" component_2="IP3"/>
<map_variables variable_1="volume_iIP3" variable_2="volume_iIP3"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="volume_i" component_2="IP3"/>
<map_variables variable_1="volume_i" variable_2="volume_i"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="volume_iIP3" component_2="volume_i"/>
<map_variables variable_1="volume_i" variable_2="volume_i"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="volume_iIP3" component_2="environment"/>
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Mathematical modelling of calcium wave propagation in airway epithelium: evidence for regenerative ATP release
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