- Author:
- pmr2.import <nobody@models.cellml.org>
- Date:
- 2006-07-09 07:43:08+12:00
- Desc:
- committing version01 of wilkins_sneyd_1998
- Permanent Source URI:
- http://models.cellml.org/workspace/wilkins_sneyd_1998/rawfile/5387045d0b9ecba598c9463c94c9545dc7dc3ea9/wilkins_sneyd_1998.cellml
<?xml version='1.0' encoding='utf-8'?>
<!-- FILE : wilkins_model_1998.xml
CREATED : 27th March 2004
LAST MODIFIED : 27th March 2004
AUTHOR : Catherine Lloyd
Bioengineering Instute
The University of Auckland
MODEL STATUS : This model conforms to the CellML 1.0 Specification released on
10th August 2001, and the 16/01/2002 CellML Metadata 1.0 Specification.
DESCRIPTION : This file contains a CellML description of Wilkins and Sneyd's 1998 mathematical model of intercellular spiral waves of calcium.
CHANGES:
--><model xmlns="http://www.cellml.org/cellml/1.0#" xmlns:cmeta="http://www.cellml.org/metadata/1.0#" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:bqs="http://www.cellml.org/bqs/1.0#" xmlns:cellml="http://www.cellml.org/cellml/1.0#" xmlns:dcterms="http://purl.org/dc/terms/" xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" cmeta:id="wilkins_sneyd_1998_version01" name="wilkins_sneyd_1998_version01">
<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
<articleinfo>
<title>Modelling Intercellular Spiral Waves of Calcium</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 is the original unchecked version of the model imported from the previous
CellML model repository, 24-Jan-2006.
</para>
</section>
<sect1 id="sec_structure">
<title>Model Structure</title>
<para>
Intercellular calcium waves have been seen to occur in several types of cells, including ciliated tracheal epithelial cells, rat brain glial cells, in liver tissue and also in the hippocampus. These calcium waves are triggered by a range of different stimuli, including mechanical or hormonal stimulation, and they are thought to play an important role in intercellular communication, helping to coordinate multicellular responses to certain stimuli. Understanding the molecular mechanism which underlie intercellular calcium waves is important for the understanding of processes such as wound healing, mechanical transduction, cell growth and information processing.
</para>
<para>
In the Wikins and Sneyd 1998 publication described here, the authors use an existing mathematical model to study the properties of intercellular calcium waves in the context of a general framework (see the figure below). This makes the model applicable to any system in which intercellular waves are propagated by coupled excitable systems. Similar systems have been studied in the context of cardiac electrophysiology, but because the calcium diffusion coefficient is so small, intercellular calcium waves have some unique properties.
</para>
<para>
The complete original paper reference is cited below:
</para>
<para>
<ulink url="http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6WMD-45J5B8H-5R&_coverDate=04%2F07%2F1998&_alid=159201875&_rdoc=1&_fmt=&_orig=search&_qd=1&_;cdi=6932&_sort=d&view=c&_acct=C000011498&_version=1&_urlVersion=0&_userid=140507&md5=1ab7a7f87f49c1687a5cefa5ca6098cb">Intercellular Spiral Waves of Calcium</ulink>, Matthew Wilkins and James Sneyd, 1998, <ulink url="http://www.sciencedirect.com/science?_ob=JournalURL&_cdi=6932&_auth=y&_acct=C000011498&_version=1&_urlVersion=0&_userid=140507&md5=c8e64d20ff203cda2255f4b6b7affe4f">
<emphasis>Journal of Theoretical Biology</emphasis>
</ulink>, 191, 299-308. (A PDF version of the article is available to subscribers on the <emphasis>Journal of Theoretical Biology</emphasis> website.) <ulink url="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&list_uids=9631570&dopt=Abstract">PubMed ID: 9631570</ulink>
</para>
<informalfigure float="0" id="fig_cell_diagram">
<mediaobject>
<imageobject>
<objectinfo>
<title>reaction diagram</title>
</objectinfo>
<imagedata fileref="wilkins_1998.png"/>
</imageobject>
<caption>
Schematic diagram showing the transmembrane calcium fluxes which are described by the mathematical model.
</caption>
</mediaobject>
</informalfigure>
</sect1>
</article>
</documentation>
<units name="micromolar">
<unit units="mole" prefix="micro"/>
<unit units="litre" exponent="-1"/>
</units>
<units name="flux">
<unit units="micromolar"/>
<unit units="second" exponent="-1"/>
</units>
<units name="micromolar_micrometre2_per_second">
<unit units="metre" prefix="micro" exponent="2"/>
<unit units="second" exponent="-1"/>
</units>
<component name="environment">
<variable units="second" public_interface="out" name="time"/>
</component>
<component name="calcium_concentration">
<variable units="micromolar" public_interface="out" name="c"/>
<variable units="micromolar_micrometre2_per_second" name="Dc" initial_value="20.0"/>
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<component name="calcium_pump">
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<variable units="flux" name="gamma" initial_value="2.0"/>
<variable units="micromolar" name="k_gamma" initial_value="0.1"/>
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<component name="calcium_flux">
<variable units="flux" public_interface="out" name="j_flux"/>
<variable units="dimensionless" name="h"/>
<variable units="dimensionless" name="b" initial_value="0.111"/>
<variable units="micromolar" name="k1" initial_value="0.7"/>
<variable units="micromolar" name="k2" initial_value="0.7"/>
<variable units="micromolar" name="k_mu" initial_value="0.7"/>
<variable units="second" name="tau_h" initial_value="2.0"/>
<variable units="flux" name="kf" initial_value="16.2"/>
<variable units="dimensionless" name="mu_p"/>
<variable units="micromolar" name="p"/>
<variable units="micromolar" public_interface="in" name="c"/>
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<math xmlns="http://www.w3.org/1998/Math/MathML">
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<ci> mu_p </ci>
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<ci> p </ci>
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</math>
</component>
<connection>
<map_components component_2="environment" component_1="calcium_concentration"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="calcium_flux"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="calcium_pump" component_1="calcium_concentration"/>
<map_variables variable_2="c" variable_1="c"/>
<map_variables variable_2="j_pump" variable_1="j_pump"/>
</connection>
<connection>
<map_components component_2="calcium_flux" component_1="calcium_concentration"/>
<map_variables variable_2="c" variable_1="c"/>
<map_variables variable_2="j_flux" variable_1="j_flux"/>
</connection>
<rdf:RDF>
<rdf:Bag rdf:about="rdf:#e42c15b0-da35-4e4a-960f-a7a38b2902a2">
<rdf:li>calcium dynamics</rdf:li>
<rdf:li>calcium waves</rdf:li>
</rdf:Bag>
<rdf:Seq rdf:about="rdf:#2eb9e3ec-d8d8-4822-9e1d-bc7bde5aaadd">
<rdf:li rdf:resource="rdf:#dd250382-cffd-4fcb-be14-4d5f0d94605a"/>
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<rdf:Description rdf:about="rdf:#5e5f0245-24ec-4c05-baa1-281ea8d21568">
<vCard:FN>Catherine Lloyd</vCard:FN>
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Wilkins and Sneyd's 1998 mathematical model of intercellular spiral waves of calcium.
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Intercellular Spiral Waves of Calcium
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<bqs:volume>191</bqs:volume>
<bqs:first_page>299</bqs:first_page>
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<dcterms:W3CDTF>1998-04-07</dcterms:W3CDTF>
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<dcterms:W3CDTF>2004-03-20</dcterms:W3CDTF>
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This is the CellML description of Wilkins and Sneyd's 1998 mathematical model of intercellular spiral waves of calcium.
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The University of Auckland, Bioengineering Institute
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