- Author:
- pmr2.import <nobody@models.cellml.org>
- Date:
- 2007-12-18 02:53:27+13:00
- Desc:
- committing version01 of karagiannis_popel_2004
- Permanent Source URI:
- https://staging.physiomeproject.org/workspace/karagiannis_popel_2004/rawfile/82d906804275016e41f4cec619355ecc06e47c60/karagiannis_popel_2004.cellml
<?xml version='1.0' encoding='utf-8'?>
<!-- FILE : karagiannis_model_2004.xml
CREATED : 10th December 2007
LAST MODIFIED : 10th December 2007
AUTHOR : Catherine Lloyd
Bioengineering Institute
The University of Auckland
MODEL STATUS : This model conforms to the CellML 1.1 Specification.
DESCRIPTION : This file contains a CellML description of Karagiannis and Popel's 2004 mathematical model of collagen type I proteolysis by matrix metalloproteinase (MMP) 2 and membrane type I MMP during the migration of a tip endothelial cell.
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="karagiannis_model_2004" name="karagiannis_model_2004">
<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
<articleinfo>
<title>A theoretical model of type I collagen proteolysis by matrix metalloproteinase (MMP) 2 and membrane type 1 MMP in the presence of tissue inhibitor of metalloproteinase 2</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 version of the model has been checked in COR and PCEnv and it runs - possibly replicating the published results. The units have been checked and they are consistent.
</para>
</section>
<sect1 id="sec_structure">
<title>Model Structure</title>
<para>
The formation of new biological vessels requires the coordinated assembly of a proliferating syncytium of endothelial cells (EC) at different developmental stages. Angiogenesis may also be an essential mechanism of blood vessel remodelling which occurs during a diverse range of physiological processes; including tissue regeneration following injury and new vessel formation during muscle exercise. It can also occur under pathological conditions such as atherosclerosis and the vascularisation of cancerous tumours.
</para>
<para>
Matrix metalloproteinases (MMPs) are a family of enzymes responsible for the proteolytic processing of extracellular matrix (ECM) structural proteins. During angiogenesis MMPs are expressed by a single endothelial cell at the tip of the new vessel. These enzymes manifest a proteolytic activity that allows the cells of the new vessle to penetrate the ECM. In the mathematical model presented here, Karagiannis and Popel investigate the proteolytic potential of such a tip endothelial cell. The model authors suggest this model provides a foundation for future quantitative studies of angiogenesis in ECMs of different compositions. The model is described in more detail in the figure below:
</para>
<para>
The complete original paper reference is cited below:
</para>
<para>
<ulink url="http://www.jbc.org/cgi/content/abstract/279/37/39105">A theoretical model of type I collagen proteolysis by matrix metalloproteinase (MMP) 2 and membrane type 1 MMP in the presence of tissue inhibitor of metalloproteinase 2</ulink>, Emmanouil D. Karagiannis and Aleksander S. Popel, 2004, <ulink url="http://www.jbc.org/">
<emphasis>The Journal of Biological Chemistry</emphasis>
</ulink>, 279, 39105-39114. (<ulink url="http://www.jbc.org/cgi/content/full/279/37/39105">Full text</ulink> and <ulink url="http://www.jbc.org/cgi/reprint/279/37/39105">PDF</ulink> versions of the article are available to subscribers on The Journal of Biological Chemistry website.) <ulink url="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&list_uids=15252025&dopt=Abstract">PubMed ID: 15252025</ulink>
</para>
<informalfigure float="0" id="fig_pathway_diagram">
<mediaobject>
<imageobject>
<objectinfo>
<title>model diagram</title>
</objectinfo>
<imagedata fileref="karagiannis_2006.png"/>
</imageobject>
</mediaobject>
<caption>A schematic diagram of the signalling pathway.</caption>
</informalfigure>
</sect1>
</article>
</documentation>
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<!--
The following RDF block contains metadata that applies to this document
as a whole, as indicated by the empty about attribute on the
<rdf:Description> element.
-->
<rdf:Description rdf:about="">
<!--
The Model Builder Metadata. The Dublin Core "creator" element is used
to indicate the person who translated the model into CellML.
-->
<dc:creator rdf:parseType="Resource">
<vCard:N rdf:parseType="Resource">
<vCard:Family>Lloyd</vCard:Family>
<vCard:Given>Catherine</vCard:Given>
<vCard:Other>May</vCard:Other>
</vCard:N>
<vCard:EMAIL rdf:parseType="Resource">
<rdf:value>c.lloyd@auckland.ac.nz</rdf:value>
<rdf:type rdf:resource="http://imc.org/vCard/3.0#internet"/>
</vCard:EMAIL>
<vCard:ORG rdf:parseType="Resource">
<vCard:Orgname>The University of Auckland</vCard:Orgname>
<vCard:Orgunit>The Bioengineering Institute</vCard:Orgunit>
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</dc:creator>
<!--
The Creation Date metadata. This is the date on which the model
was translated into CellML.
-->
<dcterms:created rdf:parseType="Resource">
<dcterms:W3CDTF>2007-12-11</dcterms:W3CDTF>
</dcterms:created>
<!--
The Modification History metadata. This lists the changes that have been
made to the document, who made the changes, and when they were made.
-->
<!-- The Publisher metadata. -->
<dc:publisher>
The University of Auckland, Bioengineering Institute
</dc:publisher>
</rdf:Description>
<!--
The following metadata refers to the model itself, as indicated by the
reference to the ID "karagiannis_model_2004", which is declared
on the <model> element.
-->
<rdf:Description rdf:about="#karagiannis_model_2004">
<!-- A human readable name for the model. -->
<dc:title>
Karagiannis and Popel's 2004 mathematical model of collagen type I proteolysis by matrix metalloproteinase (MMP) 2 and membrane type I MMP during the migration of a tip endothelial cell.
</dc:title>
<!-- A comment regarding the model. -->
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
This is a CellML description of Karagiannis and Popel's 2004 mathematical model of collagen type I proteolysis by matrix metalloproteinase (MMP) 2 and membrane type I MMP during the migration of a tip endothelial cell.
</rdf:value>
<!-- The creator of the comment. -->
<dc:creator rdf:parseType="Resource">
<vCard:FN>Catherine Lloyd</vCard:FN>
</dc:creator>
</cmeta:comment>
<!-- Keyword(s) -->
<bqs:reference rdf:parseType="Resource">
<dc:subject rdf:parseType="Resource">
<bqs:subject_type>keyword</bqs:subject_type>
<rdf:value>
<rdf:Bag>
<rdf:li>collagen</rdf:li>
<rdf:li>matrix metalloproteinase</rdf:li>
<rdf:li>signal transduction</rdf:li>
<rdf:li>cerebral aneurysm</rdf:li>
</rdf:Bag>
</rdf:value>
</dc:subject>
</bqs:reference>
<!--
The CellML Metadata Specification recommends that bibliographic metadata
is used to provide information about the original model reference. The
"identifier" attribute on the "BibliographicReference" class provides an
elegant way to identify a cited reference using a database identifier
such as Pubmed. All associated data such as author, journal title,
date, etc can be looked up on the database.
-->
<bqs:reference rdf:parseType="Resource">
<bqs:Pubmed_id>15252025</bqs:Pubmed_id>
<bqs:JournalArticle rdf:parseType="Resource">
<dc:creator>
<rdf:Seq>
<rdf:li rdf:parseType="Resource">
<bqs:Person rdf:parseType="Resource">
<vCard:N rdf:parseType="Resource">
<vCard:Family>Karagiannis</vCard:Family>
<vCard:Given>Emmanouil</vCard:Given>
<vCard:Other>D</vCard:Other>
</vCard:N>
</bqs:Person>
</rdf:li>
<rdf:li rdf:parseType="Resource">
<bqs:Person rdf:parseType="Resource">
<vCard:N rdf:parseType="Resource">
<vCard:Family>Popel</vCard:Family>
<vCard:Given>Aleksander</vCard:Given>
<vCard:Other>S</vCard:Other>
</vCard:N>
</bqs:Person>
</rdf:li>
</rdf:Seq>
</dc:creator>
<dc:title>
A theoretical model of type I collagen proteolysis by matrix metalloproteinase (MMP) 2 and membrane type 1 MMP in the presence of tissue inhibitor of metalloproteinase 2
</dc:title>
<dcterms:issued rdf:parseType="Resource">
<dcterms:W3CDTF>2004-09-10</dcterms:W3CDTF>
</dcterms:issued>
<bqs:Journal rdf:parseType="Resource">
<dc:title>
Journal of Biological Chemistry
</dc:title>
</bqs:Journal>
<bqs:volume>279</bqs:volume>
<bqs:first_page>39105</bqs:first_page>
<bqs:last_page>39114</bqs:last_page>
</bqs:JournalArticle>
</bqs:reference>
</rdf:Description>
</rdf:RDF>
<units name="molar">
<unit units="mole"/>
<unit units="litre" exponent="-1"/>
</units>
<units name="flux">
<unit units="molar"/>
<unit units="second" exponent="-1"/>
</units>
<units name="first_order_rate_constant">
<unit units="second" exponent="-1"/>
</units>
<units name="second_order_rate_constant">
<unit units="second" exponent="-1"/>
<unit units="molar" exponent="-1"/>
</units>
<component name="environment">
<variable name="time" public_interface="out" units="second"/>
</component>
<!-- Reactions -->
<!--
<component name="v1">
<variable name="v1" public_interface="out" units="flux" />
<variable name="MT1" public_interface="in" units="molar" />
<variable name="MT1_MT1" public_interface="in" units="molar" />
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<math xmlns="http://www.w3.org/1998/Math/MathML" id="1" >
<apply><eq />
<ci> v1 </ci>
<apply><minus />
<apply><times />
<ci> kon_MT1MT1 </ci>
<ci> MT1 </ci>
<ci> MT1 </ci>
</apply>
<apply><times />
<ci> koff_MT1MT1 </ci>
<ci> MT1_MT1 </ci>
</apply>
</apply>
</apply>
</math>
</component>
-->
<component name="v2">
<variable name="v2" public_interface="out" units="flux"/>
<variable name="MT1" public_interface="in" units="molar"/>
<variable name="kshed_MT1" public_interface="in" units="second_order_rate_constant"/>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="2">
<apply><eq/>
<ci> v2 </ci>
<apply><minus/>
<apply><times/>
<ci> kshed_MT1 </ci>
<ci> MT1 </ci>
<ci> MT1 </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="v3">
<variable name="v3" public_interface="out" units="flux"/>
<variable name="MT1" public_interface="in" units="molar"/>
<variable name="T2" public_interface="in" units="molar"/>
<variable name="MT1_T2" public_interface="in" units="molar"/>
<variable name="kon_MT1T2" public_interface="in" units="second_order_rate_constant"/>
<variable name="koff_MT1T2" public_interface="in" units="first_order_rate_constant"/>
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<apply><eq/>
<ci> v3 </ci>
<apply><minus/>
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<ci> MT1 </ci>
<ci> T2 </ci>
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<apply><times/>
<ci> koff_MT1T2 </ci>
<ci> MT1_T2 </ci>
</apply>
</apply>
</apply>
</math>
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<component name="v4">
<variable name="v4" public_interface="out" units="flux"/>
<variable name="M2p" public_interface="in" units="molar"/>
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<variable name="MT1_T2_M2p" public_interface="in" units="molar"/>
<variable name="kon_MT1T2M2p" public_interface="in" units="second_order_rate_constant"/>
<variable name="koff_MT1T2M2p" public_interface="in" units="first_order_rate_constant"/>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="4">
<apply><eq/>
<ci> v4 </ci>
<apply><minus/>
<apply><times/>
<ci> kon_MT1T2M2p </ci>
<ci> M2p </ci>
<ci> MT1_T2 </ci>
</apply>
<apply><times/>
<ci> koff_MT1T2M2p </ci>
<ci> MT1_T2_M2p </ci>
</apply>
</apply>
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<component name="v5">
<variable name="v5" public_interface="out" units="flux"/>
<variable name="MT1" public_interface="in" units="molar"/>
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<variable name="MT1_T2_M2p_MT1" public_interface="in" units="molar"/>
<variable name="kon_MT1T2M2pMT1" public_interface="in" units="second_order_rate_constant"/>
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<math xmlns="http://www.w3.org/1998/Math/MathML" id="5">
<apply><eq/>
<ci> v5 </ci>
<apply><minus/>
<apply><times/>
<ci> kon_MT1T2M2pMT1 </ci>
<ci> MT1 </ci>
<ci> MT1_T2_M2p </ci>
</apply>
<apply><times/>
<ci> koff_MT1T2M2pMT1 </ci>
<ci> MT1_T2_M2p_MT1 </ci>
</apply>
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</math>
</component>
<component name="v6">
<variable name="v6" public_interface="out" units="flux"/>
<variable name="MT1_T2_M2p_MT1" public_interface="in" units="molar"/>
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<math xmlns="http://www.w3.org/1998/Math/MathML" id="6">
<apply><eq/>
<ci> v6 </ci>
<apply><minus/>
<apply><times/>
<ci> kact_M2 </ci>
<ci> MT1_T2_M2p_MT1 </ci>
</apply>
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<component name="v7">
<variable name="v7" public_interface="out" units="flux"/>
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<apply><times/>
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<ci> M2_T2 </ci>
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<ci> v9 </ci>
<apply><minus/>
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<ci> M2 </ci>
<ci> C1 </ci>
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<apply><times/>
<ci> koff_M2C1 </ci>
<ci> M2_C1 </ci>
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<ci> v10 </ci>
<apply><divide/>
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<ci> kcat_M2C1 </ci>
<ci> M2 </ci>
<ci> C1 </ci>
</apply>
<apply><plus/>
<ci> km_M2C1 </ci>
<ci> C1 </ci>
</apply>
</apply>
</apply>
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</component>
<!--
<component name="v11">
<variable name="v11" public_interface="out" units="flux" />
<variable name="MT1" public_interface="in" units="molar" />
<variable name="C1" public_interface="in" units="molar" />
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<ci> koff_MT1C1 </ci>
<ci> MT1_C1 </ci>
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</apply>
</apply>
</math>
</component>
-->
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<variable name="C1" public_interface="in" units="molar"/>
<variable name="MT1" public_interface="in" units="molar"/>
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<apply><divide/>
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<ci> MT1 </ci>
<ci> C1 </ci>
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<apply><plus/>
<ci> km_MT1C1 </ci>
<ci> C1 </ci>
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<!-- substrates -->
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<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:dcterms="http://purl.org/dc/terms/">
<rdf:Description rdf:about="MT1">
<dc:title>MT1</dc:title>
<dcterms:alternative>MT1-MMP</dcterms:alternative>
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<ci> v12 </ci>
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<cn cellml:units="dimensionless"> 2.0 </cn>
<ci> v2 </ci>
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<ci> v5 </ci>
<ci> v12 </ci>
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</apply>
</apply>
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<dc:title>MT1cat</dc:title>
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<dc:title>MT1t</dc:title>
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<dc:title>T2</dc:title>
<dcterms:alternative>TIMP2</dcterms:alternative>
<dcterms:alternative>tissue inhibitor of metalloproteinases</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable name="T2" initial_value="4.0E-9" public_interface="out" units="molar"/>
<variable name="v3" public_interface="in" units="flux"/>
<variable name="v7" public_interface="in" units="flux"/>
<variable name="time" public_interface="in" units="second"/>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="17">
<apply><eq/>
<apply><diff/>
<bvar><ci> time </ci></bvar>
<ci> T2 </ci>
</apply>
<apply><minus/>
<apply><plus/>
<ci> v3 </ci>
<ci> v7 </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="MT1_T2" cmeta:id="MT1_T2">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:dcterms="http://purl.org/dc/terms/">
<rdf:Description rdf:about="MT1_T2">
<dc:title>MT1_T2</dc:title>
<dcterms:alternative>MT1-MMP-TIMP2</dcterms:alternative>
<dcterms:alternative>membrane type I matrix metalloproteinase-tissue inhibitor of metalloproteinases complex</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable name="MT1_T2" initial_value="0.0" public_interface="out" units="molar"/>
<variable name="v3" public_interface="in" units="flux"/>
<variable name="v4" public_interface="in" units="flux"/>
<variable name="time" public_interface="in" units="second"/>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="18">
<apply><eq/>
<apply><diff/>
<bvar><ci> time </ci></bvar>
<ci> MT1_T2 </ci>
</apply>
<apply><minus/>
<ci> v3 </ci>
<ci> v4 </ci>
</apply>
</apply>
</math>
</component>
<component name="M2p" cmeta:id="M2p">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:dcterms="http://purl.org/dc/terms/">
<rdf:Description rdf:about="M2p">
<dc:title>M2p</dc:title>
<dcterms:alternative>proMMP2</dcterms:alternative>
<dcterms:alternative>proenzyme diffusible matrix metalloproteinase</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable name="M2p" initial_value="50.0E-9" public_interface="out" units="molar"/>
<variable name="v4" public_interface="in" units="flux"/>
<variable name="time" public_interface="in" units="second"/>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="19">
<apply><eq/>
<apply><diff/>
<bvar><ci> time </ci></bvar>
<ci> M2p </ci>
</apply>
<apply><minus/>
<ci> v4 </ci>
</apply>
</apply>
</math>
</component>
<component name="MT1_T2_M2p" cmeta:id="MT1_T2_M2p">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:dcterms="http://purl.org/dc/terms/">
<rdf:Description rdf:about="MT1_T2_M2p">
<dc:title>MT1_T2_M2p</dc:title>
<dcterms:alternative>MT1-MMP-TIMP2-proMMP2</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable name="MT1_T2_M2p" initial_value="0.0" public_interface="out" units="molar"/>
<variable name="v4" public_interface="in" units="flux"/>
<variable name="v5" public_interface="in" units="flux"/>
<variable name="time" public_interface="in" units="second"/>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="20">
<apply><eq/>
<apply><diff/>
<bvar><ci> time </ci></bvar>
<ci> MT1_T2_M2p </ci>
</apply>
<apply><minus/>
<ci> v5 </ci>
<ci> v4 </ci>
</apply>
</apply>
</math>
</component>
<component name="MT1_T2_M2p_MT1" cmeta:id="MT1_T2_M2p_MT1">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:dcterms="http://purl.org/dc/terms/">
<rdf:Description rdf:about="MT1_T2_M2p_MT1">
<dc:title>MT1_T2_M2p_MT1</dc:title>
<dcterms:alternative>MT1-MMP-TIMP2-proMMP2-MT1-MMP</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable name="MT1_T2_M2p_MT1" initial_value="0.0" public_interface="out" units="molar"/>
<variable name="v5" public_interface="in" units="flux"/>
<variable name="v6" public_interface="in" units="flux"/>
<variable name="time" public_interface="in" units="second"/>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="21">
<apply><eq/>
<apply><diff/>
<bvar><ci> time </ci></bvar>
<ci> MT1_T2_M2p_MT1 </ci>
</apply>
<apply><minus/>
<ci> v5 </ci>
<ci> v6 </ci>
</apply>
</apply>
</math>
</component>
<component name="MT1_T2_star" cmeta:id="MT1_T2_star">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:dcterms="http://purl.org/dc/terms/">
<rdf:Description rdf:about="MT1_T2_star">
<dc:title>MT1_T2_star</dc:title>
<dcterms:alternative>inactivated MT1-MMP-TIMP2</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable name="MT1_T2_star" initial_value="0.0" public_interface="out" units="molar"/>
<variable name="v6" public_interface="in" units="flux"/>
<variable name="time" public_interface="in" units="second"/>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="22">
<apply><eq/>
<apply><diff/>
<bvar><ci> time </ci></bvar>
<ci> MT1_T2_star </ci>
</apply>
<apply><minus/>
<ci> v6 </ci>
</apply>
</apply>
</math>
</component>
<component name="M2" cmeta:id="M2">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:dcterms="http://purl.org/dc/terms/">
<rdf:Description rdf:about="M2">
<dc:title>M2</dc:title>
<dcterms:alternative>MMP2</dcterms:alternative>
<dcterms:alternative>diffusible matrix metalloproteinase</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable name="M2" initial_value="30E-12" public_interface="out" units="molar"/>
<variable name="v6" public_interface="in" units="flux"/>
<variable name="v7" public_interface="in" units="flux"/>
<variable name="v9" public_interface="in" units="flux"/>
<variable name="v10" public_interface="in" units="flux"/>
<variable name="time" public_interface="in" units="second"/>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="23">
<apply><eq/>
<apply><diff/>
<bvar><ci> time </ci></bvar>
<ci> M2 </ci>
</apply>
<apply><minus/>
<apply><plus/>
<ci> v6 </ci>
<ci> v10 </ci>
</apply>
<apply><plus/>
<ci> v7 </ci>
<ci> v9 </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="M2_T2" cmeta:id="M2_T2">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:dcterms="http://purl.org/dc/terms/">
<rdf:Description rdf:about="M2_T2">
<dc:title>M2_T2</dc:title>
<dcterms:alternative>MMP2-TIMP2</dcterms:alternative>
<dcterms:alternative>diffusible matrix metalloproteinase-tissue inhibitor of metalloproteinases complex</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable name="M2_T2" initial_value="0.0" public_interface="out" units="molar"/>
<variable name="v7" public_interface="in" units="flux"/>
<variable name="v8" public_interface="in" units="flux"/>
<variable name="time" public_interface="in" units="second"/>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="24">
<apply><eq/>
<apply><diff/>
<bvar><ci> time </ci></bvar>
<ci> M2_T2 </ci>
</apply>
<apply><minus/>
<ci> v7 </ci>
<ci> v8 </ci>
</apply>
</apply>
</math>
</component>
<component name="M2_T2_star" cmeta:id="M2_T2_star">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:dcterms="http://purl.org/dc/terms/">
<rdf:Description rdf:about="M2_T2_star">
<dc:title>M2_T2_star</dc:title>
<dcterms:alternative>inactivated MMP2-TIMP2</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable name="M2_T2_star" initial_value="0.0" public_interface="out" units="molar"/>
<variable name="v8" public_interface="in" units="flux"/>
<variable name="time" public_interface="in" units="second"/>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="25">
<apply><eq/>
<apply><diff/>
<bvar><ci> time </ci></bvar>
<ci> M2_T2_star </ci>
</apply>
<ci> v8 </ci>
</apply>
</math>
</component>
<component name="M2_C1" cmeta:id="M2_C1">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:dcterms="http://purl.org/dc/terms/">
<rdf:Description rdf:about="M2_C1">
<dc:title>M2_C1</dc:title>
<dcterms:alternative>MMP2-C1</dcterms:alternative>
<dcterms:alternative>diffusible matrix metalloproteinase-collagen type I complex</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable name="M2_C1" initial_value="0.0" public_interface="out" units="molar"/>
<variable name="v9" public_interface="in" units="flux"/>
<variable name="time" public_interface="in" units="second"/>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="24">
<apply><eq/>
<apply><diff/>
<bvar><ci> time </ci></bvar>
<ci> M2_C1 </ci>
</apply>
<ci> v9 </ci>
</apply>
</math>
</component>
<component name="C1" cmeta:id="C1">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:dcterms="http://purl.org/dc/terms/">
<rdf:Description rdf:about="C1">
<dc:title>C1</dc:title>
<dcterms:alternative>collagen type I</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable name="C1" initial_value="176E-6" public_interface="out" units="molar"/>
<variable name="v9" public_interface="in" units="flux"/>
<variable name="v10" public_interface="in" units="flux"/>
<variable name="v12" public_interface="in" units="flux"/>
<variable name="time" public_interface="in" units="second"/>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="26">
<apply><eq/>
<apply><diff/>
<bvar><ci> time </ci></bvar>
<ci> C1 </ci>
</apply>
<apply><minus/>
<apply><plus/>
<ci> v9 </ci>
<ci> v10 </ci>
<ci> v12 </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="C1D" cmeta:id="C1D">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:dcterms="http://purl.org/dc/terms/">
<rdf:Description rdf:about="C1D">
<dc:title>C1D</dc:title>
<dcterms:alternative>denatured collagen type I</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable name="C1D" initial_value="0.0" public_interface="out" units="molar"/>
<variable name="v10" public_interface="in" units="flux"/>
<variable name="v12" public_interface="in" units="flux"/>
<variable name="time" public_interface="in" units="second"/>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="27">
<apply><eq/>
<apply><diff/>
<bvar><ci> time </ci></bvar>
<ci> C1D </ci>
</apply>
<apply><plus/>
<ci> v10 </ci>
<ci> v12 </ci>
</apply>
</apply>
</math>
</component>
<!--
<component name="MT1_C1" cmeta:id="MT1_C1">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:dcterms="http://purl.org/dc/terms/">
<rdf:Description rdf:about="MT1_C1">
<dc:title>MT1_C1</dc:title>
<dcterms:alternative>MT1-MMP-collagen type I</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable name="MT1_C1" initial_value="0.0" public_interface="out" units="molar" />
<variable name="v11" public_interface="in" units="flux" />
<variable name="v12" public_interface="in" units="flux" />
<variable name="time" public_interface="in" units="second" />
<math xmlns="http://www.w3.org/1998/Math/MathML" id="28" >
<apply><eq />
<apply><diff />
<bvar><ci> time </ci></bvar>
<ci> MT1_C1 </ci>
</apply>
<apply><minus />
<ci> v11 </ci>
<ci> v12 </ci>
</apply>
</apply>
</math>
</component>
-->
<component name="model_parameters">
<variable name="kon_M2T2" public_interface="out" initial_value="5.9E6" units="second_order_rate_constant"/>
<variable name="koff_M2T2" public_interface="out" initial_value="6.3" units="first_order_rate_constant"/>
<variable name="kiso_M2T2" public_interface="out" initial_value="33.0" units="first_order_rate_constant"/>
<variable name="k_iso_M2T2" public_interface="out" initial_value="2E-8" units="first_order_rate_constant"/>
<variable name="kon_M2C1" public_interface="out" initial_value="2.6E3" units="second_order_rate_constant"/>
<variable name="koff_M2C1" public_interface="out" initial_value="2.1E-3" units="first_order_rate_constant"/>
<variable name="kcat_M2C1" public_interface="out" initial_value="4.5E-3" units="first_order_rate_constant"/>
<variable name="kact_M2" public_interface="out" initial_value="2E-2" units="first_order_rate_constant"/>
<variable name="kon_MT1T2M2p" public_interface="out" initial_value="0.14E6" units="second_order_rate_constant"/>
<variable name="koff_MT1T2M2p" public_interface="out" initial_value="4.7E-3" units="first_order_rate_constant"/>
<variable name="kon_MT1T2M2pMT1" public_interface="out" initial_value="3E3" units="second_order_rate_constant"/>
<variable name="koff_MT1T2M2pMT1" public_interface="out" initial_value="0.9E-3" units="first_order_rate_constant"/>
<variable name="kcat_MT1C1" public_interface="out" initial_value="1.97E-3" units="first_order_rate_constant"/>
<variable name="kshed_MT1" public_interface="out" initial_value="2.8E3" units="second_order_rate_constant"/>
<variable name="kon_MT1T2" public_interface="out" initial_value="3.54E6" units="second_order_rate_constant"/>
<variable name="koff_MT1T2" public_interface="out" initial_value="20.2" units="first_order_rate_constant"/>
<variable name="km_M2C1" public_interface="out" initial_value="8.5E-6" units="molar"/>
<variable name="km_MT1C1" public_interface="out" initial_value="8.5E-6" units="molar"/>
</component>
<connection>
<map_components component_1="MT1" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="MT1cat" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="MT1t" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="T2" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="MT1_T2" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="M2p" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="MT1_T2_M2p" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="MT1_T2_M2p_MT1" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="MT1_T2_star" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="M2" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="M2_T2" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="M2_T2_star" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="M2_C1" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="C1" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="C1D" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="v2" component_2="MT1"/>
<map_variables variable_1="MT1" variable_2="MT1"/>
<map_variables variable_1="v2" variable_2="v2"/>
</connection>
<connection>
<map_components component_1="v2" component_2="model_parameters"/>
<map_variables variable_1="kshed_MT1" variable_2="kshed_MT1"/>
</connection>
<connection>
<map_components component_1="v3" component_2="MT1"/>
<map_variables variable_1="MT1" variable_2="MT1"/>
<map_variables variable_1="v3" variable_2="v3"/>
</connection>
<connection>
<map_components component_1="v3" component_2="T2"/>
<map_variables variable_1="T2" variable_2="T2"/>
<map_variables variable_1="v3" variable_2="v3"/>
</connection>
<connection>
<map_components component_1="v3" component_2="MT1_T2"/>
<map_variables variable_1="MT1_T2" variable_2="MT1_T2"/>
<map_variables variable_1="v3" variable_2="v3"/>
</connection>
<connection>
<map_components component_1="v3" component_2="model_parameters"/>
<map_variables variable_1="kon_MT1T2" variable_2="kon_MT1T2"/>
<map_variables variable_1="koff_MT1T2" variable_2="koff_MT1T2"/>
</connection>
<connection>
<map_components component_1="v4" component_2="M2p"/>
<map_variables variable_1="M2p" variable_2="M2p"/>
<map_variables variable_1="v4" variable_2="v4"/>
</connection>
<connection>
<map_components component_1="v4" component_2="MT1_T2_M2p"/>
<map_variables variable_1="MT1_T2_M2p" variable_2="MT1_T2_M2p"/>
<map_variables variable_1="v4" variable_2="v4"/>
</connection>
<connection>
<map_components component_1="v4" component_2="MT1_T2"/>
<map_variables variable_1="MT1_T2" variable_2="MT1_T2"/>
<map_variables variable_1="v4" variable_2="v4"/>
</connection>
<connection>
<map_components component_1="v4" component_2="model_parameters"/>
<map_variables variable_1="kon_MT1T2M2p" variable_2="kon_MT1T2M2p"/>
<map_variables variable_1="koff_MT1T2M2p" variable_2="koff_MT1T2M2p"/>
</connection>
<connection>
<map_components component_1="v5" component_2="MT1"/>
<map_variables variable_1="MT1" variable_2="MT1"/>
<map_variables variable_1="v5" variable_2="v5"/>
</connection>
<connection>
<map_components component_1="v5" component_2="MT1_T2_M2p"/>
<map_variables variable_1="MT1_T2_M2p" variable_2="MT1_T2_M2p"/>
<map_variables variable_1="v5" variable_2="v5"/>
</connection>
<connection>
<map_components component_1="v5" component_2="MT1_T2_M2p_MT1"/>
<map_variables variable_1="MT1_T2_M2p_MT1" variable_2="MT1_T2_M2p_MT1"/>
<map_variables variable_1="v5" variable_2="v5"/>
</connection>
<connection>
<map_components component_1="v5" component_2="model_parameters"/>
<map_variables variable_1="kon_MT1T2M2pMT1" variable_2="kon_MT1T2M2pMT1"/>
<map_variables variable_1="koff_MT1T2M2pMT1" variable_2="koff_MT1T2M2pMT1"/>
</connection>
<connection>
<map_components component_1="v6" component_2="MT1_T2_M2p_MT1"/>
<map_variables variable_1="MT1_T2_M2p_MT1" variable_2="MT1_T2_M2p_MT1"/>
<map_variables variable_1="v6" variable_2="v6"/>
</connection>
<connection>
<map_components component_1="v6" component_2="model_parameters"/>
<map_variables variable_1="kact_M2" variable_2="kact_M2"/>
</connection>
<connection>
<map_components component_1="v7" component_2="M2"/>
<map_variables variable_1="M2" variable_2="M2"/>
<map_variables variable_1="v7" variable_2="v7"/>
</connection>
<connection>
<map_components component_1="v7" component_2="T2"/>
<map_variables variable_1="T2" variable_2="T2"/>
<map_variables variable_1="v7" variable_2="v7"/>
</connection>
<connection>
<map_components component_1="v7" component_2="M2_T2"/>
<map_variables variable_1="M2_T2" variable_2="M2_T2"/>
<map_variables variable_1="v7" variable_2="v7"/>
</connection>
<connection>
<map_components component_1="v7" component_2="model_parameters"/>
<map_variables variable_1="kon_M2T2" variable_2="kon_M2T2"/>
<map_variables variable_1="koff_M2T2" variable_2="koff_M2T2"/>
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<connection>
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Journal of Biological Chemistry
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A theoretical model of type I collagen proteolysis by matrix metalloproteinase (MMP) 2 and membrane type 1 MMP in the presence of tissue inhibitor of metalloproteinase 2
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Karagiannis and Popel's 2004 mathematical model of collagen type I proteolysis by matrix metalloproteinase (MMP) 2 and membrane type I MMP during the migration of a tip endothelial cell.
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