- Author:
- pmr2.import <nobody@models.cellml.org>
- Date:
- 2008-07-08 02:50:44+12:00
- Desc:
- committing version01 of vempati_karagiannis_popel_2007
- Permanent Source URI:
- http://models.cellml.org/workspace/vempati_karagiannis_popel_2007/rawfile/21bb2756461291d7c2b988a3305d82c43497a41a/vempati_karagiannis_popel_2007.cellml
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<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
<articleinfo>
<title>A Biochemical Model of Matrix Metalloproteinase 9 Activation and Inhibition</title>
<author>
<firstname>Catherine</firstname>
<surname>Lloyd</surname>
<affiliation>
<shortaffil>Bioengineering Institute, University of Auckland</shortaffil>
</affiliation>
</author>
</articleinfo>
<sect1 id="sec_structure">
<title>Model Structure</title>
<para>
This cellML model is known to run in both PCEnv and COR to recreate the results in the published paper. The units have been checked and they are consistent. Please note that many of the figures in the paper are complex and requite special simulation conditions. This particular CellMl model represents the basic core model presented in the paper. Initial conditions can be modified to generate more complex results. We thank the model author Prakash Vempati for his assistance in getting this CellML model to run.
</para>
<para>Abstract: Matrix metalloproteinases (MMPs) are a class of extracellular and membrane-bound proteases involved in an array of physiological processes including angiogenesis. We present a detailed computational model of MMP9 activation and inhibition. Our model is validated to existing biochemical experimental data. We determine kinetic rate constants for the processes of MMP9 activation by MMP3, MMP10, MMP13, and trypsin, inhibition by the tissue inhibitors of metalloproteinases (TIMPs) TIMP1 and TIMP2, and MMP9 deactivation. This computational approach allows us to investigate discrepancies in our understanding of the MMP9’s interaction with TIMP1. Specifically, we find that inhibition due to a single binding event cannot describe MMP9 inhibition by TIMP1. Temporally accurate biphasic inhibition requires either an additional isomerization step or a second lower-affinity isoform of MMP9. We also theoretically characterize the MMP3/TIMP2/proMMP9 and MMP3/TIMP1/proMMP9 systems. We speculate that these systems differ significantly in their time scales of activation and inhibition such that MMP9 is able to temporarily overshoot its final equilibrium value in the latter. Our numerical simulations suggest that the ability of proMMP9 to complex TIMP1 increases this overshoot. In all, our analysis serves as a summary of existing kinetic data for MMP9 and a foundation for future models utilizing MMP9 or other MMPs under physiologically well-defined microenvironments.</para>
<para>
<informalfigure float="0" id="fig_reaction_diagram">
<mediaobject>
<imageobject>
<objectinfo>
<title>model diagram</title>
</objectinfo>
<imagedata fileref="vempati_2007.png"/>
</imageobject>
</mediaobject>
<caption>Schematic diagram of the biochemical reaction network for MMP9 activation and inhibition spanning MMP9, MMP3, TIMP1, and TIMP2. pM9, pro-MMP9; M3, MMP3; M9, MMP9; T1, TIMP1; T2, TIMP2; Tr, Trypsin.</caption>
</informalfigure>
The complete original paper reference is cited below:
</para>
<para>
<ulink url="http://www.jbc.org/cgi/content/abstract/282/52/37585">A Biochemical Model of Matrix Metalloproteinase 9 Activation and Inhibition</ulink>, Prakash Vempati, Emmanouil D. Karagiannis, and Aleksander S. Popel , 2007, <ulink url="http://www.jbc.org/">
<emphasis>The Journal of Biological Chemistry</emphasis>
</ulink>, 282, 37585-37596. (<ulink url="http://www.jbc.org/cgi/content/full/282/52/37585">Full text</ulink> and <ulink url="http://www.jbc.org/cgi/reprint/282/52/37585">PDF</ulink> versions of the article are available to journal subscribers on the <emphasis>The Journal of Biological Chemistry</emphasis> website.) <ulink url="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=pubmed&cmd=Retrieve&dopt=AbstractPlus&list_uids=17848556&query_hl=1&itool=pubmed_docsum">PubMed ID: 17848556</ulink>
</para>
<!-- <informalfigure float="0" id="fig_reaction_diagram">
<mediaobject>
<imageobject>
<objectinfo>
<title>model diagram</title>
</objectinfo>
<imagedata fileref="../images/vempati_model_2007/vempati_2007.png"/>
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<caption>Schematic diagram ...</caption>
</informalfigure> -->
</sect1>
</article>
</documentation>
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="pM9">
<dc:title>pM9</dc:title>
<dcterms:alternative>proMMP9</dcterms:alternative>
<dcterms:alternative>promatrix metalloproteinase-9</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="M3">
<dc:title>M3</dc:title>
<dcterms:alternative>MMP3</dcterms:alternative>
<dcterms:alternative>matrix metalloproteinase-3</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="M3_pM9">
<dc:title>M3_pM9</dc:title>
<dcterms:alternative>MMP3-proMMP9</dcterms:alternative>
<dcterms:alternative>matrix metalloproteinase-3-promatrix metalloproteinase-9 complex</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="T1">
<dc:title>T1</dc:title>
<dcterms:alternative>TIMP1</dcterms:alternative>
<dcterms:alternative>tissue inhibitor of metalloproteinase-1</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
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<rdf:Description rdf:about="M3_T1">
<dc:title>M3_T1</dc:title>
<dcterms:alternative>MMP3-TIMP1</dcterms:alternative>
<dcterms:alternative>matrix metalloproteinase-3-tissue inhibitor of metalloproteinase-1 complex</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="pM9_T1">
<dc:title>pM9_T1</dc:title>
<dcterms:alternative>proMMP9-TIMP1</dcterms:alternative>
<dcterms:alternative>promatrix metalloproteinase-9-tissue inhibitor of metalloproteinase-1 complex</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="M3_pM9_T1">
<dc:title>M3_pM9_T1</dc:title>
<dcterms:alternative>MMP3-proMMP9-TIMP1</dcterms:alternative>
<dcterms:alternative>matrix metalloproteinase-3-promatrix metalloproteinase-9-tissue inhibitor of metalloproteinase-1 complex</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="M9_T1_star">
<dc:title>M9_T1_star</dc:title>
<dcterms:alternative>inactivated MMP9-TIMP1</dcterms:alternative>
<dcterms:alternative>inactivated matrix metalloproteinase-9-tissue inhibitor of metalloproteinase-1 complex</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="M9">
<dc:title>M9</dc:title>
<dcterms:alternative>MMP9</dcterms:alternative>
<dcterms:alternative>matrix metalloproteinase-9</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="M9_T1">
<dc:title>M9_T1</dc:title>
<dcterms:alternative>MMP9-TIMP1</dcterms:alternative>
<dcterms:alternative>matrix metalloproteinase-9-tissue inhibitor of metalloproteinase-1 complex</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="pM9_T1_M3">
<dc:title>pM9_T1_M3</dc:title>
<dcterms:alternative>proMMP9-TIMP1-MMP3</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="M3_pM9_T1_M3">
<dc:title>M3_pM9_T1_M3</dc:title>
<dcterms:alternative>MMP3-proMMP9-TIMP1-MMP3</dcterms:alternative>
</rdf:Description>
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<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
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<dc:title>M9_T1_M3</dc:title>
<dcterms:alternative>MMP9-TIMP1-MMP3</dcterms:alternative>
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<rdf:Description rdf:about="Tr">
<dc:title>Tr</dc:title>
<dcterms:alternative>trypsin</dcterms:alternative>
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<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
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<dc:title>Tr_pM9</dc:title>
<dcterms:alternative>trypsin-proMMP9</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
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<dcterms:alternative>trypsin-proMMP9-TIMP1-MMP3</dcterms:alternative>
</rdf:Description>
</rdf:RDF> <units name="molar">
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<unit units="litre" exponent="-1"/>
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<variable units="molar" public_interface="in" name="pM9"/>
<variable units="molar" public_interface="in" name="Tr"/>
<variable units="molar" public_interface="in" name="Tr_pM9"/>
<variable units="second_order_rate_constant" public_interface="in" name="kon_TrpM9"/>
<variable units="first_order_rate_constant" public_interface="in" name="koff_TrpM9"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>v15</ci>
<apply>
<minus/>
<apply>
<times/>
<ci>kon_TrpM9</ci>
<ci>Tr</ci>
<ci>pM9</ci>
</apply>
<apply>
<times/>
<ci>koff_TrpM9</ci>
<ci>Tr_pM9</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="v16">
<variable units="flux" public_interface="out" name="v16"/>
<variable units="molar" public_interface="in" name="Tr_pM9"/>
<variable units="first_order_rate_constant" public_interface="in" name="kact_TrpM9"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>v16</ci>
<apply>
<times/>
<ci>kact_TrpM9</ci>
<ci>Tr_pM9</ci>
</apply>
</apply>
</math>
</component>
<component name="v17">
<variable units="flux" public_interface="out" name="v17"/>
<variable units="molar" public_interface="in" name="pM9_T1"/>
<variable units="molar" public_interface="in" name="Tr"/>
<variable units="molar" public_interface="in" name="Tr_pM9_T1"/>
<variable units="second_order_rate_constant" public_interface="in" name="kon_TrpM9T1"/>
<variable units="first_order_rate_constant" public_interface="in" name="koff_TrpM9T1"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>v17</ci>
<apply>
<minus/>
<apply>
<times/>
<ci>kon_TrpM9T1</ci>
<ci>pM9_T1</ci>
<ci>Tr</ci>
</apply>
<apply>
<times/>
<ci>koff_TrpM9T1</ci>
<ci>Tr_pM9_T1</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="v18">
<variable units="flux" public_interface="out" name="v18"/>
<variable units="molar" public_interface="in" name="Tr_pM9_T1"/>
<variable units="first_order_rate_constant" public_interface="in" name="kact_TrpM9T1"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>v18</ci>
<apply>
<times/>
<ci>kact_TrpM9T1</ci>
<ci>Tr_pM9_T1</ci>
</apply>
</apply>
</math>
</component>
<component name="v19">
<variable units="flux" public_interface="out" name="v19"/>
<variable units="molar" public_interface="in" name="Tr"/>
<variable units="molar" public_interface="in" name="pM9_T1_M3"/>
<variable units="molar" public_interface="in" name="Tr_pM9_T1_M3"/>
<variable units="second_order_rate_constant" public_interface="in" name="kon_TrpM9T1M3"/>
<variable units="first_order_rate_constant" public_interface="in" name="koff_TrpM9T1M3"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>v19</ci>
<apply>
<minus/>
<apply>
<times/>
<ci>kon_TrpM9T1M3</ci>
<ci>Tr</ci>
<ci>pM9_T1_M3</ci>
</apply>
<apply>
<times/>
<ci>koff_TrpM9T1M3</ci>
<ci>Tr_pM9_T1_M3</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="v20">
<variable units="flux" public_interface="out" name="v20"/>
<variable units="molar" public_interface="in" name="Tr_pM9_T1_M3"/>
<variable units="first_order_rate_constant" public_interface="in" name="kact_TrpM9T1M3"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>v20</ci>
<apply>
<times/>
<ci>kact_TrpM9T1M3</ci>
<ci>Tr_pM9_T1_M3</ci>
</apply>
</apply>
</math>
</component>
<component name="pM9">
<variable units="molar" public_interface="out" name="pM9" initial_value="3e-7"/>
<variable units="flux" public_interface="in" name="v1"/>
<variable units="flux" public_interface="in" name="v4"/>
<variable units="flux" public_interface="in" name="v15"/>
<variable units="flux" public_interface="in" name="v11"/>
<variable units="second" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>pM9</ci>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<ci>v1</ci>
<ci>v4</ci>
<ci>v15</ci>
<ci>v11</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="M3">
<variable units="molar" public_interface="out" name="M3" initial_value="5e-8"/>
<variable units="flux" public_interface="in" name="v1"/>
<variable units="flux" public_interface="in" name="v2"/>
<variable units="flux" public_interface="in" name="v3"/>
<variable units="flux" public_interface="in" name="v5"/>
<variable units="flux" public_interface="in" name="v6"/>
<variable units="flux" public_interface="in" name="v10"/>
<variable units="flux" public_interface="in" name="v12"/>
<variable units="flux" public_interface="in" name="v13"/>
<variable units="flux" public_interface="in" name="v14"/>
<variable units="second" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>M3</ci>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<ci>v2</ci>
<ci>v6</ci>
<ci>v13</ci>
<ci>v14</ci>
</apply>
<apply>
<plus/>
<ci>v1</ci>
<ci>v3</ci>
<ci>v5</ci>
<ci>v10</ci>
<ci>v12</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="M3_pM9">
<variable units="molar" public_interface="out" name="M3_pM9" initial_value="0"/>
<variable units="flux" public_interface="in" name="v1"/>
<variable units="flux" public_interface="in" name="v2"/>
<variable units="second" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>M3_pM9</ci>
</apply>
<apply>
<minus/>
<ci>v1</ci>
<ci>v2</ci>
</apply>
</apply>
</math>
</component>
<component name="T1">
<variable units="molar" public_interface="out" name="T1" initial_value="3e-7"/>
<variable units="flux" public_interface="in" name="v3"/>
<variable units="flux" public_interface="in" name="v4"/>
<variable units="flux" public_interface="in" name="v7"/>
<variable units="second" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>T1</ci>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<ci>v3</ci>
<ci>v4</ci>
<ci>v7</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="M3_T1">
<variable units="molar" public_interface="out" name="M3_T1" initial_value="0"/>
<variable units="flux" public_interface="in" name="v3"/>
<variable units="flux" public_interface="in" name="v9"/>
<variable units="flux" public_interface="in" name="v11"/>
<variable units="second" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>M3_T1</ci>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<ci>v3</ci>
<ci>v9</ci>
</apply>
<ci>v11</ci>
</apply>
</apply>
</math>
</component>
<component name="pM9_T1">
<variable units="molar" public_interface="out" name="pM9_T1" initial_value="0"/>
<variable units="flux" public_interface="in" name="v4"/>
<variable units="flux" public_interface="in" name="v5"/>
<variable units="flux" public_interface="in" name="v10"/>
<variable units="flux" public_interface="in" name="v17"/>
<variable units="second" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>pM9_T1</ci>
</apply>
<apply>
<minus/>
<ci>v4</ci>
<apply>
<plus/>
<ci>v5</ci>
<ci>v10</ci>
<ci>v17</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="M3_pM9_T1">
<variable units="molar" public_interface="out" name="M3_pM9_T1" initial_value="0"/>
<variable units="flux" public_interface="in" name="v5"/>
<variable units="flux" public_interface="in" name="v6"/>
<variable units="second" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>M3_pM9_T1</ci>
</apply>
<apply>
<minus/>
<ci>v5</ci>
<ci>v6</ci>
</apply>
</apply>
</math>
</component>
<component name="M9_T1_star">
<variable units="molar" public_interface="out" name="M9_T1_star" initial_value="0"/>
<variable units="flux" public_interface="in" name="v7"/>
<variable units="flux" public_interface="in" name="v14"/>
<variable units="flux" public_interface="in" name="v8"/>
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<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>M9_T1_star</ci>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<ci>v7</ci>
<ci>v14</ci>
</apply>
<ci>v8</ci>
</apply>
</apply>
</math>
</component>
<component name="M9">
<variable units="molar" public_interface="out" name="M9" initial_value="0"/>
<variable units="flux" public_interface="in" name="v2"/>
<variable units="flux" public_interface="in" name="v7"/>
<variable units="flux" public_interface="in" name="v9"/>
<variable units="flux" public_interface="in" name="v16"/>
<variable units="second" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>M9</ci>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<ci>v2</ci>
<ci>v9</ci>
<ci>v16</ci>
</apply>
<ci>v7</ci>
</apply>
</apply>
</math>
</component>
<component name="M9_T1">
<variable units="molar" public_interface="out" name="M9_T1" initial_value="0"/>
<variable units="flux" public_interface="in" name="v8"/>
<variable units="flux" public_interface="in" name="v18"/>
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<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>M9_T1</ci>
</apply>
<apply>
<plus/>
<ci>v8</ci>
<ci>v18</ci>
</apply>
</apply>
</math>
</component>
<component name="pM9_T1_M3">
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<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>pM9_T1_M3</ci>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<ci>v10</ci>
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</apply>
<apply>
<plus/>
<ci>v12</ci>
<ci>v19</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="M3_pM9_T1_M3">
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<variable units="flux" public_interface="in" name="v12"/>
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<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>M3_pM9_T1_M3</ci>
</apply>
<apply>
<minus/>
<ci>v12</ci>
<ci>v13</ci>
</apply>
</apply>
</math>
</component>
<component name="M9_T1_M3">
<variable units="molar" public_interface="out" name="M9_T1_M3" initial_value="0"/>
<variable units="flux" public_interface="in" name="v9"/>
<variable units="flux" public_interface="in" name="v13"/>
<variable units="flux" public_interface="in" name="v14"/>
<variable units="flux" public_interface="in" name="v20"/>
<variable units="second" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>M9_T1_M3</ci>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<ci>v13</ci>
<ci>v20</ci>
</apply>
<apply>
<plus/>
<ci>v14</ci>
<ci>v9</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="Tr">
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<variable units="flux" public_interface="in" name="v15"/>
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<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>Tr</ci>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<ci>v16</ci>
<ci>v18</ci>
<ci>v20</ci>
</apply>
<apply>
<plus/>
<ci>v15</ci>
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</apply>
</apply>
</apply>
</math>
</component>
<component name="Tr_pM9">
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<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>Tr_pM9</ci>
</apply>
<apply>
<minus/>
<ci>v15</ci>
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</apply>
</apply>
</math>
</component>
<component name="Tr_pM9_T1">
<variable units="molar" public_interface="out" name="Tr_pM9_T1" initial_value="0"/>
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<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>Tr_pM9_T1</ci>
</apply>
<apply>
<minus/>
<ci>v17</ci>
<ci>v18</ci>
</apply>
</apply>
</math>
</component>
<component name="Tr_pM9_T1_M3">
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<math xmlns="http://www.w3.org/1998/Math/MathML">
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<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
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<ci>Tr_pM9_T1_M3</ci>
</apply>
<apply>
<minus/>
<ci>v19</ci>
<ci>v20</ci>
</apply>
</apply>
</math>
</component>
<component name="kinetic_parameters">
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<variable units="first_order_rate_constant" public_interface="out" name="koff_pM9T1" initial_value="7.48e-5"/>
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<variable units="first_order_rate_constant" public_interface="out" name="koff_pM9T1M3" initial_value="7.48e-5"/>
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<variable units="first_order_rate_constant" public_interface="out" name="koff_M3pM9" initial_value="0.001"/>
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<variable units="first_order_rate_constant" public_interface="out" name="koff_M3T1" initial_value="1.26e-4"/>
<variable units="second_order_rate_constant" public_interface="out" name="kon_M9T1_star" initial_value="5.6e6"/>
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<variable units="first_order_rate_constant" public_interface="out" name="kon_M9T1" initial_value="6.3e-4"/>
<variable units="first_order_rate_constant" public_interface="out" name="koff_M9T1" initial_value="2.5e-4"/>
<variable units="second_order_rate_constant" public_interface="out" name="kon_M3_pM9T1" initial_value="1.9e6"/>
<variable units="first_order_rate_constant" public_interface="out" name="koff_M3_pM9T1" initial_value="1.26e-4"/>
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<variable units="first_order_rate_constant" public_interface="out" name="koff_TrpM9" initial_value="0.007"/>
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<variable units="first_order_rate_constant" public_interface="out" name="kon_M9_M3T1" initial_value="7.48e-5"/>
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<variable units="first_order_rate_constant" public_interface="out" name="kact_M3pM9T1M3" initial_value="0.00057"/>
<variable units="first_order_rate_constant" public_interface="out" name="kact_M9T1M3" initial_value="1.26e-4"/>
<variable units="first_order_rate_constant" public_interface="out" name="kact_TrpM9" initial_value="0.002"/>
<variable units="first_order_rate_constant" public_interface="out" name="kact_TrpM9T1" initial_value="0.0006"/>
<variable units="first_order_rate_constant" public_interface="out" name="kact_TrpM9T1M3" initial_value="0.0006"/>
<variable units="first_order_rate_constant" public_interface="out" name="kact_M3pM9" initial_value="0.0019"/>
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<connection>
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<map_variables variable_2="pM9" variable_1="pM9"/>
<map_variables variable_2="v1" variable_1="v1"/>
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<connection>
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<map_variables variable_2="pM9" variable_1="pM9"/>
<map_variables variable_2="v4" variable_1="v4"/>
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<connection>
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<map_variables variable_2="v11" variable_1="v11"/>
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<connection>
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<connection>
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<map_variables variable_2="v1" variable_1="v1"/>
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<vCard:Given>Emmanouil</vCard:Given>
<vCard:Family>Karagiannis</vCard:Family>
<vCard:Other>D</vCard:Other>
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<rdf:Description rdf:about="rdf:#ecd31d28-374c-42e8-89cf-849a4ff204d8">
<vCard:FN>Catherine Lloyd</vCard:FN>
</rdf:Description>
<rdf:Description rdf:about="#vempati_model_2007">
<dc:title>
Vempati et al.'s 2007 biochemical model of the matrix metalloproteinase 9 activation and inhibition.
</dc:title>
<cmeta:comment rdf:resource="rdf:#4db5e780-313c-48d1-a7dd-361b8e006fa2"/>
<bqs:reference rdf:resource="rdf:#7962016d-39d0-43e8-a1f9-c67f5257bf89"/>
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<dc:creator rdf:resource="rdf:#ecd31d28-374c-42e8-89cf-849a4ff204d8"/>
<rdf:value>This is the CellML description of Vempati et al.'s 2007 biochemical model of the matrix metalloproteinase 9 activation and inhibition.</rdf:value>
</rdf:Description>
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<rdf:value>c.lloyd@auckland.ac.nz</rdf:value>
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<rdf:Description rdf:about="rdf:#5fed64e6-d0e5-445b-abca-4d865a75e437">
<vCard:Given>Aleksander</vCard:Given>
<vCard:Family>Popel</vCard:Family>
<vCard:Other>S</vCard:Other>
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<rdf:Description rdf:about="rdf:#7962016d-39d0-43e8-a1f9-c67f5257bf89">
<bqs:Pubmed_id>17848556</bqs:Pubmed_id>
<bqs:JournalArticle rdf:resource="rdf:#fb917faa-e471-4168-83dd-147a8b8ec0e7"/>
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<rdf:Description rdf:about="rdf:#6a95ebdc-836e-49e1-9d4e-ba254a9746ae">
<dcterms:W3CDTF>2008-07-08T00:00:00+00:00</dcterms:W3CDTF>
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<rdf:Description rdf:about="rdf:#e5c86249-1568-46a8-9278-522f42e31787">
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<rdf:value>This cellML model is known to run in both PCEnv and COR to recreate the results in the published paper. The units have been checked and they are consistent. Please note that many of the figures in the paper are complex and requite special simulation conditions. This particular CellMl model represents the basic core model presented in the paper. Initial conditions can be modified to generate more complex results. We thank the model author Prakash Vempati for his assistance in getting this CellML model to run.</rdf:value>
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<vCard:Orgname>The University of Auckland</vCard:Orgname>
<vCard:Orgunit>The Bioengineering Institute</vCard:Orgunit>
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<vCard:Given>Catherine</vCard:Given>
<vCard:Family>Lloyd</vCard:Family>
<vCard:Other>May</vCard:Other>
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</rdf:RDF>
</model>
