- Author:
- pmr2.import <nobody@models.cellml.org>
- Date:
- 2009-06-17 14:35:10+12:00
- Desc:
- committing version03 of huang_ferrell_1996
- Permanent Source URI:
- http://models.cellml.org/workspace/huang_ferrell_1996/rawfile/894b74cd8207449ee56d2d701688c111b20ab53d/huang_ferrell_1996.cellml
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This CellML file was generated on 10/19/2007 at 1:20:11 at PM using:
COR (0.9.31.769)
Copyright 2002-2007 Dr Alan Garny
http://COR.physiol.ox.ac.uk/ - COR@physiol.ox.ac.uk
CellML 1.0 was used to generate this cellular model
http://www.CellML.org/
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<article>
<articleinfo>
<title>The Mitogen-Activated Protein Kinase (MAPK) Cascade</title>
<author>
<firstname>James</firstname>
<surname>Lawson</surname>
<affiliation>
<shortaffil>Bioengineering Institute, University of Auckland</shortaffil>
</affiliation>
</author>
</articleinfo>
<section id="sec_status">
<title>Model Status</title>
<para>
This model has been rebuilt using the differential rate equations that Ferrel et al. use in their paper to describe the signalling pathway. This model is able to reproduce precisely the same output as that given by running the Mathematica description of the model (provided by the author) using the Mathematica NDSolve integration algorithm. This version of the model runs in both PCEnv (0.2+) and COR.
</para>
</section>
<sect1 id="sec_structure">
<title>Model Structure</title>
<para>
The mitogen-activated protein kinase (MAPK) cascade is a series of three protein kinases. Although the biological responses associated with this signalling pathway are diverse, the structure of the MAPK cascade is highly conserved between organisms (see the figure below). The cascade relays signals from the plasma membrane to targets in the cytoplasm and nucleus, often with the affect of amplifying the signal.
</para>
<para>
This model is based on Chi-Ying Huang and James Ferrell's mathematical model of the MAPK cascade, which they describe as a series of phosphorylation and dephosphorylation reactions (1996). Ordinary differential equations (ODEs) describe sequential phosphorylation by kinases and dephosphorylation by phosphatases. The ODEs are derived from the general description of enzymatic reactions based on Michaelis-Menten kinetics.
</para>
<para>
The complete original paper reference is cited below:
</para>
<para>
<ulink url="http://www.pnas.org/cgi/content/abstract/93/19/10078">Ultrasensitivity in the mitogen-activated protein cascade</ulink>, Chi-Ying F. Huang and James E. Ferrell, Jr., 1996, <ulink url="http://www.pnas.org/">
<emphasis>Proc. Natl. Acad. Sci. USA</emphasis>
</ulink>, 93, 10078-10083. (A <ulink url="http://www.pnas.org/cgi/reprint/93/19/10078.pdf">PDF</ulink> of the article is available to subscribers on the PNAS website.) <ulink url="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&list_uids=8816754&dopt=Abstract">PubMed ID: 8816754</ulink>
</para>
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<title>the conventional rendering of the MAPK cascade</title>
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<caption>A rendering of the MAPK cascade. Species are represented by rounded rectangles, and reactions by arrows. The action of a catalyst on a reaction is represented by dashed lines.</caption>
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<para>
In CellML, models are thought of as connected networks of discrete components. These components may correspond to physiologically separated regions or chemically distinct objects, or may be useful modelling abstractions. The CellML rendering of the MAPK cascade model is shown in the second figure below (the different shapes in the diagram are explained in the notation guide). The action of a catalyst on a reaction is represented by dashed lines.
</para>
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<caption>The CellML rendering of the MAPK cascade. The action of a catalyst on a reaction is demonstrated by dashed lines.</caption>
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</sect1>
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<apply>
<times/>
<ci>d4</ci>
<ci>mekstarmekpase</ci>
</apply>
<apply>
<times/>
<ci>k3</ci>
<ci>mekmosstar</ci>
</apply>
<apply>
<times/>
<ci>k6</ci>
<ci>mekstarstarmekpase</ci>
</apply>
<apply>
<times/>
<ci>d5</ci>
<ci>mekstarmosstar</ci>
</apply>
</apply>
<apply>
<times/>
<ci>a5</ci>
<ci>mekstar</ci>
<ci>mosstar</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="mekstarmekpase">
<variable units="micromolar" public_interface="out" name="mekstarmekpase" initial_value="0"/>
<variable units="second" public_interface="in" name="time"/>
<variable units="second_order_rate_constant_units" public_interface="in" name="a4"/>
<variable units="second_order_rate_constant_units" public_interface="in" name="d4"/>
<variable units="first_order_rate_constant_units" public_interface="in" name="k4"/>
<variable units="micromolar" public_interface="in" name="mekstar"/>
<variable units="micromolar" public_interface="in" name="mekpasetot"/>
<variable units="micromolar" public_interface="in" name="mekstarstarmekpase"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>mekstarmekpase</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci>a4</ci>
<ci>mekstar</ci>
<apply>
<minus/>
<apply>
<minus/>
<ci>mekpasetot</ci>
<ci>mekstarmekpase</ci>
</apply>
<ci>mekstarstarmekpase</ci>
</apply>
</apply>
<apply>
<times/>
<apply>
<plus/>
<ci>d4</ci>
<ci>k4</ci>
</apply>
<ci>mekstarmekpase</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="mekstarmosstar">
<variable units="second" public_interface="in" name="time"/>
<variable units="micromolar" public_interface="out" name="mekstarmosstar" initial_value="0"/>
<variable units="second_order_rate_constant_units" public_interface="in" name="a5"/>
<variable units="second_order_rate_constant_units" public_interface="in" name="d5"/>
<variable units="first_order_rate_constant_units" public_interface="in" name="k5"/>
<variable units="micromolar" public_interface="in" name="mekstar"/>
<variable units="micromolar" public_interface="in" name="mosstar"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>mekstarmosstar</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci>a5</ci>
<ci>mekstar</ci>
<ci>mosstar</ci>
</apply>
<apply>
<times/>
<apply>
<plus/>
<ci>d5</ci>
<ci>k5</ci>
</apply>
<ci>mekstarmosstar</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="mekstarstar">
<variable units="second" public_interface="in" name="time"/>
<variable units="micromolar" public_interface="out" name="mekstarstar" initial_value="0"/>
<variable units="first_order_rate_constant_units" public_interface="in" name="k5"/>
<variable units="micromolar" public_interface="in" name="mekstarmosstar"/>
<variable units="second_order_rate_constant_units" public_interface="in" name="a6"/>
<variable units="micromolar" public_interface="in" name="mekpasetot"/>
<variable units="micromolar" public_interface="in" name="mekstarmekpase"/>
<variable units="second_order_rate_constant_units" public_interface="in" name="d6"/>
<variable units="micromolar" public_interface="in" name="mekstarstarmekpase"/>
<variable units="second_order_rate_constant_units" public_interface="in" name="a7"/>
<variable units="micromolar" public_interface="in" name="mapktot"/>
<variable units="micromolar" public_interface="in" name="mapkstar"/>
<variable units="micromolar" public_interface="in" name="mapkstarstar"/>
<variable units="micromolar" public_interface="in" name="mapkstarmapkpase"/>
<variable units="micromolar" public_interface="in" name="mapkstarstarmapkpase"/>
<variable units="micromolar" public_interface="in" name="mapkmekstarstar"/>
<variable units="micromolar" public_interface="in" name="mapkstarmekstarstar"/>
<variable units="second_order_rate_constant_units" public_interface="in" name="d7"/>
<variable units="first_order_rate_constant_units" public_interface="in" name="k7"/>
<variable units="second_order_rate_constant_units" public_interface="in" name="d9"/>
<variable units="first_order_rate_constant_units" public_interface="in" name="k9"/>
<variable units="second_order_rate_constant_units" public_interface="in" name="a9"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>mekstarstar</ci>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<minus/>
<apply>
<times/>
<ci>k5</ci>
<ci>mekstarmosstar</ci>
</apply>
<apply>
<times/>
<ci>a6</ci>
<ci>mekstarstar</ci>
<apply>
<minus/>
<apply>
<minus/>
<ci>mekpasetot</ci>
<ci>mekstarmekpase</ci>
</apply>
<ci>mekstarstarmekpase</ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci>d6</ci>
<ci>mekstarstarmekpase</ci>
</apply>
</apply>
<apply>
<times/>
<ci>a7</ci>
<ci>mekstarstar</ci>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<minus/>
<ci>mapktot</ci>
<ci>mapkstar</ci>
</apply>
<ci>mapkstarstar</ci>
</apply>
<ci>mapkstarmapkpase</ci>
</apply>
<ci>mapkstarstarmapkpase</ci>
</apply>
<ci>mapkmekstarstar</ci>
</apply>
<ci>mapkstarmekstarstar</ci>
</apply>
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<apply>
<times/>
<apply>
<plus/>
<ci>d7</ci>
<ci>k7</ci>
</apply>
<ci>mapkmekstarstar</ci>
</apply>
<apply>
<times/>
<apply>
<plus/>
<ci>d9</ci>
<ci>k9</ci>
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<ci>mapkstarmekstarstar</ci>
</apply>
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<apply>
<times/>
<ci>a9</ci>
<ci>mapkstar</ci>
<ci>mekstarstar</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="mekstarstarmekpase">
<variable units="second" public_interface="in" name="time"/>
<variable units="micromolar" public_interface="out" name="mekstarstarmekpase" initial_value="0"/>
<variable units="second_order_rate_constant_units" public_interface="in" name="a6"/>
<variable units="micromolar" public_interface="in" name="mekstarstar"/>
<variable units="micromolar" public_interface="in" name="mekpasetot"/>
<variable units="micromolar" public_interface="in" name="mekstarmekpase"/>
<variable units="second_order_rate_constant_units" public_interface="in" name="d6"/>
<variable units="first_order_rate_constant_units" public_interface="in" name="k6"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>mekstarstarmekpase</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci>a6</ci>
<ci>mekstarstar</ci>
<apply>
<minus/>
<apply>
<minus/>
<ci>mekpasetot</ci>
<ci>mekstarmekpase</ci>
</apply>
<ci>mekstarstarmekpase</ci>
</apply>
</apply>
<apply>
<times/>
<apply>
<plus/>
<ci>d6</ci>
<ci>k6</ci>
</apply>
<ci>mekstarstarmekpase</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="mapk">
<variable units="second" public_interface="in" name="time"/>
<variable units="micromolar" public_interface="out" name="mapk" initial_value="1.2"/>
<variable units="second_order_rate_constant_units" public_interface="in" name="a7"/>
<variable units="micromolar" public_interface="in" name="mapktot"/>
<variable units="micromolar" public_interface="in" name="mapkstar"/>
<variable units="micromolar" public_interface="in" name="mapkstarstar"/>
<variable units="micromolar" public_interface="in" name="mapkstarmapkpase"/>
<variable units="micromolar" public_interface="in" name="mapkstarstarmapkpase"/>
<variable units="micromolar" public_interface="in" name="mapkmekstarstar"/>
<variable units="micromolar" public_interface="in" name="mapkstarmekstarstar"/>
<variable units="micromolar" public_interface="in" name="mekstarstar"/>
<variable units="second_order_rate_constant_units" public_interface="in" name="d7"/>
<variable units="first_order_rate_constant_units" public_interface="in" name="k8"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>mapk</ci>
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<apply>
<plus/>
<apply>
<times/>
<apply>
<minus/>
<ci>a7</ci>
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<apply>
<minus/>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<minus/>
<ci>mapktot</ci>
<ci>mapkstar</ci>
</apply>
<ci>mapkstarstar</ci>
</apply>
<ci>mapkstarmapkpase</ci>
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<ci>mapkstarstarmapkpase</ci>
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<ci>mapkmekstarstar</ci>
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<ci>mapkstarmekstarstar</ci>
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<ci>mekstarstar</ci>
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<apply>
<times/>
<ci>d7</ci>
<ci>mapkmekstarstar</ci>
</apply>
<apply>
<times/>
<ci>k8</ci>
<ci>mapkstarmapkpase</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="mapkmekstarstar">
<variable units="second" public_interface="in" name="time"/>
<variable units="micromolar" public_interface="out" name="mapkmekstarstar" initial_value="0"/>
<variable units="micromolar" public_interface="in" name="mapktot"/>
<variable units="micromolar" public_interface="in" name="mapkstar"/>
<variable units="micromolar" public_interface="in" name="mapkstarstar"/>
<variable units="micromolar" public_interface="in" name="mapkstarmapkpase"/>
<variable units="micromolar" public_interface="in" name="mapkstarstarmapkpase"/>
<variable units="micromolar" public_interface="in" name="mapkstarmekstarstar"/>
<variable units="micromolar" public_interface="in" name="mekstarstar"/>
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<variable units="first_order_rate_constant_units" public_interface="in" name="k7"/>
<variable units="second_order_rate_constant_units" public_interface="in" name="a7"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>mapkmekstarstar</ci>
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<minus/>
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<times/>
<ci>a7</ci>
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<minus/>
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<minus/>
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<minus/>
<apply>
<minus/>
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<minus/>
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<minus/>
<ci>mapktot</ci>
<ci>mapkstar</ci>
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<ci>mapkstarstar</ci>
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<ci>mapkstarmapkpase</ci>
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<ci>mapkstarstarmapkpase</ci>
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<ci>mapkmekstarstar</ci>
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<ci>mapkstarmekstarstar</ci>
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<ci>mekstarstar</ci>
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<times/>
<apply>
<plus/>
<ci>d7</ci>
<ci>k7</ci>
</apply>
<ci>mapkmekstarstar</ci>
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<component name="mapkstar">
<variable units="second" public_interface="in" name="time"/>
<variable units="micromolar" public_interface="out" name="mapkstar" initial_value="0"/>
<variable units="first_order_rate_constant_units" public_interface="in" name="k7"/>
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<variable units="micromolar" public_interface="in" name="mapkpasetot"/>
<variable units="micromolar" public_interface="in" name="mapkstarmapkpase"/>
<variable units="micromolar" public_interface="in" name="mapkstarstarmapkpase"/>
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<variable units="micromolar" public_interface="in" name="mapkstarmekstarstar"/>
<variable units="first_order_rate_constant_units" public_interface="in" name="k10"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
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<eq/>
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<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>mapkstar</ci>
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<plus/>
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<minus/>
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<plus/>
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<minus/>
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<times/>
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<ci>mapkmekstarstar</ci>
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<times/>
<ci>a8</ci>
<ci>mapkstar</ci>
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<minus/>
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<minus/>
<ci>mapkpasetot</ci>
<ci>mapkstarmapkpase</ci>
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<ci>mapkstarstarmapkpase</ci>
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<ci>mapkstarmapkpase</ci>
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<times/>
<ci>a9</ci>
<ci>mapkstar</ci>
<ci>mekstarstar</ci>
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<times/>
<ci>d9</ci>
<ci>mapkstarmekstarstar</ci>
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<apply>
<times/>
<ci>k10</ci>
<ci>mapkstarstarmapkpase</ci>
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<component name="mapkstarmekstarstar">
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<variable units="micromolar" public_interface="out" name="mapkstarmekstarstar" initial_value="0"/>
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<variable units="first_order_rate_constant_units" public_interface="in" name="k9"/>
<variable units="micromolar" public_interface="in" name="mapkstar"/>
<variable units="micromolar" public_interface="in" name="mekstarstar"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
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<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>mapkstarmekstarstar</ci>
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<minus/>
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<times/>
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<ci>mekstarstar</ci>
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<times/>
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<plus/>
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<ci>k9</ci>
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<ci>mapkstarmekstarstar</ci>
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<component name="mapkstarstar">
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<variable units="micromolar" public_interface="out" name="mapkstarstar" initial_value="0"/>
<variable units="second_order_rate_constant_units" public_interface="in" name="a10"/>
<variable units="micromolar" public_interface="in" name="mapkpasetot"/>
<variable units="micromolar" public_interface="in" name="mapkstarmapkpase"/>
<variable units="micromolar" public_interface="in" name="mapkstarstarmapkpase"/>
<variable units="second_order_rate_constant_units" public_interface="in" name="d10"/>
<variable units="first_order_rate_constant_units" public_interface="in" name="k9"/>
<variable units="micromolar" public_interface="in" name="mapkstar"/>
<variable units="micromolar" public_interface="in" name="mekstarstar"/>
<variable units="micromolar" public_interface="in" name="mapkstarmekstarstar"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
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<eq/>
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<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>mapkstarstar</ci>
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<plus/>
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<times/>
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<minus/>
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<ci>mapkstarstar</ci>
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<minus/>
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<ci>mapkstarmapkpase</ci>
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<ci>mapkstarstarmapkpase</ci>
</apply>
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<ci>mapkstarstarmapkpase</ci>
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<apply>
<times/>
<ci>k9</ci>
<ci>mapkstarmekstarstar</ci>
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</component>
<component name="mapkstarmapkpase">
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<variable units="micromolar" public_interface="out" name="mapkstarmapkpase" initial_value="0"/>
<variable units="second_order_rate_constant_units" public_interface="in" name="a8"/>
<variable units="micromolar" public_interface="in" name="mapkstar"/>
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<variable units="micromolar" public_interface="in" name="mapkstarstarmapkpase"/>
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<variable units="first_order_rate_constant_units" public_interface="in" name="k8"/>
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<diff/>
<bvar>
<ci>time</ci>
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<ci>mapkstarmapkpase</ci>
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<minus/>
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<times/>
<ci>a8</ci>
<ci>mapkstar</ci>
<apply>
<minus/>
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<minus/>
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<ci>mapkstarmapkpase</ci>
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<ci>mapkstarstarmapkpase</ci>
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<plus/>
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<ci>k8</ci>
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<ci>mapkstarmapkpase</ci>
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</apply>
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<component name="mapkstarstarmapkpase">
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<variable units="micromolar" public_interface="out" name="mapkstarstarmapkpase" initial_value="0"/>
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<variable units="micromolar" public_interface="in" name="mapkstarmapkpase"/>
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<variable units="first_order_rate_constant_units" public_interface="in" name="k10"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
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<diff/>
<bvar>
<ci>time</ci>
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<ci>mapkstarstarmapkpase</ci>
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<minus/>
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<times/>
<ci>a10</ci>
<ci>mapkstarstar</ci>
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<minus/>
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<minus/>
<ci>mapkpasetot</ci>
<ci>mapkstarmapkpase</ci>
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<ci>mapkstarstarmapkpase</ci>
</apply>
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<times/>
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<plus/>
<ci>d10</ci>
<ci>k10</ci>
</apply>
<ci>mapkstarstarmapkpase</ci>
</apply>
</apply>
</apply>
</math>
</component>
<connection>
<map_components component_2="mos" component_1="environment"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="mos" component_1="rate_constants"/>
<map_variables variable_2="a1" variable_1="a1"/>
<map_variables variable_2="d1" variable_1="d1"/>
<map_variables variable_2="k2" variable_1="k2"/>
</connection>
<connection>
<map_components component_2="mos" component_1="total_concs"/>
<map_variables variable_2="mostot" variable_1="mostot"/>
<map_variables variable_2="e1tot" variable_1="e1tot"/>
</connection>
<connection>
<map_components component_2="mos" component_1="mosstar"/>
<map_variables variable_2="mosstar" variable_1="mosstar"/>
</connection>
<connection>
<map_components component_2="mos" component_1="mose1"/>
<map_variables variable_2="mose1" variable_1="mose1"/>
</connection>
<connection>
<map_components component_2="mos" component_1="mosstare2"/>
<map_variables variable_2="mosstare2" variable_1="mosstare2"/>
</connection>
<connection>
<map_components component_2="mos" component_1="mekmosstar"/>
<map_variables variable_2="mekmosstar" variable_1="mekmosstar"/>
</connection>
<connection>
<map_components component_2="mos" component_1="mekstarmosstar"/>
<map_variables variable_2="mekstarmosstar" variable_1="mekstarmosstar"/>
</connection>
<connection>
<map_components component_2="mose1" component_1="environment"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="mose1" component_1="rate_constants"/>
<map_variables variable_2="a1" variable_1="a1"/>
<map_variables variable_2="d1" variable_1="d1"/>
<map_variables variable_2="k1" variable_1="k1"/>
</connection>
<connection>
<map_components component_2="mose1" component_1="total_concs"/>
<map_variables variable_2="mostot" variable_1="mostot"/>
<map_variables variable_2="e1tot" variable_1="e1tot"/>
</connection>
<connection>
<map_components component_2="mose1" component_1="mosstar"/>
<map_variables variable_2="mosstar" variable_1="mosstar"/>
<map_variables variable_2="mose1" variable_1="mose1"/>
</connection>
<connection>
<map_components component_2="mose1" component_1="mosstare2"/>
<map_variables variable_2="mosstare2" variable_1="mosstare2"/>
</connection>
<connection>
<map_components component_2="mose1" component_1="mekmosstar"/>
<map_variables variable_2="mekmosstar" variable_1="mekmosstar"/>
</connection>
<connection>
<map_components component_2="mose1" component_1="mekstarmosstar"/>
<map_variables variable_2="mekstarmosstar" variable_1="mekstarmosstar"/>
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