- Author:
- Catherine Lloyd <c.lloyd@auckland.ac.nz>
- Date:
- 2010-08-06 04:33:08+12:00
- Desc:
- Added RDF namespaces back into model a.
- Permanent Source URI:
- https://models.cellml.org/workspace/goldbeter_pourquie_2008/rawfile/1de828a087394d6ddad04119ad0d5812c1193df1/goldbeter_pourquie_2008_a.cellml
<?xml version="1.0"?>
<!-- FILE : goldbeter_model_2008.xml
--><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#" xmlns:ns7="http://www.cellml.org/metadata/simulation/1.0#" cmeta:id="goldbeter_model_2008" name="goldbeter_model_2008">
<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
<section id="sec_status">
<title>Model Status</title>
<para>
This CellML model runs in both PCEnv and COR to recreate the published results. The units have been checked and they are consistent. In this particular version of the model couples the Notch, Wnt and FGF signalling pathways together and so uses equations A17 and A18 in the appendix to replace equations A4 and A10 respectively.
</para>
</section>
<sect1 id="sec_structure">
<title>Model Structure</title>
<para>
ABSTRACT: The formation of somites in the course of vertebrate segmentation is governed by an oscillator known as the segmentation clock, which is characterized by a period ranging from 30 min to a few hours depending on the organism. This oscillator permits the synchronized activation of segmentation genes in successive cohorts of cells in the presomitic mesoderm in response to a periodic signal emitted by the segmentation clock, thereby defining the future segments. Recent microarray experiments [Dequeant, M.L., Glynn, E., Gaudenz, K., Wahl, M., Chen, J., Mushegian, A., Pourquie, O., 2006. A complex oscillating network of signaling genes underlies the mouse segmentation clock. Science 314, 1595-1598] indicate that the Notch, Wnt and Fibroblast Growth Factor (FGF) signaling pathways are involved in the mechanism of the segmentation clock. By means of computational modeling, we investigate the conditions in which sustained oscillations occur in these three signaling pathways. First we show that negative feedback mediated by the Lunatic Fringe protein on intracellular Notch activation can give rise to periodic behavior in the Notch pathway. We then show that negative feedback exerted by Axin2 on the degradation of beta-catenin through formation of the Axin2 destruction complex can produce oscillations in the Wnt pathway. Likewise, negative feedback on FGF signaling mediated by the phosphatase product of the gene MKP3/Dusp6 can produce oscillatory gene expression in the FGF pathway. Coupling the Wnt, Notch and FGF oscillators through common intermediates can lead to synchronized oscillations in the three signaling pathways or to complex periodic behavior, depending on the relative periods of oscillations in the three pathways. The phase relationships between cycling genes in the three pathways depend on the nature of the coupling between the pathways and on their relative autonomous periods. The model provides a framework for analyzing the dynamics of the segmentation clock in terms of a network of oscillating modules involving the Wnt, Notch and FGF signaling pathways.
</para>
<para>
The complete original paper reference is cited below:
</para>
<para>
Modeling the segmentation clock as a network of coupled oscillations in the Notch, Wnt and FGF signaling pathways, Albert Goldbeter and Olivier Pourquie, 2008, <emphasis>Journal of Theoretical Biology</emphasis>, 252, 574-585. <ulink url="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&amp;db=PubMed&amp;list_uids=18308339&amp;dopt=Abstract">PubMed ID: 18308339</ulink>
</para>
<informalfigure float="0" id="fig_reaction_diagram">
<mediaobject>
<imageobject>
<objectinfo>
<title>cell diagram</title>
</objectinfo>
<imagedata fileref="goldbeter_2008.png"/>
</imageobject>
</mediaobject>
<caption>Schematic diagram representing the model for the segmentation clock based on negative feedback loops in the coupled FGF, Wnt and Notch signalling pathways.</caption>
</informalfigure>
</sect1>
</article>
</documentation>
<units name="minute">
<unit multiplier="60" units="second"/>
</units>
<units name="first_order_rate_constant">
<unit exponent="-1" units="minute"/>
</units>
<units name="second_order_rate_constant">
<unit exponent="-1" units="nanomolar"/>
<unit exponent="-1" units="minute"/>
</units>
<units name="flux">
<unit units="nanomolar"/>
<unit exponent="-1" units="minute"/>
</units>
<units name="nanomolar">
<unit prefix="nano" units="mole"/>
<unit exponent="-1" units="litre"/>
</units>
<component name="environment">
<variable cmeta:id="environment_time" name="time" public_interface="out" units="minute"/>
</component>
<!-- Notch signalling module -->
<component cmeta:id="N" name="N">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#N">
<dc:title xmlns:dc="http://purl.org/dc/elements/1.1/">N</dc:title>
<dcterms:alternative xmlns:dcterms="http://purl.org/dc/terms/">Notch protein</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable cmeta:id="N_N" initial_value="0.5" name="N" public_interface="out" units="nanomolar"/>
<variable initial_value="1.4" name="KdN" units="nanomolar"/>
<variable initial_value="0.23" name="vsN" units="flux"/>
<variable initial_value="2.82" name="vdN" units="flux"/>
<variable name="kc" public_interface="in" units="first_order_rate_constant"/>
<variable name="KIF" public_interface="in" units="nanomolar"/>
<variable name="F" public_interface="in" units="nanomolar"/>
<variable name="epsilon" public_interface="in" units="dimensionless"/>
<variable name="j" public_interface="in" units="dimensionless"/>
<variable name="time" public_interface="in" units="minute"/>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="1">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>N</ci>
</apply>
<apply>
<times/>
<ci> epsilon </ci>
<apply>
<minus/>
<ci> vsN </ci>
<apply>
<plus/>
<apply>
<times/>
<ci> vdN </ci>
<apply>
<divide/>
<ci> N </ci>
<apply>
<plus/>
<ci> KdN </ci>
<ci> N </ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci> kc </ci>
<ci> N </ci>
<apply>
<divide/>
<apply>
<power/>
<ci> KIF </ci>
<ci> j </ci>
</apply>
<apply>
<plus/>
<apply>
<power/>
<ci> KIF </ci>
<ci> j </ci>
</apply>
<apply>
<power/>
<ci> F </ci>
<ci> j </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component cmeta:id="Na" name="Na">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#Na">
<dc:title xmlns:dc="http://purl.org/dc/elements/1.1/">Na</dc:title>
<dcterms:alternative xmlns:dcterms="http://purl.org/dc/terms/">cytosolic active Notch protein</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable initial_value="0.2" name="Na" public_interface="out" units="nanomolar"/>
<variable name="Vtr" public_interface="out" units="flux"/>
<variable initial_value="0.001" name="KdNa" units="nanomolar"/>
<variable initial_value="0.01" name="VdNa" units="flux"/>
<variable initial_value="0.1" name="kt1" units="first_order_rate_constant"/>
<variable initial_value="0.1" name="kt2" units="first_order_rate_constant"/>
<variable name="kc" public_interface="in" units="first_order_rate_constant"/>
<variable name="N" public_interface="in" units="nanomolar"/>
<variable name="Nan" public_interface="in" units="nanomolar"/>
<variable name="KIF" public_interface="in" units="nanomolar"/>
<variable name="F" public_interface="in" units="nanomolar"/>
<variable name="epsilon" public_interface="in" units="dimensionless"/>
<variable name="j" public_interface="in" units="dimensionless"/>
<variable name="time" public_interface="in" units="minute"/>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="2">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>Na</ci>
</apply>
<apply>
<times/>
<ci> epsilon </ci>
<apply>
<minus/>
<apply>
<times/>
<ci> kc </ci>
<ci> N </ci>
<apply>
<divide/>
<apply>
<power/>
<ci> KIF </ci>
<ci> j </ci>
</apply>
<apply>
<plus/>
<apply>
<power/>
<ci> KIF </ci>
<ci> j </ci>
</apply>
<apply>
<power/>
<ci> F </ci>
<ci> j </ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<plus/>
<apply>
<times/>
<ci> VdNa </ci>
<apply>
<divide/>
<ci> Na </ci>
<apply>
<plus/>
<ci> KdNa </ci>
<ci> Na </ci>
</apply>
</apply>
</apply>
<ci> Vtr </ci>
</apply>
</apply>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="2a">
<apply>
<eq/>
<ci>Vtr</ci>
<apply>
<minus/>
<apply>
<times/>
<ci> kt1 </ci>
<ci> Na </ci>
</apply>
<apply>
<times/>
<ci> kt2 </ci>
<ci> Nan </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component cmeta:id="Nan" name="Nan">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#Nan">
<dc:title xmlns:dc="http://purl.org/dc/elements/1.1/">Nan</dc:title>
<dcterms:alternative xmlns:dcterms="http://purl.org/dc/terms/">nuclear active Notch protein</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable initial_value="0.0" name="Nan" public_interface="out" units="nanomolar"/>
<variable initial_value="0.001" name="KdNan" units="nanomolar"/>
<variable initial_value="0.1" name="VdNan" units="flux"/>
<variable name="epsilon" public_interface="in" units="dimensionless"/>
<variable name="Vtr" public_interface="in" units="flux"/>
<variable name="time" public_interface="in" units="minute"/>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="3">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>Nan</ci>
</apply>
<apply>
<times/>
<ci> epsilon </ci>
<apply>
<minus/>
<ci> Vtr </ci>
<apply>
<times/>
<ci> VdNan </ci>
<apply>
<divide/>
<ci> Nan </ci>
<apply>
<plus/>
<ci> KdNan </ci>
<ci> Nan </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component cmeta:id="MF" name="MF">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#MF">
<dc:title xmlns:dc="http://purl.org/dc/elements/1.1/">MF</dc:title>
<dcterms:alternative xmlns:dcterms="http://purl.org/dc/terms/">Lunatic fringe mRNA</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable cmeta:id="MF_MF" initial_value="0.1" name="MF" public_interface="out" units="nanomolar"/>
<variable initial_value="0.768" name="KdMF" units="nanomolar"/>
<variable initial_value="2.5" name="KIG1" units="nanomolar"/>
<variable name="vsFK" units="flux"/>
<variable initial_value="3.0" name="vsF" units="flux"/>
<variable initial_value="1.92" name="vmF" units="flux"/>
<variable initial_value="0.05" name="KA" units="nanomolar"/>
<variable name="kc" public_interface="in" units="first_order_rate_constant"/>
<variable name="Nan" public_interface="in" units="nanomolar"/>
<variable name="K" public_interface="in" units="nanomolar"/>
<variable name="epsilon" public_interface="in" units="dimensionless"/>
<variable name="p" public_interface="in" units="dimensionless"/>
<variable name="time" public_interface="in" units="minute"/>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="4">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>MF</ci>
</apply>
<apply>
<times/>
<ci> epsilon </ci>
<apply>
<minus/>
<apply>
<times/>
<ci> vsFK </ci>
<apply>
<divide/>
<apply>
<power/>
<ci> Nan </ci>
<ci> p </ci>
</apply>
<apply>
<plus/>
<apply>
<power/>
<ci> KA </ci>
<ci> p </ci>
</apply>
<apply>
<power/>
<ci> Nan </ci>
<ci> p </ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci> vmF </ci>
<apply>
<divide/>
<ci> MF </ci>
<apply>
<plus/>
<ci> KdMF </ci>
<ci> MF </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="4a">
<apply>
<eq/>
<ci>vsFK</ci>
<apply>
<times/>
<ci> vsF </ci>
<apply>
<divide/>
<ci> KIG1 </ci>
<apply>
<plus/>
<ci> KIG1 </ci>
<ci> K </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component cmeta:id="F" name="F">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#F">
<dc:title xmlns:dc="http://purl.org/dc/elements/1.1/">F</dc:title>
<dcterms:alternative xmlns:dcterms="http://purl.org/dc/terms/">Lunatic fringe protein</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable cmeta:id="F_F" initial_value="0.001" name="F" public_interface="out" units="nanomolar"/>
<variable initial_value="0.37" name="KdF" units="nanomolar"/>
<variable initial_value="0.39" name="vdF" units="flux"/>
<variable initial_value="0.3" name="ksF" units="first_order_rate_constant"/>
<variable name="MF" public_interface="in" units="nanomolar"/>
<variable name="epsilon" public_interface="in" units="dimensionless"/>
<variable name="time" public_interface="in" units="minute"/>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="5">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>F</ci>
</apply>
<apply>
<times/>
<ci> epsilon </ci>
<apply>
<minus/>
<apply>
<times/>
<ci> ksF </ci>
<ci> MF </ci>
</apply>
<apply>
<times/>
<ci> vdF </ci>
<apply>
<divide/>
<ci> F </ci>
<apply>
<plus/>
<ci> KdF </ci>
<ci> F </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<!-- Wnt signalling module -->
<component cmeta:id="K" name="K">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#K">
<dc:title xmlns:dc="http://purl.org/dc/elements/1.1/">K</dc:title>
<dcterms:alternative xmlns:dcterms="http://purl.org/dc/terms/">free kinase Gsk3</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable cmeta:id="K_K" initial_value="3.0" name="K" public_interface="out" units="nanomolar"/>
<variable name="V1" public_interface="in" units="flux"/>
<variable name="theta" public_interface="in" units="dimensionless"/>
<variable name="time" public_interface="in" units="minute"/>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="6">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>K</ci>
</apply>
<apply>
<times/>
<ci> theta </ci>
<ci> V1 </ci>
</apply>
</apply>
</math>
</component>
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<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#B">
<dc:title xmlns:dc="http://purl.org/dc/elements/1.1/">B</dc:title>
<dcterms:alternative xmlns:dcterms="http://purl.org/dc/terms/">non-phosphorylated beta-catenin</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable cmeta:id="B_B" initial_value="0.1" name="B" public_interface="out" units="nanomolar"/>
<variable initial_value="0.0" name="kd1" units="first_order_rate_constant"/>
<variable initial_value="0.087" name="vsB" units="flux"/>
<variable name="VK" public_interface="in" units="flux"/>
<variable name="VP" public_interface="in" units="flux"/>
<variable name="V2" public_interface="in" units="flux"/>
<variable name="Kt" public_interface="in" units="nanomolar"/>
<variable name="AK" public_interface="in" units="nanomolar"/>
<variable name="theta" public_interface="in" units="dimensionless"/>
<variable name="time" public_interface="in" units="minute"/>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="7">
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<eq/>
<apply>
<diff/>
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<ci>time</ci>
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<ci>B</ci>
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<times/>
<ci> theta </ci>
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<apply>
<plus/>
<ci> vsB </ci>
<ci> VP </ci>
<ci> V2 </ci>
</apply>
<apply>
<plus/>
<apply>
<times/>
<ci> VK </ci>
<apply>
<divide/>
<ci> AK </ci>
<ci> Kt </ci>
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<apply>
<times/>
<ci> kd1 </ci>
<ci> B </ci>
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<rdf:Description rdf:about="#Bp">
<dc:title xmlns:dc="http://purl.org/dc/elements/1.1/">Bp</dc:title>
<dcterms:alternative xmlns:dcterms="http://purl.org/dc/terms/">phosphorylated beta-catenin</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
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<variable initial_value="7.062" name="kd2" units="first_order_rate_constant"/>
<variable name="VK" public_interface="in" units="flux"/>
<variable name="VP" public_interface="in" units="flux"/>
<variable name="Kt" public_interface="in" units="nanomolar"/>
<variable name="AK" public_interface="in" units="nanomolar"/>
<variable name="theta" public_interface="in" units="dimensionless"/>
<variable name="time" public_interface="in" units="minute"/>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="8">
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<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>Bp</ci>
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<times/>
<ci> theta </ci>
<apply>
<minus/>
<apply>
<times/>
<ci> VK </ci>
<apply>
<divide/>
<ci> AK </ci>
<ci> Kt </ci>
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<plus/>
<ci> VP </ci>
<apply>
<times/>
<ci> kd2 </ci>
<ci> Bp </ci>
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<rdf:Description rdf:about="#BN">
<dc:title xmlns:dc="http://purl.org/dc/elements/1.1/">BN</dc:title>
<dcterms:alternative xmlns:dcterms="http://purl.org/dc/terms/">nuclear beta-catenin</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
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<variable name="V2" public_interface="in" units="flux"/>
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<variable name="time" public_interface="in" units="minute"/>
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<eq/>
<apply>
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<apply>
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<ci> theta </ci>
<ci> V2 </ci>
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<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#MAx">
<dc:title xmlns:dc="http://purl.org/dc/elements/1.1/">MAx</dc:title>
<dcterms:alternative xmlns:dcterms="http://purl.org/dc/terms/">Axin2 mRNA</dcterms:alternative>
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<variable initial_value="0.06" name="v0" units="flux"/>
<variable initial_value="1.64" name="vMB" units="flux"/>
<variable initial_value="0.8" name="vmd" units="flux"/>
<variable initial_value="0.7" name="KaB" units="nanomolar"/>
<variable initial_value="0.05" name="KaXa" units="nanomolar"/>
<variable initial_value="0.48" name="Kmd" units="nanomolar"/>
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<variable name="Xa" public_interface="in" units="nanomolar"/>
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<variable name="time" public_interface="in" units="minute"/>
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<ci> vMB </ci>
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<ci> n </ci>
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<ci> n </ci>
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<apply>
<power/>
<ci> BN </ci>
<ci> n </ci>
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<ci> vMXa </ci>
<apply>
<divide/>
<apply>
<power/>
<ci> Xa </ci>
<ci> m </ci>
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<apply>
<plus/>
<apply>
<power/>
<ci> KaXa </ci>
<ci> m </ci>
</apply>
<apply>
<power/>
<ci> Xa </ci>
<ci> m </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci> vmd </ci>
<apply>
<divide/>
<ci> MAx </ci>
<apply>
<plus/>
<ci> Kmd </ci>
<ci> MAx </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component cmeta:id="A" name="A">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#A">
<dc:title xmlns:dc="http://purl.org/dc/elements/1.1/">A</dc:title>
<dcterms:alternative xmlns:dcterms="http://purl.org/dc/terms/">Axin2 protein</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable cmeta:id="A_A" initial_value="0.1" name="A" public_interface="out" units="nanomolar"/>
<variable initial_value="0.02" name="ksAx" units="first_order_rate_constant"/>
<variable initial_value="0.6" name="vdAx" units="flux"/>
<variable initial_value="0.63" name="KdAx" units="nanomolar"/>
<variable name="V1" public_interface="in" units="flux"/>
<variable name="MAx" public_interface="in" units="nanomolar"/>
<variable name="theta" public_interface="in" units="dimensionless"/>
<variable name="time" public_interface="in" units="minute"/>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="11">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>A</ci>
</apply>
<apply>
<times/>
<ci> theta </ci>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<times/>
<ci> ksAx</ci>
<ci> MAx </ci>
</apply>
<ci> V1 </ci>
</apply>
<apply>
<times/>
<ci> vdAx </ci>
<apply>
<divide/>
<ci> A </ci>
<apply>
<plus/>
<ci> KdAx </ci>
<ci> A </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="Wnt_parameters">
<variable name="AK" public_interface="out" units="nanomolar"/>
<variable name="V1" public_interface="out" units="flux"/>
<variable name="V2" public_interface="out" units="flux"/>
<variable name="VK" public_interface="out" units="flux"/>
<variable name="VP" public_interface="out" units="flux"/>
<variable initial_value="3.0" name="Kt" public_interface="out" units="nanomolar"/>
<variable initial_value="0.1" name="d1" units="first_order_rate_constant"/>
<variable initial_value="1.8" name="a1" units="second_order_rate_constant"/>
<variable initial_value="0.28" name="K1" units="nanomolar"/>
<variable initial_value="0.03" name="K2" units="nanomolar"/>
<variable initial_value="2.0" name="D" units="nanomolar"/>
<variable initial_value="0.5" name="KID" units="nanomolar"/>
<variable initial_value="0.7" name="kt3" units="first_order_rate_constant"/>
<variable initial_value="1.5" name="kt4" units="first_order_rate_constant"/>
<variable initial_value="5.08" name="VMK" units="flux"/>
<variable initial_value="1.0" name="VMP" units="flux"/>
<variable name="K" public_interface="in" units="nanomolar"/>
<variable name="A" public_interface="in" units="nanomolar"/>
<variable name="B" public_interface="in" units="nanomolar"/>
<variable name="Bp" public_interface="in" units="nanomolar"/>
<variable name="BN" public_interface="in" units="nanomolar"/>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="12">
<apply>
<eq/>
<ci> AK </ci>
<apply>
<minus/>
<ci> Kt </ci>
<ci> K </ci>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="13">
<apply>
<eq/>
<ci> V1 </ci>
<apply>
<minus/>
<apply>
<times/>
<ci> d1 </ci>
<ci> AK </ci>
</apply>
<apply>
<times/>
<ci> a1 </ci>
<ci> A </ci>
<ci> K </ci>
</apply>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="14">
<apply>
<eq/>
<ci> V2 </ci>
<apply>
<minus/>
<apply>
<times/>
<ci> kt4 </ci>
<ci> BN </ci>
</apply>
<apply>
<times/>
<ci> kt3 </ci>
<ci> B </ci>
</apply>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="15">
<apply>
<eq/>
<ci>VK</ci>
<apply>
<times/>
<ci> VMK </ci>
<apply>
<divide/>
<ci> KID </ci>
<apply>
<plus/>
<ci> KID </ci>
<ci> D </ci>
</apply>
</apply>
<apply>
<divide/>
<ci> B </ci>
<apply>
<plus/>
<ci> K1 </ci>
<ci> B </ci>
</apply>
</apply>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="16">
<apply>
<eq/>
<ci>VP</ci>
<apply>
<times/>
<ci> VMP </ci>
<apply>
<divide/>
<ci> Bp </ci>
<apply>
<plus/>
<ci> K2 </ci>
<ci> Bp </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<!-- FGF signalling module -->
<component cmeta:id="Rasa" name="Rasa">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#Rasa">
<dc:title xmlns:dc="http://purl.org/dc/elements/1.1/">Rasa</dc:title>
<dcterms:alternative xmlns:dcterms="http://purl.org/dc/terms/">active Ras</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable cmeta:id="Rasa_Rasa" initial_value="0.5" name="Rasa" public_interface="out" units="nanomolar"/>
<variable name="VaRas" public_interface="in" units="flux"/>
<variable name="VdRas" public_interface="in" units="flux"/>
<variable name="eta" public_interface="in" units="dimensionless"/>
<variable name="time" public_interface="in" units="minute"/>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="17">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>Rasa</ci>
</apply>
<apply>
<times/>
<ci> eta </ci>
<apply>
<minus/>
<ci> VaRas </ci>
<ci> VdRas </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component cmeta:id="ERKa" name="ERKa">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#ERKa">
<dc:title xmlns:dc="http://purl.org/dc/elements/1.1/">ERKa</dc:title>
<dcterms:alternative xmlns:dcterms="http://purl.org/dc/terms/">active ERK</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable cmeta:id="ERKa_ERKa" initial_value="0.2" name="ERKa" public_interface="out" units="nanomolar"/>
<variable name="VaErk" public_interface="in" units="flux"/>
<variable name="VdErk" public_interface="in" units="flux"/>
<variable name="eta" public_interface="in" units="dimensionless"/>
<variable name="time" public_interface="in" units="minute"/>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="18">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>ERKa</ci>
</apply>
<apply>
<times/>
<ci> eta </ci>
<apply>
<minus/>
<ci> VaErk </ci>
<ci> VdErk </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component cmeta:id="Xa" name="Xa">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#Xa">
<dc:title xmlns:dc="http://purl.org/dc/elements/1.1/">Xa</dc:title>
<dcterms:alternative xmlns:dcterms="http://purl.org/dc/terms/">active transcription factor X</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable cmeta:id="Xa_Xa" initial_value="0.1" name="Xa" public_interface="out" units="nanomolar"/>
<variable name="VaX" public_interface="in" units="flux"/>
<variable name="VdX" public_interface="in" units="flux"/>
<variable name="eta" public_interface="in" units="dimensionless"/>
<variable name="time" public_interface="in" units="minute"/>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="19">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>Xa</ci>
</apply>
<apply>
<times/>
<ci> eta </ci>
<apply>
<minus/>
<ci> VaX </ci>
<ci> VdX </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component cmeta:id="MDusp" name="MDusp">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#MDusp">
<dc:title xmlns:dc="http://purl.org/dc/elements/1.1/">MDusp</dc:title>
<dcterms:alternative xmlns:dcterms="http://purl.org/dc/terms/">MKP3/Dusp6 mRNA</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable cmeta:id="MDusp_MDusp" initial_value="0.1" name="MDusp" public_interface="out" units="nanomolar"/>
<variable name="VsMDusp" public_interface="in" units="flux"/>
<variable name="VdMDusp" public_interface="in" units="flux"/>
<variable name="eta" public_interface="in" units="dimensionless"/>
<variable name="time" public_interface="in" units="minute"/>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="20">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>MDusp</ci>
</apply>
<apply>
<times/>
<ci> eta </ci>
<apply>
<minus/>
<ci> VsMDusp </ci>
<ci> VdMDusp </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component cmeta:id="Dusp" name="Dusp">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#Dusp">
<dc:title xmlns:dc="http://purl.org/dc/elements/1.1/">Dusp</dc:title>
<dcterms:alternative xmlns:dcterms="http://purl.org/dc/terms/">MKP3/Dusp6 protein</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable cmeta:id="Dusp_Dusp" initial_value="0.1" name="Dusp" public_interface="out" units="nanomolar"/>
<variable initial_value="0.5" name="ksDusp" units="first_order_rate_constant"/>
<variable initial_value="2.0" name="vdDusp" units="flux"/>
<variable initial_value="0.5" name="KdDusp" units="nanomolar"/>
<variable name="MDusp" public_interface="in" units="nanomolar"/>
<variable name="eta" public_interface="in" units="dimensionless"/>
<variable name="time" public_interface="in" units="minute"/>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="21">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>Dusp</ci>
</apply>
<apply>
<times/>
<ci> eta </ci>
<apply>
<minus/>
<apply>
<times/>
<ci> ksDusp </ci>
<ci> MDusp </ci>
</apply>
<apply>
<times/>
<ci> vdDusp </ci>
<apply>
<divide/>
<ci> Dusp </ci>
<apply>
<plus/>
<ci> KdDusp </ci>
<ci> Dusp </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="FGF_parameters">
<variable name="VaRas" public_interface="out" units="flux"/>
<variable name="VdRas" public_interface="out" units="flux"/>
<variable name="VaErk" public_interface="out" units="flux"/>
<variable name="VdErk" public_interface="out" units="flux"/>
<variable name="VaX" public_interface="out" units="flux"/>
<variable name="VdX" public_interface="out" units="flux"/>
<variable name="VsMDusp" public_interface="out" units="flux"/>
<variable name="VdMDusp" public_interface="out" units="flux"/>
<variable name="Rasi" units="nanomolar"/>
<variable name="ERKi" units="nanomolar"/>
<variable name="Xi" units="nanomolar"/>
<variable initial_value="2.0" name="Rast" units="nanomolar"/>
<variable initial_value="2.0" name="ERKt" units="nanomolar"/>
<variable initial_value="2.0" name="Xt" units="nanomolar"/>
<variable initial_value="1.35" name="kcDusp" units="first_order_rate_constant"/>
<variable initial_value="4.968" name="VMaRas" units="flux"/>
<variable initial_value="0.41" name="VMdRas" units="flux"/>
<variable initial_value="3.30" name="VMaErk" units="flux"/>
<variable initial_value="1.6" name="VMaX" units="flux"/>
<variable initial_value="0.5" name="VMdX" units="flux"/>
<variable initial_value="0.9" name="VMsMDusp" units="flux"/>
<variable initial_value="0.5" name="VMdMDusp" units="flux"/>
<variable initial_value="1.0" name="Fgf" units="nanomolar"/>
<variable initial_value="0.5" name="KaFgf" units="nanomolar"/>
<variable initial_value="0.103" name="KaRas" units="nanomolar"/>
<variable initial_value="0.1" name="KdRas" units="nanomolar"/>
<variable initial_value="0.05" name="KdErk" units="nanomolar"/>
<variable initial_value="0.05" name="KaErk" units="nanomolar"/>
<variable initial_value="0.05" name="KaX" units="nanomolar"/>
<variable initial_value="0.05" name="KdX" units="nanomolar"/>
<variable initial_value="0.5" name="KaMDusp" units="nanomolar"/>
<variable initial_value="0.5" name="KdMDusp" units="nanomolar"/>
<variable initial_value="2.0" name="q" units="dimensionless"/>
<variable initial_value="2.0" name="r" units="dimensionless"/>
<variable name="Rasa" public_interface="in" units="nanomolar"/>
<variable name="ERKa" public_interface="in" units="nanomolar"/>
<variable name="Xa" public_interface="in" units="nanomolar"/>
<variable name="Dusp" public_interface="in" units="nanomolar"/>
<variable name="MDusp" public_interface="in" units="nanomolar"/>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="22">
<apply>
<eq/>
<ci> Rasi </ci>
<apply>
<minus/>
<ci> Rast </ci>
<ci> Rasa </ci>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="23">
<apply>
<eq/>
<ci> VaRas </ci>
<apply>
<times/>
<ci> VMaRas </ci>
<apply>
<divide/>
<apply>
<power/>
<ci> Fgf </ci>
<ci> r </ci>
</apply>
<apply>
<plus/>
<apply>
<power/>
<ci> KaFgf </ci>
<ci> r </ci>
</apply>
<apply>
<power/>
<ci> Fgf </ci>
<ci> r </ci>
</apply>
</apply>
</apply>
<apply>
<divide/>
<ci> Rasi </ci>
<apply>
<plus/>
<ci> KaRas </ci>
<ci> Rasi </ci>
</apply>
</apply>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="24">
<apply>
<eq/>
<ci> VdRas </ci>
<apply>
<times/>
<ci> VMdRas </ci>
<apply>
<divide/>
<ci> Rasa </ci>
<apply>
<plus/>
<ci> KdRas </ci>
<ci> Rasa </ci>
</apply>
</apply>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="25">
<apply>
<eq/>
<ci> ERKi </ci>
<apply>
<minus/>
<ci> ERKt </ci>
<ci> ERKa </ci>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="26">
<apply>
<eq/>
<ci> VaErk </ci>
<apply>
<times/>
<ci> VMaErk </ci>
<apply>
<divide/>
<ci> Rasa </ci>
<ci> Rast </ci>
</apply>
<apply>
<divide/>
<ci> ERKi </ci>
<apply>
<plus/>
<ci> KaErk </ci>
<ci> ERKi </ci>
</apply>
</apply>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="27">
<apply>
<eq/>
<ci> VdErk </ci>
<apply>
<times/>
<ci> kcDusp </ci>
<ci> Dusp </ci>
<apply>
<divide/>
<ci> ERKa </ci>
<apply>
<plus/>
<ci> KdErk </ci>
<ci> ERKa </ci>
</apply>
</apply>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="28">
<apply>
<eq/>
<ci> Xi </ci>
<apply>
<minus/>
<ci> Xt </ci>
<ci> Xa </ci>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="29">
<apply>
<eq/>
<ci> VaX </ci>
<apply>
<times/>
<ci> VMaX </ci>
<apply>
<divide/>
<ci> ERKa </ci>
<ci> ERKt </ci>
</apply>
<apply>
<divide/>
<ci> Xi </ci>
<apply>
<plus/>
<ci> KaX </ci>
<ci> Xi </ci>
</apply>
</apply>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="30">
<apply>
<eq/>
<ci> VdX </ci>
<apply>
<times/>
<ci> VMdX </ci>
<apply>
<divide/>
<ci> Xa </ci>
<apply>
<plus/>
<ci> KdX </ci>
<ci> Xa </ci>
</apply>
</apply>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="31">
<apply>
<eq/>
<ci> VsMDusp </ci>
<apply>
<times/>
<ci> VMsMDusp </ci>
<apply>
<divide/>
<apply>
<power/>
<ci> Xa </ci>
<ci> q </ci>
</apply>
<apply>
<plus/>
<apply>
<power/>
<ci> KaMDusp </ci>
<ci> q </ci>
</apply>
<apply>
<power/>
<ci> Xa </ci>
<ci> q </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="32">
<apply>
<eq/>
<ci> VdMDusp </ci>
<apply>
<times/>
<ci> VMdMDusp </ci>
<apply>
<divide/>
<ci> MDusp </ci>
<apply>
<plus/>
<ci> KdMDusp </ci>
<ci> MDusp </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="model_parameters">
<variable initial_value="3.45" name="kc" public_interface="out" units="first_order_rate_constant"/>
<variable initial_value="0.5" name="KIF" public_interface="out" units="nanomolar"/>
<variable initial_value="2.0" name="j" public_interface="out" units="dimensionless"/>
<variable initial_value="2.0" name="p" public_interface="out" units="dimensionless"/>
<variable initial_value="0.3" name="epsilon" public_interface="out" units="dimensionless"/>
<variable initial_value="1.5" name="theta" public_interface="out" units="dimensionless"/>
<variable initial_value="0.3" name="eta" public_interface="out" units="dimensionless"/>
</component>
<!-- connections -->
<connection>
<map_components component_1="N" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="Na" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="Nan" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="MF" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="F" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="K" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="B" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="Bp" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="BN" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="MAx" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="A" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="Rasa" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="ERKa" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="Xa" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="MDusp" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="Dusp" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="model_parameters" component_2="N"/>
<map_variables variable_1="kc" variable_2="kc"/>
<map_variables variable_1="KIF" variable_2="KIF"/>
<map_variables variable_1="j" variable_2="j"/>
<map_variables variable_1="epsilon" variable_2="epsilon"/>
</connection>
<connection>
<map_components component_1="F" component_2="N"/>
<map_variables variable_1="F" variable_2="F"/>
</connection>
<connection>
<map_components component_1="model_parameters" component_2="Na"/>
<map_variables variable_1="kc" variable_2="kc"/>
<map_variables variable_1="KIF" variable_2="KIF"/>
<map_variables variable_1="j" variable_2="j"/>
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