- Author:
- Hanne <Hanne@hanne-nielsens-macbook.local>
- Date:
- 2010-08-19 11:29:32+12:00
- Desc:
- Added image in eps ormat
- Permanent Source URI:
- https://models.cellml.org/workspace/goldbeter_pourquie_2008/rawfile/05713268e4b6191042ed46b82bc735ee4778e312/goldbeter_pourquie_2008_b.cellml
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<!-- 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 OpenCell and COR to recreate the published results. The units have been checked and they are consistent. This particular version of the model uncouples the Notch, Wnt and FGF signalling pathways and uses equations A4 and A10 in the appendix rather than A17 and A18.
</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, <ulink url="http://www.sciencedirect.com/science/journal/00225193">
<emphasis>Journal of Theoretical Biology</emphasis>
</ulink>, 252, 574-585. (Full text and PDF versions of the article are available to subscribers on the journal website.) <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>
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<variable units="nanomolar" public_interface="out" name="AK"/>
<variable units="flux" public_interface="out" name="V1"/>
<variable units="flux" public_interface="out" name="V2"/>
<variable units="flux" public_interface="out" name="VK"/>
<variable units="flux" public_interface="out" name="VP"/>
<variable units="nanomolar" public_interface="out" name="Kt" initial_value="3.0"/>
<variable units="first_order_rate_constant" name="d1" initial_value="0.1"/>
<variable units="second_order_rate_constant" name="a1" initial_value="1.8"/>
<variable units="nanomolar" name="K1" initial_value="0.28"/>
<variable units="nanomolar" name="K2" initial_value="0.03"/>
<variable units="nanomolar" name="D" initial_value="2.0"/>
<variable units="nanomolar" name="KID" initial_value="0.5"/>
<variable units="first_order_rate_constant" name="kt3" initial_value="0.7"/>
<variable units="first_order_rate_constant" name="kt4" initial_value="1.5"/>
<variable units="flux" name="VMK" initial_value="5.08"/>
<variable units="flux" name="VMP" initial_value="1.0"/>
<variable units="nanomolar" public_interface="in" name="K"/>
<variable units="nanomolar" public_interface="in" name="A"/>
<variable units="nanomolar" public_interface="in" name="B"/>
<variable units="nanomolar" public_interface="in" name="Bp"/>
<variable units="nanomolar" public_interface="in" name="BN"/>
<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 name="Rasa" cmeta:id="Rasa">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#Rasa">
<dc:title>Rasa</dc:title>
<dcterms:alternative>active Ras</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="nanomolar" public_interface="out" name="Rasa" initial_value="0.5"/>
<variable units="flux" public_interface="in" name="VaRas"/>
<variable units="flux" public_interface="in" name="VdRas"/>
<variable units="dimensionless" public_interface="in" name="eta"/>
<variable units="minute" public_interface="in" name="time"/>
<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 name="ERKa" cmeta:id="ERKa">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#ERKa">
<dc:title>ERKa</dc:title>
<dcterms:alternative>active ERK</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="nanomolar" public_interface="out" name="ERKa" initial_value="0.2"/>
<variable units="flux" public_interface="in" name="VaErk"/>
<variable units="flux" public_interface="in" name="VdErk"/>
<variable units="dimensionless" public_interface="in" name="eta"/>
<variable units="minute" public_interface="in" name="time"/>
<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 name="Xa" cmeta:id="Xa">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#Xa">
<dc:title>Xa</dc:title>
<dcterms:alternative>active transcription factor X</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="nanomolar" public_interface="out" name="Xa" initial_value="0.1"/>
<variable units="flux" public_interface="in" name="VaX"/>
<variable units="flux" public_interface="in" name="VdX"/>
<variable units="dimensionless" public_interface="in" name="eta"/>
<variable units="minute" public_interface="in" name="time"/>
<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 name="MDusp" cmeta:id="MDusp">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#MDusp">
<dc:title>MDusp</dc:title>
<dcterms:alternative>MKP3/Dusp6 mRNA</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="nanomolar" public_interface="out" name="MDusp" initial_value="0.1"/>
<variable units="flux" public_interface="in" name="VsMDusp"/>
<variable units="flux" public_interface="in" name="VdMDusp"/>
<variable units="dimensionless" public_interface="in" name="eta"/>
<variable units="minute" public_interface="in" name="time"/>
<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 name="Dusp" cmeta:id="Dusp">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#Dusp">
<dc:title>Dusp</dc:title>
<dcterms:alternative>MKP3/Dusp6 protein</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="nanomolar" public_interface="out" name="Dusp" initial_value="0.1"/>
<variable units="first_order_rate_constant" name="ksDusp" initial_value="0.5"/>
<variable units="flux" name="vdDusp" initial_value="2.0"/>
<variable units="nanomolar" name="KdDusp" initial_value="0.5"/>
<variable units="nanomolar" public_interface="in" name="MDusp"/>
<variable units="dimensionless" public_interface="in" name="eta"/>
<variable units="minute" public_interface="in" name="time"/>
<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 units="flux" public_interface="out" name="VaRas"/>
<variable units="flux" public_interface="out" name="VdRas"/>
<variable units="flux" public_interface="out" name="VaErk"/>
<variable units="flux" public_interface="out" name="VdErk"/>
<variable units="flux" public_interface="out" name="VaX"/>
<variable units="flux" public_interface="out" name="VdX"/>
<variable units="flux" public_interface="out" name="VsMDusp"/>
<variable units="flux" public_interface="out" name="VdMDusp"/>
<variable units="nanomolar" name="Rasi"/>
<variable units="nanomolar" name="ERKi"/>
<variable units="nanomolar" name="Xi"/>
<variable units="nanomolar" name="Rast" initial_value="2.0"/>
<variable units="nanomolar" name="ERKt" initial_value="2.0"/>
<variable units="nanomolar" name="Xt" initial_value="2.0"/>
<variable units="first_order_rate_constant" name="kcDusp" initial_value="1.35"/>
<variable units="flux" name="VMaRas" initial_value="4.968"/>
<variable units="flux" name="VMdRas" initial_value="0.41"/>
<variable units="flux" name="VMaErk" initial_value="3.30"/>
<variable units="flux" name="VMaX" initial_value="1.6"/>
<variable units="flux" name="VMdX" initial_value="0.5"/>
<variable units="flux" name="VMsMDusp" initial_value="0.9"/>
<variable units="flux" name="VMdMDusp" initial_value="0.5"/>
<variable units="nanomolar" name="Fgf" initial_value="1.0"/>
<variable units="nanomolar" name="KaFgf" initial_value="0.5"/>
<variable units="nanomolar" name="KaRas" initial_value="0.103"/>
<variable units="nanomolar" name="KdRas" initial_value="0.1"/>
<variable units="nanomolar" name="KdErk" initial_value="0.05"/>
<variable units="nanomolar" name="KaErk" initial_value="0.05"/>
<variable units="nanomolar" name="KaX" initial_value="0.05"/>
<variable units="nanomolar" name="KdX" initial_value="0.05"/>
<variable units="nanomolar" name="KaMDusp" initial_value="0.5"/>
<variable units="nanomolar" name="KdMDusp" initial_value="0.5"/>
<variable units="dimensionless" name="q" initial_value="2.0"/>
<variable units="dimensionless" name="r" initial_value="2.0"/>
<variable units="nanomolar" public_interface="in" name="Rasa"/>
<variable units="nanomolar" public_interface="in" name="ERKa"/>
<variable units="nanomolar" public_interface="in" name="Xa"/>
<variable units="nanomolar" public_interface="in" name="Dusp"/>
<variable units="nanomolar" public_interface="in" name="MDusp"/>
<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 units="first_order_rate_constant" public_interface="out" name="kc" initial_value="3.45"/>
<variable units="nanomolar" public_interface="out" name="KIF" initial_value="0.5"/>
<variable units="dimensionless" public_interface="out" name="j" initial_value="2.0"/>
<variable units="dimensionless" public_interface="out" name="p" initial_value="2.0"/>
<variable units="dimensionless" public_interface="out" name="epsilon" initial_value="0.3"/>
<variable units="dimensionless" public_interface="out" name="theta" initial_value="1.5"/>
<variable units="dimensionless" public_interface="out" name="eta" initial_value="0.3"/>
</component>
<!-- connections -->
<connection>
<map_components component_2="environment" component_1="N"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="Na"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="Nan"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="MF"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="F"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="K"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="B"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="Bp"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="BN"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="MAx"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="A"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="Rasa"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="ERKa"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="Xa"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="MDusp"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="Dusp"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="N" component_1="model_parameters"/>
<map_variables variable_2="kc" variable_1="kc"/>
<map_variables variable_2="KIF" variable_1="KIF"/>
<map_variables variable_2="j" variable_1="j"/>
<map_variables variable_2="epsilon" variable_1="epsilon"/>
</connection>
<connection>
<map_components component_2="N" component_1="F"/>
<map_variables variable_2="F" variable_1="F"/>
</connection>
<connection>
<map_components component_2="Na" component_1="model_parameters"/>
<map_variables variable_2="kc" variable_1="kc"/>
<map_variables variable_2="KIF" variable_1="KIF"/>
<map_variables variable_2="j" variable_1="j"/>
<map_variables variable_2="epsilon" variable_1="epsilon"/>
</connection>
<connection>
<map_components component_2="Na" component_1="F"/>
<map_variables variable_2="F" variable_1="F"/>
</connection>
<connection>
<map_components component_2="Na" component_1="N"/>
<map_variables variable_2="N" variable_1="N"/>
</connection>
<connection>
<map_components component_2="Na" component_1="Nan"/>
<map_variables variable_2="Nan" variable_1="Nan"/>
<map_variables variable_2="Vtr" variable_1="Vtr"/>
</connection>
<connection>
<map_components component_2="Nan" component_1="model_parameters"/>
<map_variables variable_2="epsilon" variable_1="epsilon"/>
</connection>
<connection>
<map_components component_2="MF" component_1="model_parameters"/>
<map_variables variable_2="p" variable_1="p"/>
<map_variables variable_2="epsilon" variable_1="epsilon"/>
</connection>
<connection>
<map_components component_2="MF" component_1="Nan"/>
<map_variables variable_2="Nan" variable_1="Nan"/>
</connection>
<connection>
<map_components component_2="F" component_1="model_parameters"/>
<map_variables variable_2="epsilon" variable_1="epsilon"/>
</connection>
<connection>
<map_components component_2="F" component_1="MF"/>
<map_variables variable_2="MF" variable_1="MF"/>
</connection>
<connection>
<map_components component_2="K" component_1="model_parameters"/>
<map_variables variable_2="theta" variable_1="theta"/>
</connection>
<connection>
<map_components component_2="K" component_1="Wnt_parameters"/>
<map_variables variable_2="V1" variable_1="V1"/>
<map_variables variable_2="K" variable_1="K"/>
</connection>
<connection>
<map_components component_2="B" component_1="model_parameters"/>
<map_variables variable_2="theta" variable_1="theta"/>
</connection>
<connection>
<map_components component_2="B" component_1="Wnt_parameters"/>
<map_variables variable_2="VK" variable_1="VK"/>
<map_variables variable_2="VP" variable_1="VP"/>
<map_variables variable_2="V2" variable_1="V2"/>
<map_variables variable_2="AK" variable_1="AK"/>
<map_variables variable_2="B" variable_1="B"/>
<map_variables variable_2="Kt" variable_1="Kt"/>
</connection>
<connection>
<map_components component_2="Bp" component_1="model_parameters"/>
<map_variables variable_2="theta" variable_1="theta"/>
</connection>
<connection>
<map_components component_2="Bp" component_1="Wnt_parameters"/>
<map_variables variable_2="VK" variable_1="VK"/>
<map_variables variable_2="VP" variable_1="VP"/>
<map_variables variable_2="AK" variable_1="AK"/>
<map_variables variable_2="Bp" variable_1="Bp"/>
<map_variables variable_2="Kt" variable_1="Kt"/>
</connection>
<connection>
<map_components component_2="BN" component_1="model_parameters"/>
<map_variables variable_2="theta" variable_1="theta"/>
</connection>
<connection>
<map_components component_2="BN" component_1="Wnt_parameters"/>
<map_variables variable_2="V2" variable_1="V2"/>
<map_variables variable_2="BN" variable_1="BN"/>
</connection>
<connection>
<map_components component_2="MAx" component_1="model_parameters"/>
<map_variables variable_2="theta" variable_1="theta"/>
</connection>
<connection>
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