- Author:
- pmr2.import <nobody@models.cellml.org>
- Date:
- 2009-06-08 03:54:25+12:00
- Desc:
- committing version02 of cui_kaandorp_lloyd_2008
- Permanent Source URI:
- https://models.cellml.org/workspace/cui_kaandorp_lloyd_2008/rawfile/600286361e3d94f989199af073bba30f26295eb1/cui_kaandorp_lloyd_2008_b.cellml
<?xml version='1.0' encoding='utf-8'?>
<!-- FILE : cui_kaandorp_lloyd-b_2008.xml
CREATED : 30th April 2008
LAST MODIFIED : 30th April 2008
AUTHOR : Catherine Lloyd
Bioengineering Institute
The University of Auckland
MODEL STATUS : This model conforms to the CellML 1.1 Specification.
DESCRIPTION : This file contains a CellML description of Cui and Kaandorp's 2008 mathematical model of the transcriptional response of zinc homeostasis system in E. coli.
CHANGES:
--><model xmlns="http://www.cellml.org/cellml/1.0#" xmlns:cmeta="http://www.cellml.org/metadata/1.0#" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:bqs="http://www.cellml.org/bqs/1.0#" xmlns:cellml="http://www.cellml.org/cellml/1.0#" xmlns:dcterms="http://purl.org/dc/terms/" xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" cmeta:id="cui_kaandorp_lloyd-b_2008" name="cui_kaandorp_lloyd-b_2008_version01">
<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
<articleinfo>
<title>Transcriptional response of zinc homeostasis system in E. coli</title>
<author>
<firstname>Catherine</firstname>
<surname>Lloyd</surname>
<affiliation>
<shortaffil>Bioengineering Institute, University of Auckland</shortaffil>
</affiliation>
</author>
</articleinfo>
<section id="sec_status">
<title>Model Status</title>
<para>
This 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 the zinc-buffering effects of TPEN are considered.
</para>
<para>
ValidateCellML verifies this model as valid CellML with full unit consistency.
</para>
</section>
<sect1 id="sec_structure">
<title>Model Structure</title>
<para>
Zinc plays an essential role in a large number of biological processes; including a structural role in RNA polymerase and zinc finger proteins, and a signalling role in cell proliferation and apoptosis. However, at high concentrations, zinc is toxic, and therefore intracellular zinc levels must be carefully regulated. <emphasis>Escherichia coli</emphasis> achieves intracellular zinc homeostasis by balancing the uptake and efflux of zinc across the plasma membrane. As shown in the figure below, zinc ions are transported into the cell via ZnuABC (an ABC-type transporter) and ZupT (a zinc permease), and they are removed from the cell via ZntA (a P-type ATPase) and ZitB (a cation diffusion facilitator). Zinc uptake via ZnuABC is regulated by Zur, a dimer protein which binds at least 2 zinc ions to become a repressor of <emphasis>znuABC</emphasis> gene expression. By contrast, zinc efflux through ZntA is accomplished by ZntR, a dimer protein which can bind one or two zinc ions per monomer. In its active form, ZntR binds to the promoter of the <emphasis>zntA</emphasis> gene and enhances its transcription.
</para>
<para>
In 1999-2001, Outten <emphasis>et al.</emphasis> published a series of papers presenting data from several <emphasis>in vitro</emphasis> transcription and metal-binding competition experiments in <emphasis>E. coli.</emphasis> These studies provide a detailed data set on which a mathematical model can be based. In the study described here, Cui and Kaandorp have developed such a mathematical model, and they use it to simulate the <emphasis>in vitro</emphasis> transcriptional response of zinc homeostasis system in <emphasis>E. coli.</emphasis> <ulink url="http://www.cellerator.org/">Cellerator</ulink>, an open source software, was used to automatically generate the equations, and the model was subsequently translated into CellML to facilitate future model exchange, reuse and implementation.
</para>
<informalfigure float="0" id="fig_reaction_diagram">
<mediaobject>
<imageobject>
<objectinfo>
<title>model diagram</title>
</objectinfo>
<imagedata fileref="cui_2008.png"/>
</imageobject>
</mediaobject>
<caption>A schematic diagram of the reactions described in the model of zinc homeostasis system in Escherichia coli. Extracellular zinc enters the cytoplasm through ZnuABC and ZupT, where its presence can cause Zur to bind to the znu operator and repress the transcription of the znuACB gene cluster. Excess intracellular zinc ions are exported by ZntA and ZitB, and cytosolic zinc can bind with protein ZntR to form a strong transcriptional activator of the zntA gene. Cytoplasmic zinc trafficking may involve chaperone-like proteins. Abbreviations: Zur* : active Zur; ZntR* : active ZntR; C? : (a possible zinc chaperone protein whose existence is still under debate).</caption>
</informalfigure>
<para>
The complete original paper reference is cited below:
</para>
<para>
Simulating in vitro transcriptional response of zinc homeostasis system in Escherichia coli, Jiangjun Cui, Jaap A. Kaandorp and Catherine M. Lloyd 2008,
<emphasis>BMC Systems Biology</emphasis>
, 2:89. <ulink url="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=pubmed&cmd=Retrieve&dopt=AbstractPlus&list_uids=PUBMEDID&query_hl=1&itool=pubmed_docsum">PubMed ID: PUBMEDID</ulink>
</para>
</sect1>
</article>
</documentation>
<units name="minute">
<unit units="second" multiplier="60.0"/>
</units>
<units name="molar">
<unit units="mole"/>
<unit units="litre" exponent="-1"/>
</units>
<units name="per_molar">
<unit units="molar" exponent="-1"/>
</units>
<units name="nanomolar">
<unit units="mole" prefix="nano"/>
<unit units="litre" exponent="-1"/>
</units>
<units name="first_order_rate_constant">
<unit units="second" exponent="-1"/>
</units>
<units name="second_order_rate_constant">
<unit units="nanomolar" exponent="-1"/>
<unit units="second" exponent="-1"/>
</units>
<units name="third_order_rate_constant">
<unit units="nanomolar" exponent="-2"/>
<unit units="second" exponent="-1"/>
</units>
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<variable units="second" public_interface="out" name="time"/>
</component>
<!-- The 7 ODEs describing the Zur transcription assay -->
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<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="Py">
<dc:title>Py</dc:title>
<dcterms:alternative>Zur dimer containing one zinc ion per monomer</dcterms:alternative>
<dcterms:alternative>Zn2Zur</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="nanomolar" public_interface="out" name="Py" initial_value="25.0"/>
<variable units="nanomolar" public_interface="in" name="Zn"/>
<variable units="nanomolar" public_interface="in" name="Py1"/>
<variable units="third_order_rate_constant" public_interface="in" name="r3"/>
<variable units="first_order_rate_constant" public_interface="in" name="r4"/>
<variable units="second" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
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<eq/>
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<ci>time</ci>
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<ci> Py </ci>
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<apply>
<minus/>
<apply>
<times/>
<ci> r4 </ci>
<ci> Py1 </ci>
</apply>
<apply>
<times/>
<ci> r3 </ci>
<apply>
<power/>
<ci> Zn </ci>
<cn cellml:units="dimensionless"> 2 </cn>
</apply>
<ci> Py </ci>
</apply>
</apply>
</apply>
</math>
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<component name="Py1" cmeta:id="Py1">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="Py1">
<dc:title>Py1</dc:title>
<dcterms:alternative>active Zur</dcterms:alternative>
<dcterms:alternative>Zur dimer containing two zinc ions per monomer</dcterms:alternative>
<dcterms:alternative>Zn4Zur</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="nanomolar" public_interface="out" name="Py1" initial_value="0.0"/>
<variable units="nanomolar" public_interface="in" name="Zn"/>
<variable units="nanomolar" public_interface="in" name="Py"/>
<variable units="nanomolar" public_interface="in" name="Dw"/>
<variable units="nanomolar" public_interface="in" name="Qw2"/>
<variable units="third_order_rate_constant" public_interface="in" name="r3"/>
<variable units="first_order_rate_constant" public_interface="in" name="r4"/>
<variable units="first_order_rate_constant" public_interface="in" name="k_1"/>
<variable units="second_order_rate_constant" public_interface="in" name="k1a"/>
<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> Py1 </ci>
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<apply>
<minus/>
<apply>
<plus/>
<apply>
<times/>
<ci> r3 </ci>
<apply>
<power/>
<ci> Zn </ci>
<cn cellml:units="dimensionless"> 2 </cn>
</apply>
<ci> Py </ci>
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<apply>
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<ci> k_1 </ci>
<ci> Qw2 </ci>
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<apply>
<plus/>
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<ci> r4 </ci>
<ci> Py1 </ci>
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<apply>
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<ci> k1a </ci>
<ci> Dw </ci>
<ci> Py1 </ci>
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<component name="Dw" cmeta:id="Dw">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="Dw">
<dc:title>Dw</dc:title>
<dcterms:alternative>DNA of ZnuC</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="nanomolar" public_interface="out" name="Dw" initial_value="4.0"/>
<variable units="nanomolar" public_interface="in" name="Qw2"/>
<variable units="nanomolar" public_interface="in" name="Py1"/>
<variable units="nanomolar" public_interface="in" name="Qw1"/>
<variable units="nanomolar" public_interface="in" name="Rw"/>
<variable units="second_order_rate_constant" public_interface="in" name="k1a"/>
<variable units="first_order_rate_constant" public_interface="in" name="k_1"/>
<variable units="second_order_rate_constant" public_interface="in" name="k2"/>
<variable units="first_order_rate_constant" public_interface="in" name="k_2"/>
<variable units="first_order_rate_constant" public_interface="in" name="k3"/>
<variable units="second" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
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<bvar>
<ci>time</ci>
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<ci> Dw </ci>
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<apply>
<minus/>
<apply>
<plus/>
<apply>
<times/>
<ci> k_1 </ci>
<ci> Qw2 </ci>
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<apply>
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<ci> k3 </ci>
<ci> Qw1 </ci>
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<apply>
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<ci> k_2 </ci>
<ci> Qw1 </ci>
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<apply>
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<ci> k1a </ci>
<ci> Dw </ci>
<ci> Py1 </ci>
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<apply>
<times/>
<ci> k2 </ci>
<ci> Dw </ci>
<ci> Rw </ci>
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<component name="Rw" cmeta:id="Rw">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="Rw">
<dc:title>Rw</dc:title>
<dcterms:alternative>RNA polymerase for znuC transcription</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="nanomolar" public_interface="out" name="Rw" initial_value="50.0"/>
<variable units="nanomolar" public_interface="in" name="Dw"/>
<variable units="nanomolar" public_interface="in" name="Qw1"/>
<variable units="second_order_rate_constant" public_interface="in" name="k2"/>
<variable units="first_order_rate_constant" public_interface="in" name="k_2"/>
<variable units="first_order_rate_constant" public_interface="in" name="k3"/>
<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> Rw </ci>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<times/>
<ci> k3 </ci>
<ci> Qw1 </ci>
</apply>
<apply>
<times/>
<ci> k_2 </ci>
<ci> Qw1 </ci>
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<apply>
<times/>
<ci> k2 </ci>
<ci> Dw </ci>
<ci> Rw </ci>
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</apply>
</apply>
</math>
</component>
<component name="Qw1" cmeta:id="Qw1">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="Qw1">
<dc:title>Qw1</dc:title>
<dcterms:alternative>transcription initiation complex of ZnuC</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="nanomolar" public_interface="out" name="Qw1" initial_value="0.0"/>
<variable units="nanomolar" public_interface="in" name="Dw"/>
<variable units="nanomolar" public_interface="in" name="Rw"/>
<variable units="second_order_rate_constant" public_interface="in" name="k2"/>
<variable units="first_order_rate_constant" public_interface="in" name="k_2"/>
<variable units="first_order_rate_constant" public_interface="in" name="k3"/>
<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> Qw1 </ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> k2 </ci>
<ci> Dw </ci>
<ci> Rw </ci>
</apply>
<apply>
<plus/>
<apply>
<times/>
<ci> k3 </ci>
<ci> Qw1 </ci>
</apply>
<apply>
<times/>
<ci> k_2 </ci>
<ci> Qw1 </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="Qw2" cmeta:id="Qw2">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="Qw2">
<dc:title>Qw2</dc:title>
<dcterms:alternative>Zn4Zur-DNA complex</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="nanomolar" public_interface="out" name="Qw2" initial_value="0.0"/>
<variable units="nanomolar" public_interface="in" name="Dw"/>
<variable units="nanomolar" public_interface="in" name="Py1"/>
<variable units="second_order_rate_constant" public_interface="in" name="k1a"/>
<variable units="first_order_rate_constant" public_interface="in" name="k_1"/>
<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> Qw2 </ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> k1a </ci>
<ci> Dw </ci>
<ci> Py1 </ci>
</apply>
<apply>
<times/>
<ci> k_1 </ci>
<ci> Qw2 </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="Mw" cmeta:id="Mw">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="Mw">
<dc:title>Mw</dc:title>
<dcterms:alternative>mRNA of ZnuC</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="nanomolar" public_interface="out" name="Mw" initial_value="0.0"/>
<variable units="nanomolar" public_interface="in" name="Qw1"/>
<variable units="first_order_rate_constant" public_interface="in" name="k3"/>
<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> Mw </ci>
</apply>
<apply>
<times/>
<ci> k3 </ci>
<ci> Qw1 </ci>
</apply>
</apply>
</math>
</component>
<!-- The 10 ODEs to describe the ZntR transcription assay -->
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<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="Px">
<dc:title>Px</dc:title>
<dcterms:alternative>apo-ZntR</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="nanomolar" public_interface="out" name="Px" initial_value="50.0"/>
<variable units="nanomolar" public_interface="in" name="Zn"/>
<variable units="nanomolar" public_interface="in" name="Px1"/>
<variable units="nanomolar" public_interface="in" name="Dz"/>
<variable units="nanomolar" public_interface="in" name="Qz4"/>
<variable units="second_order_rate_constant" public_interface="in" name="r1"/>
<variable units="first_order_rate_constant" public_interface="in" name="r2"/>
<variable units="second_order_rate_constant" public_interface="in" name="k1b"/>
<variable units="first_order_rate_constant" public_interface="in" name="k_1"/>
<variable units="second" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
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<eq/>
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<bvar>
<ci>time</ci>
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<ci> Px </ci>
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<minus/>
<apply>
<plus/>
<apply>
<times/>
<ci> r2 </ci>
<ci> Px1 </ci>
</apply>
<apply>
<times/>
<ci> k_1 </ci>
<ci> Qz4 </ci>
</apply>
</apply>
<apply>
<plus/>
<apply>
<times/>
<ci> r1 </ci>
<ci> Zn </ci>
<ci> Px </ci>
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<apply>
<times/>
<ci> k1b </ci>
<ci> Dz </ci>
<ci> Px </ci>
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</math>
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<dc:title>Px1</dc:title>
<dcterms:alternative>active ZntR</dcterms:alternative>
<dcterms:alternative>ZnZntR</dcterms:alternative>
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</rdf:RDF>
<variable units="nanomolar" public_interface="out" name="Px1" initial_value="0.0"/>
<variable units="nanomolar" public_interface="in" name="Zn"/>
<variable units="nanomolar" public_interface="in" name="Px"/>
<variable units="nanomolar" public_interface="in" name="Dz"/>
<variable units="nanomolar" public_interface="in" name="Qz2"/>
<variable units="second_order_rate_constant" public_interface="in" name="r1"/>
<variable units="first_order_rate_constant" public_interface="in" name="r2"/>
<variable units="second_order_rate_constant" public_interface="in" name="k1"/>
<variable units="first_order_rate_constant" public_interface="in" name="k_1"/>
<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> Px1 </ci>
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<apply>
<minus/>
<apply>
<plus/>
<apply>
<times/>
<ci> r1 </ci>
<ci> Zn </ci>
<ci> Px </ci>
</apply>
<apply>
<times/>
<ci> k_1 </ci>
<ci> Qz2 </ci>
</apply>
</apply>
<apply>
<plus/>
<apply>
<times/>
<ci> r2 </ci>
<ci> Px1 </ci>
</apply>
<apply>
<times/>
<ci> k1 </ci>
<ci> Dz </ci>
<ci> Px1 </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="Tp" cmeta:id="Tp">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="Tp">
<dc:title>Tp</dc:title>
<dcterms:alternative>TPEN</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="nanomolar" public_interface="out" name="Tp" initial_value="10000.0"/>
<variable units="nanomolar" public_interface="in" name="Zn"/>
<variable units="nanomolar" public_interface="in" name="Tp1"/>
<variable units="second_order_rate_constant" public_interface="in" name="r5"/>
<variable units="first_order_rate_constant" public_interface="in" name="r6"/>
<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> Tp </ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> r6 </ci>
<ci> Tp1 </ci>
</apply>
<apply>
<times/>
<ci> r5 </ci>
<ci> Zn </ci>
<ci> Tp </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="Tp1" cmeta:id="Tp1">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="Tp1">
<dc:title>Tp1</dc:title>
<dcterms:alternative>zinc-bound TPEN</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="nanomolar" public_interface="out" name="Tp1" initial_value="0.0"/>
<variable units="nanomolar" public_interface="in" name="Zn"/>
<variable units="nanomolar" public_interface="in" name="Tp"/>
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<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> Tp1 </ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> r5 </ci>
<ci> Zn </ci>
<ci> Tp </ci>
</apply>
<apply>
<times/>
<ci> r6 </ci>
<ci> Tp1 </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="Zn" cmeta:id="Zn">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="Zn">
<dc:title>Zn</dc:title>
<dcterms:alternative>zinc</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="nanomolar" public_interface="out" name="Zn" initial_value="10000.0"/>
<variable units="nanomolar" public_interface="in" name="Tp"/>
<variable units="nanomolar" public_interface="in" name="Tp1"/>
<variable units="nanomolar" public_interface="in" name="Px"/>
<variable units="nanomolar" public_interface="in" name="Px1"/>
<variable units="second_order_rate_constant" public_interface="in" name="r1"/>
<variable units="first_order_rate_constant" public_interface="in" name="r2"/>
<variable units="second_order_rate_constant" public_interface="in" name="r5"/>
<variable units="first_order_rate_constant" public_interface="in" name="r6"/>
<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> Zn </ci>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<times/>
<ci> r2 </ci>
<ci> Px1 </ci>
</apply>
<apply>
<times/>
<ci> r6 </ci>
<ci> Tp1 </ci>
</apply>
</apply>
<apply>
<plus/>
<apply>
<times/>
<ci> r1 </ci>
<ci> Zn </ci>
<ci> Px </ci>
</apply>
<apply>
<times/>
<ci> r5 </ci>
<ci> Zn </ci>
<ci> Tp </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="Dz" cmeta:id="Dz">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="Dz">
<dc:title>Dz</dc:title>
<dcterms:alternative>DNA of ZntA</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="nanomolar" public_interface="out" name="Dz" initial_value="2.0"/>
<variable units="nanomolar" public_interface="in" name="Qz2"/>
<variable units="nanomolar" public_interface="in" name="Px"/>
<variable units="nanomolar" public_interface="in" name="Qz1"/>
<variable units="nanomolar" public_interface="in" name="Px1"/>
<variable units="nanomolar" public_interface="in" name="Qz4"/>
<variable units="nanomolar" public_interface="in" name="Rz"/>
<variable units="second_order_rate_constant" public_interface="in" name="k1"/>
<variable units="second_order_rate_constant" public_interface="in" name="k1b"/>
<variable units="first_order_rate_constant" public_interface="in" name="k_1"/>
<variable units="second_order_rate_constant" public_interface="in" name="k2a"/>
<variable units="first_order_rate_constant" public_interface="in" name="k_2"/>
<variable units="first_order_rate_constant" public_interface="in" name="k3"/>
<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> Dz </ci>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<times/>
<ci> k_1 </ci>
<ci> Qz2 </ci>
</apply>
<apply>
<times/>
<ci> k3 </ci>
<ci> Qz1 </ci>
</apply>
<apply>
<times/>
<ci> k_2 </ci>
<ci> Qz1 </ci>
</apply>
<apply>
<times/>
<ci> k_1 </ci>
<ci> Qz4 </ci>
</apply>
</apply>
<apply>
<plus/>
<apply>
<times/>
<ci> k1b </ci>
<ci> Dz </ci>
<ci> Px </ci>
</apply>
<apply>
<times/>
<ci> k1 </ci>
<ci> Dz </ci>
<ci> Px1 </ci>
</apply>
<apply>
<times/>
<ci> k2a </ci>
<ci> Dz </ci>
<ci> Rz </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="Rz" cmeta:id="Rz">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="Rz">
<dc:title>Rz</dc:title>
<dcterms:alternative>RNA polymerase for zntA transcription</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="nanomolar" public_interface="out" name="Rz" initial_value="100.0"/>
<variable units="nanomolar" public_interface="in" name="Qz1"/>
<variable units="nanomolar" public_interface="in" name="Dz"/>
<variable units="nanomolar" public_interface="in" name="Qz3"/>
<variable units="nanomolar" public_interface="in" name="Qz4"/>
<variable units="nanomolar" public_interface="in" name="Qz5"/>
<variable units="nanomolar" public_interface="in" name="Qz2"/>
<variable units="second_order_rate_constant" public_interface="in" name="k2b"/>
<variable units="second_order_rate_constant" public_interface="in" name="k2c"/>
<variable units="second_order_rate_constant" public_interface="in" name="k2a"/>
<variable units="first_order_rate_constant" public_interface="in" name="k_2"/>
<variable units="first_order_rate_constant" public_interface="in" name="k3"/>
<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> Rz </ci>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<times/>
<ci> k3 </ci>
<ci> Qz1 </ci>
</apply>
<apply>
<times/>
<ci> k_2 </ci>
<ci> Qz1 </ci>
</apply>
<apply>
<times/>
<ci> k3 </ci>
<ci> Qz3 </ci>
</apply>
<apply>
<times/>
<ci> k_2 </ci>
<ci> Qz3 </ci>
</apply>
<apply>
<times/>
<ci> k3 </ci>
<ci> Qz5 </ci>
</apply>
<apply>
<times/>
<ci> k_2 </ci>
<ci> Qz5 </ci>
</apply>
</apply>
<apply>
<plus/>
<apply>
<times/>
<ci> k2a </ci>
<ci> Dz </ci>
<ci> Rz </ci>
</apply>
<apply>
<times/>
<ci> k2b </ci>
<ci> Qz4 </ci>
<ci> Rz </ci>
</apply>
<apply>
<times/>
<ci> k2c </ci>
<ci> Qz2 </ci>
<ci> Rz </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="Qz1" cmeta:id="Qz1">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="Qz1">
<dc:title>Qz1</dc:title>
<dcterms:alternative>transcription initiation complex formed by Dz and Rz</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="nanomolar" public_interface="out" name="Qz1" initial_value="0.0"/>
<variable units="nanomolar" public_interface="in" name="Dz"/>
<variable units="nanomolar" public_interface="in" name="Rz"/>
<variable units="second_order_rate_constant" public_interface="in" name="k2a"/>
<variable units="first_order_rate_constant" public_interface="in" name="k_2"/>
<variable units="first_order_rate_constant" public_interface="in" name="k3"/>
<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> Qz1 </ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> k2a </ci>
<ci> Dz </ci>
<ci> Rz </ci>
</apply>
<apply>
<plus/>
<apply>
<times/>
<ci> k3 </ci>
<ci> Qz1 </ci>
</apply>
<apply>
<times/>
<ci> k_2 </ci>
<ci> Qz1 </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="Qz2" cmeta:id="Qz2">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="Qz2">
<dc:title>Qz2</dc:title>
<dcterms:alternative>ZnZutA-DNA complex</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="nanomolar" public_interface="out" name="Qz2" initial_value="0.0"/>
<variable units="nanomolar" public_interface="in" name="Dz"/>
<variable units="nanomolar" public_interface="in" name="Rz"/>
<variable units="nanomolar" public_interface="in" name="Qz3"/>
<variable units="nanomolar" public_interface="in" name="Px1"/>
<variable units="second_order_rate_constant" public_interface="in" name="k1"/>
<variable units="first_order_rate_constant" public_interface="in" name="k_1"/>
<variable units="second_order_rate_constant" public_interface="in" name="k2c"/>
<variable units="first_order_rate_constant" public_interface="in" name="k3"/>
<variable units="first_order_rate_constant" public_interface="in" name="k_2"/>
<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> Qz2 </ci>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<times/>
<ci> k1 </ci>
<ci> Dz </ci>
<ci> Px1 </ci>
</apply>
<apply>
<times/>
<ci> k3 </ci>
<ci> Qz3 </ci>
</apply>
<apply>
<times/>
<ci> k_2 </ci>
<ci> Qz3 </ci>
</apply>
</apply>
<apply>
<plus/>
<apply>
<times/>
<ci> k_1 </ci>
<ci> Qz2 </ci>
</apply>
<apply>
<times/>
<ci> k2c </ci>
<ci> Qz2 </ci>
<ci> Rz </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="Qz3" cmeta:id="Qz3">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="Qz3">
<dc:title>Qz3</dc:title>
<dcterms:alternative>transcription initiation complex formed by Qz2 and Rz</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="nanomolar" public_interface="out" name="Qz3" initial_value="0.0"/>
<variable units="nanomolar" public_interface="in" name="Qz2"/>
<variable units="nanomolar" public_interface="in" name="Rz"/>
<variable units="second_order_rate_constant" public_interface="in" name="k2c"/>
<variable units="first_order_rate_constant" public_interface="in" name="k_2"/>
<variable units="first_order_rate_constant" public_interface="in" name="k3"/>
<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> Qz3 </ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> k2c </ci>
<ci> Qz2 </ci>
<ci> Rz </ci>
</apply>
<apply>
<plus/>
<apply>
<times/>
<ci> k3 </ci>
<ci> Qz3 </ci>
</apply>
<apply>
<times/>
<ci> k_2 </ci>
<ci> Qz3 </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="Qz4" cmeta:id="Qz4">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="Qz4">
<dc:title>Qz4</dc:title>
<dcterms:alternative>apo-ZntA-DNA complex</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="nanomolar" public_interface="out" name="Qz4" initial_value="0.0"/>
<variable units="nanomolar" public_interface="in" name="Dz"/>
<variable units="nanomolar" public_interface="in" name="Rz"/>
<variable units="nanomolar" public_interface="in" name="Qz5"/>
<variable units="nanomolar" public_interface="in" name="Px"/>
<variable units="second_order_rate_constant" public_interface="in" name="k1b"/>
<variable units="first_order_rate_constant" public_interface="in" name="k_1"/>
<variable units="second_order_rate_constant" public_interface="in" name="k2b"/>
<variable units="first_order_rate_constant" public_interface="in" name="k3"/>
<variable units="first_order_rate_constant" public_interface="in" name="k_2"/>
<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> Qz4 </ci>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<times/>
<ci> k1b </ci>
<ci> Dz </ci>
<ci> Px </ci>
</apply>
<apply>
<times/>
<ci> k3 </ci>
<ci> Qz5 </ci>
</apply>
<apply>
<times/>
<ci> k_2 </ci>
<ci> Qz5 </ci>
</apply>
</apply>
<apply>
<plus/>
<apply>
<times/>
<ci> k_1 </ci>
<ci> Qz4 </ci>
</apply>
<apply>
<times/>
<ci> k2b </ci>
<ci> Qz4 </ci>
<ci> Rz </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="Qz5" cmeta:id="Qz5">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="Qz5">
<dc:title>Qz5</dc:title>
<dcterms:alternative>transcription initiation complex formed by Qz4 and Rz</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="nanomolar" public_interface="out" name="Qz5" initial_value="0.0"/>
<variable units="nanomolar" public_interface="in" name="Qz4"/>
<variable units="nanomolar" public_interface="in" name="Rz"/>
<variable units="second_order_rate_constant" public_interface="in" name="k2b"/>
<variable units="first_order_rate_constant" public_interface="in" name="k_2"/>
<variable units="first_order_rate_constant" public_interface="in" name="k3"/>
<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> Qz5 </ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> k2b </ci>
<ci> Qz4 </ci>
<ci> Rz </ci>
</apply>
<apply>
<plus/>
<apply>
<times/>
<ci> k3 </ci>
<ci> Qz5 </ci>
</apply>
<apply>
<times/>
<ci> k_2 </ci>
<ci> Qz5 </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="Mz" cmeta:id="Mz">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="Mz">
<dc:title>Mz</dc:title>
<dcterms:alternative>mRNA of ZnuC</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="nanomolar" public_interface="out" name="Mz" initial_value="0.0"/>
<variable units="nanomolar" public_interface="in" name="Qz1"/>
<variable units="nanomolar" public_interface="in" name="Qz3"/>
<variable units="nanomolar" public_interface="in" name="Qz5"/>
<variable units="first_order_rate_constant" public_interface="in" name="k3"/>
<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> Mz </ci>
</apply>
<apply>
<plus/>
<apply>
<times/>
<ci> k3 </ci>
<ci> Qz1 </ci>
</apply>
<apply>
<times/>
<ci> k3 </ci>
<ci> Qz3 </ci>
</apply>
<apply>
<times/>
<ci> k3 </ci>
<ci> Qz5 </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="model_parameters">
<variable units="second_order_rate_constant" public_interface="out" name="r1" initial_value="2.73E2"/>
<variable units="first_order_rate_constant" public_interface="out" name="r2" initial_value="3.437E-4"/>
<variable units="third_order_rate_constant" public_interface="out" name="r3" initial_value="4.41E10"/>
<variable units="first_order_rate_constant" public_interface="out" name="r4" initial_value="9E-3"/>
<variable units="second_order_rate_constant" public_interface="out" name="r5" initial_value="3E4"/>
<variable units="first_order_rate_constant" public_interface="out" name="r6" initial_value="1.506E-2"/>
<variable units="second_order_rate_constant" public_interface="out" name="k1" initial_value="0.025"/>
<variable units="second_order_rate_constant" public_interface="out" name="k1a" initial_value="1.0"/>
<variable units="second_order_rate_constant" public_interface="out" name="k1b" initial_value="1.253E-2"/>
<variable units="first_order_rate_constant" public_interface="out" name="k_1" initial_value="0.9"/>
<variable units="second_order_rate_constant" public_interface="out" name="k2" initial_value="0.02"/>
<variable units="second_order_rate_constant" public_interface="out" name="k2a" initial_value="0.00005"/>
<variable units="second_order_rate_constant" public_interface="out" name="k2b" initial_value="0.0002"/>
<variable units="second_order_rate_constant" public_interface="out" name="k2c" initial_value="0.0037"/>
<variable units="first_order_rate_constant" public_interface="out" name="k_2" initial_value="0.3"/>
<variable units="first_order_rate_constant" public_interface="out" name="k3"/>
<variable units="second" name="td0" initial_value="1800.0"/>
<variable units="second" name="td" initial_value="2700"/>
<variable units="second" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci> k3 </ci>
<piecewise>
<piece>
<cn cellml:units="first_order_rate_constant"> 0.0 </cn>
<apply>
<and/>
<apply>
<geq/>
<ci> time </ci>
<cn cellml:units="second"> 0.0 </cn>
</apply>
<apply>
<lt/>
<ci> time </ci>
<ci> td0 </ci>
</apply>
</apply>
</piece>
<piece>
<cn cellml:units="first_order_rate_constant"> 0.011 </cn>
<apply>
<and/>
<apply>
<geq/>
<ci> time </ci>
<ci> td0 </ci>
</apply>
<apply>
<lt/>
<ci> time </ci>
<ci> td </ci>
</apply>
</apply>
</piece>
</piecewise>
</apply>
</math>
</component>
<connection>
<map_components component_2="environment" component_1="Py"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="Py1"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="Dw"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="Rw"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="Qw1"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="Qw2"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="Mw"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="Px"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="Px1"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="Tp"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="Tp1"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="Zn"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="Dz"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="Rz"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="Qz1"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="Qz2"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="Qz3"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="Qz4"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="Qz5"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="Mz"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="model_parameters"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="Py" component_1="Py1"/>
<map_variables variable_2="Py" variable_1="Py"/>
<map_variables variable_2="Py1" variable_1="Py1"/>
</connection>
<connection>
<map_components component_2="Py" component_1="Zn"/>
<map_variables variable_2="Zn" variable_1="Zn"/>
</connection>
<connection>
<map_components component_2="Py" component_1="model_parameters"/>
<map_variables variable_2="r3" variable_1="r3"/>
<map_variables variable_2="r4" variable_1="r4"/>
</connection>
<connection>
<map_components component_2="Py1" component_1="Dw"/>
<map_variables variable_2="Dw" variable_1="Dw"/>
<map_variables variable_2="Py1" variable_1="Py1"/>
</connection>
<connection>
<map_components component_2="Py1" component_1="Qw2"/>
<map_variables variable_2="Qw2" variable_1="Qw2"/>
<map_variables variable_2="Py1" variable_1="Py1"/>
</connection>
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