Location: Ciliberto, Tyson, 2000 @ 6869ca1112bf / ciliberto_tyson_2000.cellml

Author:

pmr2.import <nobody@models.cellml.org>

Date:

2006-07-09 07:35:09+12:00

Desc:

committing version01 of ciliberto_tyson_2000

Permanent Source URI:

http://models.cellml.org/workspace/ciliberto_tyson_2000/rawfile/6869ca1112bffbd13a5b104dccef6552515c7c01/ciliberto_tyson_2000.cellml

<?xml version='1.0' encoding='utf-8'?>
<!--  FILE :  ciliberto_model_2000.xml

CREATED :  2nd March 2004

LAST MODIFIED : 2nd March 2004

AUTHOR :  Catherine Lloyd
          Bioengineering Institute
          The University of Auckland
          
MODEL STATUS :  This model conforms to the CellML 1.0 Specification released on
10th August 2001, and the 16/1/02 CellML Metadata 1.0 Specification.

DESCRIPTION :  This file contains a CellML description of Ciliberto's 2000 mathematical model for early devlopment of the sea urchin embryo.

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="ciliberto_tyson_2000_version01" name="ciliberto_tyson_2000_version01">
<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
  <articleinfo>
  <title>Mathematical Model for the Early Development of the Sea Urchin Embryo</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 model is not currently functional (overconstrained).
          </para>
  </section>
  <sect1 id="sec_structure">
<title>Model Structure</title>

<para>
During normal mitotic cell division, eukaryotic cells will replicate their DNA during the S-phase of the cell cycle, and then divide during the M-phase.  S and M phases are temporally separated by gaps, called the G1 and G2 phases respectively.  However, in early development, when the main aim of embryo is to increase cell number by a series of rapid cell divisions, the cell cycle has a number of unique features: 
</para>
<itemizedlist>
  <listitem>
            <para>interdivision time is short and nearly constant;</para>
          </listitem>
  <listitem>
            <para>S and M phases alternate in time without intervening G1 or G2 phases;</para>
          </listitem>
  <listitem>
            <para>cell division is nearly synchronous and most cells take part;</para>
          </listitem>
  <listitem>
            <para>and the nucleocytoplasmic ration (NCR) of cells increases dramatically.</para>
          </listitem>
</itemizedlist>
<para>
It is believed that the NCR controls the cell cycle characteristics during the early stages of devlopment.  This idea has been incorporated into the following mathematical model of early devlopmental cell cycle control. 
</para>  

<para>
The molecular components involved in mitotic control have been studied extensively in the last decade, and a control system, common to all eukaryotes, has been elucidated.  This has been the subject of several mathematical models, including models which use budding yeast as the experimental organism:  
</para>
<itemizedlist>
  <listitem>
            <para>
              <ulink url="${HTML_EXMPL_NOVAK_MODEL}">Modelling the control of DNA replication in fission yeast, Novak and Tyson, 1997</ulink>
            </para>
          </listitem>
  <listitem>
            <para>
              <ulink url="${HTML_EXMPL_NOVAK_MODEL98}">Mathematical Model of the Fission Yeast Cell Cycle, Novak <emphasis>et al.</emphasis>, 1998</ulink>
            </para>
          </listitem>
  <listitem>
            <para>
              <ulink url="${HTML_EXMPL_CHEN_MODEL}">Chen <emphasis>et al.</emphasis>, Modelling the Budding Yeast Cell Cycle, 2000</ulink>
            </para>
          </listitem>
  <listitem>
            <para>
              <ulink url="${HTML_EXMPL_CILIBERTO_MODEL2}">Ciliberto <emphasis>et al.</emphasis> Modelling the Morphogenesis Checkpoint in the Budding Yeast Cell Cycle, 2003</ulink>
            </para>
          </listitem>
</itemizedlist>
<para>
and those which use the Xenopus oocyte and embryo: <ulink url="${HTML_EXMPL_CILIBERTO_MODEL}">Ciliberto <emphasis>et al.</emphasis> A Kinetic Model of the Cyclin E/Cdk2 Developmental Timer in <emphasis>Xenopus laevis</emphasis> embryos, 2003</ulink>.
</para> 

<para>
In the Ciliberto and Tyson 2000 publication described here, the authors develop a mathematical model based on the molecular interactions underlying early embryonic cell cycle control (see <xref linkend="fig_reaction_diagram"/> below).  By introducing the NCP ratio into the molecular mechanism, through model simulations the authors were able to reproduce many of the physiological features of early sea urchin development.  Since the cell cycle controls appear to be common to all eukaryotes, this model can also potentially be applied to other species. 
</para>

<para>
The model has been described here in CellML (the raw CellML description of the Ciliberto and Tyson 2000 model can be downloaded in various formats as described in <xref linkend="sec_download_this_model"/>).     
</para>

<para>
The complete original paper reference is cited below:
</para>

<para>
<ulink url="http://www.sciencedirect.com/science?_ob=ArticleURL&amp;_udi=B6WC7-45FK06D-F&amp;_user=140507&amp;_coverDate=01%2F31%2F2000&amp;_rdoc=3&amp;_fmt=high&amp;_orig=browse&amp;_srch=doc-info(%23toc%236731%232000%23999379998%23296789%23FLP%23display%23Volume)&amp;_cdi=6731&amp;_sort=d&amp;_docanchor=&amp;_ct=10&amp;_acct=C000011498&amp;_version=1&amp;_urlVersion=0&amp;_userid=140507&amp;md5=9ade0dbf059201fb36815be5648c2e06">Mathematical Model for Early Development of the Sae Urchin Embryo</ulink>, Andrea Ciliberto and John J. Tyson, 2000, <ulink url="http://www.sciencedirect.com/science/journal/00928240">
            <emphasis>Bulletin of Mathematical Biology</emphasis>
          </ulink>, 62, 37-59.  (A PDF version of the article is available to subscribers on the <emphasis>Bulletin of Mathematical Biology</emphasis> website.)  <ulink url="http://www.ncbi.nlm.nih.gov/pubmed/10824420">PubMed ID: 10824420</ulink>
</para>

<informalfigure float="0" id="fig_reaction_diagram">
<mediaobject>
  <imageobject>
    <objectinfo>
      <title>reaction diagram</title>
    </objectinfo>
    <imagedata fileref="ciliberto_2000.png"/>
  </imageobject>
</mediaobject>
<caption>The M phase control system of the cell cycle.  The upper part of the figure shows the two positive feedback loops involving active MPF (Cdc2-cyclin complex) and inactive MPF (the phosphorylated Cdc2-cyclin complex).  Cyclin is produced at a constant rate from a pool of amino acids (AA) and immediately binds to free Cdc2, producing active MPF.  All forms of cyclin - free, active and inactive MPF -  are degraded by the same process.  The lower part of the figure shows that the degradation of cyclin is the result of a negative feedback loop involving a ubiquitin-ligation complex (APC) and a putative intermediary enzyme (IE).</caption>
</informalfigure>

</sect1>
</article>
</documentation>
  
  
  <units name="minute">
    <unit units="second" multiplier="60.0"/>
  </units>
  
  <units name="first_order_rate_constant">
    <unit units="minute" exponent="-1"/>
  </units>
 
  
  <component name="environment">
    <variable units="minute" public_interface="out" name="time"/>
  </component>
  
  <component cmeta:id="Y" name="Y">
    <rdf:RDF>
      <rdf:Description rdf:about="Y">
        <dc:title>Y</dc:title>
        <dcterms:alternative>monomeric cyclin</dcterms:alternative>  
      </rdf:Description>
    </rdf:RDF> 
    <variable units="dimensionless" public_interface="out" name="Y"/>
    
    <variable units="first_order_rate_constant" name="k1" initial_value="0.024"/>
   
    <variable units="first_order_rate_constant" public_interface="in" name="k2"/>
    <variable units="first_order_rate_constant" public_interface="in" name="k3"/>
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    <variable units="minute" public_interface="in" name="time"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML"> 
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        <eq/> 
        <apply>
          <diff/> 
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            <ci>time</ci>
          </bvar> 
          <ci>Y</ci> 
        </apply>
        <apply>
          <minus/>
          <ci> k1 </ci>
          <apply>
            <plus/>
            <apply>
              <times/>
              <ci> k2 </ci>
              <ci> Y </ci>
            </apply>
            <apply>
              <times/>
              <ci> k3 </ci>
              <ci> Y </ci>
              <ci> C </ci>
            </apply>
          </apply>
        </apply>
      </apply>    
    </math>
  </component>
  
  <component cmeta:id="M" name="M">
    <rdf:RDF>
      <rdf:Description rdf:about="M">
        <dc:title>M</dc:title>
        <dcterms:alternative>active MPF</dcterms:alternative>  
      </rdf:Description>
    </rdf:RDF> 
    <variable units="dimensionless" public_interface="out" name="M"/>
    
    <variable units="first_order_rate_constant" public_interface="in" name="k2"/>
    <variable units="first_order_rate_constant" public_interface="in" name="k3"/>
    <variable units="first_order_rate_constant" public_interface="in" name="kwee"/>
    <variable units="first_order_rate_constant" public_interface="in" name="kcdc25"/>
    <variable units="dimensionless" public_interface="in" name="C"/>
    <variable units="dimensionless" public_interface="in" name="Y"/>
    <variable units="dimensionless" public_interface="in" name="preMPF"/>
    <variable units="minute" public_interface="in" name="time"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML"> 
      <apply>
        <eq/> 
        <apply>
          <diff/> 
          <bvar>
            <ci>time</ci>
          </bvar> 
          <ci>M</ci> 
        </apply>
        <apply>
          <minus/>
          <apply>
            <plus/>
            <apply>
              <times/>
              <ci> kcdc25 </ci>
              <ci> preMPF </ci>
            </apply>
            <apply>
              <times/>
              <ci> k3 </ci>
              <ci> Y </ci>
              <ci> C </ci>
            </apply>
          </apply>
          <apply>
            <plus/>
            <apply>
              <times/>
              <ci> k2 </ci>
              <ci> M </ci>
            </apply>
            <apply>
              <times/>
              <ci> kwee </ci>
              <ci> M </ci>
            </apply>
          </apply>
        </apply>
      </apply>    
    </math>
  </component>
  
  <component cmeta:id="preMPF" name="preMPF">
    <rdf:RDF>
      <rdf:Description rdf:about="preMPF">
        <dc:title>preMPF</dc:title>
        <dcterms:alternative>tyrosine phosphorylated (inactive) form of MPF</dcterms:alternative>  
      </rdf:Description>
    </rdf:RDF> 
    <variable units="dimensionless" public_interface="out" name="preMPF"/>
    
    <variable units="first_order_rate_constant" public_interface="in" name="k2"/>
    <variable units="first_order_rate_constant" public_interface="in" name="kwee"/>
    <variable units="first_order_rate_constant" public_interface="in" name="kcdc25"/>
    <variable units="dimensionless" public_interface="in" name="M"/>
    <variable units="minute" public_interface="in" name="time"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML"> 
      <apply>
        <eq/> 
        <apply>
          <diff/> 
          <bvar>
            <ci>time</ci>
          </bvar> 
          <ci>preMPF</ci> 
        </apply>
        <apply>
          <minus/>
          <apply>
            <times/>
            <ci> kwee </ci>
            <ci> M </ci>
          </apply>
          <apply>
            <plus/>
            <apply>
              <times/>
              <ci> k2 </ci>
              <ci> preMPF </ci>
            </apply>
            <apply>
              <times/>
              <ci> kcdc25 </ci>
              <ci> preMPF </ci>
            </apply>
          </apply>
        </apply>
      </apply>    
    </math>
  </component>
  
  <component cmeta:id="Cdc25P" name="Cdc25P">
    <rdf:RDF>
      <rdf:Description rdf:about="Cdc25P">
        <dc:title>Cdc25P</dc:title>
        <dcterms:alternative>phosphorylated (active) form of Cdc25</dcterms:alternative>  
      </rdf:Description>
    </rdf:RDF> 
    <variable units="dimensionless" public_interface="out" name="Cdc25P"/>
    
    <variable units="first_order_rate_constant" name="k25" initial_value="18.0"/>
    <variable units="dimensionless" name="Km25" initial_value="0.1"/>
    <variable units="first_order_rate_constant" name="k25r" initial_value="0.8"/>
    <variable units="first_order_rate_constant" name="k25ro"/>
    <variable units="dimensionless" name="Km25r" initial_value="1.0"/>
    
    <variable units="dimensionless" public_interface="in" name="p"/>
    <variable units="dimensionless" public_interface="in" name="Cdc25"/>
    <variable units="dimensionless" public_interface="in" name="M"/>
    <variable units="minute" public_interface="in" name="time"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML"> 
      <apply>
        <eq/> 
        <apply>
          <diff/> 
          <bvar>
            <ci>time</ci>
          </bvar> 
          <ci>Cdc25P</ci> 
        </apply>
        <apply>
          <minus/>
          <apply>
            <divide/>
            <apply>
              <times/>
              <ci> k25 </ci>
              <ci> M </ci>
              <ci> Cdc25 </ci>
            </apply>
            <apply>
              <plus/>
              <ci> Km25 </ci>
              <ci> Cdc25 </ci>
            </apply>
          </apply>
          <apply>
            <divide/>
            <apply>
              <times/>
              <ci> k25r </ci>
              <ci> Cdc25P </ci>
            </apply>
            <apply>
              <plus/>
              <ci> Km25r </ci>
              <ci> Cdc25P </ci>
            </apply>
          </apply>
        </apply>
      </apply>
      
      <apply>
        <eq/>
        <ci> k25r </ci>
        <apply>
          <times/>
          <ci> p </ci>
          <ci> k25ro  </ci>
        </apply>
      </apply>       
    </math>
  </component>
  
  <component cmeta:id="Wee1" name="Wee1">
    <rdf:RDF>
      <rdf:Description rdf:about="Wee1">
        <dc:title>Wee1</dc:title>
        <dcterms:alternative>unphosphorylated (active) form of Wee1</dcterms:alternative>  
      </rdf:Description>
    </rdf:RDF> 
    <variable units="dimensionless" public_interface="out" name="Wee1"/>
    
    <variable units="first_order_rate_constant" name="kw" initial_value="18.0"/>
    <variable units="dimensionless" name="Kmw" initial_value="0.1"/>
    <variable units="first_order_rate_constant" name="kwr" initial_value="0.8"/>
    <variable units="first_order_rate_constant" name="kwro"/>
    <variable units="dimensionless" name="Kmwr" initial_value="1.0"/>
    
    <variable units="dimensionless" public_interface="in" name="p"/>
    <variable units="dimensionless" public_interface="in" name="M"/>
    <variable units="dimensionless" public_interface="in" name="Wee1P"/>
    <variable units="minute" public_interface="in" name="time"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML"> 
      <apply>
        <eq/> 
        <apply>
          <diff/> 
          <bvar>
            <ci>time</ci>
          </bvar> 
          <ci>Wee1</ci> 
        </apply>
        <apply>
          <plus/>
          <apply>
            <divide/>
            <apply>
              <times/>
              <ci> kw </ci>
              <ci> M </ci>
              <ci> Wee1 </ci>
            </apply>
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              <plus/>
              <ci> Kmw </ci>
              <ci> Wee1 </ci>
            </apply>
          </apply>
          <apply>
            <divide/>
            <apply>
              <times/>
              <ci> kwr </ci>
              <ci> Wee1P </ci>
            </apply>
            <apply>
              <plus/>
              <ci> Kmwr </ci>
              <ci> Wee1P </ci>
            </apply>
          </apply>
        </apply>
      </apply> 
      
      <apply>
        <eq/>
        <ci> kwr </ci>
        <apply>
          <times/>
          <ci> p </ci>
          <ci> kwro  </ci>
        </apply>
      </apply>    
    </math>
  </component>
  
  <component cmeta:id="IEP" name="IEP">
    <rdf:RDF>
      <rdf:Description rdf:about="IEP">
        <dc:title>IEP</dc:title>
        <dcterms:alternative>phosphorylated (active) form of a putative intermediary enzyme activated by MPF that in turn activates the APC</dcterms:alternative>  
      </rdf:Description>
    </rdf:RDF> 
    <variable units="dimensionless" public_interface="out" name="IEP"/>
    
    <variable units="first_order_rate_constant" name="kie" initial_value="4.5"/>
    <variable units="dimensionless" name="Kmie" initial_value="0.01"/>
    <variable units="first_order_rate_constant" name="kier" initial_value="0.34"/>
    <variable units="dimensionless" name="Kmier" initial_value="0.01"/>
    
    <variable units="dimensionless" public_interface="in" name="IE"/>
    <variable units="dimensionless" public_interface="in" name="M"/>
    <variable units="minute" public_interface="in" name="time"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML"> 
      <apply>
        <eq/> 
        <apply>
          <diff/> 
          <bvar>
            <ci>time</ci>
          </bvar> 
          <ci>IEP</ci> 
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        <apply>
          <minus/>
          <apply>
            <divide/>
            <apply>
              <times/>
              <ci> kie </ci>
              <ci> M </ci>
              <ci> IE </ci>
            </apply>
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              <plus/>
              <ci> Kmie </ci>
              <ci> IE </ci>
            </apply>
          </apply>
          <apply>
            <divide/>
            <apply>
              <times/>
              <ci> kier </ci>
              <ci> IEP </ci>
            </apply>
            <apply>
              <plus/>
              <ci> Kmier </ci>
              <ci> IEP </ci>
            </apply>
          </apply>
        </apply>
      </apply>    
    </math>
  </component>
 
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    <rdf:RDF>
      <rdf:Description rdf:about="APC_">
        <dc:title>APC_</dc:title>
        <dcterms:alternative>active form of a ubiquitin-ligation complex</dcterms:alternative>  
      </rdf:Description>
    </rdf:RDF> 
    <variable units="dimensionless" public_interface="out" name="APC_"/>
    
    <variable units="first_order_rate_constant" name="kap" initial_value="0.3"/>
    <variable units="dimensionless" name="Kmap" initial_value="0.01"/>
    <variable units="first_order_rate_constant" name="kapr" initial_value="0.3"/>
    <variable units="dimensionless" name="Kmapr" initial_value="1.0"/>
    
    <variable units="dimensionless" public_interface="in" name="IEP"/>
    <variable units="dimensionless" public_interface="in" name="APC"/>
    <variable units="minute" public_interface="in" name="time"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML"> 
      <apply>
        <eq/> 
        <apply>
          <diff/> 
          <bvar>
            <ci>time</ci>
          </bvar> 
          <ci>APC_</ci> 
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        <apply>
          <plus/>
          <apply>
            <divide/>
            <apply>
              <times/>
              <ci> kap </ci>
              <ci> IEP </ci>
              <ci> APC </ci>
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              <plus/>
              <ci> Kmap </ci>
              <ci> APC </ci>
            </apply>
          </apply>
          <apply>
            <divide/>
            <apply>
              <times/>
              <ci> kapr </ci>
              <ci> APC_ </ci>
            </apply>
            <apply>
              <plus/>
              <ci> Kmapr </ci>
              <ci> APC_ </ci>
            </apply>
          </apply>
        </apply>
      </apply>    
    </math>
  </component>
  
  <component cmeta:id="C" name="C">
    <rdf:RDF>
      <rdf:Description rdf:about="C">
        <dc:title>C</dc:title>
        <dcterms:alternative>monomeric Cdc2</dcterms:alternative>  
      </rdf:Description>
    </rdf:RDF> 
    <variable units="dimensionless" public_interface="out" name="C"/>
    
    <variable units="dimensionless" name="Cdc2tot"/>
    
    <variable units="dimensionless" public_interface="in" name="preMPF"/>
    <variable units="dimensionless" public_interface="in" name="M"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML"> 
      <apply>
        <eq/> 
        <ci>C</ci> 
        <apply>
          <minus/>
          <ci> Cdc2tot </ci>
          <apply>
            <plus/>
            <ci> M </ci>
            <ci> preMPF </ci>
          </apply>
        </apply>
      </apply>    
    </math>
  </component>
  
  <component name="Cdc25"> 
    <variable units="dimensionless" public_interface="out" name="Cdc25"/>
    
    <variable units="dimensionless" name="Cdc25tot"/>
    
    <variable units="dimensionless" public_interface="in" name="Cdc25P"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML"> 
      <apply>
        <eq/> 
        <ci>Cdc25</ci> 
        <apply>
          <minus/>
          <ci> Cdc25tot </ci>
          <ci> Cdc25P </ci>
        </apply>
      </apply>    
    </math>
  </component>
  
  <component cmeta:id="Wee1P" name="Wee1P">
    <rdf:RDF>
      <rdf:Description rdf:about="Wee1P">
        <dc:title>Wee1P</dc:title>
        <dcterms:alternative>phosphorylated Wee1</dcterms:alternative>  
      </rdf:Description>
    </rdf:RDF> 
    <variable units="dimensionless" public_interface="out" name="Wee1P"/>
    
    <variable units="dimensionless" name="Wee1tot"/>
    
    <variable units="dimensionless" public_interface="in" name="Wee1"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML"> 
      <apply>
        <eq/> 
        <ci>Wee1P</ci> 
        <apply>
          <minus/>
          <ci> Wee1tot </ci>
          <ci> Wee1 </ci>
        </apply>
      </apply>    
    </math>
  </component>
  
  <component cmeta:id="IE" name="IE">
    <rdf:RDF>
      <rdf:Description rdf:about="IE">
        <dc:title>IE</dc:title>
        <dcterms:alternative>unphosphorylated IE</dcterms:alternative>  
      </rdf:Description>
    </rdf:RDF> 
    <variable units="dimensionless" public_interface="out" name="IE"/>
    
    <variable units="dimensionless" name="IEtot"/>
    
    <variable units="dimensionless" public_interface="in" name="IEP"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML"> 
      <apply>
        <eq/> 
        <ci>IE</ci> 
        <apply>
          <minus/>
          <ci> IEtot </ci>
          <ci> IEP </ci>
        </apply>
      </apply>    
    </math>
  </component>
  
  <component cmeta:id="APC" name="APC">
    <rdf:RDF>
      <rdf:Description rdf:about="APC">
        <dc:title>APC</dc:title>
        <dcterms:alternative>inactive form of APC</dcterms:alternative>  
      </rdf:Description>
    </rdf:RDF> 
    <variable units="dimensionless" public_interface="out" name="APC"/>
    
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