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  <h1>Repressilator: A synthetic oscillatory network of transcriptional regulators</h1>
  <table border="0" cellpadding="2" cellspacing="0">
    <thead>
      <tr>
        <th align="left" bgcolor="#EEEEEE" valign="middle">Citation</th>
      </tr>
    </thead>
    <tbody>
      <tr>
        <td>Elowitz MB, Leibler S (2000) 
          
              
              
          
              
              
              <br/>
                A synthetic oscillatory network of transcriptional regulators.
                
          
              
              
          
              
              
              <br/>Nature.403 : 335 - 338.
          
              
              
          
              
              
              <br/>
        <a href="http://www.nature.com/cgi-taf/%20%20%20%20%20%20%20%20DynaPage.taf?file=/nature/journal/v403/n6767/full/403335a0_fs.html">http:// www.nature.com/cgi-taf/DynaPage.taf?file=/nature/journal/v403/n6767/full/ 403335a0_fs.html</a>
      </td>
    </tr>
  </tbody>
</table><table border="0" cellpadding="2" cellspacing="0">
  <thead>
    <tr>
      <th align="left" bgcolor="#EEEEEE" valign="middle">Description</th>
    </tr>
  </thead>
  <tbody>
    <tr>
      <td>
        <p>This file describes the deterministic version of the repressilator system.</p>
        <p>The authors of this model (see reference) use three transcriptional repressor systems that are not part of any natural biological clock to build an oscillating network that they called the repressilator. The model system was induced in Escherichia coli.
                   </p>
        <p> In this system, LacI (variable X is the mRNA, variable PX is the protein) inhibits the tetracycline-resistance transposon 
                    tetR (Y, PY describe mRNA and protein). Protein tetR inhibits the gene Cl from phage Lambda (Z, PZ: mRNA, protein),and 
                    protein Cl inhibits lacI expression. With appropriate parameter values this system oscillates.</p>
        <p>The model is based upon the equations in Box 1 of the paper; however, these equations as printed are dimensionless, 
                    and the correct dimensions have been returned to the equations, and the parameters set to reproduce Figure 1C (left).</p>
      </td>
    </tr>
  </tbody>
</table><p>The original Model was Generated by B.E. Shapiro using Cellerator Version 1.0 update 2.1127 using Mathematica 4.2 for Mac OS X (June 4, 2002), November 27, 2002 12:15:32, using (PowerMac,PowerPC, Mac OS X,MacOSX,Darwin)</p><p>Nicolas Le Novere: Corrected version generated by SBMLeditor on Sun Aug 20 00:44:05 BST 2006. Removal of EmptySet species. Ran fine on COPASI 4.0 build 18</p><p>Bruce Shapiro: Revised with SBML editor 23 October 2006 20:39 PST. Define default units and correct reactions. The original cellerator reactions while being mathematically correct did not accurately reflect the intent of the authors.&apos; The original notes were mostly removed because they were mostly incorrect in the revised version. Tested with MathSBML 2.6.0</p><p>Nicolas Le Novere: changed the volume to 1 cubic micrometre, to allow for stochastic simulation.</p><p>Changed by Lukas Endler to use the average livetime of mRNA instead of its halflife and a corrected value of alpha and alpha0.<br/>
To clarify the equations used in this model:<br/>
The equations given in <b>box 1</b> the original publication are rescaled in three respects (lowercase letters denote the rescaled, uppercase letters the unscaled number of molecules per cell):<br/><ul>
  <li>the time is rescaled to the average mRNA lifetime, <em>t_ave: τ = t/t_ave</em>
</li><li>the mRNA concentration is rescaled to the translation efficiency <em>eff: m = M/eff</em>
</li><li>the protein concentration is rescaled to <em>Km: p = P/Km</em>
</li>
</ul><em>α</em> in the equations should be in units of rescaled proteins per promotor and cell, and  <em>β</em> is the ratio of the protein to the mRNA decay rates or the ratio of the mRNA to the protein halflife.<br/>
In this version of the model <em>α</em> and <em>β</em> are calculated correspondingly to the article, while <em>p</em> and <em>m</em> where just replaced by <em>P/Km</em> resp. <em>M/eff</em> and all equations multiplied by <em>1/t_ave</em>. Also, to make the equations easier to read, commonly used variables derived from the parameters given in the article by simple rules were introduced.<br/>
The parameters given in the article were:<br/><table border="0" cellpadding="2" cellspacing="0">
  <tr>
    <td>promotor strength (repressed) (<em>tps_repr</em>):</td>
    <td>5*10<sup>-4</sup>
  </td>
  <td>transcripts/(promotor*s)</td>
</tr><tr>
  <td>promotor strength (full) (<em>tps_active</em>):</td>
  <td>0.5</td>
  <td>transcripts/(promotor*s)</td>
</tr><tr>
  <td>mRNA half life, τ<sub>1/2,mRNA</sub>:</td>
  <td>2</td>
  <td>min</td>
</tr><tr>
  <td>protein half life, τ<sub>1/2,prot</sub>:</td>
  <td>10</td>
  <td>min</td>
</tr><tr>
  <td>K<sub>M</sub>:</td>
  <td>40 </td>
  <td>monomers/cell</td>
</tr><tr>
  <td>Hill coefficient n:</td>
  <td>2</td>
  <td/>
</tr>
</table>
from these the following constants can be derived:
<table border="0" cellpadding="2" cellspacing="0">
  <tr>
    <td>average mRNA lifetime (<em>t_ave</em>):</td>
    <td>
      <em>τ<sub>1/2,mRNA</sub>/ln(2)</em>
    </td>
    <td>= 2.89 min</td>
  </tr>
  <tr>
    <td>mRNA decay rate (<em>kd_mRNA</em>):</td>
    <td>
      <em>ln(2)/ τ<sub>1/2,mRNA</sub>
    </em>
  </td>
  <td>= 0.347 min<sup>-1</sup>
</td>
</tr><tr>
  <td>protein decay rate (<em>kd_prot</em>):</td>
  <td>
    <em>ln(2)/ τ<sub>1/2,prot</sub>
  </em>
</td>
</tr><tr>
  <td>transcription rate (<em>a_tr</em>):</td>
  <td>
    <em>tps_active*60
      </em>
  </td>
  <td>= 29.97 transcripts/min
    </td>
</tr><tr>
  <td>transcription rate (repressed) (<em>a0_tr</em>):</td>
  <td>
    <em>tps_repr*60</em>
  </td>
  <td>= 0.03 transcripts/min
    </td>
</tr><tr>
  <td>translation rate (<em>k_tl</em>):</td>
  <td>
    <em>eff*kd_mRNA</em>
  </td>
  <td>= 6.93 proteins/(mRNA*min)
    </td>
</tr><tr>
  <td>α :</td>
  <td>
    <em>a_tr*eff*τ<sub>1/2,prot</sub>/(ln(2)*K<sub>M</sub>)</em>
  </td>
  <td>= 216.4 proteins/(promotor*cell*Km)</td>
</tr><tr>
  <td>α<sub>0</sub> :</td>
  <td>
    <em>a0_tr*eff*τ<sub>1/2,prot</sub>/(ln(2)*K<sub>M</sub>)</em>
  </td>
  <td>= 0.2164 proteins/(promotor*cell*Km)</td>
</tr><tr>
  <td>β :</td>
  <td>
    <em>k_dp/k_dm</em>
  </td>
  <td>= 0.2</td>
</tr>
</table>
</p><p style="border:thin black solid">This model originates from BioModels Database: A Database of Annotated Published Models. It is copyright (c) 2005-2010 The BioModels Team.
      
      
      <br/>For more information see the 
      
      
      <a href="http://www.ebi.ac.uk/biomodels/legal.html" target="_blank">terms of use</a>.
      
      
      <br/>To cite BioModels Database, please use 
      
      
      <a href="http://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pubmed&amp;pubmedid=16381960" target="_blank"> Le Novère N., Bornstein B., Broicher A., Courtot M., Donizelli M., Dharuri H., Li L., Sauro H., Schilstra M., Shapiro B., Snoep J.L., Hucka M. (2006) BioModels Database: A Free, Centralized Database of Curated, Published, Quantitative Kinetic Models of Biochemical and Cellular Systems Nucleic Acids Res., 34: D689-D691.</a>
</p><h2>
  <a href="http://biomodels.net">biomodels.net</a>
</h2>
</body>

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      <ModelValue key="ModelValue_4" name="a_tr" simulationType="assignment">
        <Expression>
          (&lt;CN=Root,Model=Elowitz2000_Repressilator,Vector=Values[tps_active],Reference=Value&gt;-&lt;CN=Root,Model=Elowitz2000_Repressilator,Vector=Values[tps_repr],Reference=Value&gt;)*60
        </Expression>
      </ModelValue>
      <ModelValue key="ModelValue_3" name="tps_active" simulationType="fixed">
      </ModelValue>
      <ModelValue key="ModelValue_2" name="tps_repr" simulationType="fixed">
      </ModelValue>
      <ModelValue key="ModelValue_1" name="a0_tr" simulationType="assignment">
        <Expression>
          &lt;CN=Root,Model=Elowitz2000_Repressilator,Vector=Values[tps_repr],Reference=Value&gt;*60
        </Expression>
      </ModelValue>
    </ListOfModelValues>
    <ListOfReactions>
      <Reaction key="Reaction_6" name="degradation of LacI transcripts" reversible="false">
        <MiriamAnnotation>
<rdf:RDF
   xmlns:CopasiMT="http://www.copasi.org/RDF/MiriamTerms#"
   xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
  <rdf:Description rdf:about="#Reaction_6">
    <CopasiMT:isVersionOf rdf:resource="urn:miriam:obo.go:GO%3A0006402"/>
  </rdf:Description>
</rdf:RDF>

        </MiriamAnnotation>
        <ListOfSubstrates>
          <Substrate metabolite="Metabolite_10" stoichiometry="1"/>
        </ListOfSubstrates>
        <ListOfConstants>
          <Constant key="Parameter_358" name="k1" value="1"/>
        </ListOfConstants>
        <KineticLaw function="Function_13">
          <ListOfCallParameters>
            <CallParameter functionParameter="FunctionParameter_81">
              <SourceParameter reference="ModelValue_7"/>
            </CallParameter>
            <CallParameter functionParameter="FunctionParameter_79">
              <SourceParameter reference="Metabolite_10"/>
            </CallParameter>
          </ListOfCallParameters>
        </KineticLaw>
      </Reaction>
      <Reaction key="Reaction_7" name="degradation of TetR transcripts" reversible="false">
        <MiriamAnnotation>
<rdf:RDF
   xmlns:CopasiMT="http://www.copasi.org/RDF/MiriamTerms#"
   xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
  <rdf:Description rdf:about="#Reaction_7">
    <CopasiMT:isVersionOf rdf:resource="urn:miriam:obo.go:GO%3A0006402"/>
  </rdf:Description>
</rdf:RDF>

        </MiriamAnnotation>
        <ListOfSubstrates>
          <Substrate metabolite="Metabolite_11" stoichiometry="1"/>
        </ListOfSubstrates>
        <ListOfConstants>
          <Constant key="Parameter_359" name="k1" value="1"/>
        </ListOfConstants>
        <KineticLaw function="Function_13">
          <ListOfCallParameters>
            <CallParameter functionParameter="FunctionParameter_81">
              <SourceParameter reference="ModelValue_7"/>
            </CallParameter>
            <CallParameter functionParameter="FunctionParameter_79">
              <SourceParameter reference="Metabolite_11"/>
            </CallParameter>
          </ListOfCallParameters>
        </KineticLaw>
      </Reaction>
      <Reaction key="Reaction_8" name="degradation of CI transcripts" reversible="false">
        <MiriamAnnotation>
<rdf:RDF
   xmlns:CopasiMT="http://www.copasi.org/RDF/MiriamTerms#"
   xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
  <rdf:Description rdf:about="#Reaction_8">
    <CopasiMT:isVersionOf rdf:resource="urn:miriam:obo.go:GO%3A0006402"/>
  </rdf:Description>
</rdf:RDF>

        </MiriamAnnotation>
        <ListOfSubstrates>
          <Substrate metabolite="Metabolite_12" stoichiometry="1"/>
        </ListOfSubstrates>
        <ListOfConstants>
          <Constant key="Parameter_360" name="k1" value="1"/>
        </ListOfConstants>
        <KineticLaw function="Function_13">
          <ListOfCallParameters>
            <CallParameter functionParameter="FunctionParameter_81">
              <SourceParameter reference="ModelValue_7"/>
            </CallParameter>
            <CallParameter functionParameter="FunctionParameter_79">
              <SourceParameter reference="Metabolite_12"/>
            </CallParameter>
          </ListOfCallParameters>
        </KineticLaw>
      </Reaction>
      <Reaction key="Reaction_9" name="translation of LacI" reversible="false">
        <MiriamAnnotation>
<rdf:RDF
   xmlns:CopasiMT="http://www.copasi.org/RDF/MiriamTerms#"
   xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
  <rdf:Description rdf:about="#Reaction_9">
    <CopasiMT:isVersionOf rdf:resource="urn:miriam:obo.go:GO%3A0006412"/>
  </rdf:Description>
</rdf:RDF>

        </MiriamAnnotation>
        <ListOfProducts>
          <Product metabolite="Metabolite_7" stoichiometry="1"/>
        </ListOfProducts>
        <ListOfModifiers>
          <Modifier metabolite="Metabolite_10" stoichiometry="1"/>
        </ListOfModifiers>
        <ListOfConstants>
          <Constant key="Parameter_361" name="k_tl" value="1"/>
        </ListOfConstants>
        <KineticLaw function="Function_95">
          <ListOfCallParameters>
            <CallParameter functionParameter="FunctionParameter_458">
              <SourceParameter reference="Metabolite_10"/>
            </CallParameter>
            <CallParameter functionParameter="FunctionParameter_457">
              <SourceParameter reference="ModelValue_5"/>
            </CallParameter>
          </ListOfCallParameters>
        </KineticLaw>
      </Reaction>
      <Reaction key="Reaction_29" name="translation of TetR" reversible="false">
        <MiriamAnnotation>
<rdf:RDF
   xmlns:CopasiMT="http://www.copasi.org/RDF/MiriamTerms#"
   xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
  <rdf:Description rdf:about="#Reaction_29">
    <CopasiMT:isVersionOf rdf:resource="urn:miriam:obo.go:GO%3A0006412"/>
  </rdf:Description>
</rdf:RDF>

        </MiriamAnnotation>
        <ListOfProducts>
          <Product metabolite="Metabolite_8" stoichiometry="1"/>
        </ListOfProducts>
        <ListOfModifiers>
          <Modifier metabolite="Metabolite_11" stoichiometry="1"/>
        </ListOfModifiers>
        <ListOfConstants>
          <Constant key="Parameter_362" name="k_tl" value="1"/>
        </ListOfConstants>
        <KineticLaw function="Function_96">
          <ListOfCallParameters>
            <CallParameter functionParameter="FunctionParameter_361">
              <SourceParameter reference="Metabolite_11"/>
            </CallParameter>
            <CallParameter functionParameter="FunctionParameter_329">
              <SourceParameter reference="ModelValue_5"/>
            </CallParameter>
          </ListOfCallParameters>
        </KineticLaw>
      </Reaction>
      <Reaction key="Reaction_28" name="translation of CI" reversible="false">
        <MiriamAnnotation>
<rdf:RDF
   xmlns:CopasiMT="http://www.copasi.org/RDF/MiriamTerms#"
   xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
  <rdf:Description rdf:about="#Reaction_28">
    <CopasiMT:isVersionOf rdf:resource="urn:miriam:obo.go:GO%3A0006412"/>
  </rdf:Description>
</rdf:RDF>

        </MiriamAnnotation>
        <ListOfProducts>
          <Product metabolite="Metabolite_9" stoichiometry="1"/>
        </ListOfProducts>
        <ListOfModifiers>
          <Modifier metabolite="Metabolite_12" stoichiometry="1"/>
        </ListOfModifiers>
        <ListOfConstants>
          <Constant key="Parameter_363" name="k_tl" value="1"/>
        </ListOfConstants>
        <KineticLaw function="Function_97">
          <ListOfCallParameters>
            <CallParameter functionParameter="FunctionParameter_392">
              <SourceParameter reference="Metabolite_12"/>
            </CallParameter>
            <CallParameter functionParameter="FunctionParameter_412">
              <SourceParameter reference="ModelValue_5"/>
            </CallParameter>
          </ListOfCallParameters>
        </KineticLaw>
      </Reaction>
      <Reaction key="Reaction_27" name="degradation of LacI" reversible="false">
        <MiriamAnnotation>
<rdf:RDF
   xmlns:CopasiMT="http://www.copasi.org/RDF/MiriamTerms#"
   xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
  <rdf:Description rdf:about="#Reaction_27">
    <CopasiMT:isVersionOf rdf:resource="urn:miriam:obo.go:GO%3A0030163"/>
  </rdf:Description>
</rdf:RDF>

        </MiriamAnnotation>
        <ListOfSubstrates>
          <Substrate metabolite="Metabolite_7" stoichiometry="1"/>
        </ListOfSubstrates>
        <ListOfConstants>
          <Constant key="Parameter_372" name="k1" value="1"/>
        </ListOfConstants>
        <KineticLaw function="Function_13">
          <ListOfCallParameters>
            <CallParameter functionParameter="FunctionParameter_81">
              <SourceParameter reference="ModelValue_6"/>
            </CallParameter>
            <CallParameter functionParameter="FunctionParameter_79">
              <SourceParameter reference="Metabolite_7"/>
            </CallParameter>
          </ListOfCallParameters>
        </KineticLaw>
      </Reaction>
      <Reaction key="Reaction_26" name="degradation of TetR" reversible="false">
        <MiriamAnnotation>
<rdf:RDF
   xmlns:CopasiMT="http://www.copasi.org/RDF/MiriamTerms#"
   xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
  <rdf:Description rdf:about="#Reaction_26">
    <CopasiMT:isVersionOf rdf:resource="urn:miriam:obo.go:GO%3A0030163"/>
  </rdf:Description>
</rdf:RDF>

        </MiriamAnnotation>
        <ListOfSubstrates>
          <Substrate metabolite="Metabolite_8" stoichiometry="1"/>
        </ListOfSubstrates>
        <ListOfConstants>
          <Constant key="Parameter_369" name="k1" value="1"/>
        </ListOfConstants>
        <KineticLaw function="Function_13">
          <ListOfCallParameters>
            <CallParameter functionParameter="FunctionParameter_81">
              <SourceParameter reference="ModelValue_6"/>
            </CallParameter>
            <CallParameter functionParameter="FunctionParameter_79">
              <SourceParameter reference="Metabolite_8"/>
            </CallParameter>
          </ListOfCallParameters>
        </KineticLaw>
      </Reaction>
      <Reaction key="Reaction_25" name="degradation of CI" reversible="false">
        <MiriamAnnotation>
<rdf:RDF
   xmlns:CopasiMT="http://www.copasi.org/RDF/MiriamTerms#"
   xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
  <rdf:Description rdf:about="#Reaction_25">
    <CopasiMT:isVersionOf rdf:resource="urn:miriam:obo.go:GO%3A0030163"/>
  </rdf:Description>
</rdf:RDF>

        </MiriamAnnotation>
        <ListOfSubstrates>
          <Substrate metabolite="Metabolite_9" stoichiometry="1"/>
        </ListOfSubstrates>
        <ListOfConstants>
          <Constant key="Parameter_368" name="k1" value="1"/>
        </ListOfConstants>
        <KineticLaw function="Function_13">
          <ListOfCallParameters>
            <CallParameter functionParameter="FunctionParameter_81">
              <SourceParameter reference="ModelValue_6"/>
            </CallParameter>
            <CallParameter functionParameter="FunctionParameter_79">
              <SourceParameter reference="Metabolite_9"/>
            </CallParameter>
          </ListOfCallParameters>
        </KineticLaw>
      </Reaction>
      <Reaction key="Reaction_24" name="transcription of LacI" reversible="false">
        <MiriamAnnotation>
<rdf:RDF
   xmlns:CopasiMT="http://www.copasi.org/RDF/MiriamTerms#"
   xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
  <rdf:Description rdf:about="#Reaction_24">
    <CopasiMT:isVersionOf rdf:resource="urn:miriam:obo.go:GO%3A0006351"/>
  </rdf:Description>
</rdf:RDF>

        </MiriamAnnotation>
        <ListOfProducts>
          <Product metabolite="Metabolite_10" stoichiometry="1"/>
        </ListOfProducts>
        <ListOfModifiers>
          <Modifier metabolite="Metabolite_9" stoichiometry="1"/>
        </ListOfModifiers>
        <ListOfConstants>
          <Constant key="Parameter_14" name="KM" value="1"/>
          <Constant key="Parameter_9" name="a0_tr" value="1"/>
          <Constant key="Parameter_472" name="a_tr" value="1"/>
          <Constant key="Parameter_453" name="n" value="1"/>
        </ListOfConstants>
        <KineticLaw function="Function_98">
          <ListOfCallParameters>
            <CallParameter functionParameter="FunctionParameter_421">
              <SourceParameter reference="ModelValue_11"/>
            </CallParameter>
            <CallParameter functionParameter="FunctionParameter_434">
              <SourceParameter reference="Metabolite_9"/>
            </CallParameter>
            <CallParameter functionParameter="FunctionParameter_435">
              <SourceParameter reference="ModelValue_1"/>
            </CallParameter>
            <CallParameter functionParameter="FunctionParameter_436">
              <SourceParameter reference="ModelValue_4"/>
            </CallParameter>
            <CallParameter functionParameter="FunctionParameter_440">
              <SourceParameter reference="Compartment_1"/>
            </CallParameter>
            <CallParameter functionParameter="FunctionParameter_441">
              <SourceParameter reference="ModelValue_12"/>
            </CallParameter>
          </ListOfCallParameters>
        </KineticLaw>
      </Reaction>
      <Reaction key="Reaction_23" name="transcription of TetR" reversible="false">
        <MiriamAnnotation>
<rdf:RDF
   xmlns:CopasiMT="http://www.copasi.org/RDF/MiriamTerms#"
   xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
  <rdf:Description rdf:about="#Reaction_23">
    <CopasiMT:isVersionOf rdf:resource="urn:miriam:obo.go:GO%3A0006351"/>
  </rdf:Description>
</rdf:RDF>

        </MiriamAnnotation>
        <ListOfProducts>
          <Product metabolite="Metabolite_11" stoichiometry="1"/>
        </ListOfProducts>
        <ListOfModifiers>
          <Modifier metabolite="Metabolite_7" stoichiometry="1"/>
        </ListOfModifiers>
        <ListOfConstants>
          <Constant key="Parameter_452" name="KM" value="1"/>
          <Constant key="Parameter_473" name="a0_tr" value="1"/>
          <Constant key="Parameter_454" name="a_tr" value="1"/>
          <Constant key="Parameter_475" name="n" value="1"/>
        </ListOfConstants>
        <KineticLaw function="Function_99">
          <ListOfCallParameters>
            <CallParameter functionParameter="FunctionParameter_509">
              <SourceParameter reference="ModelValue_11"/>
            </CallParameter>
            <CallParameter functionParameter="FunctionParameter_510">
              <SourceParameter reference="Metabolite_7"/>
            </CallParameter>
            <CallParameter functionParameter="FunctionParameter_511">
              <SourceParameter reference="ModelValue_1"/>
            </CallParameter>
            <CallParameter functionParameter="FunctionParameter_512">
              <SourceParameter reference="ModelValue_4"/>
            </CallParameter>
            <CallParameter functionParameter="FunctionParameter_513">
              <SourceParameter reference="Compartment_1"/>
            </CallParameter>
            <CallParameter functionParameter="FunctionParameter_514">
              <SourceParameter reference="ModelValue_12"/>
            </CallParameter>
          </ListOfCallParameters>
        </KineticLaw>
      </Reaction>
      <Reaction key="Reaction_22" name="transcription of CI" reversible="false">
        <MiriamAnnotation>
<rdf:RDF
   xmlns:CopasiMT="http://www.copasi.org/RDF/MiriamTerms#"
   xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
  <rdf:Description rdf:about="#Reaction_22">
    <CopasiMT:isVersionOf rdf:resource="urn:miriam:obo.go:GO%3A0006351"/>
  </rdf:Description>
</rdf:RDF>

        </MiriamAnnotation>
        <ListOfProducts>
          <Product metabolite="Metabolite_12" stoichiometry="1"/>
        </ListOfProducts>
        <ListOfModifiers>
          <Modifier metabolite="Metabolite_8" stoichiometry="1"/>
        </ListOfModifiers>
        <ListOfConstants>
          <Constant key="Parameter_474" name="KM" value="1"/>
          <Constant key="Parameter_409" name="a0_tr" value="1"/>
          <Constant key="Parameter_410" name="a_tr" value="1"/>
          <Constant key="Parameter_450" name="n" value="1"/>
        </ListOfConstants>
        <KineticLaw function="Function_100">
          <ListOfCallParameters>
            <CallParameter functionParameter="FunctionParameter_521">
              <SourceParameter reference="ModelValue_11"/>
            </CallParameter>
            <CallParameter functionParameter="FunctionParameter_522">
              <SourceParameter reference="Metabolite_8"/>
            </CallParameter>
            <CallParameter functionParameter="FunctionParameter_523">
              <SourceParameter reference="ModelValue_1"/>
            </CallParameter>
            <CallParameter functionParameter="FunctionParameter_524">
              <SourceParameter reference="ModelValue_4"/>
            </CallParameter>
            <CallParameter functionParameter="FunctionParameter_525">
              <SourceParameter reference="Compartment_1"/>
            </CallParameter>
            <CallParameter functionParameter="FunctionParameter_526">
              <SourceParameter reference="ModelValue_12"/>
            </CallParameter>
          </ListOfCallParameters>
        </KineticLaw>
      </Reaction>
    </ListOfReactions>
    <StateTemplate>
      <StateTemplateVariable objectReference="Model_0"/>
      <StateTemplateVariable objectReference="Metabolite_7"/>
      <StateTemplateVariable objectReference="Metabolite_8"/>
      <StateTemplateVariable objectReference="Metabolite_9"/>
      <StateTemplateVariable objectReference="Metabolite_10"/>
      <StateTemplateVariable objectReference="Metabolite_11"/>
      <StateTemplateVariable objectReference="Metabolite_12"/>
      <StateTemplateVariable objectReference="ModelValue_8"/>
      <StateTemplateVariable objectReference="ModelValue_7"/>
      <StateTemplateVariable objectReference="ModelValue_6"/>
      <StateTemplateVariable objectReference="ModelValue_5"/>
      <StateTemplateVariable objectReference="ModelValue_4"/>
      <StateTemplateVariable objectReference="ModelValue_1"/>
      <StateTemplateVariable objectReference="ModelValue_16"/>
      <StateTemplateVariable objectReference="ModelValue_15"/>
      <StateTemplateVariable objectReference="ModelValue_14"/>
      <StateTemplateVariable objectReference="ModelValue_13"/>
      <StateTemplateVariable objectReference="ModelValue_12"/>
      <StateTemplateVariable objectReference="ModelValue_11"/>
      <StateTemplateVariable objectReference="ModelValue_10"/>
      <StateTemplateVariable objectReference="ModelValue_9"/>
      <StateTemplateVariable objectReference="ModelValue_3"/>
      <StateTemplateVariable objectReference="ModelValue_2"/>
      <StateTemplateVariable objectReference="Compartment_1"/>
    </StateTemplate>
    <InitialState type="initialState">
      0 0 0 0 0 20 0 2.885390081777927 0.3465735902799726 0.06931471805599453 6.931471805599453 29.97 0.03 0.2 0.2164042561333445 216.1878518772112 20 2 40 2 10 0.5 0.0005 1 
    </InitialState>
  </Model>
  <ListOfTasks>
    <Task key="Task_12" name="Steady-State" type="steadyState" scheduled="false" updateModel="false">
      <Report reference="Report_15" target="" append="1"/>
      <Problem>
        <Parameter name="JacobianRequested" type="bool" value="1"/>
        <Parameter name="StabilityAnalysisRequested" type="bool" value="1"/>
      </Problem>
      <Method name="Enhanced Newton" type="EnhancedNewton">
        <Parameter name="Resolution" type="unsignedFloat" value="1e-009"/>
        <Parameter name="Derivation Factor" type="unsignedFloat" value="0.001"/>
        <Parameter name="Use Newton" type="bool" value="1"/>
        <Parameter name="Use Integration" type="bool" value="1"/>
        <Parameter name="Use Back Integration" type="bool" value="1"/>
        <Parameter name="Accept Negative Concentrations" type="bool" value="0"/>
        <Parameter name="Iteration Limit" type="unsignedInteger" value="50"/>
        <Parameter name="Maximum duration for forward integration" type="unsignedFloat" value="1e+009"/>
        <Parameter name="Maximum duration for backward integration" type="unsignedFloat" value="1e+006"/>
      </Method>
    </Task>
    <Task key="Task_21" name="Time-Course" type="timeCourse" scheduled="false" updateModel="false">
      <Problem>
        <Parameter name="StepNumber" type="unsignedInteger" value="1000"/>
        <Parameter name="StepSize" type="float" value="1"/>
        <Parameter name="Duration" type="float" value="1000"/>
        <Parameter name="TimeSeriesRequested" type="bool" value="1"/>
        <Parameter name="OutputStartTime" type="float" value="0"/>
      </Problem>
      <Method name="Deterministic (LSODA)" type="Deterministic(LSODA)">
        <Parameter name="Integrate Reduced Model" type="bool" value="0"/>
        <Parameter name="Relative Tolerance" type="unsignedFloat" value="1e-006"/>
        <Parameter name="Absolute Tolerance" type="unsignedFloat" value="1e-012"/>
        <Parameter name="Max Internal Steps" type="unsignedInteger" value="10000"/>
      </Method>
    </Task>
    <Task key="Task_20" name="Scan" type="scan" scheduled="false" updateModel="false">
      <Problem>
        <Parameter name="Subtask" type="unsignedInteger" value="1"/>
        <ParameterGroup name="ScanItems">
        </ParameterGroup>
        <Parameter name="Output in subtask" type="bool" value="1"/>
        <Parameter name="Adjust initial conditions" type="bool" value="0"/>
      </Problem>
      <Method name="Scan Framework" type="ScanFramework">
      </Method>
    </Task>
    <Task key="Task_19" name="Elementary Flux Modes" type="fluxMode" scheduled="false" updateModel="false">
      <Report reference="Report_14" target="" append="1"/>
      <Problem>
      </Problem>
      <Method name="Bit Pattern Tree Algorithm" type="EFMBitPatternTreeMethod">
      </Method>
    </Task>
    <Task key="Task_18" name="Optimization" type="optimization" scheduled="false" updateModel="false">
      <Report reference="Report_13" target="" append="1"/>
      <Problem>
        <Parameter name="Subtask" type="cn" value="CN=Root,Vector=TaskList[Steady-State]"/>
        <ParameterText name="ObjectiveExpression" type="expression">
          
        </ParameterText>
        <Parameter name="Maximize" type="bool" value="0"/>
        <ParameterGroup name="OptimizationItemList">
        </ParameterGroup>
        <ParameterGroup name="OptimizationConstraintList">
        </ParameterGroup>
      </Problem>
      <Method name="Random Search" type="RandomSearch">
        <Parameter name="Number of Iterations" type="unsignedInteger" value="100000"/>
        <Parameter name="Random Number Generator" type="unsignedInteger" value="1"/>
        <Parameter name="Seed" type="unsignedInteger" value="0"/>
      </Method>
    </Task>
    <Task key="Task_17" name="Parameter Estimation" type="parameterFitting" scheduled="false" updateModel="false">
      <Report reference="Report_12" target="" append="1"/>
      <Problem>
        <Parameter name="Maximize" type="bool" value="0"/>
        <ParameterGroup name="OptimizationItemList">
        </ParameterGroup>
        <ParameterGroup name="OptimizationConstraintList">
        </ParameterGroup>
        <Parameter name="Steady-State" type="cn" value="CN=Root,Vector=TaskList[Steady-State]"/>
        <Parameter name="Time-Course" type="cn" value="CN=Root,Vector=TaskList[Time-Course]"/>
        <ParameterGroup name="Experiment Set">
        </ParameterGroup>
      </Problem>
      <Method name="Evolutionary Programming" type="EvolutionaryProgram">
        <Parameter name="Number of Generations" type="unsignedInteger" value="200"/>
        <Parameter name="Population Size" type="unsignedInteger" value="20"/>
        <Parameter name="Random Number Generator" type="unsignedInteger" value="1"/>
        <Parameter name="Seed" type="unsignedInteger" value="0"/>
      </Method>
    </Task>
    <Task key="Task_16" name="Metabolic Control Analysis" type="metabolicControlAnalysis" scheduled="false" updateModel="false">
      <Report reference="Report_11" target="" append="1"/>
      <Problem>
        <Parameter name="Steady-State" type="key" value="Task_12"/>
      </Problem>
      <Method name="MCA Method (Reder)" type="MCAMethod(Reder)">
        <Parameter name="Modulation Factor" type="unsignedFloat" value="1e-009"/>
      </Method>
    </Task>
    <Task key="Task_15" name="Lyapunov Exponents" type="lyapunovExponents" scheduled="false" updateModel="false">
      <Report reference="Report_10" target="" append="1"/>
      <Problem>
        <Parameter name="ExponentNumber" type="unsignedInteger" value="3"/>
        <Parameter name="DivergenceRequested" type="bool" value="1"/>
        <Parameter name="TransientTime" type="float" value="0"/>
      </Problem>
      <Method name="Wolf Method" type="WolfMethod">
        <Parameter name="Orthonormalization Interval" type="unsignedFloat" value="1"/>
        <Parameter name="Overall time" type="unsignedFloat" value="1000"/>
        <Parameter name="Relative Tolerance" type="unsignedFloat" value="1e-006"/>
        <Parameter name="Absolute Tolerance" type="unsignedFloat" value="1e-012"/>
        <Parameter name="Max Internal Steps" type="unsignedInteger" value="10000"/>
      </Method>
    </Task>
    <Task key="Task_14" name="Time Scale Separation Analysis" type="timeScaleSeparationAnalysis" scheduled="false" updateModel="false">
      <Report reference="Report_9" target="" append="1"/>
      <Problem>
        <Parameter name="StepNumber" type="unsignedInteger" value="100"/>
        <Parameter name="StepSize" type="float" value="0.01"/>
        <Parameter name="Duration" type="float" value="1"/>
        <Parameter name="TimeSeriesRequested" type="bool" value="1"/>
        <Parameter name="OutputStartTime" type="float" value="0"/>
      </Problem>
      <Method name="ILDM (LSODA,Deuflhard)" type="TimeScaleSeparation(ILDM,Deuflhard)">
        <Parameter name="Deuflhard Tolerance" type="unsignedFloat" value="1e-006"/>
      </Method>
    </Task>
    <Task key="Task_13" name="Sensitivities" type="sensitivities" scheduled="false" updateModel="false">
      <Report reference="Report_8" target="" append="1"/>
      <Problem>
        <Parameter name="SubtaskType" type="unsignedInteger" value="1"/>
        <ParameterGroup name="TargetFunctions">
          <Parameter name="SingleObject" type="cn" value=""/>
          <Parameter name="ObjectListType" type="unsignedInteger" value="7"/>
        </ParameterGroup>
        <ParameterGroup name="ListOfVariables">
          <ParameterGroup name="Variables">
            <Parameter name="SingleObject" type="cn" value=""/>
            <Parameter name="ObjectListType" type="unsignedInteger" value="41"/>
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      </Problem>
      <Method name="Sensitivities Method" type="SensitivitiesMethod">
        <Parameter name="Delta factor" type="unsignedFloat" value="0.001"/>
        <Parameter name="Delta minimum" type="unsignedFloat" value="1e-012"/>
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    <Task key="Task_22" name="Moieties" type="moieties" scheduled="false" updateModel="false">
      <Problem>
      </Problem>
      <Method name="Householder Reduction" type="Householder">
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        <Object cn="CN=Root,Vector=TaskList[Steady-State]"/>
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        <body xmlns="http://www.w3.org/1999/xhtml">
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        <body xmlns="http://www.w3.org/1999/xhtml">
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      <Footer>
        <Object cn="String=&#x0a;"/>
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        <body xmlns="http://www.w3.org/1999/xhtml">
          Automatically generated report.
        </body>
      </Comment>
      <Header>
        <Object cn="CN=Root,Vector=TaskList[Lyapunov Exponents],Object=Description"/>
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      <Footer>
        <Object cn="String=&#x0a;"/>
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        <body xmlns="http://www.w3.org/1999/xhtml">
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      <Footer>
        <Object cn="String=&#x0a;"/>
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      <Comment>
        <body xmlns="http://www.w3.org/1999/xhtml">
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        </body>
      </Comment>
      <Header>
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        <Object cn="String=&#x0a;"/>
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  </ListOfReports>
  <ListOfPlots>
    <PlotSpecification name="timecourse" type="Plot2D" active="1">
      <Parameter name="log X" type="bool" value="0"/>
      <Parameter name="log Y" type="bool" value="0"/>
      <ListOfPlotItems>
        <PlotItem name="[&quot;LacI protein&quot;]|Time" type="Curve2D">
          <Parameter name="Line type" type="unsignedInteger" value="0"/>
          <Parameter name="Recording Activity" type="string" value="during"/>
          <ListOfChannels>
            <ChannelSpec cn="CN=Root,Model=Elowitz2000_Repressilator,Reference=Time"/>
            <ChannelSpec cn="CN=Root,Model=Elowitz2000_Repressilator,Vector=Compartments[cell],Vector=Metabolites[LacI protein],Reference=Concentration"/>
          </ListOfChannels>
        </PlotItem>
        <PlotItem name="[&quot;TetR protein&quot;]|Time" type="Curve2D">
          <Parameter name="Line type" type="unsignedInteger" value="0"/>
          <Parameter name="Recording Activity" type="string" value="during"/>
          <ListOfChannels>
            <ChannelSpec cn="CN=Root,Model=Elowitz2000_Repressilator,Reference=Time"/>
            <ChannelSpec cn="CN=Root,Model=Elowitz2000_Repressilator,Vector=Compartments[cell],Vector=Metabolites[TetR protein],Reference=Concentration"/>
          </ListOfChannels>
        </PlotItem>
        <PlotItem name="[&quot;cI protein&quot;]|Time" type="Curve2D">
          <Parameter name="Line type" type="unsignedInteger" value="0"/>
          <Parameter name="Recording Activity" type="string" value="during"/>
          <ListOfChannels>
            <ChannelSpec cn="CN=Root,Model=Elowitz2000_Repressilator,Reference=Time"/>
            <ChannelSpec cn="CN=Root,Model=Elowitz2000_Repressilator,Vector=Compartments[cell],Vector=Metabolites[cI protein],Reference=Concentration"/>
          </ListOfChannels>
        </PlotItem>
      </ListOfPlotItems>
    </PlotSpecification>
    <PlotSpecification name="phaseplot" type="Plot2D" active="1">
      <Parameter name="log X" type="bool" value="0"/>
      <Parameter name="log Y" type="bool" value="0"/>
      <ListOfPlotItems>
        <PlotItem name="[&quot;cI protein&quot;]|[&quot;LacI protein&quot;]" type="Curve2D">
          <Parameter name="Line type" type="unsignedInteger" value="0"/>
          <Parameter name="Recording Activity" type="string" value="during"/>
          <ListOfChannels>
            <ChannelSpec cn="CN=Root,Model=Elowitz2000_Repressilator,Vector=Compartments[cell],Vector=Metabolites[LacI protein],Reference=Concentration"/>
            <ChannelSpec cn="CN=Root,Model=Elowitz2000_Repressilator,Vector=Compartments[cell],Vector=Metabolites[cI protein],Reference=Concentration"/>
          </ListOfChannels>
        </PlotItem>
        <PlotItem name="[&quot;TetR protein&quot;]|[&quot;cI protein&quot;]" type="Curve2D">
          <Parameter name="Line type" type="unsignedInteger" value="0"/>
          <Parameter name="Recording Activity" type="string" value="during"/>
          <ListOfChannels>
            <ChannelSpec cn="CN=Root,Model=Elowitz2000_Repressilator,Vector=Compartments[cell],Vector=Metabolites[cI protein],Reference=Concentration"/>
            <ChannelSpec cn="CN=Root,Model=Elowitz2000_Repressilator,Vector=Compartments[cell],Vector=Metabolites[TetR protein],Reference=Concentration"/>
          </ListOfChannels>
        </PlotItem>
        <PlotItem name="[&quot;LacI protein&quot;]|[&quot;TetR protein&quot;]" type="Curve2D">
          <Parameter name="Line type" type="unsignedInteger" value="0"/>
          <Parameter name="Recording Activity" type="string" value="during"/>
          <ListOfChannels>
            <ChannelSpec cn="CN=Root,Model=Elowitz2000_Repressilator,Vector=Compartments[cell],Vector=Metabolites[TetR protein],Reference=Concentration"/>
            <ChannelSpec cn="CN=Root,Model=Elowitz2000_Repressilator,Vector=Compartments[cell],Vector=Metabolites[LacI protein],Reference=Concentration"/>
          </ListOfChannels>
        </PlotItem>
      </ListOfPlotItems>
    </PlotSpecification>
  </ListOfPlots>
  <GUI>
  </GUI>
  <SBMLReference file="../BIOMD0000000012.xml">
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    <SBMLMap SBMLid="PX" COPASIkey="Metabolite_7"/>
    <SBMLMap SBMLid="PY" COPASIkey="Metabolite_8"/>
    <SBMLMap SBMLid="PZ" COPASIkey="Metabolite_9"/>
    <SBMLMap SBMLid="Reaction1" COPASIkey="Reaction_6"/>
    <SBMLMap SBMLid="Reaction10" COPASIkey="Reaction_24"/>
    <SBMLMap SBMLid="Reaction11" COPASIkey="Reaction_23"/>
    <SBMLMap SBMLid="Reaction12" COPASIkey="Reaction_22"/>
    <SBMLMap SBMLid="Reaction2" COPASIkey="Reaction_7"/>
    <SBMLMap SBMLid="Reaction3" COPASIkey="Reaction_8"/>
    <SBMLMap SBMLid="Reaction4" COPASIkey="Reaction_9"/>
    <SBMLMap SBMLid="Reaction5" COPASIkey="Reaction_29"/>
    <SBMLMap SBMLid="Reaction6" COPASIkey="Reaction_28"/>
    <SBMLMap SBMLid="Reaction7" COPASIkey="Reaction_27"/>
    <SBMLMap SBMLid="Reaction8" COPASIkey="Reaction_26"/>
    <SBMLMap SBMLid="Reaction9" COPASIkey="Reaction_25"/>
    <SBMLMap SBMLid="X" COPASIkey="Metabolite_10"/>
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    <SBMLMap SBMLid="a_tr" COPASIkey="ModelValue_4"/>
    <SBMLMap SBMLid="alpha" COPASIkey="ModelValue_14"/>
    <SBMLMap SBMLid="alpha0" COPASIkey="ModelValue_15"/>
    <SBMLMap SBMLid="beta" COPASIkey="ModelValue_16"/>
    <SBMLMap SBMLid="cell" COPASIkey="Compartment_1"/>
    <SBMLMap SBMLid="eff" COPASIkey="ModelValue_13"/>
    <SBMLMap SBMLid="k_tl" COPASIkey="ModelValue_5"/>
    <SBMLMap SBMLid="kd_mRNA" COPASIkey="ModelValue_7"/>
    <SBMLMap SBMLid="kd_prot" COPASIkey="ModelValue_6"/>
    <SBMLMap SBMLid="n" COPASIkey="ModelValue_12"/>
    <SBMLMap SBMLid="ps_0" COPASIkey="ModelValue_2"/>
    <SBMLMap SBMLid="ps_a" COPASIkey="ModelValue_3"/>
    <SBMLMap SBMLid="t_ave" COPASIkey="ModelValue_8"/>
    <SBMLMap SBMLid="tau_mRNA" COPASIkey="ModelValue_10"/>
    <SBMLMap SBMLid="tau_prot" COPASIkey="ModelValue_9"/>
  </SBMLReference>
</COPASI>
