Location: Vilar, Kueh, Barkai, Leibler, 2002 @ bfddd87b5e19 / vilar_kueh_barkai_leibler_2002.cellml

Author:
Hanne <Hanne@hanne-nielsens-macbook.local>
Date:
2010-08-09 15:15:58+12:00
Desc:
Updated xul
Permanent Source URI:
https://models.cellml.org/workspace/vilar_kueh_barkai_leibler_2002/rawfile/bfddd87b5e19b2bbd152fd7fdf68d58f2c84f86a/vilar_kueh_barkai_leibler_2002.cellml

<?xml version="1.0"?>
<model xmlns="http://www.cellml.org/cellml/1.0#" xmlns:cmeta="http://www.cellml.org/metadata/1.0#" cmeta:id="vilar_kueh_barkai_leibler_2002" name="vilar_kueh_barkai_leibler_2002">
<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
  <articleinfo>
  <title>Modelling a Genetic Oscillator</title>
  <author>
    <firstname>Catherine</firstname>
          <surname>Lloyd</surname>
    <affiliation>
      <shortaffil>Auckland Bioengineering Institute, The University of Auckland</shortaffil>
    </affiliation>
  </author>
</articleinfo>
  <section id="sec_status">
    <title>Model Status</title>
    <para>
            This CellML modelis known to run in OpenCell and COR to reproduce the results published in the paper on which it is based (figures 2 and 3).
          </para>
  </section>
  <sect1 id="sec_structure">
<title>Model Structure</title>

<para>
ABSTRACT: A wide range of organisms use circadian clocks to keep internal sense of daily time and regulate their behavior accordingly. Most of these clocks use intracellular genetic networks based on positive and negative regulatory elements. The integration of these "circuits" at the cellular level imposes strong constraints on their functioning and design. Here, we study a recently proposed model [Barkai, N. and Leibler, S. (2000) Nature (London), 403, 267-268] that incorporates just the essential elements found experimentally. We show that this type of oscillator is driven mainly by two elements: the concentration of a repressor protein and the dynamics of an activator protein forming an inactive complex with the repressor. Thus, the clock does not need to rely on mRNA dynamics to oscillate, which makes it especially resistant to fluctuations. Oscillations can be present even when the time average of the number of mRNA molecules goes below one. Under some conditions, this oscillator is not only resistant to but, paradoxically, also enhanced by the intrinsic biochemical noise.
</para>

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

<para>
Mechanisms of noise-resistance in genetic oscillators, Jose M. G. Vilar, Hao Yuan Kueh, Naama Barkai, and Stanislas Leibler, 2002,<emphasis>Proceedings of the National Academy of Sciences of the United States of America</emphasis>, 99, 5988-5992.  <ulink url="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&amp;db=PubMed&amp;list_uids=11972055&amp;dopt=Abstract">PubMed ID: 11972055</ulink>
</para>

<informalfigure float="0" id="fig_reaction_diagram">
<mediaobject>
  <imageobject>
    <objectinfo>
      <title>reaction diagram</title>
    </objectinfo>
    <imagedata fileref="vilar_2002.png"/>
  </imageobject>
</mediaobject>
<caption>Biochemical network of the circadian oscillator model.</caption>
</informalfigure>

</sect1>
</article>
</documentation>

  <units name="hour">
    <unit multiplier="3600" units="second"/>
  </units>
  
  <units base_units="yes" name="molecules"/>
  
  <units name="flux">
    <unit units="molecules"/>
	<unit exponent="-1" units="hour"/>
  </units>
  
  <units name="first_order_rate">
    <unit exponent="-1" units="hour"/>
  </units>
  
  <units name="second_order_rate">
    <unit exponent="-1" units="molecules"/>
    <unit exponent="-1" units="hour"/>
  </units>
  
  <component name="environment">
    <variable cmeta:id="environment_time" name="time" public_interface="out" units="hour"/>
  </component>

  <component name="A">
    <variable cmeta:id="A_A" initial_value="0.0" name="A" public_interface="out" units="molecules"/>
    
	<variable name="time" public_interface="in" units="hour"/>
    <variable name="RXN1" public_interface="in" units="flux"/>
    <variable name="RXN2" public_interface="in" units="flux"/>
    <variable name="RXN5" public_interface="in" units="flux"/>
    <variable name="RXN11" public_interface="in" units="flux"/>
    <variable name="RXN6" public_interface="in" units="flux"/>
    <variable name="RXN10" public_interface="in" units="flux"/>
    <variable name="RXN12" public_interface="in" units="flux"/>
	
	<math xmlns="http://www.w3.org/1998/Math/MathML" id="Deriv_A_Calc">
      <apply>
        <eq/>
        <apply>
          <diff/>
          <bvar>
            <ci>time</ci>
          </bvar>
          <ci>A</ci>
        </apply>
        <apply>
          <times/>
          <apply>
            <divide/>
            <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
            <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
          </apply>
          <apply>
            <plus/>
            <apply>
              <times/>
              <apply>
                <minus/>
                <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
              </apply>
              <ci>RXN1</ci>
            </apply>
            <apply>
              <times/>
              <apply>
                <minus/>
                <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
              </apply>
              <ci>RXN2</ci>
            </apply>
            <apply>
              <times/>
              <apply>
                <minus/>
                <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
              </apply>
              <ci>RXN5</ci>
            </apply>
            <apply>
              <times/>
              <apply>
                <minus/>
                <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
              </apply>
              <ci>RXN11</ci>
            </apply>
            <ci>RXN6</ci>
            <ci>RXN10</ci>
            <ci>RXN12</ci>
          </apply>
        </apply>
      </apply>
    </math>
  </component>
  
  <component name="C">
    <variable cmeta:id="C_C" initial_value="0.0" name="C" public_interface="out" units="molecules"/>
    
	<variable name="time" public_interface="in" units="hour"/>
    <variable name="RXN3" public_interface="in" units="flux"/>
    <variable name="RXN1" public_interface="in" units="flux"/>
    
	<math xmlns="http://www.w3.org/1998/Math/MathML" id="Deriv_C_Calc">
      <apply>
        <eq/>
        <apply>
          <diff/>
          <bvar>
            <ci>time</ci>
          </bvar>
          <ci>C</ci>
        </apply>
        <apply>
          <times/>
          <apply>
            <divide/>
            <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
            <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
          </apply>
          <apply>
            <plus/>
            <apply>
              <times/>
              <apply>
                <minus/>
                <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
              </apply>
              <ci>RXN3</ci>
            </apply>
            <ci>RXN1</ci>
          </apply>
        </apply>
      </apply>
    </math>
  </component>
  
  <component name="DA">
    <variable cmeta:id="DA_DA" initial_value="1" name="DA" public_interface="out" units="molecules"/>
    
	<variable name="time" public_interface="in" units="hour"/>
    <variable name="RXN5" public_interface="in" units="flux"/>
    <variable name="RXN7" public_interface="in" units="flux"/>
    <variable name="RXN6" public_interface="in" units="flux"/>
    
	<math xmlns="http://www.w3.org/1998/Math/MathML" id="Deriv_DA_Calc">
      <apply>
        <eq/>
        <apply>
          <diff/>
          <bvar>
            <ci>time</ci>
          </bvar>
          <ci>DA</ci>
        </apply>
        <apply>
          <times/>
          <apply>
            <divide/>
            <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
            <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
          </apply>
          <apply>
            <plus/>
            <apply>
              <times/>
              <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">-1</cn>
              <ci>RXN5</ci>
            </apply>
            <apply>
              <times/>
              <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">-1</cn>
              <ci>RXN7</ci>
            </apply>
            <ci>RXN6</ci>
            <ci>RXN7</ci>
          </apply>
        </apply>
      </apply>
    </math>
  </component>
  
  <component name="DAp">
    <variable cmeta:id="DAp_DAp" initial_value="0.0" name="DAp" public_interface="out" units="molecules"/>
    
	<variable name="time" public_interface="in" units="hour"/>
    <variable name="RXN6" public_interface="in" units="flux"/>
    <variable name="RXN8" public_interface="in" units="flux"/>
    <variable name="RXN5" public_interface="in" units="flux"/>
    
	<math xmlns="http://www.w3.org/1998/Math/MathML" id="Deriv_DAp_Calc">
      <apply>
        <eq/>
        <apply>
          <diff/>
          <bvar>
            <ci>time</ci>
          </bvar>
          <ci>DAp</ci>
        </apply>
        <apply>
          <times/>
          <apply>
            <divide/>
            <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
            <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
          </apply>
          <apply>
            <plus/>
            <apply>
              <times/>
              <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">-1</cn>
              <ci>RXN6</ci>
            </apply>
            <apply>
              <times/>
              <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">-1</cn>
              <ci>RXN8</ci>
            </apply>
            <ci>RXN5</ci>
            <ci>RXN8</ci>
          </apply>
        </apply>
      </apply>
    </math>
  </component>
  
  <component name="DR">
    <variable cmeta:id="DR_DR" initial_value="1" name="DR" public_interface="out" units="molecules"/>
    
	<variable name="time" public_interface="in" units="hour"/>
    <variable name="RXN11" public_interface="in" units="flux"/>
    <variable name="RXN12" public_interface="in" units="flux"/>
    <variable name="RXN13" public_interface="in" units="flux"/>
    
	<math xmlns="http://www.w3.org/1998/Math/MathML" id="Deriv_DR_Calc">
      <apply>
        <eq/>
        <apply>
          <diff/>
          <bvar>
            <ci>time</ci>
          </bvar>
          <ci>DR</ci>
        </apply>
        <apply>
          <times/>
          <apply>
            <divide/>
            <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
            <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
          </apply>
          <apply>
            <plus/>
            <apply>
              <times/>
              <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">-1</cn>
              <ci>RXN11</ci>
            </apply>
            <apply>
              <times/>
              <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">-1</cn>
              <ci>RXN13</ci>
            </apply>
            <ci>RXN12</ci>
            <ci>RXN13</ci>
          </apply>
        </apply>
      </apply>
    </math>
  </component>
  
  <component name="DRP">
    <variable cmeta:id="DRP_DRP" initial_value="1" name="DRP" public_interface="out" units="molecules"/>
    
	<variable name="time" public_interface="in" units="hour"/>
    <variable name="RXN12" public_interface="in" units="flux"/>
    <variable name="RXN11" public_interface="in" units="flux"/>
    <variable name="RXN14" public_interface="in" units="flux"/>
    
	<math xmlns="http://www.w3.org/1998/Math/MathML" id="Deriv_DRP_Calc">
      <apply>
        <eq/>
        <apply>
          <diff/>
          <bvar>
            <ci>time</ci>
          </bvar>
          <ci>DRP</ci>
        </apply>
        <apply>
          <times/>
          <apply>
            <divide/>
            <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
            <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
          </apply>
          <apply>
            <plus/>
            <apply>
              <times/>
              <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">-1</cn>
              <ci>RXN12</ci>
            </apply>
            <apply>
              <times/>
              <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">-1</cn>
              <ci>RXN14</ci>
            </apply>
            <ci>RXN11</ci>
            <ci>RXN14</ci>
          </apply>
        </apply>
      </apply>
    </math>
  </component>
  
  <component name="MA">
    <variable cmeta:id="MA_MA" initial_value="0.0" name="MA" public_interface="out" units="molecules"/>
    
	<variable name="time" public_interface="in" units="hour"/>
    <variable name="RXN7" public_interface="in" units="flux"/>
    <variable name="RXN8" public_interface="in" units="flux"/>
    <variable name="RXN9" public_interface="in" units="flux"/>
    <variable name="RXN10" public_interface="in" units="flux"/>
    
	<math xmlns="http://www.w3.org/1998/Math/MathML" id="Deriv_MA_Calc">
      <apply>
        <eq/>
        <apply>
          <diff/>
          <bvar>
            <ci>time</ci>
          </bvar>
          <ci>MA</ci>
        </apply>
        <apply>
          <times/>
          <apply>
            <divide/>
            <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
            <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
          </apply>
          <apply>
            <plus/>
            <apply>
              <times/>
              <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">-1</cn>
              <ci>RXN9</ci>
            </apply>
            <apply>
              <times/>
              <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">-1</cn>
              <ci>RXN10</ci>
            </apply>
            <ci>RXN7</ci>
            <ci>RXN8</ci>
            <ci>RXN10</ci>
          </apply>
        </apply>
      </apply>
    </math>
  </component>
  
  <component name="MR">
    <variable cmeta:id="MR_MR" initial_value="0.0" name="MR" public_interface="out" units="molecules"/>
    
	<variable name="time" public_interface="in" units="hour"/>
    <variable name="RXN13" public_interface="in" units="flux"/>
    <variable name="RXN14" public_interface="in" units="flux"/>
    <variable name="RXN15" public_interface="in" units="flux"/>
    <variable name="RXN16" public_interface="in" units="flux"/>
    
	<math xmlns="http://www.w3.org/1998/Math/MathML" id="Deriv_MR_Calc">
      <apply>
        <eq/>
        <apply>
          <diff/>
          <bvar>
            <ci>time</ci>
          </bvar>
          <ci>MR</ci>
        </apply>
        <apply>
          <times/>
          <apply>
            <divide/>
            <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
            <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
          </apply>
          <apply>
            <plus/>
            <apply>
              <times/>
              <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">-1</cn>
              <ci>RXN15</ci>
            </apply>
            <apply>
              <times/>
              <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">-1</cn>
              <ci>RXN16</ci>
            </apply>
            <ci>RXN13</ci>
            <ci>RXN14</ci>
            <ci>RXN16</ci>
          </apply>
        </apply>
      </apply>
    </math>
  </component>
  
  <component name="R">
    <variable cmeta:id="R_R" initial_value="0.0" name="R" public_interface="out" units="molecules"/>
    
	<variable name="time" public_interface="in" units="hour"/>
    <variable name="RXN1" public_interface="in" units="flux"/>
    <variable name="RXN3" public_interface="in" units="flux"/>
    <variable name="RXN4" public_interface="in" units="flux"/>
    <variable name="RXN16" public_interface="in" units="flux"/>
    
	<math xmlns="http://www.w3.org/1998/Math/MathML" id="Deriv_R_Calc">
      <apply>
        <eq/>
        <apply>
          <diff/>
          <bvar>
            <ci>time</ci>
          </bvar>
          <ci>R</ci>
        </apply>
        <apply>
          <times/>
          <apply>
            <divide/>
            <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
            <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
          </apply>
          <apply>
            <plus/>
            <apply>
              <times/>
              <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">-1</cn>
              <ci>RXN1</ci>
            </apply>
            <apply>
              <times/>
              <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">-1</cn>
              <ci>RXN4</ci>
            </apply>
            <ci>RXN3</ci>
            <ci>RXN16</ci>
          </apply>
        </apply>
      </apply>
    </math>
  </component>
  
  <component name="RXN1">
    <variable name="RXN1" public_interface="out" units="flux"/>
    
	<variable name="A" public_interface="in" units="molecules"/>
    <variable name="R" public_interface="in" units="molecules"/>
    <variable initial_value="2" name="Gamma_1" units="second_order_rate"/>
    
	<math xmlns="http://www.w3.org/1998/Math/MathML" id="RXN1_Calc">
      <apply>
        <eq/>
        <ci>RXN1</ci>
        <apply>
          <times/>
          <ci>A</ci>
          <ci>R</ci>
          <ci>Gamma_1</ci>
        </apply>
      </apply>
    </math>
  </component>
  
  <component name="RXN2">
    <variable name="RXN2" public_interface="out" units="flux"/>
    
	<variable name="A" public_interface="in" units="molecules"/>
    <variable initial_value="1" name="Delta_1" units="first_order_rate"/>
    
	<math xmlns="http://www.w3.org/1998/Math/MathML" id="RXN2_Calc">
      <apply>
        <eq/>
        <ci>RXN2</ci>
        <apply>
          <times/>
          <ci>A</ci>
          <ci>Delta_1</ci>
        </apply>
      </apply>
    </math>
  </component>
  
  <component name="RXN3">
    <variable name="RXN3" public_interface="out" units="flux"/>
    <variable name="C" public_interface="in" units="molecules"/>
    <variable initial_value="1" name="Delta_2" units="first_order_rate"/>
    <math xmlns="http://www.w3.org/1998/Math/MathML" id="RXN3_Calc">
      <apply>
        <eq/>
        <ci>RXN3</ci>
        <apply>
          <times/>
          <ci>C</ci>
          <ci>Delta_2</ci>
        </apply>
      </apply>
    </math>
  </component>
  
  <component name="RXN4">
    <variable name="RXN4" public_interface="out" units="flux"/>
    <variable name="R" public_interface="in" units="molecules"/>
    <variable initial_value="0.2" name="Delta_3" units="first_order_rate"/>
    <math xmlns="http://www.w3.org/1998/Math/MathML" id="RXN4_Calc">
      <apply>
        <eq/>
        <ci>RXN4</ci>
        <apply>
          <times/>
          <ci>R</ci>
          <ci>Delta_3</ci>
        </apply>
      </apply>
    </math>
  </component>
  
  <component name="RXN5">
    <variable name="RXN5" public_interface="out" units="flux"/>
    <variable name="A" public_interface="in" units="molecules"/>
    <variable name="DA" public_interface="in" units="molecules"/>
    <variable initial_value="1" name="Gamma_2" units="second_order_rate"/>
    <math xmlns="http://www.w3.org/1998/Math/MathML" id="RXN5_Calc">
      <apply>
        <eq/>
        <ci>RXN5</ci>
        <apply>
          <times/>
          <ci>A</ci>
          <ci>DA</ci>
          <ci>Gamma_2</ci>
        </apply>
      </apply>
    </math>
  </component>
  
  <component name="RXN6">
    <variable name="RXN6" public_interface="out" units="flux"/>
    <variable name="DAp" public_interface="in" units="molecules"/>
    <variable initial_value="50" name="Thetha_1" units="first_order_rate"/>
    <math xmlns="http://www.w3.org/1998/Math/MathML" id="RXN6_Calc">
      <apply>
        <eq/>
        <ci>RXN6</ci>
        <apply>
          <times/>
          <ci>DAp</ci>
          <ci>Thetha_1</ci>
        </apply>
      </apply>
    </math>
  </component>
  
  <component name="RXN7">
    <variable name="RXN7" public_interface="out" units="flux"/>
    <variable name="DA" public_interface="in" units="molecules"/>
    <variable initial_value="50" name="Alpha_1" units="first_order_rate"/>
    <math xmlns="http://www.w3.org/1998/Math/MathML" id="RXN7_Calc">
      <apply>
        <eq/>
        <ci>RXN7</ci>
        <apply>
          <times/>
          <ci>DA</ci>
          <ci>Alpha_1</ci>
        </apply>
      </apply>
    </math>
  </component>
  
  <component name="RXN8">
    <variable name="RXN8" public_interface="out" units="flux"/>
    <variable name="DAp" public_interface="in" units="molecules"/>
    <variable initial_value="500" name="Alpha_2" units="first_order_rate"/>
    <math xmlns="http://www.w3.org/1998/Math/MathML" id="RXN8_Calc">
      <apply>
        <eq/>
        <ci>RXN8</ci>
        <apply>
          <times/>
          <ci>DAp</ci>
          <ci>Alpha_2</ci>
        </apply>
      </apply>
    </math>
  </component>
  
  <component name="RXN9">
    <variable name="RXN9" public_interface="out" units="flux"/>
    <variable name="MA" public_interface="in" units="molecules"/>
    <variable initial_value="10" name="Delta_4" units="first_order_rate"/>
    <math xmlns="http://www.w3.org/1998/Math/MathML" id="RXN9_Calc">
      <apply>
        <eq/>
        <ci>RXN9</ci>
        <apply>
          <times/>
          <ci>MA</ci>
          <ci>Delta_4</ci>
        </apply>
      </apply>
    </math>
  </component>
  
  <component name="RXN10">
    <variable name="RXN10" public_interface="out" units="flux"/>
    <variable name="MA" public_interface="in" units="molecules"/>
    <variable initial_value="50" name="BetaA_1" units="first_order_rate"/>
    <math xmlns="http://www.w3.org/1998/Math/MathML" id="RXN10_Calc">
      <apply>
        <eq/>
        <ci>RXN10</ci>
        <apply>
          <times/>
          <ci>MA</ci>
          <ci>BetaA_1</ci>
        </apply>
      </apply>
    </math>
  </component>
  
  <component name="RXN11">
    <variable name="RXN11" public_interface="out" units="flux"/>
    <variable name="A" public_interface="in" units="molecules"/>
    <variable name="DR" public_interface="in" units="molecules"/>
    <variable initial_value="1" name="Gamma_3" units="second_order_rate"/>
    <math xmlns="http://www.w3.org/1998/Math/MathML" id="RXN11_Calc">
      <apply>
        <eq/>
        <ci>RXN11</ci>
        <apply>
          <times/>
          <ci>A</ci>
          <ci>DR</ci>
          <ci>Gamma_3</ci>
        </apply>
      </apply>
    </math>
  </component>
  
  <component name="RXN12">
    <variable name="RXN12" public_interface="out" units="flux"/>
    <variable name="DRP" public_interface="in" units="molecules"/>
    <variable initial_value="100" name="Theta_2" units="first_order_rate"/>
    <math xmlns="http://www.w3.org/1998/Math/MathML" id="RXN12_Calc">
      <apply>
        <eq/>
        <ci>RXN12</ci>
        <apply>
          <times/>
          <ci>DRP</ci>
          <ci>Theta_2</ci>
        </apply>
      </apply>
    </math>
  </component>
  
  <component name="RXN13">
    <variable name="RXN13" public_interface="out" units="flux"/>
    <variable name="DR" public_interface="in" units="molecules"/>
    <variable initial_value="0.01" name="Alpha_3" units="first_order_rate"/>
    <math xmlns="http://www.w3.org/1998/Math/MathML" id="RXN13_Calc">
      <apply>
        <eq/>
        <ci>RXN13</ci>
        <apply>
          <times/>
          <ci>DR</ci>
          <ci>Alpha_3</ci>
        </apply>
      </apply>
    </math>
  </component>
  
  <component name="RXN14">
    <variable name="RXN14" public_interface="out" units="flux"/>
    <variable name="DRP" public_interface="in" units="molecules"/>
    <variable initial_value="50" name="Alpha_4" units="first_order_rate"/>
    <math xmlns="http://www.w3.org/1998/Math/MathML" id="RXN14_Calc">
      <apply>
        <eq/>
        <ci>RXN14</ci>
        <apply>
          <times/>
          <ci>DRP</ci>
          <ci>Alpha_4</ci>
        </apply>
      </apply>
    </math>
  </component>
  
  <component name="RXN15">
    <variable name="RXN15" public_interface="out" units="flux"/>
    <variable name="MR" public_interface="in" units="molecules"/>
    <variable initial_value="0.5" name="Delta_5" units="first_order_rate"/>
    <math xmlns="http://www.w3.org/1998/Math/MathML" id="RXN15_Calc">
      <apply>
        <eq/>
        <ci>RXN15</ci>
        <apply>
          <times/>
          <ci>MR</ci>
          <ci>Delta_5</ci>
        </apply>
      </apply>
    </math>
  </component>
  
  <component name="RXN16">
    <variable name="RXN16" public_interface="out" units="flux"/>
    <variable name="MR" public_interface="in" units="molecules"/>
    <variable initial_value="5" name="BetaR_1" units="first_order_rate"/>
    <math xmlns="http://www.w3.org/1998/Math/MathML" id="RXN16_Calc">
      <apply>
        <eq/>
        <ci>RXN16</ci>
        <apply>
          <times/>
          <ci>MR</ci>
          <ci>BetaR_1</ci>
        </apply>
      </apply>
    </math>
  </component>
  
  <connection>
    <map_components component_1="A" component_2="RXN1"/>
    <map_variables variable_1="A" variable_2="A"/>
    <map_variables variable_1="RXN1" variable_2="RXN1"/>
  </connection>
  <connection>
    <map_components component_1="A" component_2="RXN2"/>
    <map_variables variable_1="A" variable_2="A"/>
    <map_variables variable_1="RXN2" variable_2="RXN2"/>
  </connection>
  <connection>
    <map_components component_1="A" component_2="RXN5"/>
    <map_variables variable_1="A" variable_2="A"/>
    <map_variables variable_1="RXN5" variable_2="RXN5"/>
  </connection>
  <connection>
    <map_components component_1="A" component_2="RXN11"/>
    <map_variables variable_1="A" variable_2="A"/>
    <map_variables variable_1="RXN11" variable_2="RXN11"/>
  </connection>
  <connection>
    <map_components component_1="C" component_2="RXN3"/>
    <map_variables variable_1="C" variable_2="C"/>
    <map_variables variable_1="RXN3" variable_2="RXN3"/>
  </connection>
  <connection>
    <map_components component_1="DA" component_2="RXN5"/>
    <map_variables variable_1="DA" variable_2="DA"/>
    <map_variables variable_1="RXN5" variable_2="RXN5"/>
  </connection>
  <connection>
    <map_components component_1="DA" component_2="RXN7"/>
    <map_variables variable_1="DA" variable_2="DA"/>
    <map_variables variable_1="RXN7" variable_2="RXN7"/>
  </connection>
  <connection>
    <map_components component_1="DAp" component_2="RXN6"/>
    <map_variables variable_1="DAp" variable_2="DAp"/>
    <map_variables variable_1="RXN6" variable_2="RXN6"/>
  </connection>
  <connection>
    <map_components component_1="DAp" component_2="RXN8"/>
    <map_variables variable_1="DAp" variable_2="DAp"/>
    <map_variables variable_1="RXN8" variable_2="RXN8"/>
  </connection>
  <connection>
    <map_components component_1="DR" component_2="RXN11"/>
    <map_variables variable_1="DR" variable_2="DR"/>
    <map_variables variable_1="RXN11" variable_2="RXN11"/>
  </connection>
  <connection>
    <map_components component_1="DR" component_2="RXN13"/>
    <map_variables variable_1="DR" variable_2="DR"/>
    <map_variables variable_1="RXN13" variable_2="RXN13"/>
  </connection>
  <connection>
    <map_components component_1="DRP" component_2="RXN12"/>
    <map_variables variable_1="DRP" variable_2="DRP"/>
    <map_variables variable_1="RXN12" variable_2="RXN12"/>
  </connection>
  <connection>
    <map_components component_1="DRP" component_2="RXN14"/>
    <map_variables variable_1="DRP" variable_2="DRP"/>
    <map_variables variable_1="RXN14" variable_2="RXN14"/>
  </connection>
  <connection>
    <map_components component_1="MA" component_2="RXN9"/>
    <map_variables variable_1="MA" variable_2="MA"/>
    <map_variables variable_1="RXN9" variable_2="RXN9"/>
  </connection>
  <connection>
    <map_components component_1="MA" component_2="RXN10"/>
    <map_variables variable_1="MA" variable_2="MA"/>
    <map_variables variable_1="RXN10" variable_2="RXN10"/>
  </connection>
  <connection>
    <map_components component_1="MR" component_2="RXN15"/>
    <map_variables variable_1="MR" variable_2="MR"/>
    <map_variables variable_1="RXN15" variable_2="RXN15"/>
  </connection>
  <connection>
    <map_components component_1="MR" component_2="RXN16"/>
    <map_variables variable_1="MR" variable_2="MR"/>
    <map_variables variable_1="RXN16" variable_2="RXN16"/>
  </connection>
  <connection>
    <map_components component_1="R" component_2="RXN1"/>
    <map_variables variable_1="R" variable_2="R"/>
    <map_variables variable_1="RXN1" variable_2="RXN1"/>
  </connection>
  <connection>
    <map_components component_1="environment" component_2="A"/>
    <map_variables variable_1="time" variable_2="time"/>
  </connection>
  <connection>
    <map_components component_1="environment" component_2="C"/>
    <map_variables variable_1="time" variable_2="time"/>
  </connection>
  <connection>
    <map_components component_1="environment" component_2="DA"/>
    <map_variables variable_1="time" variable_2="time"/>
  </connection>
  <connection>
    <map_components component_1="environment" component_2="DAp"/>
    <map_variables variable_1="time" variable_2="time"/>
  </connection>
  <connection>
    <map_components component_1="environment" component_2="DR"/>
    <map_variables variable_1="time" variable_2="time"/>
  </connection>
  <connection>
    <map_components component_1="environment" component_2="DRP"/>
    <map_variables variable_1="time" variable_2="time"/>
  </connection>
  <connection>
    <map_components component_1="environment" component_2="MA"/>
    <map_variables variable_1="time" variable_2="time"/>
  </connection>
  <connection>
    <map_components component_1="environment" component_2="MR"/>
    <map_variables variable_1="time" variable_2="time"/>
  </connection>
  <connection>
    <map_components component_1="environment" component_2="R"/>
    <map_variables variable_1="time" variable_2="time"/>
  </connection>
  <connection>
    <map_components component_1="RXN6" component_2="A"/>
    <map_variables variable_1="RXN6" variable_2="RXN6"/>
  </connection>
  <connection>
    <map_components component_1="RXN10" component_2="A"/>
    <map_variables variable_1="RXN10" variable_2="RXN10"/>
  </connection>
  <connection>
    <map_components component_1="RXN12" component_2="A"/>
    <map_variables variable_1="RXN12" variable_2="RXN12"/>
  </connection>
  <connection>
    <map_components component_1="RXN1" component_2="C"/>
    <map_variables variable_1="RXN1" variable_2="RXN1"/>
  </connection>
  <connection>
    <map_components component_1="RXN5" component_2="DAp"/>
    <map_variables variable_1="RXN5" variable_2="RXN5"/>
  </connection>
  <connection>
    <map_components component_1="RXN12" component_2="DR"/>
    <map_variables variable_1="RXN12" variable_2="RXN12"/>
  </connection>
  <connection>
    <map_components component_1="RXN11" component_2="DRP"/>
    <map_variables variable_1="RXN11" variable_2="RXN11"/>
  </connection>
  <connection>
    <map_components component_1="RXN7" component_2="MA"/>
    <map_variables variable_1="RXN7" variable_2="RXN7"/>
  </connection>
  <connection>
    <map_components component_1="RXN8" component_2="MA"/>
    <map_variables variable_1="RXN8" variable_2="RXN8"/>
  </connection>
  <connection>
    <map_components component_1="RXN13" component_2="MR"/>
    <map_variables variable_1="RXN13" variable_2="RXN13"/>
  </connection>
  <connection>
    <map_components component_1="RXN14" component_2="MR"/>
    <map_variables variable_1="RXN14" variable_2="RXN14"/>
  </connection>
  <connection>
    <map_components component_1="RXN3" component_2="R"/>
    <map_variables variable_1="RXN3" variable_2="RXN3"/>
  </connection>
  <connection>
    <map_components component_1="RXN4" component_2="R"/>
    <map_variables variable_1="RXN4" variable_2="RXN4"/>
    <map_variables variable_1="R" variable_2="R"/>
  </connection>
  <connection>
    <map_components component_1="RXN16" component_2="R"/>
    <map_variables variable_1="RXN16" variable_2="RXN16"/>
  </connection>
  <connection>
    <map_components component_1="RXN6" component_2="DA"/>
    <map_variables variable_1="RXN6" variable_2="RXN6"/>
  </connection>
  



<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
  <rdf:Bag rdf:about="rdf:#65c9f2d6-8697-437e-9535-4a46e163a866">
    <rdf:li>circadian rhythms</rdf:li>
    <rdf:li>noise-resistance</rdf:li>
    <rdf:li>signal transduction</rdf:li>
    <rdf:li>gene regulation</rdf:li>
    <rdf:li>genetic oscillator</rdf:li>
  </rdf:Bag>
  <rdf:Description rdf:about="rdf:#65c9f2d6-8697-437e-9535-4a46e163a866"/>
  <rdf:Seq rdf:about="rdf:#a0449968-b548-4c6a-bc6c-7a08b5c412f5">
    <rdf:li rdf:resource="rdf:#5fe56c26-ba31-4db5-9aa3-720c86d0aa17"/>
    <rdf:li rdf:resource="rdf:#e52579ff-7412-4023-a63f-4d9540642421"/>
    <rdf:li rdf:resource="rdf:#fa2451b2-21c1-44d8-9e14-e716863955a1"/>
    <rdf:li rdf:resource="rdf:#f132d8a8-6f50-499f-bee8-c0ad49da37b5"/>
  </rdf:Seq>
  <rdf:Description rdf:about="rdf:#3283e99b-42a8-4abf-95a3-bda00ffc29e5">
    <vCard:Given xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#">James</vCard:Given>
    <vCard:Family xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#">Lawson</vCard:Family>
    <vCard:Other xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#">Richard</vCard:Other>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#$fmNO53">
    <ns7:endingValue xmlns:ns7="http://www.cellml.org/metadata/simulation/1.0#">400</ns7:endingValue>
    <ns7:nonstandard-pointDensity xmlns:ns7="http://www.cellml.org/metadata/simulation/1.0#">10000</ns7:nonstandard-pointDensity>
    <ns7:maximumStepSize xmlns:ns7="http://www.cellml.org/metadata/simulation/1.0#">5</ns7:maximumStepSize>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#6b31cce9-847c-4f65-904d-2276d8008efb">
    <dcterms:W3CDTF xmlns:dcterms="http://purl.org/dc/terms/">2008-09-03T14:33:04+12:00</dcterms:W3CDTF>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#5fe56c26-ba31-4db5-9aa3-720c86d0aa17">
    <rdf:type rdf:resource="http://www.cellml.org/bqs/1.0#Person"/>
    <vCard:N xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" rdf:resource="rdf:#2b7f53de-fa65-42d7-ae08-f4fa7e3d6924"/>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#6e776b10-823c-4701-a469-3bd7d4e49f98">
    <vCard:FN xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#">James Lawson</vCard:FN>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#092ccb9f-e343-4f58-b48d-ebbe3172ed40">
    <bqs:subject_type xmlns:bqs="http://www.cellml.org/bqs/1.0#">keyword</bqs:subject_type>
    <rdf:value rdf:resource="rdf:#65c9f2d6-8697-437e-9535-4a46e163a866"/>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#f9a23f78-da42-4635-998f-9f21e3c14a88">
    <dcterms:W3CDTF xmlns:dcterms="http://purl.org/dc/terms/">2003-11-03T00:00:00+00:00</dcterms:W3CDTF>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#f132d8a8-6f50-499f-bee8-c0ad49da37b5">
    <rdf:type rdf:resource="http://www.cellml.org/bqs/1.0#Person"/>
    <vCard:N xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" rdf:resource="rdf:#6fcccf65-6d32-4645-b5ea-19ca8765eead"/>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#67b6c647-324b-49f3-a6df-cba2d32dfb1c">
    <dc:title xmlns:dc="http://purl.org/dc/elements/1.1/">PNAS</dc:title>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#4ac95772-0f07-4753-8abb-4c2d2c160772">
    <dcterms:modified xmlns:dcterms="http://purl.org/dc/terms/" rdf:resource="rdf:#6b31cce9-847c-4f65-904d-2276d8008efb"/>
    <rdf:value>added cmeta:id's to some variables</rdf:value>
    <cmeta:modifier rdf:resource="rdf:#5c0fc9b4-2538-4ab7-b46e-a69a99319b69"/>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#10cbbde9-48b9-457e-b929-269fb4394a69">
    <vCard:Given xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#">James</vCard:Given>
    <vCard:Family xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#">Lawson</vCard:Family>
    <vCard:Other xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#"/>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#2b7f53de-fa65-42d7-ae08-f4fa7e3d6924">
    <vCard:Given xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#">Jose</vCard:Given>
    <vCard:Family xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#">Vilar</vCard:Family>
    <vCard:Other xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#">G.</vCard:Other>
    <vCard:Other xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#">M.</vCard:Other>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#5eef68cf-8ff9-4789-a34d-7dbcb7051e62">
    <vCard:Given xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#">Catherine</vCard:Given>
    <vCard:Family xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#">Lloyd</vCard:Family>
    <vCard:Other xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#">May</vCard:Other>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#d2b09214-9391-49d2-add4-e6c8db79b79b">
    <vCard:FN xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#">Catherine Lloyd</vCard:FN>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#d7c31cbc-f9e8-4add-b95b-2197a5237a13">
    <dcterms:W3CDTF xmlns:dcterms="http://purl.org/dc/terms/">2008-09-01T13:12:26+12:00</dcterms:W3CDTF>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#e95de634-eb12-4283-b9c7-791c675a8038">
    <vCard:Given xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#">Hao</vCard:Given>
    <vCard:Family xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#">Kueh</vCard:Family>
    <vCard:Other xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#">Yuan</vCard:Other>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#695fc7df-e54d-47fc-832b-50c8e9ac9da2">
    <dcterms:modified xmlns:dcterms="http://purl.org/dc/terms/" rdf:resource="rdf:#4a858c75-c353-402e-9b38-9cde2c76eaca"/>
    <rdf:value>This model has been recoded using the Biomodels Database model as a template</rdf:value>
    <cmeta:modifier rdf:resource="rdf:#4e2213ae-fdc0-4cc8-9347-12ff246912c9"/>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#da246d95-923e-4768-a680-234119b8f452">
    <dc:creator xmlns:dc="http://purl.org/dc/elements/1.1/" rdf:resource="rdf:#6e776b10-823c-4701-a469-3bd7d4e49f98"/>
    <rdf:value>This model is known to run in PCEnv and COR reproduce the results published in the paper on which it is based (figures 2 and 3)</rdf:value>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#4e2213ae-fdc0-4cc8-9347-12ff246912c9">
    <vCard:N xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" rdf:resource="rdf:#ef5c8ff3-9197-4151-951e-9745118b88bc"/>
  </rdf:Description>
  <rdf:Description rdf:about="#vilar_kueh_barkai_leibler_2002">
    <ns7:simulation xmlns:ns7="http://www.cellml.org/metadata/simulation/1.0#" rdf:resource="rdf:#$dmNO53"/>
    <dc:title xmlns:dc="http://purl.org/dc/elements/1.1/">Vilar et al.'s 2002 mathematical model of a genetic oscillator.</dc:title>
    <cmeta:comment rdf:resource="rdf:#488414d1-491e-4e40-99e7-94213eab43f0"/>
    <bqs:reference xmlns:bqs="http://www.cellml.org/bqs/1.0#" rdf:resource="rdf:#1b4f8009-249a-454f-8826-add810038fd5"/>
    <bqs:reference xmlns:bqs="http://www.cellml.org/bqs/1.0#" rdf:resource="rdf:#62c278f7-6a0a-43b8-878a-dd73a10f995e"/>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#864d6fda-f4f4-4a5b-8f7a-68f12cbd2e78">
    <vCard:Given xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#">James</vCard:Given>
    <vCard:Family xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#">Lawson</vCard:Family>
    <vCard:Other xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#">Richard</vCard:Other>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#488414d1-491e-4e40-99e7-94213eab43f0">
    <dc:creator xmlns:dc="http://purl.org/dc/elements/1.1/" rdf:resource="rdf:#d2b09214-9391-49d2-add4-e6c8db79b79b"/>
    <rdf:value>This is the CellML description of Vilar et al.'s 2002 mathematical model of a genetic oscillator.</rdf:value>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#4a858c75-c353-402e-9b38-9cde2c76eaca">
    <dcterms:W3CDTF xmlns:dcterms="http://purl.org/dc/terms/">2008-02-05T11:39:57+13:00</dcterms:W3CDTF>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#fa2451b2-21c1-44d8-9e14-e716863955a1">
    <rdf:type rdf:resource="http://www.cellml.org/bqs/1.0#Person"/>
    <vCard:N xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" rdf:resource="rdf:#b167a7db-a498-4547-9a62-82b4b7baa854"/>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#3cc6b2f5-9914-4926-8768-68f3d6890eaf">
    <dcterms:modified xmlns:dcterms="http://purl.org/dc/terms/" rdf:resource="rdf:#5ba0e82b-e1ba-461d-b725-d1e1cdeeed90"/>
    <rdf:value>Added some cmeta:ids to varibles to allow referencing by a PCEnv session</rdf:value>
    <cmeta:modifier rdf:resource="rdf:#0d7bb7d7-ad0d-4691-8d18-0d1da9f4641e"/>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#5ba0e82b-e1ba-461d-b725-d1e1cdeeed90">
    <dcterms:W3CDTF xmlns:dcterms="http://purl.org/dc/terms/">2008-02-20T14:54:14+13:00</dcterms:W3CDTF>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#28f6124a-a6f7-4c0c-b56f-534161b896eb">
    <vCard:N xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" rdf:resource="rdf:#864d6fda-f4f4-4a5b-8f7a-68f12cbd2e78"/>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#4983d27d-122c-411d-bb05-f9c762139fb3">
    <vCard:Orgname xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#">The University of Auckland</vCard:Orgname>
    <vCard:Orgunit xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#">Auckland Bioengineering Institute</vCard:Orgunit>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#b0335c6f-f719-4484-8fda-eb653e9e5da5">
    <vCard:ORG xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" rdf:resource="rdf:#4983d27d-122c-411d-bb05-f9c762139fb3"/>
    <vCard:EMAIL xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" rdf:resource="rdf:#d2fceb36-78cd-492d-9226-b5a863ab0ff7"/>
    <vCard:N xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" rdf:resource="rdf:#5eef68cf-8ff9-4789-a34d-7dbcb7051e62"/>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#d2fceb36-78cd-492d-9226-b5a863ab0ff7">
    <rdf:type rdf:resource="http://imc.org/vCard/3.0#internet"/>
    <rdf:value>c.lloyd@auckland.ac.nz</rdf:value>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#$emNO53">
    <rdf:rest rdf:resource="http://www.w3.org/1999/02/22-rdf-syntax-ns#nil"/>
    <rdf:first rdf:resource="rdf:#$fmNO53"/>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#24505b47-5b9b-44f2-ba96-4637b1b38df9">
    <dcterms:modified xmlns:dcterms="http://purl.org/dc/terms/" rdf:resource="rdf:#d7c31cbc-f9e8-4add-b95b-2197a5237a13"/>
    <rdf:value>Added CellML 1.0 namespace

Removed extraneous code: initial_value="" 

Removed unnecessary initial values from RXN_X* variables with public_interface="in" 
* - X is 1-16</rdf:value>
    <cmeta:modifier rdf:resource="rdf:#28f6124a-a6f7-4c0c-b56f-534161b896eb"/>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#0d7bb7d7-ad0d-4691-8d18-0d1da9f4641e">
    <vCard:N xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" rdf:resource="rdf:#3283e99b-42a8-4abf-95a3-bda00ffc29e5"/>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#14119b20-ee64-49a1-b3f9-52383fc35b3d">
    <dc:creator xmlns:dc="http://purl.org/dc/elements/1.1/" rdf:resource="rdf:#a0449968-b548-4c6a-bc6c-7a08b5c412f5"/>
    <dc:title xmlns:dc="http://purl.org/dc/elements/1.1/">Mechanisms of noise-resistance in genetic oscillators</dc:title>
    <bqs:volume xmlns:bqs="http://www.cellml.org/bqs/1.0#">99</bqs:volume>
    <bqs:first_page xmlns:bqs="http://www.cellml.org/bqs/1.0#">5988</bqs:first_page>
    <bqs:Journal xmlns:bqs="http://www.cellml.org/bqs/1.0#" rdf:resource="rdf:#67b6c647-324b-49f3-a6df-cba2d32dfb1c"/>
    <dcterms:issued xmlns:dcterms="http://purl.org/dc/terms/" rdf:resource="rdf:#f48a996e-d61d-4f6c-a405-2e756b856c82"/>
    <bqs:last_page xmlns:bqs="http://www.cellml.org/bqs/1.0#">5992</bqs:last_page>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#e52579ff-7412-4023-a63f-4d9540642421">
    <rdf:type rdf:resource="http://www.cellml.org/bqs/1.0#Person"/>
    <vCard:N xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" rdf:resource="rdf:#e95de634-eb12-4283-b9c7-791c675a8038"/>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#f48a996e-d61d-4f6c-a405-2e756b856c82">
    <dcterms:W3CDTF xmlns:dcterms="http://purl.org/dc/terms/">2002-04-30</dcterms:W3CDTF>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#5c0fc9b4-2538-4ab7-b46e-a69a99319b69">
    <vCard:N xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" rdf:resource="rdf:#10cbbde9-48b9-457e-b929-269fb4394a69"/>
  </rdf:Description>
  <rdf:Description rdf:about="">
    <dc:publisher xmlns:dc="http://purl.org/dc/elements/1.1/">The University of Auckland, Auckland Bioengineering Institute</dc:publisher>
    <cmeta:comment rdf:resource="rdf:#da246d95-923e-4768-a680-234119b8f452"/>
    <dcterms:created xmlns:dcterms="http://purl.org/dc/terms/" rdf:resource="rdf:#f9a23f78-da42-4635-998f-9f21e3c14a88"/>
    <dc:creator xmlns:dc="http://purl.org/dc/elements/1.1/" rdf:resource="rdf:#b0335c6f-f719-4484-8fda-eb653e9e5da5"/>
    <cmeta:modification rdf:resource="rdf:#4ac95772-0f07-4753-8abb-4c2d2c160772"/>
    <cmeta:modification rdf:resource="rdf:#24505b47-5b9b-44f2-ba96-4637b1b38df9"/>
    <cmeta:modification rdf:resource="rdf:#3cc6b2f5-9914-4926-8768-68f3d6890eaf"/>
    <cmeta:modification rdf:resource="rdf:#695fc7df-e54d-47fc-832b-50c8e9ac9da2"/>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#b167a7db-a498-4547-9a62-82b4b7baa854">
    <vCard:Given xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#">Naama</vCard:Given>
    <vCard:Family xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#">Barkai</vCard:Family>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#$dmNO53">
    <ns7:boundIntervals xmlns:ns7="http://www.cellml.org/metadata/simulation/1.0#" rdf:resource="rdf:#$emNO53"/>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#1b4f8009-249a-454f-8826-add810038fd5">
    <bqs:Pubmed_id xmlns:bqs="http://www.cellml.org/bqs/1.0#">11972055</bqs:Pubmed_id>
    <bqs:JournalArticle xmlns:bqs="http://www.cellml.org/bqs/1.0#" rdf:resource="rdf:#14119b20-ee64-49a1-b3f9-52383fc35b3d"/>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#6fcccf65-6d32-4645-b5ea-19ca8765eead">
    <vCard:Given xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#">Stanislas</vCard:Given>
    <vCard:Family xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#">Leibler</vCard:Family>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#62c278f7-6a0a-43b8-878a-dd73a10f995e">
    <dc:subject xmlns:dc="http://purl.org/dc/elements/1.1/" rdf:resource="rdf:#092ccb9f-e343-4f58-b48d-ebbe3172ed40"/>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#ef5c8ff3-9197-4151-951e-9745118b88bc">
    <vCard:Given xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#">Vignesh</vCard:Given>
    <vCard:Family xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#">Kumar</vCard:Family>
    <vCard:Other xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#">B</vCard:Other>
  </rdf:Description>
</rdf:RDF>
</model>