Location: Vilar, Kueh, Barkai, Leibler, 2002 @ 92a109f266fa / vilar_kueh_barkai_leibler_2002.cellml

Author:

Hanne <Hanne@hanne-nielsens-macbook.local>

Date:

2009-12-15 11:34:01+13:00

Desc:

Added images in ai and svg format, removed non pub med references

Permanent Source URI:

https://models.physiomeproject.org/workspace/vilar_kueh_barkai_leibler_2002/rawfile/92a109f266fa26d2604fdd336066d603cc210d97/vilar_kueh_barkai_leibler_2002.cellml

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<article>
  <articleinfo>
  <title>Modelling a Genetic Oscillator</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 has been curated and is known to run in PCEnv and reproduce the results published in the paper on which it is based.
          </para>
  </section>
  <sect1 id="sec_structure">
<title>Model Structure</title>

<para>
In order to adapt to the the environment's daily cycles of light and dark many organisms, from cyanobacteria to mammals have evolved circadian rhythms.  These <emphasis>biological clocks</emphasis> have a period of about 24 hours and they regulate physiological and behavioural processes to best suit different times of the day.  Recent studies have shown that these clocks in different species share similar underlying molecular mechanisms, suggesting that they could be evolutionarily ancient and conserved (homologous).  The main common feature is the presence of gene transcription regulation networks which give rise to the gene expression oscillations.  A positive element activates genes coupled to a circadian clock, simultaneously promoting the expression of a negative element, which in turn represses the positive element (negative feedback inhibition).  When the negative element is degraded the cycle completes itself and the positive element is re-expressed.
</para>

<para>
An essential feature of circadian clocks is to maintain a constant period in spite of fluctuations in the internal and external environments.  Such robustness ensures that the clock runs accurately and that clock-dependent genes are expressed at the appropriate time of the day.  Potential disturbances include: 
<itemizedlist>
  <listitem>
              <para>fluctuations in temperature which may affect the rate of biochemical reactions;</para>
            </listitem>
  <listitem>
              <para>internal noise caused by the stochastic nature of biochemical reactions; and</para>
            </listitem>
  <listitem>
              <para>low numbers of molecules may generate random fluctuations that can destabilise the oscillatory network.</para>
            </listitem>
</itemizedlist>
Yet circadian clocks maintain a fairly constant period.
</para>

<para>
In order to better understand the potential molecular mechanisms underlying circadian clocks, Vilar <emphasis>et al.</emphasis> developed a mathematical model of a genetic oscillator (see the figure below).  The model involves two genes, an activator <emphasis>A</emphasis> and a repressor <emphasis>R</emphasis>, which are transcribed into mRNA and then translated into protein.  If the two proteins bind to each other, they form an inactivated complex, <emphasis>C</emphasis>.  The activator <emphasis>A</emphasis> binds to the promoter regions of both the <emphasis>A</emphasis> and <emphasis>R</emphasis> genes, which has the effect of increasing their transcription rate.  Thus <emphasis>A</emphasis> acts as the positive element in transcription while <emphasis>R</emphasis> acts as the negative element by sequestering the activator.
</para>

<para>
Model simulations suggest that the oscillations are driven by two components, a repressor protein and an activator-repressor complex.  The clock doesn't rely on mRNA dynamics to oscillate which makes it especially resistant to environmental fluctuations.  In fact, under certain conditions, this oscillator is not only resistant to, but also enhanced by the background biochemical noise.  
</para>

<para>
The complete 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">
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      <title>reaction diagram</title>
    </objectinfo>
    <imagedata fileref="vilar_2002.png"/>
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<caption>Biochemical network of the circadian oscillator model.</caption>
</informalfigure>

</sect1>
</article>
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    <variable units="mol" public_interface="in" name="A"/>
    <variable units="mol" public_interface="in" name="DR"/>
    <variable units="second_order_rate" name="Gamma_3" initial_value="1"/>
    <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 units="first_order_rate" public_interface="out" name="RXN12"/>
    <variable units="mol" public_interface="in" name="DRP"/>
    <variable units="first_order_rate" name="Theta_2" initial_value="100"/>
    <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 units="first_order_rate" public_interface="out" name="RXN13"/>
    <variable units="mol" public_interface="in" name="DR"/>
    <variable units="first_order_rate" name="Alpha_3" initial_value="0.01"/>
    <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 units="first_order_rate" public_interface="out" name="RXN14"/>
    <variable units="mol" public_interface="in" name="DRP"/>
    <variable units="first_order_rate" name="Alpha_4" initial_value="50"/>
    <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 units="first_order_rate" public_interface="out" name="RXN15"/>
    <variable units="mol" public_interface="in" name="MR"/>
    <variable units="first_order_rate" name="Delta_5" initial_value="0.5"/>
    <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 units="first_order_rate" public_interface="out" name="RXN16"/>
    <variable units="mol" public_interface="in" name="MR"/>
    <variable units="first_order_rate" name="BetaR_1" initial_value="5"/>
    <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_2="RXN1" component_1="A"/>
    <map_variables variable_2="A" variable_1="A"/>
    <map_variables variable_2="RXN1" variable_1="RXN1"/>
  </connection>
  <connection>
    <map_components component_2="RXN2" component_1="A"/>
    <map_variables variable_2="A" variable_1="A"/>
    <map_variables variable_2="RXN2" variable_1="RXN2"/>
  </connection>
  <connection>
    <map_components component_2="RXN5" component_1="A"/>
    <map_variables variable_2="A" variable_1="A"/>
    <map_variables variable_2="RXN5" variable_1="RXN5"/>
  </connection>
  <connection>
    <map_components component_2="RXN11" component_1="A"/>
    <map_variables variable_2="A" variable_1="A"/>
    <map_variables variable_2="RXN11" variable_1="RXN11"/>
  </connection>
  <connection>
    <map_components component_2="RXN3" component_1="C"/>
    <map_variables variable_2="C" variable_1="C"/>
    <map_variables variable_2="RXN3" variable_1="RXN3"/>
  </connection>
  <connection>
    <map_components component_2="RXN5" component_1="DA"/>
    <map_variables variable_2="DA" variable_1="DA"/>
    <map_variables variable_2="RXN5" variable_1="RXN5"/>
  </connection>
  <connection>
    <map_components component_2="RXN7" component_1="DA"/>
    <map_variables variable_2="DA" variable_1="DA"/>
    <map_variables variable_2="RXN7" variable_1="RXN7"/>
  </connection>
  <connection>
    <map_components component_2="RXN6" component_1="DAp"/>
    <map_variables variable_2="DAp" variable_1="DAp"/>
    <map_variables variable_2="RXN6" variable_1="RXN6"/>
  </connection>
  <connection>
    <map_components component_2="RXN8" component_1="DAp"/>
    <map_variables variable_2="DAp" variable_1="DAp"/>
    <map_variables variable_2="RXN8" variable_1="RXN8"/>
  </connection>
  <connection>
    <map_components component_2="RXN11" component_1="DR"/>
    <map_variables variable_2="DR" variable_1="DR"/>
    <map_variables variable_2="RXN11" variable_1="RXN11"/>
  </connection>
  <connection>
    <map_components component_2="RXN13" component_1="DR"/>
    <map_variables variable_2="DR" variable_1="DR"/>
    <map_variables variable_2="RXN13" variable_1="RXN13"/>
  </connection>
  <connection>
    <map_components component_2="RXN12" component_1="DRP"/>
    <map_variables variable_2="DRP" variable_1="DRP"/>
    <map_variables variable_2="RXN12" variable_1="RXN12"/>
  </connection>
  <connection>
    <map_components component_2="RXN14" component_1="DRP"/>
    <map_variables variable_2="DRP" variable_1="DRP"/>
    <map_variables variable_2="RXN14" variable_1="RXN14"/>
  </connection>
  <connection>
    <map_components component_2="RXN9" component_1="MA"/>
    <map_variables variable_2="MA" variable_1="MA"/>
    <map_variables variable_2="RXN9" variable_1="RXN9"/>
  </connection>
  <connection>
    <map_components component_2="RXN10" component_1="MA"/>
    <map_variables variable_2="MA" variable_1="MA"/>
    <map_variables variable_2="RXN10" variable_1="RXN10"/>
  </connection>
  <connection>
    <map_components component_2="RXN15" component_1="MR"/>
    <map_variables variable_2="MR" variable_1="MR"/>
    <map_variables variable_2="RXN15" variable_1="RXN15"/>
  </connection>
  <connection>
    <map_components component_2="RXN16" component_1="MR"/>
    <map_variables variable_2="MR" variable_1="MR"/>
    <map_variables variable_2="RXN16" variable_1="RXN16"/>
  </connection>
  <connection>
    <map_components component_2="RXN1" component_1="R"/>
    <map_variables variable_2="R" variable_1="R"/>
    <map_variables variable_2="RXN1" variable_1="RXN1"/>
  </connection>
  <connection>
    <map_components component_2="A" component_1="environment"/>
    <map_variables variable_2="time" variable_1="time"/>
  </connection>
  <connection>
    <map_components component_2="C" component_1="environment"/>
    <map_variables variable_2="time" variable_1="time"/>
  </connection>
  <connection>
    <map_components component_2="DA" component_1="environment"/>
    <map_variables variable_2="time" variable_1="time"/>
  </connection>
  <connection>
    <map_components component_2="DAp" component_1="environment"/>
    <map_variables variable_2="time" variable_1="time"/>
  </connection>
  <connection>
    <map_components component_2="DR" component_1="environment"/>
    <map_variables variable_2="time" variable_1="time"/>
  </connection>
  <connection>
    <map_components component_2="DRP" component_1="environment"/>
    <map_variables variable_2="time" variable_1="time"/>
  </connection>
  <connection>
    <map_components component_2="MA" component_1="environment"/>
    <map_variables variable_2="time" variable_1="time"/>
  </connection>
  <connection>
    <map_components component_2="MR" component_1="environment"/>
    <map_variables variable_2="time" variable_1="time"/>
  </connection>
  <connection>
    <map_components component_2="R" component_1="environment"/>
    <map_variables variable_2="time" variable_1="time"/>
  </connection>
  <connection>
    <map_components component_2="A" component_1="RXN6"/>
    <map_variables variable_2="RXN6" variable_1="RXN6"/>
  </connection>
  <connection>
    <map_components component_2="A" component_1="RXN10"/>
    <map_variables variable_2="RXN10" variable_1="RXN10"/>
  </connection>
  <connection>
    <map_components component_2="A" component_1="RXN12"/>
    <map_variables variable_2="RXN12" variable_1="RXN12"/>
  </connection>
  <connection>
    <map_components component_2="C" component_1="RXN1"/>
    <map_variables variable_2="RXN1" variable_1="RXN1"/>
  </connection>
  <connection>
    <map_components component_2="DAp" component_1="RXN5"/>
    <map_variables variable_2="RXN5" variable_1="RXN5"/>
  </connection>
  <connection>
    <map_components component_2="DR" component_1="RXN12"/>
    <map_variables variable_2="RXN12" variable_1="RXN12"/>
  </connection>
  <connection>
    <map_components component_2="DRP" component_1="RXN11"/>
    <map_variables variable_2="RXN11" variable_1="RXN11"/>
  </connection>
  <connection>
    <map_components component_2="MA" component_1="RXN7"/>
    <map_variables variable_2="RXN7" variable_1="RXN7"/>
  </connection>
  <connection>
    <map_components component_2="MA" component_1="RXN8"/>
    <map_variables variable_2="RXN8" variable_1="RXN8"/>
  </connection>
  <connection>
    <map_components component_2="MR" component_1="RXN13"/>
    <map_variables variable_2="RXN13" variable_1="RXN13"/>
  </connection>
  <connection>
    <map_components component_2="MR" component_1="RXN14"/>
    <map_variables variable_2="RXN14" variable_1="RXN14"/>
  </connection>
  <connection>
    <map_components component_2="R" component_1="RXN3"/>
    <map_variables variable_2="RXN3" variable_1="RXN3"/>
  </connection>
  <connection>
    <map_components component_2="R" component_1="RXN4"/>
    <map_variables variable_2="RXN4" variable_1="RXN4"/>
    <map_variables variable_2="R" variable_1="R"/>
  </connection>
  <connection>
    <map_components component_2="R" component_1="RXN16"/>
    <map_variables variable_2="RXN16" variable_1="RXN16"/>
  </connection>
  <connection>
    <map_components component_2="DA" component_1="RXN6"/>
    <map_variables variable_2="RXN6" variable_1="RXN6"/>
  </connection>
  <units name="hour">
    <unit units="second" multiplier="3600"/>
  </units>
  <units base_units="no" name="mol"/>
  <units name="first_order_rate">
    <unit units="hour" exponent="-1"/>
  </units>
  <units name="second_order_rate">
    <unit units="mol" exponent="-1"/>
    <unit units="hour" exponent="-1"/>
  </units>





<rdf:RDF>
  <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">
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    <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>James</vCard:Given>
    <vCard:Family>Lawson</vCard:Family>
    <vCard:Other>Richard</vCard:Other>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#$fmNO53">
    <ns7:endingValue>400</ns7:endingValue>
    <ns7:nonstandard-pointDensity>10000</ns7:nonstandard-pointDensity>
    <ns7:maximumStepSize>5</ns7:maximumStepSize>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#6b31cce9-847c-4f65-904d-2276d8008efb">
    <dcterms:W3CDTF>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"/>
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  <rdf:Description rdf:about="rdf:#6e776b10-823c-4701-a469-3bd7d4e49f98">
    <vCard:FN>James Lawson</vCard:FN>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#092ccb9f-e343-4f58-b48d-ebbe3172ed40">
    <bqs:subject_type>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>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"/>
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  </rdf:Description>
  <rdf:Description rdf:about="rdf:#67b6c647-324b-49f3-a6df-cba2d32dfb1c">
    <dc:title>PNAS</dc:title>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#4ac95772-0f07-4753-8abb-4c2d2c160772">
    <dcterms:modified 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>James</vCard:Given>
    <vCard:Family>Lawson</vCard:Family>
    <vCard:Other/>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#2b7f53de-fa65-42d7-ae08-f4fa7e3d6924">
    <vCard:Given>Jose</vCard:Given>
    <vCard:Family>Vilar</vCard:Family>
    <vCard:Other>G.</vCard:Other>
    <vCard:Other>M.</vCard:Other>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#5eef68cf-8ff9-4789-a34d-7dbcb7051e62">
    <vCard:Given>Catherine</vCard:Given>
    <vCard:Family>Lloyd</vCard:Family>
    <vCard:Other>May</vCard:Other>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#d2b09214-9391-49d2-add4-e6c8db79b79b">
    <vCard:FN>Catherine Lloyd</vCard:FN>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#d7c31cbc-f9e8-4add-b95b-2197a5237a13">
    <dcterms:W3CDTF>2008-09-01T13:12:26+12:00</dcterms:W3CDTF>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#e95de634-eb12-4283-b9c7-791c675a8038">
    <vCard:Given>Hao</vCard:Given>
    <vCard:Family>Kueh</vCard:Family>
    <vCard:Other>Yuan</vCard:Other>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#695fc7df-e54d-47fc-832b-50c8e9ac9da2">
    <dcterms:modified 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 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 rdf:resource="rdf:#ef5c8ff3-9197-4151-951e-9745118b88bc"/>
  </rdf:Description>
  <rdf:Description rdf:about="#vilar_kueh_barkai_leibler_2002">
    <ns7:simulation rdf:resource="rdf:#$dmNO53"/>
    <dc:title>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 rdf:resource="rdf:#1b4f8009-249a-454f-8826-add810038fd5"/>
    <bqs:reference rdf:resource="rdf:#62c278f7-6a0a-43b8-878a-dd73a10f995e"/>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#864d6fda-f4f4-4a5b-8f7a-68f12cbd2e78">
    <vCard:Given>James</vCard:Given>
    <vCard:Family>Lawson</vCard:Family>
    <vCard:Other>Richard</vCard:Other>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#488414d1-491e-4e40-99e7-94213eab43f0">
    <dc:creator 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>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 rdf:resource="rdf:#b167a7db-a498-4547-9a62-82b4b7baa854"/>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#3cc6b2f5-9914-4926-8768-68f3d6890eaf">
    <dcterms:modified 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>2008-02-20T14:54:14+13:00</dcterms:W3CDTF>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#28f6124a-a6f7-4c0c-b56f-534161b896eb">
    <vCard:N rdf:resource="rdf:#864d6fda-f4f4-4a5b-8f7a-68f12cbd2e78"/>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#4983d27d-122c-411d-bb05-f9c762139fb3">
    <vCard:Orgname>The University of Auckland</vCard:Orgname>
    <vCard:Orgunit>The Bioengineering Institute</vCard:Orgunit>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#b0335c6f-f719-4484-8fda-eb653e9e5da5">
    <vCard:ORG rdf:resource="rdf:#4983d27d-122c-411d-bb05-f9c762139fb3"/>
    <vCard:EMAIL rdf:resource="rdf:#d2fceb36-78cd-492d-9226-b5a863ab0ff7"/>
    <vCard:N 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"/>
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    <dcterms:modified 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"/>
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