Rendering of the source text

<?xml version="1.0" encoding="utf-8"?>

<model xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:bqs="http://www.cellml.org/bqs/1.0#" xmlns:dcterms="http://purl.org/dc/terms/" xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" name="vilar_2006" cmeta:id="vilar_2006" xmlns="http://www.cellml.org/cellml/1.0#" xmlns:cellml="http://www.cellml.org/cellml/1.0#" xmlns:cmeta="http://www.cellml.org/metadata/1.0#">
	<documentation xmlns="http://cellml.org/tmp-documentation">
		<article>
			<articleinfo>
				<title>Signal processing in the TGF-beta superfamily ligand-receptor network</title>
				<author>
					<firstname>Catherine</firstname>
					<surname>Lloyd</surname>
					<affiliation>
						<shortaffil>Bioengineering Institute, University of Auckland</shortaffil>
					</affiliation>
				</author>
			</articleinfo>
			<section id="sec_status">
				<title>Model Status</title>
				<para>
            This CellML model has been checked in both PCEnv and COR and the model runs in both to recreate figure 5A in the paper.  This particular version of the model describes a two-compartment model of receptor trafficking for one ligand.  The equations have been written to look like those in figure 4 of the paper.  Initial conditions were not provided in the paper so were taken from the SBML model in the BioModels database (<ulink url="http://www.ebi.ac.uk/biomodels-main/BIOMD0000000101">BIOMD0000000101</ulink>).  Also note that the model only runs correctly if time in minutes is defined as 3600s, and the ligand concentration is increased from 3E-5 to 0.01 at time t=2500 to ensure that the system reaches steady state. Hence, the time t=0 of the paper corresponds to t=2500 in the model (alo in accordance with the SBML model).
          </para>
			</section>
			<sect1 id="sec_structure">
				<title>Model Structure</title>
				<para>
ABSTRACT: The TGF-beta pathway plays a central role in tissue homeostasis and morphogenesis. It transduces a variety of extracellular signals into intracellular transcriptional responses that control a plethora of cellular processes, including cell growth, apoptosis, and differentiation. We use computational modeling to show that coupling of signaling with receptor trafficking results in a highly versatile signal-processing unit, able to sense by itself absolute levels of ligand, temporal changes in ligand dimensionless, and ratios of multiple ligands. This coupling controls whether the response of the receptor module is transient or permanent and whether or not different signaling channels behave independently of each other. Our computational approach unifies seemingly disparate experimental observations and suggests specific changes in receptor trafficking patterns that can lead to phenotypes that favor tumor progression.
</para>
	
<informalfigure float="0" id="fig_reaction_diagram">
<mediaobject>
  <imageobject>
    <objectinfo>
      <title>model diagram</title>
    </objectinfo>
    <imagedata fileref="vilar_2006.png"/>
  </imageobject>
</mediaobject>
<caption>Two-Compartment Model of Receptor Trafficking and Signaling.</caption>
</informalfigure>

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

<para>
Signal processing in the TGF-beta superfamily ligand-receptor network, Jose M. G. Vilar, Ronald Jansen and Chris Sander, 2006, <emphasis>PLoS Computational Biology</emphasis>, volume 2, 36-45.  <ulink url="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=pubmed&amp;cmd=Retrieve&amp;dopt=AbstractPlus&amp;list_uids=16446785&amp;query_hl=1&amp;itool=pubmed_docsum">PubMed ID: 16446785</ulink>
</para>

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

  <units name="minute">
     <unit units="second" multiplier="3600"/>
  </units>
  
  <units name="per_minute">
     <unit units="minute" exponent="-1"/>
  </units>
 
  <component name="environment">
    <variable units="minute" public_interface="out" name="time"/>
  </component> 
  
  <component name="l">
    <variable units="dimensionless" public_interface="out" name="l"/>
	
	<variable units="minute" public_interface="in" name="time"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML" id="1"> 
      <apply>
        <eq/> 
        <ci> l </ci>
        <piecewise>
          <piece>
		    <cn cellml:units="dimensionless">0.01</cn>
            <apply>
              <geq/>
              <ci>time</ci>
		      <cn cellml:units="minute">2500</cn>
            </apply>
		  </piece>
          <otherwise>
            <cn cellml:units="dimensionless">0.00003</cn>
          </otherwise>
        </piecewise>
      </apply>
    </math> 
  </component>
  
  <component name="l_RI_RII">
    <variable units="dimensionless" public_interface="out" name="l_RI_RII" initial_value="0.0"/> 
    
    <variable units="dimensionless" public_interface="in" name="l"/>
    <variable units="dimensionless" public_interface="in" name="RI"/>
	<variable units="dimensionless" public_interface="in" name="RII"/>
	<variable units="per_minute" public_interface="in" name="ka"/>
    <variable units="per_minute" public_interface="in" name="ki"/>
	<variable units="per_minute" public_interface="in" name="kcd"/>
	<variable units="per_minute" public_interface="in" name="klid"/>
	<variable units="minute" public_interface="in" name="time"/> 
    
    <math xmlns="http://www.w3.org/1998/Math/MathML" id="2"> 
      <apply>
        <eq/> 
        <apply>
          <diff/> 
          <bvar>
            <ci>time</ci>
          </bvar> 
          <ci> l_RI_RII </ci> 
        </apply>
        <apply>
          <minus/> 
		  <apply>
            <times/> 
			<ci> ka </ci>
            <ci> l </ci>
			<ci> RI </ci>
            <ci> RII </ci>
		  </apply>
		  <apply>
            <times/>
			<apply>
              <plus/> 
		      <ci> kcd </ci>
              <ci> klid </ci>
			  <ci> ki </ci>
		    </apply> 
			<ci> l_RI_RII </ci> 
          </apply>
        </apply>  
      </apply>
    </math> 
  </component>
  
  <component name="RI">
    <variable units="dimensionless" public_interface="out" name="RI" initial_value="20.0"/> 
    
    <variable units="dimensionless" public_interface="in" name="l"/>
    <variable units="dimensionless" public_interface="in" name="RI_endo"/>
	<variable units="dimensionless" public_interface="in" name="RII"/>
	<variable units="dimensionless" public_interface="in" name="l_RI_RII_endo"/>
	<variable units="per_minute" public_interface="in" name="ka"/>
    <variable units="per_minute" public_interface="in" name="kcd"/>
	<variable units="per_minute" public_interface="in" name="ki"/>
    <variable units="per_minute" public_interface="in" name="kr"/>
	<variable units="per_minute" public_interface="in" name="p_RI"/>
	<variable units="dimensionless" public_interface="in" name="alpha"/>
	<variable units="minute" public_interface="in" name="time"/> 
    
    <math xmlns="http://www.w3.org/1998/Math/MathML" id="3"> 
      <apply>
        <eq/> 
        <apply>
          <diff/> 
          <bvar>
            <ci>time</ci>
          </bvar> 
          <ci> RI </ci> 
        </apply>
        <apply>
          <minus/>
          <apply>
            <plus/> 
            <ci> p_RI </ci>			 
		    <apply>
              <times/> 
		      <ci> kr </ci>
              <ci> RI_endo </ci>
		    </apply>
			<apply>
              <times/> 
		      <ci> alpha </ci>
			  <ci> kr </ci>
              <ci> l_RI_RII_endo </ci>
		    </apply>
		  </apply>
		  <apply>
            <plus/>
			<apply>
              <times/> 
		      <ci> ka </ci>
			  <ci> l </ci>
              <ci> RI </ci>
			  <ci> RII </ci>
		    </apply>
			<apply>
              <times/> 
			  <apply>
                <plus/>
		        <ci> kcd </ci>
			    <ci> ki </ci>
		      </apply>
              <ci> RI </ci>
			</apply>
          </apply>
        </apply>  
      </apply>
    </math> 
  </component>
  
  <component name="RII">
    <variable units="dimensionless" public_interface="out" name="RII" initial_value="20.0"/> 
    
    <variable units="dimensionless" public_interface="in" name="l"/>
    <variable units="dimensionless" public_interface="in" name="RII_endo"/>
	<variable units="dimensionless" public_interface="in" name="RI"/>
	<variable units="dimensionless" public_interface="in" name="l_RI_RII_endo"/>
	<variable units="per_minute" public_interface="in" name="ka"/>
    <variable units="per_minute" public_interface="in" name="kcd"/>
	<variable units="per_minute" public_interface="in" name="ki"/>
    <variable units="per_minute" public_interface="in" name="kr"/>
	<variable units="per_minute" public_interface="in" name="p_RII"/>
	<variable units="dimensionless" public_interface="in" name="alpha"/>
	<variable units="minute" public_interface="in" name="time"/> 
    
    <math xmlns="http://www.w3.org/1998/Math/MathML" id="4"> 
      <apply>
        <eq/> 
        <apply>
          <diff/> 
          <bvar>
            <ci>time</ci>
          </bvar> 
          <ci> RII </ci> 
        </apply>
        <apply>
          <minus/>
          <apply>
            <plus/> 
            <ci> p_RII </ci>			 
		    <apply>
              <times/> 
		      <ci> kr </ci>
              <ci> RII_endo </ci>
		    </apply>
			<apply>
              <times/> 
		      <ci> alpha </ci>
			  <ci> kr </ci>
              <ci> l_RI_RII_endo </ci>
		    </apply>
		  </apply>
		  <apply>
            <plus/>
			<apply>
              <times/> 
		      <ci> ka </ci>
			  <ci> l </ci>
              <ci> RI </ci>
			  <ci> RII </ci>
		    </apply>
			<apply>
              <times/> 
			  <apply>
                <plus/>
		        <ci> kcd </ci>
			    <ci> ki </ci>
		      </apply>
              <ci> RII </ci>
			</apply>
          </apply>
        </apply>  
      </apply>
    </math> 
  </component>
  
  <component name="l_RI_RII_endo">
    <variable units="dimensionless" public_interface="out" name="l_RI_RII_endo" initial_value="40.0"/> 
    
    <variable units="dimensionless" public_interface="in" name="l_RI_RII"/>
    <variable units="per_minute" public_interface="in" name="ki"/>
    <variable units="per_minute" public_interface="in" name="kr"/>
	<variable units="minute" public_interface="in" name="time"/> 
    
    <math xmlns="http://www.w3.org/1998/Math/MathML" id="5"> 
      <apply>
        <eq/> 
        <apply>
          <diff/> 
          <bvar>
            <ci>time</ci>
          </bvar> 
          <ci> l_RI_RII_endo </ci> 
        </apply>
        <apply>
          <minus/> 
		  <apply>
            <times/> 
		    <ci> ki </ci>
            <ci> l_RI_RII </ci>
	      </apply>
		  <apply>
            <times/>
			<ci> kr </ci>
		    <ci> l_RI_RII_endo </ci> 
          </apply>
        </apply>  
      </apply>
    </math> 
  </component>
  
  <component name="RI_endo">
    <variable units="dimensionless" public_interface="out" name="RI_endo" initial_value="0.0"/> 
    
    <variable units="dimensionless" public_interface="in" name="RI"/>
    <variable units="per_minute" public_interface="in" name="ki"/>
    <variable units="per_minute" public_interface="in" name="kr"/>
	<variable units="minute" public_interface="in" name="time"/> 
    
    <math xmlns="http://www.w3.org/1998/Math/MathML" id="6"> 
      <apply>
        <eq/> 
        <apply>
          <diff/> 
          <bvar>
            <ci>time</ci>
          </bvar> 
          <ci> RI_endo </ci> 
        </apply>
        <apply>
          <minus/> 
		  <apply>
            <times/> 
		    <ci> ki </ci>
            <ci> RI </ci>
	      </apply>
		  <apply>
            <times/>
			<ci> kr </ci>
		    <ci> RI_endo </ci> 
          </apply>
        </apply>  
      </apply>
    </math> 
  </component>
  
  <component name="RII_endo">
    <variable units="dimensionless" public_interface="out" name="RII_endo" initial_value="0.0"/> 
    
    <variable units="dimensionless" public_interface="in" name="RII"/>
    <variable units="per_minute" public_interface="in" name="ki"/>
    <variable units="per_minute" public_interface="in" name="kr"/>
	<variable units="minute" public_interface="in" name="time"/> 
    
    <math xmlns="http://www.w3.org/1998/Math/MathML" id="7"> 
      <apply>
        <eq/> 
        <apply>
          <diff/> 
          <bvar>
            <ci>time</ci>
          </bvar> 
          <ci> RII_endo </ci> 
        </apply>
        <apply>
          <minus/> 
		  <apply>
            <times/> 
		    <ci> ki </ci>
            <ci> RII </ci>
	      </apply>
		  <apply>
            <times/>
			<ci> kr </ci>
		    <ci> RII_endo </ci> 
          </apply>
        </apply>  
      </apply>
    </math> 
  </component>
  
  <component name="model_parameters">
    <variable units="per_minute" public_interface="out" name="kr" initial_value="0.033333333"/>
	<variable units="per_minute" public_interface="out" name="kcd" initial_value="0.0277777778"/>
	<variable units="per_minute" public_interface="out" name="klid" initial_value="0.25"/>
	<variable units="per_minute" public_interface="out" name="ka" initial_value="1"/>
	<variable units="per_minute" public_interface="out" name="ki" initial_value="0.333333333"/>
	<variable units="per_minute" public_interface="out" name="p_RI" initial_value="8"/>
	<variable units="per_minute" public_interface="out" name="p_RII" initial_value="4"/>
	<variable units="dimensionless" public_interface="out" name="alpha" initial_value="1"/>
  </component>
  
  <connection>
    <map_components component_2="environment" component_1="l"/>
    <map_variables variable_2="time" variable_1="time"/>
  </connection>
  
  <connection>
    <map_components component_2="environment" component_1="l_RI_RII"/>
    <map_variables variable_2="time" variable_1="time"/>
  </connection>
  
  <connection>
    <map_components component_2="environment" component_1="RI"/>
    <map_variables variable_2="time" variable_1="time"/>
  </connection>
  
  <connection>
    <map_components component_2="environment" component_1="RII"/>
    <map_variables variable_2="time" variable_1="time"/>
  </connection>
  
  <connection>
    <map_components component_2="environment" component_1="l_RI_RII_endo"/>
    <map_variables variable_2="time" variable_1="time"/>
  </connection>
  
  <connection>
    <map_components component_2="environment" component_1="RI_endo"/>
    <map_variables variable_2="time" variable_1="time"/>
  </connection>
  
  <connection>
    <map_components component_2="environment" component_1="RII_endo"/>
    <map_variables variable_2="time" variable_1="time"/>
  </connection>
  
  <connection>
    <map_components component_2="l_RI_RII" component_1="l"/>
    <map_variables variable_2="l" variable_1="l"/>
  </connection>
  
  <connection>
    <map_components component_2="RI" component_1="l"/>
    <map_variables variable_2="l" variable_1="l"/>
  </connection>
  
  <connection>
    <map_components component_2="RII" component_1="l"/>
    <map_variables variable_2="l" variable_1="l"/>
  </connection>
  
  <connection>
    <map_components component_2="l_RI_RII" component_1="RI"/>
    <map_variables variable_2="RI" variable_1="RI"/>
  </connection>
  
  <connection>
    <map_components component_2="l_RI_RII" component_1="RII"/>
    <map_variables variable_2="RII" variable_1="RII"/>
  </connection>
  
  <connection>
    <map_components component_2="l_RI_RII" component_1="model_parameters"/>
    <map_variables variable_2="ka" variable_1="ka"/>
	<map_variables variable_2="kcd" variable_1="kcd"/>
	<map_variables variable_2="klid" variable_1="klid"/>
	<map_variables variable_2="ki" variable_1="ki"/>
  </connection>
  
  <connection>
    <map_components component_2="RI" component_1="RI_endo"/>
    <map_variables variable_2="RI" variable_1="RI"/>
	<map_variables variable_2="RI_endo" variable_1="RI_endo"/>
  </connection>
  
  <connection>
    <map_components component_2="RI" component_1="RII"/>
    <map_variables variable_2="RII" variable_1="RII"/>
	<map_variables variable_2="RI" variable_1="RI"/>
  </connection>
  
  <connection>
    <map_components component_2="RI" component_1="l_RI_RII_endo"/>
    <map_variables variable_2="l_RI_RII_endo" variable_1="l_RI_RII_endo"/>
  </connection>
  
  <connection>
    <map_components component_2="RI" component_1="model_parameters"/>
    <map_variables variable_2="ka" variable_1="ka"/>
	<map_variables variable_2="kcd" variable_1="kcd"/>
	<map_variables variable_2="kr" variable_1="kr"/>
	<map_variables variable_2="ki" variable_1="ki"/>
	<map_variables variable_2="alpha" variable_1="alpha"/>
	<map_variables variable_2="p_RI" variable_1="p_RI"/>
  </connection>
  
  <connection>
    <map_components component_2="RII" component_1="RII_endo"/>
    <map_variables variable_2="RII" variable_1="RII"/>
	<map_variables variable_2="RII_endo" variable_1="RII_endo"/>
  </connection>
  
  <connection>
    <map_components component_2="RII" component_1="l_RI_RII_endo"/>
    <map_variables variable_2="l_RI_RII_endo" variable_1="l_RI_RII_endo"/>
  </connection>
  
  <connection>
    <map_components component_2="RII" component_1="model_parameters"/>
    <map_variables variable_2="ka" variable_1="ka"/>
	<map_variables variable_2="kcd" variable_1="kcd"/>
	<map_variables variable_2="kr" variable_1="kr"/>
	<map_variables variable_2="ki" variable_1="ki"/>
	<map_variables variable_2="alpha" variable_1="alpha"/>
	<map_variables variable_2="p_RII" variable_1="p_RII"/>
  </connection>
  
  <connection>
    <map_components component_2="l_RI_RII_endo" component_1="l_RI_RII"/>
    <map_variables variable_2="l_RI_RII" variable_1="l_RI_RII"/>
  </connection>
  
  <connection>
    <map_components component_2="l_RI_RII_endo" component_1="model_parameters"/>
    <map_variables variable_2="kr" variable_1="kr"/>
	<map_variables variable_2="ki" variable_1="ki"/>
  </connection>
  
  <connection>
    <map_components component_2="RI_endo" component_1="model_parameters"/>
    <map_variables variable_2="kr" variable_1="kr"/>
	<map_variables variable_2="ki" variable_1="ki"/>
  </connection>
  
  <connection>
    <map_components component_2="RII_endo" component_1="model_parameters"/>
    <map_variables variable_2="kr" variable_1="kr"/>
	<map_variables variable_2="ki" variable_1="ki"/>
  </connection>

  <rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:bqs="http://www.cellml.org/bqs/1.0#" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:dcterms="http://purl.org/dc/terms/" xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#">
    <foo xmlns="http://www.example.org/foo/bar/baz" />
    <!--
      The following RDF block contains metadata that applies to this document
      as a whole, as indicated by the empty about attribute on the 
      <rdf:Description> element.
    -->
    <rdf:Description rdf:about="">
      <!--
        The Model Builder Metadata.  The Dublin Core "creator" element is used  
        to indicate the person who translated the model into CellML.
      -->
      <dc:title>Signal processing in the TGF-beta superfamily ligand-receptor network (Standard Form)</dc:title>
	  <dc:creator rdf:parseType="Resource">
        <vCard:N rdf:parseType="Resource">
          <vCard:Family>Lloyd</vCard:Family>
          <vCard:Given>Catherine</vCard:Given>
		  <vCard:Other>May</vCard:Other>
        </vCard:N>
        <vCard:EMAIL rdf:parseType="Resource">
          <rdf:value>c.lloyd@auckland@auckland.ac.nz</rdf:value>
          <rdf:type rdf:resource="http://imc.org/vCard/3.0#internet"/>
        </vCard:EMAIL>
        <vCard:ORG rdf:parseType="Resource">
          <vCard:Orgname>The University of Auckland</vCard:Orgname>
          <vCard:Orgunit>Auckland Bioengineering Institute</vCard:Orgunit>
        </vCard:ORG>
      </dc:creator>
      
      <!--
        The Creation Date metadata. This is the date on which the model
        was translated into CellML.
      -->
      <dcterms:created rdf:parseType="Resource">
        <dcterms:W3CDTF>2009-09-28</dcterms:W3CDTF>
      </dcterms:created>
      
      <!--
        The Modification History metadata. This lists the changes that have been
        made to the document, who made the changes, and when they were made.
      -->
     
    </rdf:Description>
    
    <!--
      The following metadata refers to the model itself, as indicated by the
      reference to the ID "vilar_2006", which is    
      declared on the <model> element.
    -->
    <rdf:Description rdf:about="#vilar_2006">
      <!-- A human readable name for the model. -->
      <dc:title>
        The Vilar et al. 2006 Model of Signal Processing in the TGF-beta Superfamily Ligand-Receptor Network
      </dc:title>
      
      <!-- A comment regarding the model. -->
      <cmeta:comment rdf:parseType="Resource">
        <rdf:value>
          This is the CellML description of Vilar et al.'s mathematical model of ligand-receptor binding and receptor complex internalisation in the TGF-beta superfamiliy ligand-receptor network
        </rdf:value>
        <!-- The creator of the comment. -->
        <dc:creator rdf:parseType="Resource">
          <vCard:FN>Catherine Lloyd</vCard:FN>
        </dc:creator>
      </cmeta:comment>
      
      <!--  Keyword(s) -->
      <bqs:reference rdf:parseType="Resource">
        <dc:subject rdf:parseType="Resource">
          <bqs:subject_type>keyword</bqs:subject_type>
          <rdf:value>
            <rdf:Bag>
              <rdf:li>signal transduction</rdf:li>
              <rdf:li>TGF-beta</rdf:li>
            </rdf:Bag>
          </rdf:value>
        </dc:subject>
      </bqs:reference>

      <bqs:reference rdf:parseType="Resource">
        <bqs:Pubmed_id>16446785</bqs:Pubmed_id>
        <bqs:JournalArticle rdf:parseType="Resource">
          <dc:creator>
            <rdf:Seq>
              <rdf:li rdf:parseType="Resource">
                <bqs:Person rdf:parseType="Resource">
                  <vCard:N rdf:parseType="Resource">
                    <vCard:Family>Vilar</vCard:Family>
                    <vCard:Given>Jose</vCard:Given>
                    <vCard:Other>M</vCard:Other>
					<vCard:Other>G</vCard:Other>
                  </vCard:N>
                </bqs:Person>
              </rdf:li>
              <rdf:li rdf:parseType="Resource">
                <bqs:Person rdf:parseType="Resource">
                  <vCard:N rdf:parseType="Resource">
                    <vCard:Family>Jansen</vCard:Family>
                    <vCard:Given>Ronald</vCard:Given>
				  </vCard:N>
                </bqs:Person>
              </rdf:li>
			  <rdf:li rdf:parseType="Resource">
                <bqs:Person rdf:parseType="Resource">
                  <vCard:N rdf:parseType="Resource">
                    <vCard:Family>Sander</vCard:Family>
                    <vCard:Given>Chris</vCard:Given>
                  </vCard:N>
                </bqs:Person>
              </rdf:li>
            </rdf:Seq>
          </dc:creator>
          <dc:title>
           Signal processing in the TGF-beta superfamily ligand-receptor network
          </dc:title>
          <dcterms:issued rdf:parseType="Resource">
            <dcterms:W3CDTF>2006-01</dcterms:W3CDTF>
          </dcterms:issued>
          <bqs:Journal rdf:parseType="Resource">
            <dc:title>PLoS Computational Biology</dc:title>
          </bqs:Journal>
          <bqs:volume>2</bqs:volume>
          <bqs:first_page>36</bqs:first_page>
          <bqs:last_page>45</bqs:last_page>
        </bqs:JournalArticle>
      </bqs:reference>
    </rdf:Description>
  </rdf:RDF>  
  
</model>