Location: Fallon, Lauffenburger, 2000 @ 4d2f0adb6c68 / fallon_lauffenburger_2000.cellml

Author:
James Lawson <j.lawson@auckland.ac.nz>
Date:
2009-09-16 17:16:48+12:00
Desc:
changed cmeta:id, fixed e-notation, updated curation status, updated documentation
Permanent Source URI:
http://models.cellml.org/workspace/fallon_lauffenburger_2000/rawfile/4d2f0adb6c6885e1db497276fd6bef168c250f67/fallon_lauffenburger_2000.cellml

<?xml version="1.0" encoding="utf-8"?>
<!--  FILE :fallon_lauffenburger_2000.xml

CREATED :  16th October 2002

LAST MODIFIED : 9th April 2003

AUTHOR :  Catherine Lloyd
          Bioengineering Institute
          The University of Auckland
          
MODEL STATUS :  This model conforms to the CellML 1.0 Specification released on
10th August 2001, and the 16/01/2002 CellML Metadata 1.0 Specification.

DESCRIPTION :  This file contains a CellML description of Fallon and Lauffenburger's 2000 model of the effects of ligand-receptor binding properties on interleukin-2 trafficking dynamics and T cell proliferation response.

CHANGES:  
  09/04/2003 - AAC - Added publication date information.  

-->
<model xmlns="http://www.cellml.org/cellml/1.0#" xmlns:cmeta="http://www.cellml.org/metadata/1.0#" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:bqs="http://www.cellml.org/bqs/1.0#" xmlns:cellml="http://www.cellml.org/cellml/1.0#" xmlns:dcterms="http://purl.org/dc/terms/" xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" cmeta:id="fallon_lauffenburger_2000" name="fallon_lauffenburger_2000">
<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
  <articleinfo>
  <title>Binding, Internalisation and Postendocytotic Sorting of Interleukin-2 and Its Receptor</title>
  <author>
    <firstname>Catherine</firstname>
          <surname>Lloyd</surname>
    <affiliation>
      <shortaffil>Auckland Bioengineering Institute, University of Auckland</shortaffil>
    </affiliation>
  </author>
</articleinfo>
  <section id="sec_status">
    <title>Model Status</title>
    <para>
            The model is known to run in OpenCell and COR and the results are close to those in the published paper, as generated by the original model.  The units have been checked and are consistent.  We suspect this model might generate the exact published results if the original initial conditions were used.  As it is, the paper does not state all of these values, but instead it explains that these values are calculated throughout the simulation and subsequently fed back into the model.
          </para>
  </section>
  <sect1 id="sec_structure">
<title>Model Structure</title>

<para>
Interleukin-2 (IL-2) is a growth factor which is secreted by activated T-cells and which is responsible for stimulating T-cell proliferation.  Following the binding of the cell surface IL-2 receptor to its ligand, the entire receptor-ligand complex is internalised into sorting endosomes by endocytosis.  Within these endosomes, the receptor-ligand complex may dissociate, and also, internal receptors and ligands may associate to form a new complex.  Receptor associated ligand is then subject to lysosomal degradation, while free intracellular ligand is recycled back to extracellular ligand.  In the absence of any ligand, cell surface receptors are maintained at a steady level by constitutive internalisation and biosynthesis rates.  In the presence of ligand, there are positive feedback effects.  Cell surface receptor-ligand complexes stimulate the synthesis of new receptors, and they also enhance cell proliferation.     
</para>

<para>
Eric M. Fallon and Douglas A. Lauffenburger capture these IL-2 trafficking dynamics in their computational model (see the figure below).  The model uses kinetic equations to describe receptor-ligand binding, internalisation and postendocytotic sorting of IL-2 and the IL-2-receptor complex.  Model simulations are able to predict T-cell proliferation responses to IL-2.  
</para>

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

<para>
Computational Model for Effects of Ligand/Receptor Binding Properties on Interleukin-2 Trafficking Dynamics and T Cell Proliferation Response, Eric M. Fallon and Douglas A. Lauffenburger, 2000, <emphasis>Biotechnology Progress</emphasis>, 16, 905-916.  <ulink url="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&amp;db=PubMed&amp;list_uids=11027188&amp;dopt=Abstract">PubMed ID: 11027188</ulink>  
</para>

<informalfigure float="0" id="fig_reaction_diagram">
<mediaobject>
  <imageobject>
    <objectinfo>
      <title>diagram of the ligand-receptor binding model</title>
    </objectinfo>
    <imagedata fileref="fallon_2000.png"/>
  </imageobject>
</mediaobject>
<caption>A schematic diagram of Fallon and Lauffenburger's 2000 computational model of IL-2-receptor binding and trafficking.  The model follows the path of an extracellular ligand as it is bound to a cell surface receptor, internalised, degraded or recycled.</caption>
</informalfigure>

</sect1>
</article>
</documentation>
  
    
    <!--
    Below, we define some additional units for association with variables and
    constants within the model. The identifiers are fairly self-explanatory.
  -->

   <units name="picomolar">
      <unit units="mole" prefix="pico"/>
      <unit units="litre" exponent="-1"/>
   </units>
   
   <units name="minute">
      <unit units="second" multiplier="60.0"/>
   </units>
   
   <units name="flux">
      <unit units="picomolar" exponent="1"/>
      <unit units="minute" exponent="-1"/>
   </units>
   
   <units name="first_order_rate_constant">
      <unit units="minute" exponent="-1"/>
   </units>
  
   <units name="second_order_rate_constant">
      <unit units="picomolar" exponent="-1"/>
      <unit units="minute" exponent="-1"/>
   </units>
   
   <units base_units="yes" name="cell"/>

   <units base_units="yes" name="number"/>
   
   <units name="number_per_cell">
      <unit units="number"/>
      <unit units="cell" exponent="-1"/>
   </units>

   <units name="number_per_mole">
      <unit units="number"/>
      <unit units="mole" exponent="-1"/>
   </units>

   <units name="number_per_cell_minute">
      <unit units="number"/>
      <unit units="cell" exponent="-1"/>
      <unit units="minute" exponent="-1"/>
   </units>

   <units name="L_per_cell">
      <unit units="litre"/>
      <unit units="cell" exponent="-1"/>
   </units>
   
   <units name="cell_per_L_minute">
      <unit units="cell"/>
      <unit units="litre" exponent="-1"/>
      <unit units="minute" exponent="-1"/>
   </units>
   
   <units name="cell_per_L">
      <unit units="cell"/>
      <unit units="litre" exponent="-1"/>
   </units>
  
   
   <component name="environment">
      <variable units="minute" public_interface="out" name="time"/>
   </component>

   <component cmeta:id="Rs" name="Rs">
    <rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
      <rdf:Description rdf:about="Rs">
        <dc:title>Rs</dc:title>
        <dcterms:alternative>cell surface IL-2 receptor</dcterms:alternative>
      </rdf:Description>
    </rdf:RDF> 
    <variable units="number_per_cell" public_interface="out" name="Rs" initial_value="1500.0"/>
    
    <variable units="picomolar" public_interface="in" name="L"/>
    <variable units="number_per_cell" public_interface="in" name="Cs"/>
    <variable units="number_per_cell_minute" public_interface="in" name="Vs"/>
    <variable units="second_order_rate_constant" public_interface="in" name="kf"/> 
    <variable units="first_order_rate_constant" public_interface="in" name="kr"/>
    <variable units="first_order_rate_constant" public_interface="in" name="kt"/> 
    <variable units="first_order_rate_constant" public_interface="in" name="ksyn"/> 
    <variable units="minute" public_interface="in" name="time"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML" id="1"> 
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        <eq/> 
        <apply>
          <diff/> 
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            <ci> time </ci>
          </bvar> 
          <ci> Rs </ci> 
        </apply>
        <apply>
          <minus/>
          <apply>
            <plus/>
            <apply>
              <times/>
              <apply>
                <plus/>
                <ci> kr </ci>
                <ci> ksyn </ci>
              </apply>
              <ci> Cs </ci>
            </apply>
            <ci> Vs </ci>
          </apply>
          <apply>
            <plus/>
            <apply>
              <times/>
              <ci> kf </ci>
              <ci> L </ci>
              <ci> Rs </ci>
            </apply>
            <apply>
              <times/>
              <ci> kt </ci>
              <ci> Rs </ci>
            </apply>
          </apply>
        </apply> 
      </apply> 
    </math>  
  </component>

  <component cmeta:id="Cs" name="Cs">
    <rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
      <rdf:Description rdf:about="Cs">
        <dc:title>Cs</dc:title>
        <dcterms:alternative>cell surface ligand-receptor complex</dcterms:alternative>
      </rdf:Description>
    </rdf:RDF> 
    <variable units="number_per_cell" public_interface="out" name="Cs" initial_value="1.0"/>
    
    <variable units="picomolar" public_interface="in" name="L"/>
    <variable units="number_per_cell" public_interface="in" name="Rs"/>
    <variable units="second_order_rate_constant" public_interface="in" name="kf"/> 
    <variable units="first_order_rate_constant" public_interface="in" name="kr"/>
    <variable units="first_order_rate_constant" public_interface="in" name="ke"/> 
    <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> Cs </ci> 
        </apply>
        <apply>
          <minus/>
          <apply>
            <times/>
            <ci> kf </ci>
            <ci> L </ci>
            <ci> Rs </ci>
          </apply>
          <apply>
            <times/>
            <apply>
              <plus/>
              <ci> kr </ci>
              <ci> ke </ci>
            </apply>
            <ci> Cs </ci>
          </apply>
        </apply> 
      </apply> 
    </math>  
  </component>

  <component cmeta:id="Ri" name="Ri">
    <rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
      <rdf:Description rdf:about="Ri">
        <dc:title>Ri</dc:title>
        <dcterms:alternative>intracellular IL-2 receptor</dcterms:alternative>
      </rdf:Description>
    </rdf:RDF> 
    <variable units="number_per_cell" public_interface="out" name="Ri" initial_value="300.0"/>
    
    <variable units="picomolar" public_interface="in" name="Li"/>
    <variable units="number_per_cell" public_interface="in" name="Ci"/>
    <variable units="number_per_cell" public_interface="in" name="Rs"/>
    <variable units="second_order_rate_constant" public_interface="in" name="kfe"/> 
    <variable units="first_order_rate_constant" public_interface="in" name="kre"/>
    <variable units="first_order_rate_constant" public_interface="in" name="kt"/> 
    <variable units="first_order_rate_constant" public_interface="in" name="kh"/> 
    <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/>
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            <plus/>
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              <times/>
              <ci> kre </ci>
              <ci> Ci </ci>
            </apply>
            <apply>
              <times/>
              <ci> kt </ci>
              <ci> Rs </ci>
            </apply>
          </apply>
          <apply>
            <plus/>
            <apply>
              <times/>
              <ci> kfe </ci>
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              <ci> Ri </ci>
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            <apply>
              <times/>
              <ci> kh </ci>
              <ci> Ri </ci>
            </apply>
          </apply>
        </apply> 
      </apply> 
    </math>  
  </component>

  <component cmeta:id="Ci" name="Ci">
    <rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
      <rdf:Description rdf:about="Ci">
        <dc:title>Ci</dc:title>
        <dcterms:alternative>intracellular ligand-receptor complex</dcterms:alternative>
      </rdf:Description>
    </rdf:RDF> 
    <variable units="number_per_cell" public_interface="out" name="Ci" initial_value="1.0"/>
    
    <variable units="picomolar" public_interface="in" name="Li"/>
    <variable units="number_per_cell" public_interface="in" name="Ri"/>
    <variable units="number_per_cell" public_interface="in" name="Cs"/>
    <variable units="second_order_rate_constant" public_interface="in" name="kfe"/> 
    <variable units="first_order_rate_constant" public_interface="in" name="kre"/>
    <variable units="first_order_rate_constant" public_interface="in" name="ke"/> 
    <variable units="first_order_rate_constant" public_interface="in" name="kh"/> 
    <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> Ci </ci> 
        </apply>
        <apply>
          <minus/>
          <apply>
            <plus/>
            <apply>
              <times/>
              <ci> kfe </ci>
              <ci> Li </ci>
              <ci> Ri </ci>
            </apply>
            <apply>
              <times/>
              <ci> ke </ci>
              <ci> Cs </ci>
            </apply>
          </apply>
          <apply>
            <times/>
            <apply>
              <plus/>
              <ci> kre </ci>
              <ci> kh </ci>
            </apply>
            <ci> Ci </ci>
          </apply>
        </apply> 
      </apply> 
    </math>  
  </component>

  <component cmeta:id="Li" name="Li">
    <rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
      <rdf:Description rdf:about="Li">
        <dc:title>Li</dc:title>
        <dcterms:alternative>intracellular IL-2 ligand</dcterms:alternative>
      </rdf:Description>
    </rdf:RDF> 
    <variable units="picomolar" public_interface="out" name="Li" initial_value="0.01"/>
    
    <variable units="number_per_cell" public_interface="in" name="Ci"/>
    <variable units="number_per_cell" public_interface="in" name="Ri"/>
    <variable units="second_order_rate_constant" public_interface="in" name="kfe"/> 
    <variable units="first_order_rate_constant" public_interface="in" name="kre"/>
    <variable units="first_order_rate_constant" public_interface="in" name="kx"/> 
    <variable units="L_per_cell" public_interface="in" name="Ve"/> 
    <variable units="number_per_mole" public_interface="in" name="NA"/> 
    <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> Li </ci> 
        </apply>
        <apply>
          <minus/>
          <apply>
            <divide/>
            <apply>
              <minus/>
              <apply>
                <times/>
                <ci> kre </ci>
                <ci> Ci </ci>
              </apply>
              <apply>
                <times/>
                <ci> kfe </ci>
                <ci> Li </ci>
                <ci> Ri </ci>
              </apply>
            </apply>
            <apply>
              <times/>
              <ci> Ve </ci>
              <ci> NA </ci>
            </apply>
          </apply>
          <apply>
            <times/>
            <ci> kx </ci>
            <ci> Li </ci>
          </apply>
        </apply> 
      </apply> 
    </math>  
  </component>

  <component cmeta:id="Ld" name="Ld">
    <rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
      <rdf:Description rdf:about="Ld">
        <dc:title>Ld</dc:title>
        <dcterms:alternative>degraded IL-2 ligand</dcterms:alternative>
      </rdf:Description>
    </rdf:RDF> 
    <variable units="number_per_cell" public_interface="out" name="Ld" initial_value="1.0"/>
    
    <variable units="number_per_cell" public_interface="in" name="Ci"/>
    <variable units="first_order_rate_constant" public_interface="in" name="kh"/> 
    <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> Ld </ci> 
        </apply>
        <apply>
          <times/>
          <ci> kh </ci>
          <ci> Ci </ci>
        </apply>
      </apply> 
    </math>  
  </component>

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    <rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
      <rdf:Description rdf:about="L">
        <dc:title>L</dc:title>
        <dcterms:alternative>extracellular IL-2 ligand</dcterms:alternative>
      </rdf:Description>
    </rdf:RDF> 
    <variable units="picomolar" public_interface="out" name="L" initial_value="10.0"/>
    
    <variable units="number_per_cell" public_interface="in" name="Rs"/>
    <variable units="number_per_cell" public_interface="in" name="Cs"/>
    <variable units="picomolar" public_interface="in" name="Li"/>
    <variable units="cell_per_L" public_interface="in" name="Y"/>
    <variable units="second_order_rate_constant" public_interface="in" name="kf"/> 
    <variable units="first_order_rate_constant" public_interface="in" name="kr"/>
    <variable units="first_order_rate_constant" public_interface="in" name="kx"/> 
    <variable units="L_per_cell" public_interface="in" name="Ve"/> 
    <variable units="number_per_mole" public_interface="in" name="NA"/> 
    <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> L </ci> 
        </apply>
        <apply>
          <divide/>
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            <times/>
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              <minus/>
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                <plus/>
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                  <ci> kr </ci>
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                <times/>
                <ci> kf </ci>
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    </math>  
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      <rdf:Description rdf:about="Y">
        <dc:title>Y</dc:title>
        <dcterms:alternative>cell density</dcterms:alternative>
      </rdf:Description>
    </rdf:RDF> 
    <variable units="cell_per_L" public_interface="out" name="Y" initial_value="2.5E8"/>
    
    <variable units="number_per_cell" public_interface="in" name="Cs"/>
    <variable units="minute" public_interface="in" name="time"/>
    
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          <ci> Y </ci> 
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              <minus/>
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                <divide/>
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                  <times/>
                  <cn cellml:units="dimensionless"> 600.0 </cn>
                  <ci> Cs </ci>
                </apply>
                <apply>
                  <plus/>
                  <cn cellml:units="number_per_cell"> 250.0 </cn>
                  <ci> Cs </ci>
                </apply>
              </apply>
              <cn cellml:units="dimensionless"> 200.0 </cn>
            </apply>
          </apply>
          <cn cellml:units="cell_per_L_minute" type="e-notation"> 1<sep/>3 </cn>
        </apply> 
      </apply> 
    </math>  
  </component>
  
  <component name="model_parameters">
    <variable units="first_order_rate_constant" public_interface="out" name="kr" initial_value="0.0138"/>
    <variable units="second_order_rate_constant" public_interface="out" name="kf" initial_value="0.0012432"/>
    <variable units="first_order_rate_constant" public_interface="out" name="kre" initial_value="0.1104"/>
    <variable units="second_order_rate_constant" public_interface="out" name="kfe" initial_value="0.0001104"/>
    <variable units="first_order_rate_constant" public_interface="out" name="kt" initial_value="0.007"/>
    <variable units="number_per_cell_minute" public_interface="out" name="Vs" initial_value="11"/>
    <variable units="first_order_rate_constant" public_interface="out" name="ksyn" initial_value="0.0011"/>
    <variable units="first_order_rate_constant" public_interface="out" name="ke" initial_value="0.04"/>
    <variable units="first_order_rate_constant" public_interface="out" name="kx" initial_value="0.15"/>
    <variable units="first_order_rate_constant" public_interface="out" name="kh" initial_value="0.035"/>
    <variable units="L_per_cell" public_interface="out" name="Ve" initial_value="1E-14"/>
    <variable units="number_per_mole" public_interface="out" name="NA" initial_value="6.02E23"/>
  </component>
  
   
  <connection>
    <map_components component_2="environment" component_1="Rs"/>
    <map_variables variable_2="time" variable_1="time"/>
  </connection>

  <connection>
    <map_components component_2="environment" component_1="Cs"/>
    <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="Ci"/>
    <map_variables variable_2="time" variable_1="time"/>
  </connection>
  
  <connection>
    <map_components component_2="environment" component_1="Li"/>
    <map_variables variable_2="time" variable_1="time"/>
  </connection>
  
  <connection>
    <map_components component_2="environment" component_1="Ld"/>
    <map_variables variable_2="time" variable_1="time"/>
  </connection>
  
  <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="Y"/>
    <map_variables variable_2="time" variable_1="time"/>
  </connection>

  <connection>
    <map_components component_2="Cs" component_1="Rs"/>
    <map_variables variable_2="Rs" variable_1="Rs"/>
    <map_variables variable_2="Cs" variable_1="Cs"/>
  </connection>

  <connection>
    <map_components component_2="L" component_1="Rs"/>
    <map_variables variable_2="Rs" variable_1="Rs"/>
    <map_variables variable_2="L" variable_1="L"/>
  </connection>

  <connection>
    <map_components component_2="model_parameters" component_1="Rs"/>
    <map_variables variable_2="kf" variable_1="kf"/>
    <map_variables variable_2="kr" variable_1="kr"/>
    <map_variables variable_2="ksyn" variable_1="ksyn"/>
    <map_variables variable_2="kt" variable_1="kt"/>
    <map_variables variable_2="Vs" variable_1="Vs"/>
  </connection>

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    <dc:title>Computational Model for Effects of Ligand/Receptor Binding 
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    <dc:title>Biotechnology Progress</dc:title>
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    <vCard:FN>Catherine Lloyd</vCard:FN>
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        Fallon and Lauffenburger's 2000 model of the effects of ligand-receptor 
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        proliferation response. 
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    <vCard:Given>Eric</vCard:Given>
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    <vCard:FN>Catherine Lloyd</vCard:FN>
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    <rdf:value>This is the CellML description of Fallon and Lauffenburger's 2000 
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