Rendering of the source text

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<!--  FILE :  hornberg_model_2005.xml

CREATED :  16th October 2007

LAST MODIFIED : 16th October 2007

AUTHOR :  Catherine Lloyd
          Bioengineering Institute
          The University of Auckland
          
MODEL STATUS :  This model conforms to the CellML 1.1 Specification.

DESCRIPTION :  This file contains a CellML description of Hornberg et al.'s 2005 mathematical model of the MAPK signal transduction cascade.

CHANGES:  
  
--><model xmlns="http://www.cellml.org/cellml/1.0#" xmlns:cmeta="http://www.cellml.org/metadata/1.0#" cmeta:id="hornberg_model_2005" name="hornberg_model_2005">

<documentation xmlns="http://cellml.org/tmp-documentation">

<article>
  <articleinfo>
  <title>Modelling insulin kinetics in response to oral glucose administration</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 model runs in both OpenCell and COR to recreate the published results.  Thank you to the model author Jorrit Hornberg for providing us with the original mathematica code, and also to Joe Cursons for the hours he has spent debugging the CellMl model. Please note there are several differences between the original CellML version of this model (which was based on the published paper), and the current version of the model (which was based on the Mathematica code). These differences are listed <ulink url="hornberg_model_errors.pdf">here</ulink> as a PDF document. 
          </para>
  </section>
  <sect1 id="sec_structure">
<title>Model Structure</title>

<para>
ABSTRACT: 
</para>

<para>
ABSTRACT: Oncogenesis results from changes in kinetics or in abundance of proteins in signal transduction networks. Recently, it was shown that control of signalling cannot reside in a single gene product, and might well be dispersed over many components. Which of the reactions in these complex networks are most important, and how can the existing molecular information be used to understand why particular genes are oncogenes whereas others are not? We implement a new method to help address such questions. We apply control analysis to a detailed kinetic model of the epidermal growth factor-induced mitogen-activated protein kinase network. We determine the control of each reaction with respect to three biologically relevant characteristics of the output of this network: the amplitude, duration and integrated output of the transient phosphorylation of extracellular signal-regulated kinase (ERK). We confirm that control is distributed, but far from randomly: a small proportion of reactions substantially control signalling. In particular, the activity of Raf is in control of all characteristics of the transient profile of ERK phosphorylation, which may clarify why Raf is an oncogene. Most reactions that really matter for one signalling characteristic are also important for the other characteristics. Our analysis also predicts the effects of mutations and changes in gene expression.        
</para>

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

<para>
Control of MAPK signalling: from complexity to what really matters, Jorrit J Hornberg, Bernd Binder, Frank J Bruggeman, Birgit Schoeberl, Reinhart Heinrich and Hans V Westerhoff, 2005, <emphasis>Oncogene</emphasis>, 26, 117-125. <ulink url="http://www.ncbi.nlm.nih.gov/pubmed/16007170">PubMed ID: 16007170</ulink>
</para>

<informalfigure float="0" id="fig_reaction_diagram">
<mediaobject>
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      <title>reaction diagram</title>
    </objectinfo>
    <imagedata fileref="hornberg_2005.png"/>
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</mediaobject>
<caption>Schematic diagram of the signal transduction nectwork described by the model.</caption>
</informalfigure>


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



  

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          <ci>v125</ci>
        </apply> 
      </apply> 
    </math>  
  </component>
  
  <component cmeta:id="c95" name="c95">
    <rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
      <rdf:Description rdf:about="#c95">
        <dc:title xmlns:dc="http://purl.org/dc/elements/1.1/">c95</dc:title>
        <dcterms:alternative xmlns:dcterms="http://purl.org/dc/terms/">(EGF-EGFR*)2-GAP-Grb2-Sos-ERK-PP</dcterms:alternative>  
      </rdf:Description>
    </rdf:RDF> 
    <variable cmeta:id="c95_c95" initial_value="0.0" name="c95" public_interface="out" units="molar"/>
    <variable name="v126" public_interface="in" units="flux"/> 
    <variable name="v143" public_interface="in" units="flux"/>
    <variable name="time" public_interface="in" units="second"/>
    <math xmlns="http://www.w3.org/1998/Math/MathML" id="math94"> 
      <apply>
        <eq/> 
        <apply>
          <diff/> 
          <bvar>
            <ci>time</ci>
          </bvar> 
          <ci>c95</ci> 
        </apply>
        <apply>
          <plus/>
          <ci>v126</ci>
          <ci>v143</ci>
        </apply> 
      </apply> 
    </math>  
  </component>
  
  <component cmeta:id="c96" name="c96">
    <rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
      <rdf:Description rdf:about="#c96">
        <dc:title xmlns:dc="http://purl.org/dc/elements/1.1/">c96</dc:title>
        <dcterms:alternative xmlns:dcterms="http://purl.org/dc/terms/">(EGF-EGFRi*)2-GAP-Grb2-Sos-ERKi-PP</dcterms:alternative>        
      </rdf:Description>
    </rdf:RDF> 
    <variable initial_value="0.0" name="c96" public_interface="out" units="molar"/>
    <variable name="v127" public_interface="in" units="flux"/> 
	<variable name="v146" public_interface="in" units="flux"/>
    <variable name="time" public_interface="in" units="second"/>
    <math xmlns="http://www.w3.org/1998/Math/MathML" id="math95"> 
      <apply>
        <eq/> 
        <apply>
          <diff/> 
          <bvar>
            <ci>time</ci>
          </bvar> 
          <ci>c96</ci> 
        </apply>
        <apply>
          <plus/>
          <ci>v127</ci>
          <ci>v146</ci>
        </apply>
      </apply> 
    </math>  
  </component>
  
  <component cmeta:id="c97" name="c97">
    <rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
      <rdf:Description rdf:about="#c97">
        <dc:title xmlns:dc="http://purl.org/dc/elements/1.1/">c97</dc:title>
        <dcterms:alternative xmlns:dcterms="http://purl.org/dc/terms/">(EGF-EGFR*)2-GAP-Shc*-Grb2-Sos-ERK-PP</dcterms:alternative>        
      </rdf:Description>
    </rdf:RDF> 
    <variable cmeta:id="c97_c97" initial_value="0.0" name="c97" public_interface="out" units="molar"/>
    <variable name="v128" public_interface="in" units="flux"/> 
    <variable name="v144" public_interface="in" units="flux"/>
    <variable name="time" public_interface="in" units="second"/>
    <math xmlns="http://www.w3.org/1998/Math/MathML" id="math96"> 
      <apply>
        <eq/> 
        <apply>
          <diff/> 
          <bvar>
            <ci>time</ci>
          </bvar> 
          <ci>c97</ci> 
        </apply>
        <apply>
          <plus/>
          <ci>v128</ci>
          <ci>v144</ci>
        </apply> 
      </apply> 
    </math>  
  </component>
  
  <component cmeta:id="c98" name="c98">
    <rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
      <rdf:Description rdf:about="#c98">
        <dc:title xmlns:dc="http://purl.org/dc/elements/1.1/">c98</dc:title>
        <dcterms:alternative xmlns:dcterms="http://purl.org/dc/terms/">(EGF-EGFRi*)2-GAP-Shc*-Grb2-Sos-ERKi-PP</dcterms:alternative>  
      </rdf:Description>
    </rdf:RDF> 
    <variable initial_value="0.0" name="c98" public_interface="out" units="molar"/>
    <variable name="v129" public_interface="in" units="flux"/>
    <variable name="v147" public_interface="in" units="flux"/>
    <variable name="time" public_interface="in" units="second"/>
    <math xmlns="http://www.w3.org/1998/Math/MathML" id="math97"> 
      <apply>
        <eq/> 
        <apply>
          <diff/> 
          <bvar>
            <ci>time</ci>
          </bvar> 
          <ci>c98</ci> 
        </apply>
        <apply>
          <plus/>
          <ci>v129</ci>
          <ci>v147</ci>
        </apply>
      </apply> 
    </math>  
  </component>
  
  <component cmeta:id="c99" name="c99">
    <rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
      <rdf:Description rdf:about="#c99">
        <dc:title xmlns:dc="http://purl.org/dc/elements/1.1/">c99</dc:title>
        <dcterms:alternative xmlns:dcterms="http://purl.org/dc/terms/">(EGF-EGFR*)2-GAP-Grb2-Sos-deg</dcterms:alternative>  
      </rdf:Description>
    </rdf:RDF> 
    <variable initial_value="0.0" name="c99" public_interface="out" units="molar"/>
    <variable name="v143" public_interface="in" units="flux"/> 
    <variable name="v144" public_interface="in" units="flux"/>
	<variable name="time" public_interface="in" units="second"/>
    <math xmlns="http://www.w3.org/1998/Math/MathML" id="math98"> 
      <apply>
        <eq/> 
        <apply>
          <diff/> 
          <bvar>
            <ci>time</ci>
          </bvar> 
          <ci>c99</ci> 
        </apply>
        <apply>
          <minus/>
          <apply>
            <plus/>
            <ci>v143</ci>
            <ci>v144</ci>
	      </apply>
        </apply> 
      </apply> 
    </math>  
  </component>
  
  <component cmeta:id="c100" name="c100">
    <rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
      <rdf:Description rdf:about="#c100">
        <dc:title xmlns:dc="http://purl.org/dc/elements/1.1/">c100</dc:title>
        <dcterms:alternative xmlns:dcterms="http://purl.org/dc/terms/">(EGF-EGFRi*)2-GAP-Grb2-Sos-deg</dcterms:alternative>  
      </rdf:Description>
    </rdf:RDF> 
    <variable cmeta:id="c100_c100" initial_value="0.0" name="c100" public_interface="out" units="molar"/>
    <variable name="v146" public_interface="in" units="flux"/>
    <variable name="v147" public_interface="in" units="flux"/>
    <variable name="time" public_interface="in" units="second"/>
    <math xmlns="http://www.w3.org/1998/Math/MathML" id="math99"> 
      <apply>
        <eq/> 
        <apply>
          <diff/> 
          <bvar>
            <ci>time</ci>
          </bvar> 
          <ci>c100</ci> 
        </apply>
        <apply>
          <minus/>
          <apply>
            <plus/>
            <ci>v146</ci>
            <ci>v147</ci>
          </apply> 
        </apply> 
      </apply> 
    </math>  
  </component>
  
  <component cmeta:id="c101" name="c101">
    <rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
      <rdf:Description rdf:about="#c101">
        <dc:title xmlns:dc="http://purl.org/dc/elements/1.1/">c101</dc:title>
        <dcterms:alternative xmlns:dcterms="http://purl.org/dc/terms/">Sos-ERK-PP</dcterms:alternative>  
      </rdf:Description>
    </rdf:RDF> 
    <variable initial_value="0.0" name="c101" public_interface="out" units="molar"/>
    <variable name="v130" public_interface="in" units="flux"/>
    <variable name="v145" public_interface="in" units="flux"/>
    <variable name="time" public_interface="in" units="second"/>
    <math xmlns="http://www.w3.org/1998/Math/MathML" id="math100"> 
      <apply>
        <eq/> 
        <apply>
          <diff/> 
          <bvar>
            <ci>time</ci>
          </bvar> 
          <ci>c101</ci> 
        </apply>
        <apply>
          <plus/>
          <ci>v130</ci>
          <ci>v145</ci>
        </apply> 
      </apply> 
    </math>  
  </component>
  
  <component cmeta:id="c102" name="c102">
    <rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
      <rdf:Description rdf:about="#c102">
        <dc:title xmlns:dc="http://purl.org/dc/elements/1.1/">c102</dc:title>
        <dcterms:alternative xmlns:dcterms="http://purl.org/dc/terms/">Sos-ERKi-PP</dcterms:alternative>  
      </rdf:Description>
    </rdf:RDF> 
    <variable initial_value="0.0" name="c102" public_interface="out" units="molar"/>
    <variable name="v131" public_interface="in" units="flux"/> 
    <variable name="v148" public_interface="in" units="flux"/>
    <variable name="time" public_interface="in" units="second"/>
    <math xmlns="http://www.w3.org/1998/Math/MathML" id="math101"> 
      <apply>
        <eq/> 
        <apply>
          <diff/> 
          <bvar>
            <ci>time</ci>
          </bvar> 
          <ci>c102</ci> 
        </apply>
        <apply>
          <plus/>
          <ci>v131</ci>
          <ci>v148</ci>
        </apply> 
      </apply> 
    </math>  
  </component>
  
  <component cmeta:id="c103" name="c103">
    <rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
      <rdf:Description rdf:about="#c103">
        <dc:title xmlns:dc="http://purl.org/dc/elements/1.1/">c103</dc:title>
        <dcterms:alternative xmlns:dcterms="http://purl.org/dc/terms/">Sosi</dcterms:alternative>  
      </rdf:Description>
    </rdf:RDF> 
    <variable initial_value="0.0" name="c103" public_interface="out" units="molar"/>
    <variable name="v145" public_interface="in" units="flux"/>
	<variable name="v148" public_interface="in" units="flux"/>
    <variable name="time" public_interface="in" units="second"/>
    <math xmlns="http://www.w3.org/1998/Math/MathML" id="math102"> 
      <apply>
        <eq/> 
        <apply>
          <diff/> 
          <bvar>
            <ci>time</ci>
          </bvar> 
          <ci>c103</ci> 
        </apply>
        <apply>
          <minus/>
          <apply>
            <plus/>
            <ci>v145</ci>
		    <ci>v148</ci>
		  </apply>
        </apply> 
      </apply> 
    </math>  
  </component>
  
 <!-- Reactions --> 
 
  <component name="v1">
    <variable name="v1" public_interface="out" units="flux"/>
    
    <variable name="c2" public_interface="in" units="molar"/>
    <variable name="c1" public_interface="in" units="molar"/>
    <variable name="c3" public_interface="in" units="molar"/>
    <variable name="k1" public_interface="in" units="second_order_rate_constant"/>
    <variable name="kd1" public_interface="in" units="first_order_rate_constant"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML" id="math103">
      <apply id="v1_calculation">
        <eq/>
        <ci> v1 </ci>
        <apply>
          <minus/>
          <apply>
            <times/>
            <ci> k1 </ci>
            <ci> c1 </ci>
            <ci> c2 </ci>
          </apply>
          <apply>
            <times/>
            <ci> kd1 </ci>
            <ci> c3 </ci>
          </apply>
        </apply>
      </apply>
    </math>
  </component>
  
  <component name="v2">
    <variable name="v2" public_interface="out" units="flux"/>
    
    <variable name="c4" public_interface="in" units="molar"/>
    <variable name="c3" public_interface="in" units="molar"/>
    <variable name="k2" public_interface="in" units="second_order_rate_constant"/>
    <variable name="kd2" public_interface="in" units="first_order_rate_constant"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML" id="math104">
      <apply id="v2_calculation">
        <eq/>
        <ci> v2 </ci>
        <apply>
          <minus/>
          <apply>
            <times/>
            <ci> k2 </ci>
            <ci> c3 </ci>
            <ci> c3 </ci>
          </apply>
          <apply>
            <times/>
            <ci> kd2 </ci>
            <ci> c4 </ci>
          </apply>
        </apply>
      </apply>    
    </math>
  </component>
  
  <component name="v3">
    <variable name="v3" public_interface="out" units="flux"/>
    
    <variable name="c4" public_interface="in" units="molar"/>
    <variable name="c5" public_interface="in" units="molar"/>
    <variable name="k3" public_interface="in" units="first_order_rate_constant"/>
    <variable name="kd3" public_interface="in" units="first_order_rate_constant"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML" id="math105">
      <apply id="v3_calculation">
        <eq/>
        <ci> v3 </ci>
        <apply>
          <minus/>
          <apply>
            <times/>
            <ci> k3 </ci>
            <ci> c4 </ci>
	        <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless"> 1.0 </cn>
          </apply>
          <apply>
            <times/>
            <ci> kd3 </ci>
            <ci> c5 </ci>
          </apply>
        </apply>
      </apply>    
    </math>
  </component>
  
  <component name="v4">
    <variable name="v4" public_interface="out" units="flux"/>
    
    <variable name="c7" public_interface="in" units="molar"/>
    <variable name="c12" public_interface="in" units="molar"/>
    <variable name="c23" public_interface="in" units="molar"/>
    <variable name="k4" public_interface="in" units="second_order_rate_constant"/>
    <variable name="kd4" public_interface="in" units="first_order_rate_constant"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML" id="math106">
      <apply id="v4_calculation">
        <eq/>
        <ci> v4 </ci>
        <apply>
          <minus/>
          <apply>
            <times/>
            <ci> k4 </ci>
            <ci> c23 </ci>
            <ci> c12 </ci>
          </apply>
          <apply>
            <times/>
            <ci> kd4 </ci>
            <ci> c7 </ci>
          </apply>
        </apply>
      </apply>    
    </math>
  </component>
  
  <component name="v5">
    <variable name="v5" public_interface="out" units="flux"/>
    
    <variable name="c9" public_interface="in" units="molar"/>
    <variable name="c18" public_interface="in" units="molar"/>
    <variable name="c7" public_interface="in" units="molar"/>
    <variable name="k5" public_interface="in" units="second_order_rate_constant"/>
    <variable name="kd5" public_interface="in" units="first_order_rate_constant"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML" id="math107">
      <apply id="v5_calculation">
        <eq/>
        <ci> v5 </ci>
        <apply>
          <minus/>
          <apply>
            <times/>
            <ci> k5 </ci>
            <ci> c18 </ci>
            <ci> c9 </ci>
          </apply>
          <apply>
            <times/>
            <ci> kd5 </ci>
            <ci> c7 </ci>
          </apply>
        </apply>
      </apply>    
    </math>
  </component>
  
  <component name="v6">
    <variable name="v6" public_interface="out" units="flux"/>
    
    <variable name="c6" public_interface="in" units="molar"/>
    <variable name="c2" public_interface="in" units="molar"/>
    <variable name="k6" public_interface="in" units="first_order_rate_constant"/>
    <variable name="kd6" public_interface="in" units="first_order_rate_constant"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML" id="math108">
      <apply id="v6_calculation">
        <eq/>
        <ci> v6 </ci>
        <apply>
          <minus/>
          <apply>
            <times/>
            <ci> k6 </ci>
            <ci> c2 </ci>
          </apply>
          <apply>
            <times/>
            <ci> kd6 </ci>
            <ci> c6 </ci>
          </apply>
        </apply>
      </apply>    
    </math>
  </component>
  
  <component name="v7">
    <variable name="v7" public_interface="out" units="flux"/>
    
    <variable name="c5" public_interface="in" units="molar"/>
    <variable name="c8" public_interface="in" units="molar"/>
    <variable name="k6" public_interface="in" units="first_order_rate_constant"/>
    <variable name="kd6" public_interface="in" units="first_order_rate_constant"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML" id="math109">
      <apply id="v7_calculation">
        <eq/>
        <ci> v7 </ci>
        <apply>
          <minus/>
          <apply>
            <times/>
            <ci> k6 </ci>
            <ci> c5 </ci>
          </apply>
          <apply>
            <times/>
            <ci> kd6 </ci>
            <ci> c8 </ci>
          </apply>
        </apply>
      </apply>    
    </math>
  </component>
  
  <component name="v8">
    <variable name="v8" public_interface="out" units="flux"/>
    
    <variable name="c14" public_interface="in" units="molar"/>
    <variable name="c5" public_interface="in" units="molar"/>
    <variable name="c15" public_interface="in" units="molar"/>
    <variable name="k8" public_interface="in" units="second_order_rate_constant"/>
    <variable name="kd8" public_interface="in" units="first_order_rate_constant"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML" id="math110">
      <apply id="v8_calculation">
        <eq/>
        <ci> v8 </ci>
        <apply>
          <minus/>
          <apply>
            <times/>
            <ci> k8 </ci>
            <ci> c5 </ci>
            <ci> c14 </ci>
          </apply>
          <apply>
            <times/>
            <ci> kd8 </ci>
            <ci> c15 </ci>
          </apply>
        </apply>
      </apply>    
    </math>
  </component>
  
  <component name="v9">
    <variable name="v9" public_interface="out" units="flux"/>
    <variable name="c23" public_interface="in" units="molar"/>
    <variable name="c18" public_interface="in" units="molar"/>
    <variable name="k6" public_interface="in" units="first_order_rate_constant"/>
    <variable name="kd6" public_interface="in" units="first_order_rate_constant"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML" id="math111">
      <apply id="v9_calculation">
        <eq/>
        <ci> v9 </ci>
        <apply>
          <minus/>
          <apply>
            <times/>
            <ci> k6 </ci>
            <ci> c23 </ci>
          </apply>
          <apply>
            <times/>
            <ci> kd6 </ci>
            <ci> c18 </ci>
          </apply>
        </apply>
      </apply>    
    </math>
  </component>
  
  <component name="v10">
    <variable name="v10" public_interface="out" units="flux"/>
    
    <variable name="c6" public_interface="in" units="molar"/>
    <variable name="c16" public_interface="in" units="molar"/>
    <variable name="c10" public_interface="in" units="molar"/>
    <variable name="k10b" public_interface="in" units="second_order_rate_constant"/>
    <variable name="kd10" public_interface="in" units="first_order_rate_constant"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML" id="math112">
      <apply id="v10_calculation">
        <eq/>
        <ci> v10 </ci>
        <apply>
          <minus/>
          <apply>
            <times/>
            <ci> k10b </ci>
            <ci> c6 </ci>
            <ci> c16 </ci>
          </apply>
          <apply>
            <times/>
            <ci> kd10 </ci>
            <ci> c10 </ci>
          </apply>
        </apply>
      </apply>    
    </math>
  </component>
  
  <component name="v11">
    <variable name="v11" public_interface="out" units="flux"/>
    
    <variable name="c10" public_interface="in" units="molar"/>
    <variable name="c11" public_interface="in" units="molar"/>
    <variable name="k2" public_interface="in" units="second_order_rate_constant"/>
    <variable name="kd2" public_interface="in" units="first_order_rate_constant"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML" id="math113">
      <apply id="v11_calculation">
        <eq/>
        <ci> v11 </ci>
        <apply>
          <minus/>
          <apply>
            <times/>
            <ci> k2 </ci>
            <ci> c10 </ci>
            <ci> c10 </ci>
          </apply>
          <apply>
            <times/>
            <ci> kd2 </ci>
            <ci> c11 </ci>
          </apply>
        </apply>
      </apply>    
    </math>
  </component>
  
  <component name="v12">
    <variable name="v12" public_interface="out" units="flux"/>
    
    <variable name="c11" public_interface="in" units="molar"/>
    <variable name="c8" public_interface="in" units="molar"/>
    <variable name="k3" public_interface="in" units="first_order_rate_constant"/>
    <variable name="kd3" public_interface="in" units="first_order_rate_constant"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML" id="math114">
      <apply id="v12_calculation">
        <eq/>
        <ci> v12 </ci>
        <apply>
          <minus/>
          <apply>
            <times/>
            <ci> k3 </ci>
            <ci> c11 </ci>
          </apply>
          <apply>
            <times/>
            <ci> kd3 </ci>
            <ci> c8 </ci>
          </apply>
        </apply>
      </apply>    
    </math>
  </component>
  
  <component name="v13">
    <variable name="v13" public_interface="out" units="flux"/>
    
    <variable name="c2" public_interface="in" units="molar"/>
    <variable name="k13" public_interface="in" units="first_order_rate_constant"/>
    <variable name="kd13" public_interface="in" units="first_order_rate_constant"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML" id="math115">
      <apply id="v13_calculation">
        <eq/>
        <ci> v13 </ci>
        <apply>
          <minus/>
		  <apply>
            <times/>
            <ci> k13 </ci>
		    <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="molar"> 1.0 </cn>
		  </apply>
          <apply>
            <times/>
            <ci> kd13 </ci>
            <ci> c2 </ci>
          </apply>
        </apply>
      </apply>    
    </math>
  </component>
  
  <component name="v14">
    <variable name="v14" public_interface="out" units="flux"/>
    
    <variable name="c8" public_interface="in" units="molar"/>
    <variable name="c14" public_interface="in" units="molar"/>
    <variable name="c17" public_interface="in" units="molar"/>
    <variable name="k8" public_interface="in" units="second_order_rate_constant"/>
    <variable name="kd8" public_interface="in" units="first_order_rate_constant"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML" id="math116">
      <apply id="v14_calculation">
        <eq/>
        <ci> v14 </ci>
        <apply>
          <minus/>
          <apply>
            <times/>
            <ci> k8 </ci>
            <ci> c8 </ci>
            <ci> c14 </ci>
          </apply>
          <apply>
            <times/>
            <ci> kd8 </ci>
            <ci> c17 </ci>
          </apply>
        </apply>
      </apply>    
    </math>
  </component>
    
  <component name="v15">
    <variable name="v15" public_interface="out" units="flux"/>
    
    <variable name="c9" public_interface="in" units="molar"/>
    <variable name="c12" public_interface="in" units="molar"/>
    <variable name="k15" public_interface="in" units="first_order_rate_constant"/>
    <variable name="kd15" public_interface="in" units="first_order_rate_constant"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML" id="math117">
      <apply id="v15_calculation">
        <eq/>
        <ci> v15 </ci>
        <apply>
          <minus/>
          <apply>
            <times/>
            <ci> k15 </ci>
            <ci> c9 </ci>
          </apply>
          <apply>
            <times/>
            <ci> kd15 </ci>
            <ci> c12 </ci>
          </apply>
        </apply>
      </apply>    
    </math>
  </component>
    
  <component name="v16">
    <variable name="v16" public_interface="out" units="flux"/>
    
    <variable name="c15" public_interface="in" units="molar"/>
    <variable name="c22" public_interface="in" units="molar"/>
    <variable name="c23" public_interface="in" units="molar"/>
    <variable name="k16" public_interface="in" units="second_order_rate_constant"/>
    <variable name="kd63" public_interface="in" units="first_order_rate_constant"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML" id="math118">
      <apply id="v16_calculation">
        <eq/>
        <ci> v16 </ci>
        <apply>
          <minus/>
          <apply>
            <times/>
            <ci> k16 </ci>
            <ci> c22 </ci>
            <ci> c15 </ci>
          </apply>
          <apply>
            <times/>
            <ci> kd63 </ci>
            <ci> c23 </ci>
          </apply>
        </apply>
      </apply>    
    </math>
  </component> 
  
  <component name="v17">
    <variable name="v17" public_interface="out" units="flux"/>
    
    <variable name="c23" public_interface="in" units="molar"/>
    <variable name="c24" public_interface="in" units="molar"/>
    <variable name="c25" public_interface="in" units="molar"/>
    <variable name="k17" public_interface="in" units="second_order_rate_constant"/>
    <variable name="kd17" public_interface="in" units="first_order_rate_constant"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML" id="math119">
      <apply id="v17_calculation">
        <eq/>
        <ci> v17 </ci>
        <apply>
          <minus/>
          <apply>
            <times/>
            <ci> k17 </ci>
            <ci> c24 </ci>
            <ci> c23 </ci>
          </apply>
          <apply>
            <times/>
            <ci> kd17 </ci>
            <ci> c25 </ci>
          </apply>
        </apply>
      </apply>    
    </math>
  </component>
  
  <component name="v18">
    <variable name="v18" public_interface="out" units="flux"/>
    
    <variable name="c25" public_interface="in" units="molar"/>
    <variable name="c26" public_interface="in" units="molar"/>
    <variable name="c27" public_interface="in" units="molar"/>
    <variable name="k18" public_interface="in" units="second_order_rate_constant"/>
    <variable name="kd18" public_interface="in" units="first_order_rate_constant"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML" id="math120">
      <apply id="v18_calculation">
        <eq/>
        <ci> v18 </ci>
        <apply>
          <minus/>
          <apply>
            <times/>
            <ci> k18 </ci>
            <ci> c26 </ci>
            <ci> c25 </ci>
          </apply>
          <apply>
            <times/>
            <ci> kd18 </ci>
            <ci> c27 </ci>
          </apply>
        </apply>
      </apply>    
    </math>
  </component>
  
  <component name="v19">
    <variable name="v19" public_interface="out" units="flux"/>
    
    <variable name="c25" public_interface="in" units="molar"/>
    <variable name="c28" public_interface="in" units="molar"/>
    <variable name="c27" public_interface="in" units="molar"/>
    <variable name="k19" public_interface="in" units="second_order_rate_constant"/>
    <variable name="kd19" public_interface="in" units="first_order_rate_constant"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML" id="math121">
      <apply id="v19_calculation">
        <eq/>
        <ci> v19 </ci>
        <apply>
          <minus/>
          <apply>
            <times/>
            <ci> k19 </ci>
            <ci> c28 </ci>
            <ci> c25 </ci>
          </apply>
          <apply>
            <times/>
            <ci> kd19 </ci>
            <ci> c27 </ci>
          </apply>
        </apply>
      </apply>    
    </math>
  </component>
  
  <component name="v20">
    <variable name="v20" public_interface="out" units="flux"/>
    
    <variable name="c25" public_interface="in" units="molar"/>
    <variable name="c43" public_interface="in" units="molar"/>
    <variable name="c29" public_interface="in" units="molar"/>
    <variable name="k20" public_interface="in" units="second_order_rate_constant"/>
    <variable name="kd20" public_interface="in" units="first_order_rate_constant"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML" id="math122">
      <apply id="v20_calculation">
        <eq/>
        <ci> v20 </ci>
        <apply>
          <minus/>
          <apply>
            <times/>
            <ci> k20 </ci>
            <ci> c25 </ci>
            <ci> c43 </ci>
          </apply>
          <apply>
            <times/>
            <ci> kd20 </ci>
            <ci> c29 </ci>
          </apply>
        </apply>
      </apply>    
    </math>
  </component>
  
  <component name="v21">
    <variable name="v21" public_interface="out" units="flux"/>
    
    <variable name="c25" public_interface="in" units="molar"/>
    <variable name="c26" public_interface="in" units="molar"/>
    <variable name="c29" public_interface="in" units="molar"/>
    <variable name="k21" public_interface="in" units="second_order_rate_constant"/>
    <variable name="kd21" public_interface="in" units="first_order_rate_constant"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML" id="math123">
      <apply id="v21_calculation">
        <eq/>
        <ci> v21 </ci>
        <apply>
          <minus/>
          <apply>
            <times/>
            <ci> k21 </ci>
            <ci> c25 </ci>
            <ci> c26 </ci>
          </apply>
          <apply>
            <times/>
            <ci> kd21 </ci>
            <ci> c29 </ci>
          </apply>
        </apply>
      </apply>    
    </math>
  </component>
  
  <component name="v22">
    <variable name="v22" public_interface="out" units="flux"/>
    
    <variable name="c31" public_interface="in" units="molar"/>
    <variable name="c15" public_interface="in" units="molar"/>
    <variable name="c32" public_interface="in" units="molar"/>
    <variable name="k22" public_interface="in" units="second_order_rate_constant"/>
    <variable name="kd22" public_interface="in" units="first_order_rate_constant"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML" id="math124">
      <apply id="v22_calculation">
        <eq/>
        <ci> v22 </ci>
        <apply>
          <minus/>
          <apply>
            <times/>
            <ci> k22 </ci>
            <ci> c31 </ci>
            <ci> c15 </ci>
          </apply>
          <apply>
            <times/>
            <ci> kd22 </ci>
            <ci> c32 </ci>
          </apply>
        </apply>
      </apply>    
    </math>
  </component>
  
  <component name="v23">
    <variable name="v23" public_interface="out" units="flux"/>
    
    <variable name="c32" public_interface="in" units="molar"/>
    <variable name="c33" public_interface="in" units="molar"/>
    <variable name="k23" public_interface="in" units="first_order_rate_constant"/>
    <variable name="kd23" public_interface="in" units="first_order_rate_constant"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML" id="math125">
      <apply id="v23_calculation">
        <eq/>
        <ci> v23 </ci>
        <apply>
          <minus/>
          <apply>
            <times/>
            <ci> k23 </ci>
            <ci> c32 </ci>
          </apply>
          <apply>
            <times/>
            <ci> kd23 </ci>
            <ci> c33 </ci>
          </apply>
        </apply>
      </apply>    
    </math>
  </component>
  
  <component name="v24">
    <variable name="v24" public_interface="out" units="flux"/>
    
    <variable name="c22" public_interface="in" units="molar"/>
    <variable name="c33" public_interface="in" units="molar"/>
    <variable name="c34" public_interface="in" units="molar"/>
    <variable name="k16" public_interface="in" units="second_order_rate_constant"/>
    <variable name="kd24" public_interface="in" units="first_order_rate_constant"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML" id="math126">
      <apply id="v24_calculation">
        <eq/>
        <ci> v24 </ci>
        <apply>
          <minus/>
          <apply>
            <times/>
            <ci> k16 </ci>
            <ci> c22 </ci>
            <ci> c33 </ci>
          </apply>
          <apply>
            <times/>
            <ci> kd24 </ci>
            <ci> c34 </ci>
          </apply>
        </apply>
      </apply>    
    </math>
  </component>
  
  <component name="v25">
    <variable name="v25" public_interface="out" units="flux"/>
    
    <variable name="c24" public_interface="in" units="molar"/>
    <variable name="c34" public_interface="in" units="molar"/>
    <variable name="c35" public_interface="in" units="molar"/>
    <variable name="k25" public_interface="in" units="second_order_rate_constant"/>
    <variable name="kd25" public_interface="in" units="first_order_rate_constant"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML" id="math127">
      <apply id="v25_calculation">
        <eq/>
        <ci> v25 </ci>
        <apply>
          <minus/>
          <apply>
            <times/>
            <ci> k25 </ci>
            <ci> c24 </ci>
            <ci> c34 </ci>
          </apply>
          <apply>
            <times/>
            <ci> kd25 </ci>
            <ci> c35 </ci>
          </apply>
        </apply>
      </apply>    
    </math>
  </component>

  <component name="v26">
    <variable name="v26" public_interface="out" units="flux"/>
    
    <variable name="c26" public_interface="in" units="molar"/>
    <variable name="c35" public_interface="in" units="molar"/>
    <variable name="c36" public_interface="in" units="molar"/>
    <variable name="k18" public_interface="in" units="second_order_rate_constant"/>
    <variable name="kd18" public_interface="in" units="first_order_rate_constant"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML" id="math128">
      <apply id="v26_calculation">
        <eq/>
        <ci> v26 </ci>
        <apply>
          <minus/>
          <apply>
            <times/>
            <ci> k18 </ci>
            <ci> c26 </ci>
            <ci> c35 </ci>
          </apply>
          <apply>
            <times/>
            <ci> kd18 </ci>
            <ci> c36 </ci>
          </apply>
        </apply>
      </apply>    
    </math>
  </component> 
  
  <component name="v27">
    <variable name="v27" public_interface="out" units="flux"/>
    
    <variable name="c35" public_interface="in" units="molar"/>
    <variable name="c28" public_interface="in" units="molar"/>
    <variable name="c36" public_interface="in" units="molar"/>
    <variable name="k19" public_interface="in" units="second_order_rate_constant"/>
    <variable name="kd19" public_interface="in" units="first_order_rate_constant"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML" id="math129">
      <apply id="v27_calculation">
        <eq/>
        <ci> v27 </ci>
        <apply>
          <minus/>
          <apply>
            <times/>
            <ci> k19 </ci>
            <ci> c35 </ci>
            <ci> c28 </ci>
          </apply>
          <apply>
            <times/>
            <ci> kd19 </ci>
            <ci> c36 </ci>
          </apply>
        </apply>
      </apply>    
    </math>
  </component>
  
  <component name="v28">
    <variable name="v28" public_interface="out" units="flux"/>
    
    <variable name="c28" public_interface="in" units="molar"/>
    <variable name="c41" public_interface="in" units="molar"/>
    <variable name="c42" public_interface="in" units="molar"/>
    <variable name="k28" public_interface="in" units="second_order_rate_constant"/>
    <variable name="kd28" public_interface="in" units="first_order_rate_constant"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML" id="math130">
      <apply id="v28_calculation">
        <eq/>
        <ci> v28 </ci>
        <apply>
          <minus/>
          <apply>
            <times/>
            <ci> k28 </ci>
            <ci> c28 </ci>
            <ci> c41 </ci>
          </apply>
          <apply>
            <times/>
            <ci> kd28 </ci>
            <ci> c42 </ci>
          </apply>
        </apply>
      </apply>    
    </math>
  </component>
  
  <component name="v29">
    <variable name="v29" public_interface="out" units="flux"/>
    
    <variable name="c43" public_interface="in" units="molar"/>
    <variable name="c45" public_interface="in" units="molar"/>
    <variable name="c42" public_interface="in" units="molar"/>
    <variable name="k29" public_interface="in" units="second_order_rate_constant"/>
    <variable name="kd29" public_interface="in" units="first_order_rate_constant"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML" id="math131">
      <apply id="v29_calculation">
        <eq/>
        <ci> v29 </ci>
        <apply>
          <minus/>
          <apply>
            <times/>
            <ci> k29 </ci>
            <ci> c43 </ci>
            <ci> c45 </ci>
          </apply>
          <apply>
            <times/>
            <ci> kd29 </ci>
            <ci> c42 </ci>
          </apply>
        </apply>
      </apply>    
    </math>
  </component>
  
  <component name="v30">
    <variable name="v30" public_interface="out" units="flux"/>
    
    <variable name="c35" public_interface="in" units="molar"/>
    <variable name="c43" public_interface="in" units="molar"/>
    <variable name="c37" public_interface="in" units="molar"/>
    <variable name="k20" public_interface="in" units="second_order_rate_constant"/>
    <variable name="kd20" public_interface="in" units="first_order_rate_constant"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML" id="math132">
      <apply id="v30_calculation">
        <eq/>
        <ci> v30 </ci>
        <apply>
          <minus/>
          <apply>
            <times/>
            <ci> k20 </ci>
            <ci> c35 </ci>
            <ci> c43 </ci>
          </apply>
          <apply>
            <times/>
            <ci> kd20 </ci>
            <ci> c37 </ci>
          </apply>
        </apply>
      </apply>    
    </math>
  </component>
  
  <component name="v31">
    <variable name="v31" public_interface="out" units="flux"/>
    
    <variable name="c35" public_interface="in" units="molar"/>
    <variable name="c26" public_interface="in" units="molar"/>
    <variable name="c37" public_interface="in" units="molar"/>
    <variable name="k21" public_interface="in" units="second_order_rate_constant"/>
    <variable name="kd21" public_interface="in" units="first_order_rate_constant"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML" id="math133">
      <apply id="v31_calculation">
        <eq/>
        <ci> v31 </ci>
        <apply>
          <minus/>
          <apply>
            <times/>
            <ci> k21 </ci>
            <ci> c35 </ci>
            <ci> c26 </ci>
          </apply>
          <apply>
            <times/>
            <ci> kd21 </ci>
            <ci> c37 </ci>
          </apply>
        </apply>
      </apply>    
    </math>
  </component>
  
  <component name="v32">
    <variable name="v32" public_interface="out" units="flux"/>
    
    <variable name="c38" public_interface="in" units="molar"/>
    <variable name="c15" public_interface="in" units="molar"/>
    <variable name="c35" public_interface="in" units="molar"/>
    <variable name="k32" public_interface="in" units="second_order_rate_constant"/>
    <variable name="kd32" public_interface="in" units="first_order_rate_constant"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML" id="math134">
      <apply id="v32_calculation">
        <eq/>
        <ci> v32 </ci>
        <apply>
          <minus/>
          <apply>
            <times/>
            <ci> k32 </ci>
            <ci> c38 </ci>
            <ci> c15 </ci>
          </apply>
          <apply>
            <times/>
            <ci> kd32 </ci>
            <ci> c35 </ci>
          </apply>
        </apply>
      </apply>    
    </math>
  </component>

  <component name="v33">
    <variable name="v33" public_interface="out" units="flux"/>
    
    <variable name="c40" public_interface="in" units="molar"/>
    <variable name="c30" public_interface="in" units="molar"/>
    <variable name="c38" public_interface="in" units="molar"/>
    <variable name="k33" public_interface="in" units="second_order_rate_constant"/>
    <variable name="kd33" public_interface="in" units="first_order_rate_constant"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML" id="math135">
      <apply id="v33_calculation">
        <eq/>
        <ci> v33 </ci>
        <apply>
          <minus/>
          <apply>
            <times/>
            <ci> k33 </ci>
            <ci> c40 </ci>
            <ci> c30 </ci>
          </apply>
          <apply>
            <times/>
            <ci> kd33 </ci>
            <ci> c38 </ci>
          </apply>
        </apply>
      </apply>    
    </math>
  </component> 
  
  <component name="v34">
    <variable name="v34" public_interface="out" units="flux"/>
    
    <variable name="c15" public_interface="in" units="molar"/>
    <variable name="c30" public_interface="in" units="molar"/>
    <variable name="c25" public_interface="in" units="molar"/>
    <variable name="k34" public_interface="in" units="second_order_rate_constant"/>
    <variable name="kd34" public_interface="in" units="first_order_rate_constant"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML" id="math136">
      <apply id="v34_calculation">
        <eq/>
        <ci> v34 </ci>
        <apply>
          <minus/>
          <apply>
            <times/>
            <ci> k34 </ci>
            <ci> c15 </ci>
            <ci> c30 </ci>
          </apply>
          <apply>
            <times/>
            <ci> kd34 </ci>
            <ci> c25 </ci>
          </apply>
        </apply>
      </apply>    
    </math>
  </component>
  
  <component name="v35">
    <variable name="v35" public_interface="out" units="flux"/>  
    <variable name="c24" public_interface="in" units="molar"/>
    <variable name="c22" public_interface="in" units="molar"/>
    <variable name="c30" public_interface="in" units="molar"/>
    <variable name="k35" public_interface="in" units="second_order_rate_constant"/>
    <variable name="kd35" public_interface="in" units="first_order_rate_constant"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML" id="math137">
      <apply id="v35_calculation">
        <eq/>
        <ci> v35 </ci>
        <apply>
          <minus/>
          <apply>
            <times/>
            <ci> k35 </ci>
            <ci> c24 </ci>
            <ci> c22 </ci>
          </apply>
          <apply>
            <times/>
            <ci> kd35 </ci>
            <ci> c30 </ci>
          </apply>
        </apply>
      </apply>    
    </math>
  </component>
  
  <component name="v36">
    <variable name="v36" public_interface="out" units="flux"/>   
    <variable name="c31" public_interface="in" units="molar"/>
    <variable name="c40" public_interface="in" units="molar"/>
    <variable name="k36" public_interface="in" units="first_order_rate_constant"/>
    <variable name="kd36" public_interface="in" units="first_order_rate_constant"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML" id="math138">
      <apply id="v36_calculation">
        <eq/>
        <ci> v36 </ci>
        <apply>
          <minus/>
          <apply>
            <times/>
            <ci> k36 </ci>
            <ci> c40 </ci>
          </apply>
          <apply>
            <times/>
            <ci> kd36 </ci>
            <ci> c31 </ci>
          </apply>
        </apply>
      </apply>    
    </math>
  </component>
  
  <component name="v37">
    <variable name="v37" public_interface="out" units="flux"/>
    <variable name="c15" public_interface="in" units="molar"/>
    <variable name="c40" public_interface="in" units="molar"/>
    <variable name="c33" public_interface="in" units="molar"/>
    <variable name="k37" public_interface="in" units="second_order_rate_constant"/>
    <variable name="kd37" public_interface="in" units="first_order_rate_constant"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML" id="math139">
      <apply id="v37_calculation">
        <eq/>
        <ci> v37 </ci>
        <apply>
          <minus/>
          <apply>
            <times/>
            <ci> k37 </ci>
            <ci> c15 </ci>
            <ci> c40 </ci>
          </apply>
          <apply>
            <times/>
            <ci> kd37 </ci>
            <ci> c33 </ci>
          </apply>
        </apply>
      </apply>    
    </math>
  </component>
  
  <component name="v38">
    <variable name="v38" public_interface="out" units="flux"/>
    <variable name="c22" public_interface="in" units="molar"/>
    <variable name="c40" public_interface="in" units="molar"/>
    <variable name="c39" public_interface="in" units="molar"/>
    <variable name="k16" public_interface="in" units="second_order_rate_constant"/>
    <variable name="kd24" public_interface="in" units="first_order_rate_constant"/>
    
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            <ci> kd60 </ci>
            <ci> c87 </ci>
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    <variable name="c17" public_interface="in" units="molar"/>
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    <math xmlns="http://www.w3.org/1998/Math/MathML" id="math165">
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          <minus/>
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            <times/>
            <ci> k16 </ci>
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            <ci> kd63 </ci>
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    <math xmlns="http://www.w3.org/1998/Math/MathML" id="math166">
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        <eq/>
        <ci> v64 </ci>
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          <minus/>
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            <times/>
            <ci> k17 </ci>
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    <math xmlns="http://www.w3.org/1998/Math/MathML" id="math167">
      <apply id="v65_calculation">
        <eq/>
        <ci> v65 </ci>
        <apply>
          <minus/>
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            <times/>
            <ci> k18 </ci>
            <ci> c26 </ci>
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            <ci> kd18 </ci>
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  <component name="v66">
    <variable name="v66" public_interface="out" units="flux"/>
    
    <variable name="c69" public_interface="in" units="molar"/>
    <variable name="c19" public_interface="in" units="molar"/>
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    <variable name="kd19" public_interface="in" units="first_order_rate_constant"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML" id="math168">
      <apply id="v66_calculation">
        <eq/>
        <ci> v66 </ci>
        <apply>
          <minus/>
          <apply>
            <times/>
            <ci> k19 </ci>
            <ci> c69 </ci>
            <ci> c19 </ci>
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            <times/>
            <ci> kd19 </ci>
            <ci> c20 </ci>
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    <variable name="v67" public_interface="out" units="flux"/>
    
    <variable name="c71" public_interface="in" units="molar"/>
    <variable name="c19" public_interface="in" units="molar"/>
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    <math xmlns="http://www.w3.org/1998/Math/MathML" id="math169">
      <apply id="v67_calculation">
        <eq/>
        <ci> v67 </ci>
        <apply>
          <minus/>
          <apply>
            <times/>
            <ci> k20 </ci>
            <ci> c71 </ci>
            <ci> c19 </ci>
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          <apply>
            <times/>
            <ci> kd20 </ci>
            <ci> c21 </ci>
          </apply>
        </apply>
      </apply>    
    </math>
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  <component name="v68">
    <variable name="v68" public_interface="out" units="flux"/>
    
    <variable name="c19" public_interface="in" units="molar"/>
    <variable name="c26" public_interface="in" units="molar"/>
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    <variable name="kd21" public_interface="in" units="first_order_rate_constant"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML" id="math170">
      <apply id="v68_calculation">
        <eq/>
        <ci> v68 </ci>
        <apply>
          <minus/>
          <apply>
            <times/>
            <ci> k21 </ci>
            <ci> c19 </ci>
            <ci> c26 </ci>
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          <apply>
            <times/>
            <ci> kd21 </ci>
            <ci> c21 </ci>
          </apply>
        </apply>
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    </math>
  </component>
  
  <component name="v69">
    <variable name="v69" public_interface="out" units="flux"/>
    
    <variable name="c31" public_interface="in" units="molar"/>
    <variable name="c17" public_interface="in" units="molar"/>
    <variable name="c63" public_interface="in" units="molar"/>
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    <variable name="kd22" public_interface="in" units="first_order_rate_constant"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML" id="math171">
      <apply id="v69_calculation">
        <eq/>
        <ci> v69 </ci>
        <apply>
          <minus/>
          <apply>
            <times/>
            <ci> k22 </ci>
            <ci> c31 </ci>
            <ci> c17 </ci>
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            <times/>
            <ci> kd22 </ci>
            <ci> c63 </ci>
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    </math>
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  <component name="v70">
    <variable name="v70" public_interface="out" units="flux"/>
    
    <variable name="c63" public_interface="in" units="molar"/>
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    <variable name="kd23" public_interface="in" units="first_order_rate_constant"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML" id="math172">
      <apply id="v70_calculation">
        <eq/>
        <ci> v70 </ci>
        <apply>
          <minus/>
          <apply>
            <times/>
            <ci> k23 </ci>
            <ci> c63 </ci>
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          <apply>
            <times/>
            <ci> kd23 </ci>
            <ci> c64 </ci>
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        </apply>
      </apply>    
    </math>
  </component>
  
  <component name="v71">
    <variable name="v71" public_interface="out" units="flux"/>
    
    <variable name="c22" public_interface="in" units="molar"/>
    <variable name="c64" public_interface="in" units="molar"/>
    <variable name="c65" public_interface="in" units="molar"/>
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    <math xmlns="http://www.w3.org/1998/Math/MathML" id="math173">
      <apply id="v71_calculation">
        <eq/>
        <ci> v71 </ci>
        <apply>
          <minus/>
          <apply>
            <times/>
            <ci> k16 </ci>
            <ci> c22 </ci>
            <ci> c64 </ci>
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          <apply>
            <times/>
            <ci> kd24 </ci>
            <ci> c65 </ci>
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    </math>
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  <component name="v72">
    <variable name="v72" public_interface="out" units="flux"/>
    
    <variable name="c24" public_interface="in" units="molar"/>
    <variable name="c65" public_interface="in" units="molar"/>
    <variable name="c66" public_interface="in" units="molar"/>
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    <math xmlns="http://www.w3.org/1998/Math/MathML" id="math174">
      <apply id="v72_calculation">
        <eq/>
        <ci> v72 </ci>
        <apply>
          <minus/>
          <apply>
            <times/>
            <ci> k25 </ci>
            <ci> c24 </ci>
            <ci> c65 </ci>
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          <apply>
            <times/>
            <ci> kd25 </ci>
            <ci> c66 </ci>
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    </math>
  </component>

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    <variable name="v73" public_interface="out" units="flux"/>
    
    <variable name="c26" public_interface="in" units="molar"/>
    <variable name="c66" public_interface="in" units="molar"/>
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    <math xmlns="http://www.w3.org/1998/Math/MathML" id="math175">
      <apply id="v73_calculation">
        <eq/>
        <ci> v73 </ci>
        <apply>
          <minus/>
          <apply>
            <times/>
            <ci> k18 </ci>
            <ci> c26 </ci>
            <ci> c66 </ci>
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          <apply>
            <times/>
            <ci> kd18 </ci>
            <ci> c67 </ci>
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        </apply>
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    </math>
  </component>
  
  <component name="v74">
    <variable name="v74" public_interface="out" units="flux"/>
    
    <variable name="c66" public_interface="in" units="molar"/>
    <variable name="c69" public_interface="in" units="molar"/>
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    <math xmlns="http://www.w3.org/1998/Math/MathML" id="math176">
      <apply id="v74_calculation">
        <eq/>
        <ci> v74 </ci>
        <apply>
          <minus/>
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            <times/>
            <ci> k19 </ci>
            <ci> c66 </ci>
            <ci> c69 </ci>
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            <times/>
            <ci> kd19 </ci>
            <ci> c67 </ci>
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        </apply>
      </apply>    
    </math>
  </component>
  
  <component name="v75">
    <variable name="v75" public_interface="out" units="flux"/>
    
    <variable name="c69" public_interface="in" units="molar"/>
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    <math xmlns="http://www.w3.org/1998/Math/MathML" id="math177">
      <apply id="v75_calculation">
        <eq/>
        <ci> v75 </ci>
        <apply>
          <minus/>
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            <times/>
            <ci> k28 </ci>
            <ci> c69 </ci>
            <ci> c41 </ci>
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          <apply>
            <times/>
            <ci> kd28 </ci>
            <ci> c70 </ci>
          </apply>
        </apply>
      </apply>    
    </math>
  </component>
  
  <component name="v76">
    <variable name="v76" public_interface="out" units="flux"/>
    
    <variable name="c71" public_interface="in" units="molar"/>
    <variable name="c72" public_interface="in" units="molar"/>
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    <math xmlns="http://www.w3.org/1998/Math/MathML" id="math178">
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        <eq/>
        <ci> v76 </ci>
        <apply>
          <minus/>
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            <times/>
            <ci> k29 </ci>
            <ci> c71 </ci>
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            <times/>
            <ci> kd29 </ci>
            <ci> c70 </ci>
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        </apply>
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  <component name="v77">
    <variable name="v77" public_interface="out" units="flux"/>
    
    <variable name="c71" public_interface="in" units="molar"/>
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    <math xmlns="http://www.w3.org/1998/Math/MathML" id="math179">
      <apply id="v77_calculation">
        <eq/>
        <ci> v77 </ci>
        <apply>
          <minus/>
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            <times/>
            <ci> k20 </ci>
            <ci> c71 </ci>
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            <times/>
            <ci> kd20 </ci>
            <ci> c68 </ci>
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        </apply>
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    </math>
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  <component name="v78">
    <variable name="v78" public_interface="out" units="flux"/>
    
    <variable name="c66" public_interface="in" units="molar"/>
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    <math xmlns="http://www.w3.org/1998/Math/MathML" id="math180">
      <apply id="v78_calculation">
        <eq/>
        <ci> v78 </ci>
        <apply>
          <minus/>
          <apply>
            <times/>
            <ci> k21 </ci>
            <ci> c66 </ci>
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            <times/>
            <ci> kd21 </ci>
            <ci> c68 </ci>
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        </apply>
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    </math>
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    <variable name="v79" public_interface="out" units="flux"/>
    
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    <math xmlns="http://www.w3.org/1998/Math/MathML" id="math181">
      <apply id="v79_calculation">
        <eq/>
        <ci> v79 </ci>
        <apply>
          <minus/>
          <apply>
            <times/>
            <ci> k32 </ci>
            <ci> c17 </ci>
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            <times/>
            <ci> kd32 </ci>
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    <math xmlns="http://www.w3.org/1998/Math/MathML" id="math182">
      <apply id="v80_calculation">
        <eq/>
        <ci> v80 </ci>
        <apply>
          <minus/>
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            <times/>
            <ci> k34 </ci>
            <ci> c17 </ci>
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            <times/>
            <ci> kd34 </ci>
            <ci> c19 </ci>
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    <math xmlns="http://www.w3.org/1998/Math/MathML" id="math183">
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        <eq/>
        <ci> v81 </ci>
        <apply>
          <minus/>
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            <times/>
            <ci> k37 </ci>
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            <times/>
            <ci> kd37 </ci>
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    <math xmlns="http://www.w3.org/1998/Math/MathML" id="math184">
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        <eq/>
        <ci> v82 </ci>
        <apply>
          <minus/>
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            <times/>
            <ci> k37 </ci>
            <ci> c17 </ci>
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            <times/>
            <ci> kd37 </ci>
            <ci> c65 </ci>
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  <component name="v83">
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    <math xmlns="http://www.w3.org/1998/Math/MathML" id="math185">
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        <eq/>
        <ci> v83 </ci>
        <apply>
          <minus/>
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            <times/>
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    <math xmlns="http://www.w3.org/1998/Math/MathML" id="math186">
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        <eq/>
        <ci> v84 </ci>
        <apply>
          <minus/>
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            <times/>
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            <times/>
            <ci> kd42 </ci>
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    <math xmlns="http://www.w3.org/1998/Math/MathML" id="math187">
      <apply id="v85_calculation">
        <eq/>
        <ci> v85 </ci>
        <apply>
          <minus/>
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            <times/>
            <ci> k43 </ci>
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            <times/>
            <ci> kd43 </ci>
            <ci> c73 </ci>
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        </apply>
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      <apply id="v86_calculation">
        <eq/>
        <ci> v86 </ci>
        <apply>
          <minus/>
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            <times/>
            <ci> k44 </ci>
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            <times/>
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            <ci> c74 </ci>
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        </apply>
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  <component name="v87">
    <variable name="v87" public_interface="out" units="flux"/>
    
    <variable name="c75" public_interface="in" units="molar"/>
    <variable name="c72" public_interface="in" units="molar"/>
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    <math xmlns="http://www.w3.org/1998/Math/MathML" id="math189">
      <apply id="v87_calculation">
        <eq/>
        <ci> v87 </ci>
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          <minus/>
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            <times/>
            <ci> k45 </ci>
            <ci> c75 </ci>
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            <ci> kd45 </ci>
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  <component name="v88">
    <variable name="v88" public_interface="out" units="flux"/>
    
    <variable name="c72" public_interface="in" units="molar"/>
    <variable name="c75" public_interface="in" units="molar"/>
    <variable name="c76" public_interface="in" units="molar"/>
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    <math xmlns="http://www.w3.org/1998/Math/MathML" id="math190">
      <apply id="v88_calculation">
        <eq/>
        <ci> v88 </ci>
        <apply>
          <minus/>
          <apply>
            <times/>
            <ci> k44 </ci>
            <ci> c72 </ci>
            <ci> c75 </ci>
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            <times/>
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            <ci> c76 </ci>
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  <component name="v89">
    <variable name="v89" public_interface="out" units="flux"/>
    
    <variable name="c72" public_interface="in" units="molar"/>
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    <math xmlns="http://www.w3.org/1998/Math/MathML" id="math191">
      <apply id="v89_calculation">
        <eq/>
        <ci> v89 </ci>
        <apply>
          <minus/>
          <apply>
            <times/>
            <ci> k47 </ci>
            <ci> c72 </ci>
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            <times/>
            <ci> kd47 </ci>
            <ci> c76 </ci>
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  <component name="v90">
    <variable name="v90" public_interface="out" units="flux"/>
    
    <variable name="c77" public_interface="in" units="molar"/>
    <variable name="c53" public_interface="in" units="molar"/>
    <variable name="c78" public_interface="in" units="molar"/>
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    <variable name="kd48" public_interface="in" units="first_order_rate_constant"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML" id="math192">
      <apply id="v90_calculation">
        <eq/>
        <ci> v90 </ci>
        <apply>
          <minus/>
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            <times/>
            <ci> k48 </ci>
            <ci> c77 </ci>
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            <times/>
            <ci> kd48 </ci>
            <ci> c78 </ci>
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        </apply>
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  <component name="v91">
    <variable name="v91" public_interface="out" units="flux"/>
    
    <variable name="c75" public_interface="in" units="molar"/>
    <variable name="c53" public_interface="in" units="molar"/>
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    <math xmlns="http://www.w3.org/1998/Math/MathML" id="math193">
      <apply id="v91_calculation">
        <eq/>
        <ci> v91 </ci>
        <apply>
          <minus/>
          <apply>
            <times/>
            <ci> k49 </ci>
            <ci> c75 </ci>
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            <ci> kd49 </ci>
            <ci> c78 </ci>
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  <component name="v92">
    <variable name="v92" public_interface="out" units="flux"/>
    
    <variable name="c53" public_interface="in" units="molar"/>
    <variable name="c75" public_interface="in" units="molar"/>
    <variable name="c79" public_interface="in" units="molar"/>
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    <variable name="kd50" public_interface="in" units="first_order_rate_constant"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML" id="math194">
      <apply id="v92_calculation">
        <eq/>
        <ci> v92 </ci>
        <apply>
          <minus/>
          <apply>
            <times/>
            <ci> k50 </ci>
            <ci> c53 </ci>
            <ci> c75 </ci>
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            <ci> kd50 </ci>
            <ci> c79 </ci>
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  <component name="v93">
    <variable name="v93" public_interface="out" units="flux"/>
    
    <variable name="c47" public_interface="in" units="molar"/>
    <variable name="c53" public_interface="in" units="molar"/>
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    <variable name="kd49" public_interface="in" units="first_order_rate_constant"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML" id="math195">
      <apply id="v93_calculation">
        <eq/>
        <ci> v93 </ci>
        <apply>
          <minus/>
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            <times/>
            <ci> k49 </ci>
            <ci> c47 </ci>
            <ci> c53 </ci>
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            <ci> kd49 </ci>
            <ci> c79 </ci>
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  <component name="v94">
    <variable name="v94" public_interface="out" units="flux"/>
    
    <variable name="c55" public_interface="in" units="molar"/>
    <variable name="c77" public_interface="in" units="molar"/>
    <variable name="c80" public_interface="in" units="molar"/>
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    <math xmlns="http://www.w3.org/1998/Math/MathML" id="math196">
      <apply id="v94_calculation">
        <eq/>
        <ci> v94 </ci>
        <apply>
          <minus/>
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            <times/>
            <ci> k52 </ci>
            <ci> c55 </ci>
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            <ci> kd44 </ci>
            <ci> c80 </ci>
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  <component name="v95">
    <variable name="v95" public_interface="out" units="flux"/>
    
    <variable name="c81" public_interface="in" units="molar"/>
    <variable name="c77" public_interface="in" units="molar"/>
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    <math xmlns="http://www.w3.org/1998/Math/MathML" id="math197">
      <apply id="v95_calculation">
        <eq/>
        <ci> v95 </ci>
        <apply>
          <minus/>
          <apply>
            <times/>
            <ci> k53 </ci>
            <ci> c81 </ci>
            <ci> c77 </ci>
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            <ci> c80 </ci>
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  <component name="v96">
    <variable name="v96" public_interface="out" units="flux"/>
    
    <variable name="c77" public_interface="in" units="molar"/>
    <variable name="c81" public_interface="in" units="molar"/>
    <variable name="c82" public_interface="in" units="molar"/>
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    <math xmlns="http://www.w3.org/1998/Math/MathML" id="math198">
      <apply id="v96_calculation">
        <eq/>
        <ci> v96 </ci>
        <apply>
          <minus/>
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            <times/>
            <ci> k52 </ci>
            <ci> c77 </ci>
            <ci> c81 </ci>
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            <times/>
            <ci> kd44 </ci>
            <ci> c82 </ci>
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    </math>
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  <component name="v97">
    <variable name="v97" public_interface="out" units="flux"/>
    
    <variable name="c83" public_interface="in" units="molar"/>
    <variable name="c77" public_interface="in" units="molar"/>
    <variable name="c82" public_interface="in" units="molar"/>
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    <variable name="kd55" public_interface="in" units="first_order_rate_constant"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML" id="math199">
      <apply id="v97_calculation">
        <eq/>
        <ci> v97 </ci>
        <apply>
          <minus/>
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            <times/>
            <ci> k55 </ci>
            <ci> c83 </ci>
            <ci> c77 </ci>
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            <times/>
            <ci> kd55 </ci>
            <ci> c82 </ci>
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        </apply>
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    </math>
  </component>

  <component name="v98">
    <variable name="v98" public_interface="out" units="flux"/>
    
    <variable name="c83" public_interface="in" units="molar"/>
    <variable name="c60" public_interface="in" units="molar"/>
    <variable name="c84" public_interface="in" units="molar"/>
    <variable name="k56" public_interface="in" units="second_order_rate_constant"/>
    <variable name="kd56" public_interface="in" units="first_order_rate_constant"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML" id="math200">
      <apply id="v98_calculation">
        <eq/>
        <ci> v98 </ci>
        <apply>
          <minus/>
          <apply>
            <times/>
            <ci> k56 </ci>
            <ci> c83 </ci>
            <ci> c60 </ci>
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            <times/>
            <ci> kd56 </ci>
            <ci> c84 </ci>
          </apply>
        </apply>
      </apply>    
    </math>
  </component>
  
  <component name="v99">
    <variable name="v99" public_interface="out" units="flux"/>
    
    <variable name="c81" public_interface="in" units="molar"/>
    <variable name="c60" public_interface="in" units="molar"/>
    <variable name="c84" public_interface="in" units="molar"/>
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    <variable name="kd57" public_interface="in" units="first_order_rate_constant"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML" id="math201">
      <apply id="v99_calculation">
        <eq/>
        <ci> v99 </ci>
        <apply>
          <minus/>
          <apply>
            <times/>
            <ci> k57 </ci>
            <ci> c81 </ci>
            <ci> c60 </ci>
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          <apply>
            <times/>
            <ci> kd57 </ci>
            <ci> c84 </ci>
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        </apply>
      </apply>    
    </math>
  </component>
  
  <component name="v100">
    <variable name="v100" public_interface="out" units="flux"/>
    
    <variable name="c60" public_interface="in" units="molar"/>
    <variable name="c81" public_interface="in" units="molar"/>
    <variable name="c85" public_interface="in" units="molar"/>
    <variable name="k58" public_interface="in" units="second_order_rate_constant"/>
    <variable name="kd58" public_interface="in" units="first_order_rate_constant"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML" id="math202">
      <apply id="v100_calculation">
        <eq/>
        <ci> v100 </ci>
        <apply>
          <minus/>
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            <times/>
            <ci> k58 </ci>
            <ci> c60 </ci>
            <ci> c81 </ci>
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            <times/>
            <ci> kd58 </ci>
            <ci> c85 </ci>
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        </apply>
      </apply>    
    </math>
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  <component name="v101">
    <variable name="v101" public_interface="out" units="flux"/>
    
    <variable name="c55" public_interface="in" units="molar"/>
    <variable name="c60" public_interface="in" units="molar"/>
    <variable name="c85" public_interface="in" units="molar"/>
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    <math xmlns="http://www.w3.org/1998/Math/MathML" id="math203">
      <apply id="v101_calculation">
        <eq/>
        <ci> v101 </ci>
        <apply>
          <minus/>
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            <times/>
            <ci> k57 </ci>
            <ci> c55 </ci>
            <ci> c60 </ci>
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            <times/>
            <ci> kd57 </ci>
            <ci> c85 </ci>
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        </apply>
      </apply>    
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  </component>

  <component name="v102">
    <variable name="v102" public_interface="out" units="flux"/>
    
    <variable name="c15" public_interface="in" units="molar"/>
    <variable name="c17" public_interface="in" units="molar"/>
    <variable name="k6" public_interface="in" units="first_order_rate_constant"/>
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    <math xmlns="http://www.w3.org/1998/Math/MathML" id="math204">
      <apply id="v102_calculation">
        <eq/>
        <ci> v102 </ci>
        <apply>
          <minus/>
          <apply>
            <times/>
            <ci> k6 </ci>
            <ci> c15 </ci>
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          <apply>
            <times/>
            <ci> kd6 </ci>
            <ci> c17 </ci>
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        </apply>
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  <component name="v103">
    <variable name="v103" public_interface="out" units="flux"/>
    
    <variable name="c32" public_interface="in" units="molar"/>
    <variable name="c63" public_interface="in" units="molar"/>
    <variable name="k6" public_interface="in" units="first_order_rate_constant"/>
    <variable name="kd6" public_interface="in" units="first_order_rate_constant"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML" id="math205">
      <apply id="v103_calculation">
        <eq/>
        <ci> v103 </ci>
        <apply>
          <minus/>
          <apply>
            <times/>
            <ci> k6 </ci>
            <ci> c32 </ci>
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          <apply>
            <times/>
            <ci> kd6 </ci>
            <ci> c63 </ci>
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        </apply>
      </apply>    
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  </component>

  <component name="v104">
    <variable name="v104" public_interface="out" units="flux"/>
    
    <variable name="c33" public_interface="in" units="molar"/>
    <variable name="c64" public_interface="in" units="molar"/>
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    <math xmlns="http://www.w3.org/1998/Math/MathML" id="math206">
      <apply id="v104_calculation">
        <eq/>
        <ci> v104 </ci>
        <apply>
          <minus/>
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            <times/>
            <ci> k6 </ci>
            <ci> c33 </ci>
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            <times/>
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            <ci> c64 </ci>
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  <component name="v105">
    <variable name="v105" public_interface="out" units="flux"/>
    
    <variable name="c25" public_interface="in" units="molar"/>
    <variable name="c19" public_interface="in" units="molar"/>
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    <math xmlns="http://www.w3.org/1998/Math/MathML" id="math207">
      <apply id="v105_calculation">
        <eq/>
        <ci> v105 </ci>
        <apply>
          <minus/>
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            <times/>
            <ci> k6 </ci>
            <ci> c25 </ci>
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          <apply>
            <times/>
            <ci> kd6 </ci>
            <ci> c19 </ci>
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  </component>   
  
  <component name="v106">
    <variable name="v106" public_interface="out" units="flux"/>
    
    <variable name="c25" public_interface="in" units="molar"/>
    <variable name="c12" public_interface="in" units="molar"/>
    <variable name="c88" public_interface="in" units="molar"/>
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    <math xmlns="http://www.w3.org/1998/Math/MathML" id="math208">
      <apply id="v106_calculation">
        <eq/>
        <ci> v106 </ci>
        <apply>
          <minus/>
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            <times/>
            <ci> k4 </ci>
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            <times/>
            <ci> kd4 </ci>
            <ci> c88 </ci>
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    </math>
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  <component name="v107">
    <variable name="v107" public_interface="out" units="flux"/>
    
    <variable name="c9" public_interface="in" units="molar"/>
    <variable name="c19" public_interface="in" units="molar"/>
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      <apply id="v107_calculation">
        <eq/>
        <ci> v107 </ci>
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          <minus/>
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            <times/>
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        <eq/>
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          <minus/>
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            <times/>
            <ci> k6 </ci>
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      <apply id="v110_calculation">
        <eq/>
        <ci> v110 </ci>
        <apply>
          <minus/>
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            <times/>
            <ci> k5 </ci>
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            <ci> c89 </ci>
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      <apply id="v111_calculation">
        <eq/>
        <ci> v111 </ci>
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          <minus/>
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        <ci> v128 </ci>
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            <times/>
            <ci> k60 </ci>
            <ci> c21 </ci>
          </apply>
          <apply>
            <times/>
            <ci> kd60 </ci>
            <ci> c87 </ci>
          </apply>
        </apply>
      </apply>    
    </math>
  </component>

  <component name="v137">
    <variable name="v137" public_interface="out" units="flux"/>
    
    <variable name="c63" public_interface="in" units="molar"/>
    <variable name="c87" public_interface="in" units="molar"/>
    <variable name="k60" public_interface="in" units="first_order_rate_constant"/>
    <variable name="kd60" public_interface="in" units="first_order_rate_constant"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML" id="math239">
      <apply id="v137_calculation">
        <eq/>
        <ci> v137 </ci>
        <apply>
          <minus/>
          <apply>
            <times/>
            <ci> k60 </ci>
            <ci> c63 </ci>
          </apply>
          <apply>
            <times/>
            <ci> kd60 </ci>
            <ci> c87 </ci>
          </apply>
        </apply>
      </apply>    
    </math>
  </component>

  <component name="v138">
    <variable name="v138" public_interface="out" units="flux"/>
    
    <variable name="c64" public_interface="in" units="molar"/>
    <variable name="c87" public_interface="in" units="molar"/>
    <variable name="k60" public_interface="in" units="first_order_rate_constant"/>
    <variable name="kd60" public_interface="in" units="first_order_rate_constant"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML" id="math240">
      <apply id="v138_calculation">
        <eq/>
        <ci> v138 </ci>
        <apply>
          <minus/>
          <apply>
            <times/>
            <ci> k60 </ci>
            <ci> c64 </ci>
          </apply>
          <apply>
            <times/>
            <ci> kd60 </ci>
            <ci> c87 </ci>
          </apply>
        </apply>
      </apply>    
    </math>
  </component>

  <component name="v139">
    <variable name="v139" public_interface="out" units="flux"/>
    
    <variable name="c65" public_interface="in" units="molar"/>
    <variable name="c87" public_interface="in" units="molar"/>
    <variable name="k60" public_interface="in" units="first_order_rate_constant"/>
    <variable name="kd60" public_interface="in" units="first_order_rate_constant"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML" id="math241">
      <apply id="v139_calculation">
        <eq/>
        <ci> v139 </ci>
        <apply>
          <minus/>
          <apply>
            <times/>
            <ci> k60 </ci>
            <ci> c65 </ci>
          </apply>
          <apply>
            <times/>
            <ci> kd60 </ci>
            <ci> c87 </ci>
          </apply>
        </apply>
      </apply>    
    </math>
  </component>

  <component name="v140">
    <variable name="v140" public_interface="out" units="flux"/>
    
    <variable name="c66" public_interface="in" units="molar"/>
    <variable name="c87" public_interface="in" units="molar"/>
    <variable name="k60" public_interface="in" units="first_order_rate_constant"/>
    <variable name="kd60" public_interface="in" units="first_order_rate_constant"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML" id="math242">
      <apply id="v140_calculation">
        <eq/>
        <ci> v140 </ci>
        <apply>
          <minus/>
          <apply>
            <times/>
            <ci> k60 </ci>
            <ci> c66 </ci>
          </apply>
          <apply>
            <times/>
            <ci> kd60 </ci>
            <ci> c87 </ci>
          </apply>
        </apply>
      </apply>    
    </math>
  </component>

  <component name="v141">
    <variable name="v141" public_interface="out" units="flux"/>
    
    <variable name="c67" public_interface="in" units="molar"/>
    <variable name="c87" public_interface="in" units="molar"/>
    <variable name="k60" public_interface="in" units="first_order_rate_constant"/>
    <variable name="kd60" public_interface="in" units="first_order_rate_constant"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML" id="math243">
      <apply id="v141_calculation">
        <eq/>
        <ci> v141 </ci>
        <apply>
          <minus/>
          <apply>
            <times/>
            <ci> k60 </ci>
            <ci> c67 </ci>
          </apply>
          <apply>
            <times/>
            <ci> kd60 </ci>
            <ci> c87 </ci>
          </apply>
        </apply>
      </apply>    
    </math>
  </component>

  <component name="v142">
    <variable name="v142" public_interface="out" units="flux"/>
    
    <variable name="c68" public_interface="in" units="molar"/>
    <variable name="c87" public_interface="in" units="molar"/>
    <variable name="k60" public_interface="in" units="first_order_rate_constant"/>
    <variable name="kd60" public_interface="in" units="first_order_rate_constant"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML" id="math244">
      <apply id="v142_calculation">
        <eq/>
        <ci> v142 </ci>
        <apply>
          <minus/>
          <apply>
            <times/>
            <ci> k60 </ci>
            <ci> c68 </ci>
          </apply>
          <apply>
            <times/>
            <ci> kd60 </ci>
            <ci> c87 </ci>
          </apply>
        </apply>
      </apply>    
    </math>
  </component>

  <component name="v143">
    <variable name="v143" public_interface="out" units="flux"/>
    
    <variable name="c59" public_interface="in" units="molar"/>
    <variable name="c99" public_interface="in" units="molar"/>
    <variable name="c95" public_interface="in" units="molar"/>
    <variable name="k127" public_interface="in" units="second_order_rate_constant"/>
    <variable name="kd127" public_interface="in" units="first_order_rate_constant"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML" id="math245">
      <apply id="v143_calculation">
        <eq/>
        <ci> v143 </ci>
        <apply>
          <minus/>
          <apply>
            <times/>
            <ci> k127 </ci>
            <ci> c59 </ci>
            <ci> c99 </ci>
          </apply>
          <apply>
            <times/>
            <ci> kd127 </ci>
            <ci> c95 </ci>
          </apply>
        </apply>
      </apply>    
    </math>
  </component>
   
  <component name="v144">
    <variable name="v144" public_interface="out" units="flux"/>
    
    <variable name="c59" public_interface="in" units="molar"/>
    <variable name="c99" public_interface="in" units="molar"/>
    <variable name="c97" public_interface="in" units="molar"/>
    <variable name="k127" public_interface="in" units="second_order_rate_constant"/>
    <variable name="kd127" public_interface="in" units="first_order_rate_constant"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML" id="math246">
      <apply id="v144_calculation">
        <eq/>
        <ci> v144 </ci>
        <apply>
          <minus/>
          <apply>
            <times/>
            <ci> k127 </ci>
            <ci> c59 </ci>
            <ci> c99 </ci>
          </apply>
          <apply>
            <times/>
            <ci> kd127 </ci>
            <ci> c97 </ci>
          </apply>
        </apply>
      </apply>    
    </math>
  </component>

  <component name="v145">
    <variable name="v145" public_interface="out" units="flux"/>
    
    <variable name="c59" public_interface="in" units="molar"/>
    <variable name="c103" public_interface="in" units="molar"/>
    <variable name="c101" public_interface="in" units="molar"/>
    <variable name="k127" public_interface="in" units="second_order_rate_constant"/>
    <variable name="kd127" public_interface="in" units="first_order_rate_constant"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML" id="math247">
      <apply id="v145_calculation">
        <eq/>
        <ci> v145 </ci>
        <apply>
          <minus/>
          <apply>
            <times/>
            <ci> k127 </ci>
            <ci> c59 </ci>
            <ci> c103 </ci>
          </apply>
          <apply>
            <times/>
            <ci> kd127 </ci>
            <ci> c101 </ci>
          </apply>
        </apply>
      </apply>    
    </math>
  </component>
   
  <component name="v146">
    <variable name="v146" public_interface="out" units="flux"/>
    
    <variable name="c83" public_interface="in" units="molar"/>
    <variable name="c100" public_interface="in" units="molar"/>
    <variable name="c96" public_interface="in" units="molar"/>
    <variable name="k127" public_interface="in" units="second_order_rate_constant"/>
    <variable name="kd127" public_interface="in" units="first_order_rate_constant"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML" id="math248">
      <apply id="v146_calculation">
        <eq/>
        <ci> v146 </ci>
        <apply>
          <minus/>
          <apply>
            <times/>
            <ci> k127 </ci>
            <ci> c83 </ci>
            <ci> c100 </ci>
          </apply>
          <apply>
            <times/>
            <ci> kd127 </ci>
            <ci> c96 </ci>
          </apply>
        </apply>
      </apply>    
    </math>
  </component>

  <component name="v147">
    <variable name="v147" public_interface="out" units="flux"/>
    
    <variable name="c83" public_interface="in" units="molar"/>
    <variable name="c100" public_interface="in" units="molar"/>
    <variable name="c98" public_interface="in" units="molar"/>
    <variable name="k127" public_interface="in" units="second_order_rate_constant"/>
    <variable name="kd127" public_interface="in" units="first_order_rate_constant"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML" id="math249">
      <apply id="v147_calculation">
        <eq/>
        <ci> v147 </ci>
        <apply>
          <minus/>
          <apply>
            <times/>
            <ci> k127 </ci>
            <ci> c83 </ci>
            <ci> c100 </ci>
          </apply>
          <apply>
            <times/>
            <ci> kd127 </ci>
            <ci> c98 </ci>
          </apply>
        </apply>
      </apply>    
    </math>
  </component>

  <component name="v148">
    <variable name="v148" public_interface="out" units="flux"/>
    
    <variable name="c83" public_interface="in" units="molar"/>
    <variable name="c103" public_interface="in" units="molar"/>
    <variable name="c102" public_interface="in" units="molar"/>
    <variable name="k127" public_interface="in" units="second_order_rate_constant"/>
    <variable name="kd127" public_interface="in" units="first_order_rate_constant"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML" id="math250">
      <apply id="v148_calculation">
        <eq/>
        <ci> v148 </ci>
        <apply>
          <minus/>
          <apply>
            <times/>
            <ci> k127 </ci>
            <ci> c83 </ci>
            <ci> c103 </ci>
          </apply>
          <apply>
            <times/>
            <ci> kd127 </ci>
            <ci> c102 </ci>
          </apply>
        </apply>
      </apply>    
    </math>
  </component>

  
  <component name="reaction_rates">
    <variable initial_value="3.0E7" name="k1" public_interface="out" units="second_order_rate_constant"/>
    <variable initial_value="3.84E-3" name="kd1" public_interface="out" units="first_order_rate_constant"/>
    <variable initial_value="1.66E-5" name="k2" public_interface="out" units="second_order_rate_constant"/>
    <variable initial_value="1E-1" name="kd2" public_interface="out" units="first_order_rate_constant"/>
	<variable initial_value="1E0" name="k3" public_interface="out" units="first_order_rate_constant"/>
    <variable initial_value="1E-2" name="kd3" public_interface="out" units="first_order_rate_constant"/>
    <variable initial_value="1.73E-7" name="k4" public_interface="out" units="second_order_rate_constant"/>
    <variable initial_value="1.66E-3" name="kd4" public_interface="out" units="first_order_rate_constant"/>
	<variable initial_value="1.46E-2" name="kd5" public_interface="out" units="first_order_rate_constant"/>
    <variable initial_value="0E0" name="k5" public_interface="out" units="second_order_rate_constant"/>
    <variable initial_value="5E-4" name="k6" public_interface="out" units="first_order_rate_constant"/>
    <variable initial_value="5E-3" name="kd6" public_interface="out" units="first_order_rate_constant"/>
	<variable initial_value="1.66E-6" name="k8" public_interface="out" units="second_order_rate_constant"/>
    <variable initial_value="2E-1" name="kd8" public_interface="out" units="first_order_rate_constant"/>
	<variable initial_value="5.43E-2" name="k10b" public_interface="out" units="second_order_rate_constant"/>
    <variable initial_value="1.1E-2" name="kd10" public_interface="out" units="first_order_rate_constant"/>
    <variable initial_value="2.17E0" name="k13" public_interface="out" units="first_order_rate_constant"/>
    <variable initial_value="0E0" name="kd13" public_interface="out" units="first_order_rate_constant"/>
	<variable initial_value="1E4" name="k15" public_interface="out" units="first_order_rate_constant"/>
    <variable initial_value="0E0" name="kd15" public_interface="out" units="first_order_rate_constant"/>
    <variable initial_value="1.66E-5" name="k16" public_interface="out" units="second_order_rate_constant"/>
    <variable initial_value="1.66E-5" name="k17" public_interface="out" units="second_order_rate_constant"/>
    <variable initial_value="6E-2" name="kd17" public_interface="out" units="first_order_rate_constant"/>
    <variable initial_value="2.5E-5" name="k18" public_interface="out" units="second_order_rate_constant"/>
    <variable initial_value="1.3E0" name="kd18" public_interface="out" units="first_order_rate_constant"/>
	<variable initial_value="1.66E-7" name="k19" public_interface="out" units="second_order_rate_constant"/>
    <variable initial_value="5E-1" name="kd19" public_interface="out" units="first_order_rate_constant"/>
    <variable initial_value="3.5E-6" name="k20" public_interface="out" units="second_order_rate_constant"/>
    <variable initial_value="4E-1" name="kd20" public_interface="out" units="first_order_rate_constant"/>
	<variable initial_value="3.66E-7" name="k21" public_interface="out" units="second_order_rate_constant"/>
    <variable initial_value="2.3E-2" name="kd21" public_interface="out" units="first_order_rate_constant"/>
    <variable initial_value="3.5E-5" name="k22" public_interface="out" units="second_order_rate_constant"/>
    <variable initial_value="1E-1" name="kd22" public_interface="out" units="first_order_rate_constant"/>
	<variable initial_value="6E0" name="k23" public_interface="out" units="first_order_rate_constant"/>
    <variable initial_value="6E-2" name="kd23" public_interface="out" units="first_order_rate_constant"/>
    <variable initial_value="5.5E-1" name="kd24" public_interface="out" units="first_order_rate_constant"/>
	<variable initial_value="1.66E-5" name="k25" public_interface="out" units="second_order_rate_constant"/>
    <variable initial_value="2.14E-2" name="kd25" public_interface="out" units="first_order_rate_constant"/>
    <variable initial_value="1.66E-6" name="k28" public_interface="out" units="second_order_rate_constant"/>
    <variable initial_value="5.3E-3" name="kd28" public_interface="out" units="first_order_rate_constant"/>
	<variable initial_value="1.17E-6" name="k29" public_interface="out" units="second_order_rate_constant"/>
    <variable initial_value="1E0" name="kd29" public_interface="out" units="first_order_rate_constant"/>
    <variable initial_value="4E-7" name="k32" public_interface="out" units="second_order_rate_constant"/>
    <variable initial_value="1E-1" name="kd32" public_interface="out" units="first_order_rate_constant"/>
	<variable initial_value="3.5E-5" name="k33" public_interface="out" units="second_order_rate_constant"/>
    <variable initial_value="2E-1" name="kd33" public_interface="out" units="first_order_rate_constant"/>
    <variable initial_value="7.5E-6" name="k34" public_interface="out" units="second_order_rate_constant"/>
    <variable initial_value="3E-2" name="kd34" public_interface="out" units="first_order_rate_constant"/>
	<variable initial_value="7.5E-6" name="k35" public_interface="out" units="second_order_rate_constant"/>
    <variable initial_value="1.5E-3" name="kd35" public_interface="out" units="first_order_rate_constant"/>
    <variable initial_value="5E-3" name="k36" public_interface="out" units="first_order_rate_constant"/>
    <variable initial_value="0E0" name="kd36" public_interface="out" units="first_order_rate_constant"/>
	<variable initial_value="1.5E-6" name="k37" public_interface="out" units="second_order_rate_constant"/>
    <variable initial_value="3E-1" name="kd37" public_interface="out" units="first_order_rate_constant"/>
    <variable initial_value="5E-5" name="k40" public_interface="out" units="second_order_rate_constant"/>
    <variable initial_value="6.4E-2" name="kd40" public_interface="out" units="first_order_rate_constant"/>
	<variable initial_value="5E-5" name="k41" public_interface="out" units="second_order_rate_constant"/>
    <variable initial_value="4.29E-2" name="kd41" public_interface="out" units="first_order_rate_constant"/>
    <variable initial_value="1.18E-4" name="k42" public_interface="out" units="second_order_rate_constant"/>
    <variable initial_value="2E-1" name="kd42" public_interface="out" units="first_order_rate_constant"/>
	<variable initial_value="0E0" name="k43" public_interface="out" units="second_order_rate_constant"/>
    <variable initial_value="1E0" name="kd43" public_interface="out" units="first_order_rate_constant"/>
    <variable initial_value="1.95E-5" name="k44" public_interface="out" units="second_order_rate_constant"/>
    <variable initial_value="1.83E-2" name="kd44" public_interface="out" units="first_order_rate_constant"/>
	<variable initial_value="0E0" name="k45" public_interface="out" units="second_order_rate_constant"/>
    <variable initial_value="3.5E0" name="kd45" public_interface="out" units="first_order_rate_constant"/>
    <variable initial_value="0E0" name="k47" public_interface="out" units="second_order_rate_constant"/>
    <variable initial_value="2.9E0" name="kd47" public_interface="out" units="first_order_rate_constant"/>
	<variable initial_value="2.38E-5" name="k48" public_interface="out" units="second_order_rate_constant"/>
    <variable initial_value="8E-1" name="kd48" public_interface="out" units="first_order_rate_constant"/>
    <variable initial_value="0E0" name="k49" public_interface="out" units="second_order_rate_constant"/>
    <variable initial_value="5.68E-2" name="kd49" public_interface="out" units="first_order_rate_constant"/>
	<variable initial_value="4.5E-7" name="k50" public_interface="out" units="second_order_rate_constant"/>
    <variable initial_value="5E-1" name="kd50" public_interface="out" units="first_order_rate_constant"/>
    <variable initial_value="8.91E-5" name="k52" public_interface="out" units="second_order_rate_constant"/>
    <variable initial_value="3.3E-2" name="kd52" public_interface="out" units="first_order_rate_constant"/>
	<variable initial_value="0E0" name="k53" public_interface="out" units="second_order_rate_constant"/>
    <variable initial_value="1.6E1" name="kd53" public_interface="out" units="first_order_rate_constant"/>
    <variable initial_value="0E0" name="k55" public_interface="out" units="second_order_rate_constant"/>
    <variable initial_value="5.7E0" name="kd55" public_interface="out" units="first_order_rate_constant"/>
	<variable initial_value="2.35E-5" name="k56" public_interface="out" units="second_order_rate_constant"/>
    <variable initial_value="6E-1" name="kd56" public_interface="out" units="first_order_rate_constant"/>
    <variable initial_value="0E0" name="k57" public_interface="out" units="second_order_rate_constant"/>
    <variable initial_value="2.46E-1" name="kd57" public_interface="out" units="first_order_rate_constant"/>
	<variable initial_value="8.33E-6" name="k58" public_interface="out" units="second_order_rate_constant"/>
    <variable initial_value="5E-1" name="kd58" public_interface="out" units="first_order_rate_constant"/>
    <variable initial_value="5.5E-3" name="k60" public_interface="out" units="first_order_rate_constant"/>
    <variable initial_value="0E0" name="kd60" public_interface="out" units="first_order_rate_constant"/>
	<variable initial_value="6.7E-4" name="k61" public_interface="out" units="first_order_rate_constant"/>
    <variable initial_value="0E0" name="kd61" public_interface="out" units="first_order_rate_constant"/>
    <variable initial_value="2.75E-1" name="kd63" public_interface="out" units="first_order_rate_constant"/>
	<variable initial_value="1.66E-7" name="k126" public_interface="out" units="second_order_rate_constant"/>
    <variable initial_value="2E0" name="kd126" public_interface="out" units="first_order_rate_constant"/>
    <variable initial_value="0E0" name="k127" public_interface="out" units="second_order_rate_constant"/>
    <variable initial_value="1E-4" name="kd127" public_interface="out" units="first_order_rate_constant"/>
  </component>
  
  <!-- connections -->  

  <connection>
    <map_components component_1="c1" component_2="v1"/>
    <map_variables variable_1="c1" variable_2="c1"/>
    <map_variables variable_1="v1" variable_2="v1"/>
  </connection>

  <connection>
    <map_components component_1="c2" component_2="v1"/>
    <map_variables variable_1="c2" variable_2="c2"/>
    <map_variables variable_1="v1" variable_2="v1"/>
  </connection>

  <connection>
    <map_components component_1="c2" component_2="v6"/>
    <map_variables variable_1="c2" variable_2="c2"/>
    <map_variables variable_1="v6" variable_2="v6"/>
  </connection>

  <connection>
    <map_components component_1="c2" component_2="v13"/>
    <map_variables variable_1="c2" variable_2="c2"/>
    <map_variables variable_1="v13" variable_2="v13"/>
  </connection>
  
  <connection>
    <map_components component_1="c3" component_2="v1"/>
    <map_variables variable_1="c3" variable_2="c3"/>
    <map_variables variable_1="v1" variable_2="v1"/>
  </connection>
  
  <connection>
    <map_components component_1="c3" component_2="v2"/>
    <map_variables variable_1="c3" variable_2="c3"/>
    <map_variables variable_1="v2" variable_2="v2"/>
  </connection>
  
  <connection>
    <map_components component_1="c4" component_2="v2"/>
    <map_variables variable_1="c4" variable_2="c4"/>
    <map_variables variable_1="v2" variable_2="v2"/>
  </connection>
  
  <connection>
    <map_components component_1="c4" component_2="v3"/>
    <map_variables variable_1="c4" variable_2="c4"/>
    <map_variables variable_1="v3" variable_2="v3"/>
  </connection>
  
  <connection>
    <map_components component_1="c5" component_2="v3"/>
    <map_variables variable_1="c5" variable_2="c5"/>
    <map_variables variable_1="v3" variable_2="v3"/>
  </connection>
  
  <connection>
    <map_components component_1="c5" component_2="v7"/>
    <map_variables variable_1="c5" variable_2="c5"/>
    <map_variables variable_1="v7" variable_2="v7"/>
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    <rdf:li>signal transduction</rdf:li>
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    <rdf:li>MAPK</rdf:li>
    <rdf:li>kinetic model</rdf:li>
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    <vCard:Given xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#">Bernd</vCard:Given>
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    <dc:title xmlns:dc="http://purl.org/dc/elements/1.1/">Hornberg et al.'s 2005 mathematical model of the MAPK signal transduction cascade.</dc:title>
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    <rdf:value>This CellML model runs in both PCENv and COR to recreate the published results.  Thank you to the model author Jorrit Hornberg for providing us with the original mathematica code, and also to Joe Cursons for the hours he has spent debugging the CellMl model.</rdf:value>
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    <dc:title xmlns:dc="http://purl.org/dc/elements/1.1/">Control of MAPK signalling: from complexity to what really matters</dc:title>
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