Rendering of the source text

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<!--
This CellML file was generated on 3/05/2010 at 11:33:47 at a.m. using:

COR (0.9.31.1371)
Copyright 2002-2010 Dr Alan Garny
http://cor.physiol.ox.ac.uk/ - cor@physiol.ox.ac.uk

CellML 1.0 was used to generate this model
http://www.cellml.org/
--><model xmlns="http://www.cellml.org/cellml/1.0#" xmlns:cmeta="http://www.cellml.org/metadata/1.0#" cmeta:id="bornheimer_2004" name="bornheimer_2004">
	<documentation xmlns="http://cellml.org/tmp-documentation">
		<article>
			<articleinfo>
				<title>Dynamic rerouting of the carbohydrate flux is key to counteracting oxidative stress</title>
				<author>
					<firstname>Geoffrey</firstname>
					<surname>Nunns</surname>
					<affiliation>
						<shortaffil>Bioengineering Institute, University of Auckland</shortaffil>
					</affiliation>
				</author>
			</articleinfo>
			<section id="sec_status">
				<title>Model Status</title>
				<para>
				This CellML model runs in COR and OpenCell and the units are consistent throughout. It reproduces the published results and was converted from SBML with the help of Lukas Endler. Validation was done in both CellML and Matlab, Matlab was used to simulate variations in GAP and R concentrations and to reproduce figures 3A and B. 
				 
				</para>
			</section>
			<sect1 id="sec_structure">
				<title>Model Structure</title>
				<para>
ABSTRACT: Heterotrimeric G protein signaling is regulated by signaling modules composed of heterotrimeric G proteins, active G protein-coupled receptors (Rs), which activate G proteins, and GTPase-activating proteins (GAPs), which deactivate G proteins. We term these modules GTPase-cycle modules. The local concentrations of these proteins are spatially regulated between plasma membrane microdomains and between the plasma membrane and cytosol, but no data or models are available that quantitatively explain the effect of such regulation on signaling. We present a computational model of the GTPase-cycle module that predicts that the interplay of local G protein, R, and GAP concentrations gives rise to 16 distinct signaling regimes and numerous intermediate signaling phenomena. The regimes suggest alternative modes of the GTPase-cycle module that occur based on defined local concentrations of the component proteins. In one mode, signaling occurs while G protein and receptor are unclustered and GAP eliminates signaling; in another, G protein and receptor are clustered and GAP can rapidly modulate signaling but does not eliminate it. Experimental data from multiple GTPase-cycle modules is interpreted in light of these predictions. The latter mode explains previously paradoxical data in which GAP does not alter maximal current amplitude of G protein-activated ion channels, but hastens signaling. The predictions indicate how variations in local concentrations of the component proteins create GTPase-cycle modules with distinctive phenotypes. They provide a quantitative framework for investigating how regulation of local concentrations of components of the GTPase-cycle module affects signaling.
</para>
				<para>
The original paper reference is cited below:
</para>
				<para>
Computational modeling reveals how interplay between components of a GTPase-cycle module regulates signal transduction, Scott J. Bornheimer, Mano R. Maurya, Marilyn Gist Farquhar, and Shankar Subramaniam, 2004, <emphasis>PNAS</emphasis>, volume 101, 15899-15904.  <ulink url="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=pubmed&amp;cmd=Retrieve&amp;dopt=AbstractPlus&amp;list_uids=15520372&amp;query_hl=1&amp;itool=pubmed_docsum">PubMed ID: 15520372</ulink>
				</para>
				
				<informalfigure float="0" id="fig_reaction_diagram">
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  <imageobject>
    <objectinfo>
      <title>model diagram</title>
    </objectinfo>
    <imagedata fileref="bornheimer_2004.png"/>
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<caption>Biochemical reaction scheme of the GTPase cycle.</caption>
</informalfigure>
			</sect1>
		</article>
	</documentation>
	
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   <component name="A2">
      <variable name="A2" public_interface="out" units="molar_per_second"/>
      <variable initial_value="386000" name="k1" units="per_molar_per_second"/>
      <variable initial_value="0.0408" name="k2" units="per_second"/>
      <variable name="A" public_interface="in" units="molar"/>
      <variable name="GT" public_interface="in" units="molar"/>
      <variable name="GAT" public_interface="in" units="molar"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <ci>A2</ci>
            <apply>
               <minus/>
               <apply>
                  <times/>
                  <ci>k1</ci>
                  <ci>GT</ci>
                  <ci>A</ci>
               </apply>
               <apply>
                  <times/>
                  <ci>k2</ci>
                  <ci>GAT</ci>
               </apply>
            </apply>
         </apply>
      </math>
   </component>
   <component name="A3">
      <variable name="A3" public_interface="out" units="molar_per_second"/>
      <variable initial_value="64100" name="k1" units="per_molar_per_second"/>
      <variable initial_value="0.95" name="k2" units="per_second"/>
      <variable name="A" public_interface="in" units="molar"/>
      <variable name="GD" public_interface="in" units="molar"/>
      <variable name="GAD" public_interface="in" units="molar"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <ci>A3</ci>
            <apply>
               <minus/>
               <apply>
                  <times/>
                  <ci>k1</ci>
                  <ci>GD</ci>
                  <ci>A</ci>
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               <apply>
                  <times/>
                  <ci>k2</ci>
                  <ci>GAD</ci>
               </apply>
            </apply>
         </apply>
      </math>
   </component>
   <component name="R3">
      <variable name="R3" public_interface="out" units="molar_per_second"/>
      <variable initial_value="94700000" name="k1" units="per_molar_per_second"/>
      <variable initial_value="0.00227" name="k2" units="per_second"/>
      <variable name="R" public_interface="in" units="molar"/>
      <variable name="GD" public_interface="in" units="molar"/>
      <variable name="RGD" public_interface="in" units="molar"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <ci>R3</ci>
            <apply>
               <minus/>
               <apply>
                  <times/>
                  <ci>k1</ci>
                  <ci>GD</ci>
                  <ci>R</ci>
               </apply>
               <apply>
                  <times/>
                  <ci>k2</ci>
                  <ci>RGD</ci>
               </apply>
            </apply>
         </apply>
      </math>
   </component>
   <component name="P3">
      <variable name="P3" public_interface="out" units="molar_per_second"/>
      <variable initial_value="0.013" name="k1" public_interface="out" units="per_second"/>
      <variable initial_value="2.22e-9" name="k2" units="per_molar_per_second"/>
      <variable name="Pi_" public_interface="in" units="molar"/>
      <variable name="RGT" public_interface="in" units="molar"/>
      <variable name="RGD" public_interface="in" units="molar"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <ci>P3</ci>
            <apply>
               <minus/>
               <apply>
                  <times/>
                  <ci>k1</ci>
                  <ci>RGT</ci>
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               <apply>
                  <times/>
                  <ci>k2</ci>
                  <ci>RGD</ci>
                  <ci>Pi_</ci>
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            </apply>
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      </math>
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   <component name="D3">
      <variable name="D3" public_interface="out" units="molar_per_second"/>
      <variable initial_value="2" name="k1" units="per_second"/>
      <variable initial_value="1470000" name="k2" units="per_molar_per_second"/>
      <variable name="D" public_interface="in" units="molar"/>
      <variable name="RG" public_interface="in" units="molar"/>
      <variable name="RGD" public_interface="in" units="molar"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <ci>D3</ci>
            <apply>
               <minus/>
               <apply>
                  <times/>
                  <ci>k1</ci>
                  <ci>RGD</ci>
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               <apply>
                  <times/>
                  <ci>k2</ci>
                  <ci>RG</ci>
                  <ci>D</ci>
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            </apply>
         </apply>
      </math>
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   <component name="T2">
      <variable name="T2" public_interface="out" units="molar_per_second"/>
      <variable initial_value="44700" name="k1" units="per_molar_per_second"/>
      <variable initial_value="8.32e-8" name="k2" units="per_second"/>
      <variable name="GA" public_interface="in" units="molar"/>
      <variable name="T" public_interface="in" units="molar"/>
      <variable name="GAT" public_interface="in" units="molar"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <ci>T2</ci>
            <apply>
               <minus/>
               <apply>
                  <times/>
                  <ci>k1</ci>
                  <ci>GA</ci>
                  <ci>T</ci>
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               <apply>
                  <times/>
                  <ci>k2</ci>
                  <ci>GAT</ci>
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            </apply>
         </apply>
      </math>
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      <variable name="P2" public_interface="out" units="molar_per_second"/>
      <variable initial_value="25" name="k1" public_interface="out" units="per_second"/>
      <variable initial_value="0.244" name="k2" units="per_molar_per_second"/>
      <variable name="Pi_" public_interface="in" units="molar"/>
      <variable name="GAT" public_interface="in" units="molar"/>
      <variable name="GAD" public_interface="in" units="molar"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <ci>P2</ci>
            <apply>
               <minus/>
               <apply>
                  <times/>
                  <ci>k1</ci>
                  <ci>GAT</ci>
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               <apply>
                  <times/>
                  <ci>k2</ci>
                  <ci>GAD</ci>
                  <ci>Pi_</ci>
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   <component name="D2">
      <variable name="D2" public_interface="out" units="molar_per_second"/>
      <variable initial_value="0.0001" name="k1" units="per_second"/>
      <variable initial_value="3.83" name="k2" units="per_molar_per_second"/>
      <variable name="GA" public_interface="in" units="molar"/>
      <variable name="D" public_interface="in" units="molar"/>
      <variable name="GAD" public_interface="in" units="molar"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <ci>D2</ci>
            <apply>
               <minus/>
               <apply>
                  <times/>
                  <ci>k1</ci>
                  <ci>GAD</ci>
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               <apply>
                  <times/>
                  <ci>k2</ci>
                  <ci>GA</ci>
                  <ci>D</ci>
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            </apply>
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      </math>
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   <component name="A4">
      <variable name="A4" public_interface="out" units="molar_per_second"/>
      <variable initial_value="74300" name="k1" units="per_molar_per_second"/>
      <variable initial_value="0.00572" name="k2" units="per_second"/>
      <variable name="A" public_interface="in" units="molar"/>
      <variable name="RG" public_interface="in" units="molar"/>
      <variable name="RGA" public_interface="in" units="molar"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <ci>A4</ci>
            <apply>
               <minus/>
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                  <times/>
                  <ci>k1</ci>
                  <ci>RG</ci>
                  <ci>A</ci>
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                  <times/>
                  <ci>k2</ci>
                  <ci>RGA</ci>
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   <component name="R4">
      <variable name="R4" public_interface="out" units="molar_per_second"/>
      <variable initial_value="22800000" name="k1" units="per_molar_per_second"/>
      <variable initial_value="5.43e-5" name="k2" units="per_second"/>
      <variable name="GA" public_interface="in" units="molar"/>
      <variable name="R" public_interface="in" units="molar"/>
      <variable name="RGA" public_interface="in" units="molar"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <ci>R4</ci>
            <apply>
               <minus/>
               <apply>
                  <times/>
                  <ci>k1</ci>
                  <ci>GA</ci>
                  <ci>R</ci>
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                  <times/>
                  <ci>k2</ci>
                  <ci>RGA</ci>
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         </apply>
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   <component name="T4">
      <variable name="T4" public_interface="out" units="molar_per_second"/>
      <variable initial_value="1620000" name="k1" units="per_molar_per_second"/>
      <variable initial_value="0.00875" name="k2" units="per_second"/>
      <variable name="T" public_interface="in" units="molar"/>
      <variable name="RGA" public_interface="in" units="molar"/>
      <variable name="RGAT" public_interface="in" units="molar"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <ci>T4</ci>
            <apply>
               <minus/>
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                  <times/>
                  <ci>k1</ci>
                  <ci>RGA</ci>
                  <ci>T</ci>
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                  <times/>
                  <ci>k2</ci>
                  <ci>RGAT</ci>
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   <component name="R5">
      <variable name="R5" public_interface="out" units="molar_per_second"/>
      <variable initial_value="6200000" name="k1" units="per_molar_per_second"/>
      <variable initial_value="0.0433" name="k2" units="per_second"/>
      <variable name="R" public_interface="in" units="molar"/>
      <variable name="GAT" public_interface="in" units="molar"/>
      <variable name="RGAT" public_interface="in" units="molar"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <ci>R5</ci>
            <apply>
               <minus/>
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                  <times/>
                  <ci>k1</ci>
                  <ci>GAT</ci>
                  <ci>R</ci>
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                  <times/>
                  <ci>k2</ci>
                  <ci>RGAT</ci>
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   <component name="A5">
      <variable name="A5" public_interface="out" units="molar_per_second"/>
      <variable initial_value="6300000" name="k1" units="per_molar_per_second"/>
      <variable initial_value="0.478" name="k2" units="per_second"/>
      <variable name="A" public_interface="in" units="molar"/>
      <variable name="RGT" public_interface="in" units="molar"/>
      <variable name="RGAT" public_interface="in" units="molar"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <ci>A5</ci>
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               <minus/>
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                  <times/>
                  <ci>k1</ci>
                  <ci>RGT</ci>
                  <ci>A</ci>
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                  <times/>
                  <ci>k2</ci>
                  <ci>RGAT</ci>
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         </apply>
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   <component name="P4">
      <variable name="P4" public_interface="out" units="molar_per_second"/>
      <variable initial_value="25" name="k1" public_interface="out" units="per_second"/>
      <variable initial_value="0.00297" name="k2" units="per_molar_per_second"/>
      <variable name="Pi_" public_interface="in" units="molar"/>
      <variable name="RGAT" public_interface="in" units="molar"/>
      <variable name="RGAD" public_interface="in" units="molar"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <ci>P4</ci>
            <apply>
               <minus/>
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                  <times/>
                  <ci>k1</ci>
                  <ci>RGAT</ci>
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                  <times/>
                  <ci>k2</ci>
                  <ci>RGAD</ci>
                  <ci>Pi_</ci>
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   <component name="A6">
      <variable name="A6" public_interface="out" units="molar_per_second"/>
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      <variable name="RGD" public_interface="in" units="molar"/>
      <variable name="RGAD" public_interface="in" units="molar"/>
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            <ci>A6</ci>
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               <minus/>
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                  <ci>k1</ci>
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                  <times/>
                  <ci>k2</ci>
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      <variable name="RGAD" public_interface="in" units="molar"/>
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            <ci>R6</ci>
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               <minus/>
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                  <ci>k1</ci>
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                  <times/>
                  <ci>k2</ci>
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      <variable initial_value="2940" name="k2" units="per_molar_per_second"/>
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            <ci>D4</ci>
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               <minus/>
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                  <times/>
                  <ci>k2</ci>
                  <ci>RGA</ci>
                  <ci>D</ci>
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      <map_components component_1="environment" component_2="differentials"/>
      <map_variables variable_1="time" variable_2="time"/>
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      <map_components component_1="output" component_2="differentials"/>
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      <map_variables variable_1="RGT" variable_2="RGT"/>
      <map_variables variable_1="GAT" variable_2="GAT"/>
      <map_variables variable_1="RGAT" variable_2="RGAT"/>
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      <map_components component_1="output" component_2="P1"/>
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      <map_components component_1="output" component_2="P2"/>
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      <map_components component_1="output" component_2="P3"/>
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      <map_components component_1="output" component_2="P4"/>
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      <map_variables variable_1="GT" variable_2="GT"/>
      <map_variables variable_1="GD" variable_2="GD"/>
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      <map_variables variable_1="D1" variable_2="D1"/>
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      <map_variables variable_1="GD" variable_2="GD"/>
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      <map_variables variable_1="T3" variable_2="T3"/>
      <map_variables variable_1="T" variable_2="T"/>
      <map_variables variable_1="RG" variable_2="RG"/>
      <map_variables variable_1="RGT" variable_2="RGT"/>
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      <map_variables variable_1="R2" variable_2="R2"/>
      <map_variables variable_1="R" variable_2="R"/>
      <map_variables variable_1="GT" variable_2="GT"/>
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      <map_variables variable_1="RGD" variable_2="RGD"/>
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      <map_components component_1="P3" component_2="differentials"/>
      <map_variables variable_1="P3" variable_2="P3"/>
      <map_variables variable_1="Pi_" variable_2="Pi_"/>
      <map_variables variable_1="RGT" variable_2="RGT"/>
      <map_variables variable_1="RGD" variable_2="RGD"/>
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      <map_components component_1="D3" component_2="differentials"/>
      <map_variables variable_1="D3" variable_2="D3"/>
      <map_variables variable_1="D" variable_2="D"/>
      <map_variables variable_1="RG" variable_2="RG"/>
      <map_variables variable_1="RGD" variable_2="RGD"/>
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   <connection>
      <map_components component_1="T2" component_2="differentials"/>
      <map_variables variable_1="T2" variable_2="T2"/>
      <map_variables variable_1="GA" variable_2="GA"/>
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      <map_variables variable_1="GAT" variable_2="GAT"/>
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   <connection>
      <map_components component_1="P2" component_2="differentials"/>
      <map_variables variable_1="P2" variable_2="P2"/>
      <map_variables variable_1="Pi_" variable_2="Pi_"/>
      <map_variables variable_1="GAT" variable_2="GAT"/>
      <map_variables variable_1="GAD" variable_2="GAD"/>
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      <map_components component_1="D2" component_2="differentials"/>
      <map_variables variable_1="D2" variable_2="D2"/>
      <map_variables variable_1="GA" variable_2="GA"/>
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      <map_variables variable_1="GAD" variable_2="GAD"/>
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   <connection>
      <map_components component_1="A4" component_2="differentials"/>
      <map_variables variable_1="A4" variable_2="A4"/>
      <map_variables variable_1="A" variable_2="A"/>
      <map_variables variable_1="RG" variable_2="RG"/>
      <map_variables variable_1="RGA" variable_2="RGA"/>
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   <connection>
      <map_components component_1="R4" component_2="differentials"/>
      <map_variables variable_1="R4" variable_2="R4"/>
      <map_variables variable_1="GA" variable_2="GA"/>
      <map_variables variable_1="R" variable_2="R"/>
      <map_variables variable_1="RGA" variable_2="RGA"/>
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   <connection>
      <map_components component_1="T4" component_2="differentials"/>
      <map_variables variable_1="T4" variable_2="T4"/>
      <map_variables variable_1="T" variable_2="T"/>
      <map_variables variable_1="RGA" variable_2="RGA"/>
      <map_variables variable_1="RGAT" variable_2="RGAT"/>
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   <connection>
      <map_components component_1="R5" component_2="differentials"/>
      <map_variables variable_1="R5" variable_2="R5"/>
      <map_variables variable_1="R" variable_2="R"/>
      <map_variables variable_1="GAT" variable_2="GAT"/>
      <map_variables variable_1="RGAT" variable_2="RGAT"/>
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   <connection>
      <map_components component_1="A5" component_2="differentials"/>
      <map_variables variable_1="A5" variable_2="A5"/>
      <map_variables variable_1="A" variable_2="A"/>
      <map_variables variable_1="RGT" variable_2="RGT"/>
      <map_variables variable_1="RGAT" variable_2="RGAT"/>
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   <connection>
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