Location: Chassagnole, Rais, Quentin, Fell, Mazat, 2001 @ c3057cca7199 / chassagnole_rais_quentin_fell_mazat_2001.cellml

Author:
pmr2.import <nobody@models.cellml.org>
Date:
2006-07-09 07:19:37+12:00
Desc:
committing version01 of chassagnole_rais_quentin_fell_mazat_2001
Permanent Source URI:
https://models.cellml.org/workspace/chassagnole_rais_quentin_fell_mazat_2001/rawfile/c3057cca71994933eac3cb91cd97a54aa25227e8/chassagnole_rais_quentin_fell_mazat_2001.cellml

<?xml version='1.0' encoding='utf-8'?>
<!--  FILE :  chassagnole_model_2001.xml

CREATED :  9th April 2001

LAST MODIFIED : 9th April 2003

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

DESCRIPTION :  This file contains a CellML description of Chassagnole et al's 2001 model of the threonine-synthesis metabolic pathway in the bacterium Escherichia coli.

CHANGES:  
  18/07/2002 - CML - Added more metadata.
  09/04/2003 - AAC - Added publication date information.  
--><model xmlns="http://www.cellml.org/cellml/1.0#" xmlns:cmeta="http://www.cellml.org/metadata/1.0#" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:bqs="http://www.cellml.org/bqs/1.0#" xmlns:cellml="http://www.cellml.org/cellml/1.0#" xmlns:dcterms="http://purl.org/dc/terms/" xmlns:pathway_editor="http://www.physiome.com/pathway_editor/1.0#" xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" cmeta:id="chassagnole_rais_quentin_fell_mazat_2001_version01" name="chassagnole_rais_quentin_fell_mazat_2001_version01">
<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
  <articleinfo>
  <title>The Threonine-Synthesis Pathway In Escherichia coli</title>
  <author>
    <firstname>Catherine</firstname>
          <surname>Lloyd</surname>
    <affiliation>
      <shortaffil>Bioengineering Institute, University of Auckland</shortaffil>
    </affiliation>
  </author>
</articleinfo>
  <section id="sec_status">
    <title>Model Status</title>
    <para>
            This is the original unchecked version of the model imported from the previous
            CellML model repository, 24-Jan-2006.
          </para>
  </section>
  <sect1 id="sec_structure">
<title>Model Structure</title>

<para>
Threonine is an essential amino acid for birds and mammals.  Since it can't be synthesised <emphasis>in vivo</emphasis> and must therefore be acquired through the diet, there is a considerable interest in its economic industrial production.  The five-step metabolic pathway for threonine synthesis from aspartate in the bacterium <emphasis>Escherichia coli</emphasis> (<emphasis>E. coli</emphasis>) has been well characterised.  The kinetics of all the five pathway enzymes from <emphasis>E. coli</emphasis> have previously been studied extensively, however, this information has not been applied to producing a global theoretical model of the pathway under conditions <emphasis>in vivo</emphasis>.  Not only have experimental temperatures and pH levels been well outside the physiological range, but also many studies have not considered the effects of end-product inhibition, negative feedback control or reversible reactions.
</para>

<para>
In 2001, Christophe Chassagnole, Badr Rais, Eric Quentin, David A. Fell and Jean-Pierre Mazat published a kinetic model describing the threonine-synthesis pathway in <emphasis>E. coli</emphasis> (see <xref linkend="fig_reaction_diagram"/> below).  Their aim was to summarise the kinetic behaviour of each enzyme in a single equation.  This equation accounts for the effect of the products as competitive inhibitors of the substrates in the forward reaction and where applicable, as substrates of the reverse reactions.  Co-operative feedback inhibition by threonine and lysine was also included.  Each individual rate equation was then incorporated into a complete theoretical model of the threonine pathway.  This model is able to predict the behaviour of the pathway under natural or engineered conditions.  
</para>

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

<para>
<ulink url="http://www.biochemj.org/bj/356/bj3560415.htm">An integrated study of threonine-pathway enzyme kinetics in <emphasis>Escherichia coli</emphasis>
          </ulink>, Christophe Chassagnole, Badr Rais, Eric Quentin, David A. Fell and Jean-Pierre Mazat, 2001, <ulink url="http://www.biochemj.org/">
            <emphasis>Biochemical Journal</emphasis>
          </ulink>, 356, 415-423.  (The <ulink url="http://www.biochemj.org/bj/356/0415/3560415.pdf">PDF</ulink> and <ulink url="http://www.biochemj.org/bj/356/0415/bj3560415.htm">full text</ulink> versions of the article are available on the Biochemical Journal website.)  <ulink url="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&amp;db=PubMed&amp;list_uids=11368768&amp;dopt=Abstract">PubMed ID: 11368768</ulink>
</para>

<para>
The raw CellML description of the model can be downloaded in various formats as described in <xref linkend="sec_download_this_model"/>.
</para>

<informalfigure float="0" id="fig_reaction_diagram">
<mediaobject>
  <imageobject>
    <objectinfo>
      <title>schematic diagram</title>
    </objectinfo>
    <imagedata fileref="reaction_diagram.gif"/>
  </imageobject>
</mediaobject>
<caption>Threonine-synthesis pathway from aspartate in <emphasis>E. coli</emphasis>.  The different steps are catalysed by aspartate kinases I and III (AK I and AK III), aspartate semialdehyde dehydrogenase (ASD), homoserine dehydrogenase (HDH), homoserine kinase (HK) and threonine synthase (TS).  The abbreviations used are: asp, aspartate; aspp, beta-aspartyl phosphate; ASA, aspartic beta-semialdehyde; hs, homoserine; hsp, O-phospho-homoserine; thr, threonine and lys, lysine.  Solid black lines represent the individual reaction steps of the pathway and the dashed red lines represent reaction inhibition by threonine and lysine.</caption>
</informalfigure>

</sect1>
</article>
</documentation>
  
  
  <!--
    We start the model definition with a definition of some named
    sets of units for use throughout the model.
  -->
  
  <units name="minute">
    <unit units="second" multiplier="60.0"/>
  </units>
  
  <units name="molar">
    <unit units="mole"/>
    <unit units="litre" exponent="-1"/>
  </units>
  
  <units name="millimolar">
    <unit units="mole" prefix="milli"/>
    <unit units="litre" exponent="-1"/>
  </units>
  
  <units name="per_molar">
    <unit units="molar" exponent="-1"/>
  </units>

  <units name="flux">
    <unit units="millimolar"/>
    <unit units="minute" exponent="-1"/>
  </units>

  <units name="first_order_rate_constant">
    <unit units="minute" exponent="-1"/>
  </units>
  
  <units name="second_order_rate_constant">
    <unit units="millimolar" exponent="-1"/>
    <unit units="minute" exponent="-1"/>
  </units>
  
  <component name="environment">
    <variable units="minute" public_interface="out" name="time"/>
  </component>
  
  <component cmeta:id="asp" name="asp">
    
    <variable units="millimolar" public_interface="out" name="asp"/>
    <variable units="flux" public_interface="in" name="delta_asp_rxn1"/>
    <variable units="flux" public_interface="in" name="delta_asp_rxn6"/>
    <variable units="minute" public_interface="in" name="time"/>
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply>
        <eq/>
        <apply>
          <diff/>
          <bvar>
            <ci>time</ci>
          </bvar>
          <ci>asp</ci>
        </apply>
        <apply>
          <plus/>
          <ci>delta_asp_rxn1</ci>
          <ci>delta_asp_rxn6</ci>
        </apply>
      </apply>
    </math>
  </component>
  
  <component cmeta:id="aspp" name="aspp">
    
    <variable units="millimolar" public_interface="out" name="aspp"/>
    <variable units="flux" public_interface="in" name="delta_aspp_rxn1"/>
    <variable units="flux" public_interface="in" name="delta_aspp_rxn2"/>
    <variable units="flux" public_interface="in" name="delta_aspp_rxn6"/>
    <variable units="minute" public_interface="in" name="time"/>
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply>
        <eq/>
        <apply>
          <diff/>
          <bvar>
            <ci>time</ci>
          </bvar>
          <ci>aspp</ci>
        </apply>
        <apply>
          <plus/>
          <ci>delta_aspp_rxn1</ci>
          <ci>delta_aspp_rxn2</ci>
          <ci>delta_aspp_rxn6</ci>
        </apply>
      </apply>
    </math>
  </component>
  
  <component cmeta:id="ASA" name="ASA">
    
    <variable units="millimolar" public_interface="out" name="ASA"/>
    <variable units="flux" public_interface="in" name="delta_ASA_rxn2"/>
    <variable units="flux" public_interface="in" name="delta_ASA_rxn3"/>
    <variable units="minute" public_interface="in" name="time"/>
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply>
        <eq/>
        <apply>
          <diff/>
          <bvar>
            <ci>time</ci>
          </bvar>
          <ci>ASA</ci>
        </apply>
        <apply>
          <plus/>
          <ci>delta_ASA_rxn2</ci>
          <ci>delta_ASA_rxn3</ci>
        </apply>
      </apply>
    </math>
  </component>
  
  <component cmeta:id="hs" name="hs">
    
    <variable units="millimolar" public_interface="out" name="hs"/>
    <variable units="flux" public_interface="in" name="delta_hs_rxn3"/>
    <variable units="flux" public_interface="in" name="delta_hs_rxn4"/>
    <variable units="minute" public_interface="in" name="time"/>
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply>
        <eq/>
        <apply>
          <diff/>
          <bvar>
            <ci>time</ci>
          </bvar>
          <ci>hs</ci>
        </apply>
        <apply>
          <plus/>
          <ci>delta_hs_rxn3</ci>
          <ci>delta_hs_rxn4</ci>
        </apply>
      </apply>
    </math>
  </component>
  
  <component cmeta:id="hsp" name="hsp">
    
    <variable units="millimolar" public_interface="out" name="hsp"/>
    <variable units="flux" public_interface="in" name="delta_hsp_rxn4"/>
    <variable units="flux" public_interface="in" name="delta_hsp_rxn5"/>
    <variable units="minute" public_interface="in" name="time"/>
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply>
        <eq/>
        <apply>
          <diff/>
          <bvar>
            <ci>time</ci>
          </bvar>
          <ci>hsp</ci>
        </apply>
        <apply>
          <plus/>
          <ci>delta_hsp_rxn4</ci>
          <ci>delta_hsp_rxn5</ci>
        </apply>
      </apply>
    </math>
  </component>
  
  <component cmeta:id="thr" name="thr">
    
    <variable units="millimolar" public_interface="out" name="thr"/>
    <variable units="flux" public_interface="in" name="delta_thr_rxn5"/>
    <variable units="minute" public_interface="in" name="time"/>
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply>
        <eq/>
        <apply>
          <diff/>
          <bvar>
            <ci>time</ci>
          </bvar>
          <ci>thr</ci>
        </apply>
        <ci>delta_thr_rxn5</ci>
      </apply>
    </math>
  </component>
    
  <component name="ATP">
    <variable units="millimolar" public_interface="out" name="ATP"/>
    <variable units="flux" public_interface="in" name="delta_ATP_rxn1"/>
    <variable units="flux" public_interface="in" name="delta_ATP_rxn4"/>
    <variable units="flux" public_interface="in" name="delta_ATP_rxn6"/>
    <variable units="minute" public_interface="in" name="time"/>
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply>
        <eq/>
        <apply>
          <diff/>
          <bvar>
            <ci>time</ci>
          </bvar>
          <ci>ATP</ci>
        </apply>
        <apply>
          <plus/>
          <ci>delta_ATP_rxn1</ci> 
          <ci>delta_ATP_rxn4</ci>
          <ci>delta_ATP_rxn6</ci>
        </apply>
      </apply>
    </math>
  </component>
  
  <component name="ADP">
    <variable units="millimolar" public_interface="out" name="ADP"/>
    <variable units="flux" public_interface="in" name="delta_ADP_rxn1"/>
    <variable units="flux" public_interface="in" name="delta_ADP_rxn4"/>
    <variable units="flux" public_interface="in" name="delta_ADP_rxn6"/>
    <variable units="minute" public_interface="in" name="time"/>
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply>
        <eq/>
        <apply>
          <diff/>
          <bvar>
            <ci>time</ci>
          </bvar>
          <ci>ADP</ci>
        </apply>
        <apply>
          <plus/>
          <ci>delta_ADP_rxn1</ci> 
          <ci>delta_ADP_rxn4</ci>
          <ci>delta_ADP_rxn6</ci>
        </apply>
      </apply>
    </math>
  </component>
  
  <component name="NADPH">
    <variable units="millimolar" public_interface="out" name="NADPH"/>
    <variable units="flux" public_interface="in" name="delta_NADPH_rxn2"/>
    <variable units="flux" public_interface="in" name="delta_NADPH_rxn3"/>
    <variable units="minute" public_interface="in" name="time"/>
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply>
        <eq/>
        <apply>
          <diff/>
          <bvar>
            <ci>time</ci>
          </bvar>
          <ci>NADPH</ci>
        </apply>
        <apply>
          <plus/>
          <ci>delta_NADPH_rxn2</ci> 
          <ci>delta_NADPH_rxn3</ci>
        </apply>
      </apply>
    </math>
  </component>
  
  <component name="NADP">
    <variable units="millimolar" public_interface="out" name="NADP"/>
    <variable units="flux" public_interface="in" name="delta_NADP_rxn2"/>
    <variable units="flux" public_interface="in" name="delta_NADP_rxn3"/>
    <variable units="minute" public_interface="in" name="time"/>
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply>
        <eq/>
        <apply>
          <diff/>
          <bvar>
            <ci>time</ci>
          </bvar>
          <ci>NADP</ci>
        </apply>
        <apply>
          <plus/>
          <ci>delta_NADP_rxn2</ci> 
          <ci>delta_NADP_rxn3</ci>
        </apply>
      </apply>
    </math>
  </component>
  
  <component name="Pi">
    <variable units="millimolar" public_interface="out" name="Pi"/>
    <variable units="flux" public_interface="in" name="delta_Pi_rxn2"/>
    <variable units="flux" public_interface="in" name="delta_Pi_rxn5"/>
    <variable units="minute" public_interface="in" name="time"/>
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply>
        <eq/>
        <apply>
          <diff/>
          <bvar>
            <ci>time</ci>
          </bvar>
          <ci>Pi</ci>
        </apply>
        <apply>
          <plus/>
          <ci>delta_Pi_rxn2</ci> 
          <ci>delta_Pi_rxn5</ci>
        </apply>
      </apply>
    </math>
  </component>
  
  <component name="PLP">
    <variable units="millimolar" public_interface="out" name="PLP"/>
    <variable units="flux" public_interface="in" name="delta_PLP_rxn5"/>
    <variable units="minute" public_interface="in" name="time"/>
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply>
        <eq/>
        <apply>
          <diff/>
          <bvar>
            <ci>time</ci>
          </bvar>
          <ci>PLP</ci>
        </apply>
        <ci>delta_PLP_rxn5</ci>
      </apply>
    </math>
  </component>
  
  <component name="H2O">
    <variable units="millimolar" public_interface="out" name="H2O"/>
    <variable units="flux" public_interface="in" name="delta_H2O_rxn5"/>
    <variable units="minute" public_interface="in" name="time"/>
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply>
        <eq/>
        <apply>
          <diff/>
          <bvar>
            <ci>time</ci>
          </bvar>
          <ci>H2O</ci>
        </apply>
        <ci>delta_H2O_rxn5</ci>
      </apply>
    </math>
  </component>
  
  <component cmeta:id="lys" name="lys">
    
    <variable units="millimolar" public_interface="out" name="lys"/>
  </component>
  
  <component cmeta:id="AK_I" name="AK_I">
    
    <variable units="millimolar" public_interface="out" name="AK_I"/>
  </component>
  
  <component cmeta:id="AK_III" name="AK_III">
    
    <variable units="millimolar" public_interface="out" name="AK_III"/>
  </component>
  
  <component cmeta:id="ASD" name="ASD">
    
    <variable units="millimolar" public_interface="out" name="ASD"/>
  </component>
  
  <component cmeta:id="HDH" name="HDH">
    
    <variable units="millimolar" public_interface="out" name="HDH"/>
  </component>
  
  <component cmeta:id="HK" name="HK">
    
    <variable units="millimolar" public_interface="out" name="HK"/>
  </component>
  
  <component cmeta:id="TS" name="TS">
    
    <variable units="millimolar" public_interface="out" name="TS"/>
  </component>
  
  <component name="reaction_1">
    <variable units="millimolar" public_interface="in" name="asp"/>
    <variable units="millimolar" public_interface="in" name="aspp"/>
    <variable units="millimolar" public_interface="in" name="ATP"/>
    <variable units="millimolar" public_interface="in" name="ADP"/>
    <variable units="millimolar" public_interface="in" name="thr"/>
    <variable units="millimolar" public_interface="in" name="AK_I"/>
    <variable units="millimolar" name="k_asp" initial_value="0.97"/>
    <variable units="millimolar" name="k_ATP" initial_value="0.98"/>
    <variable units="millimolar" name="k_aspp" initial_value="0.017"/>
    <variable units="millimolar" name="k_ADP" initial_value="0.25"/>
    <variable units="millimolar" name="k_ithr" initial_value="0.167"/>
    <variable units="dimensionless" name="alpha" initial_value="2.47"/>
    <variable units="dimensionless" name="h_thr" initial_value="4.09"/>
    <variable units="dimensionless" name="k_eq" initial_value="0.00064"/>
    <variable units="flux" name="V_max_AK_I"/>
    <variable units="flux" public_interface="out" name="delta_asp_rxn1"/>
    <variable units="flux" public_interface="out" name="delta_aspp_rxn1"/>
    <variable units="flux" public_interface="out" name="delta_ATP_rxn1"/>
    <variable units="flux" public_interface="out" name="delta_ADP_rxn1"/>
    <variable units="flux" name="r"/>
    <reaction reversible="yes">
      <variable_ref variable="asp">
        <role stoichiometry="1" direction="forward" delta_variable="delta_asp_rxn1" role="reactant"/>
      </variable_ref>
      <variable_ref variable="ATP">
        <role stoichiometry="1" direction="forward" delta_variable="delta_ATP_rxn1" role="reactant"/>
      </variable_ref>
      <variable_ref variable="aspp">
        <role stoichiometry="1" direction="forward" delta_variable="delta_aspp_rxn1" role="product"/>
      </variable_ref>
      <variable_ref variable="ADP">
        <role stoichiometry="1" direction="forward" delta_variable="delta_ADP_rxn1" role="product"/>
      </variable_ref> 
      <variable_ref variable="AK_I">
        <role direction="forward" role="catalyst"/>
      </variable_ref>
      <variable_ref variable="thr">
        <role direction="forward" role="inhibitor"/>
      </variable_ref>
      <variable_ref variable="r">
        <role role="rate">
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
              <eq/>
              <ci> r </ci>
              <apply>
                <divide/>
                <apply>
                  <times/>
                  <ci> V_max_AK_I </ci>
                  <apply>
                    <minus/>
                    <apply>
                      <times/>
                      <ci> asp </ci>
                      <ci> ATP </ci>
                    </apply>
                    <apply>
                      <divide/>
                      <apply>
                        <times/>
                        <ci> aspp </ci>
                        <ci> ADP </ci>
                      </apply>
                      <ci> k_eq </ci>
                    </apply>
                  </apply>
                </apply>
                <apply>
                  <times/>
                  <apply>
                    <plus/>
                    <apply>
                      <times/>
                      <ci> k_asp </ci>
                      <apply>
                        <divide/>
                        <apply>
                          <plus/>
                          <cn cellml:units="dimensionless"> 1.0 </cn>
                          <apply>
                            <power/>
                            <apply>
                              <divide/>
                              <ci> thr </ci>
                              <ci> k_ithr </ci>
                            </apply>
                            <ci> h_thr </ci>
                          </apply>
                        </apply>
                        <apply>
                          <plus/>
                          <cn cellml:units="dimensionless"> 1.0 </cn>
                          <apply>
                            <power/>
                            <apply>
                              <divide/>
                              <ci> thr </ci>
                              <apply>
                                <times/>
                                <ci> k_ithr </ci>
                                <ci> alpha </ci>
                              </apply>
                            </apply>
                            <ci> h_thr </ci>
                          </apply>
                        </apply>
                      </apply>
                    </apply>
                    <apply>
                      <times/>
                      <ci> aspp </ci>
                      <apply>
                        <divide/>
                        <ci> k_asp </ci>
                        <ci> k_aspp </ci>
                      </apply>
                    </apply>
                    <ci> asp </ci>
                  </apply>
                  <apply>
                    <plus/>
                    <apply>
                      <times/>
                      <ci> k_ATP </ci>
                      <apply>
                        <plus/>
                        <cn cellml:units="dimensionless"> 1.0 </cn>
                        <apply>
                          <divide/>
                          <ci> ADP </ci>
                          <ci> k_ADP </ci>
                        </apply>
                      </apply>
                    </apply>
                    <ci> ATP </ci>
                  </apply>
                </apply>
              </apply>
            </apply>
          </math>
        </role>
      </variable_ref>
    </reaction>
  </component>
  
  <component name="reaction_2">
    <variable units="millimolar" public_interface="in" name="aspp"/>
    <variable units="millimolar" public_interface="in" name="ASA"/>
    <variable units="millimolar" public_interface="in" name="NADPH"/>
    <variable units="millimolar" public_interface="in" name="NADP"/>
    <variable units="millimolar" public_interface="in" name="Pi"/>
    <variable units="millimolar" public_interface="in" name="ASD"/>
    <variable units="millimolar" name="k_aspp" initial_value="0.022"/>
    <variable units="millimolar" name="k_NADPH" initial_value="0.029"/>
    <variable units="millimolar" name="k_ASA" initial_value="0.11"/>
    <variable units="millimolar" name="k_NADP" initial_value="0.144"/>
    <variable units="millimolar" name="k_Pi" initial_value="10.2"/>
    <variable units="dimensionless" name="k_eq" initial_value="284000.0"/>
    <variable units="flux" name="V_max_ASD"/>
    <variable units="flux" public_interface="out" name="delta_aspp_rxn2"/>
    <variable units="flux" public_interface="out" name="delta_ASA_rxn2"/>
    <variable units="flux" public_interface="out" name="delta_NADPH_rxn2"/>
    <variable units="flux" public_interface="out" name="delta_NADP_rxn2"/>
    <variable units="flux" public_interface="out" name="delta_Pi_rxn2"/>
    <variable units="flux" name="r"/>
    <reaction reversible="yes">
      <variable_ref variable="aspp">
        <role stoichiometry="1" direction="forward" delta_variable="delta_aspp_rxn2" role="reactant"/>
      </variable_ref>
      <variable_ref variable="NADPH">
        <role stoichiometry="1" direction="forward" delta_variable="delta_NADPH_rxn2" role="reactant"/>
      </variable_ref>
      <variable_ref variable="ASA">
        <role stoichiometry="1" direction="forward" delta_variable="delta_ASA_rxn2" role="product"/>
      </variable_ref>
      <variable_ref variable="NADP">
        <role stoichiometry="1" direction="forward" delta_variable="delta_NADP_rxn2" role="product"/>
      </variable_ref> 
      <variable_ref variable="ASD">
        <role direction="forward" role="catalyst"/>
      </variable_ref>
      <variable_ref variable="Pi">
        <role stoichiometry="1" direction="forward" delta_variable="delta_Pi_rxn2" role="product"/>
      </variable_ref>
      <variable_ref variable="r">
        <role role="rate">
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
              <eq/>
              <ci> r </ci>
              <apply>
                <divide/>
                <apply>
                  <times/>
                  <ci> V_max_ASD </ci>
                  <apply>
                    <minus/>
                    <apply>
                      <times/>
                      <ci> aspp </ci>
                      <ci> NADPH </ci>
                    </apply>
                    <apply>
                      <divide/>
                      <apply>
                        <times/>
                        <ci> ASA </ci>
                        <ci> NADP </ci>
                        <ci> Pi </ci>
                      </apply>
                      <ci> k_eq </ci>
                    </apply>
                  </apply>
                </apply>
                <apply>
                  <times/>
                  <apply>
                    <plus/>
                    <apply>
                      <times/>
                      <ci> k_aspp </ci>
                      <apply>
                        <plus/>
                        <cn cellml:units="dimensionless"> 1.0 </cn>
                        <apply>
                          <divide/>
                          <ci> ASA </ci>
                          <ci> k_ASA </ci>
                        </apply>
                      </apply>
                      <apply>
                        <plus/>
                        <cn cellml:units="dimensionless"> 1.0 </cn>
                        <apply>
                          <divide/>
                          <ci> Pi </ci>
                          <ci> k_Pi </ci>
                        </apply>
                      </apply>
                    </apply>
                    <ci> aspp </ci>
                  </apply>
                  <apply>
                    <plus/>
                    <apply>
                      <times/>
                      <ci> k_NADPH </ci>
                      <apply>
                        <plus/>
                        <cn cellml:units="dimensionless"> 1.0 </cn>
                        <apply>
                          <divide/>
                          <ci> NADP </ci>
                          <ci> k_NADP </ci>
                        </apply>
                      </apply>
                    </apply>
                    <ci> NADPH </ci>
                  </apply>
                </apply>
              </apply>
            </apply>
          </math>
        </role>
      </variable_ref>
    </reaction>
  </component>
  
  <component name="reaction_3">
    <variable units="millimolar" public_interface="in" name="ASA"/>
    <variable units="millimolar" public_interface="in" name="hs"/>
    <variable units="millimolar" public_interface="in" name="NADPH"/>
    <variable units="millimolar" public_interface="in" name="NADP"/>
    <variable units="millimolar" public_interface="in" name="thr"/>
    <variable units="millimolar" public_interface="in" name="HDH"/>
    <variable units="millimolar" name="k_ASA" initial_value="0.24"/>
    <variable units="millimolar" name="k_NADPH" initial_value="0.037"/>
    <variable units="millimolar" name="k_hs" initial_value="3.39"/>
    <variable units="millimolar" name="k_NADP" initial_value="0.067"/>
    <variable units="millimolar" name="k_ithr" initial_value="0.097"/>
    <variable units="dimensionless" name="alpha" initial_value="3.93"/>
    <variable units="dimensionless" name="h" initial_value="1.41"/>
    <variable units="per_molar" name="k_eq" initial_value="100000000000.0"/>
    <variable units="flux" name="V_max_HDH"/>
    <variable units="flux" public_interface="out" name="delta_ASA_rxn3"/>
    <variable units="flux" public_interface="out" name="delta_hs_rxn3"/>
    <variable units="flux" public_interface="out" name="delta_NADPH_rxn3"/>
    <variable units="flux" public_interface="out" name="delta_NADP_rxn3"/>
    <variable units="flux" name="r"/>
    <reaction reversible="yes">
      <variable_ref variable="ASA">
        <role stoichiometry="1" direction="forward" delta_variable="delta_ASA_rxn3" role="reactant"/>
      </variable_ref>
      <variable_ref variable="NADPH">
        <role stoichiometry="1" direction="forward" delta_variable="delta_NADPH_rxn3" role="reactant"/>
      </variable_ref>
      <variable_ref variable="hs">
        <role stoichiometry="1" direction="forward" delta_variable="delta_hs_rxn3" role="product"/>
      </variable_ref>
      <variable_ref variable="NADP">
        <role stoichiometry="1" direction="forward" delta_variable="delta_NADP_rxn3" role="product"/>
      </variable_ref> 
      <variable_ref variable="HDH">
        <role direction="forward" role="catalyst"/>
      </variable_ref>
      <variable_ref variable="thr">
        <role direction="forward" role="inhibitor"/>
      </variable_ref>
      <variable_ref variable="r">
        <role role="rate">
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
              <eq/>
              <ci> r </ci>
              <apply>
                <divide/>
                <apply>
                  <times/>
                  <ci> V_max_HDH </ci>
                  <apply>
                    <minus/>
                    <apply>
                      <times/>
                      <ci> ASA </ci>
                      <ci> NADPH </ci>
                    </apply>
                    <apply>
                      <divide/>
                      <apply>
                        <times/>
                        <ci> hs </ci>
                        <ci> NADP </ci>
                      </apply>
                      <ci> k_eq </ci>
                    </apply>
                  </apply>
                </apply>
                <apply>
                  <times/>
                  <apply>
                    <divide/>
                    <apply>
                      <plus/>
                      <cn cellml:units="dimensionless"> 1.0 </cn>
                      <apply>
                        <power/>
                        <apply>
                          <divide/>
                          <ci> thr </ci>
                          <ci> k_ithr </ci>
                        </apply>
                        <ci> h </ci>
                      </apply>
                    </apply>
                    <apply>
                      <plus/>
                      <cn cellml:units="dimensionless"> 1.0 </cn>
                      <apply>
                        <power/>
                        <apply>
                          <divide/>
                          <ci> thr </ci>
                          <apply>
                            <times/>
                            <ci> alpha </ci>
                            <ci> k_ithr </ci>
                          </apply>
                        </apply>
                        <ci> h </ci>
                      </apply>
                    </apply>
                  </apply>
                  <apply>
                    <plus/>
                    <ci> k_ASA </ci>
                    <apply>
                      <times/>
                      <ci> hs </ci>
                      <apply>
                        <divide/>
                        <ci> k_ASA </ci>
                        <ci> k_hs </ci>
                      </apply>
                    </apply> 
                    <ci> ASA </ci>
                  </apply>
                  <apply>
                    <plus/>
                    <apply>
                      <times/>
                      <ci> k_NADPH </ci>
                      <apply>
                        <plus/>
                        <cn cellml:units="dimensionless"> 1.0 </cn>
                        <apply>
                          <divide/>
                          <ci> NADP </ci>
                          <ci> k_NADP </ci>
                        </apply>
                      </apply>
                    </apply>
                    <ci> NADPH </ci>
                  </apply>
                </apply>
              </apply>
            </apply>
          </math>
        </role>
      </variable_ref>
    </reaction>
  </component>
  
  <component name="reaction_4">
    <variable units="millimolar" public_interface="in" name="hs"/>
    <variable units="millimolar" public_interface="in" name="hsp"/>
    <variable units="millimolar" public_interface="in" name="ATP"/>
    <variable units="millimolar" public_interface="in" name="ADP"/>
    <variable units="millimolar" public_interface="in" name="thr"/>
    <variable units="millimolar" public_interface="in" name="lys"/>
    <variable units="millimolar" public_interface="in" name="HK"/>
    <variable units="millimolar" name="k_hs" initial_value="0.11"/>
    <variable units="millimolar" name="k_ATP" initial_value="0.072"/>
    <variable units="millimolar" name="k_ithr" initial_value="1.09"/>
    <variable units="millimolar" name="k_ilys" initial_value="9.45"/>
    <variable units="millimolar" name="k_ihs" initial_value="4.7"/>
    <variable units="millimolar" name="k_iATP" initial_value="4.35"/>
    <variable units="flux" name="V_max_HK"/>
    <variable units="flux" public_interface="out" name="delta_hs_rxn4"/>
    <variable units="flux" public_interface="out" name="delta_hsp_rxn4"/>
    <variable units="flux" public_interface="out" name="delta_ATP_rxn4"/>
    <variable units="flux" public_interface="out" name="delta_ADP_rxn4"/>
    <variable units="flux" name="r"/>
    <reaction reversible="yes">
      <variable_ref variable="hs">
        <role stoichiometry="1" direction="forward" delta_variable="delta_hs_rxn4" role="reactant"/>
      </variable_ref>
      <variable_ref variable="ATP">
        <role stoichiometry="1" direction="forward" delta_variable="delta_ATP_rxn4" role="reactant"/>
      </variable_ref>
      <variable_ref variable="hsp">
        <role stoichiometry="1" direction="forward" delta_variable="delta_hsp_rxn4" role="product"/>
      </variable_ref>
      <variable_ref variable="ADP">
        <role stoichiometry="1" direction="forward" delta_variable="delta_ADP_rxn4" role="product"/>
      </variable_ref> 
      <variable_ref variable="HK">
        <role direction="forward" role="catalyst"/>
      </variable_ref>
      <variable_ref variable="thr">
        <role direction="forward" role="inhibitor"/>
      </variable_ref>
      <variable_ref variable="lys">
        <role direction="forward" role="inhibitor"/>
      </variable_ref>
      <variable_ref variable="r">
        <role role="rate">
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
              <eq/>
              <ci> r </ci>
              <apply>
                <divide/>
                <apply>
                  <times/>
                  <ci> V_max_HK </ci>
                  <ci> hs </ci>
                  <ci> ATP </ci>
                </apply>
                <apply>
                  <times/>
                  <apply>
                    <plus/>
                    <apply>
                      <times/>
                      <ci> k_hs </ci>
                      <apply>
                        <divide/>
                        <apply>
                          <plus/>
                          <cn cellml:units="dimensionless"> 1.0 </cn>
                          <apply>
                            <divide/>
                            <ci> ATP </ci>
                            <ci> k_iATP </ci>
                          </apply>
                        </apply>
                        <apply>
                          <plus/>
                          <cn cellml:units="dimensionless"> 1.0 </cn>
                          <apply>
                            <divide/>
                            <ci> thr </ci>
                            <ci> k_ithr </ci>
                          </apply>
                        </apply>
                      </apply>
                    </apply>
                    <ci> hs </ci>
                  </apply>
                  <apply>
                    <times/>
                    <apply>
                      <plus/>
                      <apply>
                        <times/>
                        <ci> k_ATP </ci>
                        <apply>
                          <plus/>
                          <cn cellml:units="dimensionless"> 1.0 </cn>
                          <apply>
                            <divide/>
                            <ci> hs </ci>
                            <ci> k_ihs </ci>
                          </apply>
                        </apply>
                      </apply>
                      <ci> ATP </ci>
                    </apply> 
                    <apply>
                      <plus/>
                      <cn cellml:units="dimensionless"> 1.0 </cn>
                      <apply>
                        <divide/>
                        <ci> lys </ci>
                        <ci> k_ilys </ci>
                      </apply>
                    </apply>
                  </apply>
                </apply>
              </apply>
            </apply>
          </math>
        </role>
      </variable_ref>
    </reaction>
  </component>
  
  <component name="reaction_5">
    <variable units="millimolar" public_interface="in" name="hsp"/>
    <variable units="millimolar" public_interface="in" name="thr"/>
    <variable units="millimolar" public_interface="in" name="PLP"/>
    <variable units="millimolar" public_interface="in" name="H2O"/>
    <variable units="millimolar" public_interface="in" name="Pi"/>
    <variable units="millimolar" public_interface="in" name="TS"/>
    <variable units="millimolar" name="k_hsp" initial_value="0.31"/>
    <variable units="flux" name="V_max_TS"/>
    <variable units="flux" public_interface="out" name="delta_hsp_rxn5"/>
    <variable units="flux" public_interface="out" name="delta_thr_rxn5"/>
    <variable units="flux" public_interface="out" name="delta_Pi_rxn5"/>
    <variable units="flux" public_interface="out" name="delta_PLP_rxn5"/>
    <variable units="flux" public_interface="out" name="delta_H2O_rxn5"/>
    <variable units="flux" name="r"/>
    <reaction reversible="no">
      <variable_ref variable="hsp">
        <role stoichiometry="1" direction="forward" delta_variable="delta_hsp_rxn5" role="reactant"/>
      </variable_ref>
      <variable_ref variable="PLP">
        <role stoichiometry="1" direction="forward" delta_variable="delta_PLP_rxn5" role="reactant"/>
      </variable_ref>
      <variable_ref variable="H2O">
        <role stoichiometry="1" direction="forward" delta_variable="delta_H2O_rxn5" role="reactant"/>
      </variable_ref>
      <variable_ref variable="thr">
        <role stoichiometry="1" direction="forward" delta_variable="delta_thr_rxn5" role="product"/>
      </variable_ref>
      <variable_ref variable="Pi">
        <role stoichiometry="1" direction="forward" delta_variable="delta_Pi_rxn5" role="product"/>
      </variable_ref>
      <variable_ref variable="TS">
        <role direction="forward" role="catalyst"/>
      </variable_ref>
      <variable_ref variable="r">
        <role role="rate">
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
              <eq/>
              <ci> r </ci>
              <apply>
                <divide/>
                <apply>
                  <times/>
                  <ci> V_max_TS </ci>
                  <ci> hsp </ci>
                </apply>
                <apply>
                  <plus/>
                  <ci> k_hsp </ci>
                  <ci> hsp </ci>
                </apply>
              </apply>
            </apply>
          </math>
        </role>
      </variable_ref>
    </reaction>
  </component> 
  
  <component name="reaction_6">
    <variable units="millimolar" public_interface="in" name="asp"/>
    <variable units="millimolar" public_interface="in" name="aspp"/>
    <variable units="millimolar" public_interface="in" name="ATP"/>
    <variable units="millimolar" public_interface="in" name="ADP"/>
    <variable units="millimolar" public_interface="in" name="lys"/>
    <variable units="millimolar" public_interface="in" name="AK_III"/>
    <variable units="millimolar" name="k_asp" initial_value="0.32"/>
    <variable units="millimolar" name="k_ATP" initial_value="0.22"/>
    <variable units="millimolar" name="k_aspp" initial_value="0.017"/>
    <variable units="millimolar" name="k_ADP" initial_value="0.25"/>
    <variable units="millimolar" name="k_ilys" initial_value="0.391"/>
    <variable units="dimensionless" name="h_lys" initial_value="2.8"/>
    <variable units="dimensionless" name="k_eq" initial_value="0.00064"/>
    <variable units="flux" name="V_max_AK_III"/>
    <variable units="flux" public_interface="out" name="delta_asp_rxn6"/>
    <variable units="flux" public_interface="out" name="delta_aspp_rxn6"/>
    <variable units="flux" public_interface="out" name="delta_ATP_rxn6"/>
    <variable units="flux" public_interface="out" name="delta_ADP_rxn6"/>
    <variable units="flux" name="r"/>
    <reaction reversible="yes">
      <variable_ref variable="asp">
        <role stoichiometry="1" direction="forward" delta_variable="delta_asp_rxn6" role="reactant"/>
      </variable_ref>
      <variable_ref variable="ATP">
        <role stoichiometry="1" direction="forward" delta_variable="delta_ATP_rxn6" role="reactant"/>
      </variable_ref>
      <variable_ref variable="aspp">
        <role stoichiometry="1" direction="forward" delta_variable="delta_aspp_rxn6" role="product"/>
      </variable_ref>
      <variable_ref variable="ADP">
        <role stoichiometry="1" direction="forward" delta_variable="delta_ADP_rxn6" role="product"/>
      </variable_ref> 
      <variable_ref variable="AK_III">
        <role direction="forward" role="catalyst"/>
      </variable_ref>
      <variable_ref variable="lys">
        <role direction="forward" role="inhibitor"/>
      </variable_ref>
      <variable_ref variable="r">
        <role role="rate">
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
              <eq/>
              <ci> r </ci>
              <apply>
                <divide/>
                <apply>
                  <times/>
                  <ci> V_max_AK_III </ci>
                  <apply>
                    <minus/>
                    <apply>
                      <times/>
                      <ci> asp </ci>
                      <ci> ATP </ci>
                    </apply>
                    <apply>
                      <divide/>
                      <apply>
                        <times/>
                        <ci> aspp </ci>
                        <ci> ADP </ci>
                      </apply>
                      <ci> k_eq </ci>
                    </apply>
                  </apply>
                </apply>
                <apply>
                  <times/>
                  <apply>
                    <plus/>
                    <cn cellml:units="dimensionless"> 1.0 </cn>
                    <apply>
                      <power/>
                      <apply>
                        <divide/>
                        <ci> lys </ci>
                        <ci> k_ilys </ci>
                      </apply>
                      <ci> h_lys </ci>
                    </apply>
                  </apply>
                  <apply>
                    <plus/>
                    <apply>
                      <times/>
                      <ci> k_asp </ci>
                      <apply>
                        <plus/>
                        <cn cellml:units="dimensionless"> 1.0 </cn>
                        <apply>
                          <divide/>
                          <ci> aspp </ci>
                          <ci> k_aspp </ci>
                        </apply>
                      </apply>
                    </apply>
                    <ci> asp </ci>
                  </apply>
                  <apply>
                    <plus/>
                    <apply>
                      <times/>
                      <ci> k_ATP </ci>
                      <apply>
                        <plus/>
                        <cn cellml:units="dimensionless"> 1.0 </cn>
                        <apply>
                          <divide/>
                          <ci> ADP </ci>
                          <ci> k_ADP </ci>
                        </apply>
                      </apply>
                    </apply>
                    <ci> ATP </ci>
                  </apply>
                </apply>
              </apply>
            </apply>
          </math>
        </role>
      </variable_ref>
    </reaction>
  </component>
  
  <connection>
    <map_components component_2="environment" component_1="asp"/>
    <map_variables variable_2="time" variable_1="time"/>
  </connection>
  
  <connection>
    <map_components component_2="environment" component_1="aspp"/>
    <map_variables variable_2="time" variable_1="time"/>
  </connection>
  
  <connection>
    <map_components component_2="environment" component_1="ASA"/>
    <map_variables variable_2="time" variable_1="time"/>
  </connection>
  
  <connection>
    <map_components component_2="environment" component_1="hs"/>
    <map_variables variable_2="time" variable_1="time"/>
  </connection>
  
  <connection>
    <map_components component_2="environment" component_1="hsp"/>
    <map_variables variable_2="time" variable_1="time"/>
  </connection>
  
  <connection>
    <map_components component_2="environment" component_1="thr"/>
    <map_variables variable_2="time" variable_1="time"/>
  </connection>
  
  <connection>
    <map_components component_2="environment" component_1="ATP"/>
    <map_variables variable_2="time" variable_1="time"/>
  </connection>
  
  <connection>
    <map_components component_2="environment" component_1="ADP"/>
    <map_variables variable_2="time" variable_1="time"/>
  </connection>
  
  <connection>
    <map_components component_2="environment" component_1="NADP"/>
    <map_variables variable_2="time" variable_1="time"/>
  </connection>
  
  <connection>
    <map_components component_2="environment" component_1="NADPH"/>
    <map_variables variable_2="time" variable_1="time"/>
  </connection>
  
  <connection>
    <map_components component_2="environment" component_1="H2O"/>
    <map_variables variable_2="time" variable_1="time"/>
  </connection>
  
  <connection>
    <map_components component_2="environment" component_1="PLP"/>
    <map_variables variable_2="time" variable_1="time"/>
  </connection>
  
  <connection>
    <map_components component_2="environment" component_1="Pi"/>
    <map_variables variable_2="time" variable_1="time"/>
  </connection>
  
  <connection>
    <map_components component_2="reaction_1" component_1="asp"/>
    <map_variables variable_2="asp" variable_1="asp"/>
    <map_variables variable_2="delta_asp_rxn1" variable_1="delta_asp_rxn1"/>
  </connection>
  
  <connection>
    <map_components component_2="reaction_1" component_1="aspp"/>
    <map_variables variable_2="aspp" variable_1="aspp"/>
    <map_variables variable_2="delta_aspp_rxn1" variable_1="delta_aspp_rxn1"/>
  </connection>
  
  <connection>
    <map_components component_2="reaction_1" component_1="thr"/>
    <map_variables variable_2="thr" variable_1="thr"/>
  </connection>
  
  <connection>
    <map_components component_2="reaction_1" component_1="AK_I"/>
    <map_variables variable_2="AK_I" variable_1="AK_I"/>
  </connection>
  
  <connection>
    <map_components component_2="reaction_1" component_1="ATP"/>
    <map_variables variable_2="ATP" variable_1="ATP"/>
    <map_variables variable_2="delta_ATP_rxn1" variable_1="delta_ATP_rxn1"/>
  </connection>
  
  <connection>
    <map_components component_2="reaction_1" component_1="ADP"/>
    <map_variables variable_2="ADP" variable_1="ADP"/>
    <map_variables variable_2="delta_ADP_rxn1" variable_1="delta_ADP_rxn1"/>
  </connection>
  
  <connection>
    <map_components component_2="reaction_2" component_1="aspp"/>
    <map_variables variable_2="aspp" variable_1="aspp"/>
    <map_variables variable_2="delta_aspp_rxn2" variable_1="delta_aspp_rxn2"/>
  </connection>
  
  <connection>
    <map_components component_2="reaction_2" component_1="ASA"/>
    <map_variables variable_2="ASA" variable_1="ASA"/>
    <map_variables variable_2="delta_ASA_rxn2" variable_1="delta_ASA_rxn2"/>
  </connection>
  
  <connection>
    <map_components component_2="reaction_2" component_1="Pi"/>
    <map_variables variable_2="Pi" variable_1="Pi"/>
    <map_variables variable_2="delta_Pi_rxn2" variable_1="delta_Pi_rxn2"/>
  </connection>
  
  <connection>
    <map_components component_2="reaction_2" component_1="ASD"/>
    <map_variables variable_2="ASD" variable_1="ASD"/>
  </connection>
  
  <connection>
    <map_components component_2="reaction_2" component_1="NADPH"/>
    <map_variables variable_2="NADPH" variable_1="NADPH"/>
    <map_variables variable_2="delta_NADPH_rxn2" variable_1="delta_NADPH_rxn2"/>
  </connection>
  
  <connection>
    <map_components component_2="reaction_2" component_1="NADP"/>
    <map_variables variable_2="NADP" variable_1="NADP"/>
    <map_variables variable_2="delta_NADP_rxn2" variable_1="delta_NADP_rxn2"/>
  </connection>
  
  <connection>
    <map_components component_2="reaction_3" component_1="ASA"/>
    <map_variables variable_2="ASA" variable_1="ASA"/>
    <map_variables variable_2="delta_ASA_rxn3" variable_1="delta_ASA_rxn3"/>
  </connection>
  
  <connection>
    <map_components component_2="reaction_3" component_1="hs"/>
    <map_variables variable_2="hs" variable_1="hs"/>
    <map_variables variable_2="delta_hs_rxn3" variable_1="delta_hs_rxn3"/>
  </connection>
  
  <connection>
    <map_components component_2="reaction_3" component_1="thr"/>
    <map_variables variable_2="thr" variable_1="thr"/>
  </connection>
  
  <connection>
    <map_components component_2="reaction_3" component_1="HDH"/>
    <map_variables variable_2="HDH" variable_1="HDH"/>
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  <connection>
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  <connection>
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  <connection>
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  <connection>
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  <connection>
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  <connection>
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  <connection>
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  <connection>
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  <connection>
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  <connection>
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  <connection>
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  <connection>
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  <connection>
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  <connection>
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  <connection>
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  <connection>
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  <connection>
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  <connection>
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  <connection>
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  <connection>
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    <dcterms:alternative>threonine synthase</dcterms:alternative>
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    <dcterms:alternative>aspartate kinase III</dcterms:alternative>
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    <vCard:Given>David</vCard:Given>
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  <rdf:Description rdf:about="#aspp">
    <dcterms:alternative>beta_aspartyl_phosphate</dcterms:alternative>
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            An integrated study of threonine-pathway enzyme kinetics in                      Escherichia coli 
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        The University of Auckland, Bioengineering Institute
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