- Author:
- Hanne <Hanne@hanne-nielsens-macbook.local>
- Date:
- 2009-12-08 13:54:22+13:00
- Desc:
- Addedi amges in ai and svg format
- Permanent Source URI:
- https://models.physiomeproject.org/workspace/hoefnagel_starrenburg_martens_hugenholtz_kleerebezem_vanswam_bongers_westerhoff_snoep_2002/rawfile/e520bdb321846422a9d59fee83224acf68b4dfec/hoefnagel_starrenburg_martens_hugenholtz_kleerebezem_vanswam_bongers_westerhoff_snoep_2002.cellml
<?xml version='1.0' encoding='utf-8'?>
<!-- FILE : hoefnagel_model_2002.xml
CREATED : 18th August 2003
LAST MODIFIED : 18th August 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 16/1/02 CellML Metadata 1.0 Specification.
DESCRIPTION : This file contains a CellML description of Hoefnagel et al's 2002 mathematical model of pyruvate distribution in lactic acid bacteria.
CHANGES:
--><model xmlns="http://www.cellml.org/cellml/1.0#" xmlns:cmeta="http://www.cellml.org/metadata/1.0#" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:bqs="http://www.cellml.org/bqs/1.0#" xmlns:cellml="http://www.cellml.org/cellml/1.0#" xmlns:dcterms="http://purl.org/dc/terms/" xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" cmeta:id="hoefnagel_starrenburg_martens_hugenholtz_kleerebezem_vanswam_bongers_westerhoff_snoep_2002_version01" name="hoefnagel_starrenburg_martens_hugenholtz_kleerebezem_vanswam_bongers_westerhoff_snoep_2002_version01">
<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
<articleinfo>
<title>Metabolic Engineering of Lactococcus lactis</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>
Frequently, the microorganisms which are used in biotech industries to manufacture valuable compounds such as drugs, fuels, and fibres, are not naturally optimised for maximum production. In bioengineering, one frequent aim is to maximise the flux through a particular pathway. However, due to the complex, branching nature of metabolic networks, increasing metabolic flux can be difficult.
</para>
<para>
Traditionally, metabolic control analysis (MCA) has been used to identify the specific enzymes that have the most control over the metabolic flux. In MCA, enzymes are assigned a flux control coefficient. This value quantifies the influence of a particular enzyme on overall metabolic flux. However, the alleviation of <emphasis>rate-limiting</emphasis> steps, by increasing the concentration of enzymes with a high flux control coefficient, is not always successful in increasing metabolic flux.
</para>
<para>
In the Hoefnagel <emphasis>et al.</emphasis> 2002 model described here, the authors demonstrate that an integrated approach of kinetic modelling, MCA, and experimental analysis can be used to successfully model pyruvate distribution in the bacterium <emphasis>Lactococcus lactis</emphasis>. Lactic acid bacteria are used in milk fermentation, the main product of which is lactate (see <xref linkend="fig_reaction_diagram"/> below). For dairy products such as butter, diacetyl produced by <emphasis>Lactococcus lactis</emphasis> is a flavour component. Naturally, diacetyl is only produced in small quantities, and butter manufacturers try to optimise its production. A combined approach to metabolic engineering identified the enzymes with the greatest effect on metabolic flux. In turn, this highlighted which genes should be targeted in the genetic engineering of the model organism in order to maximise metabolic output.
</para>
<para>
The model has been described here in CellML (the raw CellML description of the Hoefnagel <emphasis>et al.</emphasis> model can be downloaded in various formats as described in <xref linkend="sec_download_this_model"/>).
</para>
<para>
<ulink url="http://mic.sgmjournals.org/cgi/content/abstract/148/4/1003">Metabolic engineering of lactic acid bacteria, the combined approach: kinetic modelling, metabolic control and experimental analysis</ulink>, Marcel H.N. Hoefnagel, Marjo J.C. Starrenburg, Dirk E. Martens, Jeroen Hugenholtz, Michiel Kleerebezem, Iris I. Van Swam, Roger Bongers, Hans V. Westerhoff, and Jacky L. Snoep, 2002, <ulink url="http://mic.sgmjournals.org/">
<emphasis>Microbiology</emphasis>
</ulink>, 148, 1003-1013. (<ulink url="http://mic.sgmjournals.org/cgi/content/full/148/4/1003?view=full&pmid=11932446">Full text (HTML)</ulink> and <ulink url="http://mic.sgmjournals.org/cgi/reprint/148/4/1003.pdf">PDF</ulink> versions of the article are available to subscribers on the <emphasis>Microbiology</emphasis> website.) <ulink url="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&list_uids=11932446&dopt=Abstract">PubMed ID: 11932446</ulink>
</para>
<informalfigure float="0" id="fig_reaction_diagram">
<mediaobject>
<imageobject>
<objectinfo>
<title>reaction diagram</title>
</objectinfo>
<imagedata fileref="hoefnagel_2002.png"/>
</imageobject>
</mediaobject>
<caption>A schematic diagram of the reactions included in the model to describe the distribution of carbon from pyruvate in <emphasis>L. lactis</emphasis>.</caption>
</informalfigure>
</sect1>
</article>
</documentation>
<!--
Below, we define some additional units for association with variables and
mitochondrial_membrane within the model.
-->
<units name="millimolar">
<unit units="mole" prefix="milli"/>
<unit units="litre" exponent="-1"/>
</units>
<units name="minute">
<unit units="second" multiplier="60.0"/>
</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>
<component name="environment">
<variable units="minute" public_interface="out" name="time"/>
</component>
<!--
The following components describe all the reactants and products involved in
reactions.
-->
<component cmeta:id="PYR" name="PYR">
<rdf:RDF>
<rdf:Description rdf:about="PYR">
<dc:title>PYR</dc:title>
<dcterms:alternative>pyruvate</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="millimolar" public_interface="out" name="PYR"/>
<variable units="flux" public_interface="in" name="V_GLYC"/>
<variable units="flux" public_interface="in" name="V_LDH"/>
<variable units="flux" public_interface="in" name="V_PDH"/>
<variable units="flux" public_interface="in" name="V_ALS"/>
<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>PYR</ci>
</apply>
<apply>
<minus/>
<ci>V_GLYC</ci>
<apply>
<plus/>
<ci>V_LDH</ci>
<ci>V_PDH</ci>
<apply>
<times/>
<cn cellml:units="dimensionless"> 2.0 </cn>
<ci>V_ALS</ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component cmeta:id="ACP" name="ACP">
<rdf:RDF>
<rdf:Description rdf:about="ACP">
<dc:title>ACP</dc:title>
<dcterms:alternative>acetyl phosphate</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="millimolar" public_interface="out" name="ACP"/>
<variable units="flux" public_interface="in" name="V_PTA"/>
<variable units="flux" public_interface="in" name="V_ACK"/>
<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>ACP</ci>
</apply>
<apply>
<minus/>
<ci>V_PTA</ci>
<ci>V_ACK</ci>
</apply>
</apply>
</math>
</component>
<component cmeta:id="ACAL" name="ACAL">
<rdf:RDF>
<rdf:Description rdf:about="ACAL">
<dc:title>ACAL</dc:title>
<dcterms:alternative>acetaldehyde</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="millimolar" public_interface="out" name="ACAL"/>
<variable units="flux" public_interface="in" name="V_ACALDH"/>
<variable units="flux" public_interface="in" name="V_ADH"/>
<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>ACAL</ci>
</apply>
<apply>
<minus/>
<ci>V_ACALDH</ci>
<ci>V_ADH</ci>
</apply>
</apply>
</math>
</component>
<component cmeta:id="ACLAC" name="ACLAC">
<rdf:RDF>
<rdf:Description rdf:about="ACLAC">
<dc:title>ACLAC</dc:title>
<dcterms:alternative>acetolactate</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="millimolar" public_interface="out" name="ACLAC"/>
<variable units="flux" public_interface="in" name="V_ALS"/>
<variable units="flux" public_interface="in" name="V_ALDC"/>
<variable units="flux" public_interface="in" name="V_NEALC"/>
<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>ACLAC</ci>
</apply>
<apply>
<minus/>
<ci>V_ALS</ci>
<apply>
<plus/>
<ci>V_ALDC</ci>
<ci>V_NEALC</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component cmeta:id="ACET" name="ACET">
<rdf:RDF>
<rdf:Description rdf:about="ACET">
<dc:title>ACET</dc:title>
<dcterms:alternative>acetoin</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="millimolar" public_interface="out" name="ACET"/>
<variable units="flux" public_interface="in" name="V_ALDC"/>
<variable units="flux" public_interface="in" name="V_NEALC"/>
<variable units="flux" public_interface="in" name="V_ACETDH"/>
<variable units="flux" public_interface="in" name="V_ACETEFF"/>
<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>ACET</ci>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<ci>V_ALDC</ci>
<ci>V_NEALC</ci>
</apply>
<apply>
<plus/>
<ci>V_ACETDH</ci>
<ci>V_ACETEFF</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component cmeta:id="ATP" name="ATP">
<rdf:RDF>
<rdf:Description rdf:about="ATP">
<dc:title>ATP</dc:title>
<dcterms:alternative>adenosine triphosphate</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="millimolar" public_interface="out" name="ATP"/>
<variable units="flux" public_interface="in" name="V_GLYC"/>
<variable units="flux" public_interface="in" name="V_ACK"/>
<variable units="flux" public_interface="in" name="V_ATPase"/>
<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>
<minus/>
<apply>
<plus/>
<ci>V_GLYC</ci>
<ci>V_ACK</ci>
</apply>
<ci>V_ATPase</ci>
</apply>
</apply>
</math>
</component>
<component cmeta:id="ADP" name="ADP">
<rdf:RDF>
<rdf:Description rdf:about="ADP">
<dc:title>ADP</dc:title>
<dcterms:alternative>adenosine diphosphate</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="millimolar" public_interface="out" name="ADP"/>
</component>
<component cmeta:id="NADH" name="NADH">
<rdf:RDF>
<rdf:Description rdf:about="NADH">
<dc:title>NADH</dc:title>
<dcterms:alternative>nicotinamide adenine dinucleotide</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="millimolar" public_interface="out" name="NADH"/>
<variable units="flux" public_interface="in" name="V_GLYC"/>
<variable units="flux" public_interface="in" name="V_PDH"/>
<variable units="flux" public_interface="in" name="V_LDH"/>
<variable units="flux" public_interface="in" name="V_ACALDH"/>
<variable units="flux" public_interface="in" name="V_ADH"/>
<variable units="flux" public_interface="in" name="V_ACETDH"/>
<variable units="flux" public_interface="in" name="V_NOX"/>
<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>NADH</ci>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<ci>V_GLYC</ci>
<ci>V_PDH</ci>
</apply>
<apply>
<plus/>
<ci>V_LDH</ci>
<ci>V_ACALDH</ci>
<ci>V_ADH</ci>
<ci>V_ACETDH</ci>
<ci>V_NOX</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component cmeta:id="NAD" name="NAD">
<rdf:RDF>
<rdf:Description rdf:about="NAD">
<dc:title>NAD</dc:title>
<dcterms:alternative>positive nicotinamide adenine dinucleotide</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="millimolar" public_interface="out" name="NAD"/>
</component>
<component cmeta:id="ACCOA" name="ACCOA">
<rdf:RDF>
<rdf:Description rdf:about="ACCOA">
<dc:title>ACCOA</dc:title>
<dcterms:alternative>acetyl coenzyme A</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="millimolar" public_interface="out" name="ACCOA"/>
<variable units="flux" public_interface="in" name="V_PDH"/>
<variable units="flux" public_interface="in" name="V_ACALDH"/>
<variable units="flux" public_interface="in" name="V_PTA"/>
<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>ACCOA</ci>
</apply>
<apply>
<minus/>
<ci>V_PDH</ci>
<apply>
<plus/>
<ci>V_ACALDH</ci>
<ci>V_PTA</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component cmeta:id="COA" name="COA">
<rdf:RDF>
<rdf:Description rdf:about="COA">
<dc:title>COA</dc:title>
<dcterms:alternative>coenzyme A</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="millimolar" public_interface="out" name="COA"/>
</component>
<component cmeta:id="AC" name="AC">
<rdf:RDF>
<rdf:Description rdf:about="AC">
<dc:title>AC</dc:title>
<dcterms:alternative>acetate</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="millimolar" public_interface="out" name="AC"/>
</component>
<component cmeta:id="BUT" name="BUT">
<rdf:RDF>
<rdf:Description rdf:about="BUT">
<dc:title>BUT</dc:title>
<dcterms:alternative>2,3-butanediol</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="millimolar" public_interface="out" name="BUT"/>
</component>
<component cmeta:id="ETOH" name="ETOH">
<rdf:RDF>
<rdf:Description rdf:about="ETOH">
<dc:title>ETOH</dc:title>
<dcterms:alternative>ethanol</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="millimolar" public_interface="out" name="ETOH"/>
</component>
<component cmeta:id="GLC" name="GLC">
<rdf:RDF>
<rdf:Description rdf:about="GLC">
<dc:title>GLC</dc:title>
<dcterms:alternative>glucose</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="millimolar" public_interface="out" name="GLC"/>
</component>
<component cmeta:id="LAC" name="LAC">
<rdf:RDF>
<rdf:Description rdf:about="LAC">
<dc:title>LAC</dc:title>
<dcterms:alternative>lactate</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="millimolar" public_interface="out" name="LAC"/>
</component>
<component cmeta:id="O" name="O">
<rdf:RDF>
<rdf:Description rdf:about="O">
<dc:title>O</dc:title>
<dcterms:alternative>oxygen</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="millimolar" public_interface="out" name="O"/>
</component>
<component cmeta:id="P" name="P">
<rdf:RDF>
<rdf:Description rdf:about="P">
<dc:title>P</dc:title>
<dcterms:alternative>inorganic phosphate</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="millimolar" public_interface="out" name="P"/>
</component>
<!--
The following components describe the reactions of the model.
-->
<component name="V_GLYC">
<variable units="flux" public_interface="out" name="V_GLYC"/>
<variable units="millimolar" public_interface="in" name="GLC"/>
<variable units="millimolar" public_interface="in" name="NAD"/>
<variable units="millimolar" public_interface="in" name="ADP"/>
<variable units="millimolar" public_interface="in" name="ATP"/>
<variable units="millimolar" public_interface="in" name="PYR"/>
<variable units="millimolar" public_interface="in" name="NADH"/>
<variable units="millimolar" name="Km_GLC" initial_value="0.1"/>
<variable units="millimolar" name="Km_NAD" initial_value="0.14"/>
<variable units="millimolar" name="Km_ADP" initial_value="0.047"/>
<variable units="millimolar" name="Km_PYR" initial_value="25.0"/>
<variable units="millimolar" name="Km_NADH" initial_value="0.09"/>
<variable units="millimolar" name="Km_ATP" initial_value="0.019"/>
<variable units="flux" name="V_GLYC_max" initial_value="2397.0"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="V_GLYC_calculation">
<eq/>
<ci> V_GLYC </ci>
<apply>
<divide/>
<apply>
<times/>
<ci> V_GLYC_max </ci>
<apply>
<divide/>
<ci> GLC </ci>
<ci> Km_GLC </ci>
</apply>
<apply>
<divide/>
<ci> NAD </ci>
<ci> Km_NAD </ci>
</apply>
<apply>
<divide/>
<ci> ADP </ci>
<ci> Km_ADP </ci>
</apply>
</apply>
<apply>
<times/>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<divide/>
<ci> GLC </ci>
<ci> Km_GLC </ci>
</apply>
<apply>
<divide/>
<ci> PYR </ci>
<ci> Km_PYR </ci>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<divide/>
<ci> NAD </ci>
<ci> Km_NAD </ci>
</apply>
<apply>
<divide/>
<ci> NADH </ci>
<ci> Km_NADH </ci>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<divide/>
<ci> ADP </ci>
<ci> Km_ADP </ci>
</apply>
<apply>
<divide/>
<ci> ATP </ci>
<ci> Km_ATP </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="V_LDH">
<variable units="flux" public_interface="out" name="V_LDH"/>
<variable units="millimolar" public_interface="in" name="LAC"/>
<variable units="millimolar" public_interface="in" name="NAD"/>
<variable units="millimolar" public_interface="in" name="PYR"/>
<variable units="millimolar" public_interface="in" name="NADH"/>
<variable units="millimolar" name="Keq" initial_value="21120.7"/>
<variable units="millimolar" name="Km_LAC" initial_value="100.0"/>
<variable units="millimolar" name="Km_NAD" initial_value="2.4"/>
<variable units="millimolar" name="Km_PYR" initial_value="1.5"/>
<variable units="millimolar" name="Km_NADH" initial_value="0.08"/>
<variable units="flux" name="V_LDH_max" initial_value="5118.0"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="V_LDH_calculation">
<eq/>
<ci> V_LDH </ci>
<apply>
<divide/>
<apply>
<times/>
<ci> V_LDH_max </ci>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<times/>
<ci> Km_PYR </ci>
<ci> Km_NADH </ci>
</apply>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> PYR </ci>
<ci> NADH </ci>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci> LAC </ci>
<ci> NAD </ci>
</apply>
<ci> Keq </ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<divide/>
<ci> PYR </ci>
<ci> Km_PYR </ci>
</apply>
<apply>
<divide/>
<ci> LAC </ci>
<ci> Km_LAC </ci>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<divide/>
<ci> NADH </ci>
<ci> Km_NADH </ci>
</apply>
<apply>
<divide/>
<ci> NAD </ci>
<ci> Km_NAD </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="V_PDH">
<variable units="flux" public_interface="out" name="V_PDH"/>
<variable units="millimolar" public_interface="in" name="NAD"/>
<variable units="millimolar" public_interface="in" name="COA"/>
<variable units="millimolar" public_interface="in" name="ACCOA"/>
<variable units="millimolar" public_interface="in" name="PYR"/>
<variable units="millimolar" public_interface="in" name="NADH"/>
<variable units="millimolar" name="Ki" initial_value="46.4"/>
<variable units="millimolar" name="Km_NAD" initial_value="0.4"/>
<variable units="millimolar" name="Km_COA" initial_value="0.014"/>
<variable units="millimolar" name="Km_PYR" initial_value="1.0"/>
<variable units="millimolar" name="Km_NADH" initial_value="0.1"/>
<variable units="millimolar" name="Km_ACCOA" initial_value="0.008"/>
<variable units="flux" name="V_PDH_max" initial_value="21120.7"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="V_PDH_calculation">
<eq/>
<ci> V_PDH </ci>
<apply>
<divide/>
<apply>
<times/>
<ci> V_PDH_max </ci>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<times/>
<ci> Ki </ci>
<apply>
<divide/>
<ci> NADH </ci>
<ci> NAD </ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<divide/>
<ci> PYR </ci>
<ci> Km_PYR </ci>
</apply>
<apply>
<divide/>
<ci> NAD </ci>
<ci> Km_NAD </ci>
</apply>
<apply>
<divide/>
<ci> COA </ci>
<ci> Km_COA </ci>
</apply>
</apply>
<apply>
<times/>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<divide/>
<ci> PYR </ci>
<ci> Km_PYR </ci>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<divide/>
<ci> NAD </ci>
<ci> Km_NAD </ci>
</apply>
<apply>
<divide/>
<ci> NADH </ci>
<ci> Km_NADH </ci>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<divide/>
<ci> COA </ci>
<ci> Km_COA </ci>
</apply>
<apply>
<divide/>
<ci> ACCOA </ci>
<ci> Km_ACCOA </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="V_PTA">
<variable units="flux" public_interface="out" name="V_PTA"/>
<variable units="millimolar" public_interface="in" name="P"/>
<variable units="millimolar" public_interface="in" name="COA"/>
<variable units="millimolar" public_interface="in" name="ACCOA"/>
<variable units="millimolar" public_interface="in" name="ACP"/>
<variable units="millimolar" name="Keq" initial_value="0.0281"/>
<variable units="millimolar" name="Km_P" initial_value="2.6"/>
<variable units="millimolar" name="Ki_P" initial_value="2.6"/>
<variable units="millimolar" name="Km_COA" initial_value="0.12"/>
<variable units="millimolar" name="Ki_COA" initial_value="0.029"/>
<variable units="millimolar" name="Km_ACP" initial_value="0.7"/>
<variable units="millimolar" name="Ki_ACP" initial_value="0.2"/>
<variable units="millimolar" name="Ki_ACCOA" initial_value="0.2"/>
<variable units="flux" name="V_PTA_max" initial_value="259.0"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="V_PTA_calculation">
<eq/>
<ci> V_PTA </ci>
<apply>
<divide/>
<apply>
<times/>
<ci> V_PTA_max </ci>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<times/>
<ci> Ki_ACCOA </ci>
<ci> Km_P </ci>
</apply>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> ACCOA </ci>
<ci> P </ci>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci> ACP </ci>
<ci> COA </ci>
</apply>
<ci> Keq </ci>
</apply>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<divide/>
<ci> ACCOA </ci>
<ci> Ki_ACCOA </ci>
</apply>
<apply>
<divide/>
<ci> P </ci>
<ci> Ki_P </ci>
</apply>
<apply>
<divide/>
<ci> ACP </ci>
<ci> Ki_ACP </ci>
</apply>
<apply>
<divide/>
<ci> COA </ci>
<ci> Ki_COA </ci>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci> ACCOA </ci>
<ci> P </ci>
</apply>
<apply>
<times/>
<ci> Ki_ACCOA </ci>
<ci> Km_P </ci>
</apply>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci> ACP </ci>
<ci> COA </ci>
</apply>
<apply>
<times/>
<ci> Km_ACP </ci>
<ci> Ki_COA </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="V_ACK">
<variable units="flux" public_interface="out" name="V_ACK"/>
<variable units="millimolar" public_interface="in" name="AC"/>
<variable units="millimolar" public_interface="in" name="ATP"/>
<variable units="millimolar" public_interface="in" name="ADP"/>
<variable units="millimolar" public_interface="in" name="ACP"/>
<variable units="millimolar" name="Keq" initial_value="174.2"/>
<variable units="millimolar" name="Km_AC" initial_value="7.0"/>
<variable units="millimolar" name="Km_ATP" initial_value="0.07"/>
<variable units="millimolar" name="Km_ADP" initial_value="0.5"/>
<variable units="millimolar" name="Km_ACP" initial_value="0.16"/>
<variable units="flux" name="V_ACK_max" initial_value="42.0"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="V_ACK_calculation">
<eq/>
<ci> V_ACK </ci>
<apply>
<divide/>
<apply>
<times/>
<ci> V_ACK_max </ci>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<times/>
<ci> Km_ADP </ci>
<ci> Km_ACP </ci>
</apply>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> ACP </ci>
<ci> ADP </ci>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci> AC </ci>
<ci> ATP </ci>
</apply>
<ci> Keq </ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<divide/>
<ci> ACP </ci>
<ci> Km_ACP </ci>
</apply>
<apply>
<divide/>
<ci> AC </ci>
<ci> Km_AC </ci>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<divide/>
<ci> ADP </ci>
<ci> Km_ADP </ci>
</apply>
<apply>
<divide/>
<ci> ATP </ci>
<ci> Km_ATP </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="V_ACALDH">
<variable units="flux" public_interface="out" name="V_ACALDH"/>
<variable units="millimolar" public_interface="in" name="NAD"/>
<variable units="millimolar" public_interface="in" name="NADH"/>
<variable units="millimolar" public_interface="in" name="COA"/>
<variable units="millimolar" public_interface="in" name="ACCOA"/>
<variable units="millimolar" public_interface="in" name="ACAL"/>
<variable units="millimolar" name="Keq" initial_value="1.0"/>
<variable units="millimolar" name="Km_NAD" initial_value="0.08"/>
<variable units="millimolar" name="Km_NADH" initial_value="0.025"/>
<variable units="millimolar" name="Km_COA" initial_value="0.008"/>
<variable units="millimolar" name="Km_ACCOA" initial_value="0.007"/>
<variable units="millimolar" name="Km_ACAL" initial_value="10.0"/>
<variable units="flux" name="V_ACALDH_max" initial_value="97.0"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="V_ACALDH_calculation">
<eq/>
<ci> V_ACALDH </ci>
<apply>
<divide/>
<apply>
<times/>
<ci> V_ACALDH_max </ci>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<times/>
<ci> Km_ACCOA </ci>
<ci> Km_NADH </ci>
</apply>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> ACCOA </ci>
<ci> NADH </ci>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci> NAD </ci>
<ci> COA </ci>
<ci> ACAL </ci>
</apply>
<ci> Keq </ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<divide/>
<ci> NAD </ci>
<ci> Km_NAD </ci>
</apply>
<apply>
<divide/>
<ci> NADH </ci>
<ci> Km_NADH </ci>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<divide/>
<ci> ACCOA </ci>
<ci> Km_ACCOA </ci>
</apply>
<apply>
<divide/>
<ci> COA </ci>
<ci> Km_COA </ci>
</apply>
<apply>
<divide/>
<ci> ACAL </ci>
<ci> Km_ACAL </ci>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci> ACAL </ci>
<ci> COA </ci>
</apply>
<apply>
<times/>
<ci> Km_ACAL </ci>
<ci> Km_COA </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="V_ADH">
<variable units="flux" public_interface="out" name="V_ADH"/>
<variable units="millimolar" public_interface="in" name="NAD"/>
<variable units="millimolar" public_interface="in" name="NADH"/>
<variable units="millimolar" public_interface="in" name="ETOH"/>
<variable units="millimolar" public_interface="in" name="ACAL"/>
<variable units="millimolar" name="Keq" initial_value="12354.9"/>
<variable units="millimolar" name="Km_NAD" initial_value="0.08"/>
<variable units="millimolar" name="Km_NADH" initial_value="0.05"/>
<variable units="millimolar" name="Km_ETOH" initial_value="1.0"/>
<variable units="millimolar" name="Km_ACAL" initial_value="0.03"/>
<variable units="flux" name="V_ADH_max" initial_value="162.0"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="V_ADH_calculation">
<eq/>
<ci> V_ADH </ci>
<apply>
<divide/>
<apply>
<times/>
<ci> V_ADH_max </ci>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<times/>
<ci> Km_ACAL </ci>
<ci> Km_NADH </ci>
</apply>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> ACAL </ci>
<ci> NADH </ci>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci> ETOH </ci>
<ci> NAD </ci>
</apply>
<ci> Keq </ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<divide/>
<ci> NAD </ci>
<ci> Km_NAD </ci>
</apply>
<apply>
<divide/>
<ci> NADH </ci>
<ci> Km_NADH </ci>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<divide/>
<ci> ACAL </ci>
<ci> Km_ACAL </ci>
</apply>
<apply>
<divide/>
<ci> ETOH </ci>
<ci> Km_ETOH </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="V_ALS">
<variable units="flux" public_interface="out" name="V_ALS"/>
<variable units="millimolar" public_interface="in" name="ACLAC"/>
<variable units="millimolar" public_interface="in" name="PYR"/>
<variable units="dimensionless" name="N" initial_value="2.4"/>
<variable units="millimolar" name="Keq" initial_value="9.0E12"/>
<variable units="millimolar" name="Km_ACLAC" initial_value="100.0"/>
<variable units="millimolar" name="Km_PYR" initial_value="50.0"/>
<variable units="flux" name="V_ALS_max" initial_value="600.0"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="V_ALS_calculation">
<eq/>
<ci> V_ALS </ci>
<apply>
<divide/>
<apply>
<times/>
<ci> V_ALS_max </ci>
<apply>
<divide/>
<ci> PYR </ci>
<ci> Km_PYR </ci>
</apply>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<divide/>
<ci> ACLAC </ci>
<apply>
<times/>
<ci> PYR </ci>
<ci> Keq </ci>
</apply>
</apply>
</apply>
<apply>
<power/>
<apply>
<plus/>
<apply>
<divide/>
<ci> PYR </ci>
<ci> Km_PYR </ci>
</apply>
<apply>
<divide/>
<ci> ACLAC </ci>
<ci> Km_ACLAC </ci>
</apply>
</apply>
<apply>
<minus/>
<ci> N </ci>
<cn cellml:units="dimensionless"> 1.0 </cn>
</apply>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<power/>
<apply>
<plus/>
<apply>
<divide/>
<ci> PYR </ci>
<ci> Km_PYR </ci>
</apply>
<apply>
<divide/>
<ci> ACLAC </ci>
<ci> Km_ACLAC </ci>
</apply>
</apply>
<ci> N </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="V_ALDC">
<variable units="flux" public_interface="out" name="V_ALDC"/>
<variable units="millimolar" public_interface="in" name="ACLAC"/>
<variable units="millimolar" public_interface="in" name="ACET"/>
<variable units="millimolar" name="Km_ACLAC" initial_value="10.0"/>
<variable units="millimolar" name="Km_ACET" initial_value="100.0"/>
<variable units="flux" name="V_ALDC_max" initial_value="106.0"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="V_ALDC_calculation">
<eq/>
<ci> V_ALDC </ci>
<apply>
<divide/>
<apply>
<times/>
<ci> V_ALDC_max </ci>
<apply>
<divide/>
<ci> ACLAC </ci>
<ci> Km_ACLAC </ci>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<divide/>
<ci> ACLAC </ci>
<ci> Km_ACLAC </ci>
</apply>
<apply>
<divide/>
<ci> ACET </ci>
<ci> Km_ACET </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="V_ACETEFF">
<variable units="flux" public_interface="out" name="V_ACETEFF"/>
<variable units="millimolar" public_interface="in" name="ACET"/>
<variable units="millimolar" name="Km_ACET" initial_value="5.0"/>
<variable units="flux" name="V_ACETEFF_max" initial_value="200.0"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="V_ACETEFF_calculation">
<eq/>
<ci> V_ACETEFF </ci>
<apply>
<divide/>
<apply>
<times/>
<ci> V_ACETEFF_max </ci>
<apply>
<divide/>
<ci> ACET </ci>
<ci> Km_ACET </ci>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<divide/>
<ci> ACET </ci>
<ci> Km_ACET </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="V_ACETDH">
<variable units="flux" public_interface="out" name="V_ACETDH"/>
<variable units="millimolar" public_interface="in" name="NAD"/>
<variable units="millimolar" public_interface="in" name="NADH"/>
<variable units="millimolar" public_interface="in" name="BUT"/>
<variable units="millimolar" public_interface="in" name="ACET"/>
<variable units="millimolar" name="Keq" initial_value="1400.0"/>
<variable units="millimolar" name="Km_NAD" initial_value="0.16"/>
<variable units="millimolar" name="Km_NADH" initial_value="0.02"/>
<variable units="millimolar" name="Km_BUT" initial_value="2.6"/>
<variable units="millimolar" name="Km_ACET" initial_value="0.06"/>
<variable units="flux" name="V_ACETDH_max" initial_value="105.0"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="V_ACETDH_calculation">
<eq/>
<ci> V_ACETDH </ci>
<apply>
<divide/>
<apply>
<times/>
<ci> V_ACETDH_max </ci>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<times/>
<ci> Km_ACET </ci>
<ci> Km_NADH </ci>
</apply>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> ACET </ci>
<ci> NADH </ci>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci> BUT </ci>
<ci> NAD </ci>
</apply>
<ci> Keq </ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<divide/>
<ci> ACET </ci>
<ci> Km_ACET </ci>
</apply>
<apply>
<divide/>
<ci> BUT </ci>
<ci> Km_BUT </ci>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<divide/>
<ci> NADH </ci>
<ci> Km_NADH </ci>
</apply>
<apply>
<divide/>
<ci> NAD </ci>
<ci> Km_NAD </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="V_ATPase">
<variable units="flux" public_interface="out" name="V_ATPase"/>
<variable units="millimolar" public_interface="in" name="ADP"/>
<variable units="millimolar" public_interface="in" name="ATP"/>
<variable units="dimensionless" name="N" initial_value="2.6"/>
<variable units="millimolar" name="Km_ATP" initial_value="6.2"/>
<variable units="flux" name="V_ATPase_max" initial_value="900.0"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="V_ATPase_calculation">
<eq/>
<ci> V_ATPase </ci>
<apply>
<divide/>
<apply>
<times/>
<ci> V_ATPase_max </ci>
<apply>
<power/>
<apply>
<divide/>
<ci> ATP </ci>
<apply>
<times/>
<ci> ADP </ci>
<ci> Km_ATP </ci>
</apply>
</apply>
<ci> N </ci>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<power/>
<apply>
<divide/>
<ci> ATP </ci>
<apply>
<times/>
<ci> ADP </ci>
<ci> Km_ATP </ci>
</apply>
</apply>
<ci> N </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="V_NOX">
<variable units="flux" public_interface="out" name="V_NOX"/>
<variable units="millimolar" public_interface="in" name="NAD"/>
<variable units="millimolar" public_interface="in" name="NADH"/>
<variable units="millimolar" public_interface="in" name="O"/>
<variable units="millimolar" name="Km_NAD" initial_value="1.0"/>
<variable units="millimolar" name="Km_NADH" initial_value="0.041"/>
<variable units="millimolar" name="Km_O" initial_value="0.01"/>
<variable units="flux" name="V_NOX_max" initial_value="4117.0"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="V_NOX_calculation">
<eq/>
<ci> V_NOX </ci>
<apply>
<divide/>
<apply>
<times/>
<ci> V_NOX_max </ci>
<apply>
<divide/>
<apply>
<times/>
<ci> NADH </ci>
<ci> O </ci>
</apply>
<apply>
<times/>
<ci> Km_NADH </ci>
<ci> Km_O </ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<divide/>
<ci> NADH </ci>
<ci> Km_NADH </ci>
</apply>
<apply>
<divide/>
<ci> NAD </ci>
<ci> Km_NAD </ci>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<divide/>
<ci> O </ci>
<ci> Km_O </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="V_NEALC">
<variable units="flux" public_interface="out" name="V_NEALC"/>
<variable units="millimolar" public_interface="in" name="ACLAC"/>
<variable units="first_order_rate_constant" name="k" initial_value="0.0003"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="V_NEALC_calculation">
<eq/>
<ci> V_NEALC </ci>
<apply>
<times/>
<ci> k </ci>
<ci> ACLAC </ci>
</apply>
</apply>
</math>
</component>
<connection>
<map_components component_2="V_GLYC" component_1="PYR"/>
<map_variables variable_2="PYR" variable_1="PYR"/>
<map_variables variable_2="V_GLYC" variable_1="V_GLYC"/>
</connection>
<connection>
<map_components component_2="V_LDH" component_1="PYR"/>
<map_variables variable_2="PYR" variable_1="PYR"/>
<map_variables variable_2="V_LDH" variable_1="V_LDH"/>
</connection>
<connection>
<map_components component_2="V_PDH" component_1="PYR"/>
<map_variables variable_2="PYR" variable_1="PYR"/>
<map_variables variable_2="V_PDH" variable_1="V_PDH"/>
</connection>
<connection>
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Metabolic engineering of lactic acid bacteria, the combined
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