<?xml version="1.0"?>

<!--  FILE : oxidation_of_odd_chain_fatty_acids_model.xml

CREATED :  17th June 2002

LAST MODIFIED : 22nd July 2002

AUTHOR :  Catherine Lloyd
          The 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 a generic model of
               odd-chain fatty acid oxidation.

CHANGES:  
   22/07/2002 - CML - Added more metadata.
-->

<model name="oxidation_of_odd_chain_fatty_acids_model" pathway_editor:rendering_config_file="oxidation_of_odd_chain_fatty_acids_model_CellMLrender.xml" xmlns="http://www.cellml.org/cellml/1.0#" xmlns:cellml="http://www.cellml.org/cellml/1.0#" xmlns:cmeta="http://www.cellml.org/metadata/1.0#" xmlns:pathway_editor="http://www.physiome.com/pathway_editor/1.0#">
  <rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:bqs="http://www.cellml.org/bqs/1.0#" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:dcterms="http://purl.org/dc/terms/" xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#">
    <!--
      The following RDF block contains metadata that applies to this document
      as a whole, as indicated by the empty about attribute on the 
      <rdf:Description> element.
    -->
    <rdf:Description rdf:about="">
      <!--
        The Model Builder Metadata.  The Dublin Core "creator" element is used  
        to indicate the person who translated the model into CellML.
      -->
      <dc:creator rdf:parseType="Resource">
        <vCard:N rdf:parseType="Resource">
          <vCard:Family>Lloyd</vCard:Family>
          <vCard:Given>Catherine</vCard:Given>
          <vCard:Other>May</vCard:Other>
        </vCard:N>
        <vCard:EMAIL rdf:parseType="Resource">
          <rdf:value>c.lloyd@auckland.ac.nz</rdf:value>
          <rdf:type rdf:resource="http://imc.org/vCard/3.0#internet" />
        </vCard:EMAIL>
        <vCard:ORG rdf:parseType="Resource">
          <vCard:Orgname>The University of Auckland</vCard:Orgname>
          <vCard:Orgunit>The Bioengineering Institute</vCard:Orgunit>
        </vCard:ORG>
      </dc:creator>
      
      <!--
        The Creation Date metadata. This is the date on which the model
        was translated into CellML.
      -->
      <dcterms:created rdf:parseType="Resource">
        <dcterms:W3CDTF>2002-06-17</dcterms:W3CDTF>
      </dcterms:created>
      
      <!--
        The Last Modified Date metadata. This is the date on which
        the model was last changed.
      -->
      <cmeta:modification rdf:parseType="Resource">
        <rdf:value>
          Added more metadata.
        </rdf:value>
        <cmeta:modifier rdf:parseType="Resource">
          <vCard:N rdf:parseType="Resource">
            <vCard:Family>Lloyd</vCard:Family>
            <vCard:Given>Catherine</vCard:Given>
            <vCard:Other>May</vCard:Other>
          </vCard:N>
        </cmeta:modifier>
        <dcterms:modified rdf:parseType="Resource"> 
          <dcterms:W3CDTF>2002-07-22</dcterms:W3CDTF>
        </dcterms:modified>
      </cmeta:modification>
      
      <!-- The Publisher metadata. -->
      <dc:publisher>
        The University of Auckland, Bioengineering Institute
      </dc:publisher>
    </rdf:Description>
    
    <!--
      The following metadata refers to the model itself, as indicated by the
      reference to the ID "oxidation_of_odd_chain_fatty_acids_model", which is 
      declared on the <model> element.
    -->
    <rdf:Description rdf:about="#oxidation_of_odd_chain_fatty_acids_model">
      <!-- A human readable name for the model. -->
      <dc:title>A Generic Model Of Odd-Chain Fatty Acid Oxidation</dc:title>
      
      <!-- A comment regarding the model. -->
      <cmeta:comment rdf:parseType="Resource">
        <rdf:value>
          Below is a CellML description of a general model of odd-chain fatty 
          acid oxidation.  It is not based on a specific published mathematical 
          model, but instead it is based on a textbook defined pathway.  The 
          general sequential structure and all the reactant, product and enzyme 
          components are included.  Michaelis-Menten enzyme kinetics are 
          assumed.
          
          The purpose of this description is to illustrate how CellML can be 
          used to model a general metabolic pathway.
        </rdf:value>
        <!-- The creator of the comment. -->
        <dc:creator>
          <vCard:FN>Catherine Lloyd</vCard:FN>
        </dc:creator>
      </cmeta:comment>
      
      <cmeta:species>Homo sapiens</cmeta:species>
      
      <!--  Keyword(s) -->
      <bqs:reference rdf:parseType="Resource">
        <dc:subject rdf:parseType="Resource">
          <bqs:subject_type>keyword</bqs:subject_type>
          <rdf:value>metabolism</rdf:value>
        </dc:subject>
      </bqs:reference>
      
      <bqs:Book rdf:parseType="Resource">
        <dc:creator rdf:parseType="Resource">
          <bqs:Person rdf:parseType="Resource">
            <vCard:N rdf:parseType="Resource">
              <vCard:Family>Bronk</vCard:Family>
              <vCard:Given>J</vCard:Given>
              <vCard:Other>Ramsey</vCard:Other>
            </vCard:N>
          </bqs:Person>
        </dc:creator>
        <dc:title>Human Metabolism</dc:title>
        <dcterms:issued rdf:parseType="Resource">
          <dcterms:W3CDTF>1999</dcterms:W3CDTF>
        </dcterms:issued>
        <dc:publisher rdf:parseType="Resource">
          <bqs:Organisation>Addison Wesley Longman Limited</bqs:Organisation>
          <bqs:Property rdf:parseType="Resource">
            <bqs:property_type>location</bqs:property_type>
            <rdf:value>England</rdf:value>
          </bqs:Property>
        </dc:publisher>
      </bqs:Book>
    </rdf:Description>
  </rdf:RDF>
  
  <!--
    We start the model definition with a definition of some named
    sets of units for use throughout the model.
  -->
   
   <units name="micromolar">
     <unit prefix="micro" units="mole" />
     <unit units="litre" exponent="-1" />
   </units>
   
   <units name="flux">
      <unit units="micromolar" />
      <unit units="second" exponent="-1" />
   </units>
   
   <units name="first_order_rate_constant">
     <unit units="second" exponent="-1" />
   </units>
   
   <units name="second_order_rate_constant">
     <unit units="micromolar" exponent="-1" />
     <unit units="second" exponent="-1" />
   </units>
   
   <units name="third_order_rate_constant">
     <unit units="micromolar" exponent="-2" />
     <unit units="second" exponent="-1" />
   </units>
   
  <!--  
    The following component is defined for modelling convenience.  It contains 
    all the universal variables, in this case, only time.
  -->
   <component name="global_variables">
      <variable name="time" public_interface="out" units="second" />
   </component>
  
  <!--  
    The following components describe all the metabolites - both reactants and 
    products - involved in odd-chain fatty acid oxidation.
   -->
   
   <component name="Propionyl_CoA" cmeta:id="Propionyl_CoA">
      <variable name="Propionyl_CoA" public_interface="out" initial_value="1.0" units="micromolar" />
      <variable name="delta_Propionyl_CoA_rxn0" public_interface="in" units="flux" />
      <variable name="time" public_interface="in" units="second" />
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq />
            <apply>
               <diff />
               <bvar>
                  <ci>time</ci>
               </bvar>
               <ci>Propionyl_CoA</ci>
            </apply>
            <ci>delta_Propionyl_CoA_rxn0</ci>
         </apply>
      </math>
   </component>
   
   <component name="Methylmalonyl_CoA" cmeta:id="Methylmalonyl_CoA">
      <variable name="Methylmalonyl_CoA" public_interface="out" initial_value="1.0" units="micromolar" />
      <variable name="delta_Methylmalonyl_CoA_rxn0" public_interface="in" units="flux" />
      <variable name="delta_Methylmalonyl_CoA_rxn1" public_interface="in" units="flux" />
      <variable name="time" public_interface="in" units="second" />
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq />
            <apply>
               <diff />
               <bvar>
                  <ci>time</ci>
               </bvar>
               <ci>Methylmalonyl_CoA</ci>
            </apply>
            <apply>
               <plus />
               <ci>delta_Methylmalonyl_CoA_rxn0</ci>
               <ci>delta_Methylmalonyl_CoA_rxn1</ci>
            </apply>
         </apply>
      </math>
   </component>
  
   <component name="Methylmalonyl_B12" cmeta:id="Methylmalonyl_B12">
      <variable name="Methylmalonyl_B12" public_interface="out" initial_value="1.0" units="micromolar" />
      <variable name="delta_Methylmalonyl_B12_rxn1" public_interface="in" units="flux" />
      <variable name="delta_Methylmalonyl_B12_rxn2" public_interface="in" units="flux" />
      <variable name="time" public_interface="in" units="second" />
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq />
            <apply>
               <diff />
               <bvar>
                  <ci>time</ci>
               </bvar>
               <ci>Methylmalonyl_B12</ci>
            </apply>
            <apply>
               <plus />
               <ci>delta_Methylmalonyl_B12_rxn1</ci>
               <ci>delta_Methylmalonyl_B12_rxn2</ci>
            </apply>
         </apply>
      </math>
   </component>
  
   <component name="Succinyl_CoA" cmeta:id="Succinyl_CoA">
      <variable name="Succinyl_CoA" public_interface="out" initial_value="1.0" units="micromolar" />
      <variable name="delta_Succinyl_CoA_rxn3" public_interface="in" units="flux" />
      <variable name="time" public_interface="in" units="second" />
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq />
            <apply>
               <diff />
               <bvar>
                  <ci>time</ci>
               </bvar>
               <ci>Succinyl_CoA</ci>
            </apply>
            <ci>delta_Succinyl_CoA_rxn3</ci>
         </apply>
      </math>
   </component>
  
   <component name="ATP" cmeta:id="ATP">
      <variable name="ATP" public_interface="out" initial_value="1.0" units="micromolar" />
      <variable name="delta_ATP_rxn0" public_interface="in" units="flux" />
      <variable name="time" public_interface="in" units="second" />
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq />
            <apply>
               <diff />
               <bvar>
                  <ci>time</ci>
               </bvar>
               <ci>ATP</ci>
            </apply>
            <ci>delta_ATP_rxn0</ci>
         </apply>
      </math>
   </component>
 
   <component name="ADP" cmeta:id="ADP">
      <variable name="ADP" public_interface="out" initial_value="1.0" units="micromolar" />
      <variable name="delta_ADP_rxn0" public_interface="in" units="flux" />
      <variable name="time" public_interface="in" units="second" />
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq />
            <apply>
               <diff />
               <bvar>
                  <ci>time</ci>
               </bvar>
               <ci>ADP</ci>
            </apply>
            <ci>delta_ADP_rxn0</ci>
         </apply>
      </math>
   </component>
  
   <component name="Pi" cmeta:id="Pi">
      <variable name="Pi" public_interface="out" initial_value="1.0" units="micromolar" />
      <variable name="delta_Pi_rxn0" public_interface="in" units="flux" />
      <variable name="time" public_interface="in" units="second" />
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq />
            <apply>
               <diff />
               <bvar>
                  <ci>time</ci>
               </bvar>
               <ci>Pi</ci>
            </apply>
            <ci>delta_Pi_rxn0</ci>
         </apply>
      </math>
   </component>
   
   <component name="CO2" cmeta:id="CO2">
      <variable name="CO2" public_interface="out" initial_value="1.0" units="micromolar" />
      <variable name="delta_CO2_rxn0" public_interface="in" units="flux" />
      <variable name="time" public_interface="in" units="second" />
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq />
            <apply>
               <diff />
               <bvar>
                  <ci>time</ci>
               </bvar>
               <ci>CO2</ci>
            </apply>
            <ci>delta_CO2_rxn0</ci>
         </apply>
      </math>
   </component>
  
   <component name="Deoxyadenosyl_5_B12" cmeta:id="Deoxyadenosyl_5_B12">
      <variable name="Deoxyadenosyl_5_B12" public_interface="out" initial_value="1.0" units="micromolar" />
      <variable name="delta_Deoxyadenosyl_5_B12_rxn3" public_interface="in" units="flux" />
      <variable name="delta_Deoxyadenosyl_5_B12_rxn1" public_interface="in" units="flux" />
      <variable name="time" public_interface="in" units="second" />
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq />
            <apply>
               <diff />
               <bvar>
                  <ci>time</ci>
               </bvar>
               <ci>Deoxyadenosyl_5_B12</ci>
            </apply>
            <apply>
               <plus />
               <ci>delta_Deoxyadenosyl_5_B12_rxn3</ci>
               <ci>delta_Deoxyadenosyl_5_B12_rxn1</ci>
            </apply>
         </apply>
      </math>
   </component>
  
   <component name="Succinyl_B12" cmeta:id="Succinyl_B12">
      <variable name="Succinyl_B12" public_interface="out" initial_value="1.0" units="micromolar" />
      <variable name="delta_Succinyl_B12_rxn2" public_interface="in" units="flux" />
      <variable name="delta_Succinyl_B12_rxn3" public_interface="in" units="flux" />
      <variable name="time" public_interface="in" units="second" />
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq />
            <apply>
               <diff />
               <bvar>
                  <ci>time</ci>
               </bvar>
               <ci>Succinyl_B12</ci>
            </apply>
            <apply>
               <plus />
               <ci>delta_Succinyl_B12_rxn2</ci>
               <ci>delta_Succinyl_B12_rxn3</ci>
            </apply>
         </apply>
      </math>
   </component>
  
   <component name="Deoxyadenosine_5" cmeta:id="Deoxyadenosine_5">
      <variable name="Deoxyadenosine_5" public_interface="out" initial_value="1.0" units="micromolar" />
      <variable name="delta_Deoxyadenosine_5_rxn1" public_interface="in" units="flux" />
      <variable name="delta_Deoxyadenosine_5_rxn3" public_interface="in" units="flux" />
      <variable name="time" public_interface="in" units="second" />
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq />
            <apply>
               <diff />
               <bvar>
                  <ci>time</ci>
               </bvar>
               <ci>Deoxyadenosine_5</ci>
            </apply>
            <apply>
               <plus />
               <ci>delta_Deoxyadenosine_5_rxn1</ci>
               <ci>delta_Deoxyadenosine_5_rxn3</ci>
            </apply>
         </apply>
      </math>
   </component>
   
   <!--  
    The following components describe all the enzymes and protein complexes 
    involved in odd-chain fatty acid oxidation.
   -->
   
   <component name="Methylmalonyl_CoA_mutase" cmeta:id="Methylmalonyl_CoA_mutase">
      <variable name="Methylmalonyl_CoA_mutase" public_interface="out" initial_value="1.0" units="micromolar" />
      <variable name="time" public_interface="in" units="second" />
   </component>
  
   <component name="Propionyl_CoA_carboxylase" cmeta:id="Propionyl_CoA_carboxylase">
      <variable name="Propionyl_CoA_carboxylase" public_interface="out" initial_value="1.0" units="micromolar" />
      <variable name="time" public_interface="in" units="second" />
   </component>
   
   <!--
    The following components represent the reaction steps of odd-chain fatty 
    acid oxidation.
   -->
   
   <component name="reaction0">
      <variable name="Propionyl_CoA" public_interface="in" units="micromolar" />
      <variable name="ATP" public_interface="in" units="micromolar" />
      <variable name="CO2" public_interface="in" units="micromolar" />
      <variable name="Pi" public_interface="in" units="micromolar" />
      <variable name="ADP" public_interface="in" units="micromolar" />
      <variable name="Methylmalonyl_CoA" public_interface="in" units="micromolar" />
      <variable name="Propionyl_CoA_carboxylase" public_interface="in" units="micromolar" />
      <variable name="delta_Propionyl_CoA_rxn0" public_interface="out" units="flux" />
      <variable name="delta_ATP_rxn0" public_interface="out" units="flux" />
      <variable name="delta_CO2_rxn0" public_interface="out" units="flux" />
      <variable name="delta_Pi_rxn0" public_interface="out" units="flux" />
      <variable name="delta_ADP_rxn0" public_interface="out" units="flux" />
      <variable name="delta_Methylmalonyl_CoA_rxn0" public_interface="out" units="flux" />
      <variable name="vmax0" initial_value="1.0" units="third_order_rate_constant" />
      <variable name="km0" initial_value="1.0" units="micromolar" />
      <variable name="rate" units="flux" />
      <reaction reversible="no">
         <variable_ref variable="Propionyl_CoA">
            <role role="reactant" delta_variable="delta_Propionyl_CoA_rxn0" stoichiometry="1" />
         </variable_ref>
         <variable_ref variable="ATP">
            <role role="reactant" delta_variable="delta_ATP_rxn0" stoichiometry="1" />
         </variable_ref>
         <variable_ref variable="CO2">
            <role role="reactant" delta_variable="delta_CO2_rxn0" stoichiometry="1" />
         </variable_ref>
         <variable_ref variable="Pi">
            <role role="product" delta_variable="delta_Pi_rxn0" stoichiometry="1" />
         </variable_ref>
         <variable_ref variable="ADP">
            <role role="product" delta_variable="delta_ADP_rxn0" stoichiometry="1" />
         </variable_ref>
         <variable_ref variable="Methylmalonyl_CoA">
            <role role="product" delta_variable="delta_Methylmalonyl_CoA_rxn0" stoichiometry="1" />
         </variable_ref>
         <variable_ref variable="Propionyl_CoA_carboxylase">
            <role role="catalyst" />
         </variable_ref>
         <variable_ref variable="rate">
            <role role="rate">
               <math xmlns="http://www.w3.org/1998/Math/MathML">
                  <apply>
                     <eq />
                     <ci>rate</ci>
                     <apply><divide />
                        <apply><times />
                          <ci>vmax0</ci>
                          <ci>Propionyl_CoA</ci>
                          <ci>ATP</ci>
                          <ci>CO2</ci>
                        </apply>
                        <apply><plus />
                          <ci>km0</ci>
                          <ci>Propionyl_CoA</ci>
                          <ci>ATP</ci>
                          <ci>CO2</ci>
                        </apply>
                     </apply>
                  </apply>
               </math>
            </role>
         </variable_ref>
      </reaction>
   </component>
 
   <component name="reaction1">
      <variable name="Methylmalonyl_CoA" public_interface="in" units="micromolar" />
      <variable name="Deoxyadenosyl_5_B12" public_interface="in" units="micromolar" />
      <variable name="Methylmalonyl_B12" public_interface="in" units="micromolar" />
      <variable name="Methylmalonyl_CoA_mutase" public_interface="in" units="micromolar" />
      <variable name="Deoxyadenosine_5" public_interface="in" units="micromolar" />
      <variable name="delta_Methylmalonyl_CoA_rxn1" public_interface="out" units="flux" />
      <variable name="delta_Deoxyadenosyl_5_B12_rxn1" public_interface="out" units="flux" />
      <variable name="delta_Methylmalonyl_B12_rxn1" public_interface="out" units="flux" />
      <variable name="delta_Deoxyadenosine_5_rxn1" public_interface="out" units="flux" />
      <variable name="km1" initial_value="1.0" units="micromolar" />
      <variable name="vmax1" initial_value="1.0" units="second_order_rate_constant" />
      <variable name="km1_" initial_value="1.0" units="micromolar" />
      <variable name="vmax1_" initial_value="1.0" units="second_order_rate_constant" />
      <variable name="rate" units="flux" />
      <reaction reversible="yes">
         <variable_ref variable="Methylmalonyl_CoA">
            <role role="reactant" direction="forward" delta_variable="delta_Methylmalonyl_CoA_rxn1" stoichiometry="1" />
         </variable_ref>
         <variable_ref variable="Deoxyadenosyl_5_B12">
            <role role="reactant" direction="forward" delta_variable="delta_Deoxyadenosyl_5_B12_rxn1" stoichiometry="1" />
         </variable_ref>
         <variable_ref variable="Methylmalonyl_B12">
            <role role="product" direction="forward" delta_variable="delta_Methylmalonyl_B12_rxn1" stoichiometry="1" />
         </variable_ref>
         <variable_ref variable="Deoxyadenosine_5">
            <role role="product" direction="forward" delta_variable="delta_Deoxyadenosine_5_rxn1" stoichiometry="1" />
         </variable_ref>
         <variable_ref variable="Methylmalonyl_CoA_mutase">
            <role role="catalyst" direction="forward" />
         </variable_ref>
         <variable_ref variable="rate">
            <role role="rate">
               <math xmlns="http://www.w3.org/1998/Math/MathML">
                  <apply>
                     <eq />
                     <ci>rate</ci>
                     <apply>
                        <divide />
                        <apply>
                           <minus />
                           <apply>
                              <times />
                              <ci>vmax1</ci>
                              <apply>
                                 <divide />
                                 <apply>
                                    <times />
                                    <ci>Methylmalonyl_CoA</ci>
                        &