- Author:
- pmr2.import <nobody@models.cellml.org>
- Date:
- 2006-07-09 07:45:42+12:00
- Desc:
- committing version01 of wolf_sohn_heinrich_kuriyama_2001
- Permanent Source URI:
- http://models.cellml.org/workspace/wolf_sohn_heinrich_kuriyama_2001/rawfile/b1bd8b08fdbdeb34c11e007de13c1c0b57ece4d9/wolf_sohn_heinrich_kuriyama_2001.cellml
<?xml version='1.0' encoding='utf-8'?>
<!-- FILE : wolf_model_2001.xml
CREATED : 5th 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 Wolf et al's 2001 model for metabolic oscillations in the yeast Saccharomyces cerevisiae.
CHANGES:
19/07/2002 - 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="wolf_sohn_heinrich_kuriyama_2001_version01" name="wolf_sohn_heinrich_kuriyama_2001_version01">
<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
<articleinfo>
<title>Metabolic Oscillations in Saccharomyces cerevisiae</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>
Cellular oscillations are appropriate for investigating the structure and regulatory properties of biochemical networks. Whilst calcium dynamics and glycolytic oscillations have been intensively studied (see <ulink url="${HTML_EXMPL_WOLF_MODEL}">The Wolf <emphasis>et al</emphasis>. Mathematical Model of Glycolytic Oscillations in yeast, 2000</ulink>), autonomous metabolic oscillations are a relatively new field. In their 2001 study, Jana Wolf, Ho-Yong Sohn, Reinhart Heinrich and Hiroshi Kuriyama observed autonomous metabolic oscillations in aerobic continuous cultures of <emphasis>Saccharomyces cerevisiae</emphasis>. Experimental investigation of the underlying mechanisms revealed that several pathways and regulatory couplings are involved. The authors translate a hypothetical mechanism including the sulphate assimilation pathway, ethanol degradation and respiration into a mathematical model. Simulations confirm the ability of the model to produce limit cycle oscillations which reproduce most of the characteristic features of the system.
</para>
<para>
The model includes the pathways which were found to be essential for the generation of oscillations. These are the synthesis of the amino acid cysteine by the sulfate assimilation pathway, the uptake and degradation of the carbon source ethanol, the citrate cycle and oxidative phosphorylation. Only regulatory couplings which are critical for the oscillations are considered, including the inhibitory effect of cysteine on the sulfate uptake and the inhibition of the respiratory chain by sulphide (the reaction network of the model is shown below in <xref linkend="fig_cell_diagram"/>).
</para>
<para>
The complete original paper reference is cited below:
</para>
<para>
<ulink url="http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6T36-439DRFB-7&_coverDate=06%2F22%2F2001&_alid=39766201&_rdoc=1&_fmt=summary&_orig=search&_qd=1&_cdi=4938&_sort=d&_acct=C000011498&_version=1&_urlVersion=0&_userid=140507&md5=bb87e2929d7fc00e1bbc8ab6be08655f">Mathematical analysis of a mechanism for autonomous metabolic oscillations in continuous culture of <emphasis>Saccharomyces cerevisiae</emphasis>
</ulink>, Jana Wolf, Ho-Yong Sohn, Reinhart Heinrich and Hiroshi Kuriyama, 2001, <ulink url="http://www.sciencedirect.com/science?_ob=JournalURL&_cdi=4938&_auth=y&_acct=C000011498&_version=1&_urlVersion=0&_userid=140507&md5=a119ceadbd93fd19f1efa8441096a82d">
<emphasis>FEBS Letters</emphasis>
</ulink>, 499, 230-234. (The PDF and <ulink url="http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6T36-439DRFB-7&_user=140507&_coverDate=06%2F22%2F2001&_alid=39766201&_rdoc=1&_fmt=full&_orig=search&_qd=1&_cdi=4938&_sort=d&_acct=C000011498&_version=1&_urlVersion=0&_userid=140507&md5=43097809bfa1bb4df4932ec80ec03287">full text</ulink> versions of the article are available to subscribers on the Science Direct website.) <ulink url="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&list_uids=11423122&dopt=Abstract">PubMed ID: 11423122</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_cell_diagram">
<mediaobject>
<imageobject>
<objectinfo>
<title>schematic diagram</title>
</objectinfo>
<imagedata fileref="wolf_2001.png"/>
</imageobject>
</mediaobject>
<caption>Reaction scheme of the model. The following abbreviations are introduced for the metabolites: sul: sulphate ions, aps: adenylyl sulfate, pap: 3-phosphoadenylyl sulfate, hyd: hydrogen sulphide, cys: cysteine, eth: ethanol, aco: acetyl-CoA, S1 and S2: intermediates of the citric acid cycle, oxy: oxygen, C1 and C2: protein complexes involved in oxidative phosphorylation, A3: ATP, A2: ADP, N1: NAD(P)<superscript>+</superscript>, N2: NAD(P)H, oah: O-acetylhomoserine. The cytosolic and mitochondrial compartments are characterized by the superscripts c and m, respectively.</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="millimolar">
<unit units="mole" prefix="milli"/>
<unit units="litre" 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>
<units name="third_order_rate_constant">
<unit units="millimolar" exponent="-2"/>
<unit units="minute" exponent="-1"/>
</units>
<units name="forth_order_rate_constant">
<unit units="millimolar" exponent="-3"/>
<unit units="minute" exponent="-1"/>
</units>
<units name="fifth_order_rate_constant">
<unit units="millimolar" exponent="-4"/>
<unit units="minute" exponent="-1"/>
</units>
<component name="environment">
<variable units="minute" public_interface="out" name="time"/>
</component>
<component cmeta:id="S1" name="S1">
<variable units="millimolar" public_interface="out" name="S1"/>
<variable units="flux" public_interface="in" name="delta_S1_rxn8"/>
<variable units="flux" public_interface="in" name="delta_S1_rxn9"/>
<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>S1</ci>
</apply>
<apply>
<plus/>
<ci>delta_S1_rxn8</ci>
<ci>delta_S1_rxn9</ci>
</apply>
</apply>
</math>
</component>
<component cmeta:id="S" name="S">
<variable units="millimolar" name="S" initial_value="2.0"/>
<variable units="millimolar" public_interface="in" name="S1"/>
<variable units="millimolar" public_interface="out" name="S2"/>
<variable units="minute" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>S</ci>
<apply>
<plus/>
<ci> S1 </ci>
<ci> S2 </ci>
</apply>
</apply>
</math>
</component>
<component cmeta:id="sul" name="sul">
<variable units="millimolar" public_interface="out" name="sul"/>
<variable units="flux" public_interface="in" name="delta_sul_rxn1"/>
<variable units="flux" public_interface="in" name="delta_sul_rxn2"/>
<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>sul</ci>
</apply>
<apply>
<plus/>
<ci>delta_sul_rxn1</ci>
<ci>delta_sul_rxn2</ci>
</apply>
</apply>
</math>
</component>
<component cmeta:id="aps" name="aps">
<variable units="millimolar" public_interface="out" name="aps"/>
<variable units="flux" public_interface="in" name="delta_aps_rxn2"/>
<variable units="flux" public_interface="in" name="delta_aps_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>aps</ci>
</apply>
<apply>
<plus/>
<ci>delta_aps_rxn2</ci>
<ci>delta_aps_rxn3</ci>
</apply>
</apply>
</math>
</component>
<component cmeta:id="pap" name="pap">
<variable units="millimolar" public_interface="out" name="pap"/>
<variable units="flux" public_interface="in" name="delta_pap_rxn3"/>
<variable units="flux" public_interface="in" name="delta_pap_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>pap</ci>
</apply>
<apply>
<plus/>
<ci>delta_pap_rxn3</ci>
<ci>delta_pap_rxn4</ci>
</apply>
</apply>
</math>
</component>
<component cmeta:id="hyd" name="hyd">
<variable units="millimolar" public_interface="out" name="hyd"/>
<variable units="flux" public_interface="in" name="delta_hyd_rxn4"/>
<variable units="flux" public_interface="in" name="delta_hyd_rxn5"/>
<variable units="flux" public_interface="in" name="delta_hyd_rxn17"/>
<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>hyd</ci>
</apply>
<apply>
<plus/>
<ci>delta_hyd_rxn4</ci>
<ci>delta_hyd_rxn5</ci>
<ci>delta_hyd_rxn17</ci>
</apply>
</apply>
</math>
</component>
<component cmeta:id="cys" name="cys">
<variable units="millimolar" public_interface="out" name="cys"/>
<variable units="flux" public_interface="in" name="delta_cys_rxn5"/>
<variable units="flux" public_interface="in" name="delta_cys_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>cys</ci>
</apply>
<apply>
<plus/>
<ci>delta_cys_rxn5</ci>
<ci>delta_cys_rxn6</ci>
</apply>
</apply>
</math>
</component>
<component cmeta:id="eth" name="eth">
<variable units="millimolar" public_interface="out" name="eth"/>
<variable units="flux" public_interface="in" name="delta_eth_rxn13"/>
<variable units="flux" public_interface="in" name="delta_eth_rxn7"/>
<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>eth</ci>
</apply>
<apply>
<plus/>
<ci>delta_eth_rxn13</ci>
<ci>delta_eth_rxn7</ci>
</apply>
</apply>
</math>
</component>
<component cmeta:id="aco" name="aco">
<variable units="millimolar" public_interface="out" name="aco"/>
<variable units="flux" public_interface="in" name="delta_aco_rxn7"/>
<variable units="flux" public_interface="in" name="delta_aco_rxn8"/>
<variable units="flux" public_interface="in" name="delta_aco_rxn15"/>
<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>aco</ci>
</apply>
<apply>
<plus/>
<ci>delta_aco_rxn7</ci>
<ci>delta_aco_rxn8</ci>
<ci>delta_aco_rxn15</ci>
</apply>
</apply>
</math>
</component>
<component cmeta:id="oxy" name="oxy">
<variable units="millimolar" public_interface="out" name="oxy"/>
<variable units="flux" public_interface="in" name="delta_oxy_rxn10"/>
<variable units="flux" public_interface="in" name="delta_oxy_rxn11A"/>
<variable units="flux" public_interface="in" name="delta_oxy_rxn14"/>
<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>oxy</ci>
</apply>
<apply>
<plus/>
<ci>delta_oxy_rxn10</ci>
<ci>delta_oxy_rxn11A</ci>
<ci>delta_oxy_rxn14</ci>
</apply>
</apply>
</math>
</component>
<component cmeta:id="A3_c" name="A3_c">
<variable units="millimolar" public_interface="out" name="A3_c"/>
<variable units="flux" public_interface="in" name="delta_A3_c_rxn2"/>
<variable units="flux" public_interface="in" name="delta_A3_c_rxn3"/>
<variable units="flux" public_interface="in" name="delta_A3_c_rxn12"/>
<variable units="flux" public_interface="in" name="delta_A3_c_rxn16"/>
<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>A3_c</ci>
</apply>
<apply>
<plus/>
<ci>delta_A3_c_rxn2</ci>
<ci>delta_A3_c_rxn3</ci>
<ci>delta_A3_c_rxn12</ci>
<ci>delta_A3_c_rxn16</ci>
</apply>
</apply>
</math>
</component>
<component cmeta:id="A3_m" name="A3_m">
<variable units="millimolar" public_interface="out" name="A3_m"/>
<variable units="flux" public_interface="in" name="delta_A3_m_rxn11B"/>
<variable units="flux" public_interface="in" name="delta_A3_m_rxn16"/>
<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>A3_m</ci>
</apply>
<apply>
<plus/>
<ci>delta_A3_m_rxn11B</ci>
<ci>delta_A3_m_rxn16</ci>
</apply>
</apply>
</math>
</component>
<component cmeta:id="A_c" name="A_c">
<variable units="millimolar" name="A_c" initial_value="2.0"/>
<variable units="millimolar" public_interface="out" name="A2_c"/>
<variable units="millimolar" public_interface="in" name="A3_c"/>
<variable units="minute" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>A_c</ci>
<apply>
<plus/>
<ci> A2_c </ci>
<ci> A3_c </ci>
</apply>
</apply>
</math>
</component>
<component cmeta:id="A_m" name="A_m">
<variable units="millimolar" name="A_m" initial_value="2.0"/>
<variable units="millimolar" public_interface="out" name="A2_m"/>
<variable units="millimolar" public_interface="in" name="A3_m"/>
<variable units="minute" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>A_m</ci>
<apply>
<plus/>
<ci> A2_m </ci>
<ci> A3_m </ci>
</apply>
</apply>
</math>
</component>
<component cmeta:id="N2" name="N2">
<variable units="millimolar" public_interface="out" name="N2"/>
<variable units="flux" public_interface="in" name="delta_N2_rxn4"/>
<variable units="flux" public_interface="in" name="delta_N2_rxn7"/>
<variable units="flux" public_interface="in" name="delta_N2_rxn9"/>
<variable units="flux" public_interface="in" name="delta_N2_rxn11A"/>
<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>N2</ci>
</apply>
<apply>
<plus/>
<ci>delta_N2_rxn4</ci>
<ci>delta_N2_rxn7</ci>
<ci>delta_N2_rxn9</ci>
<ci>delta_N2_rxn11A</ci>
</apply>
</apply>
</math>
</component>
<component name="N">
<variable units="millimolar" name="N" initial_value="2.0"/>
<variable units="millimolar" public_interface="out" name="N1"/>
<variable units="millimolar" public_interface="in" name="N2"/>
<variable units="minute" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci> N </ci>
<apply>
<plus/>
<ci> N1 </ci>
<ci> N2 </ci>
</apply>
</apply>
</math>
</component>
<component cmeta:id="oah" name="oah">
<variable units="millimolar" public_interface="out" name="oah"/>
<variable units="flux" public_interface="in" name="delta_oah_rxn5"/>
<variable units="flux" public_interface="in" name="delta_oah_rxn15"/>
<variable units="flux" public_interface="in" name="delta_oah_rxn18"/>
<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>oah</ci>
</apply>
<apply>
<plus/>
<ci>delta_oah_rxn5</ci>
<ci>delta_oah_rxn15</ci>
<ci>delta_oah_rxn18</ci>
</apply>
</apply>
</math>
</component>
<component name="reaction_1">
<variable units="millimolar" public_interface="in" name="sul"/>
<variable units="millimolar" public_interface="in" name="cys"/>
<variable units="flux" name="v0" initial_value="1.6"/>
<variable units="dimensionless" name="f1"/>
<variable units="dimensionless" name="n" initial_value="4.0"/>
<variable units="millimolar" name="Kc" initial_value="0.1"/>
<variable units="flux" public_interface="out" name="delta_sul_rxn1"/>
<variable units="flux" name="r"/>
<reaction reversible="no">
<variable_ref variable="sul">
<role stoichiometry="1" direction="forward" delta_variable="delta_sul_rxn1" role="reactant"/>
</variable_ref>
<variable_ref variable="cys">
<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>
<times/>
<ci> v0 </ci>
<ci> f1 </ci>
</apply>
</apply>
</math>
</role>
</variable_ref>
</reaction>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="f1_calculation">
<eq/>
<ci> f1 </ci>
<apply>
<power/>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<power/>
<apply>
<divide/>
<ci> cys </ci>
<ci> Kc </ci>
</apply>
<ci> n </ci>
</apply>
</apply>
<cn cellml:units="dimensionless"> -1.0 </cn>
</apply>
</apply>
</math>
</component>
<component name="reaction_2">
<variable units="millimolar" public_interface="in" name="sul"/>
<variable units="millimolar" public_interface="in" name="aps"/>
<variable units="millimolar" public_interface="in" name="A3_c"/>
<variable units="first_order_rate_constant" name="k_2" initial_value="0.2"/>
<variable units="flux" public_interface="out" name="delta_sul_rxn2"/>
<variable units="flux" public_interface="out" name="delta_aps_rxn2"/>
<variable units="flux" public_interface="out" name="delta_A3_c_rxn2"/>
<variable units="flux" name="r"/>
<reaction reversible="no">
<variable_ref variable="sul">
<role stoichiometry="1" direction="forward" delta_variable="delta_sul_rxn2" role="reactant"/>
</variable_ref>
<variable_ref variable="A3_c">
<role stoichiometry="1" direction="forward" delta_variable="delta_A3_c_rxn2" role="reactant"/>
</variable_ref>
<variable_ref variable="aps">
<role stoichiometry="2" direction="forward" delta_variable="delta_aps_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>
<times/>
<ci> k_2 </ci>
<ci> sul </ci>
<ci> A3_c </ci>
</apply>
</apply>
</math>
</role>
</variable_ref>
</reaction>
</component>
<component name="reaction_3">
<variable units="millimolar" public_interface="in" name="aps"/>
<variable units="millimolar" public_interface="in" name="pap"/>
<variable units="millimolar" public_interface="in" name="A3_c"/>
<variable units="millimolar" public_interface="in" name="A2_c"/>
<variable units="forth_order_rate_constant" name="k_3" initial_value="0.2"/>
<variable units="flux" public_interface="out" name="delta_aps_rxn3"/>
<variable units="flux" public_interface="out" name="delta_pap_rxn3"/>
<variable units="flux" public_interface="out" name="delta_A3_c_rxn3"/>
<variable units="flux" name="r"/>
<reaction reversible="no">
<variable_ref variable="aps">
<role stoichiometry="1" direction="forward" delta_variable="delta_aps_rxn3" role="reactant"/>
</variable_ref>
<variable_ref variable="A3_c">
<role stoichiometry="1" direction="forward" delta_variable="delta_A3_c_rxn3" role="reactant"/>
</variable_ref>
<variable_ref variable="pap">
<role stoichiometry="1" direction="forward" delta_variable="delta_pap_rxn3" role="product"/>
</variable_ref>
<variable_ref variable="A2_c">
<role direction="forward" 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>
<times/>
<ci> k_3 </ci>
<ci> aps </ci>
<ci> A3_c </ci>
</apply>
</apply>
</math>
</role>
</variable_ref>
</reaction>
</component>
<component name="reaction_4">
<variable units="millimolar" public_interface="in" name="pap"/>
<variable units="millimolar" public_interface="in" name="N2"/>
<variable units="millimolar" public_interface="in" name="hyd"/>
<variable units="millimolar" public_interface="in" name="N1"/>
<variable units="second_order_rate_constant" name="k_4" initial_value="0.2"/>
<variable units="flux" public_interface="out" name="delta_pap_rxn4"/>
<variable units="flux" public_interface="out" name="delta_N2_rxn4"/>
<variable units="flux" public_interface="out" name="delta_hyd_rxn4"/>
<variable units="flux" name="r"/>
<reaction reversible="no">
<variable_ref variable="pap">
<role stoichiometry="1" direction="forward" delta_variable="delta_pap_rxn4" role="reactant"/>
</variable_ref>
<variable_ref variable="N2">
<role stoichiometry="3" direction="forward" delta_variable="delta_N2_rxn4" role="reactant"/>
</variable_ref>
<variable_ref variable="hyd">
<role stoichiometry="1" direction="forward" delta_variable="delta_hyd_rxn4" role="product"/>
</variable_ref>
<variable_ref variable="N1">
<role direction="forward" 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>
<times/>
<ci> k_4 </ci>
<ci> pap </ci>
<ci> N2 </ci>
</apply>
</apply>
</math>
</role>
</variable_ref>
</reaction>
</component>
<component name="reaction_5">
<variable units="millimolar" public_interface="in" name="hyd"/>
<variable units="millimolar" public_interface="in" name="cys"/>
<variable units="millimolar" public_interface="in" name="oah"/>
<variable units="second_order_rate_constant" name="k_5" initial_value="0.1"/>
<variable units="flux" public_interface="out" name="delta_hyd_rxn5"/>
<variable units="flux" public_interface="out" name="delta_cys_rxn5"/>
<variable units="flux" public_interface="out" name="delta_oah_rxn5"/>
<variable units="flux" name="r"/>
<reaction reversible="no">
<variable_ref variable="hyd">
<role stoichiometry="1" direction="forward" delta_variable="delta_hyd_rxn5" role="reactant"/>
</variable_ref>
<variable_ref variable="oah">
<role stoichiometry="1" direction="forward" delta_variable="delta_oah_rxn5" role="reactant"/>
</variable_ref>
<variable_ref variable="cys">
<role stoichiometry="1" direction="forward" delta_variable="delta_cys_rxn5" 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>
<times/>
<ci> k_5 </ci>
<ci> hyd </ci>
<ci> oah </ci>
</apply>
</apply>
</math>
</role>
</variable_ref>
</reaction>
</component>
<component name="reaction_6">
<variable units="millimolar" public_interface="in" name="cys"/>
<variable units="first_order_rate_constant" name="k_6" initial_value="0.12"/>
<variable units="flux" public_interface="out" name="delta_cys_rxn6"/>
<variable units="flux" name="r"/>
<reaction reversible="no">
<variable_ref variable="cys">
<role stoichiometry="1" direction="forward" delta_variable="delta_cys_rxn6" role="reactant"/>
</variable_ref>
<variable_ref variable="r">
<role role="rate">
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci> r </ci>
<apply>
<times/>
<ci> k_6 </ci>
<ci> cys </ci>
</apply>
</apply>
</math>
</role>
</variable_ref>
</reaction>
</component>
<component name="reaction_7">
<variable units="millimolar" public_interface="in" name="eth"/>
<variable units="millimolar" public_interface="in" name="aco"/>
<variable units="millimolar" public_interface="in" name="N1"/>
<variable units="millimolar" public_interface="in" name="N2"/>
<variable units="third_order_rate_constant" name="k_7" initial_value="10.0"/>
<variable units="flux" public_interface="out" name="delta_eth_rxn7"/>
<variable units="flux" public_interface="out" name="delta_aco_rxn7"/>
<variable units="flux" public_interface="out" name="delta_N2_rxn7"/>
<variable units="flux" name="r"/>
<reaction reversible="no">
<variable_ref variable="eth">
<role stoichiometry="1" direction="forward" delta_variable="delta_eth_rxn7" role="reactant"/>
</variable_ref>
<variable_ref variable="N1">
<role direction="forward" role="reactant"/>
</variable_ref>
<variable_ref variable="aco">
<role stoichiometry="1" direction="forward" delta_variable="delta_aco_rxn7" role="product"/>
</variable_ref>
<variable_ref variable="N2">
<role stoichiometry="2" direction="forward" delta_variable="delta_N2_rxn7" 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>
<times/>
<ci> k_7 </ci>
<ci> eth </ci>
</apply>
</apply>
</math>
</role>
</variable_ref>
</reaction>
</component>
<component name="reaction_8">
<variable units="millimolar" public_interface="in" name="aco"/>
<variable units="millimolar" public_interface="in" name="S2"/>
<variable units="millimolar" public_interface="in" name="S1"/>
<variable units="second_order_rate_constant" name="k_8" initial_value="10.0"/>
<variable units="flux" public_interface="out" name="delta_S1_rxn8"/>
<variable units="flux" public_interface="out" name="delta_aco_rxn8"/>
<variable units="flux" name="r"/>
<reaction reversible="no">
<variable_ref variable="aco">
<role stoichiometry="1" direction="forward" delta_variable="delta_aco_rxn8" role="reactant"/>
</variable_ref>
<variable_ref variable="S2">
<role direction="forward" role="reactant"/>
</variable_ref>
<variable_ref variable="S1">
<role stoichiometry="1" direction="forward" delta_variable="delta_S1_rxn8" 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>
<times/>
<ci> k_8 </ci>
<ci> S2 </ci>
</apply>
</apply>
</math>
</role>
</variable_ref>
</reaction>
</component>
<component name="reaction_9">
<variable units="millimolar" public_interface="in" name="S1"/>
<variable units="millimolar" public_interface="in" name="S2"/>
<variable units="millimolar" public_interface="in" name="N1"/>
<variable units="millimolar" public_interface="in" name="N2"/>
<variable units="fifth_order_rate_constant" name="k_9" initial_value="10.0"/>
<variable units="flux" public_interface="out" name="delta_S1_rxn9"/>
<variable units="flux" public_interface="out" name="delta_N2_rxn9"/>
<variable units="flux" name="r"/>
<reaction reversible="no">
<variable_ref variable="S1">
<role stoichiometry="1" direction="forward" delta_variable="delta_S1_rxn9" role="reactant"/>
</variable_ref>
<variable_ref variable="N1">
<role direction="forward" role="reactant"/>
</variable_ref>
<variable_ref variable="S2">
<role direction="forward" role="product"/>
</variable_ref>
<variable_ref variable="N2">
<role stoichiometry="4" direction="forward" delta_variable="delta_N2_rxn9" 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>
<times/>
<ci> k_9 </ci>
<ci> S1 </ci>
<ci> N1 </ci>
</apply>
</apply>
</math>
</role>
</variable_ref>
</reaction>
</component>
<component name="reaction_10">
<variable units="millimolar" public_interface="in" name="oxy"/>
<variable units="flux" name="v10" initial_value="80.0"/>
<variable units="flux" public_interface="out" name="delta_oxy_rxn10"/>
<variable units="flux" name="r"/>
<reaction reversible="no">
<variable_ref variable="oxy">
<role stoichiometry="1" direction="forward" delta_variable="delta_oxy_rxn10" role="reactant"/>
</variable_ref>
<variable_ref variable="r">
<role role="rate">
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci> r </ci>
<ci> v10 </ci>
</apply>
</math>
</role>
</variable_ref>
</reaction>
</component>
<component name="reaction_11A">
<variable units="millimolar" public_interface="in" name="oxy"/>
<variable units="millimolar" public_interface="in" name="hyd"/>
<variable units="millimolar" public_interface="in" name="N2"/>
<variable units="millimolar" public_interface="in" name="N1"/>
<variable units="dimensionless" name="alpha" initial_value="0.1"/>
<variable units="dimensionless" name="f2"/>
<variable units="dimensionless" name="m" initial_value="4.0"/>
<variable units="millimolar" name="KH" initial_value="0.5"/>
<variable units="second_order_rate_constant" name="k_11" initial_value="10.0"/>
<variable units="flux" public_interface="out" name="delta_oxy_rxn11A"/>
<variable units="flux" public_interface="out" name="delta_N2_rxn11A"/>
<variable units="flux" public_interface="out" name="r_11A"/>
<reaction reversible="no">
<variable_ref variable="oxy">
<role stoichiometry="1" direction="forward" delta_variable="delta_oxy_rxn11A" role="reactant"/>
</variable_ref>
<variable_ref variable="N2">
<role stoichiometry="1" direction="forward" delta_variable="delta_N2_rxn11A" role="reactant"/>
</variable_ref>
<variable_ref variable="N1">
<role direction="forward" role="product"/>
</variable_ref>
<variable_ref variable="hyd">
<role direction="forward" role="inhibitor"/>
</variable_ref>
<variable_ref variable="r_11A">
<role role="rate">
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci> r_11A </ci>
<apply>
<divide/>
<apply>
<times/>
<ci> k_11 </ci>
<ci> N2 </ci>
<ci> oxy </ci>
<ci> f2 </ci>
</apply>
<apply>
<plus/>
<apply>
<times/>
<ci> alpha </ci>
<ci> N2 </ci>
</apply>
<ci> oxy </ci>
</apply>
</apply>
</apply>
</math>
</role>
</variable_ref>
</reaction>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="f2_calculation">
<eq/>
<ci> f2 </ci>
<apply>
<power/>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<power/>
<apply>
<divide/>
<ci> hyd </ci>
<ci> KH </ci>
</apply>
<ci> m </ci>
</apply>
</apply>
<cn cellml:units="dimensionless"> -1.0 </cn>
</apply>
</apply>
</math>
</component>
<component name="reaction_11B">
<variable units="millimolar" public_interface="in" name="A2_m"/>
<variable units="millimolar" public_interface="in" name="A3_m"/>
<variable units="flux" public_interface="in" name="r_11A"/>
<variable units="millimolar" name="KA" initial_value="1.0"/>
<variable units="flux" public_interface="out" name="delta_A3_m_rxn11B"/>
<variable units="flux" name="r"/>
<reaction reversible="no">
<variable_ref variable="A2_m">
<role direction="forward" role="reactant"/>
</variable_ref>
<variable_ref variable="A3_m">
<role stoichiometry="1" direction="forward" delta_variable="delta_A3_m_rxn11B" 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>
<times/>
<cn cellml:units="dimensionless"> 3.0 </cn>
<ci> r_11A </ci>
<apply>
<divide/>
<ci> A2_m </ci>
<apply>
<plus/>
<ci> KA </ci>
<ci> A2_m </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</role>
</variable_ref>
</reaction>
</component>
<component name="reaction_12">
<variable units="millimolar" public_interface="in" name="A2_c"/>
<variable units="millimolar" public_interface="in" name="A3_c"/>
<variable units="first_order_rate_constant" name="k_12" initial_value="5.0"/>
<variable units="flux" public_interface="out" name="delta_A3_c_rxn12"/>
<variable units="flux" name="r"/>
<reaction reversible="no">
<variable_ref variable="A3_c">
<role stoichiometry="1" direction="forward" delta_variable="delta_A3_c_rxn12" role="reactant"/>
</variable_ref>
<variable_ref variable="A2_c">
<role direction="forward" 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>
<times/>
<ci> k_12 </ci>
<ci> A3_c </ci>
</apply>
</apply>
</math>
</role>
</variable_ref>
</reaction>
</component>
<component name="reaction_13">
<variable units="millimolar" public_interface="in" name="eth"/>
<variable units="flux" name="v13" initial_value="4.0"/>
<variable units="flux" public_interface="out" name="delta_eth_rxn13"/>
<variable units="flux" name="r"/>
<reaction reversible="no">
<variable_ref variable="eth">
<role stoichiometry="1" direction="forward" delta_variable="delta_eth_rxn13" role="reactant"/>
</variable_ref>
<variable_ref variable="r">
<role role="rate">
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci> r </ci>
<ci> v13 </ci>
</apply>
</math>
</role>
</variable_ref>
</reaction>
</component>
<component name="reaction_14">
<variable units="millimolar" public_interface="in" name="oxy"/>
<variable units="first_order_rate_constant" name="k_14" initial_value="10.0"/>
<variable units="flux" public_interface="out" name="delta_oxy_rxn14"/>
<variable units="flux" name="r"/>
<reaction reversible="no">
<variable_ref variable="oxy">
<role stoichiometry="1" direction="forward" delta_variable="delta_oxy_rxn14" role="reactant"/>
</variable_ref>
<variable_ref variable="r">
<role role="rate">
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci> r </ci>
<apply>
<times/>
<ci> k_14 </ci>
<ci> oxy </ci>
</apply>
</apply>
</math>
</role>
</variable_ref>
</reaction>
</component>
<component name="reaction_15">
<variable units="millimolar" public_interface="in" name="oah"/>
<variable units="millimolar" public_interface="in" name="aco"/>
<variable units="first_order_rate_constant" name="k_15" initial_value="5.0"/>
<variable units="flux" public_interface="out" name="delta_oah_rxn15"/>
<variable units="flux" public_interface="out" name="delta_aco_rxn15"/>
<variable units="flux" name="r"/>
<reaction reversible="no">
<variable_ref variable="aco">
<role stoichiometry="1" direction="forward" delta_variable="delta_aco_rxn15" role="reactant"/>
</variable_ref>
<variable_ref variable="oah">
<role stoichiometry="1" direction="forward" delta_variable="delta_oah_rxn15" 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>
<times/>
<ci> k_15 </ci>
<ci> aco </ci>
</apply>
</apply>
</math>
</role>
</variable_ref>
</reaction>
</component>
<component name="reaction_16">
<variable units="millimolar" public_interface="in" name="A3_m"/>
<variable units="millimolar" public_interface="in" name="A2_c"/>
<variable units="first_order_rate_constant" name="k_16" initial_value="10.0"/>
<variable units="flux" public_interface="out" name="delta_A3_m_rxn16"/>
<variable units="flux" public_interface="out" name="delta_A3_c_rxn16"/>
<variable units="flux" name="r"/>
<reaction reversible="yes">
<variable_ref variable="A3_m">
<role stoichiometry="1" direction="forward" delta_variable="delta_A3_m_rxn16" role="reactant"/>
</variable_ref>
<variable_ref variable="A2_c">
<role stoichiometry="1" direction="forward" delta_variable="delta_A3_c_rxn16" 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>
<times/>
<ci> k_16 </ci>
<ci> A3_m </ci>
<ci> A2_c </ci>
</apply>
</apply>
</math>
</role>
</variable_ref>
</reaction>
</component>
<component name="reaction_17">
<variable units="millimolar" public_interface="in" name="hyd"/>
<variable units="first_order_rate_constant" name="k_17" initial_value="0.02"/>
<variable units="flux" public_interface="out" name="delta_hyd_rxn17"/>
<variable units="flux" name="r"/>
<reaction reversible="no">
<variable_ref variable="hyd">
<role stoichiometry="1" direction="forward" delta_variable="delta_hyd_rxn17" role="reactant"/>
</variable_ref>
<variable_ref variable="r">
<role role="rate">
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci> r </ci>
<apply>
<times/>
<ci> k_17 </ci>
<ci> hyd </ci>
</apply>
</apply>
</math>
</role>
</variable_ref>
</reaction>
</component>
<component name="reaction_18">
<variable units="millimolar" public_interface="in" name="oah"/>
<variable units="first_order_rate_constant" name="k_18" initial_value="1.0"/>
<variable units="flux" public_interface="out" name="delta_oah_rxn18"/>
<variable units="flux" name="r"/>
<reaction reversible="no">
<variable_ref variable="oah">
<role stoichiometry="1" direction="forward" delta_variable="delta_oah_rxn18" role="reactant"/>
</variable_ref>
<variable_ref variable="r">
<role role="rate">
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci> r </ci>
<apply>
<times/>
<ci> k_18 </ci>
<ci> oah </ci>
</apply>
</apply>
</math>
</role>
</variable_ref>
</reaction>
</component>
<connection>
<map_components component_2="environment" component_1="S1"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="S"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="sul"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="aps"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="pap"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="hyd"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="cys"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="eth"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="aco"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="oxy"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="A_c"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="A3_c"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="A_m"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="A3_m"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="N"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="N2"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="oah"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="reaction_8" component_1="S1"/>
<map_variables variable_2="S1" variable_1="S1"/>
<map_variables variable_2="delta_S1_rxn8" variable_1="delta_S1_rxn8"/>
</connection>
<connection>
<map_components component_2="reaction_9" component_1="S1"/>
<map_variables variable_2="S1" variable_1="S1"/>
<map_variables variable_2="delta_S1_rxn9" variable_1="delta_S1_rxn9"/>
</connection>
<connection>
<map_components component_2="reaction_8" component_1="S"/>
<map_variables variable_2="S2" variable_1="S2"/>
</connection>
<connection>
<map_components component_2="reaction_9" component_1="S"/>
<map_variables variable_2="S2" variable_1="S2"/>
</connection>
<connection>
<map_components component_2="reaction_1" component_1="sul"/>
<map_variables variable_2="sul" variable_1="sul"/>
<map_variables variable_2="delta_sul_rxn1" variable_1="delta_sul_rxn1"/>
</connection>
<connection>
<map_components component_2="reaction_2" component_1="sul"/>
<map_variables variable_2="sul" variable_1="sul"/>
<map_variables variable_2="delta_sul_rxn2" variable_1="delta_sul_rxn2"/>
</connection>
<connection>
<map_components component_2="reaction_2" component_1="aps"/>
<map_variables variable_2="aps" variable_1="aps"/>
<map_variables variable_2="delta_aps_rxn2" variable_1="delta_aps_rxn2"/>
</connection>
<connection>
<map_components component_2="reaction_3" component_1="aps"/>
<map_variables variable_2="aps" variable_1="aps"/>
<map_variables variable_2="delta_aps_rxn3" variable_1="delta_aps_rxn3"/>
</connection>
<connection>
<map_components component_2="reaction_3" component_1="pap"/>
<map_variables variable_2="pap" variable_1="pap"/>
<map_variables variable_2="delta_pap_rxn3" variable_1="delta_pap_rxn3"/>
</connection>
<connection>
<map_components component_2="reaction_4" component_1="pap"/>
<map_variables variable_2="pap" variable_1="pap"/>
<map_variables variable_2="delta_pap_rxn4" variable_1="delta_pap_rxn4"/>
</connection>
<connection>
<map_components component_2="reaction_4" component_1="hyd"/>
<map_variables variable_2="hyd" variable_1="hyd"/>
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total intermediates of the citrate acid cycle
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intermediate of the citrate acid cycle
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total cytosolic adenosine phosphates
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Mathematical analysis of a mechanism for autonomous metabolic oscillations in continuous culture of Saccharomyces cerevisae
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This is the CellML description of Wolf et al's mathematical model of
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total mitochondrial adenosine phosphates
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