- Author:
- pmr2.import <nobody@models.cellml.org>
- Date:
- 2006-07-09 07:15:43+12:00
- Desc:
- committing version01 of wolf_heinrich_2000
- Permanent Source URI:
- http://models.cellml.org/workspace/wolf_heinrich_2000/rawfile/087a6c6781800601aa7027cd171c62491307325a/wolf_heinrich_2000.cellml
<?xml version='1.0' encoding='utf-8'?>
<!-- FILE : wolf_heinrich_model_2000.xml
CREATED : 8th 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 and Heinrich's 2000 model of the effect of cellular interaction on glycolytic oscillations in yeast.
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_heinrich_2000_version01" name="wolf_heinrich_2000_version01">
<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
<articleinfo>
<title>Effect of Cellular Interaction on Glycolytic Oscillations in Yeast</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>
Glycolytic oscillations are a well studied example of rhythmic behaviour on a cellular level. They occur in a diverse array of cells including muscle, heart and pancreatic beta-cells, however the oscillations have been studied most extensively in yeast cells. Theoretical models based on experimental observations have tried to accurately define the underlying oscillatory mechanism.
</para>
<para>
In 2000, Jana Wolf and Reinhart Heinrich published a mathematical model describing the effect of cellular interaction on glycolytic oscillations in yeast (see <xref linkend="fig_reaction_diagram"/> below). Unlike earlier models of glycolytic oscillations which are restricted to single cells, Wolf and Heinrich consider the effects of intercellular interaction on glycolytic oscillations. Cells often communicate by exchanging metabolic intermediates via the external medium.
</para>
<para>
The model they present in their paper is a detailed model for anaerobic energy metabolism in yeast cells. The model includes the main steps of anaerobic glycolysis and the production of ethanol and glycerol. Transmembrane diffusion of acetaldehyde is included since it is hypothesized that this metabolite mediates the intercellular interaction.
</para>
<para>
The complete original paper reference is cited below:
</para>
<para>
<ulink url="http://www.biochemj.org/bj/345/bj3450321.htm">Effect of cellular interaction on glycolytic oscillations in yeast: a theoretical investigation</ulink>, Jana Wolf and Reinhart Heinrich, 2000, <ulink url="http://www.biochemj.org/">
<emphasis>Biochemical Journal</emphasis>
</ulink>, 345, 321-334. (The <ulink url="http://www.biochemj.org/bj/345/0321/3450321.pdf">PDF</ulink> and <ulink url="http://www.biochemj.org/bj/345/0321/bj3450321.htm">full text</ulink> versions of the article are available on the Biochemical Journal website.) <ulink url="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&list_uids=10702114&dopt=Abstract">PubMed ID: 10702114</ulink>
</para>
<para>
The raw CellML description of the model can be downloaded in various formats as described in <xref linkend="sec_download_this_model"/>.
</para>
<informalfigure float="0" id="fig_reaction_diagram">
<mediaobject>
<imageobject>
<objectinfo>
<title>schematic diagram</title>
</objectinfo>
<imagedata fileref="wolf_heinrich_2000.png"/>
</imageobject>
</mediaobject>
<caption>The scheme shows the main reactions of anaerobic glycolysis in yeast, in addition to transmembrane transport of glucose and the coupling substance (S4,ex). For further explanation of the symbols used, see the text.</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>
<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="Jo"/>
<variable units="flux" public_interface="in" name="delta_S1_rxn1"/>
<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>Jo</ci>
<ci>delta_S1_rxn1</ci>
</apply>
</apply>
</math>
</component>
<component cmeta:id="S2" name="S2">
<variable units="millimolar" public_interface="out" name="S2"/>
<variable units="flux" public_interface="in" name="delta_S2_rxn1"/>
<variable units="flux" public_interface="in" name="delta_S2_rxn2"/>
<variable units="flux" public_interface="in" name="delta_S2_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>S2</ci>
</apply>
<apply>
<plus/>
<ci>delta_S2_rxn1</ci>
<ci>delta_S2_rxn2</ci>
<ci>delta_S2_rxn6</ci>
</apply>
</apply>
</math>
</component>
<component cmeta:id="S3" name="S3">
<variable units="millimolar" public_interface="out" name="S3"/>
<variable units="flux" public_interface="in" name="delta_S3_rxn2"/>
<variable units="flux" public_interface="in" name="delta_S3_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>S3</ci>
</apply>
<apply>
<plus/>
<ci>delta_S3_rxn2</ci>
<ci>delta_S3_rxn3</ci>
</apply>
</apply>
</math>
</component>
<component cmeta:id="S4" name="S4">
<variable units="millimolar" public_interface="out" name="S4"/>
<variable units="flux" public_interface="in" name="delta_S4_rxn3"/>
<variable units="flux" public_interface="in" name="delta_S4_rxn4"/>
<variable units="flux" public_interface="in" name="J"/>
<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>S4</ci>
</apply>
<apply>
<plus/>
<ci>delta_S4_rxn3</ci>
<ci>delta_S4_rxn4</ci>
<ci>J</ci>
</apply>
</apply>
</math>
</component>
<component cmeta:id="S4_ex" name="S4_ex">
<variable units="millimolar" public_interface="out" name="S4_ex"/>
<variable units="dimensionless" name="psi" initial_value="0.1"/>
<variable units="flux" public_interface="in" name="delta_S4_ex_rxn7"/>
<variable units="flux" public_interface="in" name="J"/>
<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>S4_ex</ci>
</apply>
<apply>
<plus/>
<apply>
<times/>
<ci> psi </ci>
<ci> J </ci>
</apply>
<ci>delta_S4_ex_rxn7</ci>
</apply>
</apply>
</math>
</component>
<component cmeta:id="A3" name="A3">
<variable units="millimolar" public_interface="out" name="A3"/>
<variable units="flux" public_interface="in" name="delta_A3_rxn1"/>
<variable units="flux" public_interface="in" name="delta_A3_rxn3"/>
<variable units="flux" public_interface="in" name="delta_A3_rxn5"/>
<variable units="minute" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>A3</ci>
</apply>
<apply>
<plus/>
<ci>delta_A3_rxn1</ci>
<ci>delta_A3_rxn3</ci>
<ci>delta_A3_rxn5</ci>
</apply>
</apply>
</math>
</component>
<component cmeta:id="A" name="A">
<variable units="millimolar" name="A" initial_value="4.0"/>
<variable units="millimolar" public_interface="out" name="A2"/>
<variable units="millimolar" public_interface="in" name="A3"/>
<variable units="minute" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>A</ci>
<apply>
<plus/>
<ci> A2 </ci>
<ci> A3 </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_rxn2"/>
<variable units="flux" public_interface="in" name="delta_N2_rxn4"/>
<variable units="flux" public_interface="in" name="delta_N2_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>N2</ci>
</apply>
<apply>
<plus/>
<ci>delta_N2_rxn2</ci>
<ci>delta_N2_rxn4</ci>
<ci>delta_N2_rxn6</ci>
</apply>
</apply>
</math>
</component>
<component cmeta:id="N" name="N">
<variable units="millimolar" name="N" initial_value="1.0"/>
<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 name="reaction_1">
<variable units="millimolar" public_interface="in" name="S1"/>
<variable units="millimolar" public_interface="in" name="A3"/>
<variable units="millimolar" public_interface="in" name="S2"/>
<variable units="millimolar" public_interface="in" name="A2"/>
<variable units="millimolar" name="K_I" initial_value="0.52"/>
<variable units="second_order_rate_constant" name="k_1" initial_value="100.0"/>
<variable units="dimensionless" name="q" initial_value="4.0"/>
<variable units="dimensionless" name="f_A3"/>
<variable units="flux" public_interface="out" name="delta_S1_rxn1"/>
<variable units="flux" public_interface="out" name="delta_A3_rxn1"/>
<variable units="flux" public_interface="out" name="delta_S2_rxn1"/>
<variable units="flux" name="r"/>
<reaction reversible="no">
<variable_ref variable="S1">
<role stoichiometry="1" direction="forward" delta_variable="delta_S1_rxn1" role="reactant"/>
</variable_ref>
<variable_ref variable="A3">
<role stoichiometry="2" direction="forward" delta_variable="delta_A3_rxn1" role="reactant"/>
</variable_ref>
<variable_ref variable="S2">
<role stoichiometry="2" direction="forward" delta_variable="delta_S2_rxn1" role="product"/>
</variable_ref>
<variable_ref variable="A2">
<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_1 </ci>
<ci> S1 </ci>
<ci> A3 </ci>
<ci> f_A3 </ci>
</apply>
</apply>
</math>
</role>
</variable_ref>
</reaction>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci> f_A3 </ci>
<apply>
<power/>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<power/>
<apply>
<divide/>
<ci> A3 </ci>
<ci> K_I </ci>
</apply>
<ci> q </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="S2"/>
<variable units="millimolar" public_interface="in" name="N1"/>
<variable units="millimolar" public_interface="in" name="S3"/>
<variable units="millimolar" public_interface="in" name="N2"/>
<variable units="second_order_rate_constant" name="k_2" initial_value="6.0"/>
<variable units="flux" public_interface="out" name="delta_S2_rxn2"/>
<variable units="flux" public_interface="out" name="delta_S3_rxn2"/>
<variable units="flux" public_interface="out" name="delta_N2_rxn2"/>
<variable units="flux" name="r"/>
<reaction reversible="no">
<variable_ref variable="S2">
<role stoichiometry="1" direction="forward" delta_variable="delta_S2_rxn2" role="reactant"/>
</variable_ref>
<variable_ref variable="N1">
<role direction="forward" role="reactant"/>
</variable_ref>
<variable_ref variable="S3">
<role stoichiometry="1" direction="forward" delta_variable="delta_S3_rxn2" role="product"/>
</variable_ref>
<variable_ref variable="N2">
<role stoichiometry="1" direction="forward" delta_variable="delta_N2_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> S2 </ci>
<ci> N1 </ci>
</apply>
</apply>
</math>
</role>
</variable_ref>
</reaction>
</component>
<component name="reaction_3">
<variable units="millimolar" public_interface="in" name="S3"/>
<variable units="millimolar" public_interface="in" name="S4"/>
<variable units="millimolar" public_interface="in" name="A2"/>
<variable units="millimolar" public_interface="in" name="A3"/>
<variable units="second_order_rate_constant" name="k_3" initial_value="16.0"/>
<variable units="flux" public_interface="out" name="delta_S3_rxn3"/>
<variable units="flux" public_interface="out" name="delta_S4_rxn3"/>
<variable units="flux" public_interface="out" name="delta_A3_rxn3"/>
<variable units="flux" name="r"/>
<reaction reversible="no">
<variable_ref variable="S3">
<role stoichiometry="1" direction="forward" delta_variable="delta_S3_rxn3" role="reactant"/>
</variable_ref>
<variable_ref variable="A2">
<role direction="forward" role="reactant"/>
</variable_ref>
<variable_ref variable="S4">
<role stoichiometry="1" direction="forward" delta_variable="delta_S4_rxn3" role="product"/>
</variable_ref>
<variable_ref variable="A3">
<role stoichiometry="2" direction="forward" delta_variable="delta_A3_rxn3" 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> S3 </ci>
<ci> A2 </ci>
</apply>
</apply>
</math>
</role>
</variable_ref>
</reaction>
</component>
<component name="reaction_4">
<variable units="millimolar" public_interface="in" name="S4"/>
<variable units="millimolar" public_interface="in" name="N2"/>
<variable units="millimolar" public_interface="in" name="N1"/>
<variable units="second_order_rate_constant" name="k_4" initial_value="100.0"/>
<variable units="flux" public_interface="out" name="delta_S4_rxn4"/>
<variable units="flux" public_interface="out" name="delta_N2_rxn4"/>
<variable units="flux" public_interface="out" name="delta_S5_rxn4"/>
<variable units="flux" name="r"/>
<reaction reversible="no">
<variable_ref variable="S4">
<role stoichiometry="1" direction="forward" delta_variable="delta_S4_rxn4" role="reactant"/>
</variable_ref>
<variable_ref variable="N2">
<role stoichiometry="1" direction="forward" delta_variable="delta_N2_rxn4" role="reactant"/>
</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> S4 </ci>
<ci> N2 </ci>
</apply>
</apply>
</math>
</role>
</variable_ref>
</reaction>
</component>
<component name="reaction_5">
<variable units="millimolar" public_interface="in" name="A3"/>
<variable units="millimolar" public_interface="in" name="A2"/>
<variable units="first_order_rate_constant" name="k_5" initial_value="1.28"/>
<variable units="flux" public_interface="out" name="delta_A3_rxn5"/>
<variable units="flux" name="r"/>
<reaction reversible="no">
<variable_ref variable="A3">
<role stoichiometry="1" direction="forward" delta_variable="delta_A3_rxn5" role="reactant"/>
</variable_ref>
<variable_ref variable="A2">
<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_5 </ci>
<ci> A3 </ci>
</apply>
</apply>
</math>
</role>
</variable_ref>
</reaction>
</component>
<component name="reaction_6">
<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="second_order_rate_constant" name="k_6" initial_value="12.0"/>
<variable units="flux" public_interface="out" name="delta_S2_rxn6"/>
<variable units="flux" public_interface="out" name="delta_N2_rxn6"/>
<variable units="flux" name="r"/>
<reaction reversible="no">
<variable_ref variable="S2">
<role stoichiometry="1" direction="forward" delta_variable="delta_S2_rxn6" role="reactant"/>
</variable_ref>
<variable_ref variable="N2">
<role stoichiometry="1" direction="forward" delta_variable="delta_N2_rxn6" role="reactant"/>
</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_6 </ci>
<ci> S2 </ci>
<ci> N2 </ci>
</apply>
</apply>
</math>
</role>
</variable_ref>
</reaction>
</component>
<component name="reaction_7">
<variable units="millimolar" public_interface="in" name="S4_ex"/>
<variable units="first_order_rate_constant" name="k" initial_value="1.3"/>
<variable units="flux" public_interface="out" name="delta_S4_ex_rxn7"/>
<variable units="flux" name="r"/>
<reaction reversible="no">
<variable_ref variable="S4_ex">
<role stoichiometry="1" direction="forward" delta_variable="delta_S4_ex_rxn7" 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 </ci>
<ci> S4_ex </ci>
</apply>
</apply>
</math>
</role>
</variable_ref>
</reaction>
</component>
<component name="glucose_influx_rate">
<variable units="flux" public_interface="out" name="Jo" initial_value="3.0"/>
</component>
<component name="S4_flux_rate_across_the_plasma_membrane">
<variable units="flux" public_interface="out" name="J"/>
<variable units="first_order_rate_constant" name="k" initial_value="13.0"/>
<variable units="millimolar" public_interface="in" name="S4_ex"/>
<variable units="millimolar" public_interface="in" name="S4"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="J_calculation">
<eq/>
<ci> J </ci>
<apply>
<times/>
<ci> k </ci>
<apply>
<minus/>
<ci> S4 </ci>
<ci> S4_ex </ci>
</apply>
</apply>
</apply>
</math>
</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="S2"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="S3"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="S4"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="S4_ex"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="A"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="A3"/>
<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="glucose_influx_rate" component_1="S1"/>
<map_variables variable_2="Jo" variable_1="Jo"/>
</connection>
<connection>
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Effect of cellular interaction on glycolytic oscillations in yeast: a theoretical investigation
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