<?xml version="1.0"?>
<!--
This CellML file was generated on 12/04/2010 at 5:53:53 at p.m. using:
COR (0.9.31.1371)
Copyright 2002-2010 Dr Alan Garny
http://cor.physiol.ox.ac.uk/ - cor@physiol.ox.ac.uk
CellML 1.0 was used to generate this model
http://www.cellml.org/
-->
<model 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:dcterms="http://purl.org/dc/terms/" xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" name="wolf_2000" cmeta:id="wolf_2000" 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#">
<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
<articleinfo>
<title>Transduction of Intracellular and Intercellular Dynamics in Yeast Glycolytic Oscillations</title>
<author>
<firstname>Catherine</firstname>
<surname>Lloyd</surname>
<affiliation>
<shortaffil>Auckland Bioengineering Institute, The University of Auckland</shortaffil>
</affiliation>
</author>
</articleinfo>
<section id="sec_status">
<title>Model Status</title>
<para>
This model runs to reproduce published results in COR and OpenCell. The units are consistent throughout. This model currently reproduces Figure 4. The initial conditions were estimated and the model run to steady state to yield precise values, changing any parameters will necessitate repeating this procedure.
</para>
</section>
<sect1 id="sec_structure">
<title>Model Structure</title>
<para>
ABSTRACT: Under certain well-defined conditions, a population of yeast cells exhibits glycolytic oscillations that synchronize through intercellular acetaldehyde. This implies that the dynamic phenomenon of the oscillation propagates within and between cells. We here develop a method to establish by which route dynamics propagate through a biological reaction network. Application of the method to yeast demonstrates how the oscillations and the synchronization signal can be transduced. That transduction is not so much through the backbone of glycolysis, as via the Gibbs energy and redox coenzyme couples (ATP/ADP, and NADH/NAD), and via both intra- and intercellular acetaldehyde.
</para>
<para>
The original paper reference is cited below:
</para>
<para>
Transduction of Intracellular and Intercellular Dynamics in Yeast Glycolytic Oscillations, Jana Wolf, Jutta Passarge, Oscar J.G. Somsen, Jacky L. Snoep, Reinhart Heinrich and Hans V. Westerhoff, 2000, <emphasis>Biophysical Journal</emphasis>, 78, 1145-1153. <ulink url="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&list_uids=10692304&dopt=Abstract">PubMed ID: 10692304</ulink>
</para>
<informalfigure float="0" id="fig_reaction_diagram">
<mediaobject>
<imageobject>
<objectinfo>
<title>schematic diagram</title>
</objectinfo>
<imagedata fileref="wolf_passarge_2000.png"/>
</imageobject>
</mediaobject>
<caption>Schematic representation of the model. The nine variable model includes all shown metabolites as variables where S1 represents glucose, S2 represents fructose-1,6-bisphosphate, S3 represents the triphopshate pool, S4 represents 3-phosphoglycerate, S5 represents pyruvate, S6 represents intracellular acetaldehyde, S6,ex represents extracellular acetaldehyde, A2 is ADP, A3 is ATP, N1 is NAD<superscript>+</superscript> and N2 is NADH.</caption>
</informalfigure>
</sect1>
</article>
</documentation>
<units name="minute">
<unit multiplier="60" units="second"/>
</units>
<units name="millimolar">
<unit prefix="milli" units="mole"/>
<unit exponent="-1" units="litre"/>
</units>
<units name="flux">
<unit units="millimolar"/>
<unit exponent="-1" units="minute"/>
</units>
<units name="first_order_rate_constant">
<unit exponent="-1" units="minute"/>
</units>
<units name="second_order_rate_constant">
<unit exponent="-1" units="millimolar"/>
<unit exponent="-1" units="minute"/>
</units>
<component name="environment">
<variable cmeta:id="environment_time" name="time" public_interface="out" units="minute"/>
</component>
<component name="S1">
<variable cmeta:id="S1_S1" initial_value="1.57981839" name="S1" public_interface="out" units="millimolar"/>
<variable name="Jo" public_interface="in" units="flux"/>
<variable name="v1" public_interface="in" units="flux"/>
<variable name="time" public_interface="in" units="minute"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
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<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>S1</ci>
</apply>
<apply>
<minus/>
<ci>Jo</ci>
<ci>v1</ci>
</apply>
</apply>
</math>
</component>
<component name="S2">
<variable cmeta:id="S2_S2" initial_value="4.8279999" name="S2" public_interface="out" units="millimolar"/>
<variable name="v1" public_interface="in" units="flux"/>
<variable name="v2" public_interface="in" units="flux"/>
<variable name="time" public_interface="in" units="minute"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>S2</ci>
</apply>
<apply>
<minus/>
<ci>v1</ci>
<ci>v2</ci>
</apply>
</apply>
</math>
</component>
<component name="S3">
<variable cmeta:id="S3_S3" initial_value="0.468657507" name="S3" public_interface="out" units="millimolar"/>
<variable name="v2" public_interface="in" units="flux"/>
<variable name="v3" public_interface="in" units="flux"/>
<variable name="v8" public_interface="in" units="flux"/>
<variable name="time" public_interface="in" units="minute"/>
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<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>S3</ci>
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<apply>
<minus/>
<apply>
<times/>
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<ci>v2</ci>
</apply>
<apply>
<plus/>
<ci>v3</ci>
<ci>v8</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="S4">
<variable cmeta:id="S4_S4" initial_value="0.589391932" name="S4" public_interface="out" units="millimolar"/>
<variable name="v3" public_interface="in" units="flux"/>
<variable name="v4" public_interface="in" units="flux"/>
<variable name="time" public_interface="in" units="minute"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>S4</ci>
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<apply>
<minus/>
<ci>v3</ci>
<ci>v4</ci>
</apply>
</apply>
</math>
</component>
<component name="S5">
<variable cmeta:id="S5_S5" initial_value="8.210114438" name="S5" public_interface="out" units="millimolar"/>
<variable name="v4" public_interface="in" units="flux"/>
<variable name="v5" public_interface="in" units="flux"/>
<variable name="time" public_interface="in" units="minute"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
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<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>S5</ci>
</apply>
<apply>
<minus/>
<ci>v4</ci>
<ci>v5</ci>
</apply>
</apply>
</math>
</component>
<component name="S6">
<variable cmeta:id="S6_S6" initial_value="0.078042624" name="S6" public_interface="out" units="millimolar"/>
<variable name="v5" public_interface="in" units="flux"/>
<variable name="v6" public_interface="in" units="flux"/>
<variable name="J" public_interface="in" units="flux"/>
<variable name="time" public_interface="in" units="minute"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
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<bvar>
<ci>time</ci>
</bvar>
<ci>S6</ci>
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<apply>
<minus/>
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<apply>
<plus/>
<ci>v6</ci>
<ci>J</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="S6_ex">
<variable cmeta:id="S6_ex_S6_ex" initial_value="0.025277594" name="S6_ex" public_interface="out" units="millimolar"/>
<variable initial_value="0.1" name="phi" units="dimensionless"/>
<variable name="v9" public_interface="in" units="flux"/>
<variable name="J" public_interface="in" units="flux"/>
<variable name="time" public_interface="in" units="minute"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
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<diff/>
<bvar>
<ci>time</ci>
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<ci>S6_ex</ci>
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<apply>
<minus/>
<apply>
<times/>
<ci>phi</ci>
<ci>J</ci>
</apply>
<ci>v9</ci>
</apply>
</apply>
</math>
</component>
<component name="A3">
<variable cmeta:id="A3_A3" initial_value="1.972814237" name="A3" public_interface="out" units="millimolar"/>
<variable name="v1" public_interface="in" units="flux"/>
<variable name="v3" public_interface="in" units="flux"/>
<variable name="v4" public_interface="in" units="flux"/>
<variable name="v7" public_interface="in" units="flux"/>
<variable name="time" public_interface="in" units="minute"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>A3</ci>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<ci>v3</ci>
<ci>v4</ci>
</apply>
<apply>
<plus/>
<apply>
<times/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
<ci>v1</ci>
</apply>
<ci>v7</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="A">
<variable initial_value="4" name="A" units="millimolar"/>
<variable cmeta:id="A_A2" name="A2" public_interface="out" units="millimolar"/>
<variable name="A3" public_interface="in" units="millimolar"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>A2</ci>
<apply>
<minus/>
<ci>A</ci>
<ci>A3</ci>
</apply>
</apply>
</math>
</component>
<component name="N2">
<variable cmeta:id="N2_N2" initial_value="0.384873894" name="N2" public_interface="out" units="millimolar"/>
<variable name="v3" public_interface="in" units="flux"/>
<variable name="v6" public_interface="in" units="flux"/>
<variable name="v8" public_interface="in" units="flux"/>
<variable name="time" public_interface="in" units="minute"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>N2</ci>
</apply>
<apply>
<minus/>
<ci>v3</ci>
<apply>
<plus/>
<ci>v6</ci>
<ci>v8</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="N">
<variable initial_value="1" name="N" units="millimolar"/>
<variable cmeta:id="N_N1" name="N1" public_interface="out" units="millimolar"/>
<variable name="N2" public_interface="in" units="millimolar"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>N1</ci>
<apply>
<minus/>
<ci>N</ci>
<ci>N2</ci>
</apply>
</apply>
</math>
</component>
<component name="v1">
<variable cmeta:id="v1_v1" name="v1" public_interface="out" units="flux"/>
<variable name="S1" public_interface="in" units="millimolar"/>
<variable name="A3" public_interface="in" units="millimolar"/>
<variable initial_value="1" name="K_i" units="millimolar"/>
<variable initial_value="550" name="k_1" units="second_order_rate_constant"/>
<variable initial_value="4" name="n" units="dimensionless"/>
<variable name="f_A3" units="dimensionless"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>f_A3</ci>
<apply>
<power/>
<apply>
<plus/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
<apply>
<power/>
<apply>
<divide/>
<ci>A3</ci>
<ci>K_i</ci>
</apply>
<ci>n</ci>
</apply>
</apply>
<apply>
<minus/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>v1</ci>
<apply>
<times/>
<ci>k_1</ci>
<ci>S1</ci>
<ci>A3</ci>
<ci>f_A3</ci>
</apply>
</apply>
</math>
</component>
<component name="v2">
<variable cmeta:id="v2_v2" name="v2" public_interface="out" units="flux"/>
<variable name="S2" public_interface="in" units="millimolar"/>
<variable initial_value="9.8" name="k_2" units="first_order_rate_constant"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>v2</ci>
<apply>
<times/>
<ci>k_2</ci>
<ci>S2</ci>
</apply>
</apply>
</math>
</component>
<component name="v3">
<variable cmeta:id="v3_v3" name="v3" public_interface="out" units="flux"/>
<variable name="S3" public_interface="in" units="millimolar"/>
<variable name="S4" public_interface="in" units="millimolar"/>
<variable name="N1" public_interface="in" units="millimolar"/>
<variable name="N2" public_interface="in" units="millimolar"/>
<variable name="A2" public_interface="in" units="millimolar"/>
<variable name="A3" public_interface="in" units="millimolar"/>
<variable initial_value="323.8" name="k_GAPDH_plus" units="second_order_rate_constant"/>
<variable initial_value="57823.1" name="k_GAPDH_minus" units="second_order_rate_constant"/>
<variable initial_value="76411.1" name="k_PGK_plus" units="second_order_rate_constant"/>
<variable initial_value="23.7" name="k_PGK_minus" units="second_order_rate_constant"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>v3</ci>
<apply>
<divide/>
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<minus/>
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<times/>
<ci>k_GAPDH_plus</ci>
<ci>k_PGK_plus</ci>
<ci>S3</ci>
<ci>N1</ci>
<ci>A2</ci>
</apply>
<apply>
<times/>
<ci>k_GAPDH_minus</ci>
<ci>k_PGK_minus</ci>
<ci>S4</ci>
<ci>A3</ci>
<ci>N2</ci>
</apply>
</apply>
<apply>
<plus/>
<apply>
<times/>
<ci>k_GAPDH_minus</ci>
<ci>N2</ci>
</apply>
<apply>
<times/>
<ci>k_PGK_plus</ci>
<ci>A2</ci>
</apply>
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</math>
</component>
<component name="v4">
<variable cmeta:id="v4_v4" name="v4" public_interface="out" units="flux"/>
<variable name="S4" public_interface="in" units="millimolar"/>
<variable name="A2" public_interface="in" units="millimolar"/>
<variable initial_value="80" name="k_4" units="second_order_rate_constant"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>v4</ci>
<apply>
<times/>
<ci>k_4</ci>
<ci>S4</ci>
<ci>A2</ci>
</apply>
</apply>
</math>
</component>
<component name="v5">
<variable cmeta:id="v5_v5" name="v5" public_interface="out" units="flux"/>
<variable name="S5" public_interface="in" units="millimolar"/>
<variable initial_value="9.7" name="k_5" units="first_order_rate_constant"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
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<ci>v5</ci>
<apply>
<times/>
<ci>k_5</ci>
<ci>S5</ci>
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<component name="v6">
<variable cmeta:id="v6_v6" name="v6" public_interface="out" units="flux"/>
<variable name="S6" public_interface="in" units="millimolar"/>
<variable name="N2" public_interface="in" units="millimolar"/>
<variable initial_value="2000" name="k_6" units="second_order_rate_constant"/>
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<ci>v6</ci>
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<ci>k_6</ci>
<ci>S6</ci>
<ci>N2</ci>
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<component name="v7">
<variable cmeta:id="v7_v7" name="v7" public_interface="out" units="flux"/>
<variable name="A3" public_interface="in" units="millimolar"/>
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<variable name="N2" public_interface="in" units="millimolar"/>
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<ci>S3</ci>
<ci>N2</ci>
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<variable name="S6_ex" public_interface="in" units="millimolar"/>
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<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>v9</ci>
<apply>
<times/>
<ci>k_9</ci>
<ci>S6_ex</ci>
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</math>
</component>
<component name="glucose_influx_rate">
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</component>
<component name="S6_flux_rate_across_the_plasma_membrane">
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<variable initial_value="375" name="k" units="first_order_rate_constant"/>
<variable name="S6_ex" public_interface="in" units="millimolar"/>
<variable name="S6" public_interface="in" units="millimolar"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
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<map_variables variable_1="time" variable_2="time"/>
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<connection>
<map_components component_1="S2" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
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<connection>
<map_components component_1="S3" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="S4" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
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<connection>
<map_components component_1="S5" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="S6" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="S6_ex" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
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<connection>
<map_components component_1="A3" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="N2" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="S1" component_2="glucose_influx_rate"/>
<map_variables variable_1="Jo" variable_2="Jo"/>
</connection>
<connection>
<map_components component_1="S1" component_2="v1"/>
<map_variables variable_1="S1" variable_2="S1"/>
<map_variables variable_1="v1" variable_2="v1"/>
</connection>
<connection>
<map_components component_1="S2" component_2="v1"/>
<map_variables variable_1="v1" variable_2="v1"/>
</connection>
<connection>
<map_components component_1="S2" component_2="v2"/>
<map_variables variable_1="S2" variable_2="S2"/>
<map_variables variable_1="v2" variable_2="v2"/>
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<connection>
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<map_variables variable_1="v2" variable_2="v2"/>
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<connection>
<map_components component_1="S3" component_2="v3"/>
<map_variables variable_1="S3" variable_2="S3"/>
<map_variables variable_1="v3" variable_2="v3"/>
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<connection>
<map_components component_1="S3" component_2="v8"/>
<map_variables variable_1="S3" variable_2="S3"/>
<map_variables variable_1="v8" variable_2="v8"/>
</connection>
<connection>
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<map_variables variable_1="S4" variable_2="S4"/>
<map_variables variable_1="v3" variable_2="v3"/>
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<connection>
<map_components component_1="S4" component_2="v4"/>
<map_variables variable_1="S4" variable_2="S4"/>
<map_variables variable_1="v4" variable_2="v4"/>
</connection>
<connection>
<map_components component_1="S5" component_2="v4"/>
<map_variables variable_1="v4" variable_2="v4"/>
</connection>
<connection>
<map_components component_1="S5" component_2="v5"/>
<map_variables variable_1="S5" variable_2="S5"/>
<map_variables variable_1="v5" variable_2="v5"/>
</connection>
<connection>
<map_components component_1="S6" component_2="v5"/>
<map_variables variable_1="v5" variable_2="v5"/>
</connection>
<connection>
<map_components component_1="S6" component_2="v6"/>
<map_variables variable_1="S6" variable_2="S6"/>
<map_variables variable_1="v6" variable_2="v6"/>
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