- Author:
- Catherine Lloyd <c.lloyd@auckland.ac.nz>
- Date:
- 2010-04-28 12:43:59+12:00
- Desc:
- Updated documentation and fixed the name of the variable "pi". Model requites further curation before re-exposure.
- Permanent Source URI:
- https://staging.physiomeproject.org/workspace/westermark_lansner_2003/rawfile/72dff5ffbef911b11bb9c4ea14568ef2a65ea6f0/westermark_lansner_2003.cellml
<?xml version='1.0' encoding='utf-8'?>
<!-- FILE : westermark_model_2003.xml
CREATED : 8th October 2004
LAST MODIFIED : 8th October 2004
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 Westermark and Lansner's 2003 mathematical model of phosphofructokinase and glycolytic oscillations in the pancreatic beta-cell.
CHANGES:
--><model xmlns="http://www.cellml.org/cellml/1.0#" xmlns:cmeta="http://www.cellml.org/metadata/1.0#" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:bqs="http://www.cellml.org/bqs/1.0#" xmlns:cellml="http://www.cellml.org/cellml/1.0#" xmlns:dcterms="http://purl.org/dc/terms/" xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" cmeta:id="westermark_2003" name="westermark_2003">
<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
<articleinfo>
<title>A Model of Phosphofructokinase and Glycolytic Oscillations in the Pancreatic Beta-cell</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 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>
ABSTRACT: We have constructed a model of the upper part of the glycolysis in the pancreatic beta-cell. The model comprises the enzymatic reactions from glucokinase to glyceraldehyde-3-phosphate dehydrogenase (GAPD). Our results show, for a substantial part of the parameter space, an oscillatory behavior of the glycolysis for a large range of glucose concentrations. We show how the occurrence of oscillations depends on glucokinase, aldolase and/or GAPD activities, and how the oscillation period depends on the phosphofructokinase activity. We propose that the ratio of glucokinase and aldolase and/or GAPD activities are adequate as characteristics of the glucose responsiveness, rather than only the glucokinase activity. We also propose that the rapid equilibrium between different oligomeric forms of phosphofructokinase may reduce the oscillation period sensitivity to phosphofructokinase activity. Methodologically, we show that a satisfying description of phosphofructokinase kinetics can be achieved using the irreversible Hill equation with allosteric modifiers. We emphasize the use of parameter ranges rather than fixed values, and the use of operationally well-defined parameters in order for this methodology to be feasible. The theoretical results presented in this study apply to the study of insulin secretion mechanisms, since glycolytic oscillations have been proposed as a cause of oscillations in the ATP/ADP ratio which is linked to insulin secretion.
</para>
<para>
The original paper reference is cited below:
</para>
<para>
A Model of Phosphofructokinase and Glycolytic Oscillations in the Pancreatic Beta-cell, Pal O. Westermark and Anders Lansner, 2003, <emphasis>Biophysical Journal</emphasis>, 85, 126-139. <ulink url="http://www.ncbi.nlm.nih.gov/pubmed/12829470">PubMed ID: 12829470</ulink>
</para>
<informalfigure float="0" id="fig_reaction_diagram">
<mediaobject>
<imageobject>
<objectinfo>
<title>reaction diagram</title>
</objectinfo>
<imagedata fileref="westermark_2003.png"/>
</imageobject>
</mediaobject>
<caption>Schematic representation of the mathematical model of glycolysis. The fluxes over the enzyme catalysed reactions are denoted <emphasis>v</emphasis>.</caption>
</informalfigure>
</sect1>
</article>
</documentation>
<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="micromolar">
<unit units="mole" prefix="micro"/>
<unit units="litre" exponent="-1"/>
</units>
<units name="micromole">
<unit units="mole" prefix="micro"/>
</units>
<units name="enzyme_activity">
<unit units="micromole"/>
<unit units="gram" exponent="-1"/>
<unit units="minute" exponent="-1"/>
</units>
<units name="flux">
<unit units="micromolar"/>
<unit units="minute" exponent="-1"/>
</units>
<component name="environment">
<variable units="second" public_interface="out" name="time"/>
</component>
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<variable units="flux" public_interface="out" name="v_GK"/>
<variable units="enzyme_activity" name="V_GK" initial_value="10.0"/>
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<variable units="dimensionless" name="h_GK" initial_value="1.7"/>
<variable units="micromolar" public_interface="in" name="Glc"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
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<eq/>
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<apply>
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<divide/>
<ci> Glc </ci>
<ci> S0_5_GK </ci>
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</apply>
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<ci> Glc </ci>
<ci> S0_5_GK </ci>
</apply>
<ci> h_GK </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
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<variable units="flux" public_interface="out" name="v_GPI"/>
<variable units="dimensionless" name="Keq_GPI" initial_value="0.3"/>
<variable units="micromolar" public_interface="in" name="G6P"/>
<variable units="micromolar" public_interface="in" name="F6P"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
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<apply>
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<ci> G6P </ci>
<ci> F6P </ci>
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</math>
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<variable units="flux" public_interface="out" name="v_PFK"/>
<variable units="dimensionless" public_interface="out" name="pi_pfk"/>
<variable units="enzyme_activity" name="V_PFK" initial_value="100.0"/>
<variable units="millimolar" name="S0_5_PFK" initial_value="4.0"/>
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<variable units="micromolar" name="X0_5" initial_value="10.0"/>
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<variable units="dimensionless" name="alpha"/>
<variable units="dimensionless" name="q"/>
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<variable units="dimensionless" name="h_PFK_"/>
<variable units="dimensionless" name="h_act" initial_value="1.0"/>
<variable units="enzyme_activity" name="k_cat_K_PFK" initial_value="233.0"/>
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<variable units="millimolar" name="KO" initial_value="30.0"/>
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<variable units="micromolar" public_interface="in" name="F6P"/>
<variable units="micromolar" public_interface="in" name="Glc"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
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<ci> alpha </ci>
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<ci> S0_5_PFK </ci>
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<ci> X0_5 </ci>
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<rdf:RDF>
<rdf:Bag rdf:about="rdf:#d0754363-615c-459e-aea3-bc600904a39b">
<rdf:li>glycolysis</rdf:li>
<rdf:li>pfk</rdf:li>
<rdf:li>oscillator</rdf:li>
<rdf:li>beta cell</rdf:li>
<rdf:li>glycolytic oscillations</rdf:li>
<rdf:li>metabolism</rdf:li>
<rdf:li>pancreas</rdf:li>
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<dcterms:W3CDTF>2004-10-08</dcterms:W3CDTF>
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<dcterms:alternative>triosphosphate-phosphate isomerase reaction</dcterms:alternative>
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<vCard:Given>Pal</vCard:Given>
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<vCard:Other>O</vCard:Other>
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<vCard:Given>Anders</vCard:Given>
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<vCard:Orgname>The University of Auckland</vCard:Orgname>
<vCard:Orgunit>The Bioengineering Institute</vCard:Orgunit>
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<dcterms:alternative>fructose-1,6-bisphosphate</dcterms:alternative>
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<vCard:Given>Catherine</vCard:Given>
<vCard:Family>Lloyd</vCard:Family>
<vCard:Other>May</vCard:Other>
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<dcterms:alternative>phosphofructokinase reaction</dcterms:alternative>
<dc:title>v_PFK</dc:title>
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<dcterms:alternative>glyceraldehyde-3-phosphate</dcterms:alternative>
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This is the CellML description of Westermark and Lansner's 2003 mathematical model of phosphofructokinase and glycolytic oscillations in the pancreatic beta-cell.
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<dcterms:alternative>glyceraldehyde-3-phosphate dehydrogenase reaction</dcterms:alternative>
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<dcterms:W3CDTF>2003-07</dcterms:W3CDTF>
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<vCard:FN>Catherine Lloyd</vCard:FN>
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<dcterms:alternative>fructose-bisphosphate aldolase reaction</dcterms:alternative>
<dc:title>v_FBA</dc:title>
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<rdf:Description rdf:about="#DHAP">
<dcterms:alternative>dihydroxyacetone-phosphate</dcterms:alternative>
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<dc:title>
A Model of Phosphofructokinase and Glycolytic Oscillations in the Pancreatic Beta-cell
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<bqs:volume>85</bqs:volume>
<bqs:first_page>126</bqs:first_page>
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The University of Auckland, Auckland Bioengineering Institute
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Westermark and Lansner's 2003 mathematical model of phosphofructokinase and glycolytic oscillations in the pancreatic beta-cell.
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<cmeta:bio_entity>Pancreatic beta-cell</cmeta:bio_entity>
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<dcterms:alternative>glucose-6-phosphate isomerase reaction</dcterms:alternative>
<dc:title>v_GPI</dc:title>
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