- Author:
- Mona Zhu <devnull@localhost>
- Date:
- 2011-01-26 15:32:46+13:00
- Desc:
- Added 1.1 model
- Permanent Source URI:
- https://staging.physiomeproject.org/workspace/westermark_lansner_2003/rawfile/77884cba4662cf8f4c938b7bf356354c51efeb0d/westermark_2003_1.1.cellml
<?xml version="1.0"?>
<model xmlns="http://www.cellml.org/cellml/1.1#" xmlns:cmeta="http://www.cellml.org/metadata/1.1#" cmeta:id="westermark_2003_1.1" name="westermark_2003_1.1">
<!-- documentation -->
<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>
<author>
<firstname>Mona</firstname>
<surname>Zhu</surname>
<affiliation>
<shortaffil>Auckland Bioengineering Institute, The University of Auckland</shortaffil>
</affiliation>
</author>
</articleinfo>
<section id="sec_status">
<title>Model Status</title>
<para>
This CellML model runs in OpenCell to replicate the published results (figure 3a). It was curated with help from the equivalent SBML model from the BioModels database (BIOMD0000000236).
</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 (GAPDH). 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 GAPDH activities, and how the oscillation period depends on the phosphofructokinase activity. We propose that the ratio of glucokinase and aldolase and/or GAPDH 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 -->
<units name="minute">
<unit multiplier="60.0" units="second"/>
</units>
<units name="millimolar">
<unit prefix="milli" units="mole"/>
<unit exponent="-1" units="litre"/>
</units>
<units name="micromole">
<unit prefix="micro" units="mole"/>
</units>
<units name="enzyme_activity">
<unit units="micromole"/>
<unit exponent="-1" units="gram"/>
<unit exponent="-1" units="minute"/>
</units>
<units name="flux">
<unit units="millimolar"/>
<unit exponent="-1" units="second"/>
</units>
<!-- components -->
<component name="environment">
<variable cmeta:id="environment_time" name="time" public_interface="out" units="second"/>
</component>
<component cmeta:id="v_GK" name="v_GK">
<variable name="v_GK" public_interface="out" units="flux"/>
<variable initial_value="10.0" name="V_GK_min" private_interface="out" units="enzyme_activity"/>
<variable name="V_GK" private_interface="in" units="enzyme_activity"/>
<variable initial_value="8.0" name="Sgk" units="millimolar"/>
<variable initial_value="1.7" name="h_GK" units="dimensionless"/>
<variable name="Glc" public_interface="in" units="millimolar"/>
<variable name="min_to_sec" private_interface="out" public_interface="in" units="dimensionless"/>
<variable name="dw_per_ml" private_interface="out" public_interface="in" units="dimensionless"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci> v_GK </ci>
<apply>
<divide/>
<apply>
<times/>
<ci> V_GK </ci>
<apply>
<power/>
<apply>
<divide/>
<ci> Glc </ci>
<ci> Sgk </ci>
</apply>
<ci> h_GK </ci>
</apply>
</apply>
<apply>
<plus/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.1#" cellml:units="dimensionless"> 1.0 </cn>
<apply>
<power/>
<apply>
<divide/>
<ci> Glc </ci>
<ci> Sgk </ci>
</apply>
<ci> h_GK </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component cmeta:id="v_PFK" name="v_PFK">
<variable name="v_PFK" public_interface="out" units="flux"/>
<variable initial_value="100.0" name="V_PFK_min" private_interface="out" units="enzyme_activity"/>
<variable name="V_PFK" private_interface="in" units="enzyme_activity"/>
<variable initial_value="4.0" name="Spfk" units="millimolar"/>
<variable initial_value="0.005" name="Sfba" units="millimolar"/>
<variable initial_value="0.01" name="Xpfk" units="millimolar"/>
<variable initial_value="2.5" name="hx" units="dimensionless"/>
<variable initial_value="5.0" name="alpha" units="dimensionless"/>
<variable initial_value="2.5" name="h_PFK" units="dimensionless"/>
<variable initial_value="1.0" name="h_act" units="dimensionless"/>
<variable name="FBP" public_interface="in" units="millimolar"/>
<variable name="F6P" public_interface="in" units="millimolar"/>
<variable name="min_to_sec" private_interface="out" public_interface="in" units="dimensionless"/>
<variable name="dw_per_ml" private_interface="out" public_interface="in" units="dimensionless"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci> v_PFK </ci>
<apply>
<divide/>
<apply>
<times/>
<ci> V_PFK </ci>
<apply>
<power/>
<apply>
<divide/>
<ci> F6P </ci>
<ci> Spfk </ci>
</apply>
<apply>
<minus/>
<ci> h_PFK </ci>
<apply>
<times/>
<apply>
<minus/>
<ci> h_PFK </ci>
<ci> h_act </ci>
</apply>
<apply>
<divide/>
<apply>
<divide/>
<ci> FBP </ci>
<ci> Sfba </ci>
</apply>
<apply>
<plus/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.1#" cellml:units="dimensionless"> 1.0 </cn>
<apply>
<divide/>
<ci> FBP </ci>
<ci> Sfba </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<plus/>
<apply>
<power/>
<apply>
<divide/>
<ci> F6P </ci>
<ci> Spfk </ci>
</apply>
<apply>
<minus/>
<ci> h_PFK </ci>
<apply>
<times/>
<apply>
<minus/>
<ci> h_PFK </ci>
<ci> h_act </ci>
</apply>
<apply>
<divide/>
<apply>
<divide/>
<ci> FBP </ci>
<ci> Sfba </ci>
</apply>
<apply>
<plus/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.1#" cellml:units="dimensionless"> 1.0 </cn>
<apply>
<divide/>
<ci> FBP </ci>
<ci> Sfba </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<divide/>
<apply>
<plus/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.1#" cellml:units="dimensionless"> 1.0 </cn>
<apply>
<power/>
<apply>
<divide/>
<ci> FBP </ci>
<ci> Xpfk </ci>
</apply>
<ci> hx </ci>
</apply>
</apply>
<apply>
<plus/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.1#" cellml:units="dimensionless"> 1.0 </cn>
<apply>
<times/>
<apply>
<power/>
<ci> alpha </ci>
<apply>
<minus/>
<ci> h_PFK </ci>
<apply>
<times/>
<apply>
<minus/>
<ci> h_PFK </ci>
<ci> h_act </ci>
</apply>
<apply>
<divide/>
<apply>
<divide/>
<ci> FBP </ci>
<ci> Sfba </ci>
</apply>
<apply>
<plus/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.1#" cellml:units="dimensionless"> 1.0 </cn>
<apply>
<divide/>
<ci> FBP </ci>
<ci> Sfba </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<power/>
<apply>
<divide/>
<ci> FBP </ci>
<ci> Xpfk </ci>
</apply>
<ci> hx </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component cmeta:id="v_FBA" name="v_FBA">
<variable name="v_FBA" public_interface="out" units="flux"/>
<variable initial_value="25.0" name="V_FBA_min" private_interface="out" units="enzyme_activity"/>
<variable name="V_FBA" private_interface="in" units="enzyme_activity"/>
<variable initial_value="0.275" name="Qfba" units="millimolar"/>
<variable initial_value="0.005" name="Sfba" units="millimolar"/>
<variable initial_value="0.5" name="Pfba" units="millimolar"/>
<variable initial_value="0.1" name="Keq_FBA" units="millimolar"/>
<variable name="FBP" public_interface="in" units="millimolar"/>
<variable name="G3P" public_interface="in" units="millimolar"/>
<variable name="DHAP" public_interface="in" units="millimolar"/>
<variable name="min_to_sec" private_interface="out" public_interface="in" units="dimensionless"/>
<variable name="dw_per_ml" private_interface="out" public_interface="in" units="dimensionless"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci> v_FBA </ci>
<apply>
<divide/>
<apply>
<times/>
<ci> V_FBA </ci>
<apply>
<minus/>
<apply>
<divide/>
<ci> FBP </ci>
<ci> Sfba </ci>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci> G3P </ci>
<ci> DHAP </ci>
</apply>
<apply>
<times/>
<ci> Pfba </ci>
<ci> Qfba </ci>
<ci> Keq_FBA </ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<plus/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.1#" cellml:units="dimensionless"> 1.0 </cn>
<apply>
<divide/>
<ci> FBP </ci>
<ci> Sfba </ci>
</apply>
<apply>
<divide/>
<ci> DHAP </ci>
<ci> Qfba </ci>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci> G3P </ci>
<ci> DHAP </ci>
</apply>
<apply>
<times/>
<ci> Pfba </ci>
<ci> Qfba </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component cmeta:id="v_GAPDH" name="v_GAPDH">
<variable name="v_GAPDH" public_interface="out" units="flux"/>
<variable initial_value="250.0" name="V_GAPDH_min" private_interface="out" units="enzyme_activity"/>
<variable name="V_GAPDH" private_interface="in" units="enzyme_activity"/>
<variable initial_value="0.005" name="Sgapdh" units="millimolar"/>
<variable name="G3P" public_interface="in" units="millimolar"/>
<variable name="min_to_sec" private_interface="out" public_interface="in" units="dimensionless"/>
<variable name="dw_per_ml" private_interface="out" public_interface="in" units="dimensionless"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci> v_GAPDH </ci>
<apply>
<divide/>
<apply>
<times/>
<ci> V_GAPDH </ci>
<ci> G3P </ci>
</apply>
<apply>
<plus/>
<ci> Sgapdh </ci>
<ci> G3P </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component cmeta:id="Glc" name="Glc">
<variable cmeta:id="Glc_Glc" name="Glc" public_interface="out" units="millimolar"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci> Glc </ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.1#" cellml:units="millimolar"> 10.0 </cn>
</apply>
</math>
</component>
<component cmeta:id="G6P_F6P" name="G6P_F6P">
<variable cmeta:id="G6P_F6P_G6P_F6P" name="G6P_F6P" private_interface="in" public_interface="out" units="millimolar"/>
<variable name="v_GK" private_interface="out" public_interface="in" units="flux"/>
<variable name="v_PFK" private_interface="out" public_interface="in" units="flux"/>
<variable name="time" private_interface="out" public_interface="in" units="second"/>
<variable cmeta:id="G6P_F6P_G6P_F6P" initial_value="3.71728" name="G6P_F6P_init" private_interface="out" units="millimolar"/>
<variable initial_value="1" name="one" private_interface="out" units="dimensionless"/>
</component>
<component cmeta:id="F6P" name="F6P">
<variable cmeta:id="F6P_F6P" name="F6P" private_interface="in" public_interface="out" units="millimolar"/>
<variable initial_value="0.3" name="Keq_GPI" private_interface="out" units="dimensionless"/>
<variable name="G6P_F6P" private_interface="out" public_interface="in" units="millimolar"/>
</component>
<component cmeta:id="FBP" name="FBP">
<variable cmeta:id="FBP_FBP" name="FBP" private_interface="in" public_interface="out" units="millimolar"/>
<variable name="v_PFK" private_interface="out" public_interface="in" units="flux"/>
<variable name="v_FBA" private_interface="out" public_interface="in" units="flux"/>
<variable name="time" private_interface="out" public_interface="in" units="second"/>
<variable initial_value="0.00063612" name="FBP_init" private_interface="out" units="millimolar"/>
<variable initial_value="1" name="one" private_interface="out" units="dimensionless"/>
</component>
<component cmeta:id="DHAP_G3P" name="DHAP_G3P">
<variable name="DHAP_G3P" private_interface="in" public_interface="out" units="millimolar"/>
<variable name="v_GAPDH" private_interface="out" public_interface="in" units="flux"/>
<variable name="v_FBA" private_interface="out" public_interface="in" units="flux"/>
<variable name="time" private_interface="out" public_interface="in" units="second"/>
<variable initial_value="0.00262966" name="DHAP_G3P_init" private_interface="out" units="millimolar"/>
<variable initial_value="2" name="two" private_interface="out" units="dimensionless"/>
</component>
<component cmeta:id="DHAP" name="DHAP">
<variable cmeta:id="DHAP_DHAP" name="DHAP" public_interface="out" units="millimolar"/>
<variable name="DHAP_G3P" public_interface="in" units="millimolar"/>
<variable name="G3P" public_interface="in" units="millimolar"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci> DHAP </ci>
<apply>
<minus/>
<ci> DHAP_G3P </ci>
<ci> G3P </ci>
</apply>
</apply>
</math>
</component>
<component cmeta:id="G3P" name="G3P">
<variable cmeta:id="G3P_G3P" name="G3P" private_interface="in" public_interface="out" units="millimolar"/>
<variable initial_value="0.045455" name="Keq_TPI" private_interface="out" units="dimensionless"/>
<variable name="DHAP_G3P" private_interface="out" public_interface="in" units="millimolar"/>
</component>
<component name="model_parameters">
<variable initial_value="60.0" name="min_to_sec" public_interface="out" units="dimensionless"/>
<variable initial_value="0.3333" name="dw_per_ml" public_interface="out" units="dimensionless"/>
</component>
<!-- groups -->
<group>
<relationship_ref relationship="encapsulation"/>
<component_ref component="v_GAPDH">
<component_ref component="V_GAPDHi"/>
</component_ref>
</group>
<group>
<relationship_ref relationship="encapsulation"/>
<component_ref component="v_GK">
<component_ref component="V_GKi"/>
</component_ref>
</group>
<group>
<relationship_ref relationship="encapsulation"/>
<component_ref component="v_PFK">
<component_ref component="V_PFKi"/>
</component_ref>
</group>
<group>
<relationship_ref relationship="encapsulation"/>
<component_ref component="v_FBA">
<component_ref component="V_FBAi"/>
</component_ref>
</group>
<group>
<relationship_ref relationship="encapsulation"/>
<component_ref component="FBP">
<component_ref component="FBPi"/>
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<relationship_ref relationship="encapsulation"/>
<component_ref component="G6P_F6P">
<component_ref component="G6P_F6Pi"/>
</component_ref>
</group>
<group>
<relationship_ref relationship="encapsulation"/>
<component_ref component="DHAP_G3P">
<component_ref component="DHAP_G3Pi"/>
</component_ref>
</group>
<group>
<relationship_ref relationship="encapsulation"/>
<component_ref component="G3P">
<component_ref component="G3Pi"/>
</component_ref>
</group>
<group>
<relationship_ref relationship="encapsulation"/>
<component_ref component="F6P">
<component_ref component="F6Pi"/>
</component_ref>
</group>
<!-- imports -->
<import xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cons_law1.cellml">
<component component_ref="interface" name="V_GAPDHi"/>
</import>
<import xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cons_law1.cellml">
<component component_ref="interface" name="V_GKi"/>
</import>
<import xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cons_law1.cellml">
<component component_ref="interface" name="V_PFKi"/>
</import>
<import xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cons_law1.cellml">
<component component_ref="interface" name="V_FBAi"/>
</import>
<import xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cons_law2.cellml">
<component component_ref="interface" name="FBPi"/>
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<import xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cons_law2.cellml">
<component component_ref="interface" name="G6P_F6Pi"/>
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<import xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cons_law2.cellml">
<component component_ref="interface" name="DHAP_G3Pi"/>
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<import xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cons_law3.cellml">
<component component_ref="interface" name="G3Pi"/>
</import>
<import xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cons_law3.cellml">
<component component_ref="interface" name="F6Pi"/>
</import>
<!-- connections -->
<connection>
<map_components component_1="G6P_F6P" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="FBP" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="DHAP_G3P" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="Glc" component_2="v_GK"/>
<map_variables variable_1="Glc" variable_2="Glc"/>
</connection>
<connection>
<map_components component_1="model_parameters" component_2="v_GK"/>
<map_variables variable_1="min_to_sec" variable_2="min_to_sec"/>
<map_variables variable_1="dw_per_ml" variable_2="dw_per_ml"/>
</connection>
<connection>
<map_components component_1="v_PFK" component_2="F6P"/>
<map_variables variable_1="F6P" variable_2="F6P"/>
</connection>
<connection>
<map_components component_1="v_PFK" component_2="FBP"/>
<map_variables variable_1="FBP" variable_2="FBP"/>
<map_variables variable_1="v_PFK" variable_2="v_PFK"/>
</connection>
<connection>
<map_components component_1="model_parameters" component_2="v_PFK"/>
<map_variables variable_1="min_to_sec" variable_2="min_to_sec"/>
<map_variables variable_1="dw_per_ml" variable_2="dw_per_ml"/>
</connection>
<connection>
<map_components component_1="v_FBA" component_2="G3P"/>
<map_variables variable_1="G3P" variable_2="G3P"/>
</connection>
<connection>
<map_components component_1="v_FBA" component_2="DHAP"/>
<map_variables variable_1="DHAP" variable_2="DHAP"/>
</connection>
<connection>
<map_components component_1="v_FBA" component_2="FBP"/>
<map_variables variable_1="FBP" variable_2="FBP"/>
<map_variables variable_1="v_FBA" variable_2="v_FBA"/>
</connection>
<connection>
<map_components component_1="model_parameters" component_2="v_FBA"/>
<map_variables variable_1="min_to_sec" variable_2="min_to_sec"/>
<map_variables variable_1="dw_per_ml" variable_2="dw_per_ml"/>
</connection>
<connection>
<map_components component_1="v_GAPDH" component_2="G3P"/>
<map_variables variable_1="G3P" variable_2="G3P"/>
</connection>
<connection>
<map_components component_1="model_parameters" component_2="v_GAPDH"/>
<map_variables variable_1="min_to_sec" variable_2="min_to_sec"/>
<map_variables variable_1="dw_per_ml" variable_2="dw_per_ml"/>
</connection>
<connection>
<map_components component_1="v_GK" component_2="G6P_F6P"/>
<map_variables variable_1="v_GK" variable_2="v_GK"/>
</connection>
<connection>
<map_components component_1="v_PFK" component_2="G6P_F6P"/>
<map_variables variable_1="v_PFK" variable_2="v_PFK"/>
</connection>
<connection>
<map_components component_1="G6P_F6P" component_2="F6P"/>
<map_variables variable_1="G6P_F6P" variable_2="G6P_F6P"/>
</connection>
<connection>
<map_components component_1="v_FBA" component_2="DHAP_G3P"/>
<map_variables variable_1="v_FBA" variable_2="v_FBA"/>
</connection>
<connection>
<map_components component_1="v_GAPDH" component_2="DHAP_G3P"/>
<map_variables variable_1="v_GAPDH" variable_2="v_GAPDH"/>
</connection>
<connection>
<map_components component_1="G3P" component_2="DHAP"/>
<map_variables variable_1="G3P" variable_2="G3P"/>
</connection>
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