- Author:
- Catherine Lloyd <c.lloyd@auckland.ac.nz>
- Date:
- 2009-10-01 13:52:10+13:00
- Desc:
- Updated temp documentation and also corrected link to model image.
- Permanent Source URI:
- https://models.cellml.org/workspace/bertram_satin_zhang_smolen_sherman_2004/rawfile/f47dbf795a2064de349763bdde76998e4a55838d/bertram_satin_zhang_smolen_sherman_2004_a.cellml
<?xml version='1.0' encoding='utf-8'?>
<!-- FILE : satin_model_2004.xml
CREATED : 1st October 2004
LAST MODIFIED : 1st 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 Bertram et al.'s 2004 mathematical model of calcium and glycolysis mediated bursting modes in pancreatic islets.
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="bertram_satin_zhang_smolen_sherman_2004_version01" name="bertram_satin_zhang_smolen_sherman_2004_version01">
<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
<articleinfo>
<title>Modelling Multiple Bursting Models in Pancreatic Islets</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 model is unsuitably constrained and can not be solved in its current state.
</para>
<para>
ValidateCellML verifies this model as valid CellML, although units inconsistencies are detected.
</para>
</section>
<sect1 id="sec_structure">
<title>Model Structure</title>
<para>
ABSTRACT: Pancreatic islets of Langerhans produce bursts of electrical activity when exposed to stimulatory glucose levels. These bursts often have a regular repeating pattern, with a period of 10-60 s. In some cases, however, the bursts are episodic, clustered into bursts of bursts, which we call compound bursting. Consistent with this are recordings of free Ca2+ concentration, oxygen consumption, mitochondrial membrane potential, and intraislet glucose levels that exhibit very slow oscillations, with faster oscillations superimposed. We describe a new mathematical model of the pancreatic beta-cell that can account for these multimodal patterns. The model includes the feedback of cytosolic Ca2+ onto ion channels that can account for bursting, and a metabolic subsystem that is capable of producing slow oscillations driven by oscillations in glycolysis. This slow rhythm is responsible for the slow mode of compound bursting in the model. We also show that it is possible for glycolytic oscillations alone to drive a very slow form of bursting, which we call "glycolytic bursting." Finally, the model predicts that there is bistability between stationary and oscillatory glycolysis for a range of parameter values. We provide experimental support for this model prediction. Overall, the model can account for a diversity of islet behaviors described in the literature over the past 20 years.
</para>
<para>
Calcium and Glycolysis Mediate Multiple Bursting Modes in Pancreatic Islets, Richard Bertram, Leslie Satin, Min Zhang, Paul Smolen, and Arthur Sherman, 2004,
<emphasis>Biophysical Journal</emphasis>, 87, 3074-3087. <ulink url="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&list_uids=15347584&dopt=Abstract">PubMed ID: 15347584</ulink>
</para>
<informalfigure float="0" id="fig_cell_diagram">
<mediaobject>
<imageobject>
<objectinfo>
<title>cell diagram</title>
</objectinfo>
<imagedata fileref="satin_2004.png"/>
</imageobject>
</mediaobject>
<caption>A schematic diagram of the ionic currents and fluxes across the ER and the cell surface membranes which are described by the mathematical model.</caption>
</informalfigure>
</sect1>
</article>
</documentation>
<units name="millisecond">
<unit units="second" prefix="milli"/>
</units>
<units name="minute">
<unit units="second" multiplier="60.0"/>
</units>
<units name="millivolt">
<unit units="volt" prefix="milli"/>
</units>
<units name="micromolar">
<unit units="mole" prefix="micro"/>
<unit units="litre" exponent="-1"/>
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<units name="nanoS">
<unit units="siemens" prefix="nano"/>
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<units name="picoS">
<unit units="siemens" prefix="pico"/>
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<units name="femtoA">
<unit units="ampere" prefix="femto"/>
</units>
<units name="per_second">
<unit units="second" exponent="-1"/>
</units>
<units name="first_order_rate_constant">
<unit units="millisecond" exponent="-1"/>
</units>
<units name="micromolar_per_femtoA_millisecond">
<unit units="micromolar"/>
<unit units="femtoA" exponent="-1"/>
<unit units="millisecond" exponent="-1"/>
</units>
<units name="flux">
<unit units="micromolar"/>
<unit units="second" exponent="-1"/>
</units>
<component name="environment">
<variable units="millisecond" public_interface="out" name="time"/>
</component>
<component name="membrane">
<variable units="millivolt" public_interface="out" name="V"/>
<variable units="femtoF" name="Cm" initial_value="5300.0"/>
<variable units="millisecond" public_interface="in" name="time"/>
<variable units="femtoA" public_interface="in" name="i_Ca"/>
<variable units="femtoA" public_interface="in" name="i_K"/>
<variable units="femtoA" public_interface="in" name="i_K_Ca"/>
<variable units="femtoA" public_interface="in" name="i_K_ATP"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="membrane_voltage_diff_eq">
<eq/>
<apply>
<diff/>
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</bvar>
<ci> V </ci>
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<apply>
<divide/>
<apply>
<minus/>
<apply>
<plus/>
<ci> i_Ca </ci>
<ci> i_K </ci>
<ci> i_K_Ca </ci>
<ci> i_K_ATP </ci>
</apply>
</apply>
<ci> Cm </ci>
</apply>
</apply>
</math>
</component>
<component name="delayed_rectifier_potassium_current">
<variable units="femtoA" public_interface="out" name="i_K"/>
<variable units="millivolt" public_interface="out" name="V_K" initial_value="-75.0"/>
<variable units="picoS" name="g_K" initial_value="2700.0"/>
<variable units="millivolt" public_interface="in" private_interface="out" name="V"/>
<variable units="millisecond" public_interface="in" private_interface="out" name="time"/>
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<math xmlns="http://www.w3.org/1998/Math/MathML">
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<eq/>
<ci> i_K </ci>
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<ci> g_K </ci>
<ci> n </ci>
<apply>
<minus/>
<ci> V </ci>
<ci> V_K </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="delayed_rectifier_potassium_current_n_gate">
<variable units="dimensionless" public_interface="out" name="n"/>
<variable units="millisecond" name="tau_n" initial_value="20.0"/>
<variable units="dimensionless" name="n_infinity"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="millisecond" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="n_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> n </ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci> n_infinity </ci>
<ci> n </ci>
</apply>
<ci> tau_n </ci>
</apply>
</apply>
<apply id="n_infinity_calculation">
<eq/>
<ci> n_infinity </ci>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<plus/>
<cn cellml:units="millivolt"> 16.0 </cn>
<ci> V </ci>
</apply>
</apply>
<cn cellml:units="millivolt"> 5.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="calcium_current">
<variable units="femtoA" public_interface="out" name="i_Ca"/>
<variable units="picoS" name="g_Ca" initial_value="1000.0"/>
<variable units="millivolt" name="V_Ca" initial_value="25.0"/>
<variable units="millivolt" public_interface="in" private_interface="out" name="V"/>
<variable units="millisecond" public_interface="in" private_interface="out" name="time"/>
<variable units="dimensionless" private_interface="in" name="m_infinity"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="i_Ca_calculation">
<eq/>
<ci> i_Ca </ci>
<apply>
<times/>
<ci> g_Ca </ci>
<ci> m_infinity </ci>
<apply>
<minus/>
<ci> V </ci>
<ci> V_Ca </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="calcium_current_m_gate">
<variable units="dimensionless" public_interface="out" name="m_infinity"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="millisecond" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="m_infinity_calculation">
<eq/>
<ci> m_infinity </ci>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
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<cn cellml:units="millivolt"> 20.0 </cn>
<ci> V </ci>
</apply>
</apply>
<cn cellml:units="millivolt"> 12.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="calcium_dependent_potassium_current">
<variable units="femtoA" public_interface="out" name="i_K_Ca"/>
<variable units="picoS" name="g_K_Ca"/>
<variable units="picoS" name="g_K_Ca_" initial_value="600.0"/>
<variable units="micromolar" name="kD" initial_value="0.5"/>
<variable units="millivolt" public_interface="in" name="V_K"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="micromolar" public_interface="in" name="Ca"/>
<variable units="millisecond" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="i_K_Ca_calculation">
<eq/>
<ci> i_K_Ca </ci>
<apply>
<times/>
<ci> g_K_Ca </ci>
<apply>
<minus/>
<ci> V </ci>
<ci> V_K </ci>
</apply>
</apply>
</apply>
<apply id="g_K_Ca_eq">
<eq/>
<ci> g_K_Ca </ci>
<apply>
<times/>
<ci> g_K_Ca_ </ci>
<apply>
<divide/>
<apply>
<power/>
<ci> Ca </ci>
<cn cellml:units="dimensionless"> 5.0 </cn>
</apply>
<apply>
<plus/>
<apply>
<power/>
<ci> kD </ci>
<cn cellml:units="dimensionless"> 5.0 </cn>
</apply>
<apply>
<power/>
<ci> Ca </ci>
<cn cellml:units="dimensionless"> 5.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="nucleotide_sensitive_potassium_current">
<variable units="femtoA" public_interface="out" name="i_K_ATP"/>
<variable units="micromolar" name="MgADP"/>
<variable units="micromolar" name="ADP3"/>
<variable units="micromolar" name="ATP4"/>
<variable units="nanoS" name="g_K_ATP" initial_value="25.0"/>
<variable units="picoS" name="g_K_ATP_"/>
<variable units="dimensionless" name="O_infinity_ADP_ATP"/>
<variable units="millivolt" public_interface="in" name="V_K"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="micromolar" public_interface="in" name="ADP"/>
<variable units="micromolar" public_interface="in" name="ATP"/>
<variable units="millisecond" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="i_K_ATP_calculation">
<eq/>
<ci> i_K_ATP </ci>
<apply>
<times/>
<ci> g_K_ATP </ci>
<apply>
<minus/>
<ci> V </ci>
<ci> V_K </ci>
</apply>
</apply>
</apply>
<apply id="g_K_ATP_eq">
<eq/>
<ci> g_K_ATP </ci>
<apply>
<times/>
<ci> g_K_ATP_ </ci>
<ci> O_infinity_ADP_ATP </ci>
</apply>
</apply>
<apply id="MgADP_eq">
<eq/>
<ci> MgADP </ci>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.165 </cn>
<ci> ADP </ci>
</apply>
</apply>
<apply id="ADP3_eq">
<eq/>
<ci> ADP3 </ci>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.135 </cn>
<ci> ADP </ci>
</apply>
</apply>
<apply id="ATP4_eq">
<eq/>
<ci> ATP4 </ci>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.05 </cn>
<ci> ATP </ci>
</apply>
</apply>
<apply id="O_infinity_ADP_ATP_eq">
<eq/>
<ci> O_infinity_ADP_ATP </ci>
<apply>
<divide/>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.08 </cn>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 2.0 </cn>
<ci> MgADP </ci>
</apply>
<cn cellml:units="micromolar"> 17.0 </cn>
</apply>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.89 </cn>
<apply>
<power/>
<apply>
<divide/>
<ci> MgADP </ci>
<cn cellml:units="micromolar"> 17.0 </cn>
</apply>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
</apply>
</apply>
<apply>
<times/>
<apply>
<power/>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<divide/>
<ci> MgADP </ci>
<cn cellml:units="micromolar"> 17.0 </cn>
</apply>
</apply>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<divide/>
<ci> ADP3 </ci>
<cn cellml:units="micromolar"> 26.0 </cn>
</apply>
<apply>
<divide/>
<ci> ATP4 </ci>
<cn cellml:units="micromolar"> 1.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="cytosolic_free_calcium_concentration">
<variable units="micromolar" public_interface="out" name="Ca"/>
<variable units="dimensionless" name="fcyt" initial_value="0.01"/>
<variable units="flux" public_interface="in" name="Jmem"/>
<variable units="flux" public_interface="in" name="Jer"/>
<variable units="millisecond" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="Ca_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> Ca </ci>
</apply>
<apply>
<times/>
<ci> fcyt </ci>
<apply>
<plus/>
<ci> Jmem </ci>
<ci> Jer </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="calcium_flux_through_the_membrane">
<variable units="flux" public_interface="out" name="Jmem"/>
<variable units="micromolar_per_femtoA_millisecond" name="alpha" initial_value="4.5E-6"/>
<variable units="first_order_rate_constant" name="kPMCA" initial_value="0.2"/>
<variable units="micromolar" public_interface="in" name="Ca"/>
<variable units="femtoA" public_interface="in" name="i_Ca"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="Jmem_eq">
<eq/>
<ci> Jmem </ci>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<times/>
<ci> alpha </ci>
<ci> i_Ca </ci>
</apply>
<apply>
<times/>
<ci> kPMCA </ci>
<ci> Ca </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="net_calcium_efflux_out_of_the_ER">
<variable units="flux" public_interface="out" name="Jer"/>
<variable units="flux" public_interface="in" name="Jleak"/>
<variable units="flux" public_interface="in" name="J_SERCA"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="Jer_eq">
<eq/>
<ci> Jer </ci>
<apply>
<minus/>
<ci> Jleak </ci>
<ci> J_SERCA </ci>
</apply>
</apply>
</math>
</component>
<component name="calcium_leak_out_of_the_ER">
<variable units="flux" public_interface="out" name="Jleak"/>
<variable units="first_order_rate_constant" name="pleak" initial_value="0.0002"/>
<variable units="micromolar" public_interface="in" name="Ca"/>
<variable units="micromolar" public_interface="in" name="Ca_er"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="Jleak_eq">
<eq/>
<ci> Jleak </ci>
<apply>
<times/>
<ci> pleak </ci>
<apply>
<minus/>
<ci> Ca_er </ci>
<ci> Ca </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="calcium_influx_into_the_ER">
<variable units="flux" public_interface="out" name="J_SERCA"/>
<variable units="first_order_rate_constant" name="kSERCA" initial_value="0.4"/>
<variable units="micromolar" public_interface="in" name="Ca"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="J_SERCA_eq">
<eq/>
<ci> J_SERCA </ci>
<apply>
<times/>
<ci> kSERCA </ci>
<ci> Ca </ci>
</apply>
</apply>
</math>
</component>
<component name="ER_calcium_concentration">
<variable units="micromolar" public_interface="out" name="Ca_er"/>
<variable units="dimensionless" name="fer" initial_value="0.01"/>
<variable units="dimensionless" name="Vcyt_Ver" initial_value="31.0"/>
<variable units="flux" public_interface="in" name="Jer"/>
<variable units="millisecond" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="Ca_er_diff_eq">
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<apply>
<diff/>
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<ci> time </ci>
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<ci> Ca_er </ci>
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<ci> fer </ci>
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<ci> Vcyt_Ver </ci>
<ci> Jer </ci>
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</component>
<component name="glycolysis">
<variable units="micromolar" public_interface="out" name="G6P"/>
<variable units="micromolar" public_interface="out" name="FBP"/>
<variable units="micromolar" public_interface="out" name="F6P"/>
<variable units="flux" public_interface="out" name="R_GPDH"/>
<variable units="flux" public_interface="out" name="R_PFK"/>
<variable units="dimensionless" name="lamda1" initial_value="0.06"/>
<variable units="flux" name="Vmax" initial_value="1.0"/>
<variable units="dimensionless" name="alpha" initial_value="1.0"/>
<variable units="dimensionless" name="beta" initial_value="1.0"/>
<variable units="dimensionless" name="gamma" initial_value="1.0"/>
<variable units="dimensionless" name="delta" initial_value="0.0"/>
<variable units="dimensionless" name="epsilon" initial_value="0.0"/>
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<variable units="dimensionless" name="fraction_state"/>
<variable units="dimensionless" name="W00000"/>
<variable units="dimensionless" name="W11100"/>
<variable units="dimensionless" name="f13" initial_value="0.02"/>
<variable units="dimensionless" name="f23" initial_value="0.2"/>
<variable units="dimensionless" name="f41" initial_value="20.0"/>
<variable units="dimensionless" name="f42" initial_value="20.0"/>
<variable units="dimensionless" name="f43" initial_value="20.0"/>
<variable units="dimensionless" name="f53" initial_value="20.0"/>
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<variable units="micromolar" name="K2" initial_value="1.0"/>
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<variable units="micromolar" name="K5" initial_value="1000.0"/>
<variable units="dimensionless" name="lamda" initial_value="0.005"/>
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<variable units="micromolar" public_interface="in" name="ATP"/>
<variable units="millisecond" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
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<ci> time </ci>
</bvar>
<ci> G6P </ci>
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<apply>
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<ci> lamda </ci>
<apply>
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<ci> R_GK </ci>
<ci> R_PFK </ci>
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<apply id="FBP_diff_eq">
<eq/>
<apply>
<diff/>
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</bvar>
<ci> FBP </ci>
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<apply>
<times/>
<ci> lamda </ci>
<apply>
<minus/>
<ci> R_PFK </ci>
<apply>
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<cn cellml:units="dimensionless"> 0.5 </cn>
<ci> R_GPDH </ci>
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</apply>
</apply>
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<ci> F6P </ci>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.3 </cn>
<ci> G6P </ci>
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<apply id="R_GPDH_eq">
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<ci> R_GPDH </ci>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.2 </cn>
<apply>
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<ci> FBP </ci>
<cn cellml:units="micromolar"> 1.0 </cn>
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<cn cellml:units="dimensionless"> 0.5 </cn>
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<ci> lamda1 </ci>
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<times/>
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<ci> fraction_state </ci>
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<ci> W11100 </ci>
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</apply>
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Bertram et al.'s 2004 mathematical model of calcium and glycolysis mediated bursting modes in pancreatic islets.
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<dcterms:W3CDTF>2004-09</dcterms:W3CDTF>
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<dc:title>Biophysical Journal</dc:title>
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<vCard:Orgname>The University of Auckland</vCard:Orgname>
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<vCard:Given>James</vCard:Given>
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<dcterms:W3CDTF>2009-05-25T16:00:20+12:00</dcterms:W3CDTF>
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