- Author:
- Hanne <Hanne@hanne-nielsens-macbook.local>
- Date:
- 2010-05-25 11:00:42+12:00
- Desc:
- Added images in ai and png format
- Permanent Source URI:
- http://models.cellml.org/workspace/bertram_satin_pedersen_luciani_sherman_2007/rawfile/f76686b32d7c35aa0cb717b037a175151a0b2e0d/bertram_satin_pedersen_luciani_sherman_2007.cellml
<?xml version='1.0' encoding='utf-8'?>
<!-- FILE : bertram_model_2007.xml
CREATED : 8th August 2007
LAST MODIFIED : 8th August 2007
AUTHOR : Catherine Lloyd
Bioengineering Institute
The University of Auckland
MODEL STATUS : This model conforms to the CellML 1.1 Specification.
DESCRIPTION : This file contains a CellML description of Bertram et al.'s 2007 mathematical model of the interaction between glycolysis and mitochondrial respiration in metabolic oscillations of 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_model_2007" name="bertram_model_2007_version01">
<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
<articleinfo>
<title>Interaction of glycolysis and mitochondrial respiration in metabolic oscillations of 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 CellML model has been coded by translating the authors original XPPAUT.ode file, which can be found at http://www.math.fsu.edu/~bertram/software/islet/BJ_07/mitophan.ode. The model runs in PCEnv in COR and is able to produce the published results. The parameters have been chosen to recreate the bursting behaviour seen in figures 3 and 4 of the original paper. Some equations have inconsistent magnitudes due to the fact that some units are defined in milliseconds whereas others are defined in seconds.</para>
</section>
<sect1 id="sec_structure">
<title>Model Structure</title>
<para>Glucose metabolism plays a key signalling role in insulin-secreting pancreatic beta cells. In addition to generating ATP - the ubiquitous form of energy used to fuel many cellular processes - glucose metabolism in pancreatic beta cells is also the means by which blood glucose levels are monitored, ensuring an appropriate level of insulin secretion. ATP-sensitive potassium channels in the plasma membrane are activated by ADP and are inactivated by ATP, therefore a high ATP/ADP ratio results in a reduced number of open, ATP-sensitive, potassium channels. In turn, this results in membrane depolarisation and voltage-sensitive calcium channels open. The resulting influx of calcium ions into the cell cytosol induces insulin secretion, which in a healthy individual typically occurs in oscillatory waves. These can be fast with an oscillatory period of less than a minute, or slow with a duration of 2 to 7 minutes, or they can be a combination of fast and slow waves. This oscillatory pattern of insulin secretion appears to have a physiological function which is of particular interest since it is lost in patients with type II diabetes.</para>
<para>
Although the definitive mechanisms underlying these insulin oscillations are unknown, in the paper described here, Richard Bertram <emphasis>et al.</emphasis> suggest that calcium feedback onto ATP production or consumption is responsible for the fast component of the insulin oscillations, while oscillations in the glycolytic pathway are responsible for the slow component. Furthermore, they build these phenomena into a mathematical model that combines a model of mitochondrial metabolism with models of glycolytic oscillations, plasma membrane electrical activity, and calcium handling in the cytosol and endoplasmic reticulum (summarised in the figure below).</para>
<informalfigure float="0" id="fig_reaction_diagram">
<mediaobject>
<imageobject>
<objectinfo>
<title>model diagram</title>
</objectinfo>
<imagedata fileref="bertram_2007.png"/>
</imageobject>
</mediaobject>
<caption>Schematic diagram of the model components and the variables which are exchanged between the components.</caption>
</informalfigure>
<para>The original paper reference is cited below:</para>
<para>
Interaction of glycolysis and mitochondrial respiration in metabolic oscillations of pancreatic islets, Richard Bertram, Leslie S. Satin, Morten Gram Pedersen, Dan S. Luciani, and Arthur Sherman, 2007, <emphasis>Biophysical Journal</emphasis>, 92, 1544-1555. <ulink url="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=pubmed&cmd=Retrieve&dopt=AbstractPlus&list_uids=17172305&query_hl=1&itool=pubmed_docsum">PubMed ID: 17172305</ulink></para>
<para>
The authors highlight that the original model code can be downloaded <ulink url="http://www.math.fsu.edu/~bertram/software/islet/BJ_07/mitophan.ode">here</ulink>.</para>
</sect1>
</article>
</documentation>
<units name="minute">
<unit units="second" multiplier="60.0"/>
</units>
<units name="millisecond">
<unit units="second" prefix="milli"/>
</units>
<units name="millivolt">
<unit units="volt" prefix="milli"/>
</units>
<units name="per_millivolt">
<unit units="millivolt" exponent="-1"/>
</units>
<units name="femtofarad">
<unit units="farad" prefix="femto"/>
</units>
<units name="picosiemens">
<unit units="siemens" prefix="pico"/>
</units>
<units name="femtoampere">
<unit units="ampere" prefix="femto"/>
</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="per_micromolar">
<unit units="micromolar" exponent="-1"/>
</units>
<units name="millimolar_millisecond">
<unit units="millimolar"/>
<unit units="millisecond" exponent="-1"/>
</units>
<units name="micromolar_millisecond_millivolt">
<unit units="micromolar"/>
<unit units="millisecond" exponent="-1"/>
<unit units="millivolt" exponent="-1"/>
</units>
<units name="per_micromolar_millisecond_millivolt">
<unit units="micromolar" exponent="-1"/>
<unit units="millisecond" exponent="-1"/>
<unit units="millivolt" exponent="-1"/>
</units>
<units name="micromolar_millisecond">
<unit units="micromolar"/>
<unit units="millisecond" exponent="-1"/>
</units>
<units name="micromolar_second">
<unit units="micromolar"/>
<unit units="second" exponent="-1"/>
</units>
<units name="micromolar_millisecond_femtoampere">
<unit units="micromolar"/>
<unit units="millisecond" exponent="-1"/>
<unit units="ampere" prefix="pico" exponent="-1"/>
</units>
<units name="micromolar_millivolt">
<unit units="micromolar"/>
<unit units="millivolt" exponent="-1"/>
</units>
<units name="first_order_rate_constant">
<unit units="millisecond" exponent="-1"/>
</units>
<units name="second_order_rate_constant">
<unit units="micromolar" exponent="-1"/>
<unit units="millisecond" exponent="-1"/>
</units>
<component name="environment">
<variable units="millisecond" public_interface="out" name="time"/>
</component>
<!-- Cell model -->
<component name="membrane">
<variable units="millivolt" public_interface="out" name="Vm" initial_value="-60.0"/>
<variable units="femtofarad" name="cm" initial_value="5300.0"/>
<variable units="femtoampere" public_interface="in" name="Ica"/>
<variable units="femtoampere" public_interface="in" name="Ik"/>
<variable units="femtoampere" public_interface="in" name="Ikca"/>
<variable units="femtoampere" public_interface="in" name="Ikatp"/>
<variable units="millisecond" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci> Vm </ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<plus/>
<ci> Ik </ci>
<ci> Ica </ci>
<ci> Ikca </ci>
<ci> Ikatp </ci>
</apply>
</apply>
<ci> cm </ci>
</apply>
</apply>
</math>
</component>
<component name="Ik" cmeta:id="Ik">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="Ik">
<dc:title>Ik</dc:title>
<dcterms:alternative>voltage-dependent potassium current</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="femtoampere" public_interface="out" name="Ik"/>
<variable units="picosiemens" name="gK" initial_value="2700.0"/>
<variable units="millisecond" public_interface="in" private_interface="out" name="time"/>
<variable units="millivolt" public_interface="in" name="VK"/>
<variable units="millivolt" public_interface="in" private_interface="out" name="Vm"/>
<variable units="dimensionless" private_interface="in" name="n"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci> Ik </ci>
<apply>
<times/>
<ci> gK </ci>
<ci> n </ci>
<apply>
<minus/>
<ci> Vm </ci>
<ci> VK </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="n" cmeta:id="n">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="n">
<dc:title>n</dc:title>
<dcterms:alternative>voltage-dependent potassium current n gate</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="dimensionless" public_interface="out" name="n" initial_value="0.0"/>
<variable units="dimensionless" name="n_infinity"/>
<variable units="millisecond" name="tau_n" initial_value="20.0"/>
<variable units="millivolt" name="vn" initial_value="-16.0"/>
<variable units="millivolt" name="sn" initial_value="5.0"/>
<variable units="millisecond" public_interface="in" name="time"/>
<variable units="millivolt" public_interface="in" name="Vm"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<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>
<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/>
<ci> vn </ci>
<ci> Vm </ci>
</apply>
<ci> sn </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="Ica" cmeta:id="Ica">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="Ica">
<dc:title>Ica</dc:title>
<dcterms:alternative>voltage-dependent calcium current</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="femtoampere" public_interface="out" name="Ica"/>
<variable units="picosiemens" name="gCa" initial_value="1000.0"/>
<variable units="millisecond" public_interface="in" name="time"/>
<variable units="millivolt" public_interface="in" name="VCa"/>
<variable units="millivolt" public_interface="in" private_interface="out" name="Vm"/>
<variable units="dimensionless" private_interface="in" name="m_infinity"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci> Ica </ci>
<apply>
<times/>
<ci> gCa </ci>
<ci> m_infinity </ci>
<apply>
<minus/>
<ci> Vm </ci>
<ci> VCa </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="m" cmeta:id="m">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="m">
<dc:title>m</dc:title>
<dcterms:alternative>voltage-dependent calcium current m gate</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="dimensionless" public_interface="out" name="m_infinity"/>
<variable units="millivolt" name="v" initial_value="-20.0"/>
<variable units="millivolt" name="sm" initial_value="12.0"/>
<variable units="millivolt" public_interface="in" name="Vm"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<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/>
<ci> v </ci>
<ci> Vm </ci>
</apply>
<ci> sm </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="Ikca" cmeta:id="Ikca">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="Ikca">
<dc:title>Ikca</dc:title>
<dcterms:alternative>calcium-activated potassium current</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="femtoampere" public_interface="out" name="Ikca"/>
<variable units="picosiemens" name="gkCa" initial_value="300.0"/>
<variable units="micromolar" name="kd" initial_value="0.5"/>
<variable units="millisecond" public_interface="in" name="time"/>
<variable units="millivolt" public_interface="in" name="VK"/>
<variable units="micromolar" public_interface="in" name="c"/>
<variable units="millivolt" public_interface="in" name="Vm"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci> Ikca </ci>
<apply>
<times/>
<apply>
<divide/>
<ci> gkCa </ci>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<power/>
<apply>
<divide/>
<ci> kd </ci>
<ci> c </ci>
</apply>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
</apply>
</apply>
<apply>
<minus/>
<ci> Vm </ci>
<ci> VK </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="Ikatp" cmeta:id="Ikatp">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="Ikatp">
<dc:title>Ikatp</dc:title>
<dcterms:alternative>ATP-sensitive potassium current</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="femtoampere" public_interface="out" name="Ikatp"/>
<variable units="picosiemens" name="gkATP_" initial_value="16000.0"/>
<variable units="dimensionless" name="katpo"/>
<variable units="dimensionless" name="topo"/>
<variable units="dimensionless" name="bottomo"/>
<variable units="micromolar" name="mgadp"/>
<variable units="micromolar" name="adp3m"/>
<variable units="micromolar" name="atp4m"/>
<variable units="millisecond" public_interface="in" name="time"/>
<variable units="millivolt" public_interface="in" name="VK"/>
<variable units="micromolar" public_interface="in" name="atp"/>
<variable units="micromolar" public_interface="in" name="adp"/>
<variable units="millivolt" public_interface="in" name="Vm"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci> Ikatp </ci>
<apply>
<times/>
<ci> gkATP_ </ci>
<ci> katpo </ci>
<apply>
<minus/>
<ci> Vm </ci>
<ci> VK </ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci> katpo </ci>
<apply>
<divide/>
<ci>topo</ci>
<ci>bottomo</ci>
</apply>
</apply>
<apply>
<eq/>
<ci> topo </ci>
<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>
<apply>
<eq/>
<ci> bottomo </ci>
<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> adp3m </ci>
<cn cellml:units="micromolar"> 26.0 </cn>
</apply>
<apply>
<divide/>
<ci> atp4m </ci>
<cn cellml:units="micromolar"> 1.0 </cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci> mgadp </ci>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.165 </cn>
<ci> adp </ci>
</apply>
</apply>
<apply>
<eq/>
<ci> adp3m </ci>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.135 </cn>
<ci> adp </ci>
</apply>
</apply>
<apply>
<eq/>
<ci> atp4m </ci>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.05 </cn>
<ci> atp </ci>
</apply>
</apply>
</math>
</component>
<!-- The glycolytic model -->
<component name="JGPDH" cmeta:id="JGPDH">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="JGPDH">
<dc:title>JGPDH</dc:title>
<dcterms:alternative>rate of the glyceride 3-P dehydrogenase reaction</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="micromolar_millisecond" public_interface="out" name="JGPDH"/>
<variable units="micromolar_millisecond" name="kGPDH" initial_value="0.0005"/>
<variable units="micromolar" public_interface="in" name="FBP"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci> JGPDH </ci>
<apply>
<times/>
<ci> kGPDH </ci>
<apply>
<root/>
<apply>
<abs/>
<apply>
<divide/>
<ci> FBP </ci>
<cn cellml:units="micromolar">1</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="G6P" cmeta:id="G6P">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="G6P">
<dc:title>G6P</dc:title>
<dcterms:alternative>glucose 6-phosphate</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="micromolar" public_interface="out" name="G6P" initial_value="301.0"/>
<variable units="micromolar_millisecond" public_interface="in" name="JGK_ms"/>
<variable units="micromolar_millisecond" public_interface="in" name="JPFK_ms"/>
<variable units="millisecond" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci> G6P </ci>
</apply>
<apply>
<minus/>
<ci> JGK_ms </ci>
<ci> JPFK_ms </ci>
</apply>
</apply>
</math>
</component>
<component name="FBP" cmeta:id="FBP">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="FBP">
<dc:title>FBP</dc:title>
<dcterms:alternative>fructose 1-6-bisphosphate</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="micromolar" public_interface="out" name="FBP" initial_value="2.16"/>
<variable units="micromolar_millisecond" public_interface="in" name="JPFK_ms"/>
<variable units="micromolar_millisecond" public_interface="in" name="JGPDH"/>
<variable units="millisecond" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci> FBP </ci>
</apply>
<apply>
<minus/>
<ci> JPFK_ms </ci>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.5 </cn>
<ci> JGPDH </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="F6P" cmeta:id="F6P">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="F6P">
<dc:title>F6P</dc:title>
<dcterms:alternative>fructose 6-phosphate</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="micromolar" public_interface="out" name="F6P"/>
<variable units="micromolar" public_interface="in" name="G6P"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci> F6P </ci>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.3 </cn>
<ci> G6P </ci>
</apply>
</apply>
</math>
</component>
<component name="JPFK" cmeta:id="JPFK">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="JPFK">
<dc:title>JPFK</dc:title>
<dcterms:alternative>rate of the phosphofructokinase reaction</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="micromolar_second" public_interface="out" name="JPFK"/>
<variable units="micromolar_millisecond" public_interface="out" name="JPFK_ms"/>
<variable units="dimensionless" name="bottom1" initial_value="1"/>
<variable units="dimensionless" name="topa1" initial_value="0"/>
<variable units="micromolar" name="k1" initial_value="30"/>
<variable units="micromolar" name="k2" initial_value="1"/>
<variable units="micromolar" name="k3" initial_value="50000"/>
<variable units="micromolar" name="k4" initial_value="1000"/>
<variable units="micromolar_millisecond" name="VmaxPFK" initial_value="5.0"/>
<variable units="micromolar" public_interface="in" name="atp"/>
<variable units="dimensionless" name="weight2"/>
<variable units="dimensionless" name="topa2"/>
<variable units="dimensionless" name="bottom2"/>
<variable units="micromolar" public_interface="in" name="F6P"/>
<variable units="dimensionless" name="topa3"/>
<variable units="dimensionless" name="weight3"/>
<variable units="dimensionless" name="bottom3"/>
<variable units="dimensionless" name="f13" initial_value="0.02"/>
<variable units="dimensionless" name="f43" initial_value="20"/>
<variable units="dimensionless" name="f23" initial_value="0.2"/>
<variable units="dimensionless" name="f42" initial_value="20"/>
<variable units="dimensionless" name="f41" initial_value="20"/>
<variable units="dimensionless" name="weight4"/>
<variable units="dimensionless" name="topa4"/>
<variable units="dimensionless" name="bottom4"/>
<variable units="dimensionless" name="weight5"/>
<variable units="dimensionless" name="topa5"/>
<variable units="dimensionless" name="bottom5"/>
<variable units="dimensionless" name="weight6"/>
<variable units="dimensionless" name="topa6"/>
<variable units="dimensionless" name="bottom6"/>
<variable units="dimensionless" name="weight7"/>
<variable units="dimensionless" name="topa7"/>
<variable units="dimensionless" name="bottom7"/>
<variable units="dimensionless" name="weight8"/>
<variable units="dimensionless" name="topa8"/>
<variable units="dimensionless" name="bottom8"/>
<variable units="dimensionless" name="weight9"/>
<variable units="dimensionless" name="topa9"/>
<variable units="dimensionless" name="bottom9"/>
<variable units="dimensionless" name="weight10"/>
<variable units="dimensionless" name="topa10"/>
<variable units="dimensionless" name="bottom10"/>
<variable units="dimensionless" name="weight11"/>
<variable units="dimensionless" name="topa11"/>
<variable units="dimensionless" name="bottom11"/>
<variable units="dimensionless" name="weight12"/>
<variable units="dimensionless" name="topa12"/>
<variable units="dimensionless" name="bottom12"/>
<variable units="dimensionless" name="weight13"/>
<variable units="dimensionless" name="topa13"/>
<variable units="dimensionless" name="bottom13"/>
<variable units="dimensionless" name="weight14"/>
<variable units="dimensionless" name="topa14"/>
<variable units="dimensionless" name="bottom14"/>
<variable units="dimensionless" name="weight15"/>
<variable units="dimensionless" name="topa15"/>
<variable units="dimensionless" name="bottom15"/>
<variable units="dimensionless" name="weight16"/>
<variable units="dimensionless" name="topa16"/>
<variable units="dimensionless" name="bottom16"/>
<variable units="dimensionless" name="topb"/>
<variable units="micromolar" public_interface="in" name="FBP"/>
<variable units="micromolar" public_interface="in" name="AMP"/>
<variable units="dimensionless" name="lambda" initial_value="0.06"/>
<variable units="dimensionless" public_interface="in" name="kappa"/>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="pfk">
<apply>
<eq/>
<ci> JPFK_ms </ci>
<apply>
<times/>
<ci> kappa </ci>
<ci> JPFK </ci>
</apply>
</apply>
<apply>
<eq/>
<ci> JPFK </ci>
<apply>
<divide/>
<apply>
<plus/>
<apply>
<times/>
<ci>lambda</ci>
<ci>VmaxPFK</ci>
<ci>topa16</ci>
</apply>
<apply>
<times/>
<ci>VmaxPFK</ci>
<ci>topb</ci>
</apply>
</apply>
<ci>bottom16</ci>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="0001">
<apply>
<eq/>
<ci>weight2</ci>
<apply>
<divide/>
<apply>
<power/>
<ci>atp</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<apply>
<times/>
<ci>k4</ci>
<cn cellml:units="micromolar">1</cn>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>topa2</ci>
<ci>topa1</ci>
</apply>
<apply>
<eq/>
<ci>bottom2</ci>
<apply>
<plus/>
<ci>bottom1</ci>
<ci>weight2</ci>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="0010">
<apply>
<eq/>
<ci>weight3</ci>
<apply>
<divide/>
<apply>
<power/>
<ci>F6P</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<apply>
<times/>
<ci>k3</ci>
<cn cellml:units="micromolar">1</cn>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>topa3</ci>
<apply>
<plus/>
<ci>topa2</ci>
<ci>weight3</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>bottom3</ci>
<apply>
<plus/>
<ci>bottom2</ci>
<ci>weight3</ci>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="0011">
<apply>
<eq/>
<ci>weight4</ci>
<apply>
<divide/>
<apply>
<power/>
<apply>
<times/>
<ci>F6P</ci>
<ci>atp</ci>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
<apply>
<times/>
<ci>f43</ci>
<ci>k3</ci>
<ci>k4</ci>
<apply>
<power/>
<cn cellml:units="micromolar">1</cn>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>topa4</ci>
<apply>
<plus/>
<ci>topa3</ci>
<ci>weight4</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>bottom4</ci>
<apply>
<plus/>
<ci>bottom3</ci>
<ci>weight4</ci>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="0100">
<apply>
<eq/>
<ci>weight5</ci>
<apply>
<divide/>
<ci>FBP</ci>
<ci>k2</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>topa5</ci>
<ci>topa4</ci>
</apply>
<apply>
<eq/>
<ci>bottom5</ci>
<apply>
<plus/>
<ci>bottom4</ci>
<ci>weight5</ci>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="0101">
<apply>
<eq/>
<ci>weight6</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>FBP</ci>
<apply>
<power/>
<ci>atp</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
<apply>
<times/>
<ci>k2</ci>
<ci>k4</ci>
<ci>f42</ci>
<cn cellml:units="micromolar">1</cn>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>topa6</ci>
<ci>topa5</ci>
</apply>
<apply>
<eq/>
<ci>bottom6</ci>
<apply>
<plus/>
<ci>bottom5</ci>
<ci>weight6</ci>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="0110">
<apply>
<eq/>
<ci>weight7</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>FBP</ci>
<apply>
<power/>
<ci>F6P</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
<apply>
<times/>
<ci>k2</ci>
<ci>k3</ci>
<ci>f23</ci>
<cn cellml:units="micromolar">1</cn>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>topa7</ci>
<apply>
<plus/>
<ci>topa6</ci>
<ci>weight7</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>bottom7</ci>
<apply>
<plus/>
<ci>bottom6</ci>
<ci>weight7</ci>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="0111">
<apply>
<eq/>
<ci>weight8</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>FBP</ci>
<apply>
<power/>
<ci>F6P</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<apply>
<power/>
<ci>atp</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
<apply>
<times/>
<ci>k2</ci>
<ci>k3</ci>
<ci>k4</ci>
<ci>f23</ci>
<ci>f42</ci>
<ci>f43</ci>
<apply>
<power/>
<cn cellml:units="micromolar">1</cn>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>topa8</ci>
<apply>
<plus/>
<ci>topa7</ci>
<ci>weight8</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>bottom8</ci>
<apply>
<plus/>
<ci>bottom7</ci>
<ci>weight8</ci>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="1000">
<apply>
<eq/>
<ci>weight9</ci>
<apply>
<divide/>
<ci>AMP</ci>
<ci>k1</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>topa9</ci>
<ci>topa8</ci>
</apply>
<apply>
<eq/>
<ci>bottom9</ci>
<apply>
<plus/>
<ci>bottom8</ci>
<ci>weight9</ci>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="1001">
<apply>
<eq/>
<ci>weight10</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>AMP</ci>
<apply>
<power/>
<ci>atp</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
<apply>
<times/>
<ci>k1</ci>
<ci>k4</ci>
<ci>f41</ci>
<cn cellml:units="micromolar">1</cn>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>topa10</ci>
<ci>topa9</ci>
</apply>
<apply>
<eq/>
<ci>bottom10</ci>
<apply>
<plus/>
<ci>bottom9</ci>
<ci>weight10</ci>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="1010">
<apply>
<eq/>
<ci>weight11</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>AMP</ci>
<apply>
<power/>
<ci>F6P</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
<apply>
<times/>
<ci>k1</ci>
<ci>k3</ci>
<ci>f13</ci>
<cn cellml:units="micromolar">1</cn>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>topa11</ci>
<apply>
<plus/>
<ci>topa10</ci>
<ci>weight11</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>bottom11</ci>
<apply>
<plus/>
<ci>bottom10</ci>
<ci>weight11</ci>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="1011">
<apply>
<eq/>
<ci>weight12</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>AMP</ci>
<apply>
<power/>
<ci>F6P</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<apply>
<power/>
<ci>atp</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
<apply>
<times/>
<ci>k1</ci>
<ci>k3</ci>
<ci>k4</ci>
<ci>f13</ci>
<ci>f41</ci>
<ci>f43</ci>
<apply>
<power/>
<cn cellml:units="micromolar">1</cn>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>topa12</ci>
<apply>
<plus/>
<ci>topa11</ci>
<ci>weight12</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>bottom12</ci>
<apply>
<plus/>
<ci>bottom11</ci>
<ci>weight12</ci>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="1100">
<apply>
<eq/>
<ci>weight13</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>AMP</ci>
<ci>FBP</ci>
</apply>
<apply>
<times/>
<ci>k1</ci>
<ci>k2</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>topa13</ci>
<ci>topa12</ci>
</apply>
<apply>
<eq/>
<ci>bottom13</ci>
<apply>
<plus/>
<ci>bottom12</ci>
<ci>weight13</ci>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="1101">
<apply>
<eq/>
<ci>weight14</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>AMP</ci>
<ci>FBP</ci>
<apply>
<power/>
<ci>atp</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
<apply>
<times/>
<ci>k1</ci>
<ci>k2</ci>
<ci>k4</ci>
<ci>f42</ci>
<ci>f41</ci>
<cn cellml:units="micromolar">1</cn>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>topa14</ci>
<ci>topa13</ci>
</apply>
<apply>
<eq/>
<ci>bottom14</ci>
<apply>
<plus/>
<ci>bottom13</ci>
<ci>weight14</ci>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="1110">
<apply>
<eq/>
<ci>weight15</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>AMP</ci>
<ci>FBP</ci>
<apply>
<power/>
<ci>F6P</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
<apply>
<times/>
<ci>k1</ci>
<ci>k2</ci>
<ci>k3</ci>
<ci>f23</ci>
<ci>f13</ci>
<cn cellml:units="micromolar">1</cn>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>topa15</ci>
<ci>topa14</ci>
</apply>
<apply>
<eq/>
<ci>bottom15</ci>
<apply>
<plus/>
<ci>bottom14</ci>
<ci>weight15</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>topb</ci>
<ci>weight15</ci>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="1111">
<apply>
<eq/>
<ci>weight16</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>AMP</ci>
<ci>FBP</ci>
<apply>
<power/>
<ci>F6P</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<apply>
<power/>
<ci>atp</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
<apply>
<times/>
<ci>k1</ci>
<ci>k2</ci>
<ci>k3</ci>
<ci>k4</ci>
<ci>f23</ci>
<ci>f13</ci>
<ci>f42</ci>
<ci>f41</ci>
<ci>f43</ci>
<apply>
<power/>
<cn cellml:units="micromolar">1</cn>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>topa16</ci>
<apply>
<plus/>
<ci>topa15</ci>
<ci>weight16</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>bottom16</ci>
<apply>
<plus/>
<ci>bottom15</ci>
<ci>weight16</ci>
</apply>
</apply>
</math>
</component>
<!-- Mitochondrial model -->
<component name="JPDH" cmeta:id="JPDH">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="JPDH">
<dc:title>JPDH</dc:title>
<dcterms:alternative>rate of the pyruvate dehydrogenase reaction</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="micromolar_millisecond" public_interface="out" name="JPDH"/>
<variable units="dimensionless" name="p1" initial_value="400.0"/>
<variable units="dimensionless" name="p2" initial_value="1.0"/>
<variable units="micromolar" name="p3" initial_value="0.01"/>
<variable units="micromolar_millisecond" name="JGPDHbas" initial_value="0.0005"/>
<variable units="millimolar" public_interface="in" name="NADm"/>
<variable units="micromolar" public_interface="in" name="Cam"/>
<variable units="millimolar" public_interface="in" name="NADHm"/>
<variable units="micromolar_millisecond" public_interface="in" name="JGPDH"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci> JPDH </ci>
<apply>
<times/>
<apply>
<divide/>
<ci> p1 </ci>
<apply>
<plus/>
<ci> p2 </ci>
<apply>
<divide/>
<ci> NADHm </ci>
<ci> NADm </ci>
</apply>
</apply>
</apply>
<apply>
<divide/>
<ci> Cam </ci>
<apply>
<plus/>
<ci> p3 </ci>
<ci> Cam </ci>
</apply>
</apply>
<apply>
<plus/>
<ci> JGPDH </ci>
<ci> JGPDHbas </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="NADHm" cmeta:id="NADHm">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="NADHm">
<dc:title>NADHm</dc:title>
<dcterms:alternative>mitochondrial NADH</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="millimolar" public_interface="out" name="NADHm" initial_value="0.4"/>
<variable units="dimensionless" public_interface="in" name="gamma"/>
<variable units="micromolar_millisecond" public_interface="in" name="JPDH"/>
<variable units="micromolar_millisecond" public_interface="in" name="JO"/>
<variable units="millisecond" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci> NADHm </ci>
</apply>
<apply>
<times/>
<ci> gamma </ci>
<apply>
<minus/>
<ci> JPDH </ci>
<ci> JO </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="JO" cmeta:id="JO">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="JO">
<dc:title>JO</dc:title>
<dcterms:alternative>rate of oxygen consumption at the final stage of the electron transport chain</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="micromolar_millisecond" public_interface="out" name="JO"/>
<variable units="micromolar_millisecond" name="p4" initial_value="0.6"/>
<variable units="millimolar" name="p5" initial_value="0.1"/>
<variable units="millivolt" name="p6" initial_value="177.0"/>
<variable units="millivolt" name="p7" initial_value="5.0"/>
<variable units="millimolar" public_interface="in" name="NADHm"/>
<variable units="millivolt" public_interface="in" name="delta_psi"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci> JO </ci>
<apply>
<divide/>
<apply>
<times/>
<ci> p4 </ci>
<apply>
<divide/>
<ci> NADHm </ci>
<apply>
<plus/>
<ci> p5 </ci>
<ci> NADHm </ci>
</apply>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<ci> delta_psi </ci>
<ci> p6 </ci>
</apply>
<ci> p7 </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="NADm" cmeta:id="NADm">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="NADm">
<dc:title>NADm</dc:title>
<dcterms:alternative>mitochondrial NAD</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="millimolar" public_interface="out" name="NADm"/>
<variable units="millimolar" name="NADmtot" initial_value="10.0"/>
<variable units="millimolar" public_interface="in" name="NADHm"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci> NADm </ci>
<apply>
<minus/>
<ci> NADmtot </ci>
<ci> NADHm </ci>
</apply>
</apply>
</math>
</component>
<component name="delta_psi" cmeta:id="delta_psi">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="delta_psi">
<dc:title>delta_psi</dc:title>
<dcterms:alternative>mitochondrial inner membrane potential</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="millivolt" public_interface="out" name="delta_psi" initial_value="164.0"/>
<variable units="micromolar_millivolt" name="Cmito" initial_value="1.8"/>
<variable units="micromolar_millisecond" public_interface="in" name="JHres"/>
<variable units="micromolar_millisecond" public_interface="in" name="JHatp"/>
<variable units="micromolar_millisecond" public_interface="in" name="JANT"/>
<variable units="micromolar_millisecond" public_interface="in" name="JHleak"/>
<variable units="micromolar_millisecond" public_interface="in" name="JNaCa"/>
<variable units="micromolar_millisecond" public_interface="in" name="Juni"/>
<variable units="millisecond" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci> delta_psi </ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci> JHres </ci>
<apply>
<plus/>
<ci> JHatp </ci>
<ci> JANT </ci>
<ci> JHleak </ci>
<ci> JNaCa </ci>
<apply>
<times/>
<cn cellml:units="dimensionless"> 2.0 </cn>
<ci> Juni </ci>
</apply>
</apply>
</apply>
<ci> Cmito </ci>
</apply>
</apply>
</math>
</component>
<component name="JHres" cmeta:id="JHres">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="JHres">
<dc:title>JHres</dc:title>
<dcterms:alternative>flux through respiration-driven proton pumps</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="micromolar_millisecond" public_interface="out" name="JHres"/>
<variable units="micromolar_millisecond" name="p8" initial_value="7.0"/>
<variable units="millimolar" name="p9" initial_value="0.1"/>
<variable units="millivolt" name="p10" initial_value="177.0"/>
<variable units="millivolt" name="p11" initial_value="5.0"/>
<variable units="millimolar" public_interface="in" name="NADHm"/>
<variable units="millivolt" public_interface="in" name="delta_psi"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci> JHres </ci>
<apply>
<divide/>
<apply>
<times/>
<ci> p8 </ci>
<apply>
<divide/>
<ci> NADHm </ci>
<apply>
<plus/>
<ci> p9 </ci>
<ci> NADHm </ci>
</apply>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<ci> delta_psi </ci>
<ci> p10 </ci>
</apply>
<ci> p11 </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="JF1F0" cmeta:id="JF1F0">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="JF1F0">
<dc:title>JF1F0</dc:title>
<dcterms:alternative>rate of the F1F0 ATP synthase catalysed reaction</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="micromolar_millisecond" public_interface="out" name="JF1F0"/>
<variable units="millimolar" name="p13" initial_value="10.0"/>
<variable units="millivolt" name="p14" initial_value="190.0"/>
<variable units="millivolt" name="p15" initial_value="8.5"/>
<variable units="micromolar_millisecond" name="p16" initial_value="35.0"/>
<variable units="millimolar" public_interface="in" name="ATPm"/>
<variable units="millivolt" public_interface="in" name="delta_psi"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci> JF1F0 </ci>
<apply>
<divide/>
<apply>
<divide/>
<apply>
<times/>
<ci> p16 </ci>
<ci> p13 </ci>
</apply>
<apply>
<plus/>
<ci> p13 </ci>
<ci> ATPm </ci>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<ci> p14 </ci>
<ci> delta_psi </ci>
</apply>
<ci> p15 </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="JHatp" cmeta:id="JHatp">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="JHatp">
<dc:title>JHatp</dc:title>
<dcterms:alternative>rate of ATP-driven proton flux</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="micromolar_millisecond" public_interface="out" name="JHatp"/>
<variable units="micromolar_millisecond" public_interface="in" name="JF1F0"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci> JHatp </ci>
<apply>
<times/>
<cn cellml:units="dimensionless"> 3.0 </cn>
<ci> JF1F0 </ci>
</apply>
</apply>
</math>
</component>
<component name="JGK" cmeta:id="JGK">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="JHatp">
<dc:title>JGK</dc:title>
<dcterms:alternative>rate of the glucokinase reaction</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="micromolar_millisecond" public_interface="out" name="JGK_ms"/>
<variable units="micromolar_second" name="JGK" initial_value="0.4"/>
<variable units="dimensionless" public_interface="in" name="kappa"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci> JGK_ms </ci>
<apply>
<times/>
<ci> kappa </ci>
<ci> JGK </ci>
</apply>
</apply>
</math>
</component>
<component name="JHleak" cmeta:id="JHleak">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="JHleak">
<dc:title>JHleak</dc:title>
<dcterms:alternative>proton leakage into the mitochodria down the proton gradient</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="micromolar_millisecond" public_interface="out" name="JHleak"/>
<variable units="micromolar_millisecond_millivolt" name="p17" initial_value="0.002"/>
<variable units="micromolar_millisecond" name="p18" initial_value="-0.03"/>
<variable units="millivolt" public_interface="in" name="delta_psi"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci> JHleak </ci>
<apply>
<plus/>
<apply>
<times/>
<ci> p17 </ci>
<ci> delta_psi </ci>
</apply>
<ci> p18 </ci>
</apply>
</apply>
</math>
</component>
<component name="JANT" cmeta:id="JANT">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="JANT">
<dc:title>JANT</dc:title>
<dcterms:alternative>rate of ADP and ATP flux through the adenine nucleotide translocator</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="micromolar_millisecond" public_interface="out" name="JANT"/>
<variable units="micromolar_millisecond" name="p19" initial_value="0.35"/>
<variable units="dimensionless" name="p20" initial_value="2.0"/>
<variable units="per_millivolt" name="FRT" initial_value="0.037410133"/>
<variable units="dimensionless" public_interface="in" name="RATm"/>
<variable units="millivolt" public_interface="in" name="delta_psi"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci> JANT </ci>
<apply>
<times/>
<ci> p19 </ci>
<apply>
<divide/>
<apply>
<divide/>
<ci> RATm </ci>
<apply>
<plus/>
<ci> RATm </ci>
<ci> p20 </ci>
</apply>
</apply>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="dimensionless"> -0.5 </cn>
<ci> FRT </ci>
<ci> delta_psi </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="RATm">
<variable units="dimensionless" public_interface="out" name="RATm"/>
<variable units="millimolar" public_interface="in" name="ATPm"/>
<variable units="millimolar" public_interface="in" name="ADPm"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci> RATm </ci>
<apply>
<divide/>
<ci> ATPm </ci>
<ci> ADPm </ci>
</apply>
</apply>
</math>
</component>
<component name="Juni" cmeta:id="Juni">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="Juni">
<dc:title>Juni</dc:title>
<dcterms:alternative>calcium flux into the mitochondria through a calcium uniporter</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="micromolar_millisecond" public_interface="out" name="Juni"/>
<variable units="per_micromolar_millisecond_millivolt" name="p21" initial_value="0.04"/>
<variable units="second_order_rate_constant" name="p22" initial_value="1.1"/>
<variable units="micromolar" public_interface="in" name="c"/>
<variable units="millivolt" public_interface="in" name="delta_psi"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci> Juni </ci>
<apply>
<times/>
<apply>
<minus/>
<apply>
<times/>
<ci> p21 </ci>
<ci> delta_psi </ci>
</apply>
<ci> p22 </ci>
</apply>
<apply>
<power/>
<ci> c </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
</apply>
</apply>
</math>
</component>
<component name="JNaCa" cmeta:id="JNaCa">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="JNaCa">
<dc:title>JNaCa</dc:title>
<dcterms:alternative>calcium flux out of the mitochondria into the cytosol through the sodium-calcium ion exchanger</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="micromolar_millisecond" public_interface="out" name="JNaCa"/>
<variable units="micromolar_millisecond" name="p23" initial_value="0.01"/>
<variable units="per_millivolt" name="p24" initial_value="0.016"/>
<variable units="micromolar" public_interface="in" name="c"/>
<variable units="micromolar" public_interface="in" name="Cam"/>
<variable units="millivolt" public_interface="in" name="delta_psi"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci> JNaCa </ci>
<apply>
<times/>
<apply>
<divide/>
<ci> p23 </ci>
<ci> c </ci>
</apply>
<ci> Cam </ci>
<apply>
<exp/>
<apply>
<times/>
<ci> p24 </ci>
<ci> delta_psi </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="Cam" cmeta:id="Cam">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="Cam">
<dc:title>Cam</dc:title>
<dcterms:alternative>mitochondrial calcium concentration</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="micromolar" public_interface="out" name="Cam" initial_value="0.2"/>
<variable units="dimensionless" name="fmito" initial_value="0.01"/>
<variable units="micromolar_millisecond" public_interface="in" name="Jmito"/>
<variable units="millisecond" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci> Cam </ci>
</apply>
<apply>
<times/>
<apply>
<minus/>
<ci> fmito </ci>
</apply>
<ci> Jmito </ci>
</apply>
</apply>
</math>
</component>
<component name="Jmito">
<variable units="micromolar_millisecond" public_interface="out" name="Jmito"/>
<variable units="micromolar_millisecond" public_interface="in" name="JNaCa"/>
<variable units="micromolar_millisecond" public_interface="in" name="Juni"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci> Jmito </ci>
<apply>
<minus/>
<ci> JNaCa </ci>
<ci> Juni </ci>
</apply>
</apply>
</math>
</component>
<component name="ADPm" cmeta:id="ADPm">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="ADPm">
<dc:title>ADPm</dc:title>
<dcterms:alternative>mitochondrial ADP</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="millimolar" public_interface="out" name="ADPm" initial_value="11.1"/>
<variable units="dimensionless" public_interface="in" name="gamma"/>
<variable units="micromolar_millisecond" public_interface="in" name="JANT"/>
<variable units="micromolar_millisecond" public_interface="in" name="JF1F0"/>
<variable units="millisecond" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci> ADPm </ci>
</apply>
<apply>
<times/>
<ci> gamma </ci>
<apply>
<minus/>
<ci> JANT </ci>
<ci> JF1F0 </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="ATPm" cmeta:id="ATPm">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="ATPm">
<dc:title>ATPm</dc:title>
<dcterms:alternative>mitochondrial ATP</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="millimolar" public_interface="out" name="ATPm"/>
<variable units="millimolar" name="Amtot" initial_value="15.0"/>
<variable units="millimolar" public_interface="in" name="ADPm"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci> ATPm </ci>
<apply>
<minus/>
<ci> Amtot </ci>
<ci> ADPm </ci>
</apply>
</apply>
</math>
</component>
<component name="adp" cmeta:id="adp">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="adp">
<dc:title>adp</dc:title>
<dcterms:alternative>cytosolic ADP concentration</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="micromolar" public_interface="out" name="adp" initial_value="1137.0"/>
<variable units="dimensionless" public_interface="in" name="delta"/>
<variable units="micromolar_millisecond" public_interface="in" name="Jhyd"/>
<variable units="micromolar_millisecond" public_interface="in" name="JANT"/>
<variable units="millisecond" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci> adp </ci>
</apply>
<apply>
<plus/>
<apply>
<times/>
<apply>
<minus/>
<ci> delta </ci>
</apply>
<ci> JANT </ci>
</apply>
<ci> Jhyd </ci>
</apply>
</apply>
</math>
</component>
<component name="Jhyd" cmeta:id="Jhyd">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="Jhyd">
<dc:title>Jhyd</dc:title>
<dcterms:alternative>cytosolic hydrolysis of ATP</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="micromolar_millisecond" public_interface="out" name="Jhyd"/>
<variable units="second_order_rate_constant" name="khyd" initial_value="0.00005"/>
<variable units="first_order_rate_constant" name="khydbas" initial_value="0.00005"/>
<variable units="micromolar" public_interface="in" name="c"/>
<variable units="micromolar" public_interface="in" name="atp"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci> Jhyd </ci>
<apply>
<times/>
<apply>
<plus/>
<apply>
<times/>
<ci> khyd </ci>
<ci> c </ci>
</apply>
<ci> khydbas </ci>
</apply>
<ci> atp </ci>
</apply>
</apply>
</math>
</component>
<component name="atp" cmeta:id="atp">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="atp">
<dc:title>atp</dc:title>
<dcterms:alternative>cytosolic ATP</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="micromolar" public_interface="out" name="atp"/>
<variable units="micromolar" name="atot" initial_value="2500.0"/>
<variable units="micromolar" public_interface="in" name="adp"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci> atp </ci>
<apply>
<minus/>
<ci> atot </ci>
<ci> adp </ci>
</apply>
</apply>
</math>
</component>
<component name="c" cmeta:id="c">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="c">
<dc:title>c</dc:title>
<dcterms:alternative>cytosolic calcium</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="micromolar" public_interface="out" name="c" initial_value="0.17"/>
<variable units="dimensionless" name="fcyt" initial_value="0.01"/>
<variable units="dimensionless" public_interface="in" name="delta"/>
<variable units="micromolar_millisecond" public_interface="in" name="Jer"/>
<variable units="micromolar_millisecond" public_interface="in" name="Jmem"/>
<variable units="micromolar_millisecond" public_interface="in" name="Jmito"/>
<variable units="millisecond" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci> c </ci>
</apply>
<apply>
<times/>
<ci> fcyt </ci>
<apply>
<plus/>
<ci> Jmem </ci>
<ci> Jer </ci>
<apply>
<times/>
<ci> delta </ci>
<ci> Jmito </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="Jmem" cmeta:id="Jmem">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="Jmem">
<dc:title>Jmem</dc:title>
<dcterms:alternative>rate of calcium flux across the plasma membrane</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="micromolar_millisecond" public_interface="out" name="Jmem"/>
<variable units="first_order_rate_constant" name="kPMCA" initial_value="0.1"/>
<variable units="micromolar_millisecond_femtoampere" name="alpha" initial_value="4.5E-6"/>
<variable units="micromolar" name="Cbas" initial_value="0.05"/>
<variable units="micromolar" public_interface="in" name="c"/>
<variable units="femtoampere" public_interface="in" name="Ica"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci> Jmem </ci>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<times/>
<ci> alpha </ci>
<ci> Ica </ci>
</apply>
<apply>
<times/>
<ci> kPMCA </ci>
<apply>
<minus/>
<ci> c </ci>
<ci> Cbas </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="Jleak" cmeta:id="Jleak">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="Jleak">
<dc:title>Jleak</dc:title>
<dcterms:alternative>rate of calcium leakage out of the endoplasmic reticulum</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="micromolar_millisecond" public_interface="out" name="Jleak"/>
<variable units="first_order_rate_constant" name="pleak" initial_value="0.0002"/>
<variable units="micromolar" public_interface="in" name="c"/>
<variable units="micromolar" public_interface="in" name="Caer"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci> Jleak </ci>
<apply>
<times/>
<ci> pleak </ci>
<apply>
<minus/>
<ci> Caer </ci>
<ci> c </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="JSERCA" cmeta:id="JSERCA">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="JSERCA">
<dc:title>JSERCA</dc:title>
<dcterms:alternative>rate of calcium flux into the endoplasmic reticulum through the SERCA pumps</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="micromolar_millisecond" public_interface="out" name="JSERCA"/>
<variable units="first_order_rate_constant" name="kSERCA" initial_value="0.4"/>
<variable units="micromolar" public_interface="in" name="c"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci> JSERCA </ci>
<apply>
<times/>
<ci> kSERCA </ci>
<ci> c </ci>
</apply>
</apply>
</math>
</component>
<component name="Jer" cmeta:id="Jer">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="Jer">
<dc:title>Jer</dc:title>
<dcterms:alternative>rate of calcium flux out of the endoplasmic reticulum</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="micromolar_millisecond" public_interface="out" name="Jer"/>
<variable units="micromolar_millisecond" public_interface="in" name="Jleak"/>
<variable units="micromolar_millisecond" public_interface="in" name="JSERCA"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci> Jer </ci>
<apply>
<minus/>
<ci> Jleak </ci>
<ci> JSERCA </ci>
</apply>
</apply>
</math>
</component>
<component name="Caer" cmeta:id="Caer">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="Caer">
<dc:title>Caer</dc:title>
<dcterms:alternative>calcium</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="micromolar" public_interface="out" name="Caer" initial_value="345.0"/>
<variable units="dimensionless" name="fer" initial_value="0.01"/>
<variable units="dimensionless" name="Vc_Ver" initial_value="31.0"/>
<variable units="micromolar_millisecond" public_interface="in" name="Jer"/>
<variable units="millisecond" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci> Caer </ci>
</apply>
<apply>
<times/>
<apply>
<minus/>
<ci> fer </ci>
</apply>
<ci> Vc_Ver </ci>
<ci> Jer </ci>
</apply>
</apply>
</math>
</component>
<component name="model_parameters">
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<rdf:value>This is a CellML description of Bertram et al.'s 2007 mathematical model of the interaction between glycolysis and mitochondrial respiration in metabolic oscillations of pancreatic islets.</rdf:value>
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<vCard:Given>Morten</vCard:Given>
<vCard:Family>Pedersen</vCard:Family>
<vCard:Other>Gram</vCard:Other>
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<vCard:FN>Catherine Lloyd</vCard:FN>
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<rdf:value>Model has been fixed such that it now recreates the published results. This required a slight deviation from the equations in the published paper and the author's original .ODE code was used instead.</rdf:value>
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<rdf:value>This CellML model has been coded by translating the authors original XPPAUT .ode file, which can be found at http://www.math.fsu.edu/~bertram/software/islet/BJ_07/mitophan.ode . The model runs in PCEnv and is able to produce the published results. The parameters have been chosen to recreate the bursting behaviour seen in figures 3 and 4 of the original paper.</rdf:value>
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<vCard:Given>Arthur</vCard:Given>
<vCard:Family>Sherman</vCard:Family>
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<vCard:Given>Dan</vCard:Given>
<vCard:Family>Luciani</vCard:Family>
<vCard:Other>S</vCard:Other>
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<dc:title> Bertram et al.'s 2007 mathematical model of the interaction between glycolysis and mitochondrial respiration in metabolic oscillations of pancreatic islets. </dc:title>
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<rdf:value>c.lloyd@auckland.ac.nz</rdf:value>
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<vCard:FN>Catherine Lloyd</vCard:FN>
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<dcterms:W3CDTF>2007-11-01T17:17:08+13:00</dcterms:W3CDTF>
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