- Author:
- Erica Prentice <erica.prentice@waikato.ac.nz>
- Date:
- 2020-06-29 13:25:28+12:00
- Desc:
- init commit
- Permanent Source URI:
- https://models.cellml.org/workspace/5fb/rawfile/a2c9be2ef836d59aea1c30c69b172b76a24c8b06/Prentice at al. The Inflection Point Hypothesis.cellml
<?xml version='1.0'?>
<model cmeta:id="prentice_model_2020" name="prentice_model_2020" xmlns="http://www.cellml.org/cellml/1.0#" xmlns:cellml="http://www.cellml.org/cellml/1.0#" xmlns:cmeta="http://www.cellml.org/metadata/1.0#">
<units name="millimolar">
<unit prefix="milli" units="mole"/>
<unit exponent="-1" units="litre"/>
</units>
<units name="minute">
<unit multiplier="60.0" units="second"/>
</units>
<units name="flux">
<unit units="millimolar"/>
<unit exponent="-1" units="minute"/>
</units>
<component name="environment">
<variable name="time" public_interface="out" units="minute"/>
</component>
<component name="GLC">
<variable initial_value="10" name="GLC" public_interface="out" units="millimolar"/>
<variable name="v_GK" public_interface="in" units="flux"/>
<variable name="time" public_interface="in" units="minute"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>GLC</ci>
</apply>
<apply>
<minus/>
<ci>v_GK</ci>
</apply>
</apply>
</math>
</component>
<component name="G6P">
<variable initial_value="0" name="G6P" public_interface="out" units="millimolar"/>
<variable name="v_GK" public_interface="in" units="flux"/>
<variable name="v_PGI" public_interface="in" units="flux"/>
<variable name="time" public_interface="in" units="minute"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>G6P</ci>
</apply>
<apply>
<minus/>
<ci>v_GK</ci>
<ci>v_PGI</ci>
</apply>
</apply>
</math>
</component>
<component name="F6P">
<variable initial_value="0" name="F6P" public_interface="out" units="millimolar"/>
<variable name="v_PGI" public_interface="in" units="flux"/>
<variable name="v_PFK" public_interface="in" units="flux"/>
<variable name="time" public_interface="in" units="minute"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>F6P</ci>
</apply>
<apply>
<minus/>
<ci>v_PGI</ci>
<ci>v_PFK</ci>
</apply>
</apply>
</math>
</component>
<component name="FBP">
<variable initial_value="0" name="FBP" public_interface="out" units="millimolar"/>
<variable name="v_PFK" public_interface="in" units="flux"/>
<variable name="v_FBPA" public_interface="in" units="flux"/>
<variable name="time" public_interface="in" units="minute"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>FBP</ci>
</apply>
<apply>
<minus/>
<ci>v_PFK</ci>
<ci>v_FBPA</ci>
</apply>
</apply>
</math>
</component>
<component name="TRIO">
<variable initial_value="0" name="TRIO" public_interface="out" units="millimolar"/>
<variable name="v_FBPA" public_interface="in" units="flux"/>
<variable name="v_GAPD" public_interface="in" units="flux"/>
<variable name="time" public_interface="in" units="minute"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>TRIO</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<cn cellml:units="dimensionless">2.0</cn>
<ci>v_FBPA</ci>
</apply>
<ci>v_GAPD</ci>
</apply>
</apply>
</math>
</component>
<component name="BPG">
<variable initial_value="0" name="BPG" public_interface="out" units="millimolar"/>
<variable name="v_GAPD" public_interface="in" units="flux"/>
<variable name="time" public_interface="in" units="minute"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>BPG</ci>
</apply>
<ci>v_GAPD</ci>
</apply>
</math>
</component>
<component name="P">
<variable initial_value="100" name="P" public_interface="out" units="millimolar"/>
<variable name="time" public_interface="in" units="minute"/>
<variable name="v_GAPD" public_interface="in" units="flux"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>P</ci>
</apply>
<apply>
<minus/>
<ci>v_GAPD</ci>
</apply>
</apply>
</math>
</component>
<component name="NADH">
<variable initial_value="0" name="NADH" public_interface="out" units="millimolar"/>
<variable name="v_GAPD" public_interface="in" units="flux"/>
<variable name="time" public_interface="in" units="minute"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>NADH</ci>
</apply>
<ci>v_GAPD</ci>
</apply>
</math>
</component>
<component name="NAD">
<variable initial_value="10" name="NAD" public_interface="out" units="millimolar"/>
<variable name="v_GAPD" public_interface="in" units="flux"/>
<variable name="time" public_interface="in" units="minute"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>NAD</ci>
</apply>
<apply>
<minus/>
<ci>v_GAPD</ci>
</apply>
</apply>
</math>
</component>
<component name="DHAP">
<variable name="DHAP" public_interface="out" units="millimolar"/>
<variable initial_value="0.045" name="Keq_TPI" public_interface="out" units="dimensionless"/>
<variable name="TRIO" public_interface="in" units="millimolar"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>DHAP</ci>
<apply>
<divide/>
<ci>TRIO</ci>
<apply>
<plus/>
<cn cellml:units="dimensionless">1.0</cn>
<ci>Keq_TPI</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="GAP">
<variable name="GAP" public_interface="out" units="millimolar"/>
<variable name="Keq_TPI" public_interface="in" units="dimensionless"/>
<variable name="TRIO" public_interface="in" units="millimolar"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>GAP</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>TRIO</ci>
<ci>Keq_TPI</ci>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless">1.0</cn>
<ci>Keq_TPI</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="ADP">
<variable initial_value="0" name="ADP" public_interface="out" units="millimolar"/>
<variable name="v_GK" public_interface="in" units="flux"/>
<variable name="v_PFK" public_interface="in" units="flux"/>
<variable name="time" public_interface="in" units="minute"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>ADP</ci>
</apply>
<apply>
<plus/>
<ci>v_GK</ci>
<ci>v_PFK</ci>
</apply>
</apply>
</math>
</component>
<component name="ATP">
<variable initial_value="7" name="ATP" public_interface="out" units="millimolar"/>
<variable name="v_GK" public_interface="in" units="flux"/>
<variable name="v_PFK" public_interface="in" units="flux"/>
<variable name="time" public_interface="in" units="minute"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>ATP</ci>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<ci>v_GK</ci>
<ci>v_PFK</ci>
</apply>
</apply>
</apply>
</math>
</component>
<!-- define enzyme rates -->
<component name="v_PGI">
<variable name="v_PGI" public_interface="out" units="flux"/>
<variable initial_value="1.4" name="K_m_G6P" units="millimolar"/>
<variable initial_value="50" name="V_max" units="flux"/>
<variable name="G6P" public_interface="in" units="millimolar"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>v_PGI</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>V_max</ci>
<ci>G6P</ci>
</apply>
<apply>
<plus/>
<ci>K_m_G6P</ci>
<ci>G6P</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="v_GK">
<variable name="v_GK" public_interface="out" units="flux"/>
<variable initial_value="0.11" name="Km_GLC" units="millimolar"/>
<variable initial_value="1.7" name="K_hlf_ATP" units="millimolar"/>
<variable initial_value="1.2" name="h_ATP" units="dimensionless"/>
<variable initial_value="0.28" name="v_max" units="flux"/>
<variable name="GLC" public_interface="in" units="millimolar"/>
<variable name="ATP" public_interface="in" units="millimolar"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>v_GK</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>v_max</ci>
<apply>
<power/>
<ci>ATP</ci>
<ci>h_ATP</ci>
</apply>
<ci>GLC</ci>
</apply>
<apply>
<plus/>
<apply>
<times/>
<apply>
<power/>
<ci>K_hlf_ATP</ci>
<ci>h_ATP</ci>
</apply>
<ci>Km_GLC</ci>
</apply>
<apply>
<times/>
<apply>
<power/>
<ci>ATP</ci>
<ci>h_ATP</ci>
</apply>
<ci>GLC</ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="v_GAPD">
<variable name="v_GAPD" public_interface="out" units="flux"/>
<variable initial_value="1.3" name="V_max" units="flux"/>
<variable initial_value="2.4" name="Km_GAP" units="millimolar"/>
<!--taken from "KM" for FBP - real KM must be equal to. or lower than this. -->
<variable initial_value="0.9" name="Km_NAD" units="millimolar"/>
<variable initial_value="13" name="Km_P" units="millimolar"/>
<variable name="GAP" public_interface="in" units="millimolar"/>
<variable name="NAD" public_interface="in" units="millimolar"/>
<variable name="P" public_interface="in" units="millimolar"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>v_GAPD</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>V_max</ci>
<ci>GAP</ci>
<ci>NAD</ci>
<ci>P</ci>
</apply>
<apply>
<plus/>
<apply>
<times/>
<ci>Km_GAP</ci>
<ci>Km_NAD</ci>
<ci>Km_P</ci>
</apply>
<apply>
<times/>
<ci>GAP</ci>
<ci>NAD</ci>
<ci>P</ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="v_FBPA">
<variable name="v_FBPA" public_interface="out" units="flux"/>
<variable initial_value="4.4" name="KM_FBP" units="millimolar"/>
<variable initial_value="0.39" name="v_max" units="flux"/>
<variable initial_value="10" name="K_i_FBP" units="millimolar"/>
<variable name="FBP" public_interface="in" units="millimolar"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>v_FBPA</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>v_max</ci>
<ci>FBP</ci>
</apply>
<apply>
<plus/>
<ci>KM_FBP</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>FBP</ci>
<apply>
<plus/>
<cn cellml:units="dimensionless">1.0</cn>
<ci>FBP</ci>
</apply>
</apply>
<ci>K_i_FBP</ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="v_PFK">
<variable name="v_PFK" public_interface="out" units="flux"/>
<variable initial_value="0.035" name="v_max" units="flux"/>
<variable initial_value="0.74" name="K_hlf_F6P" units="millimolar"/>
<variable initial_value="1.7" name="h_F6P" units="dimensionless"/>
<variable initial_value="1.1" name="Km_ATP" units="millimolar"/>
<variable name="F6P" public_interface="in" units="millimolar"/>
<variable name="ATP" public_interface="in" units="millimolar"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>v_PFK</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>v_max</ci>
<apply>
<power/>
<ci>F6P</ci>
<ci>h_F6P</ci>
</apply>
<ci>ATP</ci>
</apply>
<apply>
<plus/>
<apply>
<times/>
<apply>
<power/>
<ci>K_hlf_F6P</ci>
<ci>h_F6P</ci>
</apply>
<ci>Km_ATP</ci>
</apply>
<apply>
<times/>
<apply>
<power/>
<ci>F6P</ci>
<ci>h_F6P</ci>
</apply>
<ci>ATP</ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<!-- Connections -->
<connection>
<map_components component_1="GLC" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="G6P" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="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="TRIO" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="BPG" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="P" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="NADH" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="NAD" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="ATP" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="ADP" 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"/>
<map_variables variable_1="v_GK" variable_2="v_GK"/>
</connection>
<connection>
<map_components component_1="G6P" component_2="v_GK"/>
<map_variables variable_1="v_GK" variable_2="v_GK"/>
</connection>
<connection>
<map_components component_1="G6P" component_2="v_PGI"/>
<map_variables variable_1="G6P" variable_2="G6P"/>
<map_variables variable_1="v_PGI" variable_2="v_PGI"/>
</connection>
<connection>
<map_components component_1="F6P" component_2="v_PGI"/>
<map_variables variable_1="v_PGI" variable_2="v_PGI"/>
</connection>
<connection>
<map_components component_1="F6P" component_2="v_PFK"/>
<map_variables variable_1="F6P" variable_2="F6P"/>
<map_variables variable_1="v_PFK" variable_2="v_PFK"/>
</connection>
<connection>
<map_components component_1="FBP" component_2="v_PFK"/>
<map_variables variable_1="v_PFK" variable_2="v_PFK"/>
</connection>
<connection>
<map_components component_1="FBP" component_2="v_FBPA"/>
<map_variables variable_1="FBP" variable_2="FBP"/>
<map_variables variable_1="v_FBPA" variable_2="v_FBPA"/>
</connection>
<connection>
<map_components component_1="TRIO" component_2="v_FBPA"/>
<map_variables variable_1="v_FBPA" variable_2="v_FBPA"/>
</connection>
<connection>
<map_components component_1="TRIO" component_2="v_GAPD"/>
<map_variables variable_1="v_GAPD" variable_2="v_GAPD"/>
</connection>
<connection>
<map_components component_1="BPG" component_2="v_GAPD"/>
<map_variables variable_1="v_GAPD" variable_2="v_GAPD"/>
</connection>
<connection>
<map_components component_1="ATP" component_2="v_GK"/>
<map_variables variable_1="ATP" variable_2="ATP"/>
<map_variables variable_1="v_GK" variable_2="v_GK"/>
</connection>
<connection>
<map_components component_1="ATP" component_2="v_PFK"/>
<map_variables variable_1="ATP" variable_2="ATP"/>
<map_variables variable_1="v_PFK" variable_2="v_PFK"/>
</connection>
<connection>
<map_components component_1="NADH" component_2="v_GAPD"/>
<map_variables variable_1="v_GAPD" variable_2="v_GAPD"/>
</connection>
<connection>
<map_components component_1="NAD" component_2="v_GAPD"/>
<map_variables variable_1="NAD" variable_2="NAD"/>
<map_variables variable_1="v_GAPD" variable_2="v_GAPD"/>
</connection>
<connection>
<map_components component_1="DHAP" component_2="TRIO"/>
<map_variables variable_1="TRIO" variable_2="TRIO"/>
</connection>
<connection>
<map_components component_1="GAP" component_2="TRIO"/>
<map_variables variable_1="TRIO" variable_2="TRIO"/>
</connection>
<connection>
<map_components component_1="DHAP" component_2="GAP"/>
<map_variables variable_1="Keq_TPI" variable_2="Keq_TPI"/>
</connection>
<connection>
<map_components component_1="P" component_2="v_GAPD"/>
<map_variables variable_1="P" variable_2="P"/>
</connection>
<connection>
<map_components component_1="GAP" component_2="v_GAPD"/>
<map_variables variable_1="GAP" variable_2="GAP"/>
</connection>
<connection>
<map_components component_1="ADP" component_2="v_GK"/>
<map_variables variable_1="v_GK" variable_2="v_GK"/>
</connection>
<connection>
<map_components component_1="ADP" component_2="v_PFK"/>
<map_variables variable_1="v_PFK" variable_2="v_PFK"/>
</connection>
<connection>
<map_components component_1="P" component_2="v_GAPD"/>
<map_variables variable_1="v_GAPD" variable_2="v_GAPD"/>
</connection>
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" rdf:about="#GLCo">
<dc:title xmlns:dc="http://purl.org/dc/elements/1.1/">GLCo</dc:title>
<dcterms:alternative xmlns:dcterms="http://purl.org/dc/terms/">extracellular glucose</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
</model>
