- Author:
- Tommy Yu <tommy.yu@auckland.ac.nz>
- Date:
- 2015-02-12 19:28:32+13:00
- Desc:
- Merging to remove the extra head
- Since the title is changed and in the interest of maintaining the
current structure we keep it as is.
- Permanent Source URI:
- https://models.cellml.org/w/matthiaskoenig/MetabolicComponentLibrary/rawfile/e0e2c28e2dfdfe37ea2cae3390a6ae26c28a3393/examples/nazaret_2009-MCL.cellml
<?xml version="1.0" encoding="utf-8"?>
<!--
This CellML file was generated on 4/21/2013 at 7:48:44 at PM using:
COR (0.9.31.1409)
Copyright 2002-2013 Dr Alan Garny
http://cor.physiol.ox.ac.uk/ - cor@physiol.ox.ac.uk
CellML 1.0 was used to generate this model
http://www.cellml.org/
-->
<model name="nazaret_2009_MCL" cmeta:id="nazaret_2009_MCL" xmlns="http://www.cellml.org/cellml/1.1#" xmlns:cellml="http://www.cellml.org/cellml/1.1#" xmlns:cmeta="http://www.cellml.org/metadata/1.1#">
<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
<articleinfo>
<title>Mitochondrial energetic metabolism: a simplified model of TCA cycle with ATP production</title>
<author>
<firstname>Catherine</firstname>
<surname>Lloyd</surname>
<affiliation>
<shortaffil>Auckland Bioengineering Institute, The University of Auckland</shortaffil>
</affiliation>
</author>
</articleinfo>
<section id="sec_status">
<title>Model Status</title>
<para>
This CellML runs in both OpenCell and COR. It is the unscaled version of the model, taken from equations 16-25 in the original paper. There are no published results (figures) for the unscaled model therefore we do not know whether or not this CellML model is capable of reproducing the orignal model's results.
</para>
</section>
<sect1 id="sec_structure">
<title>Model Structure</title>
<para>
ABSTRACT: Mitochondria play a central role in cellular energetic metabolism. The essential parts of this metabolism are the tricarboxylic acid (TCA) cycle, the respiratory chain and the adenosine triphosphate (ATP) synthesis machinery. Here a simplified model of these three metabolic components with a limited set of differential equations is presented. The existence of a steady state is demonstrated and results of numerical simulations are presented. The relevance of a simple model to represent actual in vivo behavior is discussed.
</para>
<para>
The original paper reference is cited below:
</para>
<para>
Mitochondrial energetic metabolism: a simplified model of TCA cycle with ATP production, Nazaret C, Heiske M, Thurley K, and Mazat JP, 2009, <emphasis>Journal of Theoretical Biology</emphasis>, 258, 455-464. <ulink url="http://www.ncbi.nlm.nih.gov/pubmed/19007794">PubMed ID: 19007794</ulink>
</para>
<informalfigure float="0" id="fig_reaction_diagram">
<mediaobject>
<imageobject>
<objectinfo>
<title>reaction diagram</title>
</objectinfo>
<imagedata fileref="nazaret_2009.png"/>
</imageobject>
</mediaobject>
<caption>Schematic diagram of the model.</caption>
</informalfigure>
</sect1>
</article>
</documentation>
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Mitochondrial energetic metabolism: a simplified model of TCA cycle with ATP production
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<variable name="NAD" units="micromolar" public_interface="in" private_interface="out"/>
<variable name="k4" units="second_order_rate_constant" private_interface="out"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>k4</ci>
<cn cellml:units="second_order_rate_constant">53</cn>
</apply>
</math>
</component>
<component name="v5">
<variable name="v5" units="micromolar_per_second" public_interface="out"/>
<variable name="ATP" units="micromolar" public_interface="in"/>
<variable name="KG" units="micromolar" public_interface="in"/>
<variable name="NAD" units="micromolar" public_interface="in"/>
<variable name="At" units="millimolar" public_interface="in"/>
<variable name="k5" units="third_order_rate_constant"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>k5</ci>
<cn cellml:units="third_order_rate_constant">82361</cn>
</apply>
<apply>
<eq/>
<ci>v5</ci>
<apply>
<times/>
<ci>k5</ci>
<ci>KG</ci>
<ci>NAD</ci>
<apply>
<minus/>
<ci>At</ci>
<ci>ATP</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="v6">
<variable name="v6" units="micromolar_per_second" public_interface="out"/>
<variable name="OAA" units="micromolar" public_interface="in"/>
<variable name="KG" units="micromolar" public_interface="in"/>
<variable name="k6" units="first_order_rate_constant"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>k6</ci>
<cn type="e-notation" cellml:units="first_order_rate_constant">3.2 <sep/>
-3</cn>
</apply>
<apply>
<eq/>
<ci>v6</ci>
<apply>
<times/>
<ci>k6</ci>
<apply>
<minus/>
<ci>OAA</ci>
<ci>KG</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="v7">
<variable name="v7" units="micromolar_per_second" public_interface="out" private_interface="in"/>
<variable name="Pyr" units="micromolar" public_interface="in" private_interface="out"/>
<variable name="ATP" units="micromolar" public_interface="in" private_interface="out"/>
<variable name="k7" units="second_order_rate_constant" private_interface="out"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>k7</ci>
<cn cellml:units="second_order_rate_constant">40</cn>
</apply>
</math>
</component>
<component name="v8">
<variable name="v8" units="micromolar_per_second" public_interface="out" private_interface="in"/>
<variable name="OAA" units="micromolar" public_interface="in" private_interface="out"/>
<variable name="k8" units="first_order_rate_constant" private_interface="out"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>k8</ci>
<cn cellml:units="first_order_rate_constant">3.6</cn>
</apply>
</math>
</component>
<component name="vANT">
<variable name="vANT" units="micromolar_per_second" public_interface="out" private_interface="in"/>
<variable name="ATP" units="micromolar" public_interface="in" private_interface="out"/>
<variable name="kANT" units="first_order_rate_constant" private_interface="out"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>kANT</ci>
<cn cellml:units="first_order_rate_constant">0.1</cn>
</apply>
</math>
</component>
<component name="vleak">
<variable name="vleak" units="micromolar_per_second" public_interface="out"/>
<variable name="delta_psi" units="millivolt" public_interface="in"/>
<variable name="kleak" units="molar_per_millivolt_per_second"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>kleak</ci>
<cn cellml:units="molar_per_millivolt_per_second">0.426</cn>
</apply>
<apply>
<eq/>
<ci>vleak</ci>
<apply>
<times/>
<ci>kleak</ci>
<ci>delta_psi</ci>
</apply>
</apply>
</math>
</component>
<component name="vresp">
<variable name="vresp" units="micromolar_per_second" public_interface="out"/>
<variable name="NAD" units="micromolar" public_interface="in"/>
<variable name="delta_psi" units="millivolt" public_interface="in"/>
<variable name="kresp" units="millimolar_per_second" initial_value="2.5"/>
<variable name="K" units="millimolar" initial_value="2"/>
<variable name="a" units="per_millivolt" initial_value="0.1"/>
<variable name="delta_psi_m" units="millivolt" initial_value="150"/>
<variable name="Nt" units="millimolar"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>Nt</ci>
<cn cellml:units="millimolar">1.07</cn>
</apply>
<apply>
<eq/>
<ci>vresp</ci>
<apply>
<divide/>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<ci>kresp</ci>
<apply>
<minus/>
<ci>Nt</ci>
<ci>NAD</ci>
</apply>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<ci>K</ci>
<ci>Nt</ci>
</apply>
<ci>NAD</ci>
</apply>
</apply>
<cn cellml:units="dimensionless">1</cn>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<times/>
<ci>a</ci>
<apply>
<minus/>
<ci>delta_psi</ci>
<ci>delta_psi_m</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="vATP">
<variable name="vATP" units="micromolar_per_second" public_interface="out"/>
<variable name="ATP" units="micromolar" public_interface="in"/>
<variable name="ATP_crit_delta_psi" units="micromolar" public_interface="in"/>
<variable name="kATP" units="millimolar_per_second" initial_value="131.9"/>
<variable name="b" units="per_micromolar" initial_value="4"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>vATP</ci>
<apply>
<times/>
<ci>kATP</ci>
<apply>
<minus/>
<apply>
<divide/>
<cn cellml:units="dimensionless">2</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<times/>
<ci>b</ci>
<apply>
<minus/>
<ci>ATP</ci>
<ci>ATP_crit_delta_psi</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<cn cellml:units="dimensionless">1</cn>
</apply>
</apply>
</apply>
</math>
</component>
<component name="ATP_crit_delta_psi">
<variable name="ATP_crit_delta_psi" units="micromolar" public_interface="out"/>
<variable name="At" units="millimolar" public_interface="in"/>
<variable name="delta_psi" units="millivolt" public_interface="in"/>
<variable name="R" units="joule_per_mole_kelvin" initial_value="8.314"/>
<variable name="T" units="kelvin" initial_value="298"/>
<variable name="F" units="coulomb_per_mole" initial_value="96485"/>
<variable name="Kapp" units="per_millimolar" initial_value="4.4e-6"/>
<variable name="Pi" units="millimolar" initial_value="2.44"/>
<variable name="delta_G_transport" units="joule_per_mole"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>ATP_crit_delta_psi</ci>
<apply>
<divide/>
<ci>At</ci>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<divide/>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">3</cn>
</apply>
<ci>delta_G_transport</ci>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci>Kapp</ci>
<ci>Pi</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>delta_G_transport</ci>
<apply>
<times/>
<cn cellml:units="dimensionless">0.0012</cn>
<ci>F</ci>
<ci>delta_psi</ci>
</apply>
</apply>
</math>
</component>
<group>
<relationship_ref relationship="encapsulation"/>
<component_ref component="v2">
<component_ref component="v2_MassActionBiIrrev"/>
</component_ref>
<component_ref component="v3">
<component_ref component="v3_MassActionBiIrrev"/>
</component_ref>
<component_ref component="v4">
<component_ref component="v4_MassActionBiIrrev"/>
</component_ref>
<component_ref component="v7">
<component_ref component="v7_MassActionBiIrrev"/>
</component_ref>
<component_ref component="v8">
<component_ref component="v8_MassActionUniIrrev"/>
</component_ref>
<component_ref component="vANT">
<component_ref component="vANT_MassActionUniIrrev"/>
</component_ref>
</group>
<connection>
<map_components component_1="v2" component_2="v2_MassActionBiIrrev"/>
<map_variables variable_1="v2" variable_2="J"/>
<map_variables variable_1="Pyr" variable_2="S1"/>
<map_variables variable_1="NAD" variable_2="S2"/>
<map_variables variable_1="k2" variable_2="k_f"/>
</connection>
<connection>
<map_components component_1="v3" component_2="v3_MassActionBiIrrev"/>
<map_variables variable_1="v3" variable_2="J"/>
<map_variables variable_1="OAA" variable_2="S1"/>
<map_variables variable_1="AcCoA" variable_2="S2"/>
<map_variables variable_1="k3" variable_2="k_f"/>
</connection>
<connection>
<map_components component_1="v4" component_2="v4_MassActionBiIrrev"/>
<map_variables variable_1="v4" variable_2="J"/>
<map_variables variable_1="Cit" variable_2="S1"/>
<map_variables variable_1="NAD" variable_2="S2"/>
<map_variables variable_1="k4" variable_2="k_f"/>
</connection>
<connection>
<map_components component_1="v7" component_2="v7_MassActionBiIrrev"/>
<map_variables variable_1="v7" variable_2="J"/>
<map_variables variable_1="Pyr" variable_2="S1"/>
<map_variables variable_1="ATP" variable_2="S2"/>
<map_variables variable_1="k7" variable_2="k_f"/>
</connection>
<connection>
<map_components component_1="v8" component_2="v8_MassActionUniIrrev"/>
<map_variables variable_1="v8" variable_2="J"/>
<map_variables variable_1="OAA" variable_2="S"/>
<map_variables variable_1="k8" variable_2="k_f"/>
</connection>
<connection>
<map_components component_1="vANT" component_2="vANT_MassActionUniIrrev"/>
<map_variables variable_1="vANT" variable_2="J"/>
<map_variables variable_1="ATP" variable_2="S"/>
<map_variables variable_1="kANT" variable_2="k_f"/>
</connection>
<connection>
<map_components component_1="Network" component_2="v1"/>
<map_variables variable_1="v1" variable_2="v1"/>
</connection>
<connection>
<map_components component_1="Network" component_2="v2"/>
<map_variables variable_1="v2" variable_2="v2"/>
<map_variables variable_1="Pyr" variable_2="Pyr"/>
<map_variables variable_1="NAD" variable_2="NAD"/>
</connection>
<connection>
<map_components component_1="Network" component_2="v3"/>
<map_variables variable_1="v3" variable_2="v3"/>
<map_variables variable_1="OAA" variable_2="OAA"/>
<map_variables variable_1="AcCoA" variable_2="AcCoA"/>
</connection>
<connection>
<map_components component_1="Network" component_2="v4"/>
<map_variables variable_1="v4" variable_2="v4"/>
<map_variables variable_1="Cit" variable_2="Cit"/>
<map_variables variable_1="NAD" variable_2="NAD"/>
</connection>
<connection>
<map_components component_1="Network" component_2="v5"/>
<map_variables variable_1="v5" variable_2="v5"/>
<map_variables variable_1="ATP" variable_2="ATP"/>
<map_variables variable_1="KG" variable_2="KG"/>
<map_variables variable_1="NAD" variable_2="NAD"/>
<map_variables variable_1="At" variable_2="At"/>
</connection>
<connection>
<map_components component_1="Network" component_2="v6"/>
<map_variables variable_1="v6" variable_2="v6"/>
<map_variables variable_1="OAA" variable_2="OAA"/>
<map_variables variable_1="KG" variable_2="KG"/>
</connection>
<connection>
<map_components component_1="Network" component_2="v7"/>
<map_variables variable_1="v7" variable_2="v7"/>
<map_variables variable_1="Pyr" variable_2="Pyr"/>
<map_variables variable_1="ATP" variable_2="ATP"/>
</connection>
<connection>
<map_components component_1="Network" component_2="v8"/>
<map_variables variable_1="v8" variable_2="v8"/>
<map_variables variable_1="OAA" variable_2="OAA"/>
</connection>
<connection>
<map_components component_1="Network" component_2="vANT"/>
<map_variables variable_1="vANT" variable_2="vANT"/>
<map_variables variable_1="ATP" variable_2="ATP"/>
</connection>
<connection>
<map_components component_1="Network" component_2="vleak"/>
<map_variables variable_1="vleak" variable_2="vleak"/>
<map_variables variable_1="delta_psi" variable_2="delta_psi"/>
</connection>
<connection>
<map_components component_1="Network" component_2="vresp"/>
<map_variables variable_1="vresp" variable_2="vresp"/>
<map_variables variable_1="NAD" variable_2="NAD"/>
<map_variables variable_1="delta_psi" variable_2="delta_psi"/>
</connection>
<connection>
<map_components component_1="Network" component_2="vATP"/>
<map_variables variable_1="vATP" variable_2="vATP"/>
<map_variables variable_1="ATP" variable_2="ATP"/>
</connection>
<connection>
<map_components component_1="ATP_crit_delta_psi" component_2="vATP"/>
<map_variables variable_1="ATP_crit_delta_psi" variable_2="ATP_crit_delta_psi"/>
</connection>
<connection>
<map_components component_1="Network" component_2="ATP_crit_delta_psi"/>
<map_variables variable_1="delta_psi" variable_2="delta_psi"/>
<map_variables variable_1="At" variable_2="At"/>
</connection>
</model>
