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<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 scaled version of the model, taken from equations 29-39 in the original paper. Unfortunately the CellMl model does not recreate the published results and it requires further curation.
</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>
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<title>reaction diagram</title>
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<caption>Schematic diagram of the model.</caption>
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</sect1>
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</apply>
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<cn cellml:units="dimensionless"> 1 </cn>
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</apply>
</math>
</component>
<component name="en_crit">
<variable cmeta:id="en_crit_en_crit" name="en_crit" public_interface="out" units="dimensionless"/>
<variable name="Kapp_dash" public_interface="in" units="dimensionless"/>
<variable name="delta_crit" public_interface="in" units="dimensionless"/>
<variable name="s" public_interface="in" units="dimensionless"/>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="21">
<apply id="en_crit_calculation"><eq/>
<ci> en_crit </ci>
<apply>
<divide/>
<ci> Kapp_dash </ci>
<apply>
<plus/>
<ci> Kapp_dash </ci>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="dimensionless"> -1 </cn>
<ci> delta_crit </ci>
<ci> s </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
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<variable name="beta2" public_interface="out" units="dimensionless"/>
<variable name="beta3" public_interface="out" units="dimensionless"/>
<variable name="beta4" public_interface="out" units="dimensionless"/>
<variable name="beta5" public_interface="out" units="dimensionless"/>
<variable name="beta6" public_interface="out" units="dimensionless"/>
<variable name="beta7" public_interface="out" units="dimensionless"/>
<variable name="beta8" public_interface="out" units="dimensionless"/>
<variable name="epsilon1" public_interface="out" units="dimensionless"/>
<variable name="epsilon2" public_interface="out" units="dimensionless"/>
<variable name="epsilon3" public_interface="out" units="dimensionless"/>
<variable name="epsilon4" public_interface="out" units="dimensionless"/>
<variable name="epsilon5" public_interface="out" units="dimensionless"/>
<variable name="epsilon6" public_interface="out" units="dimensionless"/>
<variable name="epsilon7" public_interface="out" units="dimensionless"/>
<variable name="beta_ANT" public_interface="out" units="dimensionless"/>
<variable name="beta_leak" public_interface="out" units="dimensionless"/>
<variable name="beta_resp" public_interface="out" units="dimensionless"/>
<variable name="beta_ATP" public_interface="out" units="dimensionless"/>
<variable name="delta_6" public_interface="out" units="dimensionless"/>
<variable name="delta_r1" public_interface="out" units="dimensionless"/>
<variable name="delta_r2" public_interface="out" units="dimensionless"/>
<variable name="delta_atp" public_interface="out" units="dimensionless"/>
<variable name="delta_crit" public_interface="out" units="dimensionless"/>
<variable name="Kapp_dash" public_interface="out" units="dimensionless"/>
<variable name="tau" public_interface="out" units="dimensionless"/>
<variable name="At" initial_value="4.160" units="millimolar"/>
<variable name="Nt" initial_value="1.070" units="millimolar"/>
<variable initial_value="0.161" name="Pyr_bar" units="dimensionless"/>
<variable initial_value="0.460" name="Cit_bar" units="dimensionless"/>
<variable initial_value="0.105" name="AcCoA_bar" units="dimensionless"/>
<variable initial_value="0.146" name="KG_bar" units="dimensionless"/>
<variable initial_value="0.004" name="OAA_bar" units="dimensionless"/>
<variable initial_value="38" name="k1" units="micromolar_per_second"/>
<variable initial_value="152" name="k2" units="second_order_rate_constant"/>
<variable initial_value="57142" name="k3" units="second_order_rate_constant"/>
<variable initial_value="53" name="k4" units="second_order_rate_constant"/>
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<variable initial_value="82361" name="k6" units="first_order_rate_constant"/>
<variable initial_value="3.2e-3" name="k7" units="second_order_rate_constant"/>
<variable initial_value="3.6" name="k8" units="first_order_rate_constant"/>
<variable initial_value="2.5" name="kresp" units="millimolar_per_second"/>
<variable initial_value="131.9" name="kATP" units="millimolar_per_second"/>
<variable initial_value="0.1" name="kANT" units="dimensionless"/>
<variable initial_value="0.426" name="kleak" units="molar_per_millivolt_per_second"/>
<variable initial_value="0.3975" name="Keq" units="dimensionless"/>
<variable initial_value="2" name="K" units="millimolar"/>
<variable initial_value="0.100" name="alpha" units="per_millivolt"/>
<variable initial_value="0.004" name="b" units="per_millimolar"/>
<variable initial_value="150.0" name="delta_psi_m" units="millivolt"/>
<variable initial_value="8.314" name="R" units="joule_per_mole_kelvin"/>
<variable initial_value="298" name="T" units="kelvin"/>
<variable initial_value="96485" name="F" units="coulomb_per_mole"/>
<variable initial_value="6.75e-06" name="C" units="millimolar_per_millivolt"/>
<variable initial_value="4.4e-6" name="Kapp" units="per_millimolar"/>
<variable initial_value="2.440" name="Pi" units="millimolar"/>
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<variable name="a" public_interface="in" units="dimensionless"/>
<variable name="c" public_interface="in" units="dimensionless"/>
<variable name="k" public_interface="in" units="dimensionless"/>
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<variable name="en" public_interface="in" units="dimensionless"/>
<variable name="s" public_interface="in" units="dimensionless"/>
<variable name="time" public_interface="in" units="second"/>
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<ci> beta2 </ci>
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<times/>
<apply>
<divide/>
<ci> k2 </ci>
<ci> k1 </ci>
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<ci> Nt </ci>
<ci> Pyr_bar </ci>
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</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="23">
<apply><eq/>
<ci> beta3 </ci>
<apply>
<times/>
<apply>
<divide/>
<ci> k3 </ci>
<ci> k1 </ci>
</apply>
<ci> OAA_bar </ci>
<ci> AcCoA_bar </ci>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="24">
<apply><eq/>
<ci> beta4 </ci>
<apply>
<times/>
<apply>
<divide/>
<ci> k4 </ci>
<ci> k1 </ci>
</apply>
<ci> Nt </ci>
<ci> Cit_bar </ci>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="25">
<apply><eq/>
<ci> beta5 </ci>
<apply>
<times/>
<apply>
<divide/>
<ci> k5 </ci>
<ci> k1 </ci>
</apply>
<ci> Nt </ci>
<ci> At </ci>
<ci> KG_bar </ci>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="26">
<apply><eq/>
<ci> beta6 </ci>
<apply>
<times/>
<apply>
<divide/>
<ci> k6 </ci>
<ci> k1 </ci>
</apply>
<ci> OAA_bar </ci>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="27">
<apply><eq/>
<ci> beta7 </ci>
<apply>
<times/>
<apply>
<divide/>
<ci> k7 </ci>
<ci> k1 </ci>
</apply>
<ci> At </ci>
<ci> Pyr_bar </ci>
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</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="28">
<apply><eq/>
<ci> beta8 </ci>
<apply>
<times/>
<apply>
<divide/>
<ci> k8 </ci>
<ci> k1 </ci>
</apply>
<ci> OAA_bar </ci>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="29">
<apply><eq/>
<ci> beta_ANT </ci>
<apply>
<times/>
<apply>
<divide/>
<ci> kANT </ci>
<ci> k1 </ci>
</apply>
<ci> At </ci>
</apply>
</apply>
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<math xmlns="http://www.w3.org/1998/Math/MathML" id="30">
<apply><eq/>
<ci> beta_leak </ci>
<apply>
<times/>
<apply>
<divide/>
<ci> kleak </ci>
<ci> k1 </ci>
</apply>
<ci> delta_psi_m </ci>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="31">
<apply><eq/>
<ci> beta_resp </ci>
<apply>
<divide/>
<ci> kresp </ci>
<ci> k1 </ci>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="32">
<apply><eq/>
<ci> beta_ATP </ci>
<apply>
<divide/>
<ci> kATP </ci>
<ci> k1 </ci>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="33">
<apply><eq/>
<ci> delta_6 </ci>
<apply>
<divide/>
<ci> KG_bar </ci>
<apply>
<times/>
<ci> OAA_bar </ci>
<ci> Keq </ci>
</apply>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="34">
<apply><eq/>
<ci> delta_r1 </ci>
<apply>
<divide/>
<ci> K </ci>
<ci> Nt </ci>
</apply>
</apply>
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<math xmlns="http://www.w3.org/1998/Math/MathML" id="35">
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<ci> delta_r2 </ci>
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<times/>
<ci> alpha </ci>
<ci> delta_psi_m </ci>
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<math xmlns="http://www.w3.org/1998/Math/MathML" id="36">
<apply><eq/>
<ci> delta_atp </ci>
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<times/>
<ci> b </ci>
<ci> At </ci>
</apply>
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<math xmlns="http://www.w3.org/1998/Math/MathML" id="37">
<apply><eq/>
<ci> delta_crit </ci>
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<times/>
<cn cellml:units="dimensionless"> 3 </cn>
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<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 1.2 </cn>
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<ci> delta_psi_m </ci>
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<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
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<ci> Kapp_dash </ci>
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<times/>
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<ci> Pi </ci>
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</apply>
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<math xmlns="http://www.w3.org/1998/Math/MathML" id="39">
<apply><eq/>
<ci> epsilon1 </ci>
<apply>
<divide/>
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<ci> Pyr_bar </ci>
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<ci> epsilon2 </ci>
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<divide/>
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<ci> Pyr_bar </ci>
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<math xmlns="http://www.w3.org/1998/Math/MathML" id="41">
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<divide/>
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<ci> Pyr_bar </ci>
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<divide/>
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<divide/>
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<ci> Pyr_bar </ci>
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<divide/>
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<ci> Pyr_bar </ci>
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</apply>
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<apply>
<divide/>
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<ci> tau </ci>
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<apply>
<divide/>
<ci> k1 </ci>
<ci> Pyr_bar </ci>
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<ci> time </ci>
</apply>
</apply>
</math>
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<rdf:Description rdf:about="">
<dc:title>Mitochondrial energetic metabolism: a simplified model of TCA cycle with ATP production (scaled version)</dc:title>
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<vCard:Family>Lloyd</vCard:Family>
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Mitochondrial energetic metabolism: a simplified model of TCA cycle with ATP production
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