- Author:
- Catherine Lloyd <c.lloyd@auckland.ac.nz>
- Date:
- 2010-05-27 22:53:23+12:00
- Desc:
- Made minor change to namespace.
- Permanent Source URI:
- https://models.physiomeproject.org/workspace/beard_2005/rawfile/8ec69b34c31cd1cbb53580d1853841bb333de78e/beard_2005.cellml
<?xml version="1.0"?>
<!--
This CellML file was generated on 17/12/2009 at 1:55:34 at p.m. using:
COR (0.9.31.1333)
Copyright 2002-2009 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/
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<article>
<articleinfo>
<title>A Biophysical Model of the Mitochondrial Respiratory System and Oxidative Phosphorylation, Beard, 2005</title>
<author>
<firstname>David</firstname>
<surname>Nickerson</surname>
<affiliation>
<shortaffil>Auckland Bioengineering Institute, The University of Auckland</shortaffil>
</affiliation>
</author>
</articleinfo>
<section id="sec_status">
<title>Model Status</title>
<para>
This model has been edited to correct dimensional errors and checked for other problems. It runs in COR and OpenCell to replicate results from the original matlab code. It was based on the original matlab code provided by the model authors.
</para>
</section>
<sect1 id="sec_structure">
<title>Model Structure</title>
<para>ABSTRACT: A computational model for the mitochondrial respiratory chain that appropriately balances mass, charge, and free energy transduction is introduced and analyzed based on a previously published set of data measured on isolated cardiac mitochondria. The basic components included in the model are the reactions at complexes I, III, and IV of the electron transport system, ATP synthesis at F1F0 ATPase, substrate transporters including adenine nucleotide translocase and the phosphate\u2013hydrogen co-transporter, and cation fluxes across the inner membrane including fluxes through the K+/H+ antiporter and passive H+ and K+ permeation. Estimation of 16 adjustable parameter values is based on fitting model simulations to nine independent data curves. The identified model is further validated by comparison to additional datasets measured from mitochondria isolated from rat heart and liver and observed at low oxygen concentration. To obtain reasonable fits to the available data, it is necessary to incorporate inorganic-phosphate-dependent activation of the dehydrogenase activity and the electron transport system. Specifically, it is shown that a model incorporating phosphate-dependent activation of complex III is able to reasonably reproduce the observed data. The resulting validated and verified model provides a foundation for building larger and more complex systems models and investigating complex physiological and pathophysiological interactions in cardiac energetics.
</para>
<para>
The original paper reference is cited below:
</para>
<para>A Biophysical Model of the Mitochondrial Respiratory System and Oxidative Phosphorylation, Daniel A. Beard, 2005, <emphasis>PLoS Computational Biology</emphasis>
, September 9, 1(4). <ulink url="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&list_uids=16163394&dopt=Citation">PubMed ID: 16163394</ulink>
</para>
<para>
Illustration of the Components Included in the Model of Mitochondrial Oxidative Phosphorylation:
</para>
<informalfigure float="0" id="fig_reaction_diagram1">
<mediaobject>
<imageobject>
<objectinfo>
<title>model diagram</title>
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<imagedata fileref="beard_2005a.png"/>
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<caption>A) Schematic diagram of the major components of the electron transport system, which transfers reducing potential from NADH to oxygen, and the F1F0 ATPase, which transduces energy from proton motive force to ATP, are illustrated. Complexes I, III, and IV are labeled C1, C3, and C4, respectively.
</caption>
</informalfigure>
<informalfigure float="0" id="fig_reaction_diagram2">
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<title>model diagram</title>
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<caption>B) Schematic diagram of the substrate transport process included in the model, including the ANT and PiHt on the inner membrane, and passive permeation of ATP, ADP, AMP, and phosphate across the outer membrane. The AK reaction in the IM space is shown.
</caption>
</informalfigure>
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<caption>C) Schematic diagram of the transporters for hydrogen and potassium ions on the inner membrane, including K+/H+ antiporter and passive proton and potassium fluxes. It is assumed that these cations rapidly equilibrate across the outer membrane.
</caption>
</informalfigure>
</sect1>
</article>
</documentation>
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</apply>
<apply>
<times/>
<ci>RT</ci>
<apply>
<ln/>
<apply>
<divide/>
<ci>QH2</ci>
<ci>Q</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>J_C3</ci>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<ci>x_C3</ci>
<apply>
<plus/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
<apply>
<divide/>
<ci>Pi_x</ci>
<ci>k_Pi3</ci>
</apply>
</apply>
</apply>
<apply>
<plus/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
<apply>
<divide/>
<ci>Pi_x</ci>
<ci>k_Pi4</ci>
</apply>
</apply>
</apply>
<apply>
<minus/>
<apply>
<times/>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<plus/>
<ci>dG_C3op</ci>
<apply>
<times/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">4</cn>
<ci>dG_H</ci>
</apply>
</apply>
<apply>
<times/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
<ci>F</ci>
<ci>dPsi</ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
<ci>RT</ci>
</apply>
</apply>
</apply>
<ci>Cox</ci>
</apply>
<ci>Cred</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="Electron_flux_complex_IV">
<variable cmeta:id="Electron_flux_complex_IV_J_C4" name="J_C4" public_interface="out" units="mole_per_second_per_l_mito"/>
<variable name="k_O2" public_interface="in" units="molar"/>
<variable name="x_C4" public_interface="in" units="mole_per_second_per_l_mito_per_molar"/>
<variable name="dG_C4op" units="kilojoule_per_mole"/>
<variable name="dG_C4o" public_interface="in" units="kilojoule_per_mole"/>
<variable name="Cred" public_interface="in" units="molar"/>
<variable name="Ctot" public_interface="in" units="molar"/>
<variable name="O2" public_interface="in" units="molar"/>
<variable name="dG_H" public_interface="in" units="kilojoule_per_mole"/>
<variable name="RT" public_interface="in" units="kilojoule_per_mole"/>
<variable name="Cox" public_interface="in" units="molar"/>
<variable name="F" public_interface="in" units="kilojoule_per_mole_per_millivolt"/>
<variable name="dPsi" public_interface="in" units="millivolt"/>
<variable name="H_x" public_interface="in" units="molar"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>dG_C4op</ci>
<apply>
<minus/>
<apply>
<minus/>
<ci>dG_C4o</ci>
<apply>
<times/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
<ci>RT</ci>
<apply>
<ln/>
<apply>
<divide/>
<ci>H_x</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" type="e-notation" cellml:units="molar">1 <sep/>
-7</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<times/>
<apply>
<divide/>
<ci>RT</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
</apply>
<apply>
<ln/>
<apply>
<divide/>
<ci>O2</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="molar">1</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>J_C4</ci>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<ci>x_C4</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
</apply>
<apply>
<plus/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
<apply>
<divide/>
<ci>k_O2</ci>
<ci>O2</ci>
</apply>
</apply>
</apply>
<ci>Cred</ci>
</apply>
<ci>Ctot</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<plus/>
<ci>dG_C4op</ci>
<apply>
<times/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
<ci>dG_H</ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
<ci>RT</ci>
</apply>
</apply>
</apply>
<ci>Cred</ci>
</apply>
<apply>
<times/>
<ci>Cox</ci>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<ci>F</ci>
<ci>dPsi</ci>
</apply>
<ci>RT</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="ATP_synthesis_flux">
<variable cmeta:id="ATP_synthesis_flux_J_F1" name="J_F1" public_interface="out" units="mole_per_second_per_l_mito"/>
<variable name="x_F1" public_interface="in" units="mole_per_second_per_l_mito_per_molar_per_molar"/>
<variable name="dG_F1o" public_interface="in" units="kilojoule_per_mole"/>
<variable name="K_DD" public_interface="in" units="molar"/>
<variable name="K_DT" public_interface="in" units="molar"/>
<variable name="RT" public_interface="in" units="kilojoule_per_mole"/>
<variable name="n_A" public_interface="in" units="dimensionless"/>
<variable name="dG_H" public_interface="in" units="kilojoule_per_mole"/>
<variable name="ADP_mx" public_interface="in" units="molar"/>
<variable name="Pi_x" public_interface="in" units="molar"/>
<variable name="ATP_mx" public_interface="in" units="molar"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>J_F1</ci>
<apply>
<times/>
<ci>x_F1</ci>
<apply>
<minus/>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<minus/>
<ci>dG_F1o</ci>
<apply>
<times/>
<ci>n_A</ci>
<ci>dG_H</ci>
</apply>
</apply>
</apply>
<ci>RT</ci>
</apply>
</apply>
<ci>K_DD</ci>
</apply>
<ci>K_DT</ci>
</apply>
<ci>ADP_mx</ci>
<ci>Pi_x</ci>
</apply>
<apply>
<times/>
<ci>ATP_mx</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="molar">1</cn>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="ANT_flux">
<variable name="J_ANT" public_interface="out" units="mole_per_second_per_l_mito"/>
<variable name="Psi_x" public_interface="out" units="millivolt"/>
<variable name="Psi_i" public_interface="out" units="millivolt"/>
<variable name="x_ANT" public_interface="in" units="mole_per_second_per_l_mito"/>
<variable name="ADP_fi" public_interface="in" units="molar"/>
<variable name="ATP_fi" public_interface="in" units="molar"/>
<variable name="F" public_interface="in" units="kilojoule_per_mole_per_millivolt"/>
<variable name="RT" public_interface="in" units="kilojoule_per_mole"/>
<variable name="dPsi" public_interface="in" units="millivolt"/>
<variable name="ADP_fx" public_interface="in" units="molar"/>
<variable name="ATP_fx" public_interface="in" units="molar"/>
<variable name="k_mADP" public_interface="in" units="molar"/>
<variable initial_value="1e-12" name="mincond" units="molar"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>Psi_x</ci>
<apply>
<times/>
<apply>
<minus/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">0.65</cn>
</apply>
<ci>dPsi</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>Psi_i</ci>
<apply>
<times/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">0.35</cn>
<ci>dPsi</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>J_ANT</ci>
<piecewise>
<piece>
<apply>
<divide/>
<apply>
<times/>
<ci>x_ANT</ci>
<apply>
<minus/>
<apply>
<divide/>
<ci>ADP_fi</ci>
<apply>
<plus/>
<ci>ADP_fi</ci>
<apply>
<times/>
<ci>ATP_fi</ci>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<apply>
<minus/>
<ci>F</ci>
</apply>
<ci>Psi_i</ci>
</apply>
<ci>RT</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<divide/>
<ci>ADP_fx</ci>
<apply>
<plus/>
<ci>ADP_fx</ci>
<apply>
<times/>
<ci>ATP_fx</ci>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<apply>
<minus/>
<ci>F</ci>
</apply>
<ci>Psi_x</ci>
</apply>
<ci>RT</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<ci>ADP_fi</ci>
</apply>
<apply>
<plus/>
<ci>k_mADP</ci>
<ci>ADP_fi</ci>
</apply>
</apply>
<apply>
<or/>
<apply>
<gt/>
<ci>ADP_fi</ci>
<ci>mincond</ci>
</apply>
<apply>
<gt/>
<ci>ATP_fi</ci>
<ci>mincond</ci>
</apply>
</apply>
</piece>
<otherwise>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="mole_per_second_per_l_mito">0</cn>
</otherwise>
</piecewise>
</apply>
</math>
</component>
<component name="MgATPx_binding_flux">
<variable name="J_MgATPx" public_interface="out" units="mole_per_second_per_l_mito"/>
<variable name="ATP_fx" public_interface="out" units="molar"/>
<variable name="x_MgA" public_interface="in" units="mole_per_second_per_l_mito_per_molar_per_molar"/>
<variable name="ATP_x" public_interface="in" units="molar"/>
<variable name="ATP_mx" public_interface="in" units="molar"/>
<variable name="Mg_x" public_interface="in" units="molar"/>
<variable name="K_DT" public_interface="in" units="molar"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>ATP_fx</ci>
<apply>
<minus/>
<ci>ATP_x</ci>
<ci>ATP_mx</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>J_MgATPx</ci>
<apply>
<times/>
<ci>x_MgA</ci>
<apply>
<minus/>
<apply>
<times/>
<ci>ATP_fx</ci>
<ci>Mg_x</ci>
</apply>
<apply>
<times/>
<ci>K_DT</ci>
<ci>ATP_mx</ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="MgADPx_binding_flux">
<variable name="J_MgADPx" public_interface="out" units="mole_per_second_per_l_mito"/>
<variable name="ADP_fx" public_interface="out" units="molar"/>
<variable name="ADP_x" public_interface="in" units="molar"/>
<variable name="ADP_mx" public_interface="in" units="molar"/>
<variable name="x_MgA" public_interface="in" units="mole_per_second_per_l_mito_per_molar_per_molar"/>
<variable name="K_DD" public_interface="in" units="molar"/>
<variable name="Mg_x" public_interface="in" units="molar"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>ADP_fx</ci>
<apply>
<minus/>
<ci>ADP_x</ci>
<ci>ADP_mx</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>J_MgADPx</ci>
<apply>
<times/>
<ci>x_MgA</ci>
<apply>
<minus/>
<apply>
<times/>
<ci>ADP_fx</ci>
<ci>Mg_x</ci>
</apply>
<apply>
<times/>
<ci>K_DD</ci>
<ci>ADP_mx</ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="MgATPi_binding_flux">
<variable name="J_MgATPi" public_interface="out" units="mole_per_second_per_l_mito"/>
<variable name="ATP_fi" public_interface="out" units="molar"/>
<variable name="ATP_i" public_interface="in" units="molar"/>
<variable name="ATP_mi" public_interface="in" units="molar"/>
<variable name="x_MgA" public_interface="in" units="mole_per_second_per_l_mito_per_molar_per_molar"/>
<variable name="K_DT" public_interface="in" units="molar"/>
<variable name="Mg_i" public_interface="in" units="molar"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>ATP_fi</ci>
<apply>
<minus/>
<ci>ATP_i</ci>
<ci>ATP_mi</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>J_MgATPi</ci>
<apply>
<times/>
<ci>x_MgA</ci>
<apply>
<minus/>
<apply>
<times/>
<ci>ATP_fi</ci>
<ci>Mg_i</ci>
</apply>
<apply>
<times/>
<ci>K_DT</ci>
<ci>ATP_mi</ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="MgADPi_binding_flux">
<variable name="J_MgADPi" public_interface="out" units="mole_per_second_per_l_mito"/>
<variable name="ADP_fi" public_interface="out" units="molar"/>
<variable name="ADP_i" public_interface="in" units="molar"/>
<variable name="ADP_mi" public_interface="in" units="molar"/>
<variable name="x_MgA" public_interface="in" units="mole_per_second_per_l_mito_per_molar_per_molar"/>
<variable name="K_DD" public_interface="in" units="molar"/>
<variable name="Mg_i" public_interface="in" units="molar"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>ADP_fi</ci>
<apply>
<minus/>
<ci>ADP_i</ci>
<ci>ADP_mi</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>J_MgADPi</ci>
<apply>
<times/>
<ci>x_MgA</ci>
<apply>
<minus/>
<apply>
<times/>
<ci>ADP_fi</ci>
<ci>Mg_i</ci>
</apply>
<apply>
<times/>
<ci>K_DD</ci>
<ci>ADP_mi</ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="ATP_substrate_flux">
<variable name="J_ATP" public_interface="out" units="mole_per_second_per_l_mito"/>
<variable name="ATP_e" public_interface="in" units="molar"/>
<variable name="gamma" public_interface="in" units="per_micron"/>
<variable name="p_A" public_interface="in" units="micron_per_second"/>
<variable name="ATP_i" public_interface="in" units="molar"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>J_ATP</ci>
<apply>
<times/>
<ci>gamma</ci>
<ci>p_A</ci>
<apply>
<minus/>
<ci>ATP_e</ci>
<ci>ATP_i</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="ADP_substrate_flux">
<variable name="J_ADP" public_interface="out" units="mole_per_second_per_l_mito"/>
<variable name="gamma" public_interface="in" units="per_micron"/>
<variable name="p_A" public_interface="in" units="micron_per_second"/>
<variable name="ADP_e" public_interface="in" units="molar"/>
<variable name="ADP_i" public_interface="in" units="molar"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>J_ADP</ci>
<apply>
<times/>
<ci>gamma</ci>
<ci>p_A</ci>
<apply>
<minus/>
<ci>ADP_e</ci>
<ci>ADP_i</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="AMP_substrate_flux">
<variable name="J_AMP" public_interface="out" units="mole_per_second_per_l_mito"/>
<variable name="AMP_e" public_interface="in" units="molar"/>
<variable name="gamma" public_interface="in" units="per_micron"/>
<variable name="p_A" public_interface="in" units="micron_per_second"/>
<variable name="AMP_i" public_interface="in" units="molar"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>J_AMP</ci>
<apply>
<times/>
<ci>gamma</ci>
<ci>p_A</ci>
<apply>
<minus/>
<ci>AMP_e</ci>
<ci>AMP_i</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="Pi_substrate_flux">
<variable name="J_Pi2" public_interface="out" units="mole_per_second_per_l_mito"/>
<variable name="x_Pi2" public_interface="in" units="micron_per_second"/>
<variable name="gamma" public_interface="in" units="per_micron"/>
<variable name="Pi_e" public_interface="in" units="molar"/>
<variable name="Pi_i" public_interface="in" units="molar"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>J_Pi2</ci>
<apply>
<times/>
<ci>gamma</ci>
<ci>x_Pi2</ci>
<apply>
<minus/>
<ci>Pi_e</ci>
<ci>Pi_i</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="Phosphate_hydrogen_cotransporter_flux">
<variable name="J_Pi1" public_interface="out" units="mole_per_second_per_l_mito"/>
<variable name="H2PIi" public_interface="out" units="molar"/>
<variable name="H2PIx" public_interface="out" units="molar"/>
<variable name="Pi_i" public_interface="in" units="molar"/>
<variable name="H_i" public_interface="in" units="molar"/>
<variable name="k_dHPi" public_interface="in" units="molar"/>
<variable name="Pi_x" public_interface="in" units="molar"/>
<variable name="H_x" public_interface="in" units="molar"/>
<variable name="x_Pi1" public_interface="in" units="mole_per_second_per_l_mito_per_molar"/>
<variable name="k_PiH" public_interface="in" units="molar"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>H2PIi</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>Pi_i</ci>
<ci>H_i</ci>
</apply>
<apply>
<plus/>
<ci>H_i</ci>
<ci>k_dHPi</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>H2PIx</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>Pi_x</ci>
<ci>H_x</ci>
</apply>
<apply>
<plus/>
<ci>H_x</ci>
<ci>k_dHPi</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>J_Pi1</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>x_Pi1</ci>
<apply>
<minus/>
<apply>
<times/>
<ci>H_x</ci>
<ci>H2PIi</ci>
</apply>
<apply>
<times/>
<ci>H_i</ci>
<ci>H2PIx</ci>
</apply>
</apply>
</apply>
<apply>
<plus/>
<ci>H2PIi</ci>
<ci>k_PiH</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="Adenylate_kinase_flux">
<variable name="J_AKi" public_interface="out" units="mole_per_second_per_l_mito"/>
<variable name="x_AK" public_interface="in" units="mole_per_second_per_l_mito_per_molar_per_molar"/>
<variable name="K_AK" public_interface="in" units="dimensionless"/>
<variable name="ADP_i" public_interface="in" units="molar"/>
<variable name="AMP_i" public_interface="in" units="molar"/>
<variable name="ATP_i" public_interface="in" units="molar"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>J_AKi</ci>
<apply>
<times/>
<ci>x_AK</ci>
<apply>
<minus/>
<apply>
<times/>
<ci>K_AK</ci>
<ci>ADP_i</ci>
<ci>ADP_i</ci>
</apply>
<apply>
<times/>
<ci>AMP_i</ci>
<ci>ATP_i</ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="Hydrogen_leak_flux">
<variable name="J_Hle" public_interface="out" units="mole_per_second_per_l_mito"/>
<variable name="x_Hle" public_interface="in" units="mole_per_second_per_l_mito_per_molar_per_millivolt"/>
<variable name="dPsi" public_interface="in" units="millivolt"/>
<variable name="H_i" public_interface="in" units="molar"/>
<variable name="F" public_interface="in" units="kilojoule_per_mole_per_millivolt"/>
<variable name="RT" public_interface="in" units="kilojoule_per_mole"/>
<variable name="H_x" public_interface="in" units="molar"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>J_Hle</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>x_Hle</ci>
<ci>dPsi</ci>
<apply>
<minus/>
<apply>
<times/>
<ci>H_i</ci>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<ci>F</ci>
<ci>dPsi</ci>
</apply>
<ci>RT</ci>
</apply>
</apply>
</apply>
<ci>H_x</ci>
</apply>
</apply>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<ci>F</ci>
<ci>dPsi</ci>
</apply>
<ci>RT</ci>
</apply>
</apply>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
</apply>
</apply>
</apply>
</math>
</component>
<component name="Passive_potassium_flux">
<variable name="J_K" public_interface="out" units="mole_per_second_per_l_mito"/>
<variable name="x_K" public_interface="in" units="mole_per_second_per_l_mito_per_molar_per_millivolt"/>
<variable name="dPsi" public_interface="in" units="millivolt"/>
<variable name="K_i" public_interface="in" units="molar"/>
<variable name="F" public_interface="in" units="kilojoule_per_mole_per_millivolt"/>
<variable name="RT" public_interface="in" units="kilojoule_per_mole"/>
<variable name="K_x" public_interface="in" units="molar"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>J_K</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>x_K</ci>
<ci>dPsi</ci>
<apply>
<minus/>
<apply>
<times/>
<ci>K_i</ci>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<ci>F</ci>
<ci>dPsi</ci>
</apply>
<ci>RT</ci>
</apply>
</apply>
</apply>
<ci>K_x</ci>
</apply>
</apply>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<ci>F</ci>
<ci>dPsi</ci>
</apply>
<ci>RT</ci>
</apply>
</apply>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
</apply>
</apply>
</apply>
</math>
</component>
<component name="Potassium_hydrogen_flux">
<variable name="J_KH" public_interface="out" units="mole_per_second_per_l_mito"/>
<variable name="x_KH" public_interface="in" units="mole_per_second_per_l_mito_per_molar_per_molar"/>
<variable name="K_i" public_interface="in" units="molar"/>
<variable name="K_x" public_interface="in" units="molar"/>
<variable name="H_i" public_interface="in" units="molar"/>
<variable name="H_x" public_interface="in" units="molar"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>J_KH</ci>
<apply>
<times/>
<ci>x_KH</ci>
<apply>
<minus/>
<apply>
<times/>
<ci>K_i</ci>
<ci>H_x</ci>
</apply>
<apply>
<times/>
<ci>K_x</ci>
<ci>H_i</ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="NAD_x_concentration">
<variable name="NAD_x" public_interface="out" units="molar"/>
<variable name="NADH_x" public_interface="in" units="molar"/>
<variable name="NADtot" public_interface="in" units="molar"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>NAD_x</ci>
<apply>
<minus/>
<ci>NADtot</ci>
<ci>NADH_x</ci>
</apply>
</apply>
</math>
</component>
<component name="Q_concentration">
<variable cmeta:id="Q_concentration_Q" name="Q" public_interface="out" units="molar"/>
<variable name="Qtot" public_interface="in" units="molar"/>
<variable name="QH2" public_interface="in" units="molar"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>Q</ci>
<apply>
<minus/>
<ci>Qtot</ci>
<ci>QH2</ci>
</apply>
</apply>
</math>
</component>
<component name="Cox_concentration">
<variable name="Cox" public_interface="out" units="molar"/>
<variable name="Ctot" public_interface="in" units="molar"/>
<variable name="Cred" public_interface="in" units="molar"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>Cox</ci>
<apply>
<minus/>
<ci>Ctot</ci>
<ci>Cred</ci>
</apply>
</apply>
</math>
</component>
<component name="ADP_binding">
<variable name="ADP_me" public_interface="out" units="molar"/>
<variable name="ADP_fe" public_interface="out" units="molar"/>
<variable name="ADP_e" public_interface="in" units="molar"/>
<variable name="K_DD" public_interface="in" units="molar"/>
<variable name="Mg_tot" public_interface="in" units="molar"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>ADP_fe</ci>
<apply>
<minus/>
<ci>ADP_e</ci>
<ci>ADP_me</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>ADP_me</ci>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<plus/>
<ci>K_DD</ci>
<ci>ADP_e</ci>
<ci>Mg_tot</ci>
</apply>
<apply>
<root/>
<apply>
<minus/>
<apply>
<power/>
<apply>
<plus/>
<ci>K_DD</ci>
<ci>ADP_e</ci>
<ci>Mg_tot</ci>
</apply>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
</apply>
<apply>
<times/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">4</cn>
<ci>Mg_tot</ci>
<ci>ADP_e</ci>
</apply>
</apply>
</apply>
</apply>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
</apply>
</apply>
</math>
</component>
<component name="Mg_binding">
<variable name="Mg_e" public_interface="out" units="molar"/>
<variable name="Mg_tot" public_interface="in" units="molar"/>
<variable name="Mg_i" public_interface="out" units="molar"/>
<variable name="ADP_me" public_interface="in" units="molar"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>Mg_e</ci>
<apply>
<minus/>
<ci>Mg_tot</ci>
<ci>ADP_me</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>Mg_i</ci>
<ci>Mg_e</ci>
</apply>
</math>
</component>
<component name="dH_x_dt">
<variable cmeta:id="dH_x_dt_H_x" initial_value="6.30957344480193e-8" name="H_x" public_interface="out" units="molar"/>
<variable name="x_buff" public_interface="in" units="per_molar"/>
<variable name="J_DH" public_interface="in" units="mole_per_second_per_l_mito"/>
<variable name="J_C1" public_interface="in" units="mole_per_second_per_l_mito"/>
<variable name="J_C3" public_interface="in" units="mole_per_second_per_l_mito"/>
<variable name="J_C4" public_interface="in" units="mole_per_second_per_l_mito"/>
<variable name="n_A" public_interface="in" units="dimensionless"/>
<variable name="J_F1" public_interface="in" units="mole_per_second_per_l_mito"/>
<variable name="J_Pi1" public_interface="in" units="mole_per_second_per_l_mito"/>
<variable name="J_Hle" public_interface="in" units="mole_per_second_per_l_mito"/>
<variable name="J_KH" public_interface="in" units="mole_per_second_per_l_mito"/>
<variable name="W_x" public_interface="in" units="l_water_per_l_mito"/>
<variable name="t" public_interface="in" units="second"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>H_x</ci>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci>x_buff</ci>
<ci>H_x</ci>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<minus/>
<ci>J_DH</ci>
<apply>
<times/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">5</cn>
<ci>J_C1</ci>
</apply>
</apply>
<apply>
<times/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
<ci>J_C3</ci>
</apply>
</apply>
<apply>
<times/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">4</cn>
<ci>J_C4</ci>
</apply>
</apply>
<apply>
<times/>
<apply>
<minus/>
<ci>n_A</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
</apply>
<ci>J_F1</ci>
</apply>
<apply>
<times/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
<ci>J_Pi1</ci>
</apply>
<ci>J_Hle</ci>
</apply>
<ci>J_KH</ci>
</apply>
</apply>
<ci>W_x</ci>
</apply>
</apply>
</math>
</component>
<component name="dK_x_dt">
<variable initial_value="0.14" name="K_x" public_interface="out" units="molar"/>
<variable name="J_KH" public_interface="in" units="mole_per_second_per_l_mito"/>
<variable name="J_K" public_interface="in" units="mole_per_second_per_l_mito"/>
<variable name="W_x" public_interface="in" units="l_water_per_l_mito"/>
<variable name="t" public_interface="in" units="second"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>K_x</ci>
</apply>
<apply>
<divide/>
<apply>
<plus/>
<ci>J_KH</ci>
<ci>J_K</ci>
</apply>
<ci>W_x</ci>
</apply>
</apply>
</math>
</component>
<component name="dMg_x_dt">
<variable initial_value="0.005" name="Mg_x" public_interface="out" units="molar"/>
<variable name="J_MgATPx" public_interface="in" units="mole_per_second_per_l_mito"/>
<variable name="J_MgADPx" public_interface="in" units="mole_per_second_per_l_mito"/>
<variable name="W_x" public_interface="in" units="l_water_per_l_mito"/>
<variable name="t" public_interface="in" units="second"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>Mg_x</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<minus/>
<ci>J_MgATPx</ci>
</apply>
<ci>J_MgADPx</ci>
</apply>
<ci>W_x</ci>
</apply>
</apply>
</math>
</component>
<component name="dNADH_x_dt">
<variable cmeta:id="dNADH_x_dt_NADH_x" initial_value="0.0015" name="NADH_x" public_interface="out" units="molar"/>
<variable name="J_DH" public_interface="in" units="mole_per_second_per_l_mito"/>
<variable name="J_C1" public_interface="in" units="mole_per_second_per_l_mito"/>
<variable name="W_x" public_interface="in" units="l_water_per_l_mito"/>
<variable name="t" public_interface="in" units="second"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>NADH_x</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci>J_DH</ci>
<ci>J_C1</ci>
</apply>
<ci>W_x</ci>
</apply>
</apply>
</math>
</component>
<component name="dQH2_dt">
<variable cmeta:id="dQH2_dt_QH2" initial_value="8e-4" name="QH2" public_interface="out" units="molar"/>
<variable name="J_C1" public_interface="in" units="mole_per_second_per_l_mito"/>
<variable name="J_C3" public_interface="in" units="mole_per_second_per_l_mito"/>
<variable name="W_x" public_interface="in" units="l_water_per_l_mito"/>
<variable name="t" public_interface="in" units="second"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>QH2</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci>J_C1</ci>
<ci>J_C3</ci>
</apply>
<ci>W_x</ci>
</apply>
</apply>
</math>
</component>
<component name="dCred_dt">
<variable initial_value="0.001" name="Cred" public_interface="out" units="molar"/>
<variable name="J_C3" public_interface="in" units="mole_per_second_per_l_mito"/>
<variable name="J_C4" public_interface="in" units="mole_per_second_per_l_mito"/>
<variable name="W_i" public_interface="in" units="l_water_per_l_mito"/>
<variable name="t" public_interface="in" units="second"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>Cred</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<times/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
<ci>J_C3</ci>
</apply>
<apply>
<times/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
<ci>J_C4</ci>
</apply>
</apply>
<ci>W_i</ci>
</apply>
</apply>
</math>
</component>
<component name="dATP_x_dt">
<variable initial_value="0" name="ATP_x" public_interface="out" units="molar"/>
<variable name="J_F1" public_interface="in" units="mole_per_second_per_l_mito"/>
<variable name="J_ANT" public_interface="in" units="mole_per_second_per_l_mito"/>
<variable name="W_x" public_interface="in" units="l_water_per_l_mito"/>
<variable name="t" public_interface="in" units="second"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>ATP_x</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci>J_F1</ci>
<ci>J_ANT</ci>
</apply>
<ci>W_x</ci>
</apply>
</apply>
</math>
</component>
<component name="dADP_x_dt">
<variable initial_value="0.01" name="ADP_x" public_interface="out" units="molar"/>
<variable name="J_F1" public_interface="in" units="mole_per_second_per_l_mito"/>
<variable name="J_ANT" public_interface="in" units="mole_per_second_per_l_mito"/>
<variable name="W_x" public_interface="in" units="l_water_per_l_mito"/>
<variable name="t" public_interface="in" units="second"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>ADP_x</ci>
</apply>
<apply>
<divide/>
<apply>
<plus/>
<apply>
<minus/>
<ci>J_F1</ci>
</apply>
<ci>J_ANT</ci>
</apply>
<ci>W_x</ci>
</apply>
</apply>
</math>
</component>
<component name="dATP_mx_dt">
<variable initial_value="0" name="ATP_mx" public_interface="out" units="molar"/>
<variable name="J_MgATPx" public_interface="in" units="mole_per_second_per_l_mito"/>
<variable name="W_x" public_interface="in" units="l_water_per_l_mito"/>
<variable name="t" public_interface="in" units="second"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>ATP_mx</ci>
</apply>
<apply>
<divide/>
<ci>J_MgATPx</ci>
<ci>W_x</ci>
</apply>
</apply>
</math>
</component>
<component name="dADP_mx_dt">
<variable initial_value="0" name="ADP_mx" public_interface="out" units="molar"/>
<variable name="J_MgADPx" public_interface="in" units="mole_per_second_per_l_mito"/>
<variable name="W_x" public_interface="in" units="l_water_per_l_mito"/>
<variable name="t" public_interface="in" units="second"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>ADP_mx</ci>
</apply>
<apply>
<divide/>
<ci>J_MgADPx</ci>
<ci>W_x</ci>
</apply>
</apply>
</math>
</component>
<component name="dPi_x_dt">
<variable initial_value="0.001" name="Pi_x" public_interface="out" units="molar"/>
<variable name="J_F1" public_interface="in" units="mole_per_second_per_l_mito"/>
<variable name="J_Pi1" public_interface="in" units="mole_per_second_per_l_mito"/>
<variable name="W_x" public_interface="in" units="l_water_per_l_mito"/>
<variable name="t" public_interface="in" units="second"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>Pi_x</ci>
</apply>
<apply>
<divide/>
<apply>
<plus/>
<apply>
<minus/>
<ci>J_F1</ci>
</apply>
<ci>J_Pi1</ci>
</apply>
<ci>W_x</ci>
</apply>
</apply>
</math>
</component>
<component name="dATP_i_dt">
<variable initial_value="0" name="ATP_i" public_interface="out" units="molar"/>
<variable name="J_ATP" public_interface="in" units="mole_per_second_per_l_mito"/>
<variable name="J_ANT" public_interface="in" units="mole_per_second_per_l_mito"/>
<variable name="J_AKi" public_interface="in" units="mole_per_second_per_l_mito"/>
<variable name="W_i" public_interface="in" units="l_water_per_l_mito"/>
<variable name="t" public_interface="in" units="second"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>ATP_i</ci>
</apply>
<apply>
<divide/>
<apply>
<plus/>
<ci>J_ATP</ci>
<ci>J_ANT</ci>
<ci>J_AKi</ci>
</apply>
<ci>W_i</ci>
</apply>
</apply>
</math>
</component>
<component name="dADP_i_dt">
<variable initial_value="0" name="ADP_i" public_interface="out" units="molar"/>
<variable name="J_ADP" public_interface="in" units="mole_per_second_per_l_mito"/>
<variable name="J_ANT" public_interface="in" units="mole_per_second_per_l_mito"/>
<variable name="J_AKi" public_interface="in" units="mole_per_second_per_l_mito"/>
<variable name="W_i" public_interface="in" units="l_water_per_l_mito"/>
<variable name="t" public_interface="in" units="second"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>ADP_i</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<minus/>
<ci>J_ADP</ci>
<ci>J_ANT</ci>
</apply>
<apply>
<times/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
<ci>J_AKi</ci>
</apply>
</apply>
<ci>W_i</ci>
</apply>
</apply>
</math>
</component>
<component name="dAMP_i_dt">
<variable initial_value="0" name="AMP_i" public_interface="out" units="molar"/>
<variable name="J_AMP" public_interface="in" units="mole_per_second_per_l_mito"/>
<variable name="J_AKi" public_interface="in" units="mole_per_second_per_l_mito"/>
<variable name="W_i" public_interface="in" units="l_water_per_l_mito"/>
<variable name="t" public_interface="in" units="second"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>AMP_i</ci>
</apply>
<apply>
<divide/>
<apply>
<plus/>
<ci>J_AMP</ci>
<ci>J_AKi</ci>
</apply>
<ci>W_i</ci>
</apply>
</apply>
</math>
</component>
<component name="dATP_mi_dt">
<variable initial_value="0" name="ATP_mi" public_interface="out" units="molar"/>
<variable name="J_MgATPi" public_interface="in" units="mole_per_second_per_l_mito"/>
<variable name="W_i" public_interface="in" units="l_water_per_l_mito"/>
<variable name="t" public_interface="in" units="second"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>ATP_mi</ci>
</apply>
<apply>
<divide/>
<ci>J_MgATPi</ci>
<ci>W_i</ci>
</apply>
</apply>
</math>
</component>
<component name="dADP_mi_dt">
<variable initial_value="0" name="ADP_mi" public_interface="out" units="molar"/>
<variable name="J_MgADPi" public_interface="in" units="mole_per_second_per_l_mito"/>
<variable name="W_i" public_interface="in" units="l_water_per_l_mito"/>
<variable name="t" public_interface="in" units="second"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>ADP_mi</ci>
</apply>
<apply>
<divide/>
<ci>J_MgADPi</ci>
<ci>W_i</ci>
</apply>
</apply>
</math>
</component>
<component name="dPi_i_dt">
<variable initial_value="0.001" name="Pi_i" public_interface="out" units="molar"/>
<variable name="J_Pi1" public_interface="in" units="mole_per_second_per_l_mito"/>
<variable name="J_Pi2" public_interface="in" units="mole_per_second_per_l_mito"/>
<variable name="W_i" public_interface="in" units="l_water_per_l_mito"/>
<variable name="t" public_interface="in" units="second"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>Pi_i</ci>
</apply>
<apply>
<divide/>
<apply>
<plus/>
<apply>
<minus/>
<ci>J_Pi1</ci>
</apply>
<ci>J_Pi2</ci>
</apply>
<ci>W_i</ci>
</apply>
</apply>
</math>
</component>
<component name="dPsi_dt">
<variable initial_value="160" name="dPsi" public_interface="out" units="millivolt"/>
<variable name="J_C1" public_interface="in" units="mole_per_second_per_l_mito"/>
<variable name="J_C3" public_interface="in" units="mole_per_second_per_l_mito"/>
<variable name="J_C4" public_interface="in" units="mole_per_second_per_l_mito"/>
<variable name="n_A" public_interface="in" units="dimensionless"/>
<variable name="J_F1" public_interface="in" units="mole_per_second_per_l_mito"/>
<variable name="J_ANT" public_interface="in" units="mole_per_second_per_l_mito"/>
<variable name="J_Hle" public_interface="in" units="mole_per_second_per_l_mito"/>
<variable name="J_K" public_interface="in" units="mole_per_second_per_l_mito"/>
<variable name="t" public_interface="in" units="second"/>
<variable initial_value="6.756756756756757e-6" name="C_im" units="mole_per_l_mito_per_millivolt"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>dPsi</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<times/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">4</cn>
<ci>J_C1</ci>
</apply>
<apply>
<times/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
<ci>J_C3</ci>
</apply>
<apply>
<times/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">4</cn>
<ci>J_C4</ci>
</apply>
</apply>
<apply>
<times/>
<ci>n_A</ci>
<ci>J_F1</ci>
</apply>
</apply>
<ci>J_ANT</ci>
</apply>
<ci>J_Hle</ci>
</apply>
<ci>J_K</ci>
</apply>
<ci>C_im</ci>
</apply>
</apply>
</math>
</component>
<component name="dO2_dt">
<variable initial_value="2.6e-5" name="O2" public_interface="out" units="molar"/>
<variable name="t" public_interface="in" units="second"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>O2</ci>
</apply>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="molar_per_second">0</cn>
</apply>
</math>
</component>
<connection>
<map_components component_1="dATP_x_dt" component_2="MgATPx_binding_flux"/>
<map_variables variable_1="ATP_x" variable_2="ATP_x"/>
</connection>
<connection>
<map_components component_1="dATP_mx_dt" component_2="MgATPx_binding_flux"/>
<map_variables variable_1="ATP_mx" variable_2="ATP_mx"/>
<map_variables variable_1="J_MgATPx" variable_2="J_MgATPx"/>
</connection>
<connection>
<map_components component_1="dADP_x_dt" component_2="MgADPx_binding_flux"/>
<map_variables variable_1="ADP_x" variable_2="ADP_x"/>
</connection>
<connection>
<map_components component_1="dADP_mx_dt" component_2="MgADPx_binding_flux"/>
<map_variables variable_1="ADP_mx" variable_2="ADP_mx"/>
<map_variables variable_1="J_MgADPx" variable_2="J_MgADPx"/>
</connection>
<connection>
<map_components component_1="dATP_i_dt" component_2="MgATPi_binding_flux"/>
<map_variables variable_1="ATP_i" variable_2="ATP_i"/>
</connection>
<connection>
<map_components component_1="dATP_mi_dt" component_2="MgATPi_binding_flux"/>
<map_variables variable_1="ATP_mi" variable_2="ATP_mi"/>
<map_variables variable_1="J_MgATPi" variable_2="J_MgATPi"/>
</connection>
<connection>
<map_components component_1="dADP_i_dt" component_2="MgADPi_binding_flux"/>
<map_variables variable_1="ADP_i" variable_2="ADP_i"/>
</connection>
<connection>
<map_components component_1="dADP_mi_dt" component_2="MgADPi_binding_flux"/>
<map_variables variable_1="ADP_mi" variable_2="ADP_mi"/>
<map_variables variable_1="J_MgADPi" variable_2="J_MgADPi"/>
</connection>
<connection>
<map_components component_1="Fixed_parameters" component_2="ADP_binding"/>
<map_variables variable_1="K_DD" variable_2="K_DD"/>
</connection>
<connection>
<map_components component_1="Environment" component_2="ADP_binding"/>
<map_variables variable_1="Mg_tot" variable_2="Mg_tot"/>
<map_variables variable_1="ADP_e" variable_2="ADP_e"/>
</connection>
<connection>
<map_components component_1="Environment" component_2="Mg_binding"/>
<map_variables variable_1="Mg_tot" variable_2="Mg_tot"/>
</connection>
<connection>
<map_components component_1="ADP_binding" component_2="Mg_binding"/>
<map_variables variable_1="ADP_me" variable_2="ADP_me"/>
</connection>
<connection>
<map_components component_1="Fixed_parameters" component_2="Proton_motive_force"/>
<map_variables variable_1="F" variable_2="F"/>
<map_variables variable_1="RT" variable_2="RT"/>
<map_variables variable_1="H_i" variable_2="H_i"/>
</connection>
<connection>
<map_components component_1="dPsi_dt" component_2="Proton_motive_force"/>
<map_variables variable_1="dPsi" variable_2="dPsi"/>
</connection>
<connection>
<map_components component_1="dH_x_dt" component_2="Proton_motive_force"/>
<map_variables variable_1="H_x" variable_2="H_x"/>
</connection>
<connection>
<map_components component_1="Fixed_parameters" component_2="Electron_flux_complex_I"/>
<map_variables variable_1="dG_C1o" variable_2="dG_C1o"/>
<map_variables variable_1="RT" variable_2="RT"/>
</connection>
<connection>
<map_components component_1="Adjustable_parameters" component_2="Electron_flux_complex_I"/>
<map_variables variable_1="x_C1" variable_2="x_C1"/>
</connection>
<connection>
<map_components component_1="Q_concentration" component_2="Electron_flux_complex_I"/>
<map_variables variable_1="Q" variable_2="Q"/>
</connection>
<connection>
<map_components component_1="dQH2_dt" component_2="Electron_flux_complex_I"/>
<map_variables variable_1="QH2" variable_2="QH2"/>
<map_variables variable_1="J_C1" variable_2="J_C1"/>
</connection>
<connection>
<map_components component_1="dH_x_dt" component_2="Electron_flux_complex_I"/>
<map_variables variable_1="H_x" variable_2="H_x"/>
<map_variables variable_1="J_C1" variable_2="J_C1"/>
</connection>
<connection>
<map_components component_1="dNADH_x_dt" component_2="Electron_flux_complex_I"/>
<map_variables variable_1="NADH_x" variable_2="NADH_x"/>
<map_variables variable_1="J_C1" variable_2="J_C1"/>
</connection>
<connection>
<map_components component_1="NAD_x_concentration" component_2="Electron_flux_complex_I"/>
<map_variables variable_1="NAD_x" variable_2="NAD_x"/>
</connection>
<connection>
<map_components component_1="Proton_motive_force" component_2="Electron_flux_complex_I"/>
<map_variables variable_1="dG_H" variable_2="dG_H"/>
</connection>
<connection>
<map_components component_1="dH_x_dt" component_2="Electron_flux_complex_III"/>
<map_variables variable_1="H_x" variable_2="H_x"/>
<map_variables variable_1="J_C3" variable_2="J_C3"/>
</connection>
<connection>
<map_components component_1="Q_concentration" component_2="Electron_flux_complex_III"/>
<map_variables variable_1="Q" variable_2="Q"/>
</connection>
<connection>
<map_components component_1="dQH2_dt" component_2="Electron_flux_complex_III"/>
<map_variables variable_1="QH2" variable_2="QH2"/>
<map_variables variable_1="J_C3" variable_2="J_C3"/>
</connection>
<connection>
<map_components component_1="dPi_x_dt" component_2="Electron_flux_complex_III"/>
<map_variables variable_1="Pi_x" variable_2="Pi_x"/>
</connection>
<connection>
<map_components component_1="Cox_concentration" component_2="Electron_flux_complex_III"/>
<map_variables variable_1="Cox" variable_2="Cox"/>
</connection>
<connection>
<map_components component_1="dCred_dt" component_2="Electron_flux_complex_III"/>
<map_variables variable_1="Cred" variable_2="Cred"/>
<map_variables variable_1="J_C3" variable_2="J_C3"/>
</connection>
<connection>
<map_components component_1="Adjustable_parameters" component_2="Electron_flux_complex_III"/>
<map_variables variable_1="k_Pi3" variable_2="k_Pi3"/>
<map_variables variable_1="k_Pi4" variable_2="k_Pi4"/>
<map_variables variable_1="x_C3" variable_2="x_C3"/>
</connection>
<connection>
<map_components component_1="Fixed_parameters" component_2="Electron_flux_complex_III"/>
<map_variables variable_1="dG_C3o" variable_2="dG_C3o"/>
<map_variables variable_1="F" variable_2="F"/>
<map_variables variable_1="RT" variable_2="RT"/>
</connection>
<connection>
<map_components component_1="Fixed_parameters" component_2="Electron_flux_complex_IV"/>
<map_variables variable_1="dG_C4o" variable_2="dG_C4o"/>
<map_variables variable_1="F" variable_2="F"/>
<map_variables variable_1="RT" variable_2="RT"/>
<map_variables variable_1="Ctot" variable_2="Ctot"/>
</connection>
<connection>
<map_components component_1="Adjustable_parameters" component_2="Electron_flux_complex_IV"/>
<map_variables variable_1="k_O2" variable_2="k_O2"/>
<map_variables variable_1="x_C4" variable_2="x_C4"/>
</connection>
<connection>
<map_components component_1="dH_x_dt" component_2="Electron_flux_complex_IV"/>
<map_variables variable_1="H_x" variable_2="H_x"/>
<map_variables variable_1="J_C4" variable_2="J_C4"/>
</connection>
<connection>
<map_components component_1="dO2_dt" component_2="Electron_flux_complex_IV"/>
<map_variables variable_1="O2" variable_2="O2"/>
</connection>
<connection>
<map_components component_1="dCred_dt" component_2="Electron_flux_complex_IV"/>
<map_variables variable_1="Cred" variable_2="Cred"/>
<map_variables variable_1="J_C4" variable_2="J_C4"/>
</connection>
<connection>
<map_components component_1="Cox_concentration" component_2="Electron_flux_complex_IV"/>
<map_variables variable_1="Cox" variable_2="Cox"/>
</connection>
<connection>
<map_components component_1="dPsi_dt" component_2="Electron_flux_complex_IV"/>
<map_variables variable_1="dPsi" variable_2="dPsi"/>
<map_variables variable_1="J_C4" variable_2="J_C4"/>
</connection>
<connection>
<map_components component_1="Adjustable_parameters" component_2="ATP_synthesis_flux"/>
<map_variables variable_1="x_F1" variable_2="x_F1"/>
</connection>
<connection>
<map_components component_1="Fixed_parameters" component_2="ATP_synthesis_flux"/>
<map_variables variable_1="K_DD" variable_2="K_DD"/>
<map_variables variable_1="K_DT" variable_2="K_DT"/>
<map_variables variable_1="RT" variable_2="RT"/>
<map_variables variable_1="n_A" variable_2="n_A"/>
<map_variables variable_1="dG_F1o" variable_2="dG_F1o"/>
</connection>
<connection>
<map_components component_1="Proton_motive_force" component_2="ATP_synthesis_flux"/>
<map_variables variable_1="dG_H" variable_2="dG_H"/>
</connection>
<connection>
<map_components component_1="dADP_mx_dt" component_2="ATP_synthesis_flux"/>
<map_variables variable_1="ADP_mx" variable_2="ADP_mx"/>
</connection>
<connection>
<map_components component_1="dATP_mx_dt" component_2="ATP_synthesis_flux"/>
<map_variables variable_1="ATP_mx" variable_2="ATP_mx"/>
</connection>
<connection>
<map_components component_1="dPi_x_dt" component_2="ATP_synthesis_flux"/>
<map_variables variable_1="Pi_x" variable_2="Pi_x"/>
<map_variables variable_1="J_F1" variable_2="J_F1"/>
</connection>
<connection>
<map_components component_1="Adjustable_parameters" component_2="Dehydrogenase_flux"/>
<map_variables variable_1="x_DH" variable_2="x_DH"/>
<map_variables variable_1="k_Pi1" variable_2="k_Pi1"/>
<map_variables variable_1="k_Pi2" variable_2="k_Pi2"/>
<map_variables variable_1="r" variable_2="r"/>
</connection>
<connection>
<map_components component_1="Dehydrogenase_flux" component_2="NAD_x_concentration"/>
<map_variables variable_1="NAD_x" variable_2="NAD_x"/>
</connection>
<connection>
<map_components component_1="dNADH_x_dt" component_2="Dehydrogenase_flux"/>
<map_variables variable_1="NADH_x" variable_2="NADH_x"/>
<map_variables variable_1="J_DH" variable_2="J_DH"/>
</connection>
<connection>
<map_components component_1="dPi_x_dt" component_2="Dehydrogenase_flux"/>
<map_variables variable_1="Pi_x" variable_2="Pi_x"/>
</connection>
<connection>
<map_components component_1="Adjustable_parameters" component_2="ANT_flux"/>
<map_variables variable_1="x_ANT" variable_2="x_ANT"/>
<map_variables variable_1="k_mADP" variable_2="k_mADP"/>
</connection>
<connection>
<map_components component_1="Fixed_parameters" component_2="ANT_flux"/>
<map_variables variable_1="F" variable_2="F"/>
<map_variables variable_1="RT" variable_2="RT"/>
</connection>
<connection>
<map_components component_1="MgATPx_binding_flux" component_2="ANT_flux"/>
<map_variables variable_1="ATP_fx" variable_2="ATP_fx"/>
</connection>
<connection>
<map_components component_1="MgADPx_binding_flux" component_2="ANT_flux"/>
<map_variables variable_1="ADP_fx" variable_2="ADP_fx"/>
</connection>
<connection>
<map_components component_1="MgATPi_binding_flux" component_2="ANT_flux"/>
<map_variables variable_1="ATP_fi" variable_2="ATP_fi"/>
</connection>
<connection>
<map_components component_1="MgADPi_binding_flux" component_2="ANT_flux"/>
<map_variables variable_1="ADP_fi" variable_2="ADP_fi"/>
</connection>
<connection>
<map_components component_1="dPsi_dt" component_2="ANT_flux"/>
<map_variables variable_1="dPsi" variable_2="dPsi"/>
<map_variables variable_1="J_ANT" variable_2="J_ANT"/>
</connection>
<connection>
<map_components component_1="dH_x_dt" component_2="Phosphate_hydrogen_cotransporter_flux"/>
<map_variables variable_1="H_x" variable_2="H_x"/>
<map_variables variable_1="J_Pi1" variable_2="J_Pi1"/>
</connection>
<connection>
<map_components component_1="dPi_i_dt" component_2="Phosphate_hydrogen_cotransporter_flux"/>
<map_variables variable_1="Pi_i" variable_2="Pi_i"/>
<map_variables variable_1="J_Pi1" variable_2="J_Pi1"/>
</connection>
<connection>
<map_components component_1="dPi_x_dt" component_2="Phosphate_hydrogen_cotransporter_flux"/>
<map_variables variable_1="Pi_x" variable_2="Pi_x"/>
<map_variables variable_1="J_Pi1" variable_2="J_Pi1"/>
</connection>
<connection>
<map_components component_1="Fixed_parameters" component_2="Phosphate_hydrogen_cotransporter_flux"/>
<map_variables variable_1="H_i" variable_2="H_i"/>
<map_variables variable_1="k_dHPi" variable_2="k_dHPi"/>
</connection>
<connection>
<map_components component_1="Adjustable_parameters" component_2="Phosphate_hydrogen_cotransporter_flux"/>
<map_variables variable_1="x_Pi1" variable_2="x_Pi1"/>
<map_variables variable_1="k_PiH" variable_2="k_PiH"/>
</connection>
<connection>
<map_components component_1="Adjustable_parameters" component_2="Hydrogen_leak_flux"/>
<map_variables variable_1="x_Hle" variable_2="x_Hle"/>
</connection>
<connection>
<map_components component_1="Fixed_parameters" component_2="Hydrogen_leak_flux"/>
<map_variables variable_1="F" variable_2="F"/>
<map_variables variable_1="H_i" variable_2="H_i"/>
<map_variables variable_1="RT" variable_2="RT"/>
</connection>
<connection>
<map_components component_1="dPsi_dt" component_2="Hydrogen_leak_flux"/>
<map_variables variable_1="dPsi" variable_2="dPsi"/>
<map_variables variable_1="J_Hle" variable_2="J_Hle"/>
</connection>
<connection>
<map_components component_1="dH_x_dt" component_2="Hydrogen_leak_flux"/>
<map_variables variable_1="H_x" variable_2="H_x"/>
<map_variables variable_1="J_Hle" variable_2="J_Hle"/>
</connection>
<connection>
<map_components component_1="Fixed_parameters" component_2="Potassium_hydrogen_flux"/>
<map_variables variable_1="K_i" variable_2="K_i"/>
<map_variables variable_1="H_i" variable_2="H_i"/>
</connection>
<connection>
<map_components component_1="Adjustable_parameters" component_2="Potassium_hydrogen_flux"/>
<map_variables variable_1="x_KH" variable_2="x_KH"/>
</connection>
<connection>
<map_components component_1="dK_x_dt" component_2="Potassium_hydrogen_flux"/>
<map_variables variable_1="K_x" variable_2="K_x"/>
<map_variables variable_1="J_KH" variable_2="J_KH"/>
</connection>
<connection>
<map_components component_1="dH_x_dt" component_2="Potassium_hydrogen_flux"/>
<map_variables variable_1="H_x" variable_2="H_x"/>
<map_variables variable_1="J_KH" variable_2="J_KH"/>
</connection>
<connection>
<map_components component_1="Fixed_parameters" component_2="Passive_potassium_flux"/>
<map_variables variable_1="K_i" variable_2="K_i"/>
<map_variables variable_1="F" variable_2="F"/>
<map_variables variable_1="RT" variable_2="RT"/>
</connection>
<connection>
<map_components component_1="Adjustable_parameters" component_2="Passive_potassium_flux"/>
<map_variables variable_1="x_K" variable_2="x_K"/>
</connection>
<connection>
<map_components component_1="dPsi_dt" component_2="Passive_potassium_flux"/>
<map_variables variable_1="dPsi" variable_2="dPsi"/>
<map_variables variable_1="J_K" variable_2="J_K"/>
</connection>
<connection>
<map_components component_1="dK_x_dt" component_2="Passive_potassium_flux"/>
<map_variables variable_1="K_x" variable_2="K_x"/>
<map_variables variable_1="J_K" variable_2="J_K"/>
</connection>
<connection>
<map_components component_1="Fixed_parameters" component_2="Adenylate_kinase_flux"/>
<map_variables variable_1="K_AK" variable_2="K_AK"/>
</connection>
<connection>
<map_components component_1="Adenylate_kinase_flux" component_2="Adjustable_parameters"/>
<map_variables variable_1="x_AK" variable_2="x_AK"/>
</connection>
<connection>
<map_components component_1="dADP_i_dt" component_2="Adenylate_kinase_flux"/>
<map_variables variable_1="ADP_i" variable_2="ADP_i"/>
<map_variables variable_1="J_AKi" variable_2="J_AKi"/>
</connection>
<connection>
<map_components component_1="dAMP_i_dt" component_2="Adenylate_kinase_flux"/>
<map_variables variable_1="AMP_i" variable_2="AMP_i"/>
<map_variables variable_1="J_AKi" variable_2="J_AKi"/>
</connection>
<connection>
<map_components component_1="dATP_i_dt" component_2="Adenylate_kinase_flux"/>
<map_variables variable_1="ATP_i" variable_2="ATP_i"/>
<map_variables variable_1="J_AKi" variable_2="J_AKi"/>
</connection>
<connection>
<map_components component_1="Fixed_parameters" component_2="AMP_substrate_flux"/>
<map_variables variable_1="AMP_e" variable_2="AMP_e"/>
<map_variables variable_1="gamma" variable_2="gamma"/>
</connection>
<connection>
<map_components component_1="Adjustable_parameters" component_2="AMP_substrate_flux"/>
<map_variables variable_1="p_A" variable_2="p_A"/>
</connection>
<connection>
<map_components component_1="dAMP_i_dt" component_2="AMP_substrate_flux"/>
<map_variables variable_1="AMP_i" variable_2="AMP_i"/>
<map_variables variable_1="J_AMP" variable_2="J_AMP"/>
</connection>
<connection>
<map_components component_1="Fixed_parameters" component_2="ADP_substrate_flux"/>
<map_variables variable_1="gamma" variable_2="gamma"/>
</connection>
<connection>
<map_components component_1="Environment" component_2="ADP_substrate_flux"/>
<map_variables variable_1="ADP_e" variable_2="ADP_e"/>
</connection>
<connection>
<map_components component_1="Adjustable_parameters" component_2="ADP_substrate_flux"/>
<map_variables variable_1="p_A" variable_2="p_A"/>
</connection>
<connection>
<map_components component_1="dADP_i_dt" component_2="ADP_substrate_flux"/>
<map_variables variable_1="ADP_i" variable_2="ADP_i"/>
<map_variables variable_1="J_ADP" variable_2="J_ADP"/>
</connection>
<connection>
<map_components component_1="Fixed_parameters" component_2="ATP_substrate_flux"/>
<map_variables variable_1="ATP_e" variable_2="ATP_e"/>
<map_variables variable_1="gamma" variable_2="gamma"/>
</connection>
<connection>
<map_components component_1="dATP_i_dt" component_2="ATP_substrate_flux"/>
<map_variables variable_1="ATP_i" variable_2="ATP_i"/>
<map_variables variable_1="J_ATP" variable_2="J_ATP"/>
</connection>
<connection>
<map_components component_1="Environment" component_2="Pi_substrate_flux"/>
<map_variables variable_1="Pi_e" variable_2="Pi_e"/>
</connection>
<connection>
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