- Author:
- pmr2.import <nobody@models.cellml.org>
- Date:
- 2006-07-09 07:48:39+12:00
- Desc:
- committing version01 of beard_2005
- Permanent Source URI:
- http://models.cellml.org/workspace/beard_2005/rawfile/18f4302c9a31b8d7d9cc2783c86e6565681a2223/beard_2005.cellml
<?xml version='1.0' encoding='utf-8'?>
<model xmlns="http://www.cellml.org/cellml/1.0#" xmlns:cmeta="http://www.cellml.org/metadata/1.0#" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:bqs="http://www.cellml.org/bqs/1.0#" xmlns:cellml="http://www.cellml.org/cellml/1.0#" xmlns:dcterms="http://purl.org/dc/terms/" xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" cmeta:id="beard_model_2005" name="beard_model_2005">
<documentation xmlns="http://cellml.org/tmp-documentation">
<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>Bioengineering Institute, The University of Auckland</shortaffil>
</affiliation>
</author>
</articleinfo>
<section id="sec_status">
<title>Model Status</title>
<para>
This is the original version of the model imported from the previous
CellML model repository, 24-Jan-2006. This version is known to run in PCEnv.
</para>
</section>
<sect1 id="sec_structure">
<title>Model Structure</title>
<para>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 complete original paper reference is cited below:
</para>
<para>
<ulink url="http://compbiol.plosjournals.org/perlserv/?request=get-document&doi=10.1371/journal.pcbi.0010036">A Biophysical Model of the Mitochondrial Respiratory System and Oxidative Phosphorylation</ulink>, Daniel A. Beard, 2005, <ulink url="http://compbiol.plosjournals.org/">
<emphasis>PLoS Computational Biology</emphasis>
</ulink>, 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>
</sect1>
</article>
</documentation>
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<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 units="molar" public_interface="out" private_interface="none" name="ATP_mx" initial_value="0.0"/>
<variable units="dimensionless" public_interface="in" private_interface="none" name="J_MgATPx"/>
<variable units="dimensionless" public_interface="in" private_interface="none" name="W_x"/>
<variable units="millisecond" public_interface="in" private_interface="none" name="t"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="ATP_mx_diff_Eqn">
<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 units="molar" public_interface="out" private_interface="none" name="ADP_mx" initial_value="0.0"/>
<variable units="dimensionless" public_interface="in" private_interface="none" name="J_MgADPx"/>
<variable units="dimensionless" public_interface="in" private_interface="none" name="W_x"/>
<variable units="millisecond" public_interface="in" private_interface="none" name="t"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="ADP_mx_diff_Eqn">
<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 units="molar" public_interface="out" private_interface="none" name="Pi_x" initial_value="0.0010"/>
<variable units="dimensionless" public_interface="in" private_interface="none" name="J_F1"/>
<variable units="dimensionless" public_interface="in" private_interface="none" name="J_Pi1"/>
<variable units="dimensionless" public_interface="in" private_interface="none" name="W_x"/>
<variable units="millisecond" public_interface="in" private_interface="none" name="t"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="Pi_x_diff_Eqn">
<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 units="molar" public_interface="out" private_interface="none" name="ATP_i" initial_value="0.0"/>
<variable units="dimensionless" public_interface="in" private_interface="none" name="J_ATP"/>
<variable units="dimensionless" public_interface="in" private_interface="none" name="J_ANT"/>
<variable units="dimensionless" public_interface="in" private_interface="none" name="J_AKi"/>
<variable units="dimensionless" public_interface="in" private_interface="none" name="W_i"/>
<variable units="millisecond" public_interface="in" private_interface="none" name="t"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="ATP_i_diff_Eqn">
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>ATP_i</ci>
</apply>
<apply>
<divide/>
<apply>
<plus/>
<apply>
<plus/>
<ci> J_ATP </ci>
<ci> J_ANT </ci>
</apply>
<ci> J_AKi </ci>
</apply>
<ci> W_i </ci>
</apply>
</apply>
</math>
</component>
<component name="dADP_i_dt">
<variable units="molar" public_interface="out" private_interface="none" name="ADP_i" initial_value="0.0"/>
<variable units="dimensionless" public_interface="in" private_interface="none" name="J_ADP"/>
<variable units="dimensionless" public_interface="in" private_interface="none" name="J_ANT"/>
<variable units="dimensionless" public_interface="in" private_interface="none" name="J_AKi"/>
<variable units="dimensionless" public_interface="in" private_interface="none" name="W_i"/>
<variable units="millisecond" public_interface="in" private_interface="none" name="t"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="ADP_i_diff_Eqn">
<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 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 units="molar" public_interface="out" private_interface="none" name="AMP_i" initial_value="0.0"/>
<variable units="dimensionless" public_interface="in" private_interface="none" name="J_AMP"/>
<variable units="dimensionless" public_interface="in" private_interface="none" name="J_AKi"/>
<variable units="dimensionless" public_interface="in" private_interface="none" name="W_i"/>
<variable units="millisecond" public_interface="in" private_interface="none" name="t"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="AMP_i_diff_Eqn">
<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 units="molar" public_interface="out" private_interface="none" name="ATP_mi" initial_value="0.0"/>
<variable units="dimensionless" public_interface="in" private_interface="none" name="J_MgATPi"/>
<variable units="dimensionless" public_interface="in" private_interface="none" name="W_i"/>
<variable units="millisecond" public_interface="in" private_interface="none" name="t"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="ATP_mi_diff_Eqn">
<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 units="molar" public_interface="out" private_interface="none" name="ADP_mi" initial_value="0.0"/>
<variable units="dimensionless" public_interface="in" private_interface="none" name="J_MgADPi"/>
<variable units="dimensionless" public_interface="in" private_interface="none" name="W_i"/>
<variable units="millisecond" public_interface="in" private_interface="none" name="t"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="ADP_mi_diff_Eqn">
<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 units="molar" public_interface="out" private_interface="none" name="Pi_i" initial_value="0.0010"/>
<variable units="dimensionless" public_interface="in" private_interface="none" name="J_Pi1"/>
<variable units="dimensionless" public_interface="in" private_interface="none" name="J_Pi2"/>
<variable units="dimensionless" public_interface="in" private_interface="none" name="W_i"/>
<variable units="millisecond" public_interface="in" private_interface="none" name="t"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="Pi_i_diff_Eqn">
<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 units="millivolt" public_interface="out" private_interface="none" name="dPsi" initial_value="160.0"/>
<variable units="dimensionless" public_interface="in" private_interface="none" name="J_C1"/>
<variable units="dimensionless" public_interface="in" private_interface="none" name="J_C3"/>
<variable units="dimensionless" public_interface="in" private_interface="none" name="J_C4"/>
<variable units="dimensionless" public_interface="in" private_interface="none" name="n_A"/>
<variable units="dimensionless" public_interface="in" private_interface="none" name="J_F1"/>
<variable units="dimensionless" public_interface="in" private_interface="none" name="J_ANT"/>
<variable units="dimensionless" public_interface="in" private_interface="none" name="J_Hle"/>
<variable units="dimensionless" public_interface="in" private_interface="none" name="J_K"/>
<variable units="millisecond" public_interface="in" private_interface="none" name="t"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="dPsi_diff_Eqn">
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>dPsi</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless"> 1.48e5 </cn>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 4 </cn>
<ci> J_C1 </ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless"> 2 </cn>
<ci> J_C3 </ci>
</apply>
</apply>
<apply>
<times/>
<cn 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>
</apply>
</apply>
</math>
</component>
<component name="dO2_dt">
<variable units="molar" public_interface="out" private_interface="none" name="O2" initial_value="2.6E-5"/>
<variable units="millisecond" public_interface="in" private_interface="none" name="t"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="O2_diff_Eqn">
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>O2</ci>
</apply>
<cn cellml:units="dimensionless"> 0 </cn>
</apply>
</math>
</component>
<component name="Electron_flux_complex_I">
<variable units="dimensionless" public_interface="out" private_interface="none" name="J_C1"/>
<variable units="mole_per_second_per_litre_mito" public_interface="in" private_interface="none" name="x_C1"/>
<variable units="dimensionless" public_interface="none" private_interface="none" name="dG_C1op"/>
<variable units="kilojoule_per_mole" public_interface="in" private_interface="none" name="dG_C1o"/>
<variable units="molar" public_interface="in" private_interface="none" name="NADH_x"/>
<variable units="dimensionless" public_interface="in" private_interface="none" name="NAD_x"/>
<variable units="dimensionless" public_interface="in" private_interface="none" name="dG_H"/>
<variable units="kilojoule_per_mole" public_interface="in" private_interface="none" name="RT"/>
<variable units="molar" public_interface="in" private_interface="none" name="Q"/>
<variable units="molar" public_interface="in" private_interface="none" name="QH2"/>
<variable units="molar" public_interface="in" private_interface="none" name="H_x"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="dG_C1op_Eqn">
<eq/>
<ci> dG_C1op </ci>
<apply>
<minus/>
<apply>
<minus/>
<ci> dG_C1o </ci>
<apply>
<times/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 1 </cn>
<ci> RT </ci>
</apply>
<apply>
<ln/>
<apply>
<divide/>
<ci> H_x </ci>
<cn cellml:units="dimensionless"> 1e-7 </cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci> RT </ci>
<apply>
<ln/>
<apply>
<divide/>
<ci> Q </ci>
<ci> QH2 </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="J_C1_Eqn">
<eq/>
<ci> J_C1 </ci>
<apply>
<times/>
<ci> x_C1 </ci>
<apply>
<minus/>
<apply>
<times/>
<apply>
<exp/>
<apply>
<minus/>
<apply>
<divide/>
<apply>
<plus/>
<ci> dG_C1op </ci>
<apply>
<times/>
<cn cellml:units="dimensionless"> 4 </cn>
<ci> dG_H </ci>
</apply>
</apply>
<ci> RT </ci>
</apply>
</apply>
</apply>
<ci> NADH_x </ci>
</apply>
<ci> NAD_x </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="Proton_motive_energy">
<variable units="dimensionless" public_interface="out" private_interface="none" name="dG_H"/>
<variable units="kilojoule_per_mole_per_millivolt" public_interface="in" private_interface="none" name="F"/>
<variable units="millivolt" public_interface="in" private_interface="none" name="dPsi"/>
<variable units="kilojoule_per_mole" public_interface="in" private_interface="none" name="RT"/>
<variable units="dimensionless" public_interface="in" private_interface="none" name="H_i"/>
<variable units="molar" public_interface="in" private_interface="none" name="H_x"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="dG_H_Eqn">
<eq/>
<ci> dG_H </ci>
<apply>
<plus/>
<apply>
<times/>
<ci> F </ci>
<ci> dPsi </ci>
</apply>
<apply>
<times/>
<ci> RT </ci>
<apply>
<ln/>
<apply>
<divide/>
<ci> H_i </ci>
<ci> H_x </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="Electron_flux_complex_III">
<variable units="dimensionless" public_interface="out" private_interface="none" name="J_C3"/>
<variable units="molar" public_interface="in" private_interface="none" name="k_Pi3"/>
<variable units="molar" public_interface="in" private_interface="none" name="k_Pi4"/>
<variable units="mole_per_second_per_litre_mito" public_interface="in" private_interface="none" name="x_C3"/>
<variable units="dimensionless" public_interface="none" private_interface="none" name="dG_C3op"/>
<variable units="kilojoule_per_mole" public_interface="in" private_interface="none" name="dG_C3o"/>
<variable units="dimensionless" public_interface="in" private_interface="none" name="dG_H"/>
<variable units="kilojoule_per_mole" public_interface="in" private_interface="none" name="RT"/>
<variable units="kilojoule_per_mole_per_millivolt" public_interface="in" private_interface="none" name="F"/>
<variable units="millivolt" public_interface="in" private_interface="none" name="dPsi"/>
<variable units="dimensionless" public_interface="in" private_interface="none" name="Cox"/>
<variable units="molar" public_interface="in" private_interface="none" name="Cred"/>
<variable units="molar" public_interface="in" private_interface="none" name="Q"/>
<variable units="molar" public_interface="in" private_interface="none" name="QH2"/>
<variable units="molar" public_interface="in" private_interface="none" name="H_x"/>
<variable units="molar" public_interface="in" private_interface="none" name="Pi_x"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="dG_C3op_Eqn">
<eq/>
<ci> dG_C3op </ci>
<apply>
<minus/>
<apply>
<plus/>
<ci> dG_C3o </ci>
<apply>
<times/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 2 </cn>
<ci> RT </ci>
</apply>
<apply>
<ln/>
<apply>
<divide/>
<ci> H_x </ci>
<cn cellml:units="dimensionless"> 1e-7 </cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci> RT </ci>
<apply>
<ln/>
<apply>
<divide/>
<ci> QH2 </ci>
<ci> Q </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="J_C3_Eqn">
<eq/>
<ci> J_C3 </ci>
<apply>
<times/>
<apply>
<times/>
<ci> x_C3 </ci>
<apply>
<divide/>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1 </cn>
<apply>
<divide/>
<ci> Pi_x </ci>
<ci> k_Pi3 </ci>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1 </cn>
<apply>
<divide/>
<ci> Pi_x </ci>
<ci> k_Pi4 </ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<minus/>
<apply>
<times/>
<apply>
<exp/>
<apply>
<minus/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<plus/>
<ci> dG_C3op </ci>
<apply>
<times/>
<cn cellml:units="dimensionless"> 4 </cn>
<ci> dG_H </ci>
</apply>
</apply>
<apply>
<times/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 2 </cn>
<ci> F </ci>
</apply>
<ci> dPsi </ci>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless"> 2 </cn>
<ci> RT </ci>
</apply>
</apply>
</apply>
</apply>
<ci> Cox </ci>
</apply>
<ci> Cred </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="Electron_flux_complex_IV">
<variable units="dimensionless" public_interface="out" private_interface="none" name="J_C4"/>
<variable units="molar" public_interface="in" private_interface="none" name="k_O2"/>
<variable units="mole_per_second_per_litre_mito" public_interface="in" private_interface="none" name="x_C4"/>
<variable units="dimensionless" public_interface="none" private_interface="none" name="dG_C4op"/>
<variable units="kilojoule_per_mole" public_interface="in" private_interface="none" name="dG_C4o"/>
<variable units="molar" public_interface="in" private_interface="none" name="Cred"/>
<variable units="molar" public_interface="in" private_interface="none" name="Ctot"/>
<variable units="molar" public_interface="in" private_interface="none" name="O2"/>
<variable units="dimensionless" public_interface="in" private_interface="none" name="dG_H"/>
<variable units="kilojoule_per_mole" public_interface="in" private_interface="none" name="RT"/>
<variable units="dimensionless" public_interface="in" private_interface="none" name="Cox"/>
<variable units="kilojoule_per_mole_per_millivolt" public_interface="in" private_interface="none" name="F"/>
<variable units="millivolt" public_interface="in" private_interface="none" name="dPsi"/>
<variable units="molar" public_interface="in" private_interface="none" name="H_x"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="dG_C4op_Eqn">
<eq/>
<ci> dG_C4op </ci>
<apply>
<minus/>
<apply>
<minus/>
<ci> dG_C4o </ci>
<apply>
<times/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 2 </cn>
<ci> RT </ci>
</apply>
<apply>
<ln/>
<apply>
<divide/>
<ci> H_x </ci>
<cn cellml:units="dimensionless"> 1e-7 </cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<times/>
<apply>
<divide/>
<ci> RT </ci>
<cn cellml:units="dimensionless"> 2 </cn>
</apply>
<apply>
<ln/>
<ci> O2 </ci>
</apply>
</apply>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="J_C4_Eqn">
<eq/>
<ci> J_C4 </ci>
<apply>
<times/>
<apply>
<times/>
<apply>
<times/>
<ci> x_C4 </ci>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1 </cn>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1 </cn>
<apply>
<divide/>
<ci> k_O2 </ci>
<ci> O2 </ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<divide/>
<ci> Cred </ci>
<ci> Ctot </ci>
</apply>
</apply>
<apply>
<minus/>
<apply>
<times/>
<apply>
<exp/>
<apply>
<minus/>
<apply>
<divide/>
<apply>
<plus/>
<ci> dG_C4op </ci>
<apply>
<times/>
<cn cellml:units="dimensionless"> 2 </cn>
<ci> dG_H </ci>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless"> 2 </cn>
<ci> RT </ci>
</apply>
</apply>
</apply>
</apply>
<ci> Cred </ci>
</apply>
<apply>
<times/>
<ci> Cox </ci>
<apply>
<exp/>
<apply>
<times/>
<ci> F </ci>
<apply>
<divide/>
<ci> dPsi </ci>
<ci> RT </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="ATP_synthesis_flux">
<variable units="dimensionless" public_interface="out" private_interface="none" name="J_F1"/>
<variable units="mole_per_second_per_litre_mito" public_interface="in" private_interface="none" name="x_F1"/>
<variable units="kilojoule_per_mole" public_interface="in" private_interface="none" name="dG_F1o"/>
<variable units="molar" public_interface="in" private_interface="none" name="K_DD"/>
<variable units="molar" public_interface="in" private_interface="none" name="K_DT"/>
<variable units="kilojoule_per_mole" public_interface="in" private_interface="none" name="RT"/>
<variable units="dimensionless" public_interface="in" private_interface="none" name="n_A"/>
<variable units="dimensionless" public_interface="in" private_interface="none" name="dG_H"/>
<variable units="molar" public_interface="in" private_interface="none" name="ADP_mx"/>
<variable units="molar" public_interface="in" private_interface="none" name="Pi_x"/>
<variable units="molar" public_interface="in" private_interface="none" name="ATP_mx"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="J_F1_Eqn">
<eq/>
<ci> J_F1 </ci>
<apply>
<times/>
<ci> x_F1 </ci>
<apply>
<minus/>
<apply>
<times/>
<apply>
<times/>
<apply>
<times/>
<apply>
<exp/>
<apply>
<minus/>
<apply>
<divide/>
<apply>
<minus/>
<ci> dG_F1o </ci>
<apply>
<times/>
<ci> n_A </ci>
<ci> dG_H </ci>
</apply>
</apply>
<ci> RT </ci>
</apply>
</apply>
</apply>
<apply>
<divide/>
<ci> K_DD </ci>
<ci> K_DT </ci>
</apply>
</apply>
<ci> ADP_mx </ci>
</apply>
<ci> Pi_x </ci>
</apply>
<ci> ATP_mx </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="MgATPx_binding_flux">
<variable units="dimensionless" public_interface="out" private_interface="none" name="J_MgATPx"/>
<variable units="dimensionless" public_interface="out" private_interface="none" name="ATP_fx"/>
<variable units="mole_per_second_per_litre_mito" public_interface="in" private_interface="none" name="x_MgA"/>
<variable units="molar" public_interface="in" private_interface="none" name="ATP_x"/>
<variable units="molar" public_interface="in" private_interface="none" name="ATP_mx"/>
<variable units="molar" public_interface="in" private_interface="none" name="Mg_x"/>
<variable units="molar" public_interface="in" private_interface="none" name="K_DT"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="ATP_fx_Eqn">
<eq/>
<ci> ATP_fx </ci>
<apply>
<minus/>
<ci> ATP_x </ci>
<ci> ATP_mx </ci>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="J_MgATPx_Eqn">
<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 units="dimensionless" public_interface="out" private_interface="none" name="J_MgADPx"/>
<variable units="dimensionless" public_interface="out" private_interface="none" name="ADP_fx"/>
<variable units="molar" public_interface="in" private_interface="none" name="ADP_x"/>
<variable units="molar" public_interface="in" private_interface="none" name="ADP_mx"/>
<variable units="mole_per_second_per_litre_mito" public_interface="in" private_interface="none" name="x_MgA"/>
<variable units="molar" public_interface="in" private_interface="none" name="K_DD"/>
<variable units="molar" public_interface="in" private_interface="none" name="Mg_x"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="ADP_fx_Eqn">
<eq/>
<ci> ADP_fx </ci>
<apply>
<minus/>
<ci> ADP_x </ci>
<ci> ADP_mx </ci>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="J_MgADPx_Eqn">
<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 units="dimensionless" public_interface="out" private_interface="none" name="J_MgATPi"/>
<variable units="dimensionless" public_interface="out" private_interface="none" name="ATP_fi"/>
<variable units="molar" public_interface="in" private_interface="none" name="ATP_i"/>
<variable units="molar" public_interface="in" private_interface="none" name="ATP_mi"/>
<variable units="mole_per_second_per_litre_mito" public_interface="in" private_interface="none" name="x_MgA"/>
<variable units="molar" public_interface="in" private_interface="none" name="K_DT"/>
<variable units="dimensionless" public_interface="in" private_interface="none" name="Mg_i"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="ATP_fi_Eqn">
<eq/>
<ci> ATP_fi </ci>
<apply>
<minus/>
<ci> ATP_i </ci>
<ci> ATP_mi </ci>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="J_MgATPi_Eqn">
<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 units="dimensionless" public_interface="out" private_interface="none" name="J_MgADPi"/>
<variable units="dimensionless" public_interface="out" private_interface="none" name="ADP_fi"/>
<variable units="molar" public_interface="in" private_interface="none" name="ADP_i"/>
<variable units="molar" public_interface="in" private_interface="none" name="ADP_mi"/>
<variable units="mole_per_second_per_litre_mito" public_interface="in" private_interface="none" name="x_MgA"/>
<variable units="molar" public_interface="in" private_interface="none" name="K_DD"/>
<variable units="dimensionless" public_interface="in" private_interface="none" name="Mg_i"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="ADP_fi_Eqn">
<eq/>
<ci> ADP_fi </ci>
<apply>
<minus/>
<ci> ADP_i </ci>
<ci> ADP_mi </ci>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="J_MgADPi_Eqn">
<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 units="dimensionless" public_interface="out" private_interface="none" name="J_ATP"/>
<variable units="molar" public_interface="in" private_interface="none" name="ATP_e"/>
<variable units="per_micron" public_interface="in" private_interface="none" name="gamma"/>
<variable units="micron_per_second" public_interface="in" private_interface="none" name="x_A"/>
<variable units="molar" public_interface="in" private_interface="none" name="ATP_i"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="J_ATP_Eqn">
<eq/>
<ci> J_ATP </ci>
<apply>
<times/>
<apply>
<times/>
<ci> gamma </ci>
<ci> x_A </ci>
</apply>
<apply>
<minus/>
<ci> ATP_e </ci>
<ci> ATP_i </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="ADP_substrate_flux">
<variable units="dimensionless" public_interface="out" private_interface="none" name="J_ADP"/>
<variable units="per_micron" public_interface="in" private_interface="none" name="gamma"/>
<variable units="micron_per_second" public_interface="in" private_interface="none" name="x_A"/>
<variable units="dimensionless" public_interface="in" private_interface="none" name="ADP_e"/>
<variable units="molar" public_interface="in" private_interface="none" name="ADP_i"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="J_ADP_Eqn">
<eq/>
<ci> J_ADP </ci>
<apply>
<times/>
<apply>
<times/>
<ci> gamma </ci>
<ci> x_A </ci>
</apply>
<apply>
<minus/>
<ci> ADP_e </ci>
<ci> ADP_i </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="AMP_substrate_flux">
<variable units="dimensionless" public_interface="out" private_interface="none" name="J_AMP"/>
<variable units="molar" public_interface="in" private_interface="none" name="AMP_e"/>
<variable units="per_micron" public_interface="in" private_interface="none" name="gamma"/>
<variable units="micron_per_second" public_interface="in" private_interface="none" name="x_A"/>
<variable units="molar" public_interface="in" private_interface="none" name="AMP_i"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="J_AMP_Eqn">
<eq/>
<ci> J_AMP </ci>
<apply>
<times/>
<apply>
<times/>
<ci> gamma </ci>
<ci> x_A </ci>
</apply>
<apply>
<minus/>
<ci> AMP_e </ci>
<ci> AMP_i </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="Pi_substrate_flux">
<variable units="dimensionless" public_interface="out" private_interface="none" name="J_Pi2"/>
<variable units="micron_per_second" public_interface="in" private_interface="none" name="x_Pi2"/>
<variable units="per_micron" public_interface="in" private_interface="none" name="gamma"/>
<variable units="dimensionless" public_interface="in" private_interface="none" name="Pi_e"/>
<variable units="molar" public_interface="in" private_interface="none" name="Pi_i"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="J_Pi2_Eqn">
<eq/>
<ci> J_Pi2 </ci>
<apply>
<times/>
<apply>
<times/>
<ci> gamma </ci>
<ci> x_Pi2 </ci>
</apply>
<apply>
<minus/>
<ci> Pi_e </ci>
<ci> Pi_i </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="ANT_flux">
<variable units="dimensionless" public_interface="out" private_interface="none" name="J_ANT"/>
<variable units="dimensionless" public_interface="out" private_interface="none" name="Psi_x"/>
<variable units="dimensionless" public_interface="out" private_interface="none" name="Psi_i"/>
<variable units="mole_per_second_per_litre_mito" public_interface="in" private_interface="none" name="x_ANT"/>
<variable units="dimensionless" public_interface="in" private_interface="none" name="ADP_fi"/>
<variable units="dimensionless" public_interface="in" private_interface="none" name="ATP_fi"/>
<variable units="kilojoule_per_mole_per_millivolt" public_interface="in" private_interface="none" name="F"/>
<variable units="kilojoule_per_mole" public_interface="in" private_interface="none" name="RT"/>
<variable units="millivolt" public_interface="in" private_interface="none" name="dPsi"/>
<variable units="dimensionless" public_interface="in" private_interface="none" name="ADP_fx"/>
<variable units="dimensionless" public_interface="in" private_interface="none" name="ATP_fx"/>
<variable units="molar" public_interface="in" private_interface="none" name="k_mADP"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="Psi_x_Eqn">
<eq/>
<ci> Psi_x </ci>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 0.65 </cn>
</apply>
<ci> dPsi </ci>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="Psi_i_Eqn">
<eq/>
<ci> Psi_i </ci>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.35 </cn>
<ci> dPsi </ci>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="J_ANT_Eqn">
<eq/>
<ci> J_ANT </ci>
<piecewise>
<piece>
<apply>
<times/>
<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>
<times/>
<apply>
<minus/>
<ci> F </ci>
</apply>
<apply>
<divide/>
<ci> Psi_i </ci>
<ci> RT </ci>
</apply>
</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>
<times/>
<apply>
<minus/>
<ci> F </ci>
</apply>
<apply>
<divide/>
<ci> Psi_x </ci>
<ci> RT </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<divide/>
<ci> ADP_fi </ci>
<apply>
<plus/>
<ci> ADP_fi </ci>
<ci> k_mADP </ci>
</apply>
</apply>
</apply>
<apply>
<or/>
<apply>
<gt/>
<ci>ADP_fi</ci>
<cn cellml:units="dimensionless"> 1E-12 </cn>
</apply>
<apply>
<gt/>
<ci>ATP_fi</ci>
<cn cellml:units="dimensionless"> 1E-12 </cn>
</apply>
</apply>
</piece>
<otherwise>
<cn cellml:units="dimensionless"> 0 </cn>
</otherwise>
</piecewise>
</apply>
</math>
</component>
<component name="Phosphate_hydrogen_cotransporter_flux">
<variable units="dimensionless" public_interface="out" private_interface="none" name="J_Pi1"/>
<variable units="dimensionless" public_interface="out" private_interface="none" name="H2PIi"/>
<variable units="dimensionless" public_interface="out" private_interface="none" name="H2PIx"/>
<variable units="molar" public_interface="in" private_interface="none" name="Pi_i"/>
<variable units="dimensionless" public_interface="in" private_interface="none" name="H_i"/>
<variable units="molar" public_interface="in" private_interface="none" name="k_dHPi"/>
<variable units="molar" public_interface="in" private_interface="none" name="Pi_x"/>
<variable units="molar" public_interface="in" private_interface="none" name="H_x"/>
<variable units="mole_per_second_per_litre_mito" public_interface="in" private_interface="none" name="x_Pi1"/>
<variable units="molar" public_interface="in" private_interface="none" name="k_PiH"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="H2PIi_Eqn">
<eq/>
<ci> H2PIi </ci>
<apply>
<times/>
<ci> Pi_i </ci>
<apply>
<divide/>
<ci> H_i </ci>
<apply>
<plus/>
<ci> H_i </ci>
<ci> k_dHPi </ci>
</apply>
</apply>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="H2PIx_Eqn">
<eq/>
<ci> H2PIx </ci>
<apply>
<times/>
<ci> Pi_x </ci>
<apply>
<divide/>
<ci> H_x </ci>
<apply>
<plus/>
<ci> H_x </ci>
<ci> k_dHPi </ci>
</apply>
</apply>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="J_Pi1_Eqn">
<eq/>
<ci> J_Pi1 </ci>
<apply>
<times/>
<ci> x_Pi1 </ci>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<times/>
<ci> H_x </ci>
<ci> H2PIi </ci>
</apply>
<apply>
<times/>
<ci> H_i </ci>
<ci> H2PIx </ci>
</apply>
</apply>
<apply>
<plus/>
<ci> H2PIi </ci>
<ci> k_PiH </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="Adenylate_kinase_flux">
<variable units="dimensionless" public_interface="out" private_interface="none" name="J_AKi"/>
<variable units="mole_per_second_per_litre_mito" public_interface="in" private_interface="none" name="x_AK"/>
<variable units="dimensionless" public_interface="in" private_interface="none" name="K_AK"/>
<variable units="molar" public_interface="in" private_interface="none" name="ADP_i"/>
<variable units="molar" public_interface="in" private_interface="none" name="AMP_i"/>
<variable units="molar" public_interface="in" private_interface="none" name="ATP_i"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="J_AKi_Eqn">
<eq/>
<ci> J_AKi </ci>
<apply>
<times/>
<ci> x_AK </ci>
<apply>
<minus/>
<apply>
<times/>
<apply>
<times/>
<ci> K_AK </ci>
<ci> ADP_i </ci>
</apply>
<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 units="dimensionless" public_interface="out" private_interface="none" name="J_Hle"/>
<variable units="mole_per_second_per_litre_mito" public_interface="in" private_interface="none" name="x_Hle"/>
<variable units="millivolt" public_interface="in" private_interface="none" name="dPsi"/>
<variable units="dimensionless" public_interface="in" private_interface="none" name="H_i"/>
<variable units="kilojoule_per_mole_per_millivolt" public_interface="in" private_interface="none" name="F"/>
<variable units="kilojoule_per_mole" public_interface="in" private_interface="none" name="RT"/>
<variable units="molar" public_interface="in" private_interface="none" name="H_x"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="J_Hle_Eqn">
<eq/>
<ci> J_Hle </ci>
<apply>
<times/>
<apply>
<times/>
<ci> x_Hle </ci>
<ci> dPsi </ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<times/>
<ci> H_i </ci>
<apply>
<exp/>
<apply>
<times/>
<ci> F </ci>
<apply>
<divide/>
<ci> dPsi </ci>
<ci> RT </ci>
</apply>
</apply>
</apply>
</apply>
<ci> H_x </ci>
</apply>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<times/>
<ci> F </ci>
<apply>
<divide/>
<ci> dPsi </ci>
<ci> RT </ci>
</apply>
</apply>
</apply>
<cn cellml:units="dimensionless"> 1 </cn>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="Passive_potassium_flux">
<variable units="dimensionless" public_interface="out" private_interface="none" name="J_K"/>
<variable units="mole_per_second_per_litre_mito" public_interface="in" private_interface="none" name="x_K"/>
<variable units="millivolt" public_interface="in" private_interface="none" name="dPsi"/>
<variable units="dimensionless" public_interface="in" private_interface="none" name="K_i"/>
<variable units="kilojoule_per_mole_per_millivolt" public_interface="in" private_interface="none" name="F"/>
<variable units="kilojoule_per_mole" public_interface="in" private_interface="none" name="RT"/>
<variable units="molar" public_interface="in" private_interface="none" name="K_x"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="J_K_Eqn">
<eq/>
<ci> J_K </ci>
<apply>
<times/>
<apply>
<times/>
<ci> x_K </ci>
<ci> dPsi </ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<times/>
<ci> K_i </ci>
<apply>
<exp/>
<apply>
<times/>
<ci> F </ci>
<apply>
<divide/>
<ci> dPsi </ci>
<ci> RT </ci>
</apply>
</apply>
</apply>
</apply>
<ci> K_x </ci>
</apply>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<times/>
<ci> F </ci>
<apply>
<divide/>
<ci> dPsi </ci>
<ci> RT </ci>
</apply>
</apply>
</apply>
<cn cellml:units="dimensionless"> 1 </cn>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="Potassium_hydrogen_flux">
<variable units="dimensionless" public_interface="out" private_interface="none" name="J_KH"/>
<variable units="mole_per_second_per_litre_mito" public_interface="in" private_interface="none" name="x_KH"/>
<variable units="dimensionless" public_interface="in" private_interface="none" name="K_i"/>
<variable units="molar" public_interface="in" private_interface="none" name="K_x"/>
<variable units="dimensionless" public_interface="in" private_interface="none" name="H_i"/>
<variable units="molar" public_interface="in" private_interface="none" name="H_x"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="J_KH_Eqn">
<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 units="dimensionless" public_interface="out" private_interface="none" name="NAD_x"/>
<variable units="molar" public_interface="in" private_interface="none" name="NADH_x"/>
<variable units="molar" public_interface="in" private_interface="none" name="NADtot"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="NAD_x_Eqn">
<eq/>
<ci> NAD_x </ci>
<apply>
<minus/>
<ci> NADtot </ci>
<ci> NADH_x </ci>
</apply>
</apply>
</math>
</component>
<component name="Q_concentration">
<variable units="molar" public_interface="out" private_interface="none" name="Q"/>
<variable units="molar" public_interface="in" private_interface="none" name="Qtot"/>
<variable units="molar" public_interface="in" private_interface="none" name="QH2"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="Q_Eqn">
<eq/>
<ci> Q </ci>
<apply>
<minus/>
<ci> Qtot </ci>
<ci> QH2 </ci>
</apply>
</apply>
</math>
</component>
<component name="Cox_concentration">
<variable units="dimensionless" public_interface="out" private_interface="none" name="Cox"/>
<variable units="molar" public_interface="in" private_interface="none" name="Ctot"/>
<variable units="molar" public_interface="in" private_interface="none" name="Cred"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="Cox_Eqn">
<eq/>
<ci> Cox </ci>
<apply>
<minus/>
<ci> Ctot </ci>
<ci> Cred </ci>
</apply>
</apply>
</math>
</component>
<component name="ADP_binding">
<variable units="dimensionless" public_interface="out" private_interface="none" name="ADP_me"/>
<variable units="dimensionless" public_interface="out" private_interface="none" name="ADP_fe"/>
<variable units="dimensionless" public_interface="in" private_interface="none" name="ADP_e"/>
<variable units="molar" public_interface="in" private_interface="none" name="K_DD"/>
<variable units="dimensionless" public_interface="in" private_interface="none" name="Mg_tot"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="ADP_fe_Eqn">
<eq/>
<ci> ADP_fe </ci>
<apply>
<minus/>
<ci> ADP_e </ci>
<ci> ADP_me </ci>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="ADP_me_Eqn">
<eq/>
<ci> ADP_me </ci>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<plus/>
<ci> K_DD </ci>
<ci> ADP_e </ci>
</apply>
<ci> Mg_tot </ci>
</apply>
<apply>
<power/>
<apply>
<minus/>
<apply>
<power/>
<apply>
<plus/>
<apply>
<plus/>
<ci> K_DD </ci>
<ci> ADP_e </ci>
</apply>
<ci> Mg_tot </ci>
</apply>
<cn cellml:units="dimensionless"> 2 </cn>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless"> 4 </cn>
<apply>
<times/>
<ci> Mg_tot </ci>
<ci> ADP_e </ci>
</apply>
</apply>
</apply>
<cn cellml:units="dimensionless"> 0.5 </cn>
</apply>
</apply>
<cn cellml:units="dimensionless"> 2 </cn>
</apply>
</apply>
</math>
</component>
<component name="Mg_binding">
<variable units="dimensionless" public_interface="out" private_interface="none" name="Mg_e"/>
<variable units="dimensionless" public_interface="in" private_interface="none" name="Mg_tot"/>
<variable units="dimensionless" public_interface="out" private_interface="none" name="Mg_i"/>
<variable units="dimensionless" public_interface="in" private_interface="none" name="ADP_me"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="Mg_e_Eqn">
<eq/>
<ci> Mg_e </ci>
<apply>
<minus/>
<ci> Mg_tot </ci>
<ci> ADP_me </ci>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="Mg_i_Eqn">
<eq/>
<ci> Mg_i </ci>
<ci> Mg_e </ci>
</apply>
</math>
</component>
<connection>
<map_components component_2="MgATPx_binding_flux" component_1="dATP_x_dt"/>
<map_variables variable_2="ATP_x" variable_1="ATP_x"/>
</connection>
<connection>
<map_components component_2="MgATPx_binding_flux" component_1="dATP_mx_dt"/>
<map_variables variable_2="ATP_mx" variable_1="ATP_mx"/>
<map_variables variable_2="J_MgATPx" variable_1="J_MgATPx"/>
</connection>
<connection>
<map_components component_2="MgADPx_binding_flux" component_1="dADP_x_dt"/>
<map_variables variable_2="ADP_x" variable_1="ADP_x"/>
</connection>
<connection>
<map_components component_2="MgADPx_binding_flux" component_1="dADP_mx_dt"/>
<map_variables variable_2="ADP_mx" variable_1="ADP_mx"/>
<map_variables variable_2="J_MgADPx" variable_1="J_MgADPx"/>
</connection>
<connection>
<map_components component_2="MgATPi_binding_flux" component_1="dATP_i_dt"/>
<map_variables variable_2="ATP_i" variable_1="ATP_i"/>
</connection>
<connection>
<map_components component_2="MgATPi_binding_flux" component_1="dATP_mi_dt"/>
<map_variables variable_2="ATP_mi" variable_1="ATP_mi"/>
<map_variables variable_2="J_MgATPi" variable_1="J_MgATPi"/>
</connection>
<connection>
<map_components component_2="MgADPi_binding_flux" component_1="dADP_i_dt"/>
<map_variables variable_2="ADP_i" variable_1="ADP_i"/>
</connection>
<connection>
<map_components component_2="MgADPi_binding_flux" component_1="dADP_mi_dt"/>
<map_variables variable_2="ADP_mi" variable_1="ADP_mi"/>
<map_variables variable_2="J_MgADPi" variable_1="J_MgADPi"/>
</connection>
<connection>
<map_components component_2="ADP_binding" component_1="Fixed_parameters"/>
<map_variables variable_2="K_DD" variable_1="K_DD"/>
</connection>
<connection>
<map_components component_2="ADP_binding" component_1="Environment"/>
<map_variables variable_2="Mg_tot" variable_1="Mg_tot"/>
<map_variables variable_2="ADP_e" variable_1="ADP_e"/>
</connection>
<connection>
<map_components component_2="Mg_binding" component_1="Environment"/>
<map_variables variable_2="Mg_tot" variable_1="Mg_tot"/>
</connection>
<connection>
<map_components component_2="Mg_binding" component_1="ADP_binding"/>
<map_variables variable_2="ADP_me" variable_1="ADP_me"/>
</connection>
<connection>
<map_components component_2="Proton_motive_energy" component_1="Fixed_parameters"/>
<map_variables variable_2="F" variable_1="F"/>
<map_variables variable_2="RT" variable_1="RT"/>
<map_variables variable_2="H_i" variable_1="H_i"/>
</connection>
<connection>
<map_components component_2="Proton_motive_energy" component_1="dPsi_dt"/>
<map_variables variable_2="dPsi" variable_1="dPsi"/>
</connection>
<connection>
<map_components component_2="Proton_motive_energy" component_1="dH_x_dt"/>
<map_variables variable_2="H_x" variable_1="H_x"/>
</connection>
<connection>
<map_components component_2="Electron_flux_complex_I" component_1="Fixed_parameters"/>
<map_variables variable_2="dG_C1o" variable_1="dG_C1o"/>
<map_variables variable_2="RT" variable_1="RT"/>
</connection>
<connection>
<map_components component_2="Electron_flux_complex_I" component_1="Adjustable_parameters"/>
<map_variables variable_2="x_C1" variable_1="x_C1"/>
</connection>
<connection>
<map_components component_2="Electron_flux_complex_I" component_1="Q_concentration"/>
<map_variables variable_2="Q" variable_1="Q"/>
</connection>
<connection>
<map_components component_2="Electron_flux_complex_I" component_1="dQH2_dt"/>
<map_variables variable_2="QH2" variable_1="QH2"/>
<map_variables variable_2="J_C1" variable_1="J_C1"/>
</connection>
<connection>
<map_components component_2="Electron_flux_complex_I" component_1="dH_x_dt"/>
<map_variables variable_2="H_x" variable_1="H_x"/>
<map_variables variable_2="J_C1" variable_1="J_C1"/>
</connection>
<connection>
<map_components component_2="Electron_flux_complex_I" component_1="dNADH_x_dt"/>
<map_variables variable_2="NADH_x" variable_1="NADH_x"/>
<map_variables variable_2="J_C1" variable_1="J_C1"/>
</connection>
<connection>
<map_components component_2="Electron_flux_complex_I" component_1="NAD_x_concentration"/>
<map_variables variable_2="NAD_x" variable_1="NAD_x"/>
</connection>
<connection>
<map_components component_2="Electron_flux_complex_I" component_1="Proton_motive_energy"/>
<map_variables variable_2="dG_H" variable_1="dG_H"/>
</connection>
<connection>
<map_components component_2="Electron_flux_complex_III" component_1="dH_x_dt"/>
<map_variables variable_2="H_x" variable_1="H_x"/>
<map_variables variable_2="J_C3" variable_1="J_C3"/>
</connection>
<connection>
<map_components component_2="Electron_flux_complex_III" component_1="Q_concentration"/>
<map_variables variable_2="Q" variable_1="Q"/>
</connection>
<connection>
<map_components component_2="Electron_flux_complex_III" component_1="dQH2_dt"/>
<map_variables variable_2="QH2" variable_1="QH2"/>
<map_variables variable_2="J_C3" variable_1="J_C3"/>
</connection>
<connection>
<map_components component_2="Electron_flux_complex_III" component_1="dPi_x_dt"/>
<map_variables variable_2="Pi_x" variable_1="Pi_x"/>
</connection>
<connection>
<map_components component_2="Electron_flux_complex_III" component_1="Cox_concentration"/>
<map_variables variable_2="Cox" variable_1="Cox"/>
</connection>
<connection>
<map_components component_2="Electron_flux_complex_III" component_1="dCred_dt"/>
<map_variables variable_2="Cred" variable_1="Cred"/>
<map_variables variable_2="J_C3" variable_1="J_C3"/>
</connection>
<connection>
<map_components component_2="Electron_flux_complex_III" component_1="Adjustable_parameters"/>
<map_variables variable_2="k_Pi3" variable_1="k_Pi3"/>
<map_variables variable_2="k_Pi4" variable_1="k_Pi4"/>
<map_variables variable_2="x_C3" variable_1="x_C3"/>
</connection>
<connection>
<map_components component_2="Electron_flux_complex_III" component_1="Fixed_parameters"/>
<map_variables variable_2="dG_C3o" variable_1="dG_C3o"/>
<map_variables variable_2="F" variable_1="F"/>
<map_variables variable_2="RT" variable_1="RT"/>
</connection>
<connection>
<map_components component_2="Electron_flux_complex_IV" component_1="Fixed_parameters"/>
<map_variables variable_2="dG_C4o" variable_1="dG_C4o"/>
<map_variables variable_2="F" variable_1="F"/>
<map_variables variable_2="RT" variable_1="RT"/>
<map_variables variable_2="Ctot" variable_1="Ctot"/>
</connection>
<connection>
<map_components component_2="Electron_flux_complex_IV" component_1="Adjustable_parameters"/>
<map_variables variable_2="k_O2" variable_1="k_O2"/>
<map_variables variable_2="x_C4" variable_1="x_C4"/>
</connection>
<connection>
<map_components component_2="Electron_flux_complex_IV" component_1="dH_x_dt"/>
<map_variables variable_2="H_x" variable_1="H_x"/>
<map_variables variable_2="J_C4" variable_1="J_C4"/>
</connection>
<connection>
<map_components component_2="Electron_flux_complex_IV" component_1="dO2_dt"/>
<map_variables variable_2="O2" variable_1="O2"/>
</connection>
<connection>
<map_components component_2="Electron_flux_complex_IV" component_1="dCred_dt"/>
<map_variables variable_2="Cred" variable_1="Cred"/>
<map_variables variable_2="J_C4" variable_1="J_C4"/>
</connection>
<connection>
<map_components component_2="Electron_flux_complex_IV" component_1="Cox_concentration"/>
<map_variables variable_2="Cox" variable_1="Cox"/>
</connection>
<connection>
<map_components component_2="Electron_flux_complex_IV" component_1="dPsi_dt"/>
<map_variables variable_2="dPsi" variable_1="dPsi"/>
<map_variables variable_2="J_C4" variable_1="J_C4"/>
</connection>
<connection>
<map_components component_2="ATP_synthesis_flux" component_1="Adjustable_parameters"/>
<map_variables variable_2="x_F1" variable_1="x_F1"/>
</connection>
<connection>
<map_components component_2="ATP_synthesis_flux" component_1="Fixed_parameters"/>
<map_variables variable_2="K_DD" variable_1="K_DD"/>
<map_variables variable_2="K_DT" variable_1="K_DT"/>
<map_variables variable_2="RT" variable_1="RT"/>
<map_variables variable_2="n_A" variable_1="n_A"/>
<map_variables variable_2="dG_F1o" variable_1="dG_F1o"/>
</connection>
<connection>
<map_components component_2="ATP_synthesis_flux" component_1="Proton_motive_energy"/>
<map_variables variable_2="dG_H" variable_1="dG_H"/>
</connection>
<connection>
<map_components component_2="ATP_synthesis_flux" component_1="dADP_mx_dt"/>
<map_variables variable_2="ADP_mx" variable_1="ADP_mx"/>
</connection>
<connection>
<map_components component_2="ATP_synthesis_flux" component_1="dATP_mx_dt"/>
<map_variables variable_2="ATP_mx" variable_1="ATP_mx"/>
</connection>
<connection>
<map_components component_2="ATP_synthesis_flux" component_1="dPi_x_dt"/>
<map_variables variable_2="Pi_x" variable_1="Pi_x"/>
<map_variables variable_2="J_F1" variable_1="J_F1"/>
</connection>
<connection>
<map_components component_2="Dehydrogenase_flux" component_1="Adjustable_parameters"/>
<map_variables variable_2="x_DH" variable_1="x_DH"/>
<map_variables variable_2="k_Pi1" variable_1="k_Pi1"/>
<map_variables variable_2="k_Pi2" variable_1="k_Pi2"/>
<map_variables variable_2="r" variable_1="r"/>
</connection>
<connection>
<map_components component_2="NAD_x_concentration" component_1="Dehydrogenase_flux"/>
<map_variables variable_2="NAD_x" variable_1="NAD_x"/>
</connection>
<connection>
<map_components component_2="Dehydrogenase_flux" component_1="dNADH_x_dt"/>
<map_variables variable_2="NADH_x" variable_1="NADH_x"/>
<map_variables variable_2="J_DH" variable_1="J_DH"/>
</connection>
<connection>
<map_components component_2="Dehydrogenase_flux" component_1="dPi_x_dt"/>
<map_variables variable_2="Pi_x" variable_1="Pi_x"/>
</connection>
<connection>
<map_components component_2="ANT_flux" component_1="Adjustable_parameters"/>
<map_variables variable_2="x_ANT" variable_1="x_ANT"/>
<map_variables variable_2="k_mADP" variable_1="k_mADP"/>
</connection>
<connection>
<map_components component_2="ANT_flux" component_1="Fixed_parameters"/>
<map_variables variable_2="F" variable_1="F"/>
<map_variables variable_2="RT" variable_1="RT"/>
</connection>
<connection>
<map_components component_2="ANT_flux" component_1="MgATPx_binding_flux"/>
<map_variables variable_2="ATP_fx" variable_1="ATP_fx"/>
</connection>
<connection>
<map_components component_2="ANT_flux" component_1="MgADPx_binding_flux"/>
<map_variables variable_2="ADP_fx" variable_1="ADP_fx"/>
</connection>
<connection>
<map_components component_2="ANT_flux" component_1="MgATPi_binding_flux"/>
<map_variables variable_2="ATP_fi" variable_1="ATP_fi"/>
</connection>
<connection>
<map_components component_2="ANT_flux" component_1="MgADPi_binding_flux"/>
<map_variables variable_2="ADP_fi" variable_1="ADP_fi"/>
</connection>
<connection>
<map_components component_2="ANT_flux" component_1="dPsi_dt"/>
<map_variables variable_2="dPsi" variable_1="dPsi"/>
<map_variables variable_2="J_ANT" variable_1="J_ANT"/>
</connection>
<connection>
<map_components component_2="Phosphate_hydrogen_cotransporter_flux" component_1="dH_x_dt"/>
<map_variables variable_2="H_x" variable_1="H_x"/>
<map_variables variable_2="J_Pi1" variable_1="J_Pi1"/>
</connection>
<connection>
<map_components component_2="Phosphate_hydrogen_cotransporter_flux" component_1="dPi_i_dt"/>
<map_variables variable_2="Pi_i" variable_1="Pi_i"/>
<map_variables variable_2="J_Pi1" variable_1="J_Pi1"/>
</connection>
<connection>
<map_components component_2="Phosphate_hydrogen_cotransporter_flux" component_1="dPi_x_dt"/>
<map_variables variable_2="Pi_x" variable_1="Pi_x"/>
<map_variables variable_2="J_Pi1" variable_1="J_Pi1"/>
</connection>
<connection>
<map_components component_2="Phosphate_hydrogen_cotransporter_flux" component_1="Fixed_parameters"/>
<map_variables variable_2="H_i" variable_1="H_i"/>
<map_variables variable_2="k_dHPi" variable_1="k_dHPi"/>
</connection>
<connection>
<map_components component_2="Phosphate_hydrogen_cotransporter_flux" component_1="Adjustable_parameters"/>
<map_variables variable_2="x_Pi1" variable_1="x_Pi1"/>
<map_variables variable_2="k_PiH" variable_1="k_PiH"/>
</connection>
<connection>
<map_components component_2="Hydrogen_leak_flux" component_1="Adjustable_parameters"/>
<map_variables variable_2="x_Hle" variable_1="x_Hle"/>
</connection>
<connection>
<map_components component_2="Hydrogen_leak_flux" component_1="Fixed_parameters"/>
<map_variables variable_2="F" variable_1="F"/>
<map_variables variable_2="H_i" variable_1="H_i"/>
<map_variables variable_2="RT" variable_1="RT"/>
</connection>
<connection>
<map_components component_2="Hydrogen_leak_flux" component_1="dPsi_dt"/>
<map_variables variable_2="dPsi" variable_1="dPsi"/>
<map_variables variable_2="J_Hle" variable_1="J_Hle"/>
</connection>
<connection>
<map_components component_2="Hydrogen_leak_flux" component_1="dH_x_dt"/>
<map_variables variable_2="H_x" variable_1="H_x"/>
<map_variables variable_2="J_Hle" variable_1="J_Hle"/>
</connection>
<connection>
<map_components component_2="Potassium_hydrogen_flux" component_1="Fixed_parameters"/>
<map_variables variable_2="K_i" variable_1="K_i"/>
<map_variables variable_2="H_i" variable_1="H_i"/>
</connection>
<connection>
<map_components component_2="Potassium_hydrogen_flux" component_1="Adjustable_parameters"/>
<map_variables variable_2="x_KH" variable_1="x_KH"/>
</connection>
<connection>
<map_components component_2="Potassium_hydrogen_flux" component_1="dK_x_dt"/>
<map_variables variable_2="K_x" variable_1="K_x"/>
<map_variables variable_2="J_KH" variable_1="J_KH"/>
</connection>
<connection>
<map_components component_2="Potassium_hydrogen_flux" component_1="dH_x_dt"/>
<map_variables variable_2="H_x" variable_1="H_x"/>
<map_variables variable_2="J_KH" variable_1="J_KH"/>
</connection>
<connection>
<map_components component_2="Passive_potassium_flux" component_1="Fixed_parameters"/>
<map_variables variable_2="K_i" variable_1="K_i"/>
<map_variables variable_2="F" variable_1="F"/>
<map_variables variable_2="RT" variable_1="RT"/>
</connection>
<connection>
<map_components component_2="Passive_potassium_flux" component_1="Adjustable_parameters"/>
<map_variables variable_2="x_K" variable_1="x_K"/>
</connection>
<connection>
<map_components component_2="Passive_potassium_flux" component_1="dPsi_dt"/>
<map_variables variable_2="dPsi" variable_1="dPsi"/>
<map_variables variable_2="J_K" variable_1="J_K"/>
</connection>
<connection>
<map_components component_2="Passive_potassium_flux" component_1="dK_x_dt"/>
<map_variables variable_2="K_x" variable_1="K_x"/>
<map_variables variable_2="J_K" variable_1="J_K"/>
</connection>
<connection>
<map_components component_2="Adenylate_kinase_flux" component_1="Fixed_parameters"/>
<map_variables variable_2="K_AK" variable_1="K_AK"/>
</connection>
<connection>
<map_components component_2="Adjustable_parameters" component_1="Adenylate_kinase_flux"/>
<map_variables variable_2="x_AK" variable_1="x_AK"/>
</connection>
<connection>
<map_components component_2="Adenylate_kinase_flux" component_1="dADP_i_dt"/>
<map_variables variable_2="ADP_i" variable_1="ADP_i"/>
<map_variables variable_2="J_AKi" variable_1="J_AKi"/>
</connection>
<connection>
<map_components component_2="Adenylate_kinase_flux" component_1="dAMP_i_dt"/>
<map_variables variable_2="AMP_i" variable_1="AMP_i"/>
<map_variables variable_2="J_AKi" variable_1="J_AKi"/>
</connection>
<connection>
<map_components component_2="Adenylate_kinase_flux" component_1="dATP_i_dt"/>
<map_variables variable_2="ATP_i" variable_1="ATP_i"/>
<map_variables variable_2="J_AKi" variable_1="J_AKi"/>
</connection>
<connection>
<map_components component_2="AMP_substrate_flux" component_1="Fixed_parameters"/>
<map_variables variable_2="AMP_e" variable_1="AMP_e"/>
<map_variables variable_2="gamma" variable_1="gamma"/>
</connection>
<connection>
<map_components component_2="AMP_substrate_flux" component_1="Adjustable_parameters"/>
<map_variables variable_2="x_A" variable_1="x_A"/>
</connection>
<connection>
<map_components component_2="AMP_substrate_flux" component_1="dAMP_i_dt"/>
<map_variables variable_2="AMP_i" variable_1="AMP_i"/>
<map_variables variable_2="J_AMP" variable_1="J_AMP"/>
</connection>
<connection>
<map_components component_2="ADP_substrate_flux" component_1="Fixed_parameters"/>
<map_variables variable_2="gamma" variable_1="gamma"/>
</connection>
<connection>
<map_components component_2="ADP_substrate_flux" component_1="Environment"/>
<map_variables variable_2="ADP_e" variable_1="ADP_e"/>
</connection>
<connection>
<map_components component_2="ADP_substrate_flux" component_1="Adjustable_parameters"/>
<map_variables variable_2="x_A" variable_1="x_A"/>
</connection>
<connection>
<map_components component_2="ADP_substrate_flux" component_1="dADP_i_dt"/>
<map_variables variable_2="ADP_i" variable_1="ADP_i"/>
<map_variables variable_2="J_ADP" variable_1="J_ADP"/>
</connection>
<connection>
<map_components component_2="ATP_substrate_flux" component_1="Fixed_parameters"/>
<map_variables variable_2="ATP_e" variable_1="ATP_e"/>
<map_variables variable_2="gamma" variable_1="gamma"/>
</connection>
<connection>
<map_components component_2="ATP_substrate_flux" component_1="dATP_i_dt"/>
<map_variables variable_2="ATP_i" variable_1="ATP_i"/>
<map_variables variable_2="J_ATP" variable_1="J_ATP"/>
</connection>
<connection>
<map_components component_2="Pi_substrate_flux" component_1="Environment"/>
<map_variables variable_2="Pi_e" variable_1="Pi_e"/>
</connection>
<connection>
<map_components component_2="Pi_substrate_flux" component_1="Fixed_parameters"/>
<map_variables variable_2="gamma" variable_1="gamma"/>
</connection>
<connection>
<map_components component_2="Pi_substrate_flux" component_1="Adjustable_parameters"/>
<map_variables variable_2="x_Pi2" variable_1="x_Pi2"/>
</connection>
<connection>
<map_components component_2="Pi_substrate_flux" component_1="dPi_i_dt"/>
<map_variables variable_2="Pi_i" variable_1="Pi_i"/>
<map_variables variable_2="J_Pi2" variable_1="J_Pi2"/>
</connection>
<connection>
<map_components component_2="MgATPx_binding_flux" component_1="Fixed_parameters"/>
<map_variables variable_2="K_DT" variable_1="K_DT"/>
</connection>
<connection>
<map_components component_2="MgATPx_binding_flux" component_1="Adjustable_parameters"/>
<map_variables variable_2="x_MgA" variable_1="x_MgA"/>
</connection>
<connection>
<map_components component_2="MgATPx_binding_flux" component_1="dMg_x_dt"/>
<map_variables variable_2="Mg_x" variable_1="Mg_x"/>
<map_variables variable_2="J_MgATPx" variable_1="J_MgATPx"/>
</connection>
<connection>
<map_components component_2="MgADPx_binding_flux" component_1="Fixed_parameters"/>
<map_variables variable_2="K_DD" variable_1="K_DD"/>
</connection>
<connection>
<map_components component_2="MgADPx_binding_flux" component_1="Adjustable_parameters"/>
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