- Author:
- rcai987 <devnull@localhost>
- Date:
- 2015-02-02 13:01:59+13:00
- Desc:
- Added annotations to fall_keizer_2001.cellml model
- Permanent Source URI:
- http://models.cellml.org/workspace/576/rawfile/bec4aa216e94b9a2dbf7f23317670c9cdc905711/fall_keizer_2001.cellml
<?xml version="1.0"?>
<!-- FILE : mitochondria_and_Ca_signaling_2001.xml
CREATED : 14th January 2002
LAST MODIFIED : 12th August 2003
AUTHOR : Catherine Lloyd
Department of Engineering Science
The University of Auckland
MODEL STATUS : This model conforms to the CellML 1.0 Specification released on
10th August 2001, and the 16/01/2002 CellML Metadata 1.0 Specification.
DESCRIPTION : This file contains a CellML description of Fall and Keizer's
2001 model of mitochondrial modulation of intracellular Ca2+ signaling.
CHANGES:
21/01/2002 - AAC - Updated metadata to conform to the 16/1/02 CellML Metadata
1.0 Specification.
26/02/2002 - CML - Corrected several equations.
01/03/2002 - CML - Corrected units.
22/07/2002 - CML - Added more metadata.
09/04/2003 - AAC - Added publication date information.
12/08/2003 - CML - Corrected equations.
--><model xmlns="http://www.cellml.org/cellml/1.0#" xmlns:bqs="http://www.cellml.org/bqs/1.0#" xmlns:cellml="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:dcterms="http://purl.org/dc/terms/" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" xml:base="file:///H:/fall_keizer_2001/fall_keizer_2001.cellml" cmeta:id="fall_keizer_2001" name="fall_keizer_2001">
<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
<articleinfo>
<title>Mitochondria And Ca2+ Signalling</title>
<author>
<firstname>Catherine</firstname>
<surname>Lloyd</surname>
<affiliation>
<shortaffil>Auckland Bioengineering Institute, University of Auckland</shortaffil>
</affiliation>
</author>
</articleinfo>
<section id="sec_status">
<title>Model Status</title>
<para>
This model is valid CellML but can not be integrated as it is unsuitably constrained.
</para>
</section>
<sect1 id="sec_structure">
<title>Model Structure</title>
<para>
In 2001 Christopher Fall and Joel Keizer published a detailed mathematical model to describe mitochondrial function and mitochondrial Ca<superscript>2+</superscript> handling coupled to endoplasmic reticulum (ER) based IP3-dependent Ca<superscript>2+</superscript> release. Their aim was to create a biologically realistic model of the influence of mitochondria on IP3-mediated Ca<superscript>2+</superscript> signaling. They aimed to integrate the separate IP3 receptor/channel (DeYoung-Keizer 1992) and mitochondrial Ca<superscript>2+</superscript> handling (Magnus-Keizer 1997, 1998) models into a single, common framework (see <xref linkend="fig_cell_diagram"/> below).
</para>
<para>
The complete original paper reference is cited below:
</para>
<para>
Mitochondrial Modulation of Intracellular Ca<superscript>2+</superscript> Signaling, Christopher P. Fall and Joel E. Keizer, 2001, <emphasis>J. theor. Biol.</emphasis>, 210, 151-165. <ulink url="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&list_uids=11371172&dopt=Abstract">PubMed ID: 11371172</ulink>
</para>
<informalfigure float="0" id="fig_cell_diagram">
<mediaobject>
<imageobject>
<objectinfo>
<title>diagram of the mitochondria and Ca2+ signaling model</title>
</objectinfo>
<imagedata fileref="fall_2001.png"/>
</imageobject>
</mediaobject>
<caption>Key components of the IP3-mediated intracellular Ca<superscript>2+</superscript> signaling diagram shows endoplasmic reticulum based Ca<superscript>2+</superscript> release and uptake mechanisms, mitochondrial Ca<superscript>2+</superscript> release and uptake mechanisms, in addition to other components which are not included in the mathematical model.</caption>
</informalfigure>
<informalfigure float="0" id="fig_cellml_rendering">
<mediaobject>
<imageobject>
<objectinfo>
<title>the cellml rendering of the mitochondria and Ca2+ signaling model</title>
</objectinfo>
<imagedata fileref="cellml_rendering.gif"/>
</imageobject>
</mediaobject>
<caption>The network defined in the CellML description of the mitochondria and Ca<superscript>2+</superscript> signaling model.</caption>
</informalfigure>
</sect1>
</article>
</documentation>
<!--
Below, we define some additional units for association with variables and
constants within the model. The identifiers are fairly self-explanatory.
-->
<units name="minute">
<unit multiplier="60.0" units="second"/>
</units>
<units name="per_second">
<unit exponent="-1" units="second"/>
</units>
<units name="millivolt">
<unit prefix="milli" units="volt"/>
</units>
<units name="millimolar">
<unit prefix="milli" units="mole"/>
<unit exponent="-1" units="litre"/>
</units>
<units name="per_millimolar">
<unit exponent="-1" units="millimolar"/>
</units>
<units name="micromolar">
<unit prefix="micro" units="mole"/>
<unit exponent="-1" units="litre"/>
</units>
<units name="nanomolar">
<unit prefix="nano" units="mole"/>
<unit exponent="-1" units="litre"/>
</units>
<units name="nanomole_per_mg">
<unit prefix="nano" units="mole"/>
<unit exponent="-1" prefix="milli" units="gram"/>
</units>
<units name="nanomole_per_minute_per_mg">
<unit prefix="nano" units="mole"/>
<unit exponent="-1" units="minute"/>
<unit exponent="-1" prefix="milli" units="gram"/>
</units>
<units name="nanomole_per_minute_per_millimolar">
<unit prefix="nano" units="mole"/>
<unit exponent="-1" units="minute"/>
<unit exponent="-1" units="millimolar"/>
</units>
<units name="milligram">
<unit prefix="milli" units="gram"/>
</units>
<units name="millilitre">
<unit prefix="milli" units="litre"/>
</units>
<units name="capacitance_units">
<unit prefix="nano" units="mole"/>
<unit exponent="-1" units="millivolt"/>
<unit exponent="-1" prefix="milli" units="gram"/>
</units>
<units name="conductance_units">
<unit prefix="nano" units="mole"/>
<unit exponent="-1" units="minute"/>
<unit exponent="-1" units="millivolt"/>
<unit exponent="-1" prefix="milli" units="gram"/>
</units>
<units name="millijoule_per_mole_kelvin">
<unit prefix="milli" units="joule"/>
<unit exponent="-1" units="mole"/>
<unit exponent="-1" units="kelvin"/>
</units>
<units name="coulomb_per_mole">
<unit units="coulomb"/>
<unit exponent="-1" units="mole"/>
</units>
<!--
The "environment" component is used to declare variables that are used by
all or most of the other components, in this case just "time".
-->
<component name="environment">
<variable name="time" public_interface="out" units="minute"/>
</component>
<!--
The "membrane" component is really the `root' node of our model.
-->
<component cmeta:id="id_00001" name="membrane">
<variable name="V" public_interface="out" units="millivolt"/>
<variable initial_value="50.0" name="V_B" public_interface="out" units="millivolt"/>
<variable initial_value="8314.0" name="R" public_interface="out" units="millijoule_per_mole_kelvin"/>
<variable initial_value="310.0" name="T" public_interface="out" units="kelvin"/>
<variable initial_value="96845.0" name="F" public_interface="out" units="coulomb_per_mole"/>
<variable initial_value="-0.4" name="delta_pH" public_interface="out" units="dimensionless"/>
<variable cmeta:id="id_00002" name="proton_motive_force" public_interface="out" units="nanomole_per_minute_per_mg"/>
<variable initial_value="0.2" name="g_H" public_interface="out" units="conductance_units"/>
<variable initial_value="0.00145" name="C" units="capacitance_units"/>
<variable name="pH_i" units="dimensionless"/>
<variable name="pH_m" units="dimensionless"/>
<variable name="JH_res" public_interface="in" units="nanomole_per_minute_per_mg"/>
<variable cmeta:id="id_00003" name="JH_leak" public_interface="in" units="nanomole_per_minute_per_mg"/>
<variable name="JH_F1" public_interface="in" units="nanomole_per_minute_per_mg"/>
<variable name="J_ant" public_interface="in" units="nanomole_per_minute_per_mg"/>
<variable cmeta:id="id_00004" name="J_uni" public_interface="in" units="nanomole_per_minute_per_mg"/>
<variable name="time" public_interface="in" units="minute"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="membrane_voltage_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> V </ci>
</apply>
<apply>
<times/>
<apply>
<divide/>
<cn cellml:units="dimensionless"> -1.0 </cn>
<ci> C </ci>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<ci> JH_F1 </ci>
<ci> J_ant </ci>
<ci> JH_leak </ci>
<apply>
<times/>
<ci> J_uni </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
</apply>
<ci> JH_res </ci>
</apply>
</apply>
</apply>
<apply id="delta_pH_calculation">
<eq/>
<ci> delta_pH </ci>
<apply>
<minus/>
<ci> pH_i </ci>
<ci> pH_m </ci>
</apply>
</apply>
<apply id="proton_motive_force_calculation">
<eq/>
<ci> proton_motive_force </ci>
<apply>
<minus/>
<ci> V </ci>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 2.303 </cn>
<ci> R </ci>
<ci> T </ci>
</apply>
<ci> F </ci>
</apply>
<ci> delta_pH </ci>
</apply>
</apply>
</apply>
</math>
</component>
<!-- Mitochondrial Ca2+ handling components. -->
<component cmeta:id="id_00005" name="Ca_uniporter">
<variable cmeta:id="id_00006" name="J_uni" public_interface="out" units="nanomole_per_minute_per_mg"/>
<variable initial_value="91.0" name="V_offset" public_interface="out" units="millivolt"/>
<variable cmeta:id="id_00007" initial_value="300.0" name="Jmax_uni" units="nanomole_per_minute_per_mg"/>
<variable initial_value="19.0" name="K_trans" units="micromolar"/>
<variable initial_value="0.38" name="K_act" units="micromolar"/>
<variable initial_value="110.0" name="L" units="dimensionless"/>
<variable initial_value="2.8" name="na" units="dimensionless"/>
<variable name="Ca_i" public_interface="in" units="nanomolar"/>
<variable name="R" public_interface="in" units="millijoule_per_mole_kelvin"/>
<variable name="F" public_interface="in" units="coulomb_per_mole"/>
<variable name="T" public_interface="in" units="kelvin"/>
<variable name="V" public_interface="in" units="millivolt"/>
<variable name="time" public_interface="in" units="minute"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="J_uni_calculation">
<eq/>
<ci> J_uni </ci>
<apply>
<times/>
<ci> Jmax_uni </ci>
<apply>
<divide/>
<apply>
<times/>
<apply>
<divide/>
<ci> Ca_i </ci>
<ci> K_trans </ci>
</apply>
<apply>
<power/>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<divide/>
<ci> Ca_i </ci>
<ci> K_trans </ci>
</apply>
</apply>
<cn cellml:units="dimensionless"> 3.0 </cn>
</apply>
</apply>
<apply>
<plus/>
<apply>
<power/>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<divide/>
<ci> Ca_i </ci>
<ci> K_trans </ci>
</apply>
</apply>
<cn cellml:units="dimensionless"> 4.0 </cn>
</apply>
<apply>
<divide/>
<ci> L </ci>
<apply>
<power/>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<divide/>
<ci> Ca_i </ci>
<ci> K_act </ci>
</apply>
</apply>
<ci> na </ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<divide/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 2.0 </cn>
<ci> F </ci>
<apply>
<minus/>
<ci> V </ci>
<ci> V_offset </ci>
</apply>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless"> -2.0 </cn>
<ci> F </ci>
<apply>
<minus/>
<ci> V </ci>
<ci> V_offset </ci>
</apply>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component cmeta:id="id_00008" name="Na_Ca_exchanger">
<variable initial_value="0.003" name="K_Ca" public_interface="out" units="nanomole_per_mg"/>
<variable cmeta:id="id_00009" name="J_Na_Ca" public_interface="out" units="nanomole_per_minute_per_mg"/>
<variable cmeta:id="id_00010" initial_value="25.0" name="Jmax_Na_Ca" units="nanomole_per_minute_per_mg"/>
<variable initial_value="30.0" name="Na_i" units="millimolar"/>
<variable initial_value="9.4" name="K_Na" units="millimolar"/>
<variable initial_value="0.0" name="b" units="dimensionless"/>
<variable initial_value="2.0" name="n" units="dimensionless"/>
<variable name="Ca_m" public_interface="in" units="nanomolar"/>
<variable name="V_offset" public_interface="in" units="millivolt"/>
<variable name="R" public_interface="in" units="millijoule_per_mole_kelvin"/>
<variable name="F" public_interface="in" units="coulomb_per_mole"/>
<variable name="T" public_interface="in" units="kelvin"/>
<variable name="V" public_interface="in" units="millivolt"/>
<variable name="time" public_interface="in" units="minute"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="J_Na_Ca_calculation">
<eq/>
<ci> J_Na_Ca </ci>
<apply>
<times/>
<ci> Jmax_Na_Ca </ci>
<apply>
<divide/>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<ci> b </ci>
<ci> F </ci>
<apply>
<minus/>
<ci> V </ci>
<ci> V_offset </ci>
</apply>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<apply>
<power/>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<divide/>
<ci> K_Na </ci>
<ci> Na_i </ci>
</apply>
</apply>
<ci> n </ci>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<divide/>
<ci> K_Ca </ci>
<ci> Ca_m </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<!-- Mitochondrial components that do not transport Ca2+. -->
<component cmeta:id="id_00011" name="proton_pump">
<variable name="JH_res" public_interface="out" units="nanomole_per_minute_per_mg"/>
<variable name="Jo" public_interface="out" units="nanomole_per_minute_per_mg"/>
<variable name="A_res" units="dimensionless"/>
<variable initial_value="13500000000000000.0" name="K_res" units="millimolar"/>
<variable initial_value="0.4" name="rho_res" units="nanomole_per_mg"/>
<variable initial_value="0.000000000000000002077" name="r1" units="dimensionless"/>
<variable initial_value="0.000000001728" name="r2" units="dimensionless"/>
<variable initial_value="0.00000000000000000000000001059" name="r3" units="dimensionless"/>
<variable initial_value="0.0000000006394" name="ra" units="per_second"/>
<variable initial_value="0.0000000000001762" name="rb" units="per_second"/>
<variable initial_value="0.0000000000000000002656" name="rc1" units="per_second"/>
<variable initial_value="0.000000000000000000000000008632" name="rc2" units="per_second"/>
<variable initial_value="0.85" name="g" units="dimensionless"/>
<variable name="delta_pH" public_interface="in" units="dimensionless"/>
<variable name="NAD_m" public_interface="in" units="nanomolar"/>
<variable name="NADH_m" public_interface="in" units="nanomolar"/>
<variable name="R" public_interface="in" units="millijoule_per_mole_kelvin"/>
<variable name="F" public_interface="in" units="coulomb_per_mole"/>
<variable name="T" public_interface="in" units="kelvin"/>
<variable name="V" public_interface="in" units="millivolt"/>
<variable name="V_B" public_interface="in" units="millivolt"/>
<variable name="time" public_interface="in" units="minute"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="JH_res_calculation">
<eq/>
<ci> JH_res </ci>
<apply>
<times/>
<cn cellml:units="dimensionless"> 360.0 </cn>
<ci> rho_res </ci>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<times/>
<ci> ra </ci>
<apply>
<power/>
<cn cellml:units="dimensionless"> 10.0 </cn>
<apply>
<times/>
<cn cellml:units="dimensionless"> 6.0 </cn>
<ci> delta_pH </ci>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<ci> F </ci>
<ci> A_res </ci>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci> rb </ci>
<apply>
<power/>
<cn cellml:units="dimensionless"> 10.0 </cn>
<apply>
<times/>
<cn cellml:units="dimensionless"> 6.0 </cn>
<ci> delta_pH </ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<times/>
<apply>
<plus/>
<ci> ra </ci>
<ci> rb </ci>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<ci> g </ci>
<cn cellml:units="dimensionless"> 6.0 </cn>
<ci> F </ci>
<ci> V </ci>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<plus/>
<apply>
<times/>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<times/>
<ci> r1 </ci>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<ci> F </ci>
<ci> A_res </ci>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 6.0 </cn>
<ci> F </ci>
<ci> V_B </ci>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<times/>
<apply>
<plus/>
<ci> r2 </ci>
<apply>
<times/>
<ci> r3 </ci>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<ci> F </ci>
<ci> A_res </ci>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<ci> g </ci>
<cn cellml:units="dimensionless"> 6.0 </cn>
<ci> F </ci>
<ci> V </ci>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="Jo_calculation">
<eq/>
<ci> Jo </ci>
<apply>
<times/>
<cn cellml:units="dimensionless"> 30.0 </cn>
<ci> rho_res </ci>
<apply>
<divide/>
<apply>
<plus/>
<apply>
<minus/>
<apply>
<times/>
<apply>
<plus/>
<apply>
<times/>
<ci> ra </ci>
<apply>
<power/>
<cn cellml:units="dimensionless"> 10.0 </cn>
<apply>
<times/>
<cn cellml:units="dimensionless"> 6.0 </cn>
<ci> delta_pH </ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci> rc1 </ci>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 6.0 </cn>
<ci> F </ci>
<ci> V_B </ci>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<ci> F </ci>
<ci> A_res </ci>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci> ra </ci>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<ci> g </ci>
<cn cellml:units="dimensionless"> 6.0 </cn>
<ci> F </ci>
<ci> V </ci>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci> rc2 </ci>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<ci> F </ci>
<ci> A_res </ci>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<ci> g </ci>
<cn cellml:units="dimensionless"> 6.0 </cn>
<ci> F </ci>
<ci> V </ci>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<plus/>
<apply>
<times/>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<times/>
<ci> r1 </ci>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<ci> F </ci>
<ci> A_res </ci>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 6.0 </cn>
<ci> F </ci>
<ci> V_B </ci>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<times/>
<apply>
<plus/>
<ci> r2 </ci>
<apply>
<times/>
<ci> r3 </ci>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<ci> F </ci>
<ci> A_res </ci>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<ci> g </ci>
<cn cellml:units="dimensionless"> 6.0 </cn>
<ci> F </ci>
<ci> V </ci>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="A_res_calculation">
<eq/>
<ci> A_res </ci>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
<ci> F </ci>
</apply>
<apply>
<ln/>
<apply>
<divide/>
<apply>
<times/>
<ci> K_res </ci>
<apply>
<root/>
<ci> NADH_m </ci>
</apply>
</apply>
<apply>
<root/>
<ci> NAD_m </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component cmeta:id="id_00012" name="proton_leak">
<variable cmeta:id="id_00013" name="JH_leak" public_interface="out" units="nanomole_per_minute_per_mg"/>
<variable name="g_H" public_interface="in" units="conductance_units"/>
<variable cmeta:id="id_00014" name="proton_motive_force" public_interface="in" units="nanomole_per_minute_per_mg"/>
<variable name="time" public_interface="in" units="minute"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="JH_leak_calculation">
<eq/>
<ci> JH_leak </ci>
<apply>
<times/>
<ci> g_H </ci>
<ci> proton_motive_force </ci>
</apply>
</apply>
</math>
</component>
<component cmeta:id="id_00015" name="F0_F1_ATPase">
<variable cmeta:id="id_00016" name="JH_F1" public_interface="out" units="nanomole_per_minute_per_mg"/>
<variable cmeta:id="id_00017" name="Jp_F1" public_interface="out" units="nanomole_per_minute_per_mg"/>
<variable initial_value="0.7" name="rho_F1" units="nanomole_per_mg"/>
<variable initial_value="1710000.0" name="K_F1" units="millimolar"/>
<variable name="A_F1" units="dimensionless"/>
<variable cmeta:id="id_00018" name="ADP_m_free" units="nanomolar"/>
<variable initial_value="20.0" name="Pi_m" units="millimolar"/>
<variable initial_value="0.00000001346" name="p1" units="dimensionless"/>
<variable initial_value="0.0000007739" name="p2" units="dimensionless"/>
<variable initial_value="0.00000000000000665" name="p3" units="dimensionless"/>
<variable initial_value="0.00001656" name="pa" units="per_second"/>
<variable initial_value="0.0000003373" name="pb" units="per_second"/>
<variable initial_value="0.00000000000009651" name="pc1" units="per_second"/>
<variable initial_value="0.0000000000000000004845" name="pc2" units="per_second"/>
<variable cmeta:id="id_00022" name="ATP_m" public_interface="in" units="nanomolar"/>
<variable cmeta:id="id_00019" name="ADP_m" public_interface="in" units="nanomolar"/>
<variable name="delta_pH" public_interface="in" units="dimensionless"/>
<variable name="R" public_interface="in" units="millijoule_per_mole_kelvin"/>
<variable name="F" public_interface="in" units="coulomb_per_mole"/>
<variable name="T" public_interface="in" units="kelvin"/>
<variable name="V" public_interface="in" units="millivolt"/>
<variable name="V_B" public_interface="in" units="millivolt"/>
<variable name="time" public_interface="in" units="minute"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="JH_F1_calculation">
<eq/>
<ci> JH_F1 </ci>
<apply>
<times/>
<cn cellml:units="dimensionless"> -180.0 </cn>
<ci> rho_F1 </ci>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<times/>
<ci> pa </ci>
<apply>
<power/>
<cn cellml:units="dimensionless"> 10.0 </cn>
<apply>
<times/>
<cn cellml:units="dimensionless"> 3.0 </cn>
<ci> delta_pH </ci>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<ci> F </ci>
<ci> A_F1 </ci>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci> pb </ci>
<apply>
<power/>
<cn cellml:units="dimensionless"> 10.0 </cn>
<apply>
<times/>
<cn cellml:units="dimensionless"> 3.0 </cn>
<ci> delta_pH </ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<times/>
<apply>
<plus/>
<ci> pa </ci>
<ci> pb </ci>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 3.0 </cn>
<ci> F </ci>
<ci> V </ci>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<plus/>
<apply>
<times/>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<times/>
<ci> p1 </ci>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<ci> F </ci>
<ci> A_F1 </ci>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 3.0 </cn>
<ci> F </ci>
<ci> V_B </ci>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<times/>
<apply>
<plus/>
<ci> p2 </ci>
<apply>
<times/>
<ci> p3 </ci>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<ci> F </ci>
<ci> A_F1 </ci>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 3.0 </cn>
<ci> F </ci>
<ci> V </ci>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="Jp_F1_calculation">
<eq/>
<ci> Jp_F1 </ci>
<apply>
<times/>
<cn cellml:units="dimensionless"> -60.0 </cn>
<ci> rho_F1 </ci>
<apply>
<divide/>
<apply>
<plus/>
<apply>
<minus/>
<apply>
<times/>
<apply>
<plus/>
<apply>
<times/>
<ci> pa </ci>
<apply>
<power/>
<cn cellml:units="dimensionless"> 10.0 </cn>
<apply>
<times/>
<cn cellml:units="dimensionless"> 3.0 </cn>
<ci> delta_pH </ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci> pc1 </ci>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 3.0 </cn>
<ci> F </ci>
<ci> V_B </ci>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<ci> F </ci>
<ci> A_F1 </ci>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci> pa </ci>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 3.0 </cn>
<ci> F </ci>
<ci> V </ci>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci> pc2 </ci>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<ci> F </ci>
<ci> A_F1 </ci>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 3.0 </cn>
<ci> F </ci>
<ci> V </ci>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<plus/>
<apply>
<times/>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<times/>
<ci> p1 </ci>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<ci> F </ci>
<ci> A_F1 </ci>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 3.0 </cn>
<ci> F </ci>
<ci> V_B </ci>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<times/>
<apply>
<plus/>
<ci> p2 </ci>
<apply>
<times/>
<ci> p3 </ci>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<ci> F </ci>
<ci> A_F1 </ci>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 3.0 </cn>
<ci> F </ci>
<ci> V </ci>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="A_F1_calculation">
<eq/>
<ci> A_F1 </ci>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
<ci> F </ci>
</apply>
<apply>
<ln/>
<apply>
<divide/>
<apply>
<times/>
<ci> K_F1 </ci>
<ci> ATP_m </ci>
</apply>
<apply>
<times/>
<ci> ADP_m_free </ci>
<ci> Pi_m </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="ADP_m_free_calculation">
<eq/>
<ci> ADP_m_free </ci>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.8 </cn>
<ci> ADP_m </ci>
</apply>
</apply>
</math>
</component>
<component cmeta:id="id_00023" name="ATP_ADP_exchange">
<variable cmeta:id="id_00026" name="J_ant" public_interface="out" units="nanomole_per_minute_per_mg"/>
<variable cmeta:id="id_00027" initial_value="1000.0" name="Jmax_ant" units="nanomole_per_minute_per_mg"/>
<variable initial_value="0.5" name="f" units="dimensionless"/>
<variable cmeta:id="id_00021" name="ADP_i" public_interface="in" units="nanomolar"/>
<variable cmeta:id="id_00020" name="ADP_m" public_interface="in" units="nanomolar"/>
<variable cmeta:id="id_00024" name="ATP_i" public_interface="in" units="nanomolar"/>
<variable cmeta:id="id_00025" name="ATP_m" public_interface="in" units="nanomolar"/>
<variable name="Jp_F1" public_interface="in" units="nanomole_per_minute_per_mg"/>
<variable name="R" public_interface="in" units="millijoule_per_mole_kelvin"/>
<variable name="F" public_interface="in" units="coulomb_per_mole"/>
<variable name="T" public_interface="in" units="kelvin"/>
<variable name="V" public_interface="in" units="millivolt"/>
<variable name="time" public_interface="in" units="minute"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="J_ant_calculation">
<eq/>
<ci> J_ant </ci>
<apply>
<times/>
<ci> Jmax_ant </ci>
<apply>
<divide/>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<ci> ATP_i </ci>
<ci> ADP_m </ci>
</apply>
<apply>
<times/>
<ci> ADP_i </ci>
<ci> ATP_m </ci>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<apply>
<minus/>
<ci> F </ci>
</apply>
<ci> V </ci>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<times/>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<times/>
<apply>
<divide/>
<ci> ATP_i </ci>
<ci> ADP_i </ci>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<apply>
<minus/>
<ci> f </ci>
</apply>
<ci> F </ci>
<ci> V </ci>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<divide/>
<ci> ADP_m </ci>
<ci> ATP_m </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component cmeta:id="id_00028" name="NAD_reduction">
<variable name="J_red" public_interface="out" units="nanomole_per_minute_per_mg"/>
<variable initial_value="20.0" name="J_red_basal" public_interface="out" units="nanomole_per_minute_per_mg"/>
<variable name="f_PDHa" public_interface="out" units="dimensionless"/>
<variable initial_value="15.0" name="u1" units="dimensionless"/>
<variable initial_value="1.1" name="u2" units="dimensionless"/>
<variable name="J_gly_tot" public_interface="in" units="nanomole_per_minute_per_mg"/>
<variable name="K_Ca" public_interface="in" units="nanomole_per_mg"/>
<variable name="Ca_m" public_interface="in" units="nanomolar"/>
<variable name="time" public_interface="in" units="minute"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="f_PDHa_calculation">
<eq/>
<ci> f_PDHa </ci>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<times/>
<ci> u2 </ci>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<times/>
<ci> u1 </ci>
<apply>
<power/>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<divide/>
<ci> Ca_m </ci>
<ci> K_Ca </ci>
</apply>
</apply>
<cn cellml:units="dimensionless"> -2.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="J_red_calculation">
<eq/>
<ci> J_red </ci>
<apply>
<plus/>
<ci> J_red_basal </ci>
<apply>
<times/>
<cn cellml:units="dimensionless"> 7.36 </cn>
<ci> f_PDHa </ci>
<ci> J_gly_tot </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component cmeta:id="id_00029" name="TCA_cycle_ADP_phosphorylation">
<variable name="J_ptca" public_interface="out" units="nanomole_per_minute_per_mg"/>
<variable name="f_PDHa" public_interface="in" units="dimensionless"/>
<variable name="J_red_basal" public_interface="in" units="nanomole_per_minute_per_mg"/>
<variable name="J_gly_tot" public_interface="in" units="nanomole_per_minute_per_mg"/>
<variable name="time" public_interface="in" units="minute"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="J_ptca_calculation">
<eq/>
<ci> J_ptca </ci>
<apply>
<plus/>
<apply>
<divide/>
<ci> J_red_basal </ci>
<cn cellml:units="dimensionless"> 3.0 </cn>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.84 </cn>
<ci> f_PDHa </ci>
<ci> J_gly_tot </ci>
</apply>
</apply>
</apply>
</math>
</component>
<!-- Cytosolic componets. -->
<component cmeta:id="id_00030" name="glycolytic_phosphorylation_of_ADP">
<variable cmeta:id="id_00031" name="J_gly_tot" public_interface="out" units="nanomole_per_minute_per_mg"/>
<variable initial_value="25.0" name="Glc" public_interface="out" units="nanomolar"/>
<variable initial_value="126.0" name="beta_max" units="nanomole_per_minute_per_millimolar"/>
<variable cmeta:id="id_00032" initial_value="1.66" name="beta_1" units="per_millimolar"/>
<variable cmeta:id="id_00033" initial_value="4.0" name="beta_3" units="per_millimolar"/>
<variable cmeta:id="id_00034" initial_value="2.83" name="beta_4" units="per_millimolar"/>
<variable cmeta:id="id_00035" initial_value="1.3" name="beta_5" units="per_millimolar"/>
<variable cmeta:id="id_00036" initial_value="2.66" name="beta_6" units="per_millimolar"/>
<variable cmeta:id="id_00037" initial_value="0.16" name="beta_7" units="per_millimolar"/>
<variable cmeta:id="id_00038" name="ATP_i" public_interface="in" units="nanomolar"/>
<variable name="time" public_interface="in" units="minute"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="J_gly_tot_calculation">
<eq/>
<ci> J_gly_tot </ci>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<ci> beta_max </ci>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<times/>
<ci> beta_1 </ci>
<ci> Glc </ci>
</apply>
</apply>
<ci> Glc </ci>
<ci> ATP_i </ci>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<times/>
<ci> beta_3 </ci>
<ci> ATP_i </ci>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<times/>
<ci> beta_4 </ci>
<ci> ATP_i </ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<plus/>
<apply>
<times/>
<ci> beta_5 </ci>
<ci> Glc </ci>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<times/>
<ci> beta_6 </ci>
<ci> ATP_i </ci>
</apply>
</apply>
<apply>
<times/>
<ci> beta_7 </ci>
<apply>
<power/>
<ci> Glc </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component cmeta:id="id_00039" name="hydrolysis_of_ATP">
<variable cmeta:id="id_00040" name="J_hyd" public_interface="out" units="nanomole_per_minute_per_mg"/>
<variable cmeta:id="id_00042" name="J_hyd_ss" units="nanomole_per_minute_per_mg"/>
<variable cmeta:id="id_00041" initial_value="30.1" name="Jmax_hyd" units="nanomole_per_minute_per_mg"/>
<variable cmeta:id="id_00043" name="k_hyd" units="per_millimolar"/>
<variable initial_value="8.7" name="K_Glc" units="millimolar"/>
<variable cmeta:id="id_00044" initial_value="2.7" name="n_hyd" units="dimensionless"/>
<variable name="Glc" public_interface="in" units="nanomolar"/>
<variable cmeta:id="id_00045" name="ATP_i" public_interface="in" units="nanomolar"/>
<variable name="time" public_interface="in" units="minute"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="J_hyd_calculation">
<eq/>
<ci> J_hyd </ci>
<apply>
<plus/>
<apply>
<times/>
<ci> k_hyd </ci>
<ci> ATP_i </ci>
</apply>
<ci> J_hyd_ss </ci>
</apply>
</apply>
<apply id="J_hyd_ss_calculation">
<eq/>
<ci> J_hyd_ss </ci>
<apply>
<divide/>
<ci> Jmax_hyd </ci>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<power/>
<apply>
<divide/>
<ci> K_Glc </ci>
<ci> Glc </ci>
</apply>
<ci> n_hyd </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<!-- ER Ca2+ handling components. -->
<component cmeta:id="id_00050" name="Ca_release_from_the_ER">
<variable cmeta:id="id_00051" name="J_erout" public_interface="out" units="nanomole_per_minute_per_mg"/>
<variable cmeta:id="id_00053" initial_value="3000.0" name="Jmax_IP3" units="nanomole_per_minute_per_mg"/>
<variable cmeta:id="id_00055" initial_value="0.25" name="d_IP3" units="micromolar"/>
<variable initial_value="1.0" name="d_ACT" units="micromolar"/>
<variable cmeta:id="id_00054" name="IP3" units="nanomolar"/>
<variable name="h" public_interface="in" units="dimensionless"/>
<variable name="JH_leak" public_interface="in" units="nanomole_per_minute_per_mg"/>
<variable name="Ca_i" public_interface="in" units="nanomolar"/>
<variable cmeta:id="id_00052" name="Ca_ER" public_interface="in" units="nanomolar"/>
<variable name="time" public_interface="in" units="minute"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="J_erout_calculation">
<eq/>
<ci> J_erout </ci>
<apply>
<times/>
<apply>
<plus/>
<apply>
<times/>
<ci> Jmax_IP3 </ci>
<apply>
<power/>
<apply>
<divide/>
<ci> IP3 </ci>
<apply>
<plus/>
<ci> IP3 </ci>
<ci> d_IP3 </ci>
</apply>
</apply>
<cn cellml:units="dimensionless"> 3.0 </cn>
</apply>
<apply>
<power/>
<apply>
<divide/>
<ci> Ca_i </ci>
<apply>
<plus/>
<ci> Ca_i </ci>
<ci> d_ACT </ci>
</apply>
</apply>
<cn cellml:units="dimensionless"> 3.0 </cn>
</apply>
<apply>
<power/>
<ci> h </ci>
<cn cellml:units="dimensionless"> 3.0 </cn>
</apply>
</apply>
<ci> JH_leak </ci>
</apply>
<apply>
<minus/>
<ci> Ca_ER </ci>
<ci> Ca_i </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component cmeta:id="id_00046" name="pumping_Ca_into_the_ER">
<variable cmeta:id="id_00047" name="J_serca" public_interface="out" units="nanomole_per_minute_per_mg"/>
<variable cmeta:id="id_00048" initial_value="110.0" name="Jmax_serca" units="nanomole_per_minute_per_mg"/>
<variable cmeta:id="id_00049" initial_value="0.4" name="k_serca" units="micromolar"/>
<variable name="Ca_i" public_interface="in" units="nanomolar"/>
<variable name="time" public_interface="in" units="minute"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="J_serca_calculation">
<eq/>
<ci> J_serca </ci>
<apply>
<times/>
<ci> Jmax_serca </ci>
<apply>
<divide/>
<apply>
<power/>
<ci> Ca_i </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
<apply>
<plus/>
<apply>
<power/>
<ci> k_serca </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
<apply>
<power/>
<ci> Ca_i </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="differential_equations">
<variable cmeta:id="id_00056" name="NADH_m" public_interface="out" units="nanomolar"/>
<variable cmeta:id="id_00057" name="NAD_m" public_interface="out" units="nanomolar"/>
<variable cmeta:id="id_00058" name="ADP_m" public_interface="out" units="nanomolar"/>
<variable cmeta:id="id_00060" name="ATP_m" public_interface="out" units="nanomolar"/>
<variable cmeta:id="id_00059" name="ADP_i" public_interface="out" units="nanomolar"/>
<variable cmeta:id="id_00061" name="ATP_i" public_interface="out" units="nanomolar"/>
<variable cmeta:id="id_00063" name="Ca_m" public_interface="out" units="nanomolar"/>
<variable cmeta:id="id_00062" name="Ca_ER" public_interface="out" units="nanomolar"/>
<variable cmeta:id="id_00064" name="Ca_i" public_interface="out" units="nanomolar"/>
<variable name="h" public_interface="out" units="dimensionless"/>
<variable initial_value="12.0" name="total_mitochondrial_adenosine_phosphate" units="nanomolar"/>
<variable cmeta:id="id_00065" initial_value="8.0" name="total_NAD_m" units="nanomolar"/>
<variable initial_value="37.5" name="C" units="milligram"/>
<variable initial_value="50.0" name="M" units="milligram"/>
<variable initial_value="100.0" name="E" units="milligram"/>
<variable initial_value="0.5" name="Vc" units="millilitre"/>
<variable initial_value="0.05" name="Vm" units="millilitre"/>
<variable initial_value="0.1" name="Ve" units="millilitre"/>
<variable initial_value="0.01" name="fc" units="dimensionless"/>
<variable initial_value="0.0003" name="fm" units="dimensionless"/>
<variable initial_value="0.01" name="fe" units="dimensionless"/>
<variable initial_value="1.4" name="d_INH" units="micromolar"/>
<variable initial_value="4.0" name="tau" units="second"/>
<variable name="J_red" public_interface="in" units="nanomole_per_minute_per_mg"/>
<variable name="Jo" public_interface="in" units="nanomole_per_minute_per_mg"/>
<variable cmeta:id="id_00066" name="J_ant" public_interface="in" units="nanomole_per_minute_per_mg"/>
<variable name="J_ptca" public_interface="in" units="nanomole_per_minute_per_mg"/>
<variable name="Jp_F1" public_interface="in" units="nanomole_per_minute_per_mg"/>
<variable cmeta:id="id_00067" name="J_hyd" public_interface="in" units="nanomole_per_minute_per_mg"/>
<variable name="J_gly_tot" public_interface="in" units="nanomole_per_minute_per_mg"/>
<variable name="JH_res" public_interface="in" units="nanomole_per_minute_per_mg"/>
<variable name="JH_F1" public_interface="in" units="nanomole_per_minute_per_mg"/>
<variable cmeta:id="id_00068" name="JH_leak" public_interface="in" units="nanomole_per_minute_per_mg"/>
<variable cmeta:id="id_00069" name="J_uni" public_interface="in" units="nanomole_per_minute_per_mg"/>
<variable cmeta:id="id_00070" name="J_Na_Ca" public_interface="in" units="nanomole_per_minute_per_mg"/>
<variable cmeta:id="id_00071" name="J_serca" public_interface="in" units="nanomole_per_minute_per_mg"/>
<variable name="J_erout" public_interface="in" units="nanomole_per_minute_per_mg"/>
<variable name="time" public_interface="in" units="minute"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="NADH_m_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> NADH_m </ci>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci> M </ci>
<apply>
<minus/>
<ci> J_red </ci>
<ci> Jo </ci>
</apply>
</apply>
<ci> Vm </ci>
</apply>
</apply>
<apply id="total_NAD_m_calculation">
<eq/>
<ci> total_NAD_m </ci>
<apply>
<plus/>
<ci> NADH_m </ci>
<ci> NAD_m </ci>
</apply>
</apply>
<apply id="NAD_m_calculation">
<eq/>
<ci> NAD_m </ci>
<apply>
<minus/>
<ci> total_NAD_m </ci>
<ci> NADH_m </ci>
</apply>
</apply>
<apply id="ADP_m_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> ADP_m </ci>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci> M </ci>
<apply>
<minus/>
<ci> J_ant </ci>
<apply>
<plus/>
<ci> J_ptca </ci>
<ci> Jp_F1 </ci>
</apply>
</apply>
</apply>
<ci> Vm </ci>
</apply>
</apply>
<apply id="total_mitochondrial_adenosine_phosphate_calculation">
<eq/>
<ci> total_mitochondrial_adenosine_phosphate </ci>
<apply>
<plus/>
<ci> ATP_m </ci>
<ci> ADP_m </ci>
</apply>
</apply>
<apply id="ATP_m_calculation">
<eq/>
<ci> ATP_m </ci>
<apply>
<minus/>
<ci> total_mitochondrial_adenosine_phosphate </ci>
<ci> ADP_m </ci>
</apply>
</apply>
<apply id="ADP_i_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> ADP_i </ci>
</apply>
<apply>
<divide/>
<apply>
<plus/>
<apply>
<times/>
<apply>
<minus/>
<ci> M </ci>
</apply>
<ci> J_ant </ci>
</apply>
<apply>
<times/>
<ci> C </ci>
<apply>
<minus/>
<ci> J_hyd </ci>
<ci> J_gly_tot </ci>
</apply>
</apply>
</apply>
<ci> Vc </ci>
</apply>
</apply>
<apply id="ATP_i_calculation">
<eq/>
<ci> ATP_i </ci>
<apply>
<minus/>
<cn cellml:units="millimolar"> 2.0 </cn>
<ci> ADP_i </ci>
</apply>
</apply>
<apply id="Ca_m_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> Ca_m </ci>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci> fm </ci>
<ci> M </ci>
<apply>
<minus/>
<ci> J_uni </ci>
<ci> J_Na_Ca </ci>
</apply>
</apply>
<ci> Vm </ci>
</apply>
</apply>
<apply id="Ca_ER_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> Ca_ER </ci>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci> fe </ci>
<ci> E </ci>
<apply>
<minus/>
<ci> J_serca </ci>
<ci> J_erout </ci>
</apply>
</apply>
<ci> Ve </ci>
</apply>
</apply>
<apply id="Ca_i_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> Ca_i </ci>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci> fc </ci>
<apply>
<minus/>
<apply>
<times/>
<ci> M </ci>
<apply>
<minus/>
<ci> J_Na_Ca </ci>
<ci> J_uni </ci>
</apply>
</apply>
<apply>
<times/>
<ci> E </ci>
<apply>
<minus/>
<ci> J_serca </ci>
<ci> J_erout </ci>
</apply>
</apply>
</apply>
</apply>
<ci> Vc </ci>
</apply>
</apply>
<apply id="h_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> h </ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci> d_INH </ci>
<apply>
<times/>
<apply>
<plus/>
<ci> Ca_i </ci>
<ci> d_INH </ci>
</apply>
<ci> h </ci>
</apply>
</apply>
<ci> tau </ci>
</apply>
</apply>
</math>
</component>
<group>
<relationship_ref relationship="containment"/>
<component_ref component="membrane">
<component_ref component="proton_pump"/>
<component_ref component="proton_leak"/>
<component_ref component="F0_F1_ATPase"/>
<component_ref component="ATP_ADP_exchange"/>
<component_ref component="Ca_uniporter"/>
<component_ref component="Na_Ca_exchanger"/>
<component_ref component="NAD_reduction"/>
<component_ref component="TCA_cycle_ADP_phosphorylation"/>
<component_ref component="glycolytic_phosphorylation_of_ADP"/>
<component_ref component="hydrolysis_of_ATP"/>
<component_ref component="Ca_release_from_the_ER"/>
<component_ref component="pumping_Ca_into_the_ER"/>
<component_ref component="differential_equations"/>
</component_ref>
</group>
<!--
"Time" is passed from the "environment" component into all other components.
-->
<connection>
<map_components component_1="membrane" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="environment" component_2="proton_pump"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="environment" component_2="proton_leak"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="environment" component_2="F0_F1_ATPase"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="environment" component_2="ATP_ADP_exchange"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="environment" component_2="Ca_uniporter"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="environment" component_2="Na_Ca_exchanger"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="environment" component_2="NAD_reduction"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="environment" component_2="TCA_cycle_ADP_phosphorylation"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="environment" component_2="glycolytic_phosphorylation_of_ADP"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="environment" component_2="hydrolysis_of_ATP"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="environment" component_2="Ca_release_from_the_ER"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="environment" component_2="pumping_Ca_into_the_ER"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="environment" component_2="differential_equations"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<!--
Several variables are passed between the "membrane" and its sub-components.
-->
<connection>
<map_components component_1="membrane" component_2="proton_pump"/>
<map_variables variable_1="JH_res" variable_2="JH_res"/>
<map_variables variable_1="delta_pH" variable_2="delta_pH"/>
<map_variables variable_1="V" variable_2="V"/>
<map_variables variable_1="V_B" variable_2="V_B"/>
<map_variables variable_1="R" variable_2="R"/>
<map_variables variable_1="T" variable_2="T"/>
<map_variables variable_1="F" variable_2="F"/>
</connection>
<connection>
<map_components component_1="membrane" component_2="proton_leak"/>
<map_variables variable_1="JH_leak" variable_2="JH_leak"/>
<map_variables variable_1="g_H" variable_2="g_H"/>
<map_variables variable_1="proton_motive_force" variable_2="proton_motive_force"/>
</connection>
<connection>
<map_components component_1="membrane" component_2="F0_F1_ATPase"/>
<map_variables variable_1="JH_F1" variable_2="JH_F1"/>
<map_variables variable_1="delta_pH" variable_2="delta_pH"/>
<map_variables variable_1="V" variable_2="V"/>
<map_variables variable_1="V_B" variable_2="V_B"/>
<map_variables variable_1="R" variable_2="R"/>
<map_variables variable_1="T" variable_2="T"/>
<map_variables variable_1="F" variable_2="F"/>
</connection>
<connection>
<map_components component_1="membrane" component_2="ATP_ADP_exchange"/>
<map_variables variable_1="J_ant" variable_2="J_ant"/>
<map_variables variable_1="V" variable_2="V"/>
<map_variables variable_1="R" variable_2="R"/>
<map_variables variable_1="T" variable_2="T"/>
<map_variables variable_1="F" variable_2="F"/>
</connection>
<connection>
<map_components component_1="membrane" component_2="Ca_uniporter"/>
<map_variables variable_1="J_uni" variable_2="J_uni"/>
<map_variables variable_1="V" variable_2="V"/>
<map_variables variable_1="R" variable_2="R"/>
<map_variables variable_1="T" variable_2="T"/>
<map_variables variable_1="F" variable_2="F"/>
</connection>
<connection>
<map_components component_1="membrane" component_2="Na_Ca_exchanger"/>
<map_variables variable_1="V" variable_2="V"/>
<map_variables variable_1="R" variable_2="R"/>
<map_variables variable_1="T" variable_2="T"/>
<map_variables variable_1="F" variable_2="F"/>
</connection>
<!-- A few variables are passed between the sibling components. -->
<connection>
<map_components component_1="Ca_uniporter" component_2="Na_Ca_exchanger"/>
<map_variables variable_1="V_offset" variable_2="V_offset"/>
</connection>
<connection>
<map_components component_1="Ca_uniporter" component_2="differential_equations"/>
<map_variables variable_1="J_uni" variable_2="J_uni"/>
<map_variables variable_1="Ca_i" variable_2="Ca_i"/>
</connection>
<connection>
<map_components component_1="Na_Ca_exchanger" component_2="NAD_reduction"/>
<map_variables variable_1="K_Ca" variable_2="K_Ca"/>
</connection>
<connection>
<map_components component_1="Na_Ca_exchanger" component_2="differential_equations"/>
<map_variables variable_1="J_Na_Ca" variable_2="J_Na_Ca"/>
<map_variables variable_1="Ca_m" variable_2="Ca_m"/>
</connection>
<connection>
<map_components component_1="proton_pump" component_2="differential_equations"/>
<map_variables variable_1="JH_res" variable_2="JH_res"/>
<map_variables variable_1="Jo" variable_2="Jo"/>
<map_variables variable_1="NAD_m" variable_2="NAD_m"/>
<map_variables variable_1="NADH_m" variable_2="NADH_m"/>
</connection>
<connection>
<map_components component_1="proton_leak" component_2="Ca_release_from_the_ER"/>
<map_variables variable_1="JH_leak" variable_2="JH_leak"/>
</connection>
<connection>
<map_components component_1="proton_leak" component_2="differential_equations"/>
<map_variables variable_1="JH_leak" variable_2="JH_leak"/>
</connection>
<connection>
<map_components component_1="F0_F1_ATPase" component_2="differential_equations"/>
<map_variables variable_1="JH_F1" variable_2="JH_F1"/>
<map_variables variable_1="Jp_F1" variable_2="Jp_F1"/>
<map_variables variable_1="ADP_m" variable_2="ADP_m"/>
<map_variables variable_1="ATP_m" variable_2="ATP_m"/>
</connection>
<connection>
<map_components component_1="F0_F1_ATPase" component_2="ATP_ADP_exchange"/>
<map_variables variable_1="Jp_F1" variable_2="Jp_F1"/>
</connection>
<connection>
<map_components component_1="ATP_ADP_exchange" component_2="differential_equations"/>
<map_variables variable_1="J_ant" variable_2="J_ant"/>
<map_variables variable_1="ADP_m" variable_2="ADP_m"/>
<map_variables variable_1="ATP_m" variable_2="ATP_m"/>
<map_variables variable_1="ADP_i" variable_2="ADP_i"/>
<map_variables variable_1="ATP_i" variable_2="ATP_i"/>
</connection>
<connection>
<map_components component_1="NAD_reduction" component_2="differential_equations"/>
<map_variables variable_1="J_red" variable_2="J_red"/>
<map_variables variable_1="Ca_m" variable_2="Ca_m"/>
</connection>
<connection>
<map_components component_1="NAD_reduction" component_2="TCA_cycle_ADP_phosphorylation"/>
<map_variables variable_1="J_red_basal" variable_2="J_red_basal"/>
<map_variables variable_1="f_PDHa" variable_2="f_PDHa"/>
</connection>
<connection>
<map_components component_1="NAD_reduction" component_2="glycolytic_phosphorylation_of_ADP"/>
<map_variables variable_1="J_gly_tot" variable_2="J_gly_tot"/>
</connection>
<connection>
<map_components component_1="TCA_cycle_ADP_phosphorylation" component_2="differential_equations"/>
<map_variables variable_1="J_ptca" variable_2="J_ptca"/>
</connection>
<connection>
<map_components component_1="TCA_cycle_ADP_phosphorylation" component_2="glycolytic_phosphorylation_of_ADP"/>
<map_variables variable_1="J_gly_tot" variable_2="J_gly_tot"/>
</connection>
<connection>
<map_components component_1="glycolytic_phosphorylation_of_ADP" component_2="differential_equations"/>
<map_variables variable_1="J_gly_tot" variable_2="J_gly_tot"/>
<map_variables variable_1="ATP_i" variable_2="ATP_i"/>
</connection>
<connection>
<map_components component_1="glycolytic_phosphorylation_of_ADP" component_2="hydrolysis_of_ATP"/>
<map_variables variable_1="Glc" variable_2="Glc"/>
</connection>
<connection>
<map_components component_1="hydrolysis_of_ATP" component_2="differential_equations"/>
<map_variables variable_1="J_hyd" variable_2="J_hyd"/>
<map_variables variable_1="ATP_i" variable_2="ATP_i"/>
</connection>
<connection>
<map_components component_1="Ca_release_from_the_ER" component_2="differential_equations"/>
<map_variables variable_1="J_erout" variable_2="J_erout"/>
<map_variables variable_1="Ca_i" variable_2="Ca_i"/>
<map_variables variable_1="Ca_ER" variable_2="Ca_ER"/>
<map_variables variable_1="h" variable_2="h"/>
</connection>
<connection>
<map_components component_1="pumping_Ca_into_the_ER" component_2="differential_equations"/>
<map_variables variable_1="J_serca" variable_2="J_serca"/>
<map_variables variable_1="Ca_i" variable_2="Ca_i"/>
</connection>
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