<?xml version='1.0' encoding='utf-8'?>
<!-- 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: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="fall_keizer_2001_version01" name="fall_keizer_2001_version01">
<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
<articleinfo>
<title>Mitochondria And Ca2+ Signalling</title>
<author>
<firstname>Catherine</firstname>
<surname>Lloyd</surname>
<affiliation>
<shortaffil>Bioengineering Institute, University of Auckland</shortaffil>
</affiliation>
</author>
</articleinfo>
<section id="sec_status">
<title>Model Status</title>
<para>
This is the original unchecked version of the model imported from the previous
CellML model repository, 24-Jan-2006.
</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 <ulink url="${HTML_EXMPL_IP3_CA2+_MODEL}">IP3 receptor/channel (DeYoung-Keizer 1992)</ulink> and <ulink url="${HTML_EXMPL_MITOCHONDRIAL_CA_HANDLING}">mitochondrial Ca<superscript>2+</superscript> handling (Magnus-Keizer 1997, 1998)</ulink> 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>
<ulink url="http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6WMD-457VD48-2X&_user=140507&_coverDate=05%2F21%2F2001&_alid=187119092&_rdoc=1&_fmt=summary&_orig=search&_qd=1&_cdi=6932&_sort=d&_docanchor=&view=c&_acct=C000011498&_version=1&_urlVersion=0&_userid=140507&md5=c1b4b6377cc0e91c539a5f2046bd18e0">Mitochondrial Modulation of Intracellular Ca<superscript>2+</superscript> Signaling</ulink>, Christopher P. Fall and Joel E. Keizer, 2001, <ulink url="http://www.sciencedirect.com/science?_ob=JournalURL&_cdi=6932&_auth=y&_acct=C000011498&_version=1&_urlVersion=0&_userid=140507&md5=c8e64d20ff203cda2255f4b6b7affe4f">
<emphasis>J. theor. Biol.</emphasis>
</ulink>, 210, 151-165. (A <ulink url="http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6WMD-457VD48-2X&_coverDate=05%2F21%2F2001&_alid=187119092&_rdoc=1&_fmt=&_orig=search&_qd=1&_cdi=6932&_sort=d&view=c&_acct=C000011498&_version=1&_urlVersion=0&_userid=140507&md5=c6160e53309599f9017868cecfd56646">full text (html) </ulink> and PDF versions of the article are available to subscribers on the Science Direct website.) <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>
<para>
The raw CellML description of the mitochondria and Ca<superscript>2+</superscript> signaling model can be downloaded in various formats as described in <xref linkend="sec_download_this_model"/>. For an example of a more complete documentation for an electrophysiological model, see <ulink url="${HTML_EXMPL_HHSA_INTRO}">The Hodgkin-Huxley Squid Axon Model, 1952</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 units="second" multiplier="60.0"/>
</units>
<units name="per_second">
<unit units="second" exponent="-1"/>
</units>
<units name="millivolt">
<unit units="volt" prefix="milli"/>
</units>
<units name="millimolar">
<unit units="mole" prefix="milli"/>
<unit units="litre" exponent="-1"/>
</units>
<units name="per_millimolar">
<unit units="millimolar" exponent="-1"/>
</units>
<units name="micromolar">
<unit units="mole" prefix="micro"/>
<unit units="litre" exponent="-1"/>
</units>
<units name="nanomolar">
<unit units="mole" prefix="nano"/>
<unit units="litre" exponent="-1"/>
</units>
<units name="nanomole_per_mg">
<unit units="mole" prefix="nano"/>
<unit units="gram" prefix="milli" exponent="-1"/>
</units>
<units name="nanomole_per_minute_per_mg">
<unit units="mole" prefix="nano"/>
<unit units="minute" exponent="-1"/>
<unit units="gram" prefix="milli" exponent="-1"/>
</units>
<units name="nanomole_per_minute_per_millimolar">
<unit units="mole" prefix="nano"/>
<unit units="minute" exponent="-1"/>
<unit units="millimolar" exponent="-1"/>
</units>
<units name="milligram">
<unit units="gram" prefix="milli"/>
</units>
<units name="millilitre">
<unit units="litre" prefix="milli"/>
</units>
<units name="capacitance_units">
<unit units="mole" prefix="nano"/>
<unit units="millivolt" exponent="-1"/>
<unit units="gram" prefix="milli" exponent="-1"/>
</units>
<units name="conductance_units">
<unit units="mole" prefix="nano"/>
<unit units="minute" exponent="-1"/>
<unit units="millivolt" exponent="-1"/>
<unit units="gram" prefix="milli" exponent="-1"/>
</units>
<units name="millijoule_per_mole_kelvin">
<unit units="joule" prefix="milli"/>
<unit units="mole" exponent="-1"/>
<unit units="kelvin" exponent="-1"/>
</units>
<units name="coulomb_per_mole">
<unit units="coulomb"/>
<unit units="mole" exponent="-1"/>
</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 units="minute" public_interface="out" name="time"/>
</component>
<!--
The "membrane" component is really the `root' node of our model.
-->
<component name="membrane">
<variable units="millivolt" public_interface="out" name="V"/>
<variable units="millivolt" public_interface="out" name="V_B" initial_value="50.0"/>
<variable units="millijoule_per_mole_kelvin" public_interface="out" name="R" initial_value="8314.0"/>
<variable units="kelvin" public_interface="out" name="T" initial_value="310.0"/>
<variable units="coulomb_per_mole" public_interface="out" name="F" initial_value="96845.0"/>
<variable units="dimensionless" public_interface="out" name="delta_pH" initial_value="-0.4"/>
<variable units="nanomole_per_minute_per_mg" public_interface="out" name="proton_motive_force"/>
<variable units="conductance_units" public_interface="out" name="g_H" initial_value="0.2"/>
<variable units="capacitance_units" name="C" initial_value="0.00145"/>
<variable units="dimensionless" name="pH_i"/>
<variable units="dimensionless" name="pH_m"/>
<variable units="nanomole_per_minute_per_mg" public_interface="in" name="JH_res"/>
<variable units="nanomole_per_minute_per_mg" public_interface="in" name="JH_leak"/>
<variable units="nanomole_per_minute_per_mg" public_interface="in" name="JH_F1"/>
<variable units="nanomole_per_minute_per_mg" public_interface="in" name="J_ant"/>
<variable units="nanomole_per_minute_per_mg" public_interface="in" name="J_uni"/>
<variable units="minute" public_interface="in" name="time"/>
<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 name="Ca_uniporter">
<variable units="nanomole_per_minute_per_mg" public_interface="out" name="J_uni"/>
<variable units="millivolt" public_interface="out" name="V_offset" initial_value="91.0"/>
<variable units="nanomole_per_minute_per_mg" name="Jmax_uni" initial_value="300.0"/>
<variable units="micromolar" name="K_trans" initial_value="19.0"/>
<variable units="micromolar" name="K_act" initial_value="0.38"/>
<variable units="dimensionless" name="L" initial_value="110.0"/>
<variable units="dimensionless" name="na" initial_value="2.8"/>
<variable units="nanomolar" public_interface="in" name="Ca_i"/>
<variable units="millijoule_per_mole_kelvin" public_interface="in" name="R"/>
<variable units="coulomb_per_mole" public_interface="in" name="F"/>
<variable units="kelvin" public_interface="in" name="T"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="minute" public_interface="in" name="time"/>
<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 name="Na_Ca_exchanger">
<variable units="nanomole_per_mg" public_interface="out" name="K_Ca" initial_value="0.003"/>
<variable units="nanomole_per_minute_per_mg" public_interface="out" name="J_Na_Ca"/>
<variable units="nanomole_per_minute_per_mg" name="Jmax_Na_Ca" initial_value="25.0"/>
<variable units="millimolar" name="Na_i" initial_value="30.0"/>
<variable units="millimolar" name="K_Na" initial_value="9.4"/>
<variable units="dimensionless" name="b" initial_value="0.0"/>
<variable units="dimensionless" name="n" initial_value="2.0"/>
<variable units="nanomolar" public_interface="in" name="Ca_m"/>
<variable units="millivolt" public_interface="in" name="V_offset"/>
<variable units="millijoule_per_mole_kelvin" public_interface="in" name="R"/>
<variable units="coulomb_per_mole" public_interface="in" name="F"/>
<variable units="kelvin" public_interface="in" name="T"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="minute" public_interface="in" name="time"/>
<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 name="proton_pump">
<variable units="nanomole_per_minute_per_mg" public_interface="out" name="JH_res"/>
<variable units="nanomole_per_minute_per_mg" public_interface="out" name="Jo"/>
<variable units="dimensionless" name="A_res"/>
<variable units="millimolar" name="K_res" initial_value="13500000000000000.0"/>
<variable units="nanomole_per_mg" name="rho_res" initial_value="0.4"/>
<variable units="dimensionless" name="r1" initial_value="0.000000000000000002077"/>
<variable units="dimensionless" name="r2" initial_value="0.000000001728"/>
<variable units="dimensionless" name="r3" initial_value="0.00000000000000000000000001059"/>
<variable units="per_second" name="ra" initial_value="0.0000000006394"/>
<variable units="per_second" name="rb" initial_value="0.0000000000001762"/>
<variable units="per_second" name="rc1" initial_value="0.0000000000000000002656"/>
<variable units="per_second" name="rc2" initial_value="0.000000000000000000000000008632"/>
<variable units="dimensionless" name="g" initial_value="0.85"/>
<variable units="dimensionless" public_interface="in" name="delta_pH"/>
<variable units="nanomolar" public_interface="in" name="NAD_m"/>
<variable units="nanomolar" public_interface="in" name="NADH_m"/>
<variable units="millijoule_per_mole_kelvin" public_interface="in" name="R"/>
<variable units="coulomb_per_mole" public_interface="in" name="F"/>
<variable units="kelvin" public_interface="in" name="T"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="millivolt" public_interface="in" name="V_B"/>
<variable units="minute" public_interface="in" name="time"/>
<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 name="proton_leak">
<variable units="nanomole_per_minute_per_mg" public_interface="out" name="JH_leak"/>
<variable units="conductance_units" public_interface="in" name="g_H"/>
<variable units="nanomole_per_minute_per_mg" public_interface="in" name="proton_motive_force"/>
<variable units="minute" public_interface="in" name="time"/>
<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 name="F0_F1_ATPase">
<variable units="nanomole_per_minute_per_mg" public_interface="out" name="JH_F1"/>
<variable units="nanomole_per_minute_per_mg" public_interface="out" name="Jp_F1"/>
<variable units="nanomole_per_mg" name="rho_F1" initial_value="0.7"/>
<variable units="millimolar" name="K_F1" initial_value="1710000.0"/>
<variable units="dimensionless" name="A_F1"/>
<variable units="nanomolar" name="ADP_m_free"/>
<variable units="millimolar" name="Pi_m" initial_value="20.0"/>
<variable units="dimensionless" name="p1" initial_value="0.00000001346"/>
<variable units="dimensionless" name="p2" initial_value="0.0000007739"/>
<variable units="dimensionless" name="p3" initial_value="0.00000000000000665"/>
<variable units="per_second" name="pa" initial_value="0.00001656"/>
<variable units="per_second" name="pb" initial_value="0.0000003373"/>
<variable units="per_second" name="pc1" initial_value="0.00000000000009651"/>
<variable units="per_second" name="pc2" initial_value="0.0000000000000000004845"/>
<variable units="nanomolar" public_interface="in" name="ATP_m"/>
<variable units="nanomolar" public_interface="in" name="ADP_m"/>
<variable units="dimensionless" public_interface="in" name="delta_pH"/>
<variable units="millijoule_per_mole_kelvin" public_interface="in" name="R"/>
<variable units="coulomb_per_mole" public_interface="in" name="F"/>
<variable units="kelvin" public_interface="in" name="T"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="millivolt" public_interface="in" name="V_B"/>
<variable units="minute" public_interface="in" name="time"/>
<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 name="ATP_ADP_exchange">
<variable units="nanomole_per_minute_per_mg" public_interface="out" name="J_ant"/>
<variable units="nanomole_per_minute_per_mg" name="Jmax_ant" initial_value="1000.0"/>
<variable units="dimensionless" name="f" initial_value="0.5"/>
<variable units="nanomolar" public_interface="in" name="ADP_i"/>
<variable units="nanomolar" public_interface="in" name="ADP_m"/>
<variable units="nanomolar" public_interface="in" name="ATP_i"/>
<variable units="nanomolar" public_interface="in" name="ATP_m"/>
<variable units="nanomole_per_minute_per_mg" public_interface="in" name="Jp_F1"/>
<variable units="millijoule_per_mole_kelvin" public_interface="in" name="R"/>
<variable units="coulomb_per_mole" public_interface="in" name="F"/>
<variable units="kelvin" public_interface="in" name="T"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="minute" public_interface="in" name="time"/>
<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 name="NAD_reduction">
<variable units="nanomole_per_minute_per_mg" public_interface="out" name="J_red"/>
<variable units="nanomole_per_minute_per_mg" public_interface="out" name="J_red_basal" initial_value="20.0"/>
<variable units="dimensionless" public_interface="out" name="f_PDHa"/>
<variable units="dimensionless" name="u1" initial_value="15.0"/>
<variable units="dimensionless" name="u2" initial_value="1.1"/>
<variable units="nanomole_per_minute_per_mg" public_interface="in" name="J_gly_tot"/>
<variable units="nanomole_per_mg" public_interface="in" name="K_Ca"/>
<variable units="nanomolar" public_interface="in" name="Ca_m"/>
<variable units="minute" public_interface="in" name="time"/>
<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 name="TCA_cycle_ADP_phosphorylation">
<variable units="nanomole_per_minute_per_mg" public_interface="out" name="J_ptca"/>
<variable units="dimensionless" public_interface="in" name="f_PDHa"/>
<variable units="nanomole_per_minute_per_mg" public_interface="in" name="J_red_basal"/>
<variable units="nanomole_per_minute_per_mg" public_interface="in" name="J_gly_tot"/>
<variable units="minute" public_interface="in" name="time"/>
<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 name="glycolytic_phosphorylation_of_ADP">
<variable units="nanomole_per_minute_per_mg" public_interface="out" name="J_gly_tot"/>
<variable units="nanomolar" public_interface="out" name="Glc" initial_value="25.0"/>
<variable units="nanomole_per_minute_per_millimolar" name="beta_max" initial_value="126.0"/>
<variable units="per_millimolar" name="beta_1" initial_value="1.66"/>
<variable units="per_millimolar" name="beta_3" initial_value="4.0"/>
<variable units="per_millimolar" name="beta_4" initial_value="2.83"/>
<variable units="per_millimolar" name="beta_5" initial_value="1.3"/>
<variable units="per_millimolar" name="beta_6" initial_value="2.66"/>
<variable units="per_millimolar" name="beta_7" initial_value="0.16"/>
<variable units="nanomolar" public_interface="in" name="ATP_i"/>
<variable units="minute" public_interface="in" name="time"/>
<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 name="hydrolysis_of_ATP">
<variable units="nanomole_per_minute_per_mg" public_interface="out" name="J_hyd"/>
<variable units="nanomole_per_minute_per_mg" name="J_hyd_ss"/>
<variable units="nanomole_per_minute_per_mg" name="Jmax_hyd" initial_value="30.1"/>
<variable units="per_millimolar" name="k_hyd"/>
<variable units="millimolar" name="K_Glc" initial_value="8.7"/>
<variable units="dimensionless" name="n_hyd" initial_value="2.7"/>
<variable units="nanomolar" public_interface="in" name="Glc"/>
<variable units="nanomolar" public_interface="in" name="ATP_i"/>
<variable units="minute" public_interface="in" name="time"/>
<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 name="Ca_release_from_the_ER">
<variable units="nanomole_per_minute_per_mg" public_interface="out" name="J_erout"/>
<variable units="nanomole_per_minute_per_mg" name="Jmax_IP3" initial_value="3000.0"/>
<variable units="micromolar" name="d_IP3" initial_value="0.25"/>
<variable units="micromolar" name="d_ACT" initial_value="1.0"/>
<variable units="nanomolar" name="IP3"/>
<variable units="dimensionless" public_interface="in" name="h"/>
<variable units="nanomole_per_minute_per_mg" public_interface="in" name="JH_leak"/>
<variable units="nanomolar" public_interface="in" name="Ca_i"/>
<variable units="nanomolar" public_interface="in" name="Ca_ER"/>
<variable units="minute" public_interface="in" name="time"/>
<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 name="pumping_Ca_into_the_ER">
<variable units="nanomole_per_minute_per_mg" public_interface="out" name="J_serca"/>
<variable units="nanomole_per_minute_per_mg" name="Jmax_serca" initial_value="110.0"/>
<variable units="micromolar" name="k_serca" initial_value="0.4"/>
<variable units="nanomolar" public_interface="in" name="Ca_i"/>
<variable units="minute" public_interface="in" name="time"/>
<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 units="nanomolar" public_interface="out" name="NADH_m"/>
<variable units="nanomolar" public_interface="out" name="NAD_m"/>
<variable units="nanomolar" public_interface="out" name="ADP_m"/>
<variable units="nanomolar" public_interface="out" name="ATP_m"/>
<variable units="nanomolar" public_interface="out" name="ADP_i"/>
<variable units="nanomolar" public_interface="out" name="ATP_i"/>
<variable units="nanomolar" public_interface="out" name="Ca_m"/>
<variable units="nanomolar" public_interface="out" name="Ca_ER"/>
<variable units="nanomolar" public_interface="out" name="Ca_i"/>
<variable units="dimensionless" public_interface="out" name="h"/>
<variable units="nanomolar" name="total_mitochondrial_adenosine_phosphate" initial_value="12.0"/>
<variable units="nanomolar" name="total_NAD_m" initial_value="8.0"/>
<variable units="milligram" name="C" initial_value="37.5"/>
<variable units="milligram" name="M" initial_value="50.0"/>
<variable units="milligram" name="E" initial_value="100.0"/>
<variable units="millilitre" name="Vc" initial_value="0.5"/>
<variable units="millilitre" name="Vm" initial_value="0.05"/>
<variable units="millilitre" name="Ve" initial_value="0.1"/>
<variable units="dimensionless" name="fc" initial_value="0.01"/>
<variable units="dimensionless" name="fm" initial_value="0.0003"/>
<variable units="dimensionless" name="fe" initial_value="0.01"/>
<variable units="micromolar" name="d_INH" initial_value="1.4"/>
<variable units="second" name="tau" initial_value="4.0"/>
<variable units="nanomole_per_minute_per_mg" public_interface="in" name="J_red"/>
<variable units="nanomole_per_minute_per_mg" public_interface="in" name="Jo"/>
<variable units="nanomole_per_minute_per_mg" public_interface="in" name="J_ant"/>
<variable units="nanomole_per_minute_per_mg" public_interface="in" name="J_ptca"/>
<variable units="nanomole_per_minute_per_mg" public_interface="in" name="Jp_F1"/>
<variable units="nanomole_per_minute_per_mg" public_interface="in" name="J_hyd"/>
<variable units="nanomole_per_minute_per_mg" public_interface="in" name="J_gly_tot"/>
<variable units="nanomole_per_minute_per_mg" public_interface="in" name="JH_res"/>
<variable units="nanomole_per_minute_per_mg" public_interface="in" name="JH_F1"/>
<variable units="nanomole_per_minute_per_mg" public_interface="in" name="JH_leak"/>
<variable units="nanomole_per_minute_per_mg" public_interface="in" name="J_uni"/>
<variable units="nanomole_per_minute_per_mg" public_interface="in" name="J_Na_Ca"/>
<variable units="nanomole_per_minute_per_mg" public_interface="in" name="J_serca"/>
<variable units="nanomole_per_minute_per_mg" public_interface="in" name="J_erout"/>
<variable units="minute" public_interface="in" name="time"/>
<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_2="environment" component_1="membrane"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="proton_pump" component_1="environment"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="proton_leak" component_1="environment"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="F0_F1_ATPase" component_1="environment"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="ATP_ADP_exchange" component_1="environment"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="Ca_uniporter" component_1="environment"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="Na_Ca_exchanger" component_1="environment"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="NAD_reduction" component_1="environment"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="TCA_cycle_ADP_phosphorylation" component_1="environment"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="glycolytic_phosphorylation_of_ADP" component_1="environment"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="hydrolysis_of_ATP" component_1="environment"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="Ca_release_from_the_ER" component_1="environment"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="pumping_Ca_into_the_ER" component_1="environment"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="differential_equations" component_1="environment"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<!--
Several variables are passed between the "membrane" and its sub-components.
-->
<connection>
<map_components component_2="proton_pump" component_1="membrane"/>
<map_variables variable_2="JH_res" variable_1="JH_res"/>
<map_variables variable_2="delta_pH" variable_1="delta_pH"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="V_B" variable_1="V_B"/>
<map_variables variable_2="R" variable_1="R"/>
<map_variables variable_2="T" variable_1="T"/>
<map_variables variable_2="F" variable_1="F"/>
</connection>
<connection>
<map_components component_2="proton_leak" component_1="membrane"/>
<map_variables variable_2="JH_leak" variable_1="JH_leak"/>
<map_variables variable_2="g_H" variable_1="g_H"/>
<map_variables variable_2="proton_motive_force" variable_1="proton_motive_force"/>
</connection>
<connection>
<map_components component_2="F0_F1_ATPase" component_1="membrane"/>
<map_variables variable_2="JH_F1" variable_1="JH_F1"/>
<map_variables variable_2="delta_pH" variable_1="delta_pH"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="V_B" variable_1="V_B"/>
<map_variables variable_2="R" variable_1="R"/>
<map_variables variable_2="T" variable_1="T"/>
<map_variables variable_2="F" variable_1="F"/>
</connection>
<connection>
<map_components component_2="ATP_ADP_exchange" component_1="membrane"/>
<map_variables variable_2="J_ant" variable_1="J_ant"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="R" variable_1="R"/>
<map_variables variable_2="T" variable_1="T"/>
<map_variables variable_2="F" variable_1="F"/>
</connection>
<connection>
<map_components component_2="Ca_uniporter" component_1="membrane"/>
<map_variables variable_2="J_uni" variable_1="J_uni"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="R" variable_1="R"/>
<map_variables variable_2="T" variable_1="T"/>
<map_variables variable_2="F" variable_1="F"/>
</connection>
<connection>
<map_components component_2="Na_Ca_exchanger" component_1="membrane"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="R" variable_1="R"/>
<map_variables variable_2="T" variable_1="T"/>
<map_variables variable_2="F" variable_1="F"/>
</connection>
<!-- A few variables are passed between the sibling components. -->
<connection>
<map_components component_2="Na_Ca_exchanger" component_1="Ca_uniporter"/>
<map_variables variable_2="V_offset" variable_1="V_offset"/>
</connection>
<connection>
<map_components component_2="differential_equations" component_1="Ca_uniporter"/>
<map_variables variable_2="J_uni" variable_1="J_uni"/>
<map_variables variable_2="Ca_i" variable_1="Ca_i"/>
</connection>
<connection>
<map_components component_2="NAD_reduction" component_1="Na_Ca_exchanger"/>
<map_variables variable_2="K_Ca" variable_1="K_Ca"/>
</connection>
<connection>
<map_components component_2="differential_equations" component_1="Na_Ca_exchanger"/>
<map_variables variable_2="J_Na_Ca" variable_1="J_Na_Ca"/>
<map_variables variable_2="Ca_m" variable_1="Ca_m"/>
</connection>
<connection>
<map_components component_2="differential_equations" component_1="proton_pump"/>
<map_variables variable_2="JH_res" variable_1="JH_res"/>
<map_variables variable_2="Jo" variable_1="Jo"/>
<map_variables variable_2="NAD_m" variable_1="NAD_m"/>
<map_variables variable_2="NADH_m" variable_1="NADH_m"/>
</connection>
<connection>
<map_components component_2="Ca_release_from_the_ER" component_1="proton_leak"/>
<map_variables variable_2="JH_leak" variable_1="JH_leak"/>
</connection>
<connection>
<map_components component_2="differential_equations" component_1="proton_leak"/>
<map_variables variable_2="JH_leak" variable_1="JH_leak"/>
</connection>
<connection>
<map_components component_2="differential_equations" component_1="F0_F1_ATPase"/>
<map_variables variable_2="JH_F1" variable_1="JH_F1"/>
<map_variables variable_2="Jp_F1" variable_1="Jp_F1"/>
<map_variables variable_2="ADP_m" variable_1="ADP_m"/>
<map_variables variable_2="ATP_m" variable_1="ATP_m"/>
</connection>
<connection>
<map_components component_2="ATP_ADP_exchange" component_1="F0_F1_ATPase"/>
<map_variables variable_2="Jp_F1" variable_1="Jp_F1"/>
</connection>
<connection>
<map_components component_2="differential_equations" component_1="ATP_ADP_exchange"/>
<map_variables variable_2="J_ant" variable_1="J_ant"/>
<map_variables variable_2="ADP_m" variable_1="ADP_m"/>
<map_variables variable_2="ATP_m" variable_1="ATP_m"/>
<map_variables variable_2="ADP_i" variable_1="ADP_i"/>
<map_variables variable_2="ATP_i" variable_1="ATP_i"/>
</connection>
<connection>
<map_components component_2="differential_equations" component_1="NAD_reduction"/>
<map_variables variable_2="J_red" variable_1="J_red"/>
<map_variables variable_2="Ca_m" variable_1="Ca_m"/>
</connection>
<connection>
<map_components component_2="TCA_cycle_ADP_phosphorylation" component_1="NAD_reduction"/>
<map_variables variable_2="J_red_basal" variable_1="J_red_basal"/>
<map_variables variable_2="f_PDHa" variable_1="f_PDHa"/>
</connection>
<connection>
<map_components component_2="glycolytic_phosphorylation_of_ADP" component_1="NAD_reduction"/>
<map_variables variable_2="J_gly_tot" variable_1="J_gly_tot"/>
</connection>
<connection>
<map_components component_2="differential_equations" component_1="TCA_cycle_ADP_phosphorylation"/>
<map_variables variable_2="J_ptca" variable_1="J_ptca"/>
</connection>
<connection>
<map_components component_2="glycolytic_phosphorylation_of_ADP" component_1="TCA_cycle_ADP_phosphorylation"/>
<map_variables variable_2="J_gly_tot" variable_1="J_gly_tot"/>
</connection>
<connection>
<map_components component_2="differential_equations" component_1="glycolytic_phosphorylation_of_ADP"/>
<map_variables variable_2="J_gly_tot" variable_1="J_gly_tot"/>
<map_variables variable_2="ATP_i" variable_1="ATP_i"/>
</connection>
<connection>
<map_components component_2="hydrolysis_of_ATP" component_1="glycolytic_phosphorylation_of_ADP"/>
<map_variables variable_2="Glc" variable_1="Glc"/>
</connection>
<connection>
<map_components component_2="differential_equations" component_1="hydrolysis_of_ATP"/>
<map_variables variable_2="J_hyd" variable_1="J_hyd"/>
<map_variables variable_2="ATP_i" variable_1="ATP_i"/>
</connection>
<connection>
<map_components component_2="differential_equations" component_1="Ca_release_from_the_ER"/>
<map_variables variable_2="J_erout" variable_1="J_erout"/>
<map_variables variable_2="Ca_i" variable_1="Ca_i"/>
<map_variables variable_2="Ca_ER" variable_1="Ca_ER"/>
<map_variables variable_2="h" variable_1="h"/>
</connection>
<connection>
<map_components component_2="differential_equations" component_1="pumping_Ca_into_the_ER"/>
<map_variables variable_2="J_serca" variable_1="J_serca"/>
<map_variables variable_2="Ca_i" variable_1="Ca_i"/>
</connection>
<rdf:RDF>
<rdf:Bag rdf:about="rdf:#c29bfb3e-8fd4-4f49-a193-c2b1498ee192">
<rdf:li>mitochondria</rdf:li>
<rdf:li>IP3</rdf:li>
<rdf:li>signal transduction</rdf:li>
<rdf:li>Pancreatic Beta-Cell</rdf:li>
<rdf:li>calcium dynamics</rdf:li>
<rdf:li>ip3</rdf:li>
<rdf:li>electrophysiology</rdf:li>
<rdf:li>beta cell</rdf:li>
</rdf:Bag>
<rdf:Seq rdf:about="rdf:#b3a3f2ac-46d2-4035-a6ec-447bf35a492d">
<rdf:li rdf:resource="rdf:#9f13475f-fa73-4ef0-a865-7b63688525bb"/>
<rdf:li rdf:resource="rdf:#2f12347e-cb2c-423a-a866-1a15238b32d5"/>
</rdf:Seq>
<rdf:Description rdf:about="rdf:#f3aec6c6-63ad-40a3-a0b0-94733361757d">
<dcterms:W3CDTF>2002-03-01</dcterms:W3CDTF>
</rdf:Description>
<rdf:Description rdf:about="rdf:#8e43118f-6181-4020-a06e-168048d50965">
<vCard:Given>Joel</vCard:Given>
<vCard:Family>Keizer</vCard:Family>
<vCard:Other>E</vCard:Other>
</rdf:Description>
<rdf:Description rdf:about="rdf:#88523781-7db3-4140-a982-17738d82d621">
<vCard:N rdf:resource="rdf:#8ffd332f-8a0d-470f-9d64-a6e890c156e9"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#c1e21d13-af28-472c-8c65-a59a753d4393">
<dcterms:W3CDTF>2003-08-12</dcterms:W3CDTF>
</rdf:Description>
<rdf:Description rdf:about="rdf:#44818b64-e445-4bb7-8cd0-e164c66ccb2e">
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Mitochondrial modulation of intracellular Ca2+ signaling
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Corrected equations: J_uni in Ca_uniporter component, JH_F1 in
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Mitochondrial Modulation of Intracellular Ca2+ Signalling
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This is the CellML description of Christopher Fall and Joel Keizer's
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Corrected several equations.
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