- Author:
- rcai987 <devnull@localhost>
- Date:
- 2015-02-05 13:11:02+13:00
- Desc:
- Added annotations to magnus_keizer_1998.cellml
- Permanent Source URI:
- http://models.cellml.org/workspace/magnus_keizer_1998/rawfile/588d1684e5e3737c51d1c3926b20987a6a3fc397/magnus_keizer_1998.cellml
<?xml version='1.0'?>
<!-- FILE : magnus_model_1998.xml
CREATED : 11th April 2002
LAST MODIFIED : 11th August 2003
AUTHOR : Catherine Lloyd
Bioengineering Institute
The University of Auckland
MODEL STATUS : This model conforms to the CellML 1.0 Specification released on
10th August 2001, and the 16/1/02 CellML Metadata 1.0 Specification.
DESCRIPTION : This file contains a CellML description of Magnus and Keizer's
1998 model of beta-call mitochondrial Ca2+ handling and electrical activity I. Cytoplasmic variables.
CHANGES:
18/07/2002 - CML - Added more metadata.
09/04/2003 - AAC - Added publication date information.
11/08/2003 - CML - Corrected equations.
-->
<model name="magnus_keizer_1998_version01" 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#">
<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
<articleinfo>
<title>A Model Of Beta-Cell Mitochondrial Calcium Handling And Electrical Activity</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>
When exposed to a threshold concentration of glucose, pancreatic beta-cells from a wide range of species exhibit a complicated pattern of electrical activity. Bursts of action potential spikes (the "active" phase) are observed, separated by a "silent" phase of membrane repolarisation. At even higher glucose concentrations, continuous action potentials are seen. This electrical activity has two important physiological correlates: increased cytosolic Ca<superscript>2+</superscript> concentration ([Ca<superscript>2+</superscript>]<subscript>i</subscript>) and increased rate of insulin secretion during the active phase. It is generally accepted that the rise in [Ca<superscript>2+</superscript>]<subscript>i</subscript> plays a major role in insulin secretion and that the action potential spikes during a burst are responsible for the rise in [Ca<superscript>2+</superscript>]<subscript>i</subscript>.
</para>
<para>
Because the glucose signal for insulin secretion operates via metabolism rather than through a plasma membrane-bound receptor, the details of how glucose stimulates electrical activity have been difficult to resolve. However, experimental data and theoretical models have begun to investigate the phenomenon. In 1997 Gerhard Magnus and Joel Keizer published a minimal mathematical model to describe Ca<superscript>2+</superscript> handling by mitochondria in the pancreatic beta-cell (see <ulink url="${HTML_EXMPL_MITOCHONDRIAL_CA_HANDLING}">The Magnus-Keizer Mitochondrial Ca<superscript>2+</superscript> Handling Model, 1997</ulink>). Their kinetic model incorporated six transport mechanisms in the inner mitochondrial membrane, including proton pumping via respiration and proton pumping by the F0F1-ATPase, a proton leak, adenine nucleotide exchange, the Ca<superscript>2+</superscript> uniporter and Na<superscript>+</superscript>/Ca<superscript>2+</superscript> exchange. In their 1998 model, Gerhard Magnus and Joel Keizer continue their development of a kinetic model of bursting electrical activity in the pancreatic beta-cell. Their minimal model of Ca<superscript>2+</superscript> handling is expanded to include, amongst other factors, the glucose dependence of the rate of production of mitochondrial reducing equivalents (see <xref linkend="fig_cell_diagram"/> below).
</para>
<para>
The complete original paper reference is cited below:
</para>
<para>
Model of beta-cell mitochondrial calcium handling and electrical activity. I. Cytoplasmic variables, Gerhard Magnus and Joel Keizer, 1998,<emphasis>American Journal of Physiology</emphasis>, 274, C1158-C1173. <ulink url="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&list_uids=9575813&dopt=Abstract">PubMed ID: 9575813</ulink>
</para>
<para>
The raw CellML description of the model of beta-cell mitochondrial calcium handling can be downloaded in various formats as described in <xref linkend="sec_download_this_model"/>
</para>
<informalfigure float="0" id="fig_cell_diagram">
<mediaobject>
<imageobject>
<objectinfo>
<title>diagram of the mitochondrial Ca2+ handling model</title>
</objectinfo>
<imagedata fileref="magnus_1998.png"/>
</imageobject>
</mediaobject>
<caption>A schematic representation of the bursting mechanism assumed by the Magnus-Keizer whole cell model. This diagram shows the plasma membrane currents associated with burst and spike oscillations; the area corresponding to the cytosol gives a simplified description of Ca<superscript>2+</superscript> feedback driving adenine nucleotide concentration oscillations and ATP-sensitive K<superscript>+</superscript> (K<subscript>ATP</subscript>) channel gating. Uptake of Ca<superscript>2+</superscript> by mitochondria positively affects oxidative phosphorylation by activating pyruvate dehydrogenase (PDH) and other dehydrogenases; futile cycling of Ca<superscript>2+</superscript> across the mitochondrial inner membrane periodically diminishes ATP production by lower the inner membrane voltage (delta_psi). The black arrows represent ion fluxes and the red and green arrows represent inactivation and activation (respectively) of membrane transport and other key processes.</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="millisecond">
<unit prefix="milli" units="second"/>
</units>
<units name="per_millisecond">
<unit exponent="-1" units="millisecond"/>
</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="picoS">
<unit prefix="pico" units="siemens"/>
</units>
<units name="picoS_per_mM">
<unit units="picoS"/>
<unit exponent="-1" units="millimolar"/>
</units>
<units name="picoF">
<unit prefix="pico" units="farad"/>
</units>
<units name="nanomole_per_min_mV_mg">
<unit prefix="nano" units="mole"/>
<unit exponent="-1" units="minute"/>
<unit exponent="-1" prefix="milli" units="gram"/>
<unit exponent="-1" units="millivolt"/>
</units>
<units name="nanomole_per_mg">
<unit prefix="nano" units="mole"/>
<unit exponent="-1" prefix="milli" units="gram"/>
</units>
<units name="nanomole_per_mV_mg">
<unit prefix="nano" units="mole"/>
<unit exponent="-1" prefix="milli" units="gram"/>
<unit exponent="-1" units="millivolt"/>
</units>
<units name="nanomole_per_min_mg">
<unit prefix="nano" units="mole"/>
<unit exponent="-1" units="minute"/>
<unit exponent="-1" prefix="milli" units="gram"/>
</units>
<units name="nanomole_per_min_mg_mM">
<unit prefix="nano" units="mole"/>
<unit exponent="-1" units="minute"/>
<unit exponent="-1" prefix="milli" units="gram"/>
<unit exponent="-1" units="millimolar"/>
</units>
<units name="micromolar_3">
<unit exponent="3" units="micromolar"/>
</units>
<units name="femtoA">
<unit prefix="femto" units="ampere"/>
</units>
<units name="micromolar_per_ms_fA">
<unit units="micromolar"/>
<unit exponent="-1" units="millisecond"/>
<unit exponent="-1" prefix="femto" units="ampere"/>
</units>
<units name="per_mM_mV_ms">
<unit exponent="-1" units="millimolar"/>
<unit exponent="-1" units="millivolt"/>
<unit exponent="-1" units="millisecond"/>
</units>
<units name="mM_min_mg_per_ms_nmol">
<unit units="millimolar"/>
<unit units="minute"/>
<unit prefix="milli" units="gram"/>
<unit exponent="-1" units="millisecond"/>
<unit exponent="-1" prefix="nano" units="mole"/>
</units>
<units name="uM_min_mg_per_ms_nmol">
<unit units="micromolar"/>
<unit units="minute"/>
<unit prefix="milli" units="gram"/>
<unit exponent="-1" units="millisecond"/>
<unit exponent="-1" prefix="nano" units="mole"/>
</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="millisecond"/>
</component>
<!-- plasma membrane equations. -->
<component name="plasma_membrane">
<variable name="V" 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="6157.0" name="C" units="picoF"/>
<variable name="time" public_interface="in" units="millisecond"/>
<variable cmeta:id="id_000000003" name="i_K_dr" public_interface="in" units="femtoA"/>
<variable name="i_K_ATP" public_interface="in" units="femtoA"/>
<variable cmeta:id="id_000000088" name="i_Ca_f" public_interface="in" units="femtoA"/>
<variable cmeta:id="id_000000087" name="i_Ca_s" public_interface="in" units="femtoA"/>
<variable cmeta:id="id_000000039" name="i_NS" public_interface="in" units="femtoA"/>
<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>
<divide/>
<apply>
<minus/>
<apply>
<plus/>
<ci> i_K_dr </ci>
<ci> i_K_ATP </ci>
<ci> i_Ca_f </ci>
<ci> i_Ca_s </ci>
<ci> i_NS </ci>
</apply>
</apply>
<ci> C </ci>
</apply>
</apply>
</math>
</component>
<component cmeta:id="id_000000001" name="delayed_rectifier_K_channel_current">
<variable cmeta:id="id_000000002" name="i_K_dr" public_interface="out" units="femtoA"/>
<variable cmeta:id="id_000000005" initial_value="-75.0" name="V_K" public_interface="out" units="millivolt"/>
<variable cmeta:id="id_000000004" initial_value="5000.0" name="g_K_dr" units="picoS"/>
<variable name="time" private_interface="out" public_interface="in" units="millisecond"/>
<variable name="V" private_interface="out" public_interface="in" units="millivolt"/>
<variable name="n" private_interface="in" units="dimensionless"/>
<variable name="I" private_interface="in" units="dimensionless"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="i_K_dr_calculation">
<eq/>
<ci> i_K_dr </ci>
<apply>
<times/>
<ci> g_K_dr </ci>
<ci> n </ci>
<ci> I </ci>
<apply>
<minus/>
<ci> V </ci>
<ci> V_K </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component cmeta:id="id_000000006" name="delayed_rectifier_K_channel_current_n_gate">
<variable cmeta:id="id_000000007" name="n" public_interface="out" units="dimensionless"/>
<variable cmeta:id="id_000000008" name="n_infinity" units="dimensionless"/>
<variable cmeta:id="id_000000009" name="tau_n" units="millisecond"/>
<variable name="V" public_interface="in" units="millivolt"/>
<variable name="time" public_interface="in" units="millisecond"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="n_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> n </ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci> n_infinity </ci>
<ci> n </ci>
</apply>
<ci> tau_n </ci>
</apply>
</apply>
<apply id="n_infinity_calculation">
<eq/>
<ci> n_infinity </ci>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<cn cellml:units="millivolt"> -20.0 </cn>
<ci> V </ci>
</apply>
<cn cellml:units="millivolt"> 5.3 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="tau_n_calculation">
<eq/>
<ci> tau_n </ci>
<apply>
<divide/>
<cn cellml:units="millisecond"> 50.0 </cn>
<apply>
<plus/>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 75.0 </cn>
</apply>
<cn cellml:units="millivolt"> 65.0 </cn>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 75.0 </cn>
</apply>
</apply>
<cn cellml:units="millivolt"> 20.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component cmeta:id="id_000000010" name="delayed_rectifier_K_channel_current_I_gate">
<variable cmeta:id="id_000000012" name="I" public_interface="out" units="dimensionless"/>
<variable cmeta:id="id_000000013" name="I_infinity" units="dimensionless"/>
<variable cmeta:id="id_000000011" initial_value="2600.0" name="tau_I" units="millisecond"/>
<variable name="V" public_interface="in" units="millivolt"/>
<variable name="time" public_interface="in" units="millisecond"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="I_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> I </ci>
</apply>
<apply>
<minus/>
<apply>
<divide/>
<apply>
<minus/>
<ci> I </ci>
<ci> I_infinity </ci>
</apply>
<ci> tau_I </ci>
</apply>
</apply>
</apply>
<apply id="I_infinity_calculation">
<eq/>
<ci> I_infinity </ci>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<cn cellml:units="millivolt"> 36.0 </cn>
<ci> V </ci>
</apply>
<cn cellml:units="millivolt"> 4.5 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component cmeta:id="id_000000014" name="K_ATP_channel_current">
<variable cmeta:id="id_000000015" name="i_K_ATP" public_interface="out" units="femtoA"/>
<variable cmeta:id="id_000000016" initial_value="70000.0" name="g_K_ATP" units="picoS"/>
<variable cmeta:id="id_000000017" name="O_K_ATP" units="dimensionless"/>
<variable initial_value="17.0" name="K_dd" units="micromolar"/>
<variable initial_value="26.0" name="K_td" units="micromolar"/>
<variable initial_value="1.0" name="K_tt" units="micromolar"/>
<variable name="MgADP_i" units="millimolar"/>
<variable name="V_K" public_interface="in" units="millivolt"/>
<variable name="time" public_interface="in" units="millisecond"/>
<variable name="V" public_interface="in" units="millivolt"/>
<variable name="ADP3_i" public_interface="in" units="millimolar"/>
<variable name="ATP4_i" public_interface="in" units="millimolar"/>
<variable name="ADP_i" public_interface="in" units="millimolar"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="i_K_ATP_calculation">
<eq/>
<ci> i_K_ATP </ci>
<apply>
<times/>
<ci> g_K_ATP </ci>
<ci> O_K_ATP </ci>
<apply>
<minus/>
<ci> V </ci>
<ci> V_K </ci>
</apply>
</apply>
</apply>
<apply id="O_K_ATP_calculation">
<eq/>
<ci> O_K_ATP </ci>
<apply>
<divide/>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.8 </cn>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 2.0 </cn>
<ci> MgADP_i </ci>
</apply>
<ci> K_dd </ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.89 </cn>
<apply>
<power/>
<apply>
<divide/>
<ci> MgADP_i </ci>
<ci> K_dd </ci>
</apply>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
</apply>
</apply>
<apply>
<times/>
<apply>
<power/>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<divide/>
<ci> MgADP_i </ci>
<ci> K_dd </ci>
</apply>
</apply>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<divide/>
<ci> ADP3_i </ci>
<ci> K_td </ci>
</apply>
<apply>
<divide/>
<ci> ATP4_i </ci>
<ci> K_tt </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="MgADP_i_calculation">
<eq/>
<ci> MgADP_i </ci>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.55 </cn>
<cn cellml:units="dimensionless"> 0.3 </cn>
<ci> ADP_i </ci>
</apply>
</apply>
</math>
</component>
<component cmeta:id="id_000000018" name="fast_Ca_channel_current">
<variable cmeta:id="id_000000019" name="i_Ca_f" public_interface="out" units="femtoA"/>
<variable cmeta:id="id_000000020" initial_value="4116.0" name="g_Ca" public_interface="out" units="picoS_per_mM"/>
<variable name="O_f" private_interface="out" units="dimensionless"/>
<variable name="k_plus_1" private_interface="out" units="per_millisecond"/>
<variable name="k_minus_1" private_interface="out" units="per_millisecond"/>
<variable name="k_plus_2" private_interface="out" units="per_millisecond"/>
<variable initial_value="65.0" name="k_minus_2" private_interface="out" units="per_millisecond"/>
<variable initial_value="0.02" name="k_plus_3" private_interface="out" units="per_millisecond"/>
<variable initial_value="0.005" name="k_minus_3" private_interface="out" units="per_millisecond"/>
<variable initial_value="2.5" name="Ca_o" private_interface="out" public_interface="out" units="millimolar"/>
<variable name="Ca_d" private_interface="out" units="millimolar"/>
<variable name="O_infinity" private_interface="out" units="dimensionless"/>
<variable initial_value="1.3" name="tau_Ca_f" units="millisecond"/>
<variable name="time" private_interface="out" public_interface="in" units="millisecond"/>
<variable name="V" private_interface="out" public_interface="in" units="millivolt"/>
<variable name="R" public_interface="in" units="millijoule_per_mole_kelvin"/>
<variable name="T" public_interface="in" units="kelvin"/>
<variable name="F" public_interface="in" units="coulomb_per_mole"/>
<variable name="C" private_interface="in" units="dimensionless"/>
<variable name="B" private_interface="in" units="dimensionless"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="i_Ca_f_calculation">
<eq/>
<ci> i_Ca_f </ci>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.27 </cn>
<ci> g_Ca </ci>
<ci> O_f </ci>
<apply>
<divide/>
<apply>
<times/>
<ci> Ca_o </ci>
<ci> V </ci>
</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>
<ci> V </ci>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="O_f_calculation">
<eq/>
<ci> O_f </ci>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<plus/>
<ci> C </ci>
<ci> B </ci>
</apply>
</apply>
</apply>
<apply id="k_plus_1_calculation">
<eq/>
<ci> k_plus_1 </ci>
<apply>
<divide/>
<ci> O_infinity </ci>
<ci> tau_Ca_f </ci>
</apply>
</apply>
<apply id="k_minus_1_calculation">
<eq/>
<ci> k_minus_1 </ci>
<apply>
<divide/>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> O_infinity </ci>
</apply>
<ci> tau_Ca_f </ci>
</apply>
</apply>
<apply id="O_infinity_calculation">
<eq/>
<ci> O_infinity </ci>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<plus/>
<cn cellml:units="millivolt"> 15.0 </cn>
<ci> V </ci>
</apply>
</apply>
<cn cellml:units="millivolt"> 6.2 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="Ca_d_calculation">
<eq/>
<ci> Ca_d </ci>
<apply>
<times/>
<apply>
<divide/>
<cn cellml:units="per_mM_mV_ms"> -3.02 </cn>
<ci> k_plus_2 </ci>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci> Ca_o </ci>
<ci> V </ci>
</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>
<ci> V </ci>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component cmeta:id="id_000000021" name="fast_Ca_channel_current_C_gate">
<variable name="C" public_interface="out" units="dimensionless"/>
<variable name="O_infinity" public_interface="in" units="dimensionless"/>
<variable name="Ca_d" public_interface="in" units="millimolar"/>
<variable name="k_plus_1" public_interface="in" units="per_millisecond"/>
<variable name="k_minus_1" public_interface="in" units="per_millisecond"/>
<variable name="k_plus_2" public_interface="in" units="per_millisecond"/>
<variable name="k_minus_2" public_interface="in" units="per_millisecond"/>
<variable name="Ca_o" public_interface="in" units="millimolar"/>
<variable name="O_f" public_interface="in" units="dimensionless"/>
<variable name="V" public_interface="in" units="millivolt"/>
<variable name="time" public_interface="in" units="millisecond"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="C_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> C </ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> k_minus_1 </ci>
<apply>
<divide/>
<ci> k_minus_2 </ci>
<apply>
<plus/>
<apply>
<times/>
<ci> k_plus_2 </ci>
<ci> Ca_d </ci>
<ci> V </ci>
</apply>
<ci> k_minus_2 </ci>
</apply>
</apply>
<ci> O_f </ci>
</apply>
<apply>
<times/>
<ci> k_plus_1 </ci>
<ci> C </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component cmeta:id="id_000000022" name="fast_Ca_channel_current_B_gate">
<variable name="B" public_interface="out" units="dimensionless"/>
<variable name="Ca_d" public_interface="in" units="millimolar"/>
<variable name="O_f" public_interface="in" units="dimensionless"/>
<variable name="k_plus_2" public_interface="in" units="per_millisecond"/>
<variable name="k_minus_2" public_interface="in" units="per_millisecond"/>
<variable name="k_plus_3" public_interface="in" units="per_millisecond"/>
<variable name="k_minus_3" public_interface="in" units="per_millisecond"/>
<variable name="V" public_interface="in" units="millivolt"/>
<variable name="time" public_interface="in" units="millisecond"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="B_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> B </ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> k_plus_3 </ci>
<apply>
<divide/>
<apply>
<times/>
<ci> k_plus_2 </ci>
<ci> Ca_d </ci>
<ci> V </ci>
</apply>
<apply>
<plus/>
<apply>
<times/>
<ci> k_plus_2 </ci>
<ci> Ca_d </ci>
<ci> V </ci>
</apply>
<ci> k_minus_2 </ci>
</apply>
</apply>
<ci> O_f </ci>
</apply>
<apply>
<times/>
<ci> k_minus_3 </ci>
<ci> B </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component cmeta:id="id_000000023" name="slow_Ca_channel_current">
<variable cmeta:id="id_000000024" name="i_Ca_s" public_interface="out" units="femtoA"/>
<variable cmeta:id="id_000000025" name="O_s" units="dimensionless"/>
<variable name="g_Ca" public_interface="in" units="picoS_per_mM"/>
<variable name="time" private_interface="out" public_interface="in" units="millisecond"/>
<variable name="V" private_interface="out" public_interface="in" units="millivolt"/>
<variable name="R" public_interface="in" units="millijoule_per_mole_kelvin"/>
<variable name="T" public_interface="in" units="kelvin"/>
<variable name="F" public_interface="in" units="coulomb_per_mole"/>
<variable name="Ca_o" public_interface="in" units="millimolar"/>
<variable name="J" private_interface="in" units="dimensionless"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="i_Ca_s_calculation">
<eq/>
<ci> i_Ca_s </ci>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.73 </cn>
<ci> g_Ca </ci>
<ci> O_s </ci>
<apply>
<divide/>
<apply>
<times/>
<ci> Ca_o </ci>
<ci> V </ci>
</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>
<ci> V </ci>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="O_s_calculation">
<eq/>
<ci> O_s </ci>
<apply>
<divide/>
<ci> J </ci>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<plus/>
<cn cellml:units="millivolt"> 11.0 </cn>
<ci> V </ci>
</apply>
</apply>
<cn cellml:units="millivolt"> 3.6 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component cmeta:id="id_000000026" name="slow_Ca_channel_current_J_gate">
<variable name="J" public_interface="out" units="dimensionless"/>
<variable name="J_infinity" units="dimensionless"/>
<variable name="tau_J" units="millisecond"/>
<variable initial_value="50000.0" name="TJ" units="millisecond"/>
<variable initial_value="1500.0" name="Tmin" units="millisecond"/>
<variable name="V" public_interface="in" units="millivolt"/>
<variable name="time" public_interface="in" units="millisecond"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="J_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> J </ci>
</apply>
<apply>
<minus/>
<apply>
<divide/>
<apply>
<minus/>
<ci> J </ci>
<ci> J_infinity </ci>
</apply>
<ci> tau_J </ci>
</apply>
</apply>
</apply>
<apply id="J_infinity_calculation">
<eq/>
<ci> J_infinity </ci>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 50.0 </cn>
</apply>
<cn cellml:units="millivolt"> 6.3 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="tau_J_calculation">
<eq/>
<ci> tau_J </ci>
<apply>
<plus/>
<apply>
<divide/>
<ci> TJ </ci>
<apply>
<plus/>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 50.0 </cn>
</apply>
<cn cellml:units="millivolt"> 6.3 </cn>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 50.0 </cn>
</apply>
</apply>
<cn cellml:units="millivolt"> 6.3 </cn>
</apply>
</apply>
</apply>
</apply>
<ci> Tmin </ci>
</apply>
</apply>
</math>
</component>
<component cmeta:id="id_000000027" name="non_selective_cation_channel_current">
<variable cmeta:id="id_000000028" name="i_NS" public_interface="out" units="femtoA"/>
<variable cmeta:id="id_000000029" initial_value="0.5" name="K_NS" units="millimolar"/>
<variable cmeta:id="id_000000030" initial_value="24.0" name="g_NS" units="picoS_per_mM"/>
<variable name="time" public_interface="in" units="millisecond"/>
<variable name="V" public_interface="in" units="millivolt"/>
<variable name="R" public_interface="in" units="millijoule_per_mole_kelvin"/>
<variable name="T" public_interface="in" units="kelvin"/>
<variable name="F" public_interface="in" units="coulomb_per_mole"/>
<variable name="Ca_o" public_interface="in" units="millimolar"/>
<variable name="ATP_i" public_interface="in" units="millimolar"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="i_NS_calculation">
<eq/>
<ci> i_NS </ci>
<apply>
<times/>
<apply>
<divide/>
<ci> g_NS </ci>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<divide/>
<ci> K_NS </ci>
<ci> ATP_i </ci>
</apply>
</apply>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci> Ca_o </ci>
<ci> V </ci>
</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>
<ci> V </ci>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component cmeta:id="id_000000031" name="cytosolic_ADP">
<variable cmeta:id="id_000000033" name="ATP_i" public_interface="out" units="millimolar"/>
<variable cmeta:id="id_000000032" name="ADP_i" public_interface="out" units="millimolar"/>
<variable name="glu" public_interface="out" units="millimolar"/>
<variable initial_value="0.00000153" name="gamma1" units="mM_min_mg_per_ms_nmol"/>
<variable initial_value="50.0" name="tau_hyd" units="second"/>
<variable initial_value="2.7" name="n_hyd" units="dimensionless"/>
<variable name="J_hyd" units="nanomole_per_min_mg"/>
<variable initial_value="41.0" name="k_hyd" units="nanomole_per_min_mg_mM"/>
<variable name="delta_J_hyd" units="nanomole_per_min_mg"/>
<variable name="delta_J_hyd_ss" units="nanomole_per_min_mg"/>
<variable initial_value="30.1" name="delta_J_hyd_max" units="nanomole_per_min_mg"/>
<variable name="Jp_gly" units="nanomole_per_min_mg"/>
<variable name="delta_J_gly_total" units="nanomole_per_min_mg"/>
<variable initial_value="8.7" name="K_glu" units="millimolar"/>
<variable cmeta:id="id_000000042" name="J_ANT" public_interface="in" units="nanomole_per_min_mg"/>
<variable name="time" public_interface="in" units="millisecond"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="ADP_i_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> ADP_i </ci>
</apply>
<apply>
<times/>
<ci> gamma1 </ci>
<apply>
<minus/>
<ci> J_hyd </ci>
<apply>
<plus/>
<ci> J_ANT </ci>
<ci> Jp_gly </ci>
</apply>
</apply>
</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="J_hyd_calculation">
<eq/>
<ci> J_hyd </ci>
<apply>
<plus/>
<apply>
<times/>
<ci> k_hyd </ci>
<ci> ATP_i </ci>
</apply>
<ci> delta_J_hyd </ci>
</apply>
</apply>
<apply id="Jp_gly_calculation">
<eq/>
<ci> Jp_gly </ci>
<apply>
<times/>
<cn cellml:units="dimensionless"> 2.0 </cn>
<ci> delta_J_gly_total </ci>
</apply>
</apply>
<apply id="delta_J_hyd_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> delta_J_hyd </ci>
</apply>
<apply>
<times/>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> tau_hyd </ci>
</apply>
<apply>
<minus/>
<ci> delta_J_hyd_ss </ci>
<ci> delta_J_hyd </ci>
</apply>
</apply>
</apply>
<apply id="delta_J_hyd_ss_calculation">
<eq/>
<ci> delta_J_hyd_ss </ci>
<apply>
<divide/>
<ci> delta_J_hyd_max </ci>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<power/>
<apply>
<divide/>
<ci> K_glu </ci>
<ci> glu </ci>
</apply>
<ci> n_hyd </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component cmeta:id="id_000000034" name="cytosolic_Ca">
<variable cmeta:id="id_000000035" name="Ca_i" public_interface="out" units="micromolar"/>
<variable initial_value="0.00153" name="gamma2" units="uM_min_mg_per_ms_nmol"/>
<variable initial_value="0.00000678" name="alpha" units="micromolar_per_ms_fA"/>
<variable initial_value="0.19" name="k_Ca" units="per_millisecond"/>
<variable initial_value="0.01" name="f_i" units="dimensionless"/>
<variable cmeta:id="id_000000040" name="i_NS" public_interface="in" units="femtoA"/>
<variable name="i_Ca_f" public_interface="in" units="femtoA"/>
<variable name="i_Ca_s" public_interface="in" units="femtoA"/>
<variable name="J_uni" public_interface="in" units="nanomole_per_min_mg"/>
<variable name="J_NaCa" public_interface="in" units="nanomole_per_min_mg"/>
<variable name="time" public_interface="in" units="millisecond"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="Ca_i_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> Ca_i </ci>
</apply>
<apply>
<times/>
<ci> f_i </ci>
<apply>
<minus/>
<apply>
<times/>
<apply>
<minus/>
<ci> alpha </ci>
</apply>
<apply>
<plus/>
<ci> i_NS </ci>
<ci> i_Ca_f </ci>
<ci> i_Ca_s </ci>
</apply>
</apply>
<apply>
<plus/>
<apply>
<times/>
<ci> gamma2 </ci>
<apply>
<minus/>
<ci> J_uni </ci>
<ci> J_NaCa </ci>
</apply>
</apply>
<apply>
<times/>
<ci> k_Ca </ci>
<ci> Ca_i </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component cmeta:id="id_000000045" name="mitochondrial_membrane">
<variable initial_value="50.0" name="delta_psi" public_interface="out" units="millivolt"/>
<variable name="proton_motive_force" public_interface="out" units="nanomole_per_min_mg"/>
<variable initial_value="0.2" name="g_H" public_interface="out" units="nanomole_per_min_mV_mg"/>
<variable initial_value="-0.4" name="delta_pH" public_interface="out" units="dimensionless"/>
<variable initial_value="0.00145" name="Cmito" units="nanomole_per_mV_mg"/>
<variable name="pH_i" units="dimensionless"/>
<variable name="pH_m" units="dimensionless"/>
<variable cmeta:id="id_000000054" name="JH_leak" public_interface="in" units="nanomole_per_min_mg"/>
<variable name="JH_res" public_interface="in" units="nanomole_per_min_mg"/>
<variable cmeta:id="id_000000061" name="JH_F1" public_interface="in" units="nanomole_per_min_mg"/>
<variable cmeta:id="id_000000046" name="J_ANT" public_interface="in" units="nanomole_per_min_mg"/>
<variable cmeta:id="id_000000048" name="J_uni" public_interface="in" units="nanomole_per_min_mg"/>
<variable name="J_NaCa" public_interface="in" units="nanomole_per_min_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="millisecond"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="mitochondrial_membrane_voltage_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> delta_psi </ci>
</apply>
<apply>
<times/>
<apply>
<divide/>
<cn cellml:units="dimensionless"> -1.0 </cn>
<apply>
<times/>
<cn cellml:units="dimensionless"> 60000.0 </cn>
<ci> Cmito </ci>
</apply>
</apply>
<apply>
<plus/>
<apply>
<minus/>
<ci> JH_res </ci>
</apply>
<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>
<ci> J_NaCa </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>
<component name="proton_pump">
<variable name="JH_res" public_interface="out" units="nanomole_per_min_mg"/>
<variable name="J_o" public_interface="out" units="nanomole_per_min_mg"/>
<variable name="A_res" units="dimensionless"/>
<variable initial_value="135000000000000000.0" 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 cmeta:id="id_000000064" name="NAD_m" public_interface="in" units="nanomolar"/>
<variable cmeta:id="id_000000063" name="NADH_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="delta_psi" 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>
<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> 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>
<minus/>
<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>
<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> delta_psi </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="J_o_calculation">
<eq/>
<ci> J_o </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> delta_psi </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> delta_psi </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_000000065" name="proton_leak">
<variable cmeta:id="id_000000066" name="JH_leak" public_interface="out" units="nanomole_per_min_mg"/>
<variable name="g_H" public_interface="in" units="nanomole_per_min_mV_mg"/>
<variable name="proton_motive_force" public_interface="in" units="nanomole_per_min_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_000000055" name="F0_F1_ATPase">
<variable cmeta:id="id_000000056" name="JH_F1" public_interface="out" units="nanomole_per_min_mg"/>
<variable cmeta:id="id_000000057" name="Jp_F1" public_interface="out" units="nanomole_per_min_mg"/>
<variable cmeta:id="id_000000058" initial_value="0.7" name="rho_F1" units="nanomole_per_mg"/>
<variable cmeta:id="id_000000059" initial_value="1710000.0" name="K_F1" units="millimolar"/>
<variable cmeta:id="id_000000060" name="A_F1" units="dimensionless"/>
<variable name="ATP_m_free" units="nanomolar"/>
<variable 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 name="ATP_m" public_interface="in" units="nanomolar"/>
<variable 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="delta_psi" 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>
<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>
<minus/>
<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>
<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> delta_psi </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> delta_psi </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> delta_psi </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_000000067" name="mitochondrial_NADH">
<variable cmeta:id="id_000000068" name="NADH_m" public_interface="out" units="nanomolar"/>
<variable cmeta:id="id_000000069" name="NAD_m" public_interface="out" units="nanomolar"/>
<variable initial_value="126.0" name="beta_max" units="nanomole_per_min_mg_mM"/>
<variable initial_value="1.66" name="beta1" units="per_millimolar"/>
<variable initial_value="0.0249" name="beta2" units="per_millimolar"/>
<variable initial_value="4.0" name="beta3" units="per_millimolar"/>
<variable initial_value="2.83" name="beta4" units="per_millimolar"/>
<variable initial_value="1.3" name="beta5" units="per_millimolar"/>
<variable initial_value="2.66" name="beta6" units="per_millimolar"/>
<variable initial_value="0.16" name="beta7" units="per_millimolar"/>
<variable initial_value="1.1" name="u2" units="dimensionless"/>
<variable initial_value="15.0" name="u1" units="dimensionless"/>
<variable name="J_red" units="nanomole_per_min_mg"/>
<variable name="delta_J_red_I" units="nanomole_per_min_mg"/>
<variable name="delta_J_red_II" units="nanomole_per_min_mg"/>
<variable initial_value="20.0" name="J_red_basal" units="nanomole_per_min_mg"/>
<variable name="delta_J_gly_total" units="nanomole_per_min_mg"/>
<variable name="f_glu" units="dimensionless"/>
<variable name="f_PDHa" units="dimensionless"/>
<variable initial_value="0.05" name="K_Ca2" units="micromolar"/>
<variable name="J_o" public_interface="in" units="nanomole_per_min_mg"/>
<variable name="glu" public_interface="in" units="millimolar"/>
<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="delta_pH" public_interface="in" units="dimensionless"/>
<variable name="delta_psi" public_interface="in" units="millivolt"/>
<variable cmeta:id="id_000000070" name="Ca_m" public_interface="in" units="millimolar"/>
<variable cmeta:id="id_000000041" name="i_NS" public_interface="in" units="femtoA"/>
<variable cmeta:id="id_000000071" name="ATP_i" public_interface="in" units="millimolar"/>
<variable cmeta:id="id_000000072" name="i_Ca_f" public_interface="in" units="femtoA"/>
<variable cmeta:id="id_000000073" name="i_Ca_s" public_interface="in" units="femtoA"/>
<variable name="time" public_interface="in" units="millisecond"/>
<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>
<times/>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<cn cellml:units="dimensionless"> 60000.0 </cn>
</apply>
<apply>
<minus/>
<ci> J_red </ci>
<ci> J_o </ci>
</apply>
</apply>
</apply>
<apply id="NAD_m_calculation">
<eq/>
<ci> NAD_m </ci>
<apply>
<minus/>
<cn cellml:units="nanomole_per_mg"> 8.0 </cn>
<ci> NADH_m </ci>
</apply>
</apply>
<apply id="J_red_calculation">
<eq/>
<ci> J_red </ci>
<apply>
<plus/>
<ci> J_red_basal </ci>
<ci> delta_J_red_I </ci>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.66 </cn>
<ci> delta_J_red_II </ci>
</apply>
</apply>
</apply>
<apply id="delta_J_red_I_calculation">
<eq/>
<ci> delta_J_red_I </ci>
<apply>
<times/>
<cn cellml:units="dimensionless"> 4.52 </cn>
<ci> f_glu</ci>
<ci> delta_J_gly_total </ci>
</apply>
</apply>
<apply id="delta_J_red_II_calculation">
<eq/>
<ci> delta_J_red_II </ci>
<apply>
<times/>
<cn cellml:units="dimensionless"> 2.84 </cn>
<ci> f_glu </ci>
<ci> delta_J_gly_total </ci>
</apply>
</apply>
<apply id="f_glu_calculation">
<eq/>
<ci> f_glu </ci>
<ci> f_PDHa </ci>
</apply>
<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_Ca2 </ci>
</apply>
</apply>
<cn cellml:units="dimensionless"> -2.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="delta_J_gly_total_calculation">
<eq/>
<ci> delta_J_gly_total </ci>
<apply>
<divide/>
<apply>
<times/>
<ci> beta_max </ci>
<ci> beta2 </ci>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<times/>
<ci> beta1 </ci>
<ci> glu </ci>
</apply>
</apply>
<ci> glu </ci>
<ci> ATP_i </ci>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<times/>
<ci> beta3 </ci>
<ci> ATP_i </ci>
</apply>
<apply>
<times/>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<times/>
<ci> beta4 </ci>
<ci> ATP_i </ci>
</apply>
</apply>
<apply>
<times/>
<ci> beta5 </ci>
<ci> glu </ci>
</apply>
</apply>
<apply>
<times/>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<times/>
<ci> beta6 </ci>
<ci> ATP_i </ci>
</apply>
</apply>
<apply>
<times/>
<ci> beta7 </ci>
<apply>
<power/>
<ci> glu </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component cmeta:id="id_000000074" name="ATP_ADP_exchange">
<variable cmeta:id="id_000000044" name="J_ANT" public_interface="out" units="nanomole_per_min_mg"/>
<variable name="ADP3_i" public_interface="out" units="nanomolar"/>
<variable name="ATP4_i" public_interface="out" units="nanomolar"/>
<variable cmeta:id="id_000000043" initial_value="1000.0" name="Jmax_ANT" units="nanomole_per_min_mg"/>
<variable cmeta:id="id_000000078" name="ATP_m" units="nanomolar"/>
<variable cmeta:id="id_000000079" name="ATP4_m" units="nanomolar"/>
<variable name="ADP3_m" units="nanomolar"/>
<variable initial_value="0.5" name="f" units="dimensionless"/>
<variable cmeta:id="id_000000075" name="ADP_i" public_interface="in" units="nanomolar"/>
<variable cmeta:id="id_000000077" name="ATP_i" public_interface="in" units="nanomolar"/>
<variable cmeta:id="id_000000076" name="ADP_m" public_interface="in" units="nanomolar"/>
<variable cmeta:id="id_000000062" name="Jp_F1" public_interface="in" units="nanomole_per_min_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> ATP4_i </ci>
<ci> ADP3_m </ci>
</apply>
<apply>
<times/>
<ci> ADP3_i </ci>
<ci> ATP4_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> ATP4_i </ci>
<ci> ADP3_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> ADP3_m </ci>
<ci> ATP4_m </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="ADP3_m_calculation">
<eq/>
<ci> ADP3_m </ci>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.45 </cn>
<cn cellml:units="dimensionless"> 0.8 </cn>
<ci> ADP_m </ci>
</apply>
</apply>
<apply id="ADP3_i_calculation">
<eq/>
<ci> ADP3_i </ci>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.45 </cn>
<cn cellml:units="dimensionless"> 0.3 </cn>
<ci> ADP_i </ci>
</apply>
</apply>
<apply id="ATP4_m_calculation">
<eq/>
<ci> ATP4_m </ci>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.05 </cn>
<ci> ATP_m </ci>
</apply>
</apply>
<apply id="ATP4_i_calculation">
<eq/>
<ci> ATP4_i </ci>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.05 </cn>
<ci> ATP_i </ci>
</apply>
</apply>
</math>
</component>
<component cmeta:id="id_000000080" name="mitochondrial_ADP">
<variable cmeta:id="id_000000082" name="ATP_m" public_interface="out" units="nanomolar"/>
<variable cmeta:id="id_000000081" name="ADP_m" public_interface="out" units="nanomolar"/>
<variable name="Jp_TCA" units="nanomole_per_min_mg"/>
<variable name="Jp_F1" public_interface="in" units="nanomole_per_min_mg"/>
<variable cmeta:id="id_000000047" name="J_ANT" public_interface="in" units="nanomole_per_min_mg"/>
<variable name="time" public_interface="in" units="second"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="ADP_m_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> ADP_m </ci>
</apply>
<apply>
<times/>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<cn cellml:units="dimensionless"> 60000.0 </cn>
</apply>
<apply>
<minus/>
<ci> J_ANT </ci>
<apply>
<plus/>
<ci> Jp_TCA </ci>
<ci> Jp_F1 </ci>
</apply>
</apply>
</apply>
</apply>
<apply id="ATP_m_calculation">
<eq/>
<ci> ATP_m </ci>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 12.0 </cn>
<ci> ADP_m </ci>
</apply>
</apply>
</math>
</component>
<component cmeta:id="id_000000049" name="Ca_uniporter">
<variable cmeta:id="id_000000051" name="J_uni" public_interface="out" units="nanomole_per_min_mg"/>
<variable initial_value="91.0" name="delta_psi_offset" public_interface="out" units="millivolt"/>
<variable cmeta:id="id_000000050" initial_value="400.0" name="Jmax_uni" units="nanomole_per_min_mg"/>
<variable initial_value="6.0" name="K_trans" units="micromolar"/>
<variable initial_value="0.38" name="K_act" units="micromolar"/>
<variable initial_value="50.0" 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>
<minus/>
<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> delta_psi_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> delta_psi_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_000000083" name="NaCa_exchanger">
<variable cmeta:id="id_000000085" name="J_NaCa" public_interface="out" units="nanomole_per_min_mg"/>
<variable initial_value="0.0003" name="fm" public_interface="out" units="dimensionless"/>
<variable cmeta:id="id_000000084" initial_value="5.5" name="Jmax_NaCa" units="nanomole_per_min_mg"/>
<variable initial_value="30.0" name="Na_i" units="millimolar"/>
<variable initial_value="9.4" name="K_Na" units="millimolar"/>
<variable initial_value="0.003" name="K_Ca" units="nanomole_per_mg"/>
<variable initial_value="0.5" name="b" units="dimensionless"/>
<variable initial_value="3.0" name="n" units="dimensionless"/>
<variable cmeta:id="id_000000036" name="Ca_m" public_interface="in" units="nanomolar"/>
<variable cmeta:id="id_000000052" name="J_uni" public_interface="in" units="nanomole_per_min_mg"/>
<variable name="delta_psi_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_NaCa_calculation">
<eq/>
<ci> J_NaCa </ci>
<apply>
<times/>
<ci> Jmax_NaCa </ci>
<apply>
<divide/>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<ci> b </ci>
<ci> F </ci>
<apply>
<minus/>
<ci> V </ci>
<ci> delta_psi_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>
<component cmeta:id="id_000000037" name="mitochondrial_Ca">
<variable cmeta:id="id_000000038" name="Ca_m" public_interface="out" units="micromolar"/>
<variable name="fm" public_interface="in" units="dimensionless"/>
<variable cmeta:id="id_000000053" name="J_uni" public_interface="in" units="nanomole_per_min_mg"/>
<variable cmeta:id="id_000000086" name="J_NaCa" public_interface="in" units="nanomole_per_min_mg"/>
<variable name="time" public_interface="in" units="second"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="Ca_m_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> Ca_m </ci>
</apply>
<apply>
<times/>
<apply>
<divide/>
<ci> fm </ci>
<cn cellml:units="dimensionless"> 60000.0 </cn>
</apply>
<apply>
<minus/>
<ci> J_uni </ci>
<ci> J_NaCa </ci>
</apply>
</apply>
</apply>
</math>
</component>
<group>
<relationship_ref relationship="containment"/>
<component_ref component="plasma_membrane">
<component_ref component="delayed_rectifier_K_channel_current">
<component_ref component="delayed_rectifier_K_channel_current_n_gate"/>
<component_ref component="delayed_rectifier_K_channel_current_I_gate"/>
</component_ref>
<component_ref component="K_ATP_channel_current"/>
<component_ref component="fast_Ca_channel_current">
<component_ref component="fast_Ca_channel_current_C_gate"/>
<component_ref component="fast_Ca_channel_current_B_gate"/>
</component_ref>
<component_ref component="slow_Ca_channel_current">
<component_ref component="slow_Ca_channel_current_J_gate"/>
</component_ref>
<component_ref component="non_selective_cation_channel_current"/>
<component_ref component="cytosolic_ADP"/>
<component_ref component="cytosolic_Ca"/>
<component_ref component="mitochondrial_membrane">
<component_ref component="mitochondrial_NADH"/>
<component_ref component="mitochondrial_ADP"/>
<component_ref component="mitochondrial_Ca"/>
<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="NaCa_exchanger"/>
</component_ref>
</component_ref>
</group>
<group>
<relationship_ref relationship="encapsulation"/>
<component_ref component="delayed_rectifier_K_channel_current">
<component_ref component="delayed_rectifier_K_channel_current_n_gate"/>
<component_ref component="delayed_rectifier_K_channel_current_I_gate"/>
</component_ref>
<component_ref component="fast_Ca_channel_current">
<component_ref component="fast_Ca_channel_current_C_gate"/>
<component_ref component="fast_Ca_channel_current_B_gate"/>
</component_ref>
<component_ref component="slow_Ca_channel_current">
<component_ref component="slow_Ca_channel_current_J_gate"/>
</component_ref>
</group>
<connection>
<map_components component_1="plasma_membrane" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="mitochondrial_membrane" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="delayed_rectifier_K_channel_current" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="K_ATP_channel_current" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="fast_Ca_channel_current" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="slow_Ca_channel_current" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="non_selective_cation_channel_current" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="cytosolic_ADP" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="cytosolic_Ca" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="mitochondrial_NADH" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="mitochondrial_ADP" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="mitochondrial_Ca" 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="NaCa_exchanger"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="delayed_rectifier_K_channel_current" component_2="plasma_membrane"/>
<map_variables variable_1="V" variable_2="V"/>
<map_variables variable_1="i_K_dr" variable_2="i_K_dr"/>
</connection>
<connection>
<map_components component_1="K_ATP_channel_current" component_2="plasma_membrane"/>
<map_variables variable_1="V" variable_2="V"/>
<map_variables variable_1="i_K_ATP" variable_2="i_K_ATP"/>
</connection>
<connection>
<map_components component_1="fast_Ca_channel_current" component_2="plasma_membrane"/>
<map_variables variable_1="V" variable_2="V"/>
<map_variables variable_1="i_Ca_f" variable_2="i_Ca_f"/>
<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="slow_Ca_channel_current" component_2="plasma_membrane"/>
<map_variables variable_1="V" variable_2="V"/>
<map_variables variable_1="i_Ca_s" variable_2="i_Ca_s"/>
<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="non_selective_cation_channel_current" component_2="plasma_membrane"/>
<map_variables variable_1="V" variable_2="V"/>
<map_variables variable_1="i_NS" variable_2="i_NS"/>
<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="mitochondrial_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="delta_psi" variable_2="delta_psi"/>
</connection>
<connection>
<map_components component_1="plasma_membrane" component_2="proton_pump"/>
<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="mitochondrial_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="mitochondrial_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="delta_psi" variable_2="delta_psi"/>
</connection>
<connection>
<map_components component_1="plasma_membrane" component_2="F0_F1_ATPase"/>
<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="mitochondrial_membrane" component_2="ATP_ADP_exchange"/>
<map_variables variable_1="J_ANT" variable_2="J_ANT"/>
</connection>
<connection>
<map_components component_1="plasma_membrane" component_2="ATP_ADP_exchange"/>
<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="mitochondrial_membrane" component_2="Ca_uniporter"/>
<map_variables variable_1="J_uni" variable_2="J_uni"/>
</connection>
<connection>
<map_components component_1="plasma_membrane" component_2="Ca_uniporter"/>
<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="plasma_membrane" component_2="mitochondrial_NADH"/>
<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="plasma_membrane" component_2="NaCa_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>
<connection>
<map_components component_1="mitochondrial_membrane" component_2="NaCa_exchanger"/>
<map_variables variable_1="J_NaCa" variable_2="J_NaCa"/>
</connection>
<connection>
<map_components component_1="mitochondrial_membrane" component_2="plasma_membrane"/>
<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="delayed_rectifier_K_channel_current" component_2="K_ATP_channel_current"/>
<map_variables variable_1="V_K" variable_2="V_K"/>
</connection>
<connection>
<map_components component_1="K_ATP_channel_current" component_2="cytosolic_ADP"/>
<map_variables variable_1="ADP_i" variable_2="ADP_i"/>
</connection>
<connection>
<map_components component_1="K_ATP_channel_current" component_2="ATP_ADP_exchange"/>
<map_variables variable_1="ADP3_i" variable_2="ADP3_i"/>
<map_variables variable_1="ATP4_i" variable_2="ATP4_i"/>
</connection>
<connection>
<map_components component_1="fast_Ca_channel_current" component_2="cytosolic_Ca"/>
<map_variables variable_1="i_Ca_f" variable_2="i_Ca_f"/>
</connection>
<connection>
<map_components component_1="fast_Ca_channel_current" component_2="mitochondrial_NADH"/>
<map_variables variable_1="i_Ca_f" variable_2="i_Ca_f"/>
</connection>
<connection>
<map_components component_1="fast_Ca_channel_current" component_2="slow_Ca_channel_current"/>
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