- Author:
- Hanne <Hanne@hanne-nielsens-macbook.local>
- Date:
- 2009-12-09 12:41:49+13:00
- Desc:
- Added images in ai and svg format, removed non pub med references
- Permanent Source URI:
- https://staging.physiomeproject.org/workspace/magnus_keizer_1997/rawfile/64c61ee85a9827c3e492c1d16facdcca9afa3726/magnus_keizer_1997.cellml
<?xml version='1.0' encoding='utf-8'?>
<!-- FILE : mitochondrial_Ca_handling_1997.xml
CREATED : 11th 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 16/1/02 CellML Metadata 1.0 Specification.
DESCRIPTION : This file contains a CellML description of Magnus and Keizer's
1997 minimal model of beta-call mitochondrial Ca2+ handling.
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="magnus_keizer_1997_version01" name="magnus_keizer_1997_version01">
<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
<articleinfo>
<title>Mitochondrial Ca2+ Handling</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 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. Their kinetic model includes 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 (see <xref linkend="fig_cell_diagram"/> below).
</para>
<para>
The complete original paper reference is cited below:
</para>
<para>
Minimal model of beta-cell mitochondrial Ca<superscript>2+</superscript> handling, Gerhard Magnus and Joel Keizer, 1997, 273, C717-C733. <ulink url="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&list_uids=9277370&dopt=Abstract">PubMed ID: 9277370</ulink>
</para>
<para>
The raw CellML description of the mitochondrial Ca<superscript>2+</superscript> handling 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 mitochondrial Ca2+ handling model showing ionic currents across the mitochondrial membrane</title>
</objectinfo>
<imagedata fileref="magnus_1997.png"/>
</imageobject>
</mediaobject>
<caption>
A schematic representation of the ion fluxes through the mitochondrial inner membrane that are included in the Magnus-Keizer minimal model.
</caption>
</informalfigure>
<informalfigure float="0" id="fig_cellml_rendering">
<mediaobject>
<imageobject>
<objectinfo>
<title>the cellml rendering of the mitochondrial Ca2+ handling model</title>
</objectinfo>
<imagedata fileref="cellml_rendering.gif"/>
</imageobject>
</mediaobject>
<caption>The network defined in the CellML description of the mitochondrial Ca<superscript>2+</superscript> handling 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="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="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="Cmito" 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> Cmito </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>
<component name="proton_pump">
<variable units="nanomole_per_minute_per_mg" public_interface="out" name="JH_res"/>
<variable units="nanomole_per_minute_per_mg" name="Jo"/>
<variable units="dimensionless" name="A_res"/>
<variable units="millimolar" name="K_res" initial_value="135000000000000000.0"/>
<variable units="nanomolar" name="total_NAD_m" initial_value="8.0"/>
<variable units="nanomolar" name="NAD_m"/>
<variable units="nanomolar" name="NADH_m"/>
<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="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>
<apply id="total_NAD_m_calculation">
<eq/>
<ci> total_NAD_m </ci>
<apply>
<plus/>
<ci> NADH_m </ci>
<ci> NAD_m </ci>
</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="total_mitochondrial_adenosine_phosphate" initial_value="12.0"/>
<variable units="nanomolar" name="ATP_m"/>
<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="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="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="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="nanomolar" public_interface="out" name="ADP_m"/>
<variable units="nanomole_per_minute_per_mg" name="Jmax_ant" initial_value="1000.0"/>
<variable units="nanomolar" name="ATP_i"/>
<variable units="nanomolar" name="ATP_m"/>
<variable units="nanomolar" name="ADP_i"/>
<variable units="nanomolar" name="ATP4_i"/>
<variable units="nanomolar" name="ATP4_m"/>
<variable units="nanomolar" name="ADP3_i"/>
<variable units="nanomolar" name="ADP3_m"/>
<variable units="dimensionless" name="f" initial_value="0.5"/>
<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> 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="ADP_m_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> ADP_m </ci>
</apply>
<apply>
<minus/>
<ci> J_ant </ci>
<ci> Jp_F1 </ci>
</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"> 1.0 </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 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="nanomolar" name="Ca_i"/>
<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="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_minute_per_mg" name="J_Na_Ca"/>
<variable units="nanomole_per_minute_per_mg" name="Jmax_Na_Ca" initial_value="25.0"/>
<variable units="nanomolar" name="Ca_m"/>
<variable units="millimolar" name="Na_i" initial_value="30.0"/>
<variable units="millimolar" name="K_Na" initial_value="9.4"/>
<variable units="nanomole_per_mg" name="K_Ca" initial_value="0.003"/>
<variable units="dimensionless" name="b" initial_value="0.0"/>
<variable units="dimensionless" name="n" initial_value="2.0"/>
<variable units="dimensionless" name="fm" initial_value="0.0003"/>
<variable units="nanomole_per_minute_per_mg" public_interface="in" name="J_uni"/>
<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>
<apply id="Ca_m_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> Ca_m </ci>
</apply>
<apply>
<times/>
<ci> fm </ci>
<apply>
<minus/>
<ci> J_uni </ci>
<ci> J_Na_Ca </ci>
</apply>
</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>
</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>
<!--
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="F0_F1_ATPase" component_1="ATP_ADP_exchange"/>
<map_variables variable_2="Jp_F1" variable_1="Jp_F1"/>
<map_variables variable_2="ADP_m" variable_1="ADP_m"/>
</connection>
<connection>
<map_components component_2="Ca_uniporter" component_1="Na_Ca_exchanger"/>
<map_variables variable_2="J_uni" variable_1="J_uni"/>
<map_variables variable_2="V_offset" variable_1="V_offset"/>
</connection>
<rdf:RDF>
<rdf:Bag rdf:about="rdf:#df76ce61-71c2-4484-9b8f-854f452b6296">
<rdf:li>calcium dynamics</rdf:li>
<rdf:li>electrophysiology</rdf:li>
<rdf:li>beta cell</rdf:li>
<rdf:li>Pancreatic Beta-Cell</rdf:li>
<rdf:li>mitochondria</rdf:li>
</rdf:Bag>
<rdf:Seq rdf:about="rdf:#c32682c9-4637-4464-aec1-7e4b6f3517b5">
<rdf:li rdf:resource="rdf:#3b7a4359-a8ee-4876-bb82-61e19edb1e77"/>
<rdf:li rdf:resource="rdf:#b9be7b77-0a0e-426c-af52-fa6f1876cb07"/>
</rdf:Seq>
<rdf:Description rdf:about="rdf:#e70859a4-9460-4d0a-87ea-1068cb187d47">
<vCard:Given>Catherine</vCard:Given>
<vCard:Family>Lloyd</vCard:Family>
<vCard:Other>May</vCard:Other>
</rdf:Description>
<rdf:Description rdf:about="rdf:#114b67e1-ead5-4e5a-8d8b-e2cb6ef4785b">
<vCard:Orgname>The University of Auckland</vCard:Orgname>
<vCard:Orgunit>The Bioengineering Research Group</vCard:Orgunit>
</rdf:Description>
<rdf:Description rdf:about="rdf:#02ff6efd-a443-4a54-9bdb-1c652734beab">
<dcterms:modified rdf:resource="rdf:#c5a0b75f-8ea6-4206-84a1-86571f27b085"/>
<rdf:value>
Corrected units.
</rdf:value>
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Minimal Model of beta-cell mitochondrial Ca2+ handling
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Corrected equations: JH_F1 in F0_F1_ATPase component, J_uni in
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This is the CellML description of Gerhard Magnus and Joel Keizer's
1997 minimal model of beta-call mitochondrial Ca2+ handling. They
developed a simplified mathematical model to describe Ca2+ handling by
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Minimal model of beta-cell mitochondrial Ca2+ handling
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Corrected several equations.
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Added more metadata.
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Updated metadata to conform to the 16/1/02 CellML Metadata 1.0
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The University of Auckland, Bioengineering Research Group
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