- Author:
- rcai987 <devnull@localhost>
- Date:
- 2015-02-02 13:03:56+13:00
- Desc:
- Added annotations to fridyland_tamarina_philipson_2003.cellml model
- Permanent Source URI:
- http://models.cellml.org/workspace/fridlyand_tamarina_philipson_2003/rawfile/c0bc0382dc05eca7b252df50d363445468825c26/fridlyand_tamarina_philipson_2003.cellml
<?xml version="1.0"?>
<!-- FILE : fridlyand_model_2003.xml
CREATED : 14th November 2002
LAST MODIFIED : 14th November 2003
AUTHOR : Catherine Lloyd
The Bioengineering Institute
The University of Auckland
MODEL STATUS : This model conforms to the CellML 1.0 Specification released on
10th August 2001, and the CellML Metadata 1.0 Specification released on 16th
January, 2002.
DESCRIPTION : This file contains a CellML description of Fridlyand et al's 2003 mathematical model of Ca2+ fluxes in pancreatic beta-cells.
CHANGES:
--><model xmlns="http://www.cellml.org/cellml/1.0#" xmlns:bqs="http://www.cellml.org/bqs/1.0#" xmlns:cellml="http://www.cellml.org/cellml/1.0#" xmlns:cmeta="http://www.cellml.org/metadata/1.0#" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:dcterms="http://purl.org/dc/terms/" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" xml:base="file:///H:/fridlyand_tamarina_philipson_2003/fridlyand_tamarina_philipson_2003.cellml" cmeta:id="fridlyand_tamarina_philipson_2003_version01" name="fridlyand_tamarina_philipson_2003_version01">
<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
<articleinfo>
<title>Modelling Ca2+ Flux in Pancreatic Beta-cells</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>
An increase in the concentration of intracellular free calcium ([Ca<superscript>2+</superscript>]<subscript>i</subscript>) is an essential signal for the initiation of insulin secretion in pancreatic beta-cells. This increase is primarily due to the opening of Ca<superscript>2+</superscript> channels in the plasma membrane in response to glucose. Glucose metabolism leads to an increase in the cytosolic ATP:ADP ratio, which in turn causes the ATP-sensitive potassium channels to close. The beta-cell membrane becomes depolarised, Ca<superscript>2+</superscript> channels open, and Ca<superscript>2+</superscript> enters the cell. These events underlie the glucose-induced electrical activity, which in pancreatic islets, consists of Ca<superscript>2+</superscript>-dependent action potentials.
</para>
<para>
There is an abundance of literature that describes beta-cell electrical activity and its relationship to [Ca<superscript>2+</superscript>]<subscript>i</subscript>. Complex and cyclic spike-burst activity, and corresponding [Ca<superscript>2+</superscript>]<subscript>i</subscript> oscillations in pancreatic islets and beta-cell clusters are induced in response to a rise in extracellular glucose concentration. Intermediate glucose concentrations induce both fast and slow oscillations. The authors of this current study: Fridlyand, Tamarina and Philipson, have previously studied slow and fast [Ca<superscript>2+</superscript>]<subscript>i</subscript> oscillations in islets in response to a variety of conditions. However, the experimental results were complex, and precise understanding was limited by the large number of channels and pumps in the beta-cell plasma membrane that were simultaneously working.
</para>
<para>
In order to better understand the molecular mechanisms underlying this behaviour, in this publication Fridlyand <emphasis>et al.</emphasis> have developed a mathematical model of the Ca<superscript>2+</superscript> fluxes in pancreatic beta-cells. Several other mathematical models of glucose-induced insulin secretion, with corresponding descriptions of glucose transport, metabolism and ion regulation, have been published. These include:
</para>
<itemizedlist>
<listitem>
<para>
<ulink url="${HTML_EXMPL_CHAY_MODEL97}">Extracellular and Intracellular Calcium Effects on Pancreatic Beta Cells, Chay, 1997</ulink>;</para>
</listitem>
<listitem>
<para>
<ulink url="${HTML_EXMPL_GALL_MODEL}">Na<superscript>+</superscript>/Ca<superscript>2+</superscript> Exchange in Models for Pancreatic Beta-Cells, Gall and Susa, 1999</ulink>; and</para>
</listitem>
<listitem>
<para>
<ulink url="${HTML_EXMPL_BERTRAM_MODEL}">The Phantom Burster Model for Pancreatic Beta-Cells, Bertram <emphasis>et al.</emphasis>, 2000</ulink>.</para>
</listitem>
</itemizedlist>
<para>
However, most of these models are focused on describing one specific phenomenon. They only include a very limited set of channels and pumps, and therefore it is difficult to apply them to a another situation. In addition, since their publication, new experimental data has become available, and these new findings should be included in a theoretical model. For this reason Fridlyand <emphasis>et al.</emphasis> have developed the new mathematical model described here (see the raw CellML description of the Fridlyand <emphasis>et al.</emphasis> 2003 model in <xref linkend="sec_download_this_model"/>). They have adopted the more complex style of modelling that has previously been used successfully to describe the electrophysiology of cardiac myocytes and other cell types (for example in <ulink url="${HTML_EXMPL_NYGREN_ATRIAL_MODEL}">Human Atrial Cell Model, Nygren <emphasis>et al.</emphasis> 1998</ulink> and in <ulink url="${HTML_EXMPL_RICE_MODEL2}">Modelling Interval-Force Relations in Cardiac Muscle, Rice <emphasis>et al.</emphasis>, 2000</ulink>). </para>
<para>
Their new model includes a wider range of channels and pumps, as well as endoplasmic reticulum (ER) Ca<superscript>2+</superscript> sequestration mechanisms (see <xref linkend="fig_cell_diagram"/> below). Using this model they were able to simulate whole cell electrical activity and [Ca<superscript>2+</superscript>]<subscript>i</subscript>, free calcium in the ER ([Ca<superscript>2+</superscript>]<subscript>ER</subscript>), intracellular Na<superscript> +</superscript> ([Na<superscript>+</superscript>]<subscript>i</subscript>), cytosolic ATP ([ATP]<subscript>i</subscript>), and inositol triphosphate ([IP<subscript>3</subscript>]<subscript>i</subscript>) concentrations. However, they acknowledge that this model does not consider metabolic processes or insulin secretion.
</para>
<para>
The complete original paper reference is cited below:
</para>
<para>
<ulink url="http://ajpendo.physiology.org/cgi/content/abstract/285/1/E138">Modeling of Ca<superscript>2+</superscript> flux in pancreatic beta-cells: role of the plasma membrane and intracellular stores</ulink>, Leonid E. Fridlyand, Natalia Tamarina, and Louis H. Philipson, 2003, <ulink url="http://ajpendo.physiology.org/">
<emphasis>American Journal of Physiology</emphasis>
</ulink>, 285, E138-E154. (<ulink url="http://ajpendo.physiology.org/cgi/content/full/285/1/E138">Full text (HTML)</ulink> and <ulink url="http://ajpendo.physiology.org/cgi/reprint/285/1/E138.pdf">PDF</ulink> versions of the article are available on the <emphasis>American Jounal of Physiology</emphasis> website.) <ulink url="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&list_uids=12644446&dopt=Abstract">PubMed ID: 12644446</ulink>
</para>
<informalfigure float="0" id="fig_cell_diagram">
<mediaobject>
<imageobject>
<objectinfo>
<title>cell diagram</title>
</objectinfo>
<imagedata fileref="fridlyand_2003.png"/>
</imageobject>
</mediaobject>
<caption>Schematic representation of currents and ion fluxes, through the plasma membrane and the endoplasmic reticulum membrane, which have been included in the whole beta-cell mathematical model.</caption>
</informalfigure>
</sect1>
</article>
</documentation>
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<component name="environment">
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<component cmeta:id="id_00001" name="membrane">
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<variable initial_value="100.0" name="b1" units="first_order_rate_constant"/>
<variable initial_value="0.0001" name="b2" units="second_order_rate_constant"/>
<variable initial_value="1.72E-17" name="b3" units="forth_order_rate_constant"/>
<variable initial_value="0.0002" name="b4" units="second_order_rate_constant"/>
<variable initial_value="0.03" name="b5_" units="first_order_rate_constant"/>
<variable name="b5" units="first_order_rate_constant"/>
<variable initial_value="6.0E-7" name="b6" units="second_order_rate_constant"/>
<variable name="B2" units="first_order_rate_constant"/>
<variable name="B3" units="first_order_rate_constant"/>
<variable name="B4" units="first_order_rate_constant"/>
<variable name="B6" units="first_order_rate_constant"/>
<variable name="D" units="dimensionless"/>
<variable name="V" public_interface="in" units="millivolt"/>
<variable name="R" public_interface="in" units="joule_per_kilomole_kelvin"/>
<variable name="F" public_interface="in" units="coulomb_per_mole"/>
<variable name="T" public_interface="in" units="kelvin"/>
<variable name="Nai" public_interface="in" units="micromolar"/>
<variable name="Nao" public_interface="in" units="micromolar"/>
<variable name="ATPi" public_interface="in" units="micromolar"/>
<variable name="ADPi" public_interface="in" units="micromolar"/>
<variable name="Ko" public_interface="in" units="micromolar"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="i_NaK_calculation">
<eq/>
<ci> i_NaK </ci>
<apply>
<times/>
<ci> P_NaK </ci>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<times/>
<ci> F1 </ci>
<ci> f2 </ci>
<ci> f3 </ci>
<ci> F4 </ci>
<ci> F5 </ci>
<ci> f6 </ci>
</apply>
<apply>
<times/>
<ci> b1 </ci>
<ci> B2 </ci>
<ci> B3 </ci>
<ci> B4 </ci>
<ci> b5 </ci>
<ci> B6 </ci>
</apply>
</apply>
<ci> D </ci>
</apply>
</apply>
</apply>
<apply id="D_calculation">
<eq/>
<ci> D </ci>
<apply>
<plus/>
<apply>
<times/>
<ci> f2 </ci>
<ci> f3 </ci>
<ci> F4 </ci>
<ci> F5 </ci>
<ci> f6 </ci>
</apply>
<apply>
<times/>
<ci> b1 </ci>
<ci> f3 </ci>
<ci> F4 </ci>
<ci> F5 </ci>
<ci> f6 </ci>
</apply>
<apply>
<times/>
<ci> b1 </ci>
<ci> B2 </ci>
<ci> F4 </ci>
<ci> F5 </ci>
<ci> f6 </ci>
</apply>
<apply>
<times/>
<ci> b1 </ci>
<ci> B2 </ci>
<ci> B3 </ci>
<ci> F5 </ci>
<ci> f6 </ci>
</apply>
<apply>
<times/>
<ci> b1 </ci>
<ci> B2 </ci>
<ci> B3 </ci>
<ci> B4 </ci>
<ci> f6 </ci>
</apply>
<apply>
<times/>
<ci> b1 </ci>
<ci> B2 </ci>
<ci> B3 </ci>
<ci> B4 </ci>
<ci> b5 </ci>
</apply>
</apply>
</apply>
<apply id="F1_calculation">
<eq/>
<ci> F1 </ci>
<apply>
<times/>
<ci> f1 </ci>
<apply>
<power/>
<ci> Nai </ci>
<cn cellml:units="dimensionless"> 3.0 </cn>
</apply>
</apply>
</apply>
<apply id="F4_calculation">
<eq/>
<ci> F4 </ci>
<apply>
<times/>
<ci> f4 </ci>
<apply>
<power/>
<ci> Ko </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
</apply>
</apply>
<apply id="F5_calculation">
<eq/>
<ci> F5 </ci>
<apply>
<times/>
<ci> f5 </ci>
<ci> ATPi </ci>
</apply>
</apply>
<apply id="f5_calculation">
<eq/>
<ci> f5 </ci>
<apply>
<times/>
<ci> f5_ </ci>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<ci> V </ci>
<ci> F </ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless"> 2.0 </cn>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="B2_calculation">
<eq/>
<ci> B2 </ci>
<apply>
<times/>
<ci> b2 </ci>
<ci> ATPi </ci>
</apply>
</apply>
<apply id="B3_calculation">
<eq/>
<ci> B3 </ci>
<apply>
<times/>
<ci> b3 </ci>
<apply>
<power/>
<ci> Nai </ci>
<cn cellml:units="dimensionless"> 3.0 </cn>
</apply>
</apply>
</apply>
<apply id="B4_calculation">
<eq/>
<ci> B4 </ci>
<apply>
<times/>
<ci> b4 </ci>
<ci> P </ci>
</apply>
</apply>
<apply id="B6_calculation">
<eq/>
<ci> B6 </ci>
<apply>
<times/>
<ci> b6 </ci>
<apply>
<power/>
<ci> K_supi </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
</apply>
</apply>
<apply id="b5_calculation">
<eq/>
<ci> b5 </ci>
<apply>
<times/>
<ci> b5_ </ci>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<times/>
<ci> V </ci>
<ci> F </ci>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless"> 2.0 </cn>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component cmeta:id="id_00052" name="voltage_dependent_potassium_current">
<variable cmeta:id="id_00053" name="i_KDr" public_interface="out" units="femtoA"/>
<variable cmeta:id="id_00054" name="V_K" public_interface="out" units="millivolt"/>
<variable cmeta:id="id_00055" initial_value="3000.0" name="gm_KDr" 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="R" public_interface="in" units="joule_per_kilomole_kelvin"/>
<variable name="F" public_interface="in" units="coulomb_per_mole"/>
<variable name="T" public_interface="in" units="kelvin"/>
<variable name="Ki" public_interface="in" units="micromolar"/>
<variable name="Ko" public_interface="in" units="micromolar"/>
<variable name="n" private_interface="in" units="dimensionless"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="i_KDr_calculation">
<eq/>
<ci> i_KDr </ci>
<apply>
<times/>
<ci> gm_KDr </ci>
<ci> n </ci>
<apply>
<minus/>
<ci> V </ci>
<ci> V_K </ci>
</apply>
</apply>
</apply>
<apply id="V_K_calculation">
<eq/>
<ci> V_K </ci>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
<ci> F </ci>
</apply>
<apply>
<ln/>
<apply>
<divide/>
<ci> Ko </ci>
<ci> Ki </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component cmeta:id="id_00056" name="voltage_dependent_potassium_current_n_gate">
<variable cmeta:id="id_00057" initial_value="0.00123" name="n" public_interface="out" units="dimensionless"/>
<variable cmeta:id="id_00058" name="tau_n" units="dimensionless"/>
<variable cmeta:id="id_00059" name="n_infinity" units="dimensionless"/>
<variable cmeta:id="id_00060" initial_value="-14.0" name="Vn" units="millivolt"/>
<variable cmeta:id="id_00061" initial_value="-75.0" name="Vtau" units="millivolt"/>
<variable cmeta:id="id_00062" initial_value="7.0" name="Sn" units="millivolt"/>
<variable initial_value="65.0" name="a" units="millivolt"/>
<variable initial_value="20.0" name="b" units="millivolt"/>
<variable initial_value="20.0" name="c" 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/>
<ci> Vn </ci>
<ci> V </ci>
</apply>
<ci> Sn </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="tau_n_calculation">
<eq/>
<ci> tau_n </ci>
<apply>
<divide/>
<ci> c </ci>
<apply>
<plus/>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<ci> V </ci>
<ci> Vtau </ci>
</apply>
<ci> a </ci>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<ci> Vtau </ci>
<ci> V </ci>
</apply>
<ci> b </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component cmeta:id="id_00069" name="calcium_dependent_potassium_current">
<variable cmeta:id="id_00070" name="i_KCa" public_interface="out" units="femtoA"/>
<variable cmeta:id="id_00071" initial_value="130.0" name="gm_KCa" units="picoS"/>
<variable cmeta:id="id_00072" name="V_K" public_interface="in" units="millivolt"/>
<variable name="V" public_interface="in" units="millivolt"/>
<variable name="Cai" private_interface="out" public_interface="in" units="micromolar"/>
<variable name="fCa" private_interface="in" units="dimensionless"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="i_KCa_calculation">
<eq/>
<ci> i_KCa </ci>
<apply>
<times/>
<ci> gm_KCa </ci>
<ci> fCa </ci>
<apply>
<minus/>
<ci> V </ci>
<ci> V_K </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component cmeta:id="id_00073" name="calcium_dependent_potassium_current_fCa_gate">
<variable cmeta:id="id_00074" name="fCa" public_interface="out" units="dimensionless"/>
<variable cmeta:id="id_00075" initial_value="0.1" name="K_KCa" units="micromolar"/>
<variable name="Cai" public_interface="in" units="micromolar"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="fCa_calculation">
<eq/>
<ci> fCa </ci>
<apply>
<divide/>
<apply>
<power/>
<ci> Cai </ci>
<cn cellml:units="dimensionless"> 4.0 </cn>
</apply>
<apply>
<plus/>
<apply>
<power/>
<ci> Cai </ci>
<cn cellml:units="dimensionless"> 4.0 </cn>
</apply>
<apply>
<power/>
<ci> K_KCa </ci>
<cn cellml:units="dimensionless"> 4.0 </cn>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component cmeta:id="id_00063" name="ATP_dependent_potassium_current">
<variable cmeta:id="id_00064" name="i_KATP" public_interface="out" units="femtoA"/>
<variable cmeta:id="id_00065" initial_value="24000.0" name="gm_KATP" units="picoS"/>
<variable cmeta:id="id_00066" name="O_KATP" units="dimensionless"/>
<variable initial_value="17.0" name="Kdd" units="micromolar"/>
<variable initial_value="26.0" name="Ktd" units="micromolar"/>
<variable initial_value="1.0" name="Ktt" units="micromolar"/>
<variable name="V" public_interface="in" units="millivolt"/>
<variable name="V_K" public_interface="in" units="millivolt"/>
<variable name="ADPi" public_interface="in" units="micromolar"/>
<variable name="ATPi" public_interface="in" units="micromolar"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="i_KATP_calculation">
<eq/>
<ci> i_KATP </ci>
<apply>
<times/>
<ci> gm_KATP </ci>
<ci> O_KATP </ci>
<apply>
<minus/>
<ci> V </ci>
<ci> V_K </ci>
</apply>
</apply>
</apply>
<apply id="O_KATP_calculation">
<eq/>
<ci> O_KATP </ci>
<apply>
<divide/>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.08 </cn>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.33 </cn>
<ci> ADPi </ci>
</apply>
<ci> Kdd </ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.89 </cn>
<apply>
<power/>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 0.165 </cn>
<apply>
<divide/>
<ci> ADPi </ci>
<ci> Kdd </ci>
</apply>
</apply>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
</apply>
</apply>
<apply>
<times/>
<apply>
<power/>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 0.165 </cn>
<apply>
<divide/>
<ci> ADPi </ci>
<ci> Kdd </ci>
</apply>
</apply>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.135 </cn>
<ci> ADPi </ci>
</apply>
<ci> Ktd </ci>
</apply>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.05 </cn>
<ci> ATPi </ci>
</apply>
<ci> Ktt </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component cmeta:id="id_00077" name="SERCA_pump">
<variable cmeta:id="id_00078" name="Jer_p" public_interface="out" units="flux"/>
<variable cmeta:id="id_00079" initial_value="0.105" name="P_CaER" units="flux"/>
<variable cmeta:id="id_00080" initial_value="0.5" name="K_Carp" units="micromolar"/>
<variable name="Cai" public_interface="in" units="micromolar"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="Jer_p_calculation">
<eq/>
<ci> Jer_p </ci>
<apply>
<times/>
<ci> P_CaER </ci>
<apply>
<divide/>
<apply>
<power/>
<ci> Cai </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
<apply>
<plus/>
<apply>
<power/>
<ci> Cai </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
<apply>
<power/>
<ci> K_Carp </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component cmeta:id="id_00081" name="IP3_metabolism">
<variable cmeta:id="id_00082" initial_value="0.33" name="IP3i" public_interface="out" units="micromolar"/>
<variable initial_value="0.0003" name="kIP" units="flux"/>
<variable initial_value="0.00004" name="kdIP" units="first_order_rate_constant"/>
<variable cmeta:id="id_00083" initial_value="0.4" name="K_IPCa" units="micromolar"/>
<variable name="Cai" public_interface="in" units="micromolar"/>
<variable name="time" public_interface="in" units="millisecond"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="IP3_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> IP3i </ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> kIP </ci>
<apply>
<divide/>
<apply>
<power/>
<ci> Cai </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
<apply>
<plus/>
<apply>
<power/>
<ci> Cai </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
<apply>
<power/>
<ci> K_IPCa </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci> kdIP </ci>
<ci> IP3i </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="CaER_mobilisation">
<variable name="J_out" public_interface="out" units="flux"/>
<variable cmeta:id="id_00087" initial_value="0.0001" name="P_leak" units="picol_per_ms"/>
<variable cmeta:id="id_00086" initial_value="0.0012" name="P_IP3" units="picol_per_ms"/>
<variable name="O_infinity" units="dimensionless"/>
<variable initial_value="3.2" name="K_RCa" units="micromolar"/>
<variable cmeta:id="id_00084" initial_value="0.077" name="K_IP3" units="micromolar"/>
<variable cmeta:id="id_00085" name="IP3i" public_interface="in" units="micromolar"/>
<variable name="Cai" public_interface="in" units="micromolar"/>
<variable name="CaER" public_interface="in" units="micromolar"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci> J_out </ci>
<apply>
<times/>
<apply>
<plus/>
<ci> P_leak </ci>
<apply>
<times/>
<ci> P_IP3 </ci>
<ci> O_infinity </ci>
</apply>
</apply>
<apply>
<minus/>
<ci> CaER </ci>
<ci> Cai </ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci> O_infinity </ci>
<apply>
<times/>
<apply>
<divide/>
<ci> Cai </ci>
<apply>
<plus/>
<ci> Cai </ci>
<ci> K_RCa </ci>
</apply>
</apply>
<apply>
<divide/>
<apply>
<power/>
<ci> IP3i </ci>
<cn cellml:units="dimensionless"> 3.0 </cn>
</apply>
<apply>
<plus/>
<apply>
<power/>
<ci> IP3i </ci>
<cn cellml:units="dimensionless"> 3.0 </cn>
</apply>
<apply>
<power/>
<ci> K_IP3 </ci>
<cn cellml:units="dimensionless"> 3.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component cmeta:id="id_00044" name="calcium_and_sodium_dynamics">
<variable initial_value="0.085" name="Cai" public_interface="out" units="micromolar"/>
<variable initial_value="22.8" name="CaER" public_interface="out" units="micromolar"/>
<variable initial_value="9858.0" name="Nai" public_interface="out" units="micromolar"/>
<variable initial_value="0.01" name="fi" units="dimensionless"/>
<variable initial_value="0.03" name="fer" units="dimensionless"/>
<variable initial_value="0.0001" name="ksg" units="first_order_rate_constant"/>
<variable initial_value="0.280" name="Ver" units="picol"/>
<variable name="Vi" public_interface="in" units="picol"/>
<variable cmeta:id="id_00021" name="i_VCa" public_interface="in" units="femtoA"/>
<variable cmeta:id="id_00034" name="i_NaCa" public_interface="in" units="femtoA"/>
<variable name="i_Ca_pump" public_interface="in" units="femtoA"/>
<variable cmeta:id="id_00049" name="i_NaK" public_interface="in" units="femtoA"/>
<variable cmeta:id="id_00043" name="i_Na" public_interface="in" units="femtoA"/>
<variable cmeta:id="id_00011" name="i_CRAN" public_interface="in" units="femtoA"/>
<variable name="F" public_interface="in" units="coulomb_per_mole"/>
<variable name="J_out" public_interface="in" units="flux"/>
<variable name="Jer_p" public_interface="in" units="flux"/>
<variable name="time" public_interface="in" units="millisecond"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="Cai_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> Cai </ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> fi </ci>
<apply>
<plus/>
<apply>
<minus/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<minus/>
<ci> i_VCa </ci>
</apply>
<apply>
<times/>
<ci> i_NaCa </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
</apply>
<apply>
<times/>
<ci> i_Ca_pump </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless"> 2.0 </cn>
<ci> F </ci>
<ci> Vi </ci>
</apply>
</apply>
<ci> Jer_p </ci>
</apply>
<apply>
<divide/>
<ci> J_out </ci>
<ci> Vi </ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci> ksg </ci>
<ci> Cai </ci>
</apply>
</apply>
</apply>
<apply id="CaER_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> CaER </ci>
</apply>
<apply>
<times/>
<apply>
<divide/>
<ci> fer </ci>
<ci> Ver </ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> Jer_p </ci>
<ci> Vi </ci>
</apply>
<ci> J_out </ci>
</apply>
</apply>
</apply>
<apply id="Nai_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> Nai </ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 3.0 </cn>
<ci> i_NaCa </ci>
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<apply>
<times/>
<cn cellml:units="dimensionless"> 3.0 </cn>
<ci> i_NaK </ci>
</apply>
<ci> i_Na </ci>
<ci> i_CRAN </ci>
</apply>
</apply>
<apply>
<times/>
<ci> Vi </ci>
<ci> F </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component cmeta:id="id_00090" name="ATP_homeostasis">
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<variable cmeta:id="id_00091" name="ADPi" public_interface="out" units="millimolar"/>
<variable cmeta:id="id_00092" name="k_ADP" units="first_order_rate_constant"/>
<variable cmeta:id="id_00067" initial_value="0.00005" name="k_ATP" units="first_order_rate_constant"/>
<variable cmeta:id="id_00089" initial_value="0.00005" name="k_ATP_Ca" units="second_order_rate_constant"/>
<variable initial_value="4000.0" name="Ao" units="micromolar"/>
<variable name="Vi" public_interface="in" units="picol"/>
<variable name="Cai" public_interface="in" units="micromolar"/>
<variable cmeta:id="id_00027" name="i_Ca_pump" public_interface="in" units="femtoA"/>
<variable cmeta:id="id_00010" name="i_CRAN" public_interface="in" units="femtoA"/>
<variable cmeta:id="id_00050" name="i_NaK" public_interface="in" units="femtoA"/>
<variable name="F" public_interface="in" units="coulomb_per_mole"/>
<variable name="Jer_p" public_interface="in" units="flux"/>
<variable name="time" public_interface="in" units="millisecond"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="ATPi_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> ATPi </ci>
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<apply>
<minus/>
<apply>
<times/>
<ci> k_ADP </ci>
<ci> ADPi </ci>
</apply>
<apply>
<plus/>
<apply>
<divide/>
<apply>
<plus/>
<ci> i_NaK </ci>
<ci> i_CRAN </ci>
</apply>
<apply>
<times/>
<ci> Vi </ci>
<ci> F </ci>
</apply>
</apply>
<apply>
<divide/>
<ci> Jer_p </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
<apply>
<times/>
<apply>
<plus/>
<apply>
<times/>
<ci> k_ATP_Ca </ci>
<ci> Cai </ci>
</apply>
<ci> k_ATP </ci>
</apply>
<ci> ATPi </ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci> ADPi </ci>
<apply>
<minus/>
<ci> Ao </ci>
<ci> ATPi </ci>
</apply>
</apply>
</math>
</component>
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<connection>
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<connection>
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<connection>
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<connection>
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<connection>
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<connection>
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