- Author:
- pmr2.import <nobody@models.cellml.org>
- Date:
- 2009-06-17 14:14:09+12:00
- Desc:
- committing version01 of fridlyand_tamarina_philipson_2003
- Permanent Source URI:
- https://models.cellml.org/workspace/fridlyand_tamarina_philipson_2003/rawfile/4f36f7fb799a7cbe4b727683e2801feca451f0aa/fridlyand_tamarina_philipson_2003.cellml
<?xml version='1.0' encoding='utf-8'?>
<!-- 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: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="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="whole_cell_calcium_current_p_VCa_gate">
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<variable units="millivolt" name="V_Cah" initial_value="-19.0"/>
<variable units="millivolt" name="K_Cah" initial_value="9.5"/>
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<component name="PM_calcium_pumps">
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<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 name="voltage_dependent_potassium_current">
<variable units="femtoA" public_interface="out" name="i_KDr"/>
<variable units="millivolt" public_interface="out" name="V_K"/>
<variable units="picoS" name="gm_KDr" initial_value="3000.0"/>
<variable units="millisecond" public_interface="in" private_interface="out" name="time"/>
<variable units="millivolt" public_interface="in" private_interface="out" name="V"/>
<variable units="joule_per_kilomole_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="micromolar" public_interface="in" name="Ki"/>
<variable units="micromolar" public_interface="in" name="Ko"/>
<variable units="dimensionless" private_interface="in" name="n"/>
<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 name="voltage_dependent_potassium_current_n_gate">
<variable units="dimensionless" public_interface="out" name="n" initial_value="0.00123"/>
<variable units="dimensionless" name="tau_n"/>
<variable units="dimensionless" name="n_infinity"/>
<variable units="millivolt" name="Vn" initial_value="-14.0"/>
<variable units="millivolt" name="Vtau" initial_value="-75.0"/>
<variable units="millivolt" name="Sn" initial_value="7.0"/>
<variable units="millivolt" name="a" initial_value="65.0"/>
<variable units="millivolt" name="b" initial_value="20.0"/>
<variable units="millisecond" name="c" initial_value="20.0"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="millisecond" public_interface="in" name="time"/>
<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 name="calcium_dependent_potassium_current">
<variable units="femtoA" public_interface="out" name="i_KCa"/>
<variable units="picoS" name="gm_KCa" initial_value="130.0"/>
<variable units="millivolt" public_interface="in" name="V_K"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="micromolar" public_interface="in" private_interface="out" name="Cai"/>
<variable units="dimensionless" private_interface="in" name="fCa"/>
<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 name="calcium_dependent_potassium_current_fCa_gate">
<variable units="dimensionless" public_interface="out" name="fCa"/>
<variable units="micromolar" name="K_KCa" initial_value="0.1"/>
<variable units="micromolar" public_interface="in" name="Cai"/>
<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 name="ATP_dependent_potassium_current">
<variable units="femtoA" public_interface="out" name="i_KATP"/>
<variable units="picoS" name="gm_KATP" initial_value="24000.0"/>
<variable units="dimensionless" name="O_KATP"/>
<variable units="micromolar" name="Kdd" initial_value="17.0"/>
<variable units="micromolar" name="Ktd" initial_value="26.0"/>
<variable units="micromolar" name="Ktt" initial_value="1.0"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="millivolt" public_interface="in" name="V_K"/>
<variable units="micromolar" public_interface="in" name="ADPi"/>
<variable units="micromolar" public_interface="in" name="ATPi"/>
<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 name="SERCA_pump">
<variable units="flux" public_interface="out" name="Jer_p"/>
<variable units="flux" name="P_CaER" initial_value="0.105"/>
<variable units="micromolar" name="K_Carp" initial_value="0.5"/>
<variable units="micromolar" public_interface="in" name="Cai"/>
<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 name="IP3_metabolism">
<variable units="micromolar" public_interface="out" name="IP3i" initial_value="0.33"/>
<variable units="flux" name="kIP" initial_value="0.0003"/>
<variable units="first_order_rate_constant" name="kdIP" initial_value="0.00004"/>
<variable units="micromolar" name="K_IPCa" initial_value="0.4"/>
<variable units="micromolar" public_interface="in" name="Cai"/>
<variable units="millisecond" public_interface="in" name="time"/>
<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 units="flux" public_interface="out" name="J_out"/>
<variable units="picol_per_ms" name="P_leak" initial_value="0.0001"/>
<variable units="picol_per_ms" name="P_IP3" initial_value="0.0012"/>
<variable units="dimensionless" name="O_infinity"/>
<variable units="micromolar" name="K_RCa" initial_value="3.2"/>
<variable units="micromolar" name="K_IP3" initial_value="0.077"/>
<variable units="micromolar" public_interface="in" name="IP3i"/>
<variable units="micromolar" public_interface="in" name="Cai"/>
<variable units="micromolar" public_interface="in" name="CaER"/>
<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 name="calcium_and_sodium_dynamics">
<variable units="micromolar" public_interface="out" name="Cai" initial_value="0.085"/>
<variable units="micromolar" public_interface="out" name="CaER" initial_value="22.8"/>
<variable units="micromolar" public_interface="out" name="Nai" initial_value="9858.0"/>
<variable units="dimensionless" name="fi" initial_value="0.01"/>
<variable units="dimensionless" name="fer" initial_value="0.03"/>
<variable units="first_order_rate_constant" name="ksg" initial_value="0.0001"/>
<variable units="picol" name="Ver" initial_value="0.280"/>
<variable units="picol" public_interface="in" name="Vi"/>
<variable units="femtoA" public_interface="in" name="i_VCa"/>
<variable units="femtoA" public_interface="in" name="i_NaCa"/>
<variable units="femtoA" public_interface="in" name="i_Ca_pump"/>
<variable units="femtoA" public_interface="in" name="i_NaK"/>
<variable units="femtoA" public_interface="in" name="i_Na"/>
<variable units="femtoA" public_interface="in" name="i_CRAN"/>
<variable units="coulomb_per_mole" public_interface="in" name="F"/>
<variable units="flux" public_interface="in" name="J_out"/>
<variable units="flux" public_interface="in" name="Jer_p"/>
<variable units="millisecond" public_interface="in" name="time"/>
<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>
</apply>
<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 name="ATP_homeostasis">
<variable units="micromolar" public_interface="out" name="ATPi" initial_value="932.1"/>
<variable units="millimolar" public_interface="out" name="ADPi"/>
<variable units="first_order_rate_constant" name="k_ADP"/>
<variable units="first_order_rate_constant" name="k_ATP" initial_value="0.00005"/>
<variable units="second_order_rate_constant" name="k_ATP_Ca" initial_value="0.00005"/>
<variable units="micromolar" name="Ao" initial_value="4000.0"/>
<variable units="picol" public_interface="in" name="Vi"/>
<variable units="micromolar" public_interface="in" name="Cai"/>
<variable units="femtoA" public_interface="in" name="i_Ca_pump"/>
<variable units="femtoA" public_interface="in" name="i_CRAN"/>
<variable units="femtoA" public_interface="in" name="i_NaK"/>
<variable units="coulomb_per_mole" public_interface="in" name="F"/>
<variable units="flux" public_interface="in" name="Jer_p"/>
<variable units="millisecond" public_interface="in" name="time"/>
<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>
</apply>
<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/>
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The University of Auckland, The Bioengineering Institute
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Modeling of Ca2+ flux in pancreatic beta-cells: role of the plasma
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Fridlyand et al's 2003 mathematical model of Ca2+ fluxes in pancreatic
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