- Author:
- pmr2.import <nobody@models.cellml.org>
- Date:
- 2006-07-09 07:35:26+12:00
- Desc:
- committing version01 of chay_1997
- Permanent Source URI:
- https://models.cellml.org/workspace/chay_1997/rawfile/0ce7426d4bbc3cc2a1a50b2847354f8c16199b08/chay_1997.cellml
<?xml version='1.0' encoding='utf-8'?>
<!-- FILE : chay_model_1997.xml
CREATED : 7th May 2002
LAST MODIFIED : 9th April 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 16/01/2002 CellML Metadata 1.0 Specification.
DESCRIPTION : This file contains a CellML description of Chay et al's
1997 mathematical model of the effects of extracellular and intracellular calcium on pancreatic beta cells.
CHANGES:
22/07/2002 - CML - Added more metadata.
09/04/2003 - AAC - Added publication date information.
--><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="chay_1997_version01" name="chay_1997_version01">
<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
<articleinfo>
<title>Extracellular And Intracellular Calcium Effects On 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>
When exposed to a threshold concentration of glucose, pancreatic beta-cells 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 is influenced by the extracellular calcium concentration ([Ca<superscript>2+</superscript>]<subscript>o</subscript>). Specifically, in a mouse pancreatic beta-cell in a medium containing a moderate amount of glucose, an increase in [Ca<superscript>2+</superscript>]<subscript>o</subscript> lowers the repolarisation potential, raises the plateau potential and shortens the spike and plateau durations. The mechanisms underlying these affects are not well understood.
</para>
<para>
In her 1997 paper, Teresa Chay elucidates the role of extracellular calcium concentration in influencing electrical activity, intracellular calcium concentration, and the luminal calcium concentration in the intracellular calcium store of pancreatic beta-cells. She studies the extracellular calcium effect using a mathematical model which includes seven currents across the plasma membrane and two calcium fluxes across the membrane of the endoplasmic reticulum (ER) (see <xref linkend="fig_cell_diagram"/> below).
</para>
<para>
The complete original paper reference is cited below:
</para>
<para>
<ulink url="http://www.biophysj.org/cgi/content/abstract/73/3/1673">Effects of extracellular Calcium on Electrical Bursting and Intracellular and Luminal Calcium Oscillations in Insulin Secreting Pancreatic Beta-Cells</ulink>, Teresa Ree Chay, 1997, <ulink url="http://www.biophysj.org/">
<emphasis>Biophysical Journal</emphasis>
</ulink>, 73, 1673-1688. <ulink url="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&list_uids=9284334&dopt=Abstract">PubMed ID: 9284334</ulink>
</para>
<para>
The raw CellML description of the model 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="cell_diagram.gif"/>
</imageobject>
</mediaobject>
<caption>A schematic representation of the current and fluxes captured by the Chay 1997 pancreatic beta-cell model. This diagram shows the plasma membrane currents associated with burst and spike oscillations: the fast current, I<subscript>fast</subscript>; the calcium current, I <subscript>Ca<superscript>2+</superscript>
</subscript>; the cationic nonselective inward current, I<subscript>NS</subscript>; the delayed-rectifying K<superscript>+</superscript> current, I<subscript>K(dr)</subscript>, the calcium-sensitive K<superscript>+</superscript> current, I<subscript>K(Ca)</subscript>; the ATP-sensitive K<superscript>+</superscript> current, I<subscript>K(ATP)</subscript>; and the Na<superscript>+</superscript> leak current, I<subscript>Na(L)</subscript>. The ER intracellular Ca<superscript>2+</superscript> store is also shown with its associated transmembrane calcium fluxes: calcium release, J<subscript>rel</subscript>; and calcium uptake by the Ca<superscript>2+</superscript>-ATPase, J<subscript>pump</subscript>.</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="per_second">
<unit units="second" exponent="-1"/>
</units>
<units name="millivolt">
<unit units="volt" prefix="milli"/>
</units>
<units name="micromolar">
<unit units="mole" prefix="micro"/>
<unit units="litre" exponent="-1"/>
</units>
<units name="microS_per_cm2">
<unit units="siemens" prefix="micro"/>
<unit units="metre" prefix="centi" exponent="-2"/>
</units>
<units name="microF_per_cm2">
<unit units="farad" prefix="micro"/>
<unit units="metre" prefix="centi" exponent="-2"/>
</units>
<units name="nanoA_per_cm2">
<unit units="ampere" prefix="nano"/>
<unit units="metre" prefix="centi" exponent="-2"/>
</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="second" public_interface="out" name="time"/>
</component>
<component name="membrane">
<variable units="millivolt" public_interface="out" name="V"/>
<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="microF_per_cm2" name="Cm" initial_value="1.0"/>
<variable units="second" public_interface="in" name="time"/>
<variable units="nanoA_per_cm2" public_interface="in" name="i_K_dr"/>
<variable units="nanoA_per_cm2" public_interface="in" name="i_K_Ca"/>
<variable units="nanoA_per_cm2" public_interface="in" name="i_K_ATP"/>
<variable units="nanoA_per_cm2" public_interface="in" name="i_fast"/>
<variable units="nanoA_per_cm2" public_interface="in" name="i_Ca"/>
<variable units="nanoA_per_cm2" public_interface="in" name="i_NS"/>
<variable units="nanoA_per_cm2" public_interface="in" name="i_NaL"/>
<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_Ca </ci>
<ci> i_K_ATP </ci>
<ci> i_fast </ci>
<ci> i_Ca </ci>
<ci> i_NS </ci>
<ci> i_NaL </ci>
</apply>
</apply>
<ci> Cm </ci>
</apply>
</apply>
</math>
</component>
<component name="fast_current">
<variable units="nanoA_per_cm2" public_interface="out" name="i_fast"/>
<variable units="microS_per_cm2" name="g_fast" initial_value="600.0"/>
<variable units="millivolt" name="V_fast" initial_value="80.0"/>
<variable units="second" public_interface="in" private_interface="out" name="time"/>
<variable units="millivolt" public_interface="in" private_interface="out" name="V"/>
<variable units="dimensionless" private_interface="in" name="m_infinity"/>
<variable units="dimensionless" private_interface="in" name="h"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="i_fast_calculation">
<eq/>
<ci> i_fast </ci>
<apply>
<times/>
<ci> g_fast </ci>
<apply>
<power/>
<ci> m_infinity </ci>
<cn cellml:units="dimensionless"> 3.0 </cn>
</apply>
<ci> h </ci>
<apply>
<minus/>
<ci> V </ci>
<ci> V_fast </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="fast_current_m_gate">
<variable units="dimensionless" public_interface="out" name="m_infinity"/>
<variable units="millivolt" name="Vm" initial_value="-25.0"/>
<variable units="millivolt" name="Sm" initial_value="9.0"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="second" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="m_infinity_calculation">
<eq/>
<ci> m_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> V </ci>
<ci> Vm </ci>
</apply>
<ci> Sm </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="fast_current_h_gate">
<variable units="dimensionless" public_interface="out" name="h"/>
<variable units="per_second" name="lamda_h" initial_value="2.5"/>
<variable units="second" name="tau_h"/>
<variable units="dimensionless" name="h_infinity"/>
<variable units="millivolt" name="Vh" initial_value="-25.0"/>
<variable units="millivolt" name="Sh" initial_value="9.0"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="second" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="h_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> h </ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci> h_infinity </ci>
<ci> h </ci>
</apply>
<ci> tau_h </ci>
</apply>
</apply>
<apply id="h_infinity_calculation">
<eq/>
<ci> h_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> V </ci>
<ci> Vh </ci>
</apply>
<ci> Sh </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="tau_h_calculation">
<eq/>
<ci> tau_h </ci>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<times/>
<ci> lamda_h </ci>
<apply>
<plus/>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<ci> Vh </ci>
<ci> V </ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless"> 2.0 </cn>
<ci> Sh </ci>
</apply>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<ci> V </ci>
<ci> Vh </ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless"> 2.0 </cn>
<ci> Sh </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="calcium_current">
<variable units="nanoA_per_cm2" public_interface="out" name="i_Ca"/>
<variable units="micromolar" public_interface="out" private_interface="out" name="K_Ca" initial_value="1.0"/>
<variable units="nanoA_per_cm2" name="P_Ca" initial_value="2.0"/>
<variable units="micromolar" name="Ca_o" initial_value="2500.0"/>
<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="second" public_interface="in" private_interface="out" name="time"/>
<variable units="millivolt" public_interface="in" private_interface="out" name="V"/>
<variable units="micromolar" public_interface="in" private_interface="out" name="Ca_i"/>
<variable units="dimensionless" private_interface="in" name="f_infinity"/>
<variable units="dimensionless" private_interface="in" name="d"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="i_Ca_calculation">
<eq/>
<ci> i_Ca </ci>
<apply>
<times/>
<ci> P_Ca </ci>
<ci> d </ci>
<ci> f_infinity </ci>
<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>
<divide/>
<apply>
<minus/>
<ci> Ca_o </ci>
<apply>
<times/>
<ci> Ca_i </ci>
<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>
<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 name="calcium_current_d_gate">
<variable units="dimensionless" public_interface="out" name="d"/>
<variable units="per_second" name="lamda_d" initial_value="12.5"/>
<variable units="second" name="tau_d"/>
<variable units="dimensionless" name="d_infinity"/>
<variable units="millivolt" name="Vd" initial_value="-10.0"/>
<variable units="millivolt" name="Sd" initial_value="5.0"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="second" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="d_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> d </ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci> d_infinity </ci>
<ci> d </ci>
</apply>
<ci> tau_d </ci>
</apply>
</apply>
<apply id="d_infinity_calculation">
<eq/>
<ci> d_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> V </ci>
<ci> Vd </ci>
</apply>
<ci> Sd </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="tau_d_calculation">
<eq/>
<ci> tau_d </ci>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<times/>
<ci> lamda_d </ci>
<apply>
<plus/>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<ci> Vd </ci>
<ci> V </ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless"> 2.0 </cn>
<ci> Sd </ci>
</apply>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<ci> V </ci>
<ci> Vd </ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless"> 2.0 </cn>
<ci> Sd </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="calcium_current_f_gate">
<variable units="dimensionless" public_interface="out" name="f_infinity"/>
<variable units="micromolar" public_interface="in" name="K_Ca"/>
<variable units="micromolar" public_interface="in" name="Ca_i"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="f_infinity_calculation">
<eq/>
<ci> f_infinity </ci>
<apply>
<divide/>
<ci> K_Ca </ci>
<apply>
<plus/>
<ci> K_Ca </ci>
<ci> Ca_i </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="cationic_nonselective_inward_current">
<variable units="nanoA_per_cm2" public_interface="out" name="i_NS"/>
<variable units="microS_per_cm2" name="g_NS" initial_value="5.0"/>
<variable units="micromolar" name="K_NS" initial_value="50.0"/>
<variable units="millivolt" name="VNS" initial_value="-20.0"/>
<variable units="micromolar" public_interface="in" name="Ca_lum"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="second" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="i_NS_calculation">
<eq/>
<ci> i_NS </ci>
<apply>
<times/>
<ci> g_NS </ci>
<apply>
<divide/>
<apply>
<power/>
<ci> K_NS </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
<apply>
<plus/>
<apply>
<power/>
<ci> K_NS </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
<apply>
<power/>
<ci> Ca_lum </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
</apply>
</apply>
<apply>
<minus/>
<apply>
<divide/>
<apply>
<minus/>
<ci> V </ci>
<ci> VNS </ci>
</apply>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.1 </cn>
<apply>
<minus/>
<ci> VNS </ci>
<ci> V </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<cn cellml:units="millivolt"> 10.0 </cn>
</apply>
</apply>
</apply>
</math>
</component>
<component name="delayed_rectifier_K_channel_current">
<variable units="nanoA_per_cm2" public_interface="out" name="i_K_dr"/>
<variable units="millivolt" public_interface="out" name="V_K" initial_value="-75.0"/>
<variable units="microS_per_cm2" name="g_K_dr" initial_value="600.0"/>
<variable units="second" public_interface="in" private_interface="out" name="time"/>
<variable units="millivolt" public_interface="in" private_interface="out" name="V"/>
<variable units="dimensionless" private_interface="in" name="n"/>
<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>
<apply>
<minus/>
<ci> V </ci>
<ci> V_K </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="delayed_rectifier_K_channel_current_n_gate">
<variable units="dimensionless" public_interface="out" name="n"/>
<variable units="per_second" name="lamda_n" initial_value="12.5"/>
<variable units="millivolt" name="Vn" initial_value="-18.0"/>
<variable units="millivolt" name="Sn" initial_value="14.0"/>
<variable units="dimensionless" name="n_infinity"/>
<variable units="second" name="tau_n"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="second" 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> V </ci>
<ci> Vn </ci>
</apply>
<ci> Sn </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="tau_n_calculation">
<eq/>
<ci> tau_n </ci>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<times/>
<ci> lamda_n </ci>
<apply>
<plus/>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<ci> Vn </ci>
<ci> V </ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless"> 2.0 </cn>
<ci> Sn </ci>
</apply>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<ci> V </ci>
<ci> Vn </ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless"> 2.0 </cn>
<ci> Sn </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="Ca_sensitive_K_current">
<variable units="nanoA_per_cm2" public_interface="out" name="i_K_Ca"/>
<variable units="microS_per_cm2" name="g_K_Ca" initial_value="5.0"/>
<variable units="micromolar" public_interface="in" name="K_Ca"/>
<variable units="second" public_interface="in" name="time"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="millivolt" public_interface="in" name="V_K"/>
<variable units="micromolar" public_interface="in" name="Ca_i"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="i_K_Ca_calculation">
<eq/>
<ci> i_K_Ca </ci>
<apply>
<times/>
<ci> g_K_Ca </ci>
<apply>
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<ci> Ca_i </ci>
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<apply>
<plus/>
<apply>
<power/>
<ci> K_Ca </ci>
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</apply>
<apply>
<power/>
<ci> Ca_i </ci>
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</apply>
</apply>
</apply>
<apply>
<minus/>
<ci> V </ci>
<ci> V_K </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="ATP_sensitive_K_current">
<variable units="nanoA_per_cm2" public_interface="out" name="i_K_ATP"/>
<variable units="microS_per_cm2" name="g_K_ATP" initial_value="2.0"/>
<variable units="second" public_interface="in" name="time"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="millivolt" public_interface="in" name="V_K"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="i_K_ATP_calculation">
<eq/>
<ci> i_K_ATP </ci>
<apply>
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<ci> g_K_ATP </ci>
<apply>
<minus/>
<ci> V </ci>
<ci> V_K </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="Na_leak_current">
<variable units="nanoA_per_cm2" public_interface="out" name="i_NaL"/>
<variable units="microS_per_cm2" name="g_NaL" initial_value="2.0"/>
<variable units="millivolt" name="V_Na" initial_value="80.0"/>
<variable units="second" public_interface="in" name="time"/>
<variable units="millivolt" public_interface="in" name="V"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="i_NaL_calculation">
<eq/>
<ci> i_NaL </ci>
<apply>
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<ci> g_NaL </ci>
<apply>
<minus/>
<ci> V </ci>
<ci> V_Na </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="cytosolic_calcium">
<variable units="micromolar" public_interface="out" name="Ca_i"/>
<variable units="micromolar" public_interface="out" name="Ca_lum"/>
<variable units="per_second" name="k_rel" initial_value="0.2"/>
<variable units="per_second" name="k_Ca" initial_value="7.0"/>
<variable units="per_second" name="k_pump" initial_value="30.0"/>
<variable units="dimensionless" name="omega" initial_value="0.2"/>
<variable units="nanoA_per_cm2" public_interface="in" name="i_Ca"/>
<variable units="second" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="Ca_i_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
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<ci> Ca_i </ci>
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<apply>
<minus/>
<apply>
<times/>
<ci> k_rel </ci>
<apply>
<minus/>
<ci> Ca_lum </ci>
<ci> Ca_i </ci>
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</apply>
<apply>
<plus/>
<apply>
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<ci> omega </ci>
<ci> i_Ca </ci>
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<apply>
<times/>
<ci> k_Ca </ci>
<ci> Ca_i </ci>
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<apply>
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<ci> k_pump </ci>
<ci> Ca_i </ci>
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</apply>
</apply>
</apply>
<apply id="Ca_lum_diff_eq">
<eq/>
<apply>
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<ci> time </ci>
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<ci> Ca_lum </ci>
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<apply>
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<apply>
<minus/>
<apply>
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<ci> k_rel </ci>
<apply>
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<ci> Ca_lum </ci>
<ci> Ca_i </ci>
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</apply>
</apply>
<apply>
<times/>
<ci> k_pump </ci>
<ci> Ca_i </ci>
</apply>
</apply>
</apply>
</math>
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<component_ref component="fast_current_h_gate"/>
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<component_ref component="calcium_current_f_gate"/>
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<component_ref component="cationic_nonselective_inward_current"/>
<component_ref component="delayed_rectifier_K_channel_current">
<component_ref component="delayed_rectifier_K_channel_current_n_gate"/>
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<component_ref component="Ca_sensitive_K_current"/>
<component_ref component="ATP_sensitive_K_current"/>
<component_ref component="Na_leak_current"/>
<component_ref component="cytosolic_calcium"/>
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<group>
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<component_ref component="fast_current_h_gate"/>
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<component_ref component="calcium_current">
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<component_ref component="calcium_current_f_gate"/>
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<component_ref component="delayed_rectifier_K_channel_current">
<component_ref component="delayed_rectifier_K_channel_current_n_gate"/>
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<connection>
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</connection>
<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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<connection>
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<map_variables variable_2="i_fast" variable_1="i_fast"/>
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<connection>
<map_components component_2="membrane" component_1="calcium_current"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="i_Ca" variable_1="i_Ca"/>
<map_variables variable_2="R" variable_1="R"/>
<map_variables variable_2="T" variable_1="T"/>
<map_variables variable_2="F" variable_1="F"/>
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<connection>
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<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="i_NS" variable_1="i_NS"/>
</connection>
<connection>
<map_components component_2="membrane" component_1="delayed_rectifier_K_channel_current"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="i_K_dr" variable_1="i_K_dr"/>
</connection>
<connection>
<map_components component_2="membrane" component_1="Ca_sensitive_K_current"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="i_K_Ca" variable_1="i_K_Ca"/>
</connection>
<connection>
<map_components component_2="membrane" component_1="ATP_sensitive_K_current"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="i_K_ATP" variable_1="i_K_ATP"/>
</connection>
<connection>
<map_components component_2="membrane" component_1="Na_leak_current"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="i_NaL" variable_1="i_NaL"/>
</connection>
<connection>
<map_components component_2="cytosolic_calcium" component_1="calcium_current"/>
<map_variables variable_2="i_Ca" variable_1="i_Ca"/>
<map_variables variable_2="Ca_i" variable_1="Ca_i"/>
</connection>
<connection>
<map_components component_2="cytosolic_calcium" component_1="Ca_sensitive_K_current"/>
<map_variables variable_2="Ca_i" variable_1="Ca_i"/>
</connection>
<connection>
<map_components component_2="Ca_sensitive_K_current" component_1="calcium_current"/>
<map_variables variable_2="K_Ca" variable_1="K_Ca"/>
</connection>
<connection>
<map_components component_2="ATP_sensitive_K_current" component_1="delayed_rectifier_K_channel_current"/>
<map_variables variable_2="V_K" variable_1="V_K"/>
</connection>
<connection>
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<map_variables variable_2="V_K" variable_1="V_K"/>
</connection>
<connection>
<map_components component_2="cytosolic_calcium" component_1="cationic_nonselective_inward_current"/>
<map_variables variable_2="Ca_lum" variable_1="Ca_lum"/>
</connection>
<connection>
<map_components component_2="fast_current_m_gate" component_1="fast_current"/>
<map_variables variable_2="m_infinity" variable_1="m_infinity"/>
<map_variables variable_2="time" variable_1="time"/>
<map_variables variable_2="V" variable_1="V"/>
</connection>
<connection>
<map_components component_2="fast_current_h_gate" component_1="fast_current"/>
<map_variables variable_2="h" variable_1="h"/>
<map_variables variable_2="time" variable_1="time"/>
<map_variables variable_2="V" variable_1="V"/>
</connection>
<connection>
<map_components component_2="calcium_current_f_gate" component_1="calcium_current"/>
<map_variables variable_2="f_infinity" variable_1="f_infinity"/>
<map_variables variable_2="Ca_i" variable_1="Ca_i"/>
<map_variables variable_2="K_Ca" variable_1="K_Ca"/>
</connection>
<connection>
<map_components component_2="calcium_current_d_gate" component_1="calcium_current"/>
<map_variables variable_2="d" variable_1="d"/>
<map_variables variable_2="time" variable_1="time"/>
<map_variables variable_2="V" variable_1="V"/>
</connection>
<connection>
<map_components component_2="delayed_rectifier_K_channel_current_n_gate" component_1="delayed_rectifier_K_channel_current"/>
<map_variables variable_2="n" variable_1="n"/>
<map_variables variable_2="time" variable_1="time"/>
<map_variables variable_2="V" variable_1="V"/>
</connection>
<rdf:RDF>
<rdf:Bag rdf:about="rdf:#a2cc4365-2f2f-4903-9cbc-dc863978ea00">
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The University of Auckland, Bioengineering Institute
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This is the CellML description of Chay et al's 1997 mathematical model of the effects of extracellular and intracellular calcium on
pancreatic beta cells.
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The Chay et al 1997 mathematical model of the effects of extracellular
and intracellular calcium on pancreatic beta cells.
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<cmeta:bio_entity>Pancreatic Beta-cell</cmeta:bio_entity>
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<vCard:Given>Catherine</vCard:Given>
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Effects of extracellular calcium on electrical bursting and intracellular and luminal calcium oscillations in insulin secreting pancreatic beta-cells
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Added publication date information.
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<dc:title>Biophysical Journal</dc:title>
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