- Author:
- pmr2.import <nobody@models.cellml.org>
- Date:
- 2007-06-18 23:34:14+12:00
- Desc:
- committing version03 of chay_1997
- Permanent Source URI:
- https://models.cellml.org/workspace/chay_1997/rawfile/2d78827d7ce385023c6b6a11a682553eba10a7f9/chay_1997.cellml
<?xml version='1.0' encoding='utf-8'?>
<!--
This CellML file was generated on 16/11/2006 at 15:57:30 using:
COR (0.9.31.397)
Copyright 2002-2006 Oxford Cardiac Electrophysiology Group
http://COR.physiol.ox.ac.uk/ - COR@physiol.ox.ac.uk
CellML 1.0 was used to generate this cellular model
http://www.CellML.org/
--><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#" xmlns:ns7="http://www.cellml.org/metadata/simulation/1.0#" cmeta:id="chay_1997_version01" name="chay_1997_version03">
<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>Oxford University</shortaffil>
</affiliation>
</author>
</articleinfo>
<section id="sec_status">
<title>Model Status</title>
<para>
This model has been validated by Penny Noble of Oxford University and is known to run in PCEnv and COR. This model is able to reproduce the figures presented in the Chay 1997 paper and this version has a PCEnv session file associated with it. The value for the variable 'Ca_o' in the component 'calcium_current' can be altered to 0, 2.5, 5 or 7.5 mM to reproduce figures 5 a,b,c,d, respectively.
</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>
<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>
<component name="environment">
<variable units="second" public_interface="out" name="time" cmeta:id="environment_time"/>
</component>
<component name="membrane">
<variable units="millivolt" public_interface="out" cmeta:id="membrane_V" name="V" initial_value="-38.34146"/>
<variable units="millijoule_per_mole_kelvin" public_interface="out" name="R" initial_value="8314"/>
<variable units="kelvin" public_interface="out" name="T" initial_value="310"/>
<variable units="coulomb_per_mole" public_interface="out" name="F" initial_value="96485"/>
<variable units="microF_per_cm2" name="Cm" initial_value="1"/>
<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>
<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"/>
<variable units="millivolt" name="V_fast" initial_value="80"/>
<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>
<eq/>
<ci>i_fast</ci>
<apply>
<times/>
<ci>g_fast</ci>
<apply>
<power/>
<ci>m_infinity</ci>
<cn cellml:units="dimensionless">3</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"/>
<variable units="millivolt" name="Sm" initial_value="9"/>
<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>
<eq/>
<ci>m_infinity</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<ci>Vm</ci>
<ci>V</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" initial_value="0.214723"/>
<variable units="per_second" name="lamda_h" initial_value="12.5"/>
<variable units="second" name="tau_h"/>
<variable units="dimensionless" name="h_infinity"/>
<variable units="millivolt" name="Vh" initial_value="-48"/>
<variable units="millivolt" name="Sh" initial_value="-7"/>
<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>
<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>
<eq/>
<ci>h_infinity</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<ci>Vh</ci>
<ci>V</ci>
</apply>
<ci>Sh</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>tau_h</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</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</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</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"/>
<variable units="nanoA_per_cm2" name="P_Ca" initial_value="2"/>
<variable units="micromolar" name="Ca_o" initial_value="2500"/>
<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>
<eq/>
<ci>i_Ca</ci>
<apply>
<divide/>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<ci>P_Ca</ci>
<ci>d</ci>
<ci>f_infinity</ci>
<cn cellml:units="dimensionless">2</cn>
<ci>F</ci>
<ci>V</ci>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
<apply>
<minus/>
<ci>Ca_o</ci>
<apply>
<times/>
<ci>Ca_i</ci>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<ci>F</ci>
<ci>V</ci>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<ci>F</ci>
<ci>V</ci>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="calcium_current_d_gate">
<variable units="dimensionless" public_interface="out" name="d" initial_value="0.0031711238"/>
<variable units="per_second" name="lamda_d" initial_value="2.5"/>
<variable units="second" name="tau_d"/>
<variable units="dimensionless" name="d_infinity"/>
<variable units="millivolt" name="Vd" initial_value="-10"/>
<variable units="millivolt" name="Sd" initial_value="5"/>
<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>
<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>
<eq/>
<ci>d_infinity</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<ci>Vd</ci>
<ci>V</ci>
</apply>
<ci>Sd</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>tau_d</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</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</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</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>
<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"/>
<variable units="micromolar" name="K_NS" initial_value="50"/>
<variable units="millivolt" name="VNS" initial_value="-20"/>
<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>
<eq/>
<ci>i_NS</ci>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<ci>g_NS</ci>
<apply>
<power/>
<ci>K_NS</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
<apply>
<plus/>
<apply>
<power/>
<ci>K_NS</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<apply>
<power/>
<ci>Ca_lum</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
<apply>
<minus/>
<apply>
<divide/>
<apply>
<minus/>
<ci>V</ci>
<ci>VNS</ci>
</apply>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</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</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"/>
<variable units="microS_per_cm2" name="g_K_dr" initial_value="600"/>
<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>
<eq/>
<ci>i_K_dr</ci>
<apply>
<times/>
<ci>g_K_dr</ci>
<apply>
<power/>
<ci>n</ci>
<cn cellml:units="dimensionless">4</cn>
</apply>
<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" initial_value="0.1836403"/>
<variable units="per_second" name="lamda_n" initial_value="12.5"/>
<variable units="millivolt" name="Vn" initial_value="-18"/>
<variable units="millivolt" name="Sn" initial_value="14"/>
<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>
<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>
<eq/>
<ci>n_infinity</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<ci>Vn</ci>
<ci>V</ci>
</apply>
<ci>Sn</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>tau_n</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</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</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</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"/>
<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>
<eq/>
<ci>i_K_Ca</ci>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<ci>g_K_Ca</ci>
<apply>
<power/>
<ci>Ca_i</ci>
<cn cellml:units="dimensionless">3</cn>
</apply>
</apply>
<apply>
<plus/>
<apply>
<power/>
<ci>K_Ca</ci>
<cn cellml:units="dimensionless">3</cn>
</apply>
<apply>
<power/>
<ci>Ca_i</ci>
<cn cellml:units="dimensionless">3</cn>
</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"/>
<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>
<eq/>
<ci>i_K_ATP</ci>
<apply>
<times/>
<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="0.3"/>
<variable units="millivolt" name="V_Na" initial_value="80"/>
<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>
<eq/>
<ci>i_NaL</ci>
<apply>
<times/>
<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" cmeta:id="cytosolic_calcium_Ca_i" name="Ca_i" initial_value="0.6959466"/>
<variable units="micromolar" public_interface="out" cmeta:id="cytosolic_calcium_Ca_lum" name="Ca_lum" initial_value="102.686"/>
<variable units="per_second" name="k_rel" initial_value="0.2"/>
<variable units="per_second" name="k_Ca" initial_value="7"/>
<variable units="per_second" name="k_pump" initial_value="30"/>
<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>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>Ca_i</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci>k_rel</ci>
<apply>
<minus/>
<ci>Ca_lum</ci>
<ci>Ca_i</ci>
</apply>
</apply>
<apply>
<plus/>
<apply>
<times/>
<ci>omega</ci>
<ci>i_Ca</ci>
</apply>
<apply>
<times/>
<ci>k_Ca</ci>
<ci>Ca_i</ci>
</apply>
<apply>
<times/>
<ci>k_pump</ci>
<ci>Ca_i</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>Ca_lum</ci>
</apply>
<apply>
<plus/>
<apply>
<times/>
<apply>
<minus/>
<ci>k_rel</ci>
</apply>
<apply>
<minus/>
<ci>Ca_lum</ci>
<ci>Ca_i</ci>
</apply>
</apply>
<apply>
<times/>
<ci>k_pump</ci>
<ci>Ca_i</ci>
</apply>
</apply>
</apply>
</math>
</component>
<group>
<relationship_ref relationship="containment"/>
<component_ref component="membrane">
<component_ref component="fast_current">
<component_ref component="fast_current_m_gate"/>
<component_ref component="fast_current_h_gate"/>
</component_ref>
<component_ref component="calcium_current">
<component_ref component="calcium_current_d_gate"/>
<component_ref component="calcium_current_f_gate"/>
</component_ref>
<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"/>
</component_ref>
<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"/>
</component_ref>
</group>
<group>
<relationship_ref relationship="encapsulation"/>
<component_ref component="fast_current">
<component_ref component="fast_current_m_gate"/>
<component_ref component="fast_current_h_gate"/>
</component_ref>
<component_ref component="calcium_current">
<component_ref component="calcium_current_d_gate"/>
<component_ref component="calcium_current_f_gate"/>
</component_ref>
<component_ref component="delayed_rectifier_K_channel_current">
<component_ref component="delayed_rectifier_K_channel_current_n_gate"/>
</component_ref>
</group>
<connection>
<map_components component_2="environment" component_1="membrane"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="fast_current"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="calcium_current"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="cationic_nonselective_inward_current"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="delayed_rectifier_K_channel_current"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="Ca_sensitive_K_current"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="ATP_sensitive_K_current"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="Na_leak_current"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="cytosolic_calcium"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="membrane" component_1="fast_current"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="i_fast" variable_1="i_fast"/>
</connection>
<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"/>
</connection>
<connection>
<map_components component_2="membrane" component_1="cationic_nonselective_inward_current"/>
<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>
<map_components component_2="Ca_sensitive_K_current" component_1="delayed_rectifier_K_channel_current"/>
<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">
<rdf:li>calcium dynamics</rdf:li>
<rdf:li>electrophysiological</rdf:li>
</rdf:Bag>
<rdf:Seq rdf:about="rdf:#7c75d0fe-e2ea-4306-a36b-863632500f4e">
<rdf:li rdf:resource="rdf:#67a4c2be-a043-42a0-a2cf-156b3b7c7598"/>
</rdf:Seq>
<rdf:Description rdf:about="">
<dc:publisher>The University of Auckland, Bioengineering Institute</dc:publisher>
<cmeta:comment rdf:resource="rdf:#51b1bcf0-cb86-4c8f-98b4-4911bf6ce72b"/>
<dcterms:created rdf:resource="rdf:#0ff67c11-a57c-4f33-a48d-dadbbb2ae5a2"/>
<dc:creator rdf:resource="rdf:#3b95224c-b8cc-46e7-b213-fd20a4b346e3"/>
<cmeta:modification rdf:resource="rdf:#a9e42612-b725-4ad8-9afa-a890ed4f3591"/>
<cmeta:modification rdf:resource="rdf:#d42f3492-3ace-4f88-b29a-67b923201a1e"/>
<cmeta:modification rdf:resource="rdf:#f0b2acc8-21ca-4887-9cbf-715041bcbc45"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#865e3c5c-bc6a-4431-a1f8-a2503b2aeba1">
<dc:title>Biophysical Journal</dc:title>
</rdf:Description>
<rdf:Description rdf:about="rdf:#272ea005-0b0b-45fb-a45a-3f7efecb9fea">
<dcterms:W3CDTF>2007-06-19T11:36:53+12:00</dcterms:W3CDTF>
</rdf:Description>
<rdf:Description rdf:about="rdf:#adedec42-59c5-4dad-8f6c-177511d9560d">
<dcterms:W3CDTF>2002-07-22</dcterms:W3CDTF>
</rdf:Description>
<rdf:Description rdf:about="rdf:#1df83312-5912-493b-8df9-acad7a980fbc">
<vCard:N rdf:resource="rdf:#b87b0808-5081-44e3-9bde-1b28762f3c10"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#689427f3-1fc8-4435-ad61-e81e4670cdec">
<vCard:Given>Catherine</vCard:Given>
<vCard:Family>Lloyd</vCard:Family>
<vCard:Other>May</vCard:Other>
</rdf:Description>
<rdf:Description rdf:about="rdf:#3b95224c-b8cc-46e7-b213-fd20a4b346e3">
<vCard:ORG rdf:resource="rdf:#6904a13f-ab67-4726-b3fa-06de9624350c"/>
<vCard:EMAIL rdf:resource="rdf:#f9f9e858-a37e-404e-884c-2b591352e0a8"/>
<vCard:N rdf:resource="rdf:#689427f3-1fc8-4435-ad61-e81e4670cdec"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#6478f744-71f1-4704-a5b3-3dd797e0c780">
<vCard:FN>Catherine Lloyd</vCard:FN>
</rdf:Description>
<rdf:Description rdf:about="rdf:#3ee27592-159c-4faa-9c7a-22d32346dc0b">
<dcterms:W3CDTF>2003-04-09</dcterms:W3CDTF>
</rdf:Description>
<rdf:Description rdf:about="rdf:#$tzI6R1">
<rdf:rest rdf:resource="http://www.w3.org/1999/02/22-rdf-syntax-ns#nil"/>
<rdf:first rdf:resource="rdf:#$uzI6R1"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#d42f3492-3ace-4f88-b29a-67b923201a1e">
<dcterms:modified rdf:resource="rdf:#adedec42-59c5-4dad-8f6c-177511d9560d"/>
<rdf:value>Added more metadata.</rdf:value>
<cmeta:modifier rdf:resource="rdf:#1df83312-5912-493b-8df9-acad7a980fbc"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#b87b0808-5081-44e3-9bde-1b28762f3c10">
<vCard:Given>Catherine</vCard:Given>
<vCard:Family>Lloyd</vCard:Family>
<vCard:Other>May</vCard:Other>
</rdf:Description>
<rdf:Description rdf:about="rdf:#f0b2acc8-21ca-4887-9cbf-715041bcbc45">
<dcterms:modified rdf:resource="rdf:#272ea005-0b0b-45fb-a45a-3f7efecb9fea"/>
<rdf:value>Added cmeta:id's to several variables to allow their use by a session file. (PCEnv does this automatically when a session of a model is exported and the model file saved.)</rdf:value>
<cmeta:modifier rdf:resource="rdf:#c3e37a47-326f-4f3c-81bc-def220c86f52"/>
</rdf:Description>
<rdf:Description rdf:about="#chay_1997_version01">
<ns7:simulation rdf:resource="rdf:#$szI6R1"/>
<dc:title>The Chay et al 1997 mathematical model of the effects of extracellular
and intracellular calcium on pancreatic beta cells.</dc:title>
<cmeta:bio_entity>Pancreatic Beta-cell</cmeta:bio_entity>
<cmeta:comment rdf:resource="rdf:#429b7f97-dc30-475b-8868-3fde2aa83dbe"/>
<bqs:reference rdf:resource="rdf:#0855ba44-9c92-4224-8182-c79ef9d998e0"/>
<bqs:reference rdf:resource="rdf:#7951457b-585b-4a43-b328-16035242f6ce"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#429b7f97-dc30-475b-8868-3fde2aa83dbe">
<dc:creator rdf:resource="rdf:#6478f744-71f1-4704-a5b3-3dd797e0c780"/>
<rdf:value>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.</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#7951457b-585b-4a43-b328-16035242f6ce">
<bqs:Pubmed_id>9284334</bqs:Pubmed_id>
<bqs:JournalArticle rdf:resource="rdf:#d6d4a8ec-88ec-4cd1-9817-ea9a61a359bd"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#d6d4a8ec-88ec-4cd1-9817-ea9a61a359bd">
<dc:creator rdf:resource="rdf:#7c75d0fe-e2ea-4306-a36b-863632500f4e"/>
<dc:title>Effects of extracellular calcium on electrical bursting and intracellular and luminal calcium oscillations in insulin secreting pancreatic beta-cells</dc:title>
<bqs:volume>73</bqs:volume>
<bqs:first_page>1673</bqs:first_page>
<bqs:Journal rdf:resource="rdf:#865e3c5c-bc6a-4431-a1f8-a2503b2aeba1"/>
<dcterms:issued rdf:resource="rdf:#0c360212-f816-4351-950a-a117f862a672"/>
<bqs:last_page>1688</bqs:last_page>
</rdf:Description>
<rdf:Description rdf:about="rdf:#f9f9e858-a37e-404e-884c-2b591352e0a8">
<rdf:type rdf:resource="http://imc.org/vCard/3.0#internet"/>
<rdf:value>c.lloyd@auckland.ac.nz</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#a9e42612-b725-4ad8-9afa-a890ed4f3591">
<dcterms:modified rdf:resource="rdf:#3ee27592-159c-4faa-9c7a-22d32346dc0b"/>
<rdf:value>Added publication date information.</rdf:value>
<cmeta:modifier rdf:resource="rdf:#c963df5c-bb43-490d-baa3-587ac6d67bb0"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#67a4c2be-a043-42a0-a2cf-156b3b7c7598">
<rdf:type rdf:resource="http://www.cellml.org/bqs/1.0#Person"/>
<vCard:N rdf:resource="rdf:#ee0877ce-1228-4f62-ad4d-fda0e45f0e1e"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#$szI6R1">
<ns7:boundIntervals rdf:resource="rdf:#$tzI6R1"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#0c360212-f816-4351-950a-a117f862a672">
<dcterms:W3CDTF>1997-09</dcterms:W3CDTF>
</rdf:Description>
<rdf:Description rdf:about="rdf:#9957dbbd-a1b4-40c7-b49e-502606ec0c36">
<vCard:Given>James</vCard:Given>
<vCard:Family>Lawson</vCard:Family>
<vCard:Other>Richard</vCard:Other>
</rdf:Description>
<rdf:Description rdf:about="rdf:#0ff67c11-a57c-4f33-a48d-dadbbb2ae5a2">
<dcterms:W3CDTF>2002-05-07T00:00:00+00:00</dcterms:W3CDTF>
</rdf:Description>
<rdf:Description rdf:about="rdf:#51b1bcf0-cb86-4c8f-98b4-4911bf6ce72b">
<dc:creator rdf:resource="rdf:#3faafe87-4cf5-41d2-8b7d-7cf1581c10ac"/>
<rdf:value>This model is able to reproduce the figures presented in the Chay 1997 paper and this version has a PCEnv session file associated with it.
The session shows three electrophysiological graphs (x-axis is time in seconds): membrane potential (mV), intracellular cytosolic calcium and intracellular (luminal / endoplasmic reticulum) calcium. The value for the variable 'Ca_o' in the component 'calcium_current' can be altered to 0, 2.5, 5 or 7.5 mM to reproduce figures 5 a,b,c,d, respectively.</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#$uzI6R1">
<ns7:endingValue>100</ns7:endingValue>
<ns7:nonstandard-pointDensity>1000000</ns7:nonstandard-pointDensity>
<ns7:maximumStepSize>0.01</ns7:maximumStepSize>
</rdf:Description>
<rdf:Description rdf:about="rdf:#6bfba5f6-415b-466a-aff1-49fd37869b6e">
<bqs:subject_type>keyword</bqs:subject_type>
<rdf:value rdf:resource="rdf:#a2cc4365-2f2f-4903-9cbc-dc863978ea00"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#3faafe87-4cf5-41d2-8b7d-7cf1581c10ac">
<vCard:FN>James Lawson</vCard:FN>
</rdf:Description>
<rdf:Description rdf:about="rdf:#6904a13f-ab67-4726-b3fa-06de9624350c">
<vCard:Orgname>The University of Auckland</vCard:Orgname>
<vCard:Orgunit>The Bioengineering Institute</vCard:Orgunit>
</rdf:Description>
<rdf:Description rdf:about="rdf:#0855ba44-9c92-4224-8182-c79ef9d998e0">
<dc:subject rdf:resource="rdf:#6bfba5f6-415b-466a-aff1-49fd37869b6e"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#c3e37a47-326f-4f3c-81bc-def220c86f52">
<vCard:N rdf:resource="rdf:#9957dbbd-a1b4-40c7-b49e-502606ec0c36"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#8180d95a-0164-47c3-bb69-9939c6a0c5ec">
<vCard:Given>Autumn</vCard:Given>
<vCard:Family>Cuellar</vCard:Family>
<vCard:Other>A</vCard:Other>
</rdf:Description>
<rdf:Description rdf:about="rdf:#ee0877ce-1228-4f62-ad4d-fda0e45f0e1e">
<vCard:Given>Teresa</vCard:Given>
<vCard:Family>Chay</vCard:Family>
<vCard:Other>Ree</vCard:Other>
</rdf:Description>
<rdf:Description rdf:about="rdf:#c963df5c-bb43-490d-baa3-587ac6d67bb0">
<vCard:N rdf:resource="rdf:#8180d95a-0164-47c3-bb69-9939c6a0c5ec"/>
</rdf:Description>
</rdf:RDF>
</model>
