<?xml version="1.0"?>
<!-- FILE : greenstein_model_1_1_2000.xml
CREATED : 17th September 2003
LAST MODIFIED : 17th September 2003
AUTHOR : Catherine Lloyd
Bioengineering Institute
The University of Auckland
MODEL STATUS : This model conforms to the CellML 1.1 Specification and the CellML Metadata 1.0 Specification released on 16th January, 2002.
DESCRIPTION : This file contains a CellML description of Greenstein et al's 2000 mathematical model of the role of the transient outward current Ito1 in shaping action potential morphology and duration. It imports the Winslow et al 1999 model using the import and reuse features of CellML 1.1.
CHANGES:
-->
<model
name="greenstein_model_1_1_2000"
cmeta:id="greenstein_model_1_1_2000"
xmlns="http://www.cellml.org/cellml/1.1#"
xmlns:cellml="http://www.cellml.org/cellml/1.1#"
xmlns:cmeta="http://www.cellml.org/metadata/1.0#"
xmlns:xlink="http://www.w3.org/1999/xlink">
<rdf:RDF
xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
xmlns:cmeta="http://www.cellml.org/metadata/1.0#"
xmlns:bqs="http://www.cellml.org/bqs/1.1#"
xmlns:dc="http://purl.org/dc/elements/1.1/"
xmlns:dcterms="http://purl.org/dc/terms/"
xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#">
<!--
The following RDF block contains metadata that applies to this document
as a whole, as indicated by the empty about attribute on the
<rdf:Description> element.
-->
<rdf:Description rdf:about="">
<!--
The Model Builder Metadata. The Dublin Core "creator" element is used
to indicate the person who translated the model into CellML.
-->
<dc:creator rdf:parseType="Resource">
<vCard:N rdf:parseType="Resource">
<vCard:Family>Lloyd</vCard:Family>
<vCard:Given>Catherine</vCard:Given>
<vCard:Other>May</vCard:Other>
</vCard:N>
<vCard:EMAIL rdf:parseType="Resource">
<rdf:value>c.lloyd@auckland.ac.nz</rdf:value>
<rdf:type rdf:resource="http://imc.org/vCard/3.0#internet" />
</vCard:EMAIL>
<vCard:ORG rdf:parseType="Resource">
<vCard:Orgname>The University of Auckland</vCard:Orgname>
<vCard:Orgunit>The Bioengineering Institute</vCard:Orgunit>
</vCard:ORG>
</dc:creator>
<!--
The Creation Date metadata. This is the date on which the model
was translated into CellML.
-->
<dcterms:created rdf:parseType="Resource">
<dcterms:W3CDTF>2003-09-17</dcterms:W3CDTF>
</dcterms:created>
<!--
The Modification History metadata. This lists the changes that have been
made to the document, who made the changes, and when they were made.
-->
<!-- The Publisher metadata. -->
<dc:publisher>
The University of Auckland, Bioengineering Institute
</dc:publisher>
</rdf:Description>
<!--
The following metadata refers to the model itself, as indicated by the
reference to the ID "greenstein_model_1_1_2000", which is declared on
the <model> element.
-->
<rdf:Description rdf:about="#greenstein_model_1_1_2000">
<!-- A human readable name for the model. -->
<dc:title>
Greenstein et al's 2000 mathematical model of the role of the transient outward current Ito1 in shaping action potential morphology and duration.
</dc:title>
<!-- A comment regarding the model. -->
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
This is the CellML description of Greenstein et al's 2000 mathematical model of the role of the transient outward current Ito1 in shaping action potential morphology and duration. It imports the Winslow et al 1999 model using the import and reuse features of CellML 1.1.
</rdf:value>
<!-- The creator of the comment. -->
<dc:creator rdf:parseType="Resource">
<vCard:FN>Catherine Lloyd</vCard:FN>
</dc:creator>
</cmeta:comment>
<!-- The model is relevant to canines. -->
<cmeta:species>Canine</cmeta:species>
<cmeta:bio_entity>Ventricular Myocyte</cmeta:bio_entity>
<!--
The CellML Metadata Specification recommends that bibliographic metadata
is used to provide information about the original model reference. The
"identifier" attribute on the "BibliographicReference" class provides an
elegant way to identify a cited reference using a database identifier such as Pubmed. All associated data such as author, journal title,
date, etc can be looked up on the database.
-->
<bqs:reference rdf:parseType="Resource">
<bqs:Pubmed_id>11090548</bqs:Pubmed_id>
<bqs:JournalArticle rdf:parseType="Resource">
<dc:creator>
<rdf:Seq>
<rdf:li rdf:parseType="Resource">
<bqs:Person rdf:parseType="Resource">
<vCard:N rdf:parseType="Resource">
<vCard:Family>Greenstein</vCard:Family>
<vCard:Given>Joseph</vCard:Given>
<vCard:Other>L</vCard:Other>
</vCard:N>
</bqs:Person>
</rdf:li>
<rdf:li rdf:parseType="Resource">
<bqs:Person rdf:parseType="Resource">
<vCard:N rdf:parseType="Resource">
<vCard:Family>Wu</vCard:Family>
<vCard:Given>Richard</vCard:Given>
</vCard:N>
</bqs:Person>
</rdf:li>
<rdf:li rdf:parseType="Resource">
<bqs:Person rdf:parseType="Resource">
<vCard:N rdf:parseType="Resource">
<vCard:Family>Po</vCard:Family>
<vCard:Given>Sunny</vCard:Given>
</vCard:N>
</bqs:Person>
</rdf:li>
<rdf:li rdf:parseType="Resource">
<bqs:Person rdf:parseType="Resource">
<vCard:N rdf:parseType="Resource">
<vCard:Family>Tomaselli</vCard:Family>
<vCard:Given>Gordon</vCard:Given>
<vCard:Other>F</vCard:Other>
</vCard:N>
</bqs:Person>
</rdf:li>
<rdf:li rdf:parseType="Resource">
<bqs:Person rdf:parseType="Resource">
<vCard:N rdf:parseType="Resource">
<vCard:Family>Winslow</vCard:Family>
<vCard:Given>Raimond</vCard:Given>
<vCard:Other>L</vCard:Other>
</vCard:N>
</bqs:Person>
</rdf:li>
</rdf:Seq>
</dc:creator>
<dc:title>
Role of the Calcium-Independent Transient Outward Current Ito1 in
Shaping Action Potential Morphology and Duration.
</dc:title>
<dcterms:issued rdf:parseType="Resource">
<dcterms:W3CDTF>2000-11-24</dcterms:W3CDTF>
</dcterms:issued>
<bqs:Journal rdf:parseType="Resource">
<dc:title>Circulation Research</dc:title>
</bqs:Journal>
<bqs:volume>87</bqs:volume>
<bqs:first_page>1026</bqs:first_page>
<bqs:last_page>1033</bqs:last_page>
</bqs:JournalArticle>
</bqs:reference>
</rdf:Description>
</rdf:RDF>
<import xlink:href="http://www.cellml.org/examples/models/winslow_model_1999.xml">
<units name="millisecond" units_ref="millisecond" />
<units name="millivolt" units_ref="millivolt" />
<units name="per_millisecond" units_ref="per_millisecond" />
<units name="per_millivolt" units_ref="per_millivolt" />
<units name="per_millivolt_millisecond" units_ref="per_millivolt_millisecond" />
<units name="milliS_per_microF" units_ref="milliS_per_microF" />
<units name="microA_per_microF" units_ref="microA_per_microF" />
<units name="millimolar" units_ref="millimolar" />
<units name="joule_per_mole_kelvin" units_ref="joule_per_mole_kelvin" />
<units name="coulomb_per_millimole" units_ref="coulomb_per_millimole" />
<units name="microF_per_cm2" units_ref="microF_per_cm2" />
<component name="environment" component_ref="environment" />
<component name="membrane" component_ref="membrane" />
<component name="fast_sodium_current" component_ref="fast_sodium_current" />
<component name="rapid_activating_delayed_rectifiyer_K_current" component_ref="rapid_activating_delayed_rectifiyer_K_current" />
<component name="slow_activating_delayed_rectifiyer_K_current" component_ref="slow_activating_delayed_rectifiyer_K_current" />
<component name="time_independent_potassium_current" component_ref="time_independent_potassium_current" />
<component name="plateau_potassium_current" component_ref="plateau_potassium_current" />
<component name="Na_Ca_exchanger" component_ref="Na_Ca_exchanger" />
<component name="sodium_potassium_pump" component_ref="sodium_potassium_pump" />
<component name="sarcolemmal_calcium_pump" component_ref="sarcolemmal_calcium_pump" />
<component name="calcium_background_current" component_ref="calcium_background_current" />
<component name="sodium_background_current" component_ref="sodium_background_current" />
<component name="L_type_Ca_current" component_ref="L_type_Ca_current" />
<component name="RyR_channel" component_ref="RyR_channel" />
<component name="SERCA2a_pump" component_ref="SERCA2a_pump" />
<component name="intracellular_Ca_fluxes" component_ref="intracellular_Ca_fluxes" />
<component name="intracellular_ion_concentrations" component_ref="intracellular_ion_concentrations" />
<component name="standard_ionic_concentrations" component_ref="standard_ionic_concentrations" />
</import>
<!--
Below, we define an additional unit for use in the importing Greenstein 1.1 model.
-->
<units name="mm_per_s">
<unit prefix="milli" units="metre" />
<unit units="second" exponent="-1" />
</units>
<!-- The new components -->
<component name="transient_outward_potassium_current">
<variable name="i_to1" public_interface="out" units="microA_per_microF" />
<variable name="time" public_interface="in" private_interface="out" units="millisecond" />
<variable name="V" public_interface="in" private_interface="out" units="millivolt" />
<variable name="E_K" public_interface="in" private_interface="out" units="millivolt" />
<variable name="Nai" public_interface="in" private_interface="out" units="millimolar" />
<variable name="Nao" public_interface="in" private_interface="out" units="millimolar" />
<variable name="Ki" public_interface="in" private_interface="out" units="millimolar" />
<variable name="Ko" public_interface="in" private_interface="out" units="millimolar" />
<variable name="R" public_interface="in" private_interface="out" units="joule_per_mole_kelvin" />
<variable name="T" public_interface="in" private_interface="out" units="kelvin" />
<variable name="F" public_interface="in" private_interface="out" units="coulomb_per_millimole" />
<variable name="C_sc" public_interface="in" private_interface="out" units="microF_per_cm2" />
<variable name="i_Kv4_3" private_interface="in" units="microA_per_microF" />
<variable name="i_Kv1_4" private_interface="in" units="microA_per_microF" />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="i_to1_calculation"><eq />
<ci> i_to1 </ci>
<apply><plus />
<ci> i_Kv4_3 </ci>
<ci> i_Kv1_4 </ci>
</apply>
</apply>
</math>
</component>
<component name="Kv4_3_current">
<variable name="i_Kv4_3" public_interface="out" units="microA_per_microF" />
<variable name="g_Kv4_3" units="milliS_per_microF" />
<variable name="P_open" units="dimensionless" />
<variable name="P_C0" units="dimensionless" />
<variable name="P_C1" units="dimensionless" />
<variable name="P_C2" units="dimensionless" />
<variable name="P_C3" units="dimensionless" />
<variable name="P_CI0" units="dimensionless" />
<variable name="P_CI1" units="dimensionless" />
<variable name="P_CI2" units="dimensionless" />
<variable name="P_CI3" units="dimensionless" />
<variable name="P_O" units="dimensionless" />
<variable name="P_OI" units="dimensionless" />
<variable name="a_a" initial_value="0.02898" units="per_millivolt" />
<variable name="b_a" initial_value="0.04684" units="per_millivolt" />
<variable name="a_i" initial_value="3.7302E-4" units="per_millivolt" />
<variable name="b_i" initial_value="5.374E-8" units="per_millivolt" />
<variable name="alpha_a0" initial_value="0.5437" units="per_millisecond" />
<variable name="beta_a0" initial_value="0.08019" units="per_millisecond" />
<variable name="alpha_i0" initial_value="0.04984" units="per_millisecond" />
<variable name="beta_i0" initial_value="8.1948E-4" units="per_millisecond" />
<variable name="alpha_a" units="per_millisecond" />
<variable name="beta_a" units="per_millisecond" />
<variable name="alpha_i" units="per_millisecond" />
<variable name="beta_i" units="per_millisecond" />
<variable name="f1" initial_value="1.8936" units="dimensionless" />
<variable name="f2" initial_value="14.225" units="dimensionless" />
<variable name="f3" initial_value="158.574" units="dimensionless" />
<variable name="f4" initial_value="142.937" units="dimensionless" />
<variable name="b1" initial_value="6.7735" units="dimensionless" />
<variable name="b2" initial_value="15.621" units="dimensionless" />
<variable name="b3" initial_value="28.753" units="dimensionless" />
<variable name="b4" initial_value="524.576" units="dimensionless" />
<variable name="time" public_interface="in" units="millisecond" />
<variable name="V" public_interface="in" units="millivolt" />
<variable name="E_K" public_interface="in" units="millivolt" />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="i_Kv4_3_calculation"><eq />
<ci> i_Kv4_3 </ci>
<apply><times />
<ci> g_Kv4_3 </ci>
<ci> P_open </ci>
<apply><minus />
<ci> V </ci>
<ci> E_K </ci>
</apply>
</apply>
</apply>
<apply id="P_open_calculation"><eq />
<ci> P_open </ci>
<apply><plus />
<ci> P_O </ci>
<ci> P_OI </ci>
</apply>
</apply>
<apply id="P_C0_diff_eq"><eq />
<apply><diff />
<bvar><ci> time </ci></bvar>
<ci> P_C0 </ci>
</apply>
<apply><minus />
<apply><plus />
<apply><times />
<ci> alpha_i </ci>
<ci> P_CI0 </ci>
</apply>
<apply><times />
<ci> beta_a </ci>
<ci> P_C1 </ci>
</apply>
</apply>
<apply><times />
<apply><plus />
<ci> beta_i </ci>
<apply><times />
<cn cellml:units="dimensionless"> 4.0 </cn>
<ci> alpha_a </ci>
</apply>
</apply>
<ci> P_C0 </ci>
</apply>
</apply>
</apply>
<apply id="P_C1_diff_eq"><eq />
<apply><diff />
<bvar><ci> time </ci></bvar>
<ci> P_C1 </ci>
</apply>
<apply><minus />
<apply><plus />
<apply><times />
<apply><divide />
<ci> alpha_i </ci>
<ci> b1 </ci>
</apply>
<ci> P_CI1 </ci>
</apply>
<apply><times />
<cn cellml:units="dimensionless"> 4.0 </cn>
<ci> alpha_a </ci>
<ci> P_C0 </ci>
</apply>
<apply><times />
<cn cellml:units="dimensionless"> 2.0 </cn>
<ci> beta_a </ci>
<ci> P_C2 </ci>
</apply>
</apply>
<apply><times />
<apply><plus />
<apply><times />
<ci> f1 </ci>
<ci> beta_i </ci>
</apply>
<ci> beta_a </ci>
<apply><times />
<cn cellml:units="dimensionless"> 3.0 </cn>
<ci> alpha_a </ci>
</apply>
</apply>
<ci> P_C1 </ci>
</apply>
</apply>
</apply>
<apply id="P_C2_diff_eq"><eq />
<apply><diff />
<bvar><ci> time </ci></bvar>
<ci> P_C2 </ci>
</apply>
<apply><minus />
<apply><plus />
<apply><times />
<apply><divide />
<ci> alpha_i </ci>
<ci> b2 </ci>
</apply>
<ci> P_CI2 </ci>
</apply>
<apply><times />
<cn cellml:units="dimensionless"> 3.0 </cn>
<ci> alpha_a </ci>
<ci> P_C1 </ci>
</apply>
<apply><times />
<cn cellml:units="dimensionless"> 3.0 </cn>
<ci> beta_a </ci>
<ci> P_C3 </ci>
</apply>
</apply>
<apply><times />
<apply><plus />
<apply><times />
<ci> f2 </ci>
<ci> beta_i </ci>
</apply>
<apply><times />
<cn cellml:units="dimensionless"> 2.0 </cn>
<ci> beta_a </ci>
</apply>
<apply><times />
<cn cellml:units="dimensionless"> 2.0 </cn>
<ci> alpha_a </ci>
</apply>
</apply>
<ci> P_C2 </ci>
</apply>
</apply>
</apply>
<apply id="P_C3_diff_eq"><eq />
<apply><diff />
<bvar><ci> time </ci></bvar>
<ci> P_C3 </ci>
</apply>
<apply><minus />
<apply><plus />
<apply><times />
<apply><divide />
<ci> alpha_i </ci>
<ci> b3 </ci>
</apply>
<ci> P_CI3 </ci>
</apply>
<apply><times />
<cn cellml:units="dimensionless"> 2.0 </cn>
<ci> alpha_a </ci>
<ci> P_C2 </ci>
</apply>
<apply><times />
<cn cellml:units="dimensionless"> 4.0 </cn>
<ci> beta_a </ci>
<ci> P_O </ci>
</apply>
</apply>
<apply><times />
<apply><plus />
<apply><times />
<ci> f3 </ci>
<ci> beta_i </ci>
</apply>
<apply><times />
<cn cellml:units="dimensionless"> 3.0 </cn>
<ci> beta_a </ci>
</apply>
<ci> alpha_a </ci>
</apply>
<ci> P_C3 </ci>
</apply>
</apply>
</apply>
<apply id="P_O_diff_eq"><eq />
<apply><diff />
<bvar><ci> time </ci></bvar>
<ci> P_O </ci>
</apply>
<apply><minus />
<apply><plus />
<apply><times />
<ci> alpha_a </ci>
<ci> P_C3 </ci>
</apply>
<apply><times />
<apply><divide />
<ci> alpha_i </ci>
<ci> b4 </ci>
</apply>
<ci> P_OI </ci>
</apply>
</apply>
<apply><times />
<apply><plus />
<apply><times />
<ci> f4 </ci>
<ci> beta_i </ci>
</apply>
<apply><times />
<cn cellml:units="dimensionless"> 4.0 </cn>
<ci> beta_a </ci>
</apply>
</apply>
<ci> P_O </ci>
</apply>
</apply>
</apply>
<apply id="P_CI0_diff_eq"><eq />
<apply><diff />
<bvar><ci> time </ci></bvar>
<ci> P_CI0 </ci>
</apply>
<apply><minus />
<apply><plus />
<apply><times />
<ci> beta_i </ci>
<ci> P_C0 </ci>
</apply>
<apply><times />
<apply><divide />
<ci> beta_a </ci>
<ci> f1 </ci>
</apply>
<ci> P_C1 </ci>
</apply>
</apply>
<apply><times />
<apply><plus />
<ci> alpha_i </ci>
<apply><times />
<ci> b1 </ci>
<cn cellml:units="dimensionless"> 4.0 </cn>
<ci> alpha_a </ci>
</apply>
</apply>
<ci> P_CI0 </ci>
</apply>
</apply>
</apply>
<apply id="P_CI1_diff_eq"><eq />
<apply><diff />
<bvar><ci> time </ci></bvar>
<ci> P_CI1 </ci>
</apply>
<apply><minus />
<apply><plus />
<apply><times />
<apply><divide />
<apply><times />
<ci> f1 </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
<ci> beta_a </ci>
</apply>
<ci> f2 </ci>
</apply>
<ci> P_CI2 </ci>
</apply>
<apply><times />
<ci> b1 </ci>
<cn cellml:units="dimensionless"> 4.0 </cn>
<ci> alpha_a </ci>
<ci> P_CI0 </ci>