- Author:
- David Nickerson <david.nickerson@gmail.com>
- Date:
- 2021-09-15 23:15:11+12:00
- Desc:
- update jupyter notebook with FK model results
- Permanent Source URI:
- https://staging.physiomeproject.org/workspace/a1/rawfile/797bc599b7ec66eef984e817d4ce138aabd116a6/models/1975_mcallister/1975_mcallister_noble_tsien.xml
<?xml version="1.0" encoding="iso-8859-1"?>
<!-- FILE : MNT_purkinje_fibre_model_1975.xml
CREATED : September 2001
LAST MODIFIED : 5th April 2003
AUTHOR : Catherine Lloyd
Department of Engineering Science
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 16
January 2002.
DESCRIPTION : This file contains a CellML description of cardiac action
potentials in purkinje fibres, based on the McAllister-Noble-Tsien model, 1975.
CHANGES:
19/10/2001 - CML - Removed document type definition as this is declared as
optional according to the W3C recommendation.
24/10/2001 - CML - Made changes to some of the metadata, bringing them up to
date with the most recent working draft (26th September) of
the Metadata specification.
10/12/2001 - CML - Changed equations after checking with the mathml validator.
03/01/2002 - CML - Altered parent-child relationships as x1 and x2 were made
to be gates of the plateau potassium currents.
20/01/2002 - AAC - Updated metadata to conform to the 16/01/2002 CellML
Metadata Specification.
28/02/2002 - CML - Corrected units.
19/07/2002 - CML - Added more metadata.
05/04/2003 - AAC - Changed the model name so the model loads in the database
easier.
-->
<model
name="mcallister_noble_tsien_model_1975"
cmeta:id="MNT_purkinje_fibre_model_1975"
xmlns="http://www.cellml.org/cellml/1.0#"
xmlns:cellml="http://www.cellml.org/cellml/1.0#"
xmlns:cmeta="http://www.cellml.org/metadata/1.0#">
<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/1.0#"
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 Research Group</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>2001-09-27</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.
-->
<cmeta:modification rdf:parseType="Resource">
<rdf:value>
Changed some units and added a stimulus current.
</rdf:value>
<cmeta:modifier rdf:parseType="Resource">
<vCard:N rdf:parseType="Resource">
<vCard:Family>Nickerson</vCard:Family>
<vCard:Given>David</vCard:Given>
<vCard:Other>P</vCard:Other>
</vCard:N>
</cmeta:modifier>
<dcterms:modified rdf:parseType="Resource">
<dcterms:W3CDTF>2003-10-13</dcterms:W3CDTF>
</dcterms:modified>
</cmeta:modification>
<cmeta:modification rdf:parseType="Resource">
<rdf:value>
Changed the model name so the model loads in the database easier.
</rdf:value>
<cmeta:modifier rdf:parseType="Resource">
<vCard:N rdf:parseType="Resource">
<vCard:Family>Cuellar</vCard:Family>
<vCard:Given>Autumn</vCard:Given>
<vCard:Other>A</vCard:Other>
</vCard:N>
</cmeta:modifier>
<dcterms:modified rdf:parseType="Resource">
<dcterms:W3CDTF>2003-04-05</dcterms:W3CDTF>
</dcterms:modified>
</cmeta:modification>
<cmeta:modification rdf:parseType="Resource">
<rdf:value>
Added more metadata.
</rdf:value>
<cmeta:modifier 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>
</cmeta:modifier>
<dcterms:modified rdf:parseType="Resource">
<dcterms:W3CDTF>2002-07-19</dcterms:W3CDTF>
</dcterms:modified>
</cmeta:modification>
<cmeta:modification rdf:parseType="Resource">
<rdf:value>
Corrected units
</rdf:value>
<cmeta:modifier 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>
</cmeta:modifier>
<dcterms:modified rdf:parseType="Resource">
<dcterms:W3CDTF>2002-02-28</dcterms:W3CDTF>
</dcterms:modified>
</cmeta:modification>
<cmeta:modification rdf:parseType="Resource">
<rdf:value>
Updated metadata to conform to the 16/01/2002 CellML Metadata 1.0
Specification.
</rdf:value>
<cmeta:modifier rdf:parseType="Resource">
<vCard:N rdf:parseType="Resource">
<vCard:Family>Cuellar</vCard:Family>
<vCard:Given>Autumn</vCard:Given>
<vCard:Other>A.</vCard:Other>
</vCard:N>
</cmeta:modifier>
<dcterms:modified rdf:parseType="Resource">
<dcterms:W3CDTF>2002-01-20</dcterms:W3CDTF>
</dcterms:modified>
</cmeta:modification>
<cmeta:modification rdf:parseType="Resource">
<rdf:value>
Altered parent-child relationships as x1 and x2 were made to be gates
of the plateau potassium currents.
</rdf:value>
<cmeta:modifier 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>
</cmeta:modifier>
<dcterms:modified rdf:parseType="Resource">
<dcterms:W3CDTF>2002-01-03</dcterms:W3CDTF>
</dcterms:modified>
</cmeta:modification>
<cmeta:modification rdf:parseType="Resource">
<rdf:value>
Changed equations after checking with the mathml validator.
</rdf:value>
<cmeta:modifier 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>
</cmeta:modifier>
<dcterms:modified rdf:parseType="Resource">
<dcterms:W3CDTF>2001-12-10</dcterms:W3CDTF>
</dcterms:modified>
</cmeta:modification>
<cmeta:modification rdf:parseType="Resource">
<rdf:value>
Made changes to some of the metadata, bringing them up to date with
the most recent working draft (26th September) of the Metadata
Specification.
</rdf:value>
<cmeta:modifier 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>
</cmeta:modifier>
<dcterms:modified rdf:parseType="Resource">
<dcterms:W3CDTF>2001-10-24</dcterms:W3CDTF>
</dcterms:modified>
</cmeta:modification>
<cmeta:modification rdf:parseType="Resource">
<rdf:value>
Removed document type definition as this is declared as optional
according to the W3C recommendation.
</rdf:value>
<cmeta:modifier 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>
</cmeta:modifier>
<dcterms:modified rdf:parseType="Resource">
<dcterms:W3CDTF>2001-10-19</dcterms:W3CDTF>
</dcterms:modified>
</cmeta:modification>
<!-- The Publisher metadata. -->
<dc:publisher>
The University of Auckland, Bioengineering Research Group
</dc:publisher>
</rdf:Description>
<!--
The following metadata refers to the model itself, as indicated by the
reference to the ID "MNT_purkinje_fibre_model_1975", which is
declared on the <model> element.
-->
<rdf:Description rdf:about="#MNT_purkinje_fibre_model_1975">
<!-- A human readable name for the model. -->
<dc:title>
The McAllister-Noble-Tsien Model of Cardiac Action Potentials in
Purkinje fibres, 1975
</dc:title>
<!-- A comment regarding the model. -->
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
This is the CellML description of McAllister, Noble and Tsien's
mathematical model of cardiac action potentials of Purkinje fibres.
It describes transmembrane ionic currents in terms of Hodgkin-Huxley type equations. It is a significant development of the Noble (1962)
model as more currents are added based on new experimental data.
</rdf:value>
<!-- The creator of the comment. -->
<dc:creator rdf:parseType="Resource">
<vCard:FN>Catherine Lloyd</vCard:FN>
</dc:creator>
</cmeta:comment>
<cmeta:bio_entity>Purkinje Fibre</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>1185607</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>McAllister</vCard:Family>
<vCard:Given>R</vCard:Given>
<vCard:Other>E</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>Noble</vCard:Family>
<vCard:Given>Denis</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>Tsien</vCard:Family>
<vCard:Given>R</vCard:Given>
<vCard:Other>W</vCard:Other>
</vCard:N>
</bqs:Person>
</rdf:li>
</rdf:Seq>
</dc:creator>
<dc:title>
Reconstruction of the electrical activity of cardiac purkinje fibres
</dc:title>
<dcterms:issued rdf:parseType="Resource">
<dcterms:W3CDTF>1975-09</dcterms:W3CDTF>
</dcterms:issued>
<bqs:Journal rdf:parseType="Resource">
<dc:title>Journal of Physiology</dc:title>
</bqs:Journal>
<bqs:volume>251</bqs:volume>
<bqs:first_page>1</bqs:first_page>
<bqs:last_page>59</bqs:last_page>
</bqs:JournalArticle>
</bqs:reference>
</rdf:Description>
</rdf:RDF>
<!--
Below, are defined some additional units for association with variables and
constants within the model. The identifiers are fairly self-explanatory.
-->
<units name="ms">
<unit prefix="milli" units="second" />
</units>
<units name="per_ms">
<unit prefix="milli" units="second" exponent="-1" />
</units>
<units name="mV">
<unit prefix="milli" units="volt" />
</units>
<units name="per_mV">
<unit prefix="milli" units="volt" exponent="-1" />
</units>
<units name="per_mV_ms">
<unit units="mV" exponent="-1" />
<unit units="ms" exponent="-1" />
</units>
<units name="mS_per_mm2">
<unit prefix="milli" units="siemens" />
<unit prefix="milli" units="metre" exponent="-2" />
</units>
<units name="uF_per_mm2">
<unit prefix="micro" units="farad" />
<unit prefix="milli" units="metre" exponent="-2" />
</units>
<units name="uA_per_mm2">
<unit prefix="micro" units="ampere" />
<unit prefix="milli" units="metre" exponent="-2" />
</units>
<units name="concentration_units">
<unit prefix="nano" units="mole" />
<unit prefix="milli" units="metre" exponent="-3" />
</units>
<component name="interface" cmeta:id="interface">
<variable name="time" public_interface="in" private_interface="out" units="ms" />
<variable name="I_stim" public_interface="in" private_interface="out" units="uA_per_mm2"/>
</component>
<!--
The "membrane" component is really the `root' node of our model.
It defines the action potential variable "V" among other things.
-->
<component name="membrane" cmeta:id="membrane">
<rdf:RDF
xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
xmlns:cmeta="http://www.cellml.org/metadata/1.0#">
<rdf:Description rdf:about="#membrane">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The main component of the model, containing the definition of the
model's action potential.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<!-- These variables are defined here and used in other components. -->
<variable cmeta:id="Vm" name="V" initial_value="-80.0" public_interface="out" units="mV" />
<!-- These variables are defined here and only used internally. -->
<variable name="C" initial_value="0.1" units="uF_per_mm2" />
<!-- These variables are imported from other components. -->
<variable name="time" public_interface="in" units="ms" />
<variable name="i_Na" public_interface="in" units="uA_per_mm2" />
<variable name="i_si" public_interface="in" units="uA_per_mm2" />
<variable name="i_K2" public_interface="in" units="uA_per_mm2" />
<variable name="i_x1" public_interface="in" units="uA_per_mm2" />
<variable name="i_x2" public_interface="in" units="uA_per_mm2" />
<variable name="i_qr" public_interface="in" units="uA_per_mm2" />
<variable name="i_K1" public_interface="in" units="uA_per_mm2" />
<variable name="i_Na_b" public_interface="in" units="uA_per_mm2" />
<variable name="i_Cl_b" public_interface="in" units="uA_per_mm2" />
<variable name="I_stim" public_interface="in" units="uA_per_mm2" />
<!--
The membrane voltage (V) is calculated as an ordinary
differential equation in terms of the currents.
-->
<rdf:RDF
xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
xmlns:cmeta="http://www.cellml.org/metadata/1.0#">
<rdf:Description rdf:about="#membrane_voltage_diff_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The kinetics of the transmembrane potential, defined as the sum of
the trans-sarcolemmal currents and an applied stimulus current.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="membrane_voltage_diff_eq">
<apply id="membrane_voltage_diff_eq"><eq />
<apply><diff />
<bvar><ci> time </ci></bvar>
<ci> V </ci>
</apply>
<apply><divide />
<apply><minus />
<ci>I_stim</ci>
<apply><plus />
<ci> i_Na </ci>
<ci> i_si </ci>
<ci> i_K2 </ci>
<ci> i_x1 </ci>
<ci> i_x2 </ci>
<ci> i_qr </ci>
<ci> i_K1 </ci>
<ci> i_Na_b </ci>
<ci> i_Cl_b </ci>
</apply>
</apply>
<ci> C </ci>
</apply>
</apply>
</math>
</component>
<!--
The "fast_sodium_current" component contains the differential equations
governing the influx of sodium ions through the cell surface membrane
into the cell.
-->
<component name="fast_sodium_current" cmeta:id="fast_sodium_current">
<rdf:RDF
xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
xmlns:cmeta="http://www.cellml.org/metadata/1.0#">
<rdf:Description rdf:about="#fast_sodium_current">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The fast sodium current, primarily responsible for the upstroke of
the action potential.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<!-- These variables are defined here and used in other components. -->
<variable name="i_Na" public_interface="out" units="uA_per_mm2" />
<variable
name="E_Na" public_interface="out"
initial_value="40.0" units="mV" />
<!-- This variable is defined here and only used internally. -->
<variable name="g_Na" initial_value="1.5" units="mS_per_mm2" />
<!--
Time is imported from the "interface", and membrane potential is
imported from the "membrane" component. These variables are used in the
"sodium_current" parent component, which also acts as an interface,
passing the variables to its encapsulated gate components.
-->
<variable
name="time" public_interface="in"
private_interface="out" units="ms" />
<variable
name="V" public_interface="in"
private_interface="out" units="mV" />
<!-- These variables are imported from encapsulated components. -->
<variable name="m" private_interface="in" units="dimensionless" />
<variable name="h" private_interface="in" units="dimensionless" />
<rdf:RDF
xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
xmlns:cmeta="http://www.cellml.org/metadata/1.0#">
<rdf:Description rdf:about="#i_Na_calculation_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
Calculation of the fast sodium current.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="i_Na_calculation_eq">
<apply id="i_Na_calculation"><eq />
<ci> i_Na </ci>
<apply><times />
<ci> g_Na </ci>
<apply><power />
<ci> m </ci>
<cn cellml:units="dimensionless"> 3.0 </cn>
</apply>
<ci> h </ci>
<apply><minus />
<ci> V </ci>
<ci> E_Na </ci>
</apply>
</apply>
</apply>
</math>
</component>
<!--
The "fast_sodium_current_m_gate" is the activation m gate encapsulated
inside the "fast sodium current" component.
-->
<component name="fast_sodium_current_m_gate"
cmeta:id="fast_sodium_current_m_gate">
<rdf:RDF
xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
xmlns:cmeta="http://www.cellml.org/metadata/1.0#">
<rdf:Description rdf:about="#fast_sodium_current_m_gate">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The voltage-dependent activation gate for the fast sodium channel -
the m gate.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<!-- This variable is defined here and used in other components. -->
<variable name="m" initial_value="0.019" public_interface="out" units="dimensionless" />
<!-- These variables are defined here and only used internally. -->
<variable name="alpha_m" units="per_ms" />
<variable name="beta_m" units="per_ms" />
<!--
These variables are imported from the "interface" and the "membrane" via
the "fast_sodium_current" component.
-->
<variable name="V" public_interface="in" units="mV" />
<variable name="time" public_interface="in" units="ms" />
<rdf:RDF
xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
xmlns:cmeta="http://www.cellml.org/metadata/1.0#">
<rdf:Description rdf:about="#alpha_m_calculation_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The opening rate of the m gate.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="alpha_m_calculation_eq">
<apply id="alpha_m_calculation"><eq />
<ci> alpha_m </ci>
<apply><divide />
<apply><plus />
<ci> V </ci>
<cn cellml:units="mV"> 47.0 </cn>
</apply>
<apply><minus />
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply><exp />
<apply><minus />
<apply><divide />
<apply><plus />
<ci> V </ci>
<cn cellml:units="mV"> 47.0 </cn>
</apply>
<cn cellml:units="mV"> 10.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
<rdf:RDF
xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
xmlns:cmeta="http://www.cellml.org/metadata/1.0#">
<rdf:Description rdf:about="#beta_m_calculation_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The closing rate of the m gate.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="beta_m_calculation_eq">
<apply id="beta_m_calculation"><eq />
<ci> beta_m </ci>
<apply><times />
<cn cellml:units="per_ms"> 40.0 </cn>
<apply><exp />
<apply><minus />
<apply><divide />
<apply><plus />
<ci> V </ci>
<cn cellml:units="mV"> 72.0 </cn>
</apply>
<cn cellml:units="mV"> 17.86 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
<rdf:RDF
xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
xmlns:cmeta="http://www.cellml.org/metadata/1.0#">
<rdf:Description rdf:about="#dm_dt_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The kinetics of the m gate.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="dm_dt_eq">
<apply id="dm_dt"><eq />
<apply><diff />
<bvar><ci> time </ci></bvar>
<ci> m </ci>
</apply>
<apply><minus />
<apply><times />
<ci> alpha_m </ci>
<apply><minus />
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> m </ci>
</apply>
</apply>
<apply><times />
<ci> beta_m </ci>
<ci> m </ci>
</apply>
</apply>
</apply>
</math>
</component>
<!--
The "fast_sodium_current_h_gate" component is the inactivation h gate
encapsulated in the "fast sodium current" component.
-->
<component name="fast_sodium_current_h_gate"
cmeta:id="fast_sodium_current_h_gate">
<rdf:RDF
xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
xmlns:cmeta="http://www.cellml.org/metadata/1.0#">
<rdf:Description rdf:about="#fast_sodium_current_h_gate">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The voltage-dependent inactivation gate for the fast sodium channel
- the h gate.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<!-- This variable is defined here and used in other components. -->
<variable
name="h" initial_value="0.863" public_interface="out"
units="dimensionless" />
<!-- These variables are defined here and only used internally. -->
<variable name="alpha_h" units="per_ms" />
<variable name="beta_h" units="per_ms" />
<!--
These variables are imported from the "interface" and the "membrane" via
the "fast_sodium_current" component.
-->
<variable name="V" public_interface="in" units="mV" />
<variable name="time" public_interface="in" units="ms" />
<rdf:RDF
xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
xmlns:cmeta="http://www.cellml.org/metadata/1.0#">
<rdf:Description rdf:about="#alpha_h_calculation_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The opening rate of the h gate.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="alpha_h_calculation_eq">
<apply id="alpha_h_calculation"><eq />
<ci> alpha_h </ci>
<apply><times />
<cn cellml:units="per_ms"> 0.0085 </cn>
<apply><exp />
<apply><minus />
<apply><divide />
<apply><plus />
<ci> V </ci>
<cn cellml:units="mV"> 71.0 </cn>
</apply>
<cn cellml:units="mV"> 5.435 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
<rdf:RDF
xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
xmlns:cmeta="http://www.cellml.org/metadata/1.0#">
<rdf:Description rdf:about="#beta_h_calculation_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The closing rate of the h gate.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="beta_h_calculation_eq">
<apply id="beta_h_calculation"><eq />
<ci> beta_h </ci>
<apply><divide />
<cn cellml:units="per_ms"> 2.5 </cn>
<apply><plus />
<apply><exp />
<apply><minus />
<apply><divide />
<apply><plus />
<ci> V </ci>
<cn cellml:units="mV"> 10.0 </cn>
</apply>
<cn cellml:units="mV"> 12.2 </cn>
</apply>
</apply>
</apply>
<cn cellml:units="dimensionless"> 1.0 </cn>
</apply>
</apply>
</apply>
</math>
<rdf:RDF
xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
xmlns:cmeta="http://www.cellml.org/metadata/1.0#">
<rdf:Description rdf:about="#dh_dt_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The kinetics of the h gate.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="dh_dt_eq">
<apply id="dh_dt"><eq />
<apply><diff />
<bvar><ci> time </ci></bvar>
<ci> h </ci>
</apply>
<apply><minus />
<apply><times />
<ci> alpha_h </ci>
<apply><minus />
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> h </ci>
</apply>
</apply>
<apply><times />
<ci> beta_h </ci>
<ci> h </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="secondary_inward_current"
cmeta:id="secondary_inward_current">
<rdf:RDF
xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
xmlns:cmeta="http://www.cellml.org/metadata/1.0#">
<rdf:Description rdf:about="#secondary_inward_current">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The secondary (or sometimes slow) inward current activates much more
slowly than the sodium current and it is responsible for holding up
the plateau after the initial activation and for controlling the
duration of the action potential. At the time of this model, it was
assumed that the flux of both Na and Ca ions through the cell
membrane was responsible for this current. This channel has an
activation gate d and an inactivation gate f. It was observed in
earlier experiments that a portion of this current would not
completely inactivate. This is represented by the second term in
the secondary current equation which has an activation variable d1,
but no deactivation variable.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<!-- This variable is defined here and used in other components. -->
<variable name="i_si" public_interface="out" units="uA_per_mm2" />
<!-- These variables are defined here and only used internally. -->
<variable name="g_si" initial_value="0.008" units="mS_per_mm2" />
<variable name="g_si_" initial_value="0.0004" units="mS_per_mm2" />
<variable name="E_si" initial_value="70.0" units="mV" />
<!--
Time is imported from the "interface", and membrane potential is
imported from the "membrane" component. These variables are used in the
"secondary_inward_current" parent component, which also acts as an
interface, passing the variables to its encapsulated gate component.
-->
<variable
name="time" public_interface="in"
private_interface="out" units="ms" />
<variable
name="V" public_interface="in"
private_interface="out" units="mV" />
<!-- These variables are imported from encapsulated components. -->
<variable name="d" private_interface="in" units="dimensionless" />
<variable name="f" private_interface="in" units="dimensionless" />
<variable name="d1" private_interface="in" units="dimensionless" />
<rdf:RDF
xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
xmlns:cmeta="http://www.cellml.org/metadata/1.0#">
<rdf:Description rdf:about="#i_si_calculation_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
Calculation of the second inward current.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="i_si_calculation_eq">
<apply id="i_si_calculation"><eq />
<ci> i_si </ci>
<apply><plus />
<apply><times />
<ci> g_si </ci>
<ci> d </ci>
<ci> f </ci>
<apply><minus />
<ci> V </ci>
<ci> E_si </ci>
</apply>
</apply>
<apply><times />
<ci> g_si_ </ci>
<ci> d1 </ci>
<apply><minus />
<ci> V </ci>
<ci> E_si </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<!--
The "secondary_inward_current_d_gate" component is the d gate encapsulated
in the "secondary inward current" component.
-->
<component name="secondary_inward_current_d_gate"
cmeta:id="secondary_inward_current_d_gate">
<rdf:RDF
xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
xmlns:cmeta="http://www.cellml.org/metadata/1.0#">
<rdf:Description rdf:about="#secondary_inward_current_d_gate">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The voltage-dependent activation gate for the secondary inward
current - the d gate.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<!-- This variable is defined here and used in other components. -->
<variable
name="d" initial_value="0.002" public_interface="out"
units="dimensionless" />
<!-- These variables are defined here and only used internally. -->
<variable name="alpha_d" units="per_ms" />
<variable name="beta_d" units="per_ms" />
<!--
These variables are imported from the "interface" and the "membrane" via
the "slow_inward_current" component.
-->
<variable name="V" public_interface="in" units="mV" />
<variable name="time" public_interface="in" units="ms" />
<rdf:RDF
xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
xmlns:cmeta="http://www.cellml.org/metadata/1.0#">
<rdf:Description rdf:about="#alpha_d_calculation_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The opening rate of the d gate.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="alpha_d_calculation_eq">
<apply id="alpha_d_calculation"><eq />
<ci> alpha_d </ci>
<apply><divide />
<apply><plus />
<ci> V </ci>
<cn cellml:units="mV"> 40.0 </cn>
</apply>
<apply><times />
<cn cellml:units="mV"> 500.0 </cn>
<apply><minus />
<cn cellml:units="ms"> 1.0 </cn>
<apply><exp />
<apply><minus />
<apply><divide />
<apply><plus />
<ci> V </ci>
<cn cellml:units="mV"> 40.0 </cn>
</apply>
<cn cellml:units="mV"> 10.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
<rdf:RDF
xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
xmlns:cmeta="http://www.cellml.org/metadata/1.0#">
<rdf:Description rdf:about="#beta_d_calculation_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The closing rate of the d gate.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="beta_d_calculation_eq">
<apply id="beta_d_calculation"><eq />
<ci> beta_d </ci>
<apply><times />
<cn cellml:units="per_ms"> 0.02 </cn>
<apply><exp />
<apply><minus />
<apply><divide />
<apply><plus />
<ci> V </ci>
<cn cellml:units="mV"> 40.0 </cn>
</apply>
<cn cellml:units="mV"> 11.26 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
<rdf:RDF
xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
xmlns:cmeta="http://www.cellml.org/metadata/1.0#">
<rdf:Description rdf:about="#dd_dt_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The kinetics of the d gate.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="dd_dt_eq">
<apply id="dd_dt"><eq />
<apply><diff />
<bvar><ci> time </ci></bvar>
<ci> d </ci>
</apply>
<apply><minus />
<apply><times />
<ci> alpha_d </ci>
<apply><minus />
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> d </ci>
</apply>
</apply>
<apply><times />
<ci> beta_d </ci>
<ci> d </ci>
</apply>
</apply>
</apply>
</math>
</component>
<!--
The "secondary_inward_current_f_gate" component is the f gate encapsulated
in the "secondary inward current" component.
-->
<component name="secondary_inward_current_f_gate"
cmeta:id="secondary_inward_current_f_gate">
<rdf:RDF
xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
xmlns:cmeta="http://www.cellml.org/metadata/1.0#">
<rdf:Description rdf:about="#secondary_inward_current_f_gate">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The voltage-dependent inactivation gate for the secondary inward
current - the f gate.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<!-- This variable is defined here and used in other components. -->
<variable
name="f" public_interface="out"
initial_value="0.794" units="dimensionless" />
<!-- These variables are defined here and only used internally. -->
<variable name="alpha_f" units="per_ms" />
<variable name="beta_f" units="per_ms" />
<!-- These variables are imported from parent and sibling components. -->
<variable name="V" public_interface="in" units="mV" />
<variable name="time" public_interface="in" units="ms" />
<rdf:RDF
xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
xmlns:cmeta="http://www.cellml.org/metadata/1.0#">
<rdf:Description rdf:about="#alpha_f_calculation_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The opening rate of the f gate.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="alpha_f_calculation_eq">
<apply id="alpha_f_calculation"><eq />
<ci> alpha_f </ci>
<apply><times />
<cn cellml:units="per_ms"> 0.000987 </cn>
<apply><exp />
<apply><minus />
<apply><divide />
<apply><plus />
<ci> V </ci>
<cn cellml:units="mV"> 60.0 </cn>
</apply>
<cn cellml:units="mV"> 25.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
<rdf:RDF
xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
xmlns:cmeta="http://www.cellml.org/metadata/1.0#">
<rdf:Description rdf:about="#beta_f_calculation_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The closing rate of the f gate.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="beta_f_calculation_eq">
<apply id="beta_f_calculation"><eq />
<ci> beta_f </ci>
<apply><divide />
<cn cellml:units="per_ms"> 0.02 </cn>
<apply><plus />
<apply><exp />
<apply><minus />
<apply><divide />
<apply><plus />
<ci> V </ci>
<cn cellml:units="mV"> 26.0 </cn>
</apply>
<cn cellml:units="mV"> 11.5 </cn>
</apply>
</apply>
</apply>
<cn cellml:units="dimensionless"> 1.0 </cn>
</apply>
</apply>
</apply>
</math>
<rdf:RDF
xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
xmlns:cmeta="http://www.cellml.org/metadata/1.0#">
<rdf:Description rdf:about="#df_dt_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The kinetics of the f gate.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="df_dt_eq">
<apply id="df_dt"><eq />
<apply><diff />
<bvar><ci> time </ci></bvar>
<ci> f </ci>
</apply>
<apply><minus />
<apply><times />
<ci> alpha_f </ci>
<apply><minus />
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> f </ci>
</apply>
</apply>
<apply><times />
<ci> beta_f </ci>
<ci> f </ci>
</apply>
</apply>
</apply>
</math>
</component>
<!--
The "secondary_inward_current_d1_gate" component is the d1 gate encapsulated
in the "secondary inward current" component.
-->
<component name="secondary_inward_current_d1_gate"
cmeta:id="secondary_inward_current_d1_gate">
<rdf:RDF
xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
xmlns:cmeta="http://www.cellml.org/metadata/1.0#">
<rdf:Description rdf:about="#secondary_inward_current_d1_gate">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The activation variable for the slow component of the secondard
inward current - the d1 gate (corresponds to the d' variable in
the MNT paper.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<!-- This variable is defined here and used in other components. -->
<variable
name="d1" public_interface="out"
units="dimensionless" />
<!-- These variables are imported from other components. -->
<variable name="V" public_interface="in" units="mV" />
<variable name="time" public_interface="in" units="ms" />
<rdf:RDF
xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
xmlns:cmeta="http://www.cellml.org/metadata/1.0#">
<rdf:Description rdf:about="#d1_calculation_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
Calculation of the activation variable d1.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="d1_calculation_eq">
<apply id="d1_calculation"><eq />
<ci> d1 </ci>
<apply><divide />
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply><plus />
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply><exp />
<apply><minus />
<apply><divide />
<apply><plus />
<ci> V </ci>
<cn cellml:units="mV"> 40.0 </cn>
</apply>
<cn cellml:units="mV"> 6.667 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<!--
The pacemaker potassium current describes an outward flux of potassium ions
in terms of a single gate variable, s.
-->
<component name="pacemaker_potassium_current"
cmeta:id="pacemaker_potassium_current">
<rdf:RDF
xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
xmlns:cmeta="http://www.cellml.org/metadata/1.0#">
<rdf:Description rdf:about="#pacemaker_potassium_current">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
A potassium current activated over the "pace-maker" range of
potentials. Provides the pacemaker function of the model.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<!-- These variables are defined here and used in other components. -->
<variable name="i_K2" public_interface="out" units="uA_per_mm2" />
<variable name="I_K2" public_interface="out" units="uA_per_mm2" />
<!-- This variable is defined here and only used internally. -->
<variable name="E_K" initial_value="-110.0" units="mV" />
<!-- These variables are imported from parent and sibling components. -->
<variable
name="time" public_interface="in"
private_interface="out" units="ms" />
<variable
name="V" public_interface="in"
private_interface="out" units="mV" />
<!-- These variables are imported from encapsulated components. -->
<variable name="s" private_interface="in" units="dimensionless" />
<rdf:RDF
xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
xmlns:cmeta="http://www.cellml.org/metadata/1.0#">
<rdf:Description rdf:about="#i_K2_calculation_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
Calculation of the pacemaker current.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="i_K2_calculation_eq">
<apply id="i_K2_calculation"><eq />
<ci> i_K2 </ci>
<apply><times />
<ci> I_K2 </ci>
<ci> s </ci>
</apply>
</apply>
</math>
<rdf:RDF
xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
xmlns:cmeta="http://www.cellml.org/metadata/1.0#">
<rdf:Description rdf:about="#I_K2_max_calculation_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The maximal pacemaker current.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="I_K2_max_calculation_eq">
<apply id="I_K2_calculation"><eq />
<ci> I_K2 </ci>
<apply><times />
<cn cellml:units="uA_per_mm2"> 0.028 </cn>
<apply><divide />
<apply><minus />
<apply><exp />
<apply><divide />
<apply><minus />
<ci> V </ci>
<ci> E_K </ci>
</apply>
<cn cellml:units="mV"> 25.0 </cn>
</apply>
</apply>
<cn cellml:units="dimensionless"> 1.0 </cn>
</apply>
<apply><plus />
<apply><exp />
<apply><divide />
<apply><plus />
<ci> V </ci>
<cn cellml:units="mV"> 60.0 </cn>
</apply>
<cn cellml:units="mV"> 12.5 </cn>
</apply>
</apply>
<apply><exp />
<apply><divide />
<apply><plus />
<ci> V </ci>
<cn cellml:units="mV"> 60.0 </cn>
</apply>
<cn cellml:units="mV"> 25.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<!--
The s gate component is encapsulated within the pacemaker potassium current.
-->
<component name="pacemaker_potassium_current_s_gate"
cmeta:id="pacemaker_potassium_current_s_gate">
<rdf:RDF
xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
xmlns:cmeta="http://www.cellml.org/metadata/1.0#">
<rdf:Description rdf:about="#pacemaker_potassium_current_s_gate">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The voltage-dependent gating variable for the pacemaker current -
the s gate.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<!-- This variable is defined here and used in other components. -->
<variable name="s" initial_value="0.763" public_interface="out" units="dimensionless" />
<!-- These variables are defined here and only used internally. -->
<variable name="alpha_s" units="per_ms" />
<variable name="beta_s" units="per_ms" />
<variable name="E_s" initial_value="-52.0" units="mV" />
<!-- These variables are imported from parent and sibling components. -->
<variable name="V" public_interface="in" units="mV" />
<variable name="time" public_interface="in" units="ms" />
<rdf:RDF
xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
xmlns:cmeta="http://www.cellml.org/metadata/1.0#">
<rdf:Description rdf:about="#alpha_s_calculation_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The opening rate of the s gate.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="alpha_s_calculation_eq">
<apply id="alpha_s_calculation"><eq />
<ci> alpha_s </ci>
<apply><divide />
<apply><times />
<cn cellml:units="per_ms"> 0.001 </cn>
<apply><minus />
<ci> V </ci>
<ci> E_s </ci>
</apply>
</apply>
<apply><minus />
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply><exp />
<apply><minus />
<apply><divide />
<apply><minus />
<ci> V </ci>
<ci> E_s </ci>
</apply>
<cn cellml:units="mV"> 5.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
<rdf:RDF
xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
xmlns:cmeta="http://www.cellml.org/metadata/1.0#">
<rdf:Description rdf:about="#beta_s_calculation_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The closing rate of the s gate.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="beta_s_calculation_eq">
<apply id="beta_s_calculation"><eq />
<ci> beta_s </ci>
<apply><times />
<cn cellml:units="per_ms"> 0.00005 </cn>
<apply><exp />
<apply><minus />
<apply><divide />
<apply><minus />
<ci> V </ci>
<ci> E_s </ci>
</apply>
<cn cellml:units="mV"> 15.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
<rdf:RDF
xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
xmlns:cmeta="http://www.cellml.org/metadata/1.0#">
<rdf:Description rdf:about="#ds_dt_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The kinetics of the s gate.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="ds_dt_eq">
<apply id="ds_dt"><eq />
<apply><diff />
<bvar><ci> time </ci></bvar>
<ci> s </ci>
</apply>
<apply><minus />
<apply><times />
<ci> alpha_s </ci>
<apply><minus />
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> s </ci>
</apply>
</apply>
<apply><times />
<ci> beta_s </ci>
<ci> s </ci>
</apply>
</apply>
</apply>
</math>
</component>
<!--
The equations for the plateau potassium currents (x1 and x2) are based on
experiments performed by Noble and Tsien (1969) which showed that additional
potassium currents were activated in the plateau range of potentials. They
appear to play an essential role in membrane repolarisation.
-->
<component name="plateau_potassium_current1"
cmeta:id="plateau_potassium_current1">
<rdf:RDF
xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
xmlns:cmeta="http://www.cellml.org/metadata/1.0#">
<rdf:Description rdf:about="#plateau_potassium_current1">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The equations for the plateau potassium currents (x1 and x2) are
based on experiments performed by Noble and Tsien (1969) which
showed that additional potassium currents were activated in the
plateau range of potentials. They appear to play an essential role
in membrane repolarisation.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<!-- This variable is defined here and used in other components. -->
<variable name="i_x1" public_interface="out" units="uA_per_mm2" />
<!-- This variable is defined here and only used internally. -->
<variable name="I_x1" units="uA_per_mm2" />
<!-- These variables are imported from parent and sibling components. -->
<variable
name="time" public_interface="in"
private_interface="out" units="ms" />
<variable
name="V" public_interface="in"
private_interface="out" units="mV" />
<!-- This variable is imported from an encapsulated component. -->
<variable name="x1" private_interface="in" units="dimensionless" />
<rdf:RDF
xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
xmlns:cmeta="http://www.cellml.org/metadata/1.0#">
<rdf:Description rdf:about="#i_x1_calculation_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
Calculation of the first plateau potassium current.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="i_x1_calculation_eq">
<apply id="i_x1_calculation"><eq />
<ci> i_x1 </ci>
<apply><times />
<ci> x1 </ci>
<ci> I_x1 </ci>
</apply>
</apply>
</math>
<rdf:RDF
xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
xmlns:cmeta="http://www.cellml.org/metadata/1.0#">
<rdf:Description rdf:about="#I_x1_max_calculation_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
Calculation of the maximal first plateau potassium current.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="I_x1_max_calculation_eq">
<apply id="I_x1_calculation"><eq />
<ci> I_x1 </ci>
<apply><times />
<cn cellml:units="uA_per_mm2"> 0.012 </cn>
<apply><divide />
<apply><minus />
<apply><exp />
<apply><divide />
<apply><plus />
<ci> V </ci>
<cn cellml:units="mV"> 95.0 </cn>
</apply>
<cn cellml:units="mV"> 25.0 </cn>
</apply>
</apply>
<cn cellml:units="dimensionless"> 1.0 </cn>
</apply>
<apply><exp />
<apply><divide />
<apply><plus />
<ci> V </ci>
<cn cellml:units="mV"> 45.0 </cn>
</apply>
<cn cellml:units="mV"> 25.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<!--
The x1 gate component is encapsulated within the plateau potassium current
1.
-->
<component name="plateau_potassium_current1_x1_gate"
cmeta:id="plateau_potassium_current1_x1_gate">
<rdf:RDF
xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
xmlns:cmeta="http://www.cellml.org/metadata/1.0#">
<rdf:Description rdf:about="#plateau_potassium_current1_x1_gate">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The voltage-dependent gating variable for the first plateau
potassium current - the x1 gate.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<!-- This variable is defined here and used in other components. -->
<variable name="x1" initial_value="0.051" public_interface="out" units="dimensionless" />
<!-- These variables are defined here and only used internally. -->
<variable name="alpha_x1" units="per_ms" />
<variable name="beta_x1" units="per_ms" />
<!-- These variables are imported from parent and sibling components. -->
<variable name="V" public_interface="in" units="mV" />
<variable name="time" public_interface="in" units="ms" />
<rdf:RDF
xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
xmlns:cmeta="http://www.cellml.org/metadata/1.0#">
<rdf:Description rdf:about="#alpha_x1_calculation_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The opening rate of the x1 gate.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="alpha_x1_calculation_eq">
<apply id="alpha_x1_calculation"><eq />
<ci> alpha_x1 </ci>
<apply><times />
<cn cellml:units="per_ms"> 5e-4 </cn>
<apply><divide />
<apply><exp />
<apply><divide />
<apply><plus />
<ci> V </ci>
<cn cellml:units="mV"> 50.0 </cn>
</apply>
<cn cellml:units="mV"> 12.1 </cn>
</apply>
</apply>
<apply><plus />
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply><exp />
<apply><divide />
<apply><plus />
<ci> V </ci>
<cn cellml:units="mV"> 50.0 </cn>
</apply>
<cn cellml:units="mV"> 17.5 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
<rdf:RDF
xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
xmlns:cmeta="http://www.cellml.org/metadata/1.0#">
<rdf:Description rdf:about="#beta_x1_calculation_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The closing rate of the x1 gate.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="beta_x1_calculation_eq">
<apply id="beta_x1_calculation"><eq />
<ci> beta_x1 </ci>
<apply><times />
<cn cellml:units="per_ms"> 0.0013 </cn>
<apply><divide />
<apply><exp />
<apply><minus />
<apply><divide />
<apply><plus />
<ci> V </ci>
<cn cellml:units="mV"> 20.0 </cn>
</apply>
<cn cellml:units="mV"> 16.67 </cn>
</apply>
</apply>
</apply>
<apply><plus />
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply><exp />
<apply><minus />
<apply><divide />
<apply><plus />
<ci> V </ci>
<cn cellml:units="mV"> 20.0 </cn>
</apply>
<cn cellml:units="mV"> 20.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
<rdf:RDF
xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
xmlns:cmeta="http://www.cellml.org/metadata/1.0#">
<rdf:Description rdf:about="#dx1_dt_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The kinetics of the x1 gate.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="dx1_dt_eq">
<apply id="dx1_dt"><eq />
<apply><diff />
<bvar><ci> time </ci></bvar>
<ci> x1 </ci>
</apply>
<apply><minus />
<apply><times />
<ci> alpha_x1 </ci>
<apply><minus />
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> x1 </ci>
</apply>
</apply>
<apply><times />
<ci> beta_x1 </ci>
<ci> x1 </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="plateau_potassium_current2"
cmeta:id="plateau_potassium_current2">
<rdf:RDF
xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
xmlns:cmeta="http://www.cellml.org/metadata/1.0#">
<rdf:Description rdf:about="#plateau_potassium_current2">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The second of the plateau potassium currents.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<!-- This variable is defined here and used in other components. -->
<variable name="i_x2" public_interface="out" units="uA_per_mm2" />
<!-- This variable is defined here and only used internally. -->
<variable name="I_x2" units="uA_per_mm2" />
<!-- These variables are imported from parent and sibling components. -->
<variable
name="time" public_interface="in"
private_interface="out" units="ms" />
<variable
name="V" public_interface="in"
private_interface="out" units="mV" />
<!-- This variable is imported from an encapsulated component. -->
<variable name="x2" private_interface="in" units="dimensionless" />
<rdf:RDF
xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
xmlns:cmeta="http://www.cellml.org/metadata/1.0#">
<rdf:Description rdf:about="#i_x2_calculation_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
Calculation of the second plateau potassium current.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="i_x2_calculation_eq">
<apply id="i_x2_calculation"><eq />
<ci> i_x2 </ci>
<apply><times />
<ci> x2 </ci>
<ci> I_x2 </ci>
</apply>
</apply>
</math>
<rdf:RDF
xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
xmlns:cmeta="http://www.cellml.org/metadata/1.0#">
<rdf:Description rdf:about="#I_x2_max_calculation_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The linear maximal second plateau potassium current.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="I_x2_max_calculation_eq">
<apply id="I_x2_calculation"><eq />
<ci> I_x2 </ci>
<apply><plus />
<cn cellml:units="uA_per_mm2"> 0.25 </cn>
<apply><times />
<cn cellml:units="mS_per_mm2"> 0.00385 </cn>
<ci> V </ci>
</apply>
</apply>
</apply>
</math>
</component>
<!--
The x2 gate component is encapsulated within the plateau potassium current
2.
-->
<component name="plateau_potassium_current2_x2_gate"
cmeta:id="plateau_potassium_current2_x2_gate">
<rdf:RDF
xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
xmlns:cmeta="http://www.cellml.org/metadata/1.0#">
<rdf:Description rdf:about="#plateau_potassium_current2_x2_gate">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The gating variable for the second plateau potassium current - the
x2 gate.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<!-- This variable is defined here and used in other components. -->
<variable name="x2" initial_value="0.006" public_interface="out" units="dimensionless" />
<!-- These variables are defined here and only used internally. -->
<variable name="alpha_x2" units="per_ms" />
<variable name="beta_x2" units="per_ms" />
<!-- These variables are imported from parent and sibling components. -->
<variable name="V" public_interface="in" units="mV" />
<variable name="time" public_interface="in" units="ms" />
<rdf:RDF
xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
xmlns:cmeta="http://www.cellml.org/metadata/1.0#">
<rdf:Description rdf:about="#alpha_x2_calculation_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The opening rate for the x2 gate.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="alpha_x2_calculation_eq">
<apply id="alpha_x2_calculation"><eq />
<ci> alpha_x2 </ci>
<apply><times />
<cn cellml:units="per_ms"> 0.000127 </cn>
<apply><divide />
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply><plus />
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply><exp />
<apply><minus />
<apply><divide />
<apply><plus />
<ci> V </ci>
<cn cellml:units="mV"> 19.0 </cn>
</apply>
<cn cellml:units="mV"> 5.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
<rdf:RDF
xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
xmlns:cmeta="http://www.cellml.org/metadata/1.0#">
<rdf:Description rdf:about="#beta_x2_calculation_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The closing rate for the x2 gate.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="beta_x2_calculation_eq">
<apply id="beta_x2_calculation"><eq />
<ci> beta_x2 </ci>
<apply><times />
<cn cellml:units="per_ms"> 0.0003 </cn>
<apply><divide />
<apply><exp />
<apply><minus />
<apply><divide />
<apply><plus />
<ci> V </ci>
<cn cellml:units="mV"> 20.0 </cn>
</apply>
<cn cellml:units="mV"> 16.67 </cn>
</apply>
</apply>
</apply>
<apply><plus />
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply><exp />
<apply><minus />
<apply><divide />
<apply><plus />
<ci> V </ci>
<cn cellml:units="mV"> 20.0 </cn>
</apply>
<cn cellml:units="mV"> 25.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
<rdf:RDF
xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
xmlns:cmeta="http://www.cellml.org/metadata/1.0#">
<rdf:Description rdf:about="#dx2_dt_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The kinetics of the x2 gate.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="dx2_dt_eq">
<apply id="dx2_dt"><eq />
<apply><diff />
<bvar><ci> time </ci></bvar>
<ci> x2 </ci>
</apply>
<apply><minus />
<apply><times />
<ci> alpha_x2 </ci>
<apply><minus />
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> x2 </ci>
</apply>
</apply>
<apply><times />
<ci> beta_x2 </ci>
<ci> x2 </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="transient_chloride_current"
cmeta:id="transient_chloride_current">
<rdf:RDF
xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
xmlns:cmeta="http://www.cellml.org/metadata/1.0#">
<rdf:Description rdf:about="#transient_chloride_current">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The transient chloride current (i_qr) is responsible for the rapid
repolarisation from the peak of the depolarisation spike of the
action potential, to the start of the plateau. The current has 2
gating variables, q and r.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<!-- These variables are defined here and used in other components. -->
<variable name="i_qr" public_interface="out" units="uA_per_mm2" />
<variable
name="E_Cl" public_interface="out"
initial_value="-70.0" units="mV" />
<!-- This variable is defined here and only used internally. -->
<variable name="g_qr" initial_value="0.05" units="mS_per_mm2" />
<!-- These variables are imported from parent and sibling components. -->
<variable
name="time" public_interface="in"
private_interface="out" units="ms" />
<variable
name="V" public_interface="in"
private_interface="out" units="mV" />
<!-- These variables are imported from encapsulated components. -->
<variable name="q" private_interface="in" units="dimensionless" />
<variable name="r" private_interface="in" units="dimensionless" />
<rdf:RDF
xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
xmlns:cmeta="http://www.cellml.org/metadata/1.0#">
<rdf:Description rdf:about="#i_qr_calculation_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
Calculation of the transient chloride current.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="i_qr_calculation_eq">
<apply id="i_qr_calculation"><eq />
<ci> i_qr </ci>
<apply><times />
<ci> g_qr </ci>
<ci> q </ci>
<ci> r </ci>
<apply><minus />
<ci> V </ci>
<ci> E_Cl </ci>
</apply>
</apply>
</apply>
</math>
</component>
<!-- The encapsulated q gate. -->
<component name="transient_chloride_current_q_gate"
cmeta:id="transient_chloride_current_q_gate">
<rdf:RDF
xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
xmlns:cmeta="http://www.cellml.org/metadata/1.0#">
<rdf:Description rdf:about="#transient_chloride_current_q_gate">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The voltage-dependent activation gate for the transient chloride
channel - the q gate.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<!-- This variable is defined here and used in other components. -->
<variable
name="q" initial_value="0.0" public_interface="out"
units="dimensionless" />
<!-- These variables are defined here and only used internally. -->
<variable name="alpha_q" units="per_ms" />
<variable name="beta_q" units="per_ms" />
<!-- These variables are imported from parent and sibling components. -->
<variable name="V" public_interface="in" units="mV" />
<variable name="time" public_interface="in" units="ms" />
<rdf:RDF
xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
xmlns:cmeta="http://www.cellml.org/metadata/1.0#">
<rdf:Description rdf:about="#alpha_q_calculation_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The opening rate for the q gate.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="alpha_q_calculation_eq">
<apply id="alpha_q_calculation"><eq />
<ci> alpha_q </ci>
<apply><times />
<cn cellml:units="per_mV_ms"> 0.008 </cn>
<apply><divide />
<ci> V </ci>
<apply><minus />
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply><exp />
<apply><minus />
<apply><divide />
<ci> V </ci>
<cn cellml:units="mV"> 10.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
<rdf:RDF
xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
xmlns:cmeta="http://www.cellml.org/metadata/1.0#">
<rdf:Description rdf:about="#beta_q_calculation_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The closing rate for the q gate.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="beta_q_calculation_eq">
<apply id="beta_q_calculation"><eq />
<ci> beta_q </ci>
<apply><times />
<cn cellml:units="per_ms"> 0.08 </cn>
<apply><exp />
<apply><minus />
<apply><divide />
<ci> V </ci>
<cn cellml:units="mV"> 11.26 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
<rdf:RDF
xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
xmlns:cmeta="http://www.cellml.org/metadata/1.0#">
<rdf:Description rdf:about="#dq_dt_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The kinetics of the q gate.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="dq_dt_eq">
<apply id="dq_dt"><eq />
<apply><diff />
<bvar><ci> time </ci></bvar>
<ci> q </ci>
</apply>
<apply><minus />
<apply><times />
<ci> alpha_q </ci>
<apply><minus />
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> q </ci>
</apply>
</apply>
<apply><times />
<ci> beta_q </ci>
<ci> q </ci>
</apply>
</apply>
</apply>
</math>
</component>
<!-- The encapsualted r gate. -->
<component name="transient_chloride_current_r_gate"
cmeta:id="transient_chloride_current_r_gate">
<rdf:RDF
xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
xmlns:cmeta="http://www.cellml.org/metadata/1.0#">
<rdf:Description rdf:about="#transient_chloride_current_r_gate">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The voltage-dependent inactivation gate for the transient chloride
current - the r gate.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<!-- This variable is defined here and used in other components. -->
<variable
name="r" initial_value="0.126" public_interface="out"
units="dimensionless" />
<!-- These variables are defined here and only used internally. -->
<variable name="alpha_r" units="per_ms" />
<variable name="beta_r" units="per_ms" />
<!-- These variables are imported from parent and sibling components. -->
<variable name="V" public_interface="in" units="mV" />
<variable name="time" public_interface="in" units="ms" />
<rdf:RDF
xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
xmlns:cmeta="http://www.cellml.org/metadata/1.0#">
<rdf:Description rdf:about="#alpha_r_calculation_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The opening rate for the r gate.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="alpha_r_calculation_eq">
<apply id="alpha_r_calculation"><eq />
<ci> alpha_r </ci>
<apply><times />
<cn cellml:units="per_ms"> 0.00018 </cn>
<apply><exp />
<apply><minus />
<apply><divide />
<apply><plus/>
<ci> V </ci>
<cn cellml:units="mV">80</cn>
</apply>
<cn cellml:units="mV"> 25.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
<rdf:RDF
xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
xmlns:cmeta="http://www.cellml.org/metadata/1.0#">
<rdf:Description rdf:about="#beta_r_calculation_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The closing rate for the r gate.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="beta_r_calculation_eq">
<apply id="beta_r_calculation"><eq />
<ci> beta_r </ci>
<apply><divide />
<cn cellml:units="per_ms"> 0.02 </cn>
<apply><plus />
<apply><exp />
<apply><minus />
<apply><divide />
<apply><plus />
<ci> V </ci>
<cn cellml:units="mV"> 26 </cn>
</apply>
<cn cellml:units="mV"> 11.5 </cn>
</apply>
</apply>
</apply>
<cn cellml:units="dimensionless"> 1.0 </cn>
</apply>
</apply>
</apply>
</math>
<rdf:RDF
xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
xmlns:cmeta="http://www.cellml.org/metadata/1.0#">
<rdf:Description rdf:about="#dr_dt_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The kinetics of the r gate.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="dr_dt_eq">
<apply id="dr_dt"><eq />
<apply><diff />
<bvar><ci> time </ci></bvar>
<ci> r </ci>
</apply>
<apply><minus />
<apply><times />
<ci> alpha_r </ci>
<apply><minus />
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> r </ci>
</apply>
</apply>
<apply><times />
<ci> beta_r </ci>
<ci> r </ci>
</apply>
</apply>
</apply>
</math>
</component>
<!--
The outward time-independent (or background) ionic current is carried
predominately by potassium ions and is represented by i_K1.
-->
<component name="time_independent_outward_current"
cmeta:id="time_independent_outward_current">
<rdf:RDF
xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
xmlns:cmeta="http://www.cellml.org/metadata/1.0#">
<rdf:Description rdf:about="#time_independent_outward_current">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The time-independent (background) current carried by potassium ions.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<!-- This variable is defined here and used in other components. -->
<variable name="i_K1" public_interface="out" units="uA_per_mm2" />
<!-- This variable is defined here and only used internally. -->
<variable name="E_K1" initial_value="-30.0" units="mV" />
<!-- These variables are imported from other components. -->
<variable name="time" public_interface="in" units="ms" />
<variable name="V" public_interface="in" units="mV" />
<variable name="I_K2" public_interface="in" units="uA_per_mm2" />
<rdf:RDF
xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
xmlns:cmeta="http://www.cellml.org/metadata/1.0#">
<rdf:Description rdf:about="#i_K1_calculation_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
Calculation of the time-independent potassium current.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="i_K1_calculation_eq">
<apply id="i_K1_calculation"><eq />
<ci> i_K1 </ci>
<apply><plus />
<apply><divide />
<ci> I_K2 </ci>
<cn cellml:units="dimensionless"> 2.8 </cn>
</apply>
<apply><times />
<cn cellml:units="uA_per_mm2"> 0.002 </cn>
<apply><divide />
<apply><minus />
<ci> V </ci>
<ci> E_K1 </ci>
</apply>
<apply><minus />
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply><exp />
<apply><minus />
<apply><divide />
<apply><minus />
<ci> V </ci>
<ci> E_K1 </ci>
</apply>
<cn cellml:units="mV"> 25.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<!--
The "sodium_background_current" is a time-independent diffusion of Na ions
down their electrochemical gradient, through the cell surface membrane into
the cytosol.
-->
<component name="sodium_background_current"
cmeta:id="sodium_background_current">
<rdf:RDF
xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
xmlns:cmeta="http://www.cellml.org/metadata/1.0#">
<rdf:Description rdf:about="#sodium_background_current">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The sodium background current is a time-independent diffusion of Na
ions down their electrochemical gradient, through the cell surface
membrane into the cytosol.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<!-- This variable is defined here and used in other components. -->
<variable name="i_Na_b" public_interface="out" units="uA_per_mm2" />
<!-- This variable is defined here and only used internally. -->
<variable name="g_Nab" initial_value="0.00105" units="mS_per_mm2" />
<!--
Time and membrane potential are imported from the "interface" and the
"membrane" components. The reversal potential is imported from the
"fast_sodium_current" component.
-->
<variable name="time" public_interface="in" units="ms" />
<variable name="V" public_interface="in" units="mV" />
<variable name="E_Na" public_interface="in" units="mV" />
<rdf:RDF
xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
xmlns:cmeta="http://www.cellml.org/metadata/1.0#">
<rdf:Description rdf:about="#i_Na_b_calculation_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
Calculation of the sodium background current.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="i_Na_b_calculation_eq">
<apply id="i_Na_b_calculation"><eq />
<ci> i_Na_b </ci>
<apply><times />
<ci> g_Nab </ci>
<apply><minus />
<ci> V </ci>
<ci> E_Na </ci>
</apply>
</apply>
</apply>
</math>
</component>
<!--
The "chloride_background_current" contributes to maintaining the plateau and
helps to determine the action potential duration.
-->
<component name="chloride_background_current"
cmeta:id="chloride_background_current">
<rdf:RDF
xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
xmlns:cmeta="http://www.cellml.org/metadata/1.0#">
<rdf:Description rdf:about="#chloride_background_current">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The chloride background current contributes to maintaining the
plateau and helps to determine the action potential duration.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<!-- This variable is defined here and used in other components. -->
<variable name="i_Cl_b" public_interface="out" units="uA_per_mm2" />
<!-- These variables are defined here and only used internally. -->
<variable name="g_Clb" initial_value="0.0001" units="mS_per_mm2" />
<!--
Time and memebrane potential are imported from the "interface" and the
"membrane" components. The reversal potential is imported from the
"transient_chloride_current" component.
-->
<variable name="time" public_interface="in" units="ms" />
<variable name="V" public_interface="in" units="mV" />
<variable name="E_Cl" public_interface="in" units="mV" />
<rdf:RDF
xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
xmlns:cmeta="http://www.cellml.org/metadata/1.0#">
<rdf:Description rdf:about="#i_Cl_b_calculation_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
Calculation of the background chloride current.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="i_Cl_b_calculation_eq">
<apply id="i_Cl_b_calculation"><eq />
<ci> i_Cl_b </ci>
<apply><times />
<ci> g_Clb </ci>
<apply><minus />
<ci> V </ci>
<ci> E_Cl </ci>
</apply>
</apply>
</apply>
</math>
</component>
<!--
The following <group> element specifies how the components representing
activation and inactivation gates are encapsulated inside their parent
currents.
-->
<group>
<relationship_ref relationship="encapsulation" />
<component_ref component="interface">
<component_ref component="membrane"/>
<component_ref component="fast_sodium_current">
<component_ref component="fast_sodium_current_m_gate" />
<component_ref component="fast_sodium_current_h_gate" />
</component_ref>
<component_ref component="secondary_inward_current">
<component_ref component="secondary_inward_current_d_gate" />
<component_ref component="secondary_inward_current_f_gate" />
<component_ref component="secondary_inward_current_d1_gate" />
</component_ref>
<component_ref component="pacemaker_potassium_current">
<component_ref component="pacemaker_potassium_current_s_gate" />
</component_ref>
<component_ref component="transient_chloride_current">
<component_ref component="transient_chloride_current_q_gate" />
<component_ref component="transient_chloride_current_r_gate" />
</component_ref>
<component_ref component="plateau_potassium_current1">
<component_ref component="plateau_potassium_current1_x1_gate" />
</component_ref>
<component_ref component="plateau_potassium_current2">
<component_ref component="plateau_potassium_current2_x2_gate" />
</component_ref>
<component_ref component="time_independent_outward_current" />
<component_ref component="sodium_background_current" />
<component_ref component="chloride_background_current" />
</component_ref>
</group>
<!--
"time" is passed from the "interface" component into the
"membrane" and current components.
-->
<connection>
<map_components
component_1="membrane" component_2="interface" />
<map_variables variable_1="time" variable_2="time" />
<map_variables variable_1="I_stim" variable_2="I_stim" />
</connection>
<connection>
<map_components
component_1="fast_sodium_current" component_2="interface" />
<map_variables variable_1="time" variable_2="time" />
</connection>
<connection>
<map_components
component_1="secondary_inward_current" component_2="interface" />
<map_variables variable_1="time" variable_2="time" />
</connection>
<connection>
<map_components
component_1="pacemaker_potassium_current" component_2="interface" />
<map_variables variable_1="time" variable_2="time" />
</connection>
<connection>
<map_components
component_1="plateau_potassium_current1" component_2="interface" />
<map_variables variable_1="time" variable_2="time" />
</connection>
<connection>
<map_components
component_1="plateau_potassium_current2" component_2="interface" />
<map_variables variable_1="time" variable_2="time" />
</connection>
<connection>
<map_components
component_1="transient_chloride_current" component_2="interface" />
<map_variables variable_1="time" variable_2="time" />
</connection>
<connection>
<map_components
component_1="time_independent_outward_current" component_2="interface" />
<map_variables variable_1="time" variable_2="time" />
</connection>
<connection>
<map_components
component_1="sodium_background_current" component_2="interface" />
<map_variables variable_1="time" variable_2="time" />
</connection>
<connection>
<map_components
component_1="chloride_background_current" component_2="interface" />
<map_variables variable_1="time" variable_2="time" />
</connection>
<!--
Several variables are passed between the "membrane" and its sub-components.
-->
<connection>
<map_components
component_1="membrane" component_2="fast_sodium_current" />
<map_variables variable_1="V" variable_2="V" />
<map_variables variable_1="i_Na" variable_2="i_Na" />
</connection>
<connection>
<map_components
component_1="secondary_inward_current" component_2="membrane" />
<map_variables variable_1="V" variable_2="V" />
<map_variables variable_1="i_si" variable_2="i_si" />
</connection>
<connection>
<map_components
component_1="pacemaker_potassium_current" component_2="membrane" />
<map_variables variable_1="V" variable_2="V" />
<map_variables variable_1="i_K2" variable_2="i_K2" />
</connection>
<connection>
<map_components
component_1="plateau_potassium_current1" component_2="membrane" />
<map_variables variable_1="V" variable_2="V" />
<map_variables variable_1="i_x1" variable_2="i_x1" />
</connection>
<connection>
<map_components
component_1="plateau_potassium_current2" component_2="membrane" />
<map_variables variable_1="V" variable_2="V" />
<map_variables variable_1="i_x2" variable_2="i_x2" />
</connection>
<connection>
<map_components
component_1="transient_chloride_current" component_2="membrane" />
<map_variables variable_1="V" variable_2="V" />
<map_variables variable_1="i_qr" variable_2="i_qr" />
</connection>
<connection>
<map_components
component_1="time_independent_outward_current" component_2="membrane" />
<map_variables variable_1="V" variable_2="V" />
<map_variables variable_1="i_K1" variable_2="i_K1" />
</connection>
<connection>
<map_components
component_1="sodium_background_current" component_2="membrane" />
<map_variables variable_1="V" variable_2="V" />
<map_variables variable_1="i_Na_b" variable_2="i_Na_b" />
</connection>
<connection>
<map_components
component_1="chloride_background_current" component_2="membrane" />
<map_variables variable_1="V" variable_2="V" />
<map_variables variable_1="i_Cl_b" variable_2="i_Cl_b" />
</connection>
<!-- A few variables are passed between the other components. -->
<connection>
<map_components
component_1="sodium_background_current" component_2="fast_sodium_current" />
<map_variables variable_1="E_Na" variable_2="E_Na" />
</connection>
<connection>
<map_components
component_1="time_independent_outward_current" component_2="pacemaker_potassium_current" />
<map_variables variable_1="I_K2" variable_2="I_K2" />
</connection>
<connection>
<map_components
component_1="transient_chloride_current" component_2="chloride_background_current" />
<map_variables variable_1="E_Cl" variable_2="E_Cl" />
</connection>
<!--
Several variables are passed between parent components and their
encapsulated gates.
-->
<connection>
<map_components
component_1="fast_sodium_current" component_2="fast_sodium_current_m_gate" />
<map_variables variable_1="m" variable_2="m" />
<map_variables variable_1="time" variable_2="time" />
<map_variables variable_1="V" variable_2="V" />
</connection>
<connection>
<map_components
component_1="fast_sodium_current" component_2="fast_sodium_current_h_gate" />
<map_variables variable_1="h" variable_2="h" />
<map_variables variable_1="time" variable_2="time" />
<map_variables variable_1="V" variable_2="V" />
</connection>
<connection>
<map_components
component_1="secondary_inward_current" component_2="secondary_inward_current_d_gate" />
<map_variables variable_1="d" variable_2="d" />
<map_variables variable_1="time" variable_2="time" />
<map_variables variable_1="V" variable_2="V" />
</connection>
<connection>
<map_components
component_1="secondary_inward_current" component_2="secondary_inward_current_f_gate" />
<map_variables variable_1="f" variable_2="f" />
<map_variables variable_1="time" variable_2="time" />
<map_variables variable_1="V" variable_2="V" />
</connection>
<connection>
<map_components
component_1="secondary_inward_current" component_2="secondary_inward_current_d1_gate" />
<map_variables variable_1="d1" variable_2="d1" />
<map_variables variable_1="time" variable_2="time" />
<map_variables variable_1="V" variable_2="V" />
</connection>
<connection>
<map_components
component_1="pacemaker_potassium_current" component_2="pacemaker_potassium_current_s_gate" />
<map_variables variable_1="s" variable_2="s" />
<map_variables variable_1="time" variable_2="time" />
<map_variables variable_1="V" variable_2="V" />
</connection>
<connection>
<map_components
component_1="transient_chloride_current" component_2="transient_chloride_current_q_gate" />
<map_variables variable_1="q" variable_2="q" />
<map_variables variable_1="time" variable_2="time" />
<map_variables variable_1="V" variable_2="V" />
</connection>
<connection>
<map_components
component_1="transient_chloride_current" component_2="transient_chloride_current_r_gate" />
<map_variables variable_1="r" variable_2="r" />
<map_variables variable_1="time" variable_2="time" />
<map_variables variable_1="V" variable_2="V" />
</connection>
<connection>
<map_components
component_1="plateau_potassium_current1" component_2="plateau_potassium_current1_x1_gate" />
<map_variables variable_1="x1" variable_2="x1" />
<map_variables variable_1="time" variable_2="time" />
<map_variables variable_1="V" variable_2="V" />
</connection>
<connection>
<map_components
component_1="plateau_potassium_current2" component_2="plateau_potassium_current2_x2_gate" />
<map_variables variable_1="x2" variable_2="x2" />
<map_variables variable_1="time" variable_2="time" />
<map_variables variable_1="V" variable_2="V" />
</connection>
</model>
