- Author:
- David Nickerson <david.nickerson@gmail.com>
- Date:
- 2021-09-16 00:41:19+12:00
- Desc:
- Updating Noble 1962 model:
* Exposing the membrane potential to the top-level model;
* adding SED-ML for the paced and pacemaker variants of the model.
Using OpenCOR Snapshot release 2021-09-14.
- Permanent Source URI:
- https://models.fieldml.org/workspace/a1/rawfile/f954e59183314cd37f86c8832dc81317d01c8ec5/models/1977_beeler/model.xml
<?xml version="1.0" encoding="iso-8859-1"?>
<!-- FILE : beeler_reuter_mammalian_ventricle_1977.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 16/01/2002 CellML Metadata 1.0 Specification.
DESCRIPTION : This file contains a CellML description of the mammalian
ventricular action potential, based on the Beeler-Reuter model, 1977.
CHANGES:
19/10/2001 - CML - Removed document type definition as this is declared as
optional according to the WC3 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.
07/12/2001 - CML - Changed some equations after using the MathML validator.
21/01/2002 - AAC - Updated metadata to conform to the 16/01/02 CellML Metadata
1.0 Specification.
28/02/2002 - CML - Corrected the membrane voltage differential equation.
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="beeler_reuter_model_1977"
cmeta:id="beeler_reuter_mammalian_ventricle_1977"
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#">
<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>2001-09-10</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>
Adding an addition current to the interface which can be used to add new currents to the membrane potential equation. Also exposing the INa variable so that the addition current can be used to cancel out the default INa with either the EJ or DR variants of INa.
</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>2009-06-23</dcterms:W3CDTF>
</dcterms:modified>
</cmeta:modification>
<cmeta:modification rdf:parseType="Resource">
<rdf:value>
Modified the units and corrected mathematics. Also added a stimulus
current to allow for pacing.
</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>2003-07-22</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:value>
Corrected the membrane voltage differential equation.
</rdf:value>
<cmeta:modifier>
<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>
<dcterms:W3CDTF>2002-02-28</dcterms:W3CDTF>
</dcterms:modified>
</cmeta:modification>
<cmeta:modification>
<rdf:value>
Updated metadata to conform to the 16/01/2002 CellML Metadata 1.0
Specification.
</rdf:value>
<cmeta:modifier>
<vCard:N>
<vCard:Family>Cuellar</vCard:Family>
<vCard:Given>Autumn</vCard:Given>
<vCard:Other>A.</vCard:Other>
</vCard:N>
</cmeta:modifier>
<dcterms:modified>
<dcterms:W3CDTF>2002-01-21</dcterms:W3CDTF>
</dcterms:modified>
</cmeta:modification>
<cmeta:modification>
<rdf:value>
Changed some equations after using the MathML validator.
</rdf:value>
<cmeta:modifier>
<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>
<dcterms:W3CDTF>2001-12-07</dcterms:W3CDTF>
</dcterms:modified>
</cmeta:modification>
<cmeta:modification>
<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>
<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>
<dcterms:W3CDTF>2001-10-24</dcterms:W3CDTF>
</dcterms:modified>
</cmeta:modification>
<cmeta:modification>
<rdf:value>
Removed document type definition as this is declared as optional
according to the WC3 recommendation.
</rdf:value>
<cmeta:modifier>
<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>
<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 "beeler_reuter_mammalian_ventricle_1977", which is
declared on the <model> element.
-->
<rdf:Description rdf:about="#beeler_reuter_mammalian_ventricle_1977">
<!-- A human readable name for the model. -->
<dc:title>
The Beeler-Reuter Model of Membrane Action Potentials of Mammalian
Ventricular Myocytes, 1977
</dc:title>
<!-- A comment regarding the model. -->
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
This is the CellML description of Beeler and Reuter's mathematical
model of membrane action potentials of mammalian ventricular
myocardial fibres. It describes four ionic currents in terms of
Hodkin-Huxley type equations.
</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 all mammals. -->
<cmeta:species>Mammalia</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>874889</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>Beeler</vCard:Family>
<vCard:Given>G</vCard:Given>
<vCard:Other>W</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>Reuter</vCard:Family>
<vCard:Given>H</vCard:Given>
</vCard:N>
</bqs:Person>
</rdf:li>
</rdf:Seq>
</dc:creator>
<dc:title>
Reconstruction of the action potential of ventricular myocardial
fibres
</dc:title>
<dcterms:issued rdf:parseType="Resource">
<dcterms:W3CDTF>1977</dcterms:W3CDTF>
</dcterms:issued>
<bqs:Journal rdf:parseType="Resource">
<dc:title>Journal of Physiology</dc:title>
</bqs:Journal>
<bqs:volume>268</bqs:volume>
<bqs:first_page>177</bqs:first_page>
<bqs:last_page>210</bqs:last_page>
</bqs:JournalArticle>
</bqs:reference>
</rdf:Description>
</rdf:RDF>
<!--
Below, we define 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>
<units name="per_concentration_units">
<unit units="concentration_units" exponent="-1" />
</units>
<units name="conversion_units">
<unit units="uA_per_mm2" exponent="-1"/>
<unit units="concentration_units"/>
<unit units="per_ms" exponent="-1"/>
</units>
<!--
The "interface" component is used to declare variables that are used by
all or most of the other components, in this case just "time".
-->
<component name="interface" cmeta:id="interface">
<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="#interface">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The interface which encapsulates the model.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<variable name="time" public_interface="in" private_interface="out" units="ms" />
<variable name="Istim" public_interface="in" private_interface="out" units="uA_per_mm2"/>
<variable name="Iadd" public_interface="in" private_interface="out" units="uA_per_mm2"/>
<variable name="INa" public_interface="out" private_interface="in" units="uA_per_mm2"/>
<variable name="V" public_interface="out" private_interface="in" units="mV"/>
</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>
This component is the `root' node of our model.
It defines the action potential variable `V'.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<!-- These variables are defined here and used in other components. -->
<variable
name="V" public_interface="out"
initial_value="-84.624" units="mV" cmeta:id="Vm"/>
<!-- This variable is defined here and only used internally. -->
<variable name="C" initial_value="0.01" 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_s" public_interface="in" units="uA_per_mm2" />
<variable name="i_x1" public_interface="in" units="uA_per_mm2" />
<variable name="i_K1" public_interface="in" units="uA_per_mm2" />
<variable name="Istim" public_interface="in" units="uA_per_mm2"/>
<variable name="Iadd" 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 ODE governing the membrane potential -- given by the summation
of the ionic currents and an applied stimulus.
</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>Istim</ci>
<apply><plus />
<ci> i_Na </ci>
<ci> i_s </ci>
<ci> i_x1 </ci>
<ci> i_K1 </ci>
<ci>Iadd</ci>
</apply>
</apply>
<ci>C</ci>
</apply>
</apply>
</math>
</component>
<!--
The "sodium_current" component contains the differential equations
governing the influx of sodium ions through the cell surface membrane into
the cell. This sodium current is primarily responsible for the rapid
upstroke of the action potential during membrane depolarisation.
Note that no initial values are needed on many variables as they are
all directly dependent on the membrane voltage.
-->
<component name="sodium_current" cmeta:id="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="#sodium_current">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The "sodium_current" component contains the differential equations
governing the influx of sodium ions through the cell surface
membrane into the cell. This sodium current is primarily
responsible for the rapid upstroke of the action potential during
membrane depolarisation. Note that no initial values are needed on
many variables as they are all directly dependent on the membrane
voltage.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<!-- This variable is defined here and used in other components. -->
<variable cmeta:id="INa" name="i_Na" public_interface="out" units="uA_per_mm2" />
<!-- These variables are defined here and only used internally. -->
<variable name="g_Na" initial_value="4.0e-2" units="mS_per_mm2" />
<variable name="E_Na" initial_value="50.0" units="mV" />
<variable name="g_Nac" initial_value="3.0e-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" />
<variable name="j" 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 sodium current in terms of the conductance,
membrane potential, and gating variables.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="i_Na_calculation_eq">
<!--
The following equation calculates the sodium current in terms
of the conductance, the membrane voltage, and the gate variables.
-->
<apply id="i_Na_calculation"><eq />
<ci> i_Na </ci>
<apply><times />
<apply><plus />
<apply><times />
<ci> g_Na </ci>
<apply><power />
<ci> m </ci>
<cn cellml:units="dimensionless"> 3.0 </cn>
</apply>
<ci> h </ci>
<ci> j </ci>
</apply>
<ci> g_Nac </ci>
</apply>
<apply><minus />
<ci> V </ci>
<ci> E_Na </ci>
</apply>
</apply>
</apply>
</math>
</component>
<!--
The "sodium_current_m_gate" is the m gate encapsulated inside the sodium
current
-->
<component name="sodium_current_m_gate" cmeta:id="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="#sodium_current_m_gate">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The definition of the voltage-dependent activation gating
kinetics for the sodium ion 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" public_interface="out"
initial_value="0.011" 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 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_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">
<!--
The rate constants on the m and h gates are functions
of membrane voltage.
-->
<apply id="alpha_m_calculation"><eq />
<ci> alpha_m </ci>
<apply><divide />
<apply><times />
<cn cellml:units="per_mV_ms"> -1 </cn>
<apply><plus />
<ci> V </ci>
<cn cellml:units="mV"> 47.0 </cn>
</apply>
</apply>
<apply><minus />
<apply><exp />
<apply><times />
<cn cellml:units="per_mV"> -0.1 </cn>
<apply><plus />
<ci> V </ci>
<cn cellml:units="mV"> 47.0 </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="#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><times />
<cn cellml:units="per_mV"> -0.056 </cn>
<apply><plus />
<ci> V </ci>
<cn cellml:units="mV"> 72.0 </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="#dm_dt_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The actual kinetic equation for 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 "sodium_current_h_gate" component is the h gate encapsulated in
the sodium current.
-->
<component name="sodium_current_h_gate" cmeta:id="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="#sodium_current_h_gate">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The voltage-dependent inactivation gate for the 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" public_interface="out"
initial_value="0.988" 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 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_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"> 0.126 </cn>
<apply><exp />
<apply><times />
<cn cellml:units="per_mV"> -0.25 </cn>
<apply><plus />
<ci> V </ci>
<cn cellml:units="mV"> 77.0 </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_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"> 1.7 </cn>
<apply><plus />
<apply><exp />
<apply><times />
<cn cellml:units="per_mV"> -0.082 </cn>
<apply><plus />
<ci> V </ci>
<cn cellml:units="mV"> 22.5 </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="#dh_dt_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The gating 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>
<!--
The "sodium_current_j_gate" component is the j gate encapsulated in
the sodium current.
-->
<component name="sodium_current_j_gate" cmeta:id="sodium_current_j_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="#sodium_current_j_gate">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The voltage dependent slow inactivation sodium channel gate - the j
gate.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<!-- This variable is defined here and used in other components. -->
<variable
name="j" public_interface="out"
initial_value="0.975" units="dimensionless" />
<!-- These variables are defined here and only used internally. -->
<variable name="alpha_j" units="per_ms" />
<variable name="beta_j" 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_j_calculation_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The opening rate for the j gate.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="alpha_j_calculation_eq">
<apply id="alpha_j_calculation"><eq />
<ci> alpha_j </ci>
<apply><divide />
<apply><times />
<cn cellml:units="per_ms"> 0.055 </cn>
<apply><exp />
<apply><times />
<cn cellml:units="per_mV"> -0.25 </cn>
<apply><plus />
<ci> V </ci>
<cn cellml:units="mV"> 78.0 </cn>
</apply>
</apply>
</apply>
</apply>
<apply><plus />
<apply><exp />
<apply><times />
<cn cellml:units="per_mV"> -0.2 </cn>
<apply><plus />
<ci> V </ci>
<cn cellml:units="mV"> 78.0 </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="#beta_j_calculation_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The closing rate for the j gate.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="beta_j_calculation_eq">
<apply id="beta_j_calculation"><eq />
<ci> beta_j </ci>
<apply><divide />
<cn cellml:units="per_ms"> 0.3 </cn>
<apply><plus />
<apply><exp />
<apply><times />
<cn cellml:units="per_mV"> -0.1 </cn>
<apply><plus />
<ci> V </ci>
<cn cellml:units="mV"> 32.0 </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="#dj_dt_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The kinetics of the j gate.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="dj_dt_eq">
<apply id="dj_dt"><eq />
<apply><diff />
<bvar><ci> time </ci></bvar>
<ci> j </ci>
</apply>
<apply><minus />
<apply><times />
<ci> alpha_j </ci>
<apply><minus />
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> j </ci>
</apply>
</apply>
<apply><times />
<ci> beta_j </ci>
<ci> j </ci>
</apply>
</apply>
</apply>
</math>
</component>
<!-- The "slow_inward_current " component contains the differential
equations governing the transient inward ionic current. This current is
predominately carried by calcium ions and it is largely responsible for
maintaining the plateau of the action potential. -->
<component name="slow_inward_current" cmeta:id="slow_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="#slow_inward_current">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The "slow_inward_current" component contains the differential
equations governing the transient inward ionic current. This current
is predominately carried by calcium ions and it is largely
responsible for maintaining the plateau of the action potential.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<!-- This variable is defined here and used in other components. -->
<variable name="i_s" public_interface="out" units="uA_per_mm2" />
<!-- These variables are defined here and only used internally. -->
<variable name="g_s" initial_value="9.0e-4" units="mS_per_mm2" />
<variable name="E_s" units="mV" />
<variable name="Cai" initial_value="1.0e-4" units="concentration_units" />
<!-- 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="d" private_interface="in" units="dimensionless" />
<variable name="f" 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="#E_s_calculation_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The reversal potential for the slow inward current.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="E_s_calculation_eq">
<!--
The following equation determines the reversal potential of the
slow inward current.
-->
<apply id="E_s_calculation"><eq />
<ci> E_s </ci>
<apply><minus />
<cn cellml:units="mV"> -82.3 </cn>
<apply><times />
<cn cellml:units="mV"> 13.0287 </cn>
<apply><ln />
<apply><times/>
<ci> Cai </ci>
<cn cellml:units="per_concentration_units">0.001</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="#i_s_calculation_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
Calculation of the slow inward current.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="i_s_calculation_eq">
<!--
The following equation calculates the slow inward current in terms of
the conductance, the membrane voltage and the gate variables.
-->
<apply id="i_s_calculation"><eq />
<ci> i_s </ci>
<apply><times />
<ci> g_s </ci>
<ci> d </ci>
<ci> f </ci>
<apply><minus />
<ci> V </ci>
<ci> E_s </ci>
</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="#dCai_dt_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The change in calcium ion concentration.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="dCai_dt_eq">
<!-- Change in {Ca}i (intracellular calcium concentration) is given in
terms of the slow inward current as: -->
<apply id="dCai_dt"><eq />
<apply><diff />
<bvar><ci> time </ci></bvar>
<ci> Cai </ci>
</apply>
<apply><plus />
<apply><times />
<cn cellml:units="conversion_units"> -0.01 </cn>
<ci> i_s </ci>
</apply>
<apply><times />
<cn cellml:units="per_ms"> 0.07 </cn>
<apply><minus />
<cn cellml:units="concentration_units"> 0.0001 </cn>
<ci> Cai </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<!--
The "slow_inward_current_d_gate" component is the d gate encapsulated in
the slow inward current.
-->
<component name="slow_inward_current_d_gate"
cmeta:id="slow_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="#slow_inward_current_d_gate">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The voltage-dependent activation gate for the slow 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" public_interface="out"
initial_value="0.003" 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 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_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">
<!--
The rate constants on the d gate are functions of membrane voltage.
-->
<apply id="alpha_d_calculation"><eq />
<ci> alpha_d </ci>
<apply><divide />
<apply><times />
<cn cellml:units="per_ms"> 0.095 </cn>
<apply><exp />
<apply><minus />
<apply><divide />
<apply><minus />
<ci> V </ci>
<cn cellml:units="mV"> 5.0 </cn>
</apply>
<cn cellml:units="mV"> 100.0 </cn>
</apply>
</apply>
</apply>
</apply>
<apply><plus />
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply><exp />
<apply><minus />
<apply><divide />
<apply><minus />
<ci> V </ci>
<cn cellml:units="mV"> 5.0 </cn>
</apply>
<cn cellml:units="mV"> 13.89 </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_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><divide />
<apply><times />
<cn cellml:units="per_ms"> 0.07 </cn>
<apply><exp />
<apply><minus />
<apply><divide />
<apply><plus />
<ci> V </ci>
<cn cellml:units="mV"> 44.0 </cn>
</apply>
<cn cellml:units="mV"> 59.0 </cn>
</apply>
</apply>
</apply>
</apply>
<apply><plus />
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply><exp />
<apply><divide />
<apply><plus />
<ci> V </ci>
<cn cellml:units="mV"> 44.0 </cn>
</apply>
<cn cellml:units="mV"> 20.0 </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="#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 "slow_inward_current_f_gate" component is the f gate encapsulated in
the slow inward current.
-->
<component name="slow_inward_current_f_gate"
cmeta:id="slow_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="#slow_inward_current_f_gate">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The voltage-dependent inactivation gate for the slow 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="0.994" 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">
<!--
The rate constants on the f gate are functions of membrane voltage.
-->
<apply id="alpha_f_calculation"><eq />
<ci> alpha_f </ci>
<apply><divide />
<apply><times />
<cn cellml:units="per_ms"> 0.012 </cn>
<apply><exp />
<apply><minus />
<apply><divide />
<apply><plus />
<ci> V </ci>
<cn cellml:units="mV"> 28.0 </cn>
</apply>
<cn cellml:units="mV"> 125.0 </cn>
</apply>
</apply>
</apply>
</apply>
<apply><plus />
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply><exp />
<apply><divide />
<apply><plus />
<ci> V </ci>
<cn cellml:units="mV"> 28.0 </cn>
</apply>
<cn cellml:units="mV"> 6.67 </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 />
<apply><times />
<cn cellml:units="per_ms"> 0.0065 </cn>
<apply><exp />
<apply><minus />
<apply><divide />
<apply><plus />
<ci> V </ci>
<cn cellml:units="mV"> 30.0 </cn>
</apply>
<cn cellml:units="mV"> 50.0 </cn>
</apply>
</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"> 30.0 </cn>
</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="#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 "time_dependent_outward_current" component contains the
differential equations governing the voltage- and time-dependent outward
current. This current is predominately carried by potassium ions and it
is involved in the plateau of the action potential and in the
re-polarisation phase.
-->
<component name="time_dependent_outward_current"
cmeta:id="time_dependent_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_dependent_outward_current">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The "time_dependent_outward_current" component contains the
differential equations governing the voltage- and time-dependent
outward current. This current is predominately carried by potassium
ions and it is involved in the plateau of the action potential and
in the re-polarisation phase.
</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" />
<!-- 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 encapsulated components. -->
<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 time-dependent outward current.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="i_x1_calculation_eq">
<!--
The following equation calculates the time-dependent outward current
in terms of the membrane voltage.
-->
<apply id="i_x1_calculation"><eq />
<ci> i_x1 </ci>
<apply><times />
<ci> x1 </ci>
<cn cellml:units="dimensionless"> 0.008 </cn>
<apply><divide />
<apply><minus />
<apply><exp />
<apply><times />
<cn cellml:units="per_mV"> 0.04 </cn>
<apply><plus />
<ci> V </ci>
<cn cellml:units="mV"> 77.0 </cn>
</apply>
</apply>
</apply>
<cn cellml:units="dimensionless"> 1.0 </cn>
</apply>
<apply><exp />
<apply><times />
<cn cellml:units="per_mV"> 0.04 </cn>
<apply><plus />
<ci> V </ci>
<cn cellml:units="mV"> 35.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="time_dependent_outward_current_x1_gate"
cmeta:id="time_dependent_outward_current_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="#time_dependent_outward_current_x1_gate">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The voltage-dependent gating variable for the time-dependent outward
current - the x1 gate.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<variable name="x1" initial_value="0" public_interface="out" units="dimensionless" />
<variable name="alpha_x1" units="per_ms" />
<variable name="beta_x1" units="per_ms" />
<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"> 0.0005 </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"> 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="#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="per_mV"> 1.0 </cn>
<ci> x1 </ci>
</apply>
</apply>
<apply><times />
<ci> beta_x1 </ci>
<ci> x1 </ci>
</apply>
</apply>
</apply>
</math>
</component>
<!--
The "time_independent_outward_current" component contains the
equations governing the voltage-dependent, time-independent
outward current. This current is carried by potassium ions and it is
involved in the plateau of the action potential and in the
re-polarisation phase. Because the current is time-independent, it
can also be described as a background current.
-->
<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_outward_current" component contains the
equations governing the voltage-dependent, time-independent outward
current. This current is carried by potassium ions and it is
involved in the plateau of the action potential and in the
re-polarisation phase. Because the current is time-independent, it
can also be described as a background current.
</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" />
<!-- These variables are imported from other components. -->
<variable name="time" public_interface="in" units="ms" />
<variable name="V" public_interface="in" units="mV" />
<!--
The following equation calculates the time-independent outward
potassium current in terms of membrane voltage.
-->
<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 outward 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><times />
<cn cellml:units="dimensionless"> 0.0035 </cn>
<apply><plus />
<apply><times />
<cn cellml:units="per_ms"> 4.0 </cn>
<apply><divide />
<apply><minus />
<apply><exp />
<apply><times />
<cn cellml:units="per_mV"> 0.04 </cn>
<apply><plus />
<ci> V </ci>
<cn cellml:units="mV"> 85.0 </cn>
</apply>
</apply>
</apply>
<cn cellml:units="dimensionless"> 1.0 </cn>
</apply>
<apply><plus />
<apply><exp />
<apply><times />
<cn cellml:units="per_mV"> 0.08 </cn>
<apply><plus />
<ci> V </ci>
<cn cellml:units="mV"> 53 </cn>
</apply>
</apply>
</apply>
<apply><exp />
<apply><times />
<cn cellml:units="per_mV"> 0.04 </cn>
<apply><plus />
<ci> V </ci>
<cn cellml:units="mV"> 53.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply><times />
<cn cellml:units="per_ms"> 0.2 </cn>
<apply><divide />
<apply><plus />
<ci> V </ci>
<cn cellml:units="mV"> 23.0 </cn>
</apply>
<apply><minus />
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply><exp />
<apply><times />
<cn cellml:units="per_mV"> -0.04 </cn>
<apply><plus />
<ci> V </ci>
<cn cellml:units="mV"> 23.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<!--
The following <group> element specifies how the components representing
activation and inactivation coefficients are encapsulated inside the
sodium and potassium channel components.
-->
<group>
<relationship_ref relationship="encapsulation" />
<component_ref component="interface">
<component_ref component="membrane"/>
<component_ref component="sodium_current">
<component_ref component="sodium_current_m_gate" />
<component_ref component="sodium_current_h_gate" />
<component_ref component="sodium_current_j_gate" />
</component_ref>
<component_ref component="slow_inward_current">
<component_ref component="slow_inward_current_d_gate" />
<component_ref component="slow_inward_current_f_gate" />
</component_ref>
<component_ref component="time_dependent_outward_current">
<component_ref component="time_dependent_outward_current_x1_gate" />
</component_ref>
<component_ref component="time_independent_outward_current"/>
</component_ref>
</group>
<!--
The connections hold the actual mappings between variables declared in
different components. When more than one variable is mapped between two
components, all variable mappings must be listed in the same connection
element (there can only be one connection between two components). The
variables are assumed to be listed in the same order within the two
<component_ref> elements. The modeler should NOT rely on matching the
names of the variables in the two components.
-->
<!--
"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="Istim" variable_2="Istim" />
<map_variables variable_1="Iadd" variable_2="Iadd"/>
<map_variables variable_1="V" variable_2="V"/>
</connection>
<connection>
<map_components
component_1="sodium_current" component_2="interface" />
<map_variables variable_1="time" variable_2="time" />
<map_variables variable_1="i_Na" variable_2="INa"/>
</connection>
<connection>
<map_components
component_1="slow_inward_current" component_2="interface" />
<map_variables variable_1="time" variable_2="time" />
</connection>
<connection>
<map_components
component_1="time_dependent_outward_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>
<!--
A number of variables are passed between the "membrane" and its four
sub-components, the "sodium_current", "slow_inward_current",
"time_dependent_outward_current" and the "time_independent_outward_current".
-->
<connection>
<map_components
component_1="membrane" component_2="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="membrane" component_2="slow_inward_current" />
<map_variables variable_1="V" variable_2="V" />
<map_variables variable_1="i_s" variable_2="i_s" />
</connection>
<connection>
<map_components
component_1="membrane" component_2="time_dependent_outward_current" />
<map_variables variable_1="V" variable_2="V" />
<map_variables variable_1="i_x1" variable_2="i_x1" />
</connection>
<connection>
<map_components
component_1="membrane" component_2="time_independent_outward_current" />
<map_variables variable_1="V" variable_2="V" />
<map_variables variable_1="i_K1" variable_2="i_K1" />
</connection>
<!--
Various gating variables are passed between the "sodium_current" and
"slow_inward_current" components and the encapsulated "beeler_reuter_gate"
components.
-->
<connection>
<map_components
component_1="sodium_current" component_2="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="sodium_current" component_2="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="sodium_current" component_2="sodium_current_j_gate" />
<map_variables variable_1="j" variable_2="j" />
<map_variables variable_1="time" variable_2="time" />
<map_variables variable_1="V" variable_2="V" />
</connection>
<connection>
<map_components
component_1="time_dependent_outward_current" component_2="time_dependent_outward_current_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="slow_inward_current" component_2="slow_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="slow_inward_current" component_2="slow_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>
</model>
