- Author:
- David Nickerson <david.nickerson@gmail.com>
- Date:
- 2021-09-16 01:20:40+12:00
- Desc:
- Upadte jupyter notebook with MNT and DFN comparison figure
- Permanent Source URI:
- https://models.fieldml.org/workspace/a1/rawfile/ae7a0b93f4ee5fda3d81ba97eb459f958b2819c9/models/1985_difrancesco/1985_difrancesco_noble.xml
<?xml version="1.0" encoding="iso-8859-1"?>
<!-- FILE : DFN_purkinje_fibre_model_1985.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 16th January 2002.
DESCRIPTION : This file contains a CellML description of cardiac action
potentials in purkinje fibres, based on the Di Francesco-Noble model, 1985.
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.
07/12/2001 - CML - Changed equations after using mathml validator.
03/01/2002 - CML - Created two extra components for extracellular sodium and
extracellular calcium concentrations. Then changed the Nao
and Cao variable public interfaces and the connections
between components appropriately.
21/01/2002 - AAC - Updated metadata to conform with the 16/1/02 CellML
Metadata 1.0 Specification.
25/02/2002 - CML - Corrected several equations.
06/05/2002 - CML - Added some initial values.
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="difrancesco_noble_model_1985"
cmeta:id="DFN_purkinje_fibre_model_1985"
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#"
xmlns:cs="http://www.cellml.org/metadata/simulation/1.0#">
<!--
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>2001-09-28</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>
Getting the model solving and correcting a bunch of errors and fixing
up the units and moving everything to "per-unit-area" type equations.
</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>2003-10-28</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>
Added some initial values from Penny Noble's documentation.
</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>2002-05-06</dcterms:W3CDTF>
</dcterms:modified>
</cmeta:modification>
<cmeta:modification rdf:parseType="Resource">
<rdf:value>
Corrected several equations.
</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>2002-02-25</dcterms:W3CDTF>
</dcterms:modified>
</cmeta:modification>
<cmeta:modification rdf:parseType="Resource">
<rdf:value>
Updated metadata to conform to the 16/1/02 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>2002-01-21</dcterms:W3CDTF>
</dcterms:modified>
</cmeta:modification>
<cmeta:modification rdf:parseType="Resource">
<rdf:value>
Created two extra components for extracellular sodium and
extracellular calcium concentrations. Then changed the Nao and Cao
variable public interfaces and the connections between components
appropriately.
</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 using 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>2001-12-07</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 "DFN_purkinje_fibre_model_1985", which is
declared on the <model> element.
-->
<rdf:Description rdf:about="#DFN_purkinje_fibre_model_1985">
<!-- A human readable name for the model. -->
<dc:title>
The Di Francesco-Noble Model of Cardiac Action Potentials in Purkinje
fibres, 1985
</dc:title>
<!-- A comment regarding the model. -->
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
This is the CellML description of Di Francesco and Noble's
mathematical model of cardiac action potentials of Purkinje fibres.
It is a significant development on the MNT model (1975), and it
remains the most complete of all Purkinje fibre ionic current models
to date. It is a complete replacement for the MNT model. In
particular it considers changes in the interpretation of the i_K2
system, includes more accurate experimental data concerning the fast
sodium current and it starts to account for fluctuations in ionic
concentrations. In addition, a start is made on accounting for
intracellular calcium movement between the sarcoplasmic reticulum and
the myoplasm. Corrections for the model can be found in an appendix at
the end of Earm & Noble, Proc. Roy. Soc. B, Vol 240(1297), 1990.
</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>2578676</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>DiFrancesco</vCard:Family>
<vCard:Given>D</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>Noble</vCard:Family>
<vCard:Given>D</vCard:Given>
</vCard:N>
</bqs:Person>
</rdf:li>
</rdf:Seq>
</dc:creator>
<dc:title>
A model of cardiac electrical activity incorporating ionic pumps and concentration changes
</dc:title>
<dcterms:issued rdf:parseType="Resource">
<dcterms:W3CDTF>1985-01-10</dcterms:W3CDTF>
</dcterms:issued>
<bqs:Journal rdf:parseType="Resource">
<dc:title>
Philosophical Transactions of the Royal Society of London Series B
</dc:title>
</bqs:Journal>
<bqs:volume>307</bqs:volume>
<bqs:first_page>353</bqs:first_page>
<bqs:last_page>398</bqs:last_page>
</bqs:JournalArticle>
</bqs:reference>
<cs:simulation>
<rdf:Description rdf:ID="simulation">
<cs:multistepMethod>bdf</cs:multistepMethod>
<cs:iterationMethod>functional</cs:iterationMethod>
<cs:boundIntervals rdf:parseType="Collection">
<rdf:Description>
<cs:boundVariable>
<rdf:Description rdf:about="#time"/>
</cs:boundVariable>
<cs:maximumStepSize rdf:datatype="http://www.w3.org/2001/XMLSchema#double">
0.01
</cs:maximumStepSize>
<cs:tabulationStepSize rdf:datatype="http://www.w3.org/2001/XMLSchema#double">
1.0
</cs:tabulationStepSize>
<cs:startingValue rdf:datatype="http://www.w3.org/2001/XMLSchema#double">
0
</cs:startingValue>
<cs:endingValue rdf:datatype="http://www.w3.org/2001/XMLSchema#double">
5000
</cs:endingValue>
</rdf:Description>
</cs:boundIntervals>
</rdf:Description>
</cs:simulation>
</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="mm">
<unit prefix="micro" units="mole" />
<unit units="litre" exponent="-1" />
</units>
<units name="per_mm">
<unit prefix="micro" units="mole" />
<unit units="litre" exponent="-1" />
</units>
<units name="ms">
<unit prefix="milli" units="second" />
</units>
<units name="per_ms">
<unit units="ms" exponent="-1" />
</units>
<units name="mV">
<unit prefix="milli" units="volt" />
</units>
<units name="per_mV">
<unit units="mV" 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 units="mm" exponent="-2" />
</units>
<units name="uF_per_mm2">
<unit prefix="micro" units="farad" />
<unit units="mm" exponent="-2" />
</units>
<units name="uA_per_mm2">
<unit prefix="micro" units="ampere" />
<unit units="mm" exponent="-2" />
</units>
<units name="uA_per_mm2_per_mM">
<unit prefix="micro" units="ampere" />
<unit units="mm" exponent="-2" />
<unit units="mM" exponent="-1" />
</units>
<units name="mM">
<unit prefix="nano" units="mole" />
<unit units="mm" exponent="-3" />
</units>
<units name="mM_per_ms">
<unit units="mM" />
<unit units="ms" exponent="-1" />
</units>
<units name="per_ms_per_mM">
<unit units="ms" exponent="-1" />
<unit units="mM" exponent="-1" />
</units>
<units name="mM2">
<unit units="mM" exponent="2" />
</units>
<units name="gas_constant_units">
<unit prefix="pico" units="joule" />
<unit prefix="nano" units="mole" exponent="-1" />
<unit units="kelvin" exponent="-1" />
</units>
<units name="faradays_constant_units">
<unit prefix="nano" units="coulomb" />
<unit prefix="nano" units="mole" exponent="-1" />
</units>
<!--
The "environment" component is used to declare variables that are used by
all or most of the other components, in this case just "time".
-->
<component name="environment" cmeta:id="environment">
<variable name="time" cmeta:id="time" public_interface="out" units="ms" />
</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 membrane component is the main component for this model,
containing the differential equation for the transmembrane potential
(the 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" public_interface="out"
initial_value="-87.0" units="mV" />
<variable
name="R" public_interface="out"
initial_value="8314.41" units="gas_constant_units" />
<variable
name="T" public_interface="out"
initial_value="310.0" units="kelvin" />
<variable
name="F" public_interface="out"
initial_value="96485.3" units="faradays_constant_units" />
<!-- This variable is defined here and only used internally. -->
<variable name="C" initial_value="0.08466" units="uF_per_mm2" />
<!-- These variables are imported from other components. -->
<variable name="time" public_interface="in" units="ms" />
<variable name="i_f" public_interface="in" units="uA_per_mm2" />
<variable name="i_K" public_interface="in" units="uA_per_mm2" />
<variable name="i_K1" public_interface="in" units="uA_per_mm2" />
<variable name="i_to" public_interface="in" units="uA_per_mm2" />
<variable name="i_Na_b" public_interface="in" units="uA_per_mm2" />
<variable name="i_Ca_b" public_interface="in" units="uA_per_mm2" />
<variable name="i_NaK" public_interface="in" units="uA_per_mm2" />
<variable name="i_NaCa" public_interface="in" units="uA_per_mm2" />
<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_stim" initial_value="0.0" 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 action potential equation consists of the sum of the
trans-sarcolemmal currents plus an applied stimulus, which may be
used to pace the cell model.
</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_f </ci>
<ci> i_K </ci>
<ci> i_K1 </ci>
<ci> i_to </ci>
<ci> i_Na_b </ci>
<ci> i_Ca_b </ci>
<ci> i_NaK </ci>
<ci> i_NaCa </ci>
<ci> i_Na </ci>
<ci> i_si </ci>
</apply>
</apply>
<ci> C </ci>
</apply>
</apply>
</math>
</component>
<!-- The hyperpolarising-activated current (i_f) is a Na-K current. -->
<component name="hyperpolarising_activated_current"
cmeta:id="hyperpolarising_activated_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="#hyperpolarising_activated_current">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The "funny" current - activated by hyperpolarisation rather than
depolarisation, and consisting of sodium and potassium components.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<!-- These variables are defined here and used in other components. -->
<variable name="i_f" public_interface="out" units="uA_per_mm2" />
<variable name="i_fK" public_interface="out" units="uA_per_mm2" />
<variable name="i_fNa" public_interface="out" units="uA_per_mm2" />
<variable name="E_Na" public_interface="out" units="mV" />
<variable name="E_K" public_interface="out" units="mV" />
<!-- These variables are defined here and only used internally. -->
<variable name="g_f_Na" initial_value="3.39e-3" units="mS_per_mm2" />
<variable name="g_f_K" initial_value="3.39e-3" units="mS_per_mm2" />
<variable name="I_fK" units="uA_per_mm2" />
<variable name="I_fNa" units="uA_per_mm2" />
<variable name="Km_f" initial_value="45.0" units="mM" />
<!-- These variables are imported from other components. -->
<variable
name="time" public_interface="in"
private_interface="out" units="ms" />
<variable
name="V" public_interface="in"
private_interface="out" units="mV" />
<variable name="R" public_interface="in" units="gas_constant_units" />
<variable name="T" public_interface="in" units="kelvin" />
<variable name="F" public_interface="in" units="faradays_constant_units" />
<variable name="Kc" public_interface="in" units="mM" />
<variable name="Ki" public_interface="in" units="mM" />
<variable name="Nai" public_interface="in" units="mM" />
<variable name="Nao" public_interface="in" units="mM" />
<!-- These variables are imported from encapsulated components. -->
<variable name="y" 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_f_calculation_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The total current is simply the sum of the two component currents.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="i_f_calculation_eq">
<apply id="i_f_calculation"><eq />
<ci> i_f </ci>
<apply><plus />
<ci> i_fK </ci>
<ci> i_fNa </ci>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="i_fK_calculation"><eq />
<ci> i_fK </ci>
<apply><times />
<ci> y </ci>
<ci> I_fK </ci>
</apply>
</apply>
<apply id="i_fNa_calculation"><eq />
<ci> i_fNa </ci>
<apply><times />
<ci> y </ci>
<ci> I_fNa </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_fK_calculation_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The maximal potassium current.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="I_fK_calculation_eq">
<apply id="I_fK_calculation"><eq />
<ci> I_fK </ci>
<apply><times />
<apply><divide />
<ci> Kc </ci>
<apply><plus />
<ci> Kc </ci>
<ci> Km_f </ci>
</apply>
</apply>
<apply><times />
<ci> g_f_K </ci>
<apply><minus />
<ci> V </ci>
<ci> E_K </ci>
</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_fNa_calculation_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The maximal sodium current.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="I_fNa_calculation_eq">
<apply id="I_fNa_calculation"><eq />
<ci> I_fNa </ci>
<apply><times />
<apply><divide />
<ci> Kc </ci>
<apply><plus />
<ci> Kc </ci>
<ci> Km_f </ci>
</apply>
</apply>
<apply><times />
<ci> g_f_Na </ci>
<apply><minus />
<ci> V </ci>
<ci> E_Na </ci>
</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="#E_f_calculation_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The reversal potentials for the two ions.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="E_f_calculation_eq">
<apply id="E_Na_calculation"><eq />
<ci> E_Na </ci>
<apply><times />
<apply><divide />
<apply><times />
<ci> R </ci>
<ci> T </ci>
</apply>
<ci> F </ci>
</apply>
<apply><ln />
<apply><divide />
<ci> Nao </ci>
<ci> Nai </ci>
</apply>
</apply>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="E_K_calculation"><eq />
<ci> E_K </ci>
<apply><times />
<apply><divide />
<apply><times />
<ci> R </ci>
<ci> T </ci>
</apply>
<ci> F </ci>
</apply>
<apply><ln />
<apply><divide />
<ci> Kc </ci>
<ci> Ki </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<!--
The y gate is encapsulated within the hyperpolarising-activated current.
-->
<component name="hyperpolarising_activated_current_y_gate"
cmeta:id="hyperpolarising_activated_current_y_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="#hyperpolarising_activated_current_y_gate">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The activation variable for the "funny" current - the y gate.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<!-- This variable is defined here and used in other components. -->
<variable
name="y" public_interface="out"
initial_value="0.2" units="dimensionless" />
<!-- These variables are defined here and only used internally. -->
<variable name="alpha_y" units="per_ms" />
<variable name="beta_y" 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_y_calculation_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The opening rate for the y gate.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="alpha_y_calculation_eq">
<apply id="alpha_y_calculation"><eq />
<ci> alpha_y </ci>
<apply><times />
<cn cellml:units="per_ms"> 0.05e-3 </cn>
<apply><exp />
<apply><times />
<cn cellml:units="per_mV"> -0.067 </cn>
<apply><plus />
<ci> V </ci>
<cn cellml:units="mV"> 42.0 </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_y_calculation_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The closing rate for the y gate.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="beta_y_calculation_eq">
<apply id="beta_y_calculation"><eq />
<ci> beta_y </ci>
<apply><divide />
<apply><times/>
<cn cellml:units="per_ms">1.0e-3</cn>
<apply><plus />
<ci> V </ci>
<cn cellml:units="mV"> 42.0 </cn>
</apply>
</apply>
<apply><minus />
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply><exp />
<apply><times />
<cn cellml:units="per_mV"> -0.2 </cn>
<apply><plus />
<ci> V </ci>
<cn cellml:units="mV"> 42.0 </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="#y_kinetics">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The Hodgkin-Huxley type kinetics for the y gate.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="y_kinetics">
<apply id="dy_dt"><eq />
<apply><diff />
<bvar><ci> time </ci></bvar>
<ci> y </ci>
</apply>
<apply><minus />
<apply><times />
<ci> alpha_y </ci>
<apply><minus />
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> y </ci>
</apply>
</apply>
<apply><times />
<ci> beta_y </ci>
<ci> y </ci>
</apply>
</apply>
</apply>
</math>
</component>
<!--
The time-dependent (delayed) potassium current is equivalent to the plateau
potassium current (1) in the MNT model. It is controlled by a single gate,
x.
-->
<component name="time_dependent_potassium_current"
cmeta:id="time_dependent_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="#time_dependent_potassium_current">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The time-dependent potassium current, a current dependent on both
potassium ion concentration and membrane potential.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<!-- This variable is defined here and used in other components. -->
<variable name="i_K" public_interface="out" units="uA_per_mm2" />
<!-- These variables are defined here and only used internally. -->
<!--<variable name="K" units="dimensionless" />-->
<variable name="I_K" units="uA_per_mm2" />
<variable name="i_K_max" initial_value="0.2032" units="uA_per_mm2" />
<!-- These variables are imported from other components. -->
<variable
name="time" public_interface="in"
private_interface="out" units="ms" />
<variable
name="V" public_interface="in"
private_interface="out" units="mV" />
<variable name="Ki" public_interface="in" units="mM" />
<variable name="Kc" public_interface="in" units="mM" />
<variable name="R" public_interface="in" units="gas_constant_units" />
<variable name="T" public_interface="in" units="kelvin" />
<variable name="F" public_interface="in" units="faradays_constant_units" />
<!-- This variable is imported from an encapsulated component. -->
<variable name="x" 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_K_calculation_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
Calculation of the time-dependent potassium current.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="i_K_calculation_eq">
<apply id="i_K_calculation"><eq />
<ci> i_K </ci>
<apply><times />
<ci> x </ci>
<ci> I_K </ci>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="I_K_calculation"><eq />
<ci> I_K </ci>
<apply><times />
<ci> i_K_max </ci>
<apply><divide />
<apply><minus />
<ci> Ki </ci>
<apply><times />
<ci> Kc </ci>
<apply><exp />
<apply><minus/>
<apply><divide />
<apply><times/>
<ci> V </ci>
<ci> F </ci>
</apply>
<apply><times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<cn cellml:units="mM"> 140.0 </cn>
</apply>
</apply>
</apply>
</math>
</component>
<!-- The x gate encapsulated within the time-dependent potassium current. -->
<component name="time_dependent_potassium_current_x_gate"
cmeta:id="time_dependent_potassium_current_x_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_potassium_current_x_gate">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The voltage-dependent activation variable for the time-dependent
potassium current, the x gate.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<!-- This variable is defined here and used in other components. -->
<variable
name="x" public_interface="out"
initial_value="0.01" units="dimensionless" />
<!-- These variables are defined here and only used internally. -->
<variable name="alpha_x" units="per_ms" />
<variable name="beta_x" units="per_ms" />
<!-- These variables are imported from other components. -->
<variable name="time" public_interface="in" units="ms" />
<variable name="V" 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="#alpha_x_calculation_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The opening rate of the x gate.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="alpha_x_calculation_eq">
<apply id="alpha_x_calculation"><eq />
<ci> alpha_x </ci>
<apply><times />
<cn cellml:units="per_ms"> 0.5e-3 </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_x_calculation_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The closing rate of the x gate.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="beta_x_calculation_eq">
<apply id="beta_x_calculation"><eq />
<ci> beta_x </ci>
<apply><times />
<cn cellml:units="per_ms"> 1.3e-3 </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="#dx_dt_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The kinetics of the x gate.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="dx_dt_eq">
<apply id="dx_dt"><eq />
<apply><diff />
<bvar><ci> time </ci></bvar>
<ci> x </ci>
</apply>
<apply><minus />
<apply><times />
<ci> alpha_x </ci>
<apply><minus />
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> x </ci>
</apply>
</apply>
<apply><times />
<ci> beta_x </ci>
<ci> x </ci>
</apply>
</apply>
</apply>
</math>
</component>
<!-- The time-independent (background) potassium current (i_K1). -->
<component name="time_independent_potassium_current"
cmeta:id="time_independent_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="#time_independent_potassium_current">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The time-independent background potassium 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 defined here and only used internally. -->
<variable name="g_K1" initial_value="1.0385" units="mS_per_mm2" />
<variable name="Km_K1" initial_value="210.0" units="mM" />
<!-- 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="E_K" public_interface="in" units="mV" />
<variable name="Kc" public_interface="in" units="mM" />
<variable name="R" public_interface="in" units="gas_constant_units" />
<variable name="T" public_interface="in" units="kelvin" />
<variable name="F" public_interface="in" units="faradays_constant_units" />
<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 postassium 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 />
<ci> g_K1 </ci>
<apply><divide />
<ci> Kc </ci>
<apply><plus />
<ci> Kc </ci>
<ci> Km_K1 </ci>
</apply>
</apply>
<apply><divide />
<apply><minus />
<ci> V </ci>
<ci> E_K </ci>
</apply>
<apply><plus />
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply><exp />
<apply><divide />
<apply><times />
<apply><minus />
<apply><plus />
<ci> V </ci>
<cn cellml:units="mV"> 10.0 </cn>
</apply>
<ci> E_K </ci>
</apply>
<ci> F </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
<apply><times />
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<!--
The transient outward current (i_to) replaces the i_qr chloride-based
current of the MNT model. This current is a calcium-activated, outward
rectifier. It has an inactivation gate, r.
-->
<component name="transient_outward_current"
cmeta:id="transient_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="#transient_outward_current">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The transient outward current (i_to) replaces the i_qr
chloride-based current of the MNT model. This current is a
calcium-activated, outward rectifier. It has an inactivation gate,
r.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<!-- This variable is defined here and used in other components. -->
<variable name="i_to" public_interface="out" units="uA_per_mm2" />
<!-- These variables are defined here and only used internally. -->
<variable name="Km_to" initial_value="10.0" units="mM" />
<variable name="Km_Ca" initial_value="0.5e-3" units="mM" />
<variable name="g_to" initial_value="0.316e-3" units="mS_per_mm2" />
<!-- These variables are imported from other components. -->
<variable
name="time" public_interface="in"
private_interface="out" units="ms" />
<variable
name="V" public_interface="in"
private_interface="out" units="mV" />
<variable name="R" public_interface="in" units="gas_constant_units" />
<variable name="T" public_interface="in" units="kelvin" />
<variable name="F" public_interface="in" units="faradays_constant_units" />
<variable name="Kc" public_interface="in" units="mM" />
<variable name="Ki" public_interface="in" units="mM" />
<variable name="Cai" public_interface="in" units="mM" />
<!-- this variable is imported from an encapsulated component. -->
<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_to_calculation_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
Calculation of the transient outward current.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="i_to_calculation_eq">
<apply id="i_to_calculation"><eq />
<ci> i_to </ci>
<apply><times />
<ci> r </ci>
<ci> g_to </ci>
<apply><plus />
<cn cellml:units="mM"> 0.2 </cn>
<apply><divide />
<ci> Kc </ci>
<apply><plus />
<ci> Km_to </ci>
<ci> Kc </ci>
</apply>
</apply>
</apply>
<apply><divide />
<ci> Cai </ci>
<apply><plus />
<ci> Km_Ca </ci>
<ci> Cai </ci>
</apply>
</apply>
<apply><divide />
<apply><plus />
<ci> V </ci>
<cn cellml:units="mV"> 10.0 </cn>
</apply>
<apply><minus />
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply><exp />
<apply><times />
<cn cellml:units="per_mV"> -0.2 </cn>
<apply><plus />
<ci> V </ci>
<cn cellml:units="mV"> 10.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply><minus />
<apply><times />
<ci> Ki </ci>
<apply><exp />
<apply><times />
<cn cellml:units="per_mV"> 0.02 </cn>
<ci> V </ci>
</apply>
</apply>
</apply>
<apply><times />
<ci> Kc </ci>
<apply><exp />
<apply><times />
<cn cellml:units="per_mV"> -0.02 </cn>
<ci> V </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<!-- The inactivation process is described by the following r component. -->
<component name="transient_outward_current_r_gate"
cmeta:id="transient_outward_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_outward_current_r_gate">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The activation variable for the transient outward current.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<!-- this variable is defined here and used in other components -->
<variable
name="r" public_interface="out"
initial_value="1.0" 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 of 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"> 0.033e-3 </cn>
<apply><exp />
<apply><divide />
<apply><minus />
<ci> V </ci>
</apply>
<cn cellml:units="mV"> 17.0 </cn>
</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 of 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"> 33.0e-3 </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"> 10.0 </cn>
</apply>
<cn cellml:units="mV"> 8.0 </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="#dr_dt_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The kinetics for 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 sodium background current is a simple, time-independent current which
is similar to the i_Na_b of the MNT model. i_Ch_b is a background current
due to choline, or some other sodium substitute.
-->
<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>
A linear resting sodium flux.
</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="0.203e-3" units="mS_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" />
<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 background sodium 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 calcium background current is in the same form as the sodium background
current.
-->
<component name="calcium_background_current"
cmeta:id="calcium_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="#calcium_background_current">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
A resting background leakage calcium flux.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<!-- These variables are defined here and used in other components. -->
<variable name="i_Ca_b" public_interface="out" units="uA_per_mm2" />
<variable name="E_Ca" public_interface="out" units="mV" />
<!-- This variable is defined here and only used internally. -->
<variable name="g_Cab" initial_value="0.0226e-3" units="mS_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" />
<variable name="R" public_interface="in" units="gas_constant_units" />
<variable name="T" public_interface="in" units="kelvin" />
<variable name="F" public_interface="in" units="faradays_constant_units" />
<variable name="Cai" public_interface="in" units="mM" />
<variable name="Cao" public_interface="in" units="mM" />
<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_Ca_b_calculation_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
Calculation of the calcium leakage current.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="i_Ca_b_calculation_eq">
<apply id="i_Ca_b_calculation"><eq />
<ci> i_Ca_b </ci>
<apply><times />
<ci> g_Cab </ci>
<apply><minus />
<ci> V </ci>
<ci> E_Ca </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="#E_Ca_calculation_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The calcium reversal potential.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="E_Ca_calculation_eq">
<apply id="E_Ca_calculation"><eq />
<ci> E_Ca </ci>
<apply><times />
<apply><divide />
<apply><times />
<ci> R </ci>
<ci> T </ci>
</apply>
<apply><times />
<ci> F </ci>
<cn cellml:units="dimensionless">2.0</cn>
</apply>
</apply>
<apply><ln />
<apply><divide />
<ci> Cao </ci>
<ci> Cai </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<!--
The Na-K exchange pump couples the free energy released by the hydrolysis of
ATP to transfer sodium and potassium ions across the cell membrane against
their electrochemical gradients. 3 Na ions are pumped out for every 2 K
ions pumped into the cell.
-->
<component name="sodium_potassium_pump" cmeta:id="sodium_potassium_pump">
<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_potassium_pump">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The Na-K exchange pump couples the free energy released by the
hydrolysis of ATP to transfer sodium and potassium ions across the
cell membrane against their electrochemical gradients. 3 Na ions are
pumped out for every 2 K ions pumped into the cell.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<!-- This variable is defined here and used in other components. -->
<variable name="i_NaK" public_interface="out" units="uA_per_mm2" />
<!-- This variable is defined here and only used internally. -->
<variable name="I_NaK" initial_value="0.141" units="uA_per_mm2" />
<variable name="K_mK" initial_value="1.0" units="mM" />
<variable name="K_mNa" initial_value="40.0" units="mM" />
<!-- 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="Nai" public_interface="in" units="mM" />
<variable name="Kc" public_interface="in" units="mM" />
<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_NaK_calculation_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
Calculation of the Na/K-pump current.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="i_NaK_calculation_eq">
<apply id="i_NaK_calculation"><eq />
<ci> i_NaK </ci>
<apply><times />
<ci> I_NaK </ci>
<apply><divide />
<ci> Kc </ci>
<apply><plus />
<ci> K_mK </ci>
<ci> Kc </ci>
</apply>
</apply>
<apply><divide />
<ci> Nai </ci>
<apply><plus />
<ci> K_mNa </ci>
<ci> Nai </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<!--
The equation for the Na-Ca exchange current assumes that i_NaCa depends
soley on the sodium and calcium ion electrochemical gradients and the
transmembrane potential. The stoichiometry of the exchange is 3Na : 1Ca,
producing a net outward current.
-->
<component name="Na_Ca_exchanger" cmeta:id="Na_Ca_exchanger">
<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="#Na_Ca_exchanger">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The DFN paper gives two alternative equations for the
i_NaCa current. The simplest makes the current a sine function of
the total energy gradient. The more realistic model uses an
equation which is likely to reproduce better dependence of i_NaCa
on intracellular calcium ions. We utilise the more complex version
here.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<!-- This variable is defined here and used in other components. -->
<variable name="i_NaCa" public_interface="out" units="uA_per_mm2" />
<variable
name="n_NaCa" public_interface="out"
initial_value="3.0" units="dimensionless" />
<!-- These variables are defined here and only used internally. -->
<variable name="k_NaCa" initial_value="0.0226e-3" units="uA_per_mm2" />
<!--<variable name="E_NaCa" units="mV" />-->
<variable name="d_NaCa" initial_value="0.001" units="dimensionless" />
<variable name="gamma" initial_value="0.5" units="dimensionless" />
<!--<variable name="n" units="dimensionless" />-->
<!-- These variables are imported in from other components. -->
<variable name="time" public_interface="in" units="ms" />
<variable name="V" public_interface="in" units="mV" />
<variable name="R" public_interface="in" units="gas_constant_units" />
<variable name="T" public_interface="in" units="kelvin" />
<variable name="F" public_interface="in" units="faradays_constant_units" />
<variable name="Cao" public_interface="in" units="mM" />
<variable name="Cai" public_interface="in" units="mM" />
<variable name="E_Na" public_interface="in" units="mV" />
<variable name="Nai" public_interface="in" units="mM" />
<variable name="Nao" public_interface="in" units="mM" />
<variable name="E_Ca" public_interface="in" units="mV" />
<!-- The current is given as: -->
<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="#Na_Ca_exchanger_calculation2_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
Calculation of the exchanger current.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="Na_Ca_exchanger_calculation2_eq">
<!--
<apply id="Na_Ca_exchanger_calculation1"><eq />
<ci> i_NaCa </ci>
<apply><times />
<ci> K_NaCa </ci>
<apply><sinh />
<apply><divide />
<apply><times />
<apply><minus />
<ci> V </ci>
<ci> E_NaCa </ci>
</apply>
<ci> F </ci>
</apply>
<apply><times />
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="E_NaCa_calculation"><eq />
<ci> E_NaCa </ci>
<apply><divide />
<apply><minus />
<apply><times />
<ci> n_NaCa </ci>
<ci> E_Na </ci>
</apply>
<apply><times />
<cn cellml:units="dimensionless"> 2.0 </cn>
<ci> E_Ca </ci>
</apply>
</apply>
<apply><minus />
<ci> n_NaCa </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
</apply>
</apply>
-->
<apply id="Na_Ca_exchanger_calculation2"><eq />
<ci> i_NaCa </ci>
<apply><times />
<ci> k_NaCa </ci>
<apply><divide />
<apply><minus />
<apply><times />
<apply><exp />
<apply><divide />
<apply><times />
<ci> gamma </ci>
<apply><minus />
<ci> n_NaCa </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
<ci> V </ci>
<ci> F </ci>
</apply>
<apply><times />
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
<apply><power />
<ci> Nai </ci>
<ci> n_NaCa </ci>
</apply>
<ci> Cao </ci>
</apply>
<apply><times />
<apply><exp />
<apply><divide />
<apply><times />
<cn cellml:units="dimensionless"> -1.0 </cn>
<apply><minus />
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> gamma </ci>
</apply>
<apply><minus />
<ci> n_NaCa </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
<ci> V </ci>
<ci> F </ci>
</apply>
<apply><times />
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
<apply><power />
<ci> Nao </ci>
<ci> n_NaCa </ci>
</apply>
<ci> Cai </ci>
</apply>
</apply>
<apply><plus />
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply><times />
<ci> d_NaCa </ci>
<apply><plus />
<apply><times />
<ci> Cai </ci>
<apply><power />
<ci> Nao </ci>
<ci> n_NaCa </ci>
</apply>
</apply>
<apply><times />
<ci> Cao </ci>
<apply><power />
<ci> Nai </ci>
<ci> n_NaCa </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<!--
The DFN model retains a two-variable mode; of the sodium kinetics, with new
equations for the gates m and h. It is acknowledged however that the model
does not represent the slower components of Na inactivation and recovery.
It is also assumed that the sodium channel shows a 12% permeability to k
ions.
-->
<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 DFN model retains a two-variable model of the sodium kinetics,
with new equations for the gates m and h. It is acknowledged however
that the model does not represent the slower components of Na
inactivation and recovery. It is also assumed that the sodium
channel shows a 12% permeability to K ions.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<!-- This variable is defined here and used in other components. -->
<variable 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="0.846" units="mS_per_mm2" />
<variable name="E_mh" units="mV" />
<!-- These variables are imported from other components. -->
<variable
name="time" public_interface="in"
private_interface="out" units="ms" />
<variable
name="V" public_interface="in"
private_interface="out" units="mV" />
<variable name="R" public_interface="in" units="gas_constant_units" />
<variable name="T" public_interface="in" units="kelvin" />
<variable name="F" public_interface="in" units="faradays_constant_units" />
<variable name="Nao" public_interface="in" units="mM" />
<variable name="Nai" public_interface="in" units="mM" />
<variable name="Kc" public_interface="in" units="mM" />
<variable name="Ki" public_interface="in" units="mM" />
<!-- 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_mh </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="#E_mh_calculation_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The reversal potential of the fast sodium channel, assuming a 12%
permeability of potassium ions.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="E_mh_calculation_eq">
<apply id="E_mh_calculation"><eq />
<ci> E_mh </ci>
<apply><times />
<apply><divide />
<apply><times />
<ci> R </ci>
<ci> T </ci>
</apply>
<ci> F </ci>
</apply>
<apply><ln />
<apply><divide />
<apply><plus />
<ci> Nao </ci>
<apply><times />
<cn cellml:units="dimensionless"> 0.12 </cn>
<ci> Kc </ci>
</apply>
</apply>
<apply><plus />
<ci> Nai </ci>
<apply><times />
<cn cellml:units="dimensionless"> 0.12 </cn>
<ci> Ki </ci>
</apply>
</apply>
</apply>
</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" public_interface="out"
initial_value="0.01" 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 "environment" 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><times />
<cn cellml:units="per_mV_ms"> 200.0e-3 </cn>
<apply><plus />
<ci> V </ci>
<cn cellml:units="mV"> 41.0 </cn>
</apply>
</apply>
<apply><minus />
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply><exp />
<apply><times />
<cn cellml:units="dimensionless"> -0.1 </cn>
<apply><plus />
<ci> V </ci>
<cn cellml:units="mV"> 41.0 </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"> 8000.0e-3 </cn>
<apply><exp />
<apply><times />
<cn cellml:units="dimensionless"> -0.056 </cn>
<apply><plus />
<ci> V </ci>
<cn cellml:units="mV"> 66.0 </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 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 current
- 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="0.98" 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 "environment" 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"> 20.0e-3 </cn>
<apply><exp />
<apply><times />
<cn cellml:units="dimensionless"> -0.125 </cn>
<apply><plus />
<ci> V </ci>
<cn cellml:units="mV"> 75.0 </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"> 2000.0e-3 </cn>
<apply><plus/>
<cn cellml:units="dimensionless">1.0</cn>
<apply><times />
<cn cellml:units="dimensionless"> 320.0 </cn>
<apply><exp />
<apply><times />
<cn cellml:units="dimensionless"> -0.1 </cn>
<apply><plus />
<ci> V </ci>
<cn cellml:units="mV"> 75.0 </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="#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>
<!--
Like the MNT model, the kinetics of the secondary inward current are still
described in terms of two gate variables d and f, but the time constants for
activation and inactivation processes are much shorter. The fast component,
i_si of this current has been divided into the individual ion movements of
Ca, K and Na.
-->
<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>
Like the MNT model, the kinetics of the secondary inward current are
still described in terms of two gate variables d and f, but the time
constants for activation and inactivation processes are much
shorter. The fast component, i_si of this current has been divided
into the individual ion movements of Ca, K and Na. This current
would later be called the L-type calcium current.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<!-- These variables are defined here and used in other components. -->
<variable name="i_si" public_interface="out" units="uA_per_mm2" />
<variable name="i_siCa" public_interface="out" units="uA_per_mm2" />
<variable name="i_siK" public_interface="out" units="uA_per_mm2" />
<variable name="i_siNa" public_interface="out" units="uA_per_mm2" />
<!-- This variable is defined here and only used internally. -->
<variable name="P_Ca" initial_value="16.93e-3" units="uA_per_mm2_per_mM" />
<variable name="P_CaK" initial_value="0.01" units="dimensionless" />
<variable name="P_CaNa" initial_value="0.01" units="dimensionless" />
<!-- These variables are imported from other components. -->
<variable
name="time" public_interface="in"
private_interface="out" units="ms" />
<variable
name="V" public_interface="in"
private_interface="out" units="mV" />
<variable name="R" public_interface="in" units="gas_constant_units" />
<variable name="T" public_interface="in" units="kelvin" />
<variable name="F" public_interface="in" units="faradays_constant_units" />
<variable name="Nao" public_interface="in" units="mM" />
<variable name="Nai" public_interface="in" units="mM" />
<variable name="Kc" public_interface="in" units="mM" />
<variable name="Ki" public_interface="in" units="mM" />
<variable name="Cao" public_interface="in" units="mM" />
<variable name="Cai" public_interface="in" private_interface="out" units="mM" />
<!-- 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="f2" 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>
The total i_si current is simply the sum of the component calcium,
potassium, and sodium currents.
</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 />
<ci> i_siCa </ci>
<ci> i_siK </ci>
<ci> i_siNa </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_siCa_calculation_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
Calculation of the calcium component 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_siCa_calculation_eq">
<apply id="i_siCa_calculation"><eq />
<ci> i_siCa </ci>
<apply><times />
<ci> d </ci>
<ci> f </ci>
<ci> f2 </ci>
<apply><divide />
<apply><times />
<cn cellml:units="dimensionless"> 4.0 </cn>
<ci> P_Ca </ci>
<apply><minus />
<ci> V </ci>
<cn cellml:units="mV"> 50.0 </cn>
</apply>
<apply><divide />
<ci> F </ci>
<apply><times />
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
<apply><minus />
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply><exp />
<apply><divide />
<apply><times />
<cn cellml:units="dimensionless"> -1.0 </cn>
<apply><minus />
<ci> V </ci>
<cn cellml:units="mV"> 50.0 </cn>
</apply>
<ci> F </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
<apply><times />
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply><minus />
<apply><times />
<ci> Cai </ci>
<apply><exp />
<apply><divide />
<apply><times />
<cn cellml:units="dimensionless"> 50.0 </cn>
<ci> F </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
<apply><times />
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
</apply>
<apply><times />
<ci> Cao </ci>
<apply><exp />
<apply><divide />
<apply><times />
<cn cellml:units="dimensionless"> -2.0 </cn>
<apply><minus />
<ci> V </ci>
<cn cellml:units="mV"> 50.0 </cn>
</apply>
<ci> F </ci>
</apply>
<apply><times />
<ci> R </ci>
<ci> T </ci>
</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="#i_siK_calculation_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
Calculation of the potassium component 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_siK_calculation_eq">
<apply id="i_siK_calculation"><eq />
<ci> i_siK </ci>
<apply><times />
<ci> d </ci>
<ci> f </ci>
<ci> f2 </ci>
<apply><divide />
<apply><times />
<ci>P_CaK</ci>
<ci> P_Ca </ci>
<apply><minus />
<ci> V </ci>
<cn cellml:units="mV"> 50.0 </cn>
</apply>
<apply><divide />
<ci> F </ci>
<apply><times />
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
<apply><minus />
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply><exp />
<apply><divide />
<apply><times />
<cn cellml:units="dimensionless"> -1.0 </cn>
<apply><minus />
<ci> V </ci>
<cn cellml:units="mV"> 50.0 </cn>
</apply>
<ci> F </ci>
</apply>
<apply><times />
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply><minus />
<apply><times />
<ci> Ki </ci>
<apply><exp />
<apply><divide />
<apply><times />
<cn cellml:units="dimensionless"> 50.0 </cn>
<ci> F </ci>
</apply>
<apply><times />
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
</apply>
<apply><times />
<ci> Kc </ci>
<apply><exp />
<apply><divide />
<apply><times />
<cn cellml:units="dimensionless"> -1.0 </cn>
<apply><minus />
<ci> V </ci>
<cn cellml:units="mV"> 50.0 </cn>
</apply>
<ci> F </ci>
</apply>
<apply><times />
<ci> R </ci>
<ci> T </ci>
</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="#i_siNa_calculation_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
Calculation of the sodium component 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_siNa_calculation_eq">
<apply id="i_siNa_calculation"><eq />
<ci> i_siNa </ci>
<apply><times />
<ci> d </ci>
<ci> f </ci>
<ci> f2 </ci>
<apply><divide />
<apply><times />
<ci>P_CaNa</ci>
<ci> P_Ca </ci>
<apply><minus />
<ci> V </ci>
<cn cellml:units="mV"> 50.0 </cn>
</apply>
<apply><divide />
<ci> F </ci>
<apply><times />
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
<apply><minus />
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply><exp />
<apply><divide />
<apply><times />
<cn cellml:units="dimensionless"> -1.0 </cn>
<apply><minus />
<ci> V </ci>
<cn cellml:units="mV"> 50.0 </cn>
</apply>
<ci> F </ci>
</apply>
<apply><times />
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply><minus />
<apply><times />
<ci> Nai </ci>
<apply><exp />
<apply><divide />
<apply><times />
<cn cellml:units="dimensionless"> 50.0 </cn>
<ci> F </ci>
</apply>
<apply><times />
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
</apply>
<apply><times />
<ci> Nao </ci>
<apply><exp />
<apply><divide />
<apply><times />
<cn cellml:units="dimensionless"> -1.0 </cn>
<apply><minus />
<ci> V </ci>
<cn cellml:units="mV"> 50.0 </cn>
</apply>
<ci> F </ci>
</apply>
<apply><times />
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
</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 second 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="0.005" 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 "environment" and the "membrane" via
the "secondary_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><times />
<cn cellml:units="per_mV_ms"> 30.0e-3 </cn>
<apply><divide />
<apply><plus />
<ci> V </ci>
<cn cellml:units="mV"> 19.0 </cn>
</apply>
<apply><minus />
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply><exp />
<apply><divide />
<apply><times />
<cn cellml:units="dimensionless"> -1.0 </cn>
<apply><plus />
<ci> V </ci>
<cn cellml:units="mV"> 19.0 </cn>
</apply>
</apply>
<cn cellml:units="mV"> 4.0 </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_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_mV_ms"> 12.0e-3 </cn>
<apply><divide />
<apply><plus />
<ci> V </ci>
<cn cellml:units="mV"> 19.0 </cn>
</apply>
<apply><minus />
<apply><exp />
<apply><divide />
<apply><plus />
<ci> V </ci>
<cn cellml:units="mV"> 19.0 </cn>
</apply>
<cn cellml:units="mV"> 10.0 </cn>
</apply>
</apply>
<cn cellml:units="dimensionless"> 1.0 </cn>
</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 second 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="1.0" 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" />
<variable name="Cai" public_interface="in" units="mM" />
<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_mV_ms"> 6.25e-3 </cn>
<apply><divide />
<apply><plus />
<ci> V </ci>
<cn cellml:units="mV"> 34.0 </cn>
</apply>
<apply><minus />
<apply><exp />
<apply><divide />
<apply><plus />
<ci> V </ci>
<cn cellml:units="mV"> 34.0 </cn>
</apply>
<cn cellml:units="mV"> 4.0 </cn>
</apply>
</apply>
<cn cellml:units="dimensionless"> 1.0 </cn>
</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"> 50.0e-3 </cn>
<apply><plus />
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply><exp />
<apply><divide />
<apply><times />
<cn cellml:units="dimensionless"> -1.0 </cn>
<apply><plus />
<ci> V </ci>
<cn cellml:units="mV"> 34.0 </cn>
</apply>
</apply>
<cn cellml:units="mV"> 4.0 </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="#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 DFN model also includes a description of Ca-dependent inactivation.
When calcium ions bind to a regulatory site on the channel protein, they
induce a conformational change such that the channel no longer conducts,
and the secondary current slows or ceases.
-->
<component name="secondary_inward_current_f2_gate"
cmeta:id="secondary_inward_current_f2_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_f2_gate">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The DFN model also includes a description of Ca-dependent
inactivation. When calcium ions bind to a regulatory site on the
channel protein, they induce a conformational change such that the
channel no longer conducts, and the secondary current slows or
ceases.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<!-- This variable is defined here and used in other components. -->
<variable
name="f2" public_interface="out"
initial_value="1.0" units="dimensionless" />
<!-- These variables are defined here and only used internally. -->
<variable name="alpha_f2" initial_value="5.0e-3" units="per_ms" />
<variable name="beta_f2" units="per_ms" />
<variable name="K_mf2" initial_value="1.0e-3" units="mM" />
<!-- 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" />
<variable name="Cai" public_interface="in" units="mM" />
<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="#df2_dt_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The kinetics of the f2 gate.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="df2_dt_eq">
<apply id="df2_dt"><eq />
<apply><diff />
<bvar><ci> time </ci></bvar>
<ci> f2 </ci>
</apply>
<apply><minus />
<apply><times />
<ci> alpha_f2 </ci>
<apply><minus />
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> f2 </ci>
</apply>
</apply>
<apply><times />
<ci> beta_f2 </ci>
<ci> f2 </ci>
</apply>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="beta_f2_calculation"><eq />
<ci> beta_f2 </ci>
<apply><divide />
<apply><times />
<ci> Cai </ci>
<ci> alpha_f2 </ci>
</apply>
<ci> K_mf2 </ci>
</apply>
</apply>
</math>
</component>
<!--
Additionally, the DFN model attempted to quantify the changes in several ion
concentrations, as well as the [Ca]i of earlier models.
-->
<component name="extracellular_sodium_concentration"
cmeta:id="extracellular_sodium_concentration">
<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="#extracellular_sodium_concentration">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
A representation of extracellular sodium ion concentration, held
constant in this model.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<!-- This variable is defined here and used in other components -->
<variable
name="Nao" public_interface="out"
initial_value="140.0" units="mM" />
</component>
<component name="intracellular_sodium_concentration"
cmeta:id="intracellular_sodium_concentration">
<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="#intracellular_sodium_concentration">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
This component contains the description of intracellular sodium
concentration change.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<!-- This variable is defined here and used in other components -->
<variable
name="Nai" public_interface="out"
initial_value="8.0" units="mM" />
<!-- These variables are imported from other components. -->
<variable name="V_i" public_interface="in" units="dimensionless" />
<variable name="Am" public_interface="in" units="per_mm" />
<variable name="time" public_interface="in" units="ms" />
<variable name="F" public_interface="in" units="faradays_constant_units" />
<variable name="i_Na" public_interface="in" units="uA_per_mm2" />
<variable name="i_Na_b" public_interface="in" units="uA_per_mm2" />
<variable name="i_siNa" public_interface="in" units="uA_per_mm2" />
<variable name="i_NaK" public_interface="in" units="uA_per_mm2" />
<variable name="i_fNa" public_interface="in" units="uA_per_mm2" />
<variable name="i_NaCa" public_interface="in" units="uA_per_mm2" />
<variable name="n_NaCa" public_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="#sodium_diff_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The rate of change of intracellular sodium concentration is the sum
of the ions entering the intracellular volume via the sodium
transmembrane currents.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="sodium_diff_eq">
<apply id="sodium_diff_eq"><eq />
<apply><diff />
<bvar><ci> time </ci></bvar>
<ci> Nai </ci>
</apply>
<apply><divide />
<apply><minus />
<apply><times/>
<ci>Am</ci>
<apply><plus />
<ci> i_Na </ci>
<ci> i_Na_b </ci>
<ci> i_fNa </ci>
<ci> i_siNa </ci>
<apply><times />
<ci> i_NaK </ci>
<cn cellml:units="dimensionless"> 3.0 </cn>
</apply>
<apply><times />
<ci> i_NaCa </ci>
<apply><divide />
<ci> n_NaCa </ci>
<apply><minus />
<ci> n_NaCa </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply><times />
<ci> V_i </ci>
<ci> F </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="extracellular_calcium_concentration"
cmeta:id="extracellular_calcium_concentration">
<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="#extracellular_calcium_concentration">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
A representation of extracellular calcium ion concentration, held
constant in this model.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<!-- This variable is defined here and used in other components -->
<variable
name="Cao" public_interface="out"
initial_value="2.0" units="mM" />
</component>
<!--
Changes in [Ca]i were first modelled in the BR model and has only been
slightly developed in the DFN model. Calcium is sequestered in the
sarcoplasmic reticulum ([Ca]up). A fraction is transferred to a release
store in the junctional SR ([Ca]rel) before being released into the
intracellular space. The Ca concentrations in each of these various
stores is modelled together with the transfer between the calcium sites
and the ca transfer across the cell membrane via the other ionic
currents.
-->
<component name="intracellular_calcium_concentration"
cmeta:id="intracellular_calcium_concentration">
<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="#intracellular_calcium_concentration">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
Changes in [Ca]i were first modelled in the BR model and has only
been slightly developed in the DFN model. Calcium is sequestered in
the sarcoplasmic reticulum ([Ca]up). A fraction is transferred to a
release store in the junctional SR ([Ca]rel) before being released
into the intracellular space. The Ca concentrations in each of these
various stores is modelled together with the transfer between the
calcium sites and the Ca transfer across the cell membrane via the
other ionic currents.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<!-- This variable is defined here and used in other components -->
<variable
name="Cai" public_interface="out"
initial_value="0.00005" units="mM" />
<!-- These variables are defined here and only used internally. -->
<variable name="Am" public_interface="in" units="per_mm" />
<variable name="V_up" public_interface="in" units="dimensionless" />
<variable name="V_rel" public_interface="in" units="dimensionless" />
<variable name="V_i" public_interface="in" units="dimensionless" />
<variable name="i_up" units="mM_per_ms" />
<variable name="i_tr" units="mM_per_ms" />
<variable name="i_rel" units="mM_per_ms" />
<variable name="alpha_up" units="per_ms_per_mM" />
<variable name="alpha_tr" units="per_ms" />
<variable name="alpha_rel" units="per_ms" />
<variable name="Ca_up" initial_value="2.0" units="mM" />
<variable name="Ca_rel" initial_value="1.0" units="mM" />
<variable name="Ca_up_max" initial_value="5.0" units="mM" />
<variable name="K_mCa" initial_value="1.0e-6" units="mM2" />
<variable name="p" initial_value="1.0" units="dimensionless" />
<variable name="alpha_p" units="per_ms" />
<variable name="beta_p" units="per_ms" />
<variable name="tau_up" initial_value="25.0" units="ms" />
<variable name="tau_rep" initial_value="2.0e+3" units="ms" />
<variable name="tau_rel" initial_value="50.0" units="ms" />
<!-- 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="F" public_interface="in" units="faradays_constant_units" />
<variable name="i_Ca_b" public_interface="in" units="uA_per_mm2" />
<variable name="i_siCa" public_interface="in" units="uA_per_mm2" />
<variable name="i_NaCa" public_interface="in" units="uA_per_mm2" />
<variable name="n_NaCa" public_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_up_calculation_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The calcium current into the uptake store.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="i_up_calculation_eq">
<apply id="i_up_calculation"><eq />
<ci> i_up </ci>
<apply><times />
<ci> alpha_up </ci>
<ci> Cai </ci>
<apply><minus />
<ci> Ca_up_max </ci>
<ci> Ca_up </ci>
</apply>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="alpha_up_calculation_eq">
<apply id="alpha_up_calculation"><eq />
<ci> alpha_up </ci>
<apply><divide />
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply><times />
<ci> tau_up </ci>
<ci> Ca_up_max </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="#i_tr_calculation_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The calcium current between the uptake and release stores, which
uses a voltage-dependent activation variable - the p gate.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="i_tr_calculation_eq">
<apply id="i_tr_calculation"><eq />
<ci> i_tr </ci>
<apply><times />
<ci> alpha_tr </ci>
<ci> p </ci>
<apply><minus />
<ci> Ca_up </ci>
<ci> Ca_rel </ci>
</apply>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="alpha_tr_calculation"><eq />
<ci> alpha_tr </ci>
<apply><divide />
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> tau_rep </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="#alpha_p_calculation_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The opening rate of the p gate.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="alpha_p_calculation_eq">
<apply id="alpha_p_calculation"><eq />
<ci> alpha_p </ci>
<apply><times />
<cn cellml:units="per_mV_ms"> 0.625e-3 </cn>
<apply><divide />
<apply><plus />
<ci> V </ci>
<cn cellml:units="mV"> 34.0 </cn>
</apply>
<apply><minus />
<apply><exp />
<apply><divide />
<apply><plus />
<ci> V </ci>
<cn cellml:units="mV"> 34.0 </cn>
</apply>
<cn cellml:units="mV"> 4.0 </cn>
</apply>
</apply>
<cn cellml:units="dimensionless"> 1.0 </cn>
</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_p_calculation_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The closing rate of the p gate.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="beta_p_calculation_eq">
<apply id="beta_p_calculation"><eq />
<ci> beta_p </ci>
<apply><divide />
<cn cellml:units="per_ms"> 5.0e-3 </cn>
<apply><plus />
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply><exp />
<apply><divide />
<apply><times />
<cn cellml:units="dimensionless"> -1.0 </cn>
<apply><plus />
<ci> V </ci>
<cn cellml:units="mV"> 34.0 </cn>
</apply>
</apply>
<cn cellml:units="mV"> 4.0 </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="#dp_dt_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The kinetics of the p gate.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="dp_dt_eq">
<apply id="dp_dt"><eq />
<apply><diff />
<bvar><ci> time </ci></bvar>
<ci> p </ci>
</apply>
<apply><minus />
<apply><times />
<ci> alpha_p </ci>
<apply><minus />
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> p </ci>
</apply>
</apply>
<apply><times />
<ci> beta_p </ci>
<ci> p </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="#i_rel_calculation_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The calcium release current from the SR into the cytosol.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="i_rel_calculation_eq">
<apply id="i_rel_calculation"><eq />
<ci> i_rel </ci>
<apply><times />
<ci> alpha_rel </ci>
<ci> Ca_rel </ci>
<apply><divide />
<apply><power />
<ci> Cai </ci>
<cn cellml:units="dimensionless">2.0</cn>
</apply>
<apply><plus />
<apply><power />
<ci> Cai </ci>
<cn cellml:units="dimensionless">2.0</cn>
</apply>
<ci> K_mCa </ci>
</apply>
</apply>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="alpha_rel_calculation"><eq />
<ci> alpha_rel </ci>
<apply><divide />
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> tau_rel </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="#Ca_up_diff_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The rate of change of calcium concentration in the uptake store.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="Ca_up_diff_eq">
<apply id="Ca_up_diff_eq"><eq />
<apply><diff />
<bvar><ci> time </ci></bvar>
<ci> Ca_up </ci>
</apply>
<apply><minus/>
<apply><times/>
<ci>i_up</ci>
<apply><divide/>
<ci>V_i</ci>
<ci>V_up</ci>
</apply>
</apply>
<apply><times/>
<ci>i_tr</ci>
<apply><divide/>
<ci>V_rel</ci>
<ci>V_up</ci>
</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="#Ca_rel_diff_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The rate of change of calcium concentration in the release store.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="Ca_rel_diff_eq">
<apply id="Ca_rel_diff_eq"><eq />
<apply><diff />
<bvar><ci> time </ci></bvar>
<ci> Ca_rel </ci>
</apply>
<apply><minus/>
<ci>i_tr</ci>
<ci>i_rel</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="#Cai_diff_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The rate of change of intracellular calcium concentration.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="Cai_diff_eq">
<apply id="Cai_diff_eq"><eq />
<apply><diff />
<bvar><ci> time </ci></bvar>
<ci> Cai </ci>
</apply>
<apply><minus />
<apply><times/>
<ci>i_rel</ci>
<apply><divide/>
<ci>V_rel</ci>
<ci>V_i</ci>
</apply>
</apply>
<apply><plus/>
<ci>i_up</ci>
<apply><divide />
<apply><times/>
<ci>Am</ci>
<apply><minus />
<apply><plus />
<ci> i_siCa </ci>
<ci> i_Ca_b </ci>
</apply>
<apply><divide />
<apply><times />
<cn cellml:units="dimensionless"> 2.0 </cn>
<ci> i_NaCa </ci>
</apply>
<apply><minus />
<ci> n_NaCa </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
</apply>
</apply>
</apply>
<apply><times />
<cn cellml:units="dimensionless"> 2.0 </cn>
<ci> V_i </ci>
<ci> F </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<!--
The DFN model assumes that the potassium ion concentration is homogeneous
throughout the three-compartment model.
-->
<component name="extracellular_potassium_concentration"
cmeta:id="extracellular_potassium_concentration">
<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="#extracellular_potassium_concentration">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
A representation of extracellular potassium ion concentration based
on a homogeneous three-compartment model.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<!-- This variable is defined here and used in other components -->
<variable
name="Kc" public_interface="out"
initial_value="4.0" units="mM" />
<!-- These variables are defined here and only used internally. -->
<variable name="Am" public_interface="in" units="per_mm" />
<variable name="V_i" public_interface="in" units="dimensionless" />
<variable name="Kb" initial_value="4.0" units="mM" />
<variable name="i_mK" public_interface="out" units="uA_per_mm2" />
<variable name="P" initial_value="0.7" units="dimensionless" />
<!-- These variables are imported from other components. -->
<variable name="time" public_interface="in" units="ms" />
<variable name="F" public_interface="in" units="faradays_constant_units" />
<variable name="i_K1" public_interface="in" units="uA_per_mm2" />
<variable name="i_K" public_interface="in" units="uA_per_mm2" />
<variable name="i_fK" public_interface="in" units="uA_per_mm2" />
<variable name="i_siK" public_interface="in" units="uA_per_mm2" />
<variable name="i_NaK" public_interface="in" units="uA_per_mm2" />
<variable name="i_to" 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="#Kc_diff_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The rate of change in the cleft potassium concentration is the
combination of potassium ions crossing the cellular membrane and
ions diffusing into the volume from the bulk extracellular stores.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="Kc_diff_eq">
<apply id="Kc_diff_eq"><eq />
<apply><diff />
<bvar><ci> time </ci></bvar>
<ci> Kc </ci>
</apply>
<apply><plus />
<apply><minus />
<apply><times />
<ci> P </ci>
<apply><minus />
<ci> Kc </ci>
<ci> Kb </ci>
</apply>
</apply>
</apply>
<apply><divide />
<apply><times/>
<ci>Am</ci>
<ci> i_mK </ci>
</apply>
<apply><times />
<ci> V_i </ci>
<ci> F </ci>
</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_mK_calculation_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The total transmembrane potassium current.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="i_mK_calculation_eq">
<apply id="i_mK_calculation"><eq />
<ci> i_mK </ci>
<apply><minus />
<apply><plus />
<ci> i_K1 </ci>
<ci> i_K </ci>
<ci> i_fK </ci>
<ci> i_siK </ci>
<ci> i_to </ci>
</apply>
<apply><times />
<cn cellml:units="dimensionless"> 2.0 </cn>
<ci> i_NaK </ci>
</apply>
</apply>
</apply>
</math>
</component>
<!--
The intracellular potassium concentration is related to the total potassium
ion membrane flux.
-->
<component name="intracellular_potassium_concentration"
cmeta:id="intracellular_potassium_concentration">
<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="#intracellular_potassium_concentration">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The change in intracellular potassium ion concentration.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<!-- This variable is defined here and used in other components -->
<variable
name="Ki" public_interface="out"
initial_value="140.0" units="mM" />
<!-- These variables are defined here and only used internally. -->
<variable name="Am" public_interface="in" units="per_mm" />
<variable name="V_i" public_interface="in" units="dimensionless" />
<variable name="i_mK" public_interface="in" units="uA_per_mm2" />
<!-- These variables are imported from other components. -->
<variable name="time" public_interface="in" units="ms" />
<variable name="F" public_interface="in" units="faradays_constant_units" />
<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="#Ki_diff_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The rate of change of intracellular potassium concentration is the
sum of the ions crossing the membrane.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="Ki_diff_eq">
<apply id="Ki_diff_eq"><eq />
<apply><diff />
<bvar><ci> time </ci></bvar>
<ci> Ki </ci>
</apply>
<apply><divide />
<apply><minus />
<apply><times/>
<ci>Am</ci>
<ci> i_mK </ci>
</apply>
</apply>
<apply><times />
<ci> V_i </ci>
<ci> F </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="volumes" cmeta:id="volumes">
<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="#volumes">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
A component used to group the geometry parameters and calculations.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<variable name="radius" initial_value="50e-3" units="mm"/>
<variable name="length" initial_value="2" units="mm"/>
<variable name="V_ecs" initial_value="0.1" units="dimensionless"/>
<variable name="Am" initial_value="40.0" public_interface="out" units="per_mm"/>
<variable name="V_i" public_interface="out" units="dimensionless" />
<variable name="V_e" public_interface="out" units="dimensionless" />
<variable name="V_up" public_interface="out" units="dimensionless" />
<variable name="V_rel" public_interface="out" 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="#V_i_calculation_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The intracellular volume fraction.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="V_i_calculation_eq">
<apply id="V_i_calculation"><eq />
<ci>V_i</ci>
<apply><minus/>
<cn cellml:units="dimensionless">1.0</cn>
<ci>V_ecs</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="#V_e_calculation_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The extracellular volume fraction.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="V_e_calculation_eq">
<apply id="V_e_calculation"><eq />
<ci>V_e</ci>
<ci>V_ecs</ci>
</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="#V_up_calculation_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The calcium uptake store volume fraction.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="V_up_calculation_eq">
<apply id="V_up_calculation"><eq />
<ci>V_up</ci>
<apply><times/>
<cn cellml:units="dimensionless">0.05</cn>
<ci>V_i</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="#V_rel_calculation_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The calcium release store volume fraction.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="V_rel_calculation_eq">
<apply id="V_rel_calculation"><eq />
<ci>V_rel</ci>
<apply><times/>
<cn cellml:units="dimensionless">0.02</cn>
<ci>V_i</ci>
</apply>
</apply>
</math>
</component>
<!--
The following <group> element specifies a single containment hierarchy
that encompasses all of the components in the model, with the exception of
the "environment" component.
-->
<group>
<relationship_ref relationship="containment" />
<component_ref component="membrane">
<component_ref component="hyperpolarising_activated_current">
<component_ref component="hyperpolarising_activated_current_y_gate" />
</component_ref>
<component_ref component="time_dependent_potassium_current">
<component_ref component="time_dependent_potassium_current_x_gate" />
</component_ref>
<component_ref component="time_independent_potassium_current" />
<component_ref component="transient_outward_current">
<component_ref component="transient_outward_current_r_gate" />
</component_ref>
<component_ref component="sodium_background_current" />
<component_ref component="calcium_background_current" />
<component_ref component="sodium_potassium_pump" />
<component_ref component="Na_Ca_exchanger" />
<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_f2_gate" />
</component_ref>
<component_ref component="intracellular_sodium_concentration" />
<component_ref component="extracellular_sodium_concentration" />
<component_ref component="intracellular_calcium_concentration" />
<component_ref component="extracellular_calcium_concentration" />
<component_ref component="extracellular_potassium_concentration" />
<component_ref component="intracellular_potassium_concentration" />
</component_ref>
</group>
<!--
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="hyperpolarising_activated_current">
<component_ref component="hyperpolarising_activated_current_y_gate" />
</component_ref>
<component_ref component="time_dependent_potassium_current">
<component_ref component="time_dependent_potassium_current_x_gate" />
</component_ref>
<component_ref component="transient_outward_current">
<component_ref component="transient_outward_current_r_gate" />
</component_ref>
<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_f2_gate" />
</component_ref>
</group>
<!--
"time" is passed from the "environment" component into the
"membrane" and current components.
-->
<connection>
<map_components
component_1="membrane" component_2="environment" />
<map_variables variable_1="time" variable_2="time" />
</connection>
<connection>
<map_components
component_1="hyperpolarising_activated_current" component_2="environment" />
<map_variables variable_1="time" variable_2="time" />
</connection>
<connection>
<map_components
component_1="time_dependent_potassium_current" component_2="environment" />
<map_variables variable_1="time" variable_2="time" />
</connection>
<connection>
<map_components
component_1="time_independent_potassium_current" component_2="environment" />
<map_variables variable_1="time" variable_2="time" />
</connection>
<connection>
<map_components
component_1="transient_outward_current" component_2="environment" />
<map_variables variable_1="time" variable_2="time" />
</connection>
<connection>
<map_components
component_1="sodium_background_current" component_2="environment" />
<map_variables variable_1="time" variable_2="time" />
</connection>
<connection>
<map_components
component_1="calcium_background_current" component_2="environment" />
<map_variables variable_1="time" variable_2="time" />
</connection>
<connection>
<map_components
component_1="sodium_potassium_pump" component_2="environment" />
<map_variables variable_1="time" variable_2="time" />
</connection>
<connection>
<map_components
component_1="Na_Ca_exchanger" component_2="environment" />
<map_variables variable_1="time" variable_2="time" />
</connection>
<connection>
<map_components
component_1="fast_sodium_current" component_2="environment" />
<map_variables variable_1="time" variable_2="time" />
</connection>
<connection>
<map_components
component_1="secondary_inward_current" component_2="environment" />
<map_variables variable_1="time" variable_2="time" />
</connection>
<connection>
<map_components
component_1="intracellular_sodium_concentration" component_2="environment" />
<map_variables variable_1="time" variable_2="time" />
</connection>
<connection>
<map_components
component_1="intracellular_calcium_concentration" component_2="environment" />
<map_variables variable_1="time" variable_2="time" />
</connection>
<connection>
<map_components
component_1="extracellular_potassium_concentration" component_2="environment" />
<map_variables variable_1="time" variable_2="time" />
</connection>
<connection>
<map_components
component_1="transient_outward_current" component_2="extracellular_potassium_concentration" />
<map_variables variable_1="i_to" variable_2="i_to" />
</connection>
<connection>
<map_components
component_1="intracellular_potassium_concentration" component_2="environment" />
<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="hyperpolarising_activated_current" component_2="membrane" />
<map_variables variable_1="V" variable_2="V" />
<map_variables variable_1="R" variable_2="R" />
<map_variables variable_1="T" variable_2="T" />
<map_variables variable_1="F" variable_2="F" />
<map_variables variable_1="i_f" variable_2="i_f" />
</connection>
<connection>
<map_components
component_1="time_dependent_potassium_current" component_2="membrane" />
<map_variables variable_1="V" variable_2="V" />
<map_variables variable_1="i_K" variable_2="i_K" />
<map_variables variable_1="R" variable_2="R" />
<map_variables variable_1="T" variable_2="T" />
<map_variables variable_1="F" variable_2="F" />
</connection>
<connection>
<map_components
component_1="time_independent_potassium_current" component_2="membrane" />
<map_variables variable_1="V" variable_2="V" />
<map_variables variable_1="R" variable_2="R" />
<map_variables variable_1="T" variable_2="T" />
<map_variables variable_1="F" variable_2="F" />
<map_variables variable_1="i_K1" variable_2="i_K1" />
</connection>
<connection>
<map_components
component_1="transient_outward_current" component_2="membrane" />
<map_variables variable_1="V" variable_2="V" />
<map_variables variable_1="R" variable_2="R" />
<map_variables variable_1="T" variable_2="T" />
<map_variables variable_1="F" variable_2="F" />
<map_variables variable_1="i_to" variable_2="i_to" />
</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="calcium_background_current" component_2="membrane" />
<map_variables variable_1="V" variable_2="V" />
<map_variables variable_1="R" variable_2="R" />
<map_variables variable_1="T" variable_2="T" />
<map_variables variable_1="F" variable_2="F" />
<map_variables variable_1="i_Ca_b" variable_2="i_Ca_b" />
</connection>
<connection>
<map_components
component_1="sodium_potassium_pump" component_2="membrane" />
<map_variables variable_1="V" variable_2="V" />
<map_variables variable_1="i_NaK" variable_2="i_NaK" />
</connection>
<connection>
<map_components
component_1="Na_Ca_exchanger" component_2="membrane" />
<map_variables variable_1="V" variable_2="V" />
<map_variables variable_1="i_NaCa" variable_2="i_NaCa" />
<map_variables variable_1="R" variable_2="R" />
<map_variables variable_1="F" variable_2="F" />
<map_variables variable_1="T" variable_2="T" />
</connection>
<connection>
<map_components
component_1="fast_sodium_current" component_2="membrane" />
<map_variables variable_1="V" variable_2="V" />
<map_variables variable_1="i_Na" variable_2="i_Na" />
<map_variables variable_1="R" variable_2="R" />
<map_variables variable_1="F" variable_2="F" />
<map_variables variable_1="T" variable_2="T" />
</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" />
<map_variables variable_1="R" variable_2="R" />
<map_variables variable_1="F" variable_2="F" />
<map_variables variable_1="T" variable_2="T" />
</connection>
<connection>
<map_components
component_1="intracellular_sodium_concentration" component_2="membrane" />
<map_variables variable_1="F" variable_2="F" />
</connection>
<connection>
<map_components
component_1="intracellular_calcium_concentration" component_2="membrane" />
<map_variables variable_1="V" variable_2="V" />
<map_variables variable_1="F" variable_2="F" />
</connection>
<connection>
<map_components
component_1="extracellular_potassium_concentration" component_2="membrane" />
<map_variables variable_1="F" variable_2="F" />
</connection>
<connection>
<map_components
component_1="intracellular_potassium_concentration" component_2="membrane" />
<map_variables variable_1="F" variable_2="F" />
</connection>
<!-- A few variables are passed between the other components. -->
<connection>
<map_components
component_1="hyperpolarising_activated_current" component_2="extracellular_potassium_concentration" />
<map_variables variable_1="Kc" variable_2="Kc" />
<map_variables variable_1="i_fK" variable_2="i_fK" />
</connection>
<connection>
<map_components
component_1="hyperpolarising_activated_current" component_2="intracellular_potassium_concentration" />
<map_variables variable_1="Ki" variable_2="Ki" />
</connection>
<connection>
<map_components
component_1="hyperpolarising_activated_current" component_2="time_independent_potassium_current" />
<map_variables variable_1="E_K" variable_2="E_K" />
</connection>
<connection>
<map_components
component_1="hyperpolarising_activated_current" component_2="sodium_background_current" />
<map_variables variable_1="E_Na" variable_2="E_Na" />
</connection>
<connection>
<map_components
component_1="hyperpolarising_activated_current" component_2="Na_Ca_exchanger" />
<map_variables variable_1="E_Na" variable_2="E_Na" />
</connection>
<connection>
<map_components
component_1="hyperpolarising_activated_current" component_2="intracellular_sodium_concentration" />
<map_variables variable_1="i_fNa" variable_2="i_fNa" />
<map_variables variable_1="Nai" variable_2="Nai" />
</connection>
<connection>
<map_components
component_1="hyperpolarising_activated_current" component_2="extracellular_sodium_concentration" />
<map_variables variable_1="Nao" variable_2="Nao" />
</connection>
<connection>
<map_components
component_1="calcium_background_current" component_2="Na_Ca_exchanger" />
<map_variables variable_1="E_Ca" variable_2="E_Ca" />
</connection>
<connection>
<map_components
component_1="calcium_background_current" component_2="extracellular_calcium_concentration" />
<map_variables variable_1="Cao" variable_2="Cao" />
</connection>
<connection>
<map_components
component_1="time_dependent_potassium_current" component_2="extracellular_potassium_concentration" />
<map_variables variable_1="Kc" variable_2="Kc" />
<map_variables variable_1="i_K" variable_2="i_K" />
</connection>
<connection>
<map_components
component_1="time_dependent_potassium_current" component_2="intracellular_potassium_concentration" />
<map_variables variable_1="Ki" variable_2="Ki" />
</connection>
<connection>
<map_components
component_1="time_independent_potassium_current" component_2="extracellular_potassium_concentration" />
<map_variables variable_1="Kc" variable_2="Kc" />
<map_variables variable_1="i_K1" variable_2="i_K1" />
</connection>
<connection>
<map_components
component_1="transient_outward_current" component_2="extracellular_potassium_concentration" />
<map_variables variable_1="Kc" variable_2="Kc" />
</connection>
<connection>
<map_components
component_1="transient_outward_current" component_2="intracellular_potassium_concentration" />
<map_variables variable_1="Ki" variable_2="Ki" />
</connection>
<connection>
<map_components
component_1="transient_outward_current" component_2="intracellular_calcium_concentration" />
<map_variables variable_1="Cai" variable_2="Cai" />
</connection>
<connection>
<map_components
component_1="sodium_background_current" component_2="intracellular_sodium_concentration" />
<map_variables variable_1="i_Na_b" variable_2="i_Na_b" />
</connection>
<connection>
<map_components
component_1="calcium_background_current" component_2="intracellular_calcium_concentration" />
<map_variables variable_1="i_Ca_b" variable_2="i_Ca_b" />
<map_variables variable_1="Cai" variable_2="Cai" />
</connection>
<connection>
<map_components
component_1="sodium_potassium_pump" component_2="extracellular_potassium_concentration" />
<map_variables variable_1="i_NaK" variable_2="i_NaK" />
<map_variables variable_1="Kc" variable_2="Kc" />
</connection>
<connection>
<map_components
component_1="sodium_potassium_pump" component_2="intracellular_sodium_concentration" />
<map_variables variable_1="i_NaK" variable_2="i_NaK" />
<map_variables variable_1="Nai" variable_2="Nai" />
</connection>
<connection>
<map_components
component_1="Na_Ca_exchanger" component_2="extracellular_sodium_concentration" />
<map_variables variable_1="Nao" variable_2="Nao" />
</connection>
<connection>
<map_components
component_1="Na_Ca_exchanger" component_2="extracellular_calcium_concentration" />
<map_variables variable_1="Cao" variable_2="Cao" />
</connection>
<connection>
<map_components
component_1="Na_Ca_exchanger" component_2="intracellular_sodium_concentration" />
<map_variables variable_1="n_NaCa" variable_2="n_NaCa" />
<map_variables variable_1="i_NaCa" variable_2="i_NaCa" />
<map_variables variable_1="Nai" variable_2="Nai" />
</connection>
<connection>
<map_components
component_1="Na_Ca_exchanger" component_2="intracellular_calcium_concentration" />
<map_variables variable_1="n_NaCa" variable_2="n_NaCa" />
<map_variables variable_1="i_NaCa" variable_2="i_NaCa" />
<map_variables variable_1="Cai" variable_2="Cai" />
</connection>
<connection>
<map_components
component_1="fast_sodium_current" component_2="intracellular_sodium_concentration" />
<map_variables variable_1="i_Na" variable_2="i_Na" />
<map_variables variable_1="Nai" variable_2="Nai" />
</connection>
<connection>
<map_components
component_1="fast_sodium_current" component_2="extracellular_sodium_concentration" />
<map_variables variable_1="Nao" variable_2="Nao" />
</connection>
<connection>
<map_components
component_1="fast_sodium_current" component_2="intracellular_potassium_concentration" />
<map_variables variable_1="Ki" variable_2="Ki" />
</connection>
<connection>
<map_components
component_1="fast_sodium_current" component_2="extracellular_potassium_concentration" />
<map_variables variable_1="Kc" variable_2="Kc" />
</connection>
<connection>
<map_components
component_1="secondary_inward_current" component_2="intracellular_calcium_concentration" />
<map_variables variable_1="i_siCa" variable_2="i_siCa" />
<map_variables variable_1="Cai" variable_2="Cai" />
</connection>
<connection>
<map_components
component_1="secondary_inward_current" component_2="extracellular_calcium_concentration" />
<map_variables variable_1="Cao" variable_2="Cao" />
</connection>
<connection>
<map_components
component_1="secondary_inward_current" component_2="extracellular_sodium_concentration" />
<map_variables variable_1="Nao" variable_2="Nao" />
</connection>
<connection>
<map_components
component_1="secondary_inward_current" component_2="extracellular_potassium_concentration" />
<map_variables variable_1="i_siK" variable_2="i_siK" />
<map_variables variable_1="Kc" variable_2="Kc" />
</connection>
<connection>
<map_components
component_1="secondary_inward_current" component_2="intracellular_sodium_concentration" />
<map_variables variable_1="i_siNa" variable_2="i_siNa" />
<map_variables variable_1="Nai" variable_2="Nai" />
</connection>
<connection>
<map_components
component_1="secondary_inward_current" component_2="intracellular_potassium_concentration" />
<map_variables variable_1="Ki" variable_2="Ki" />
</connection>
<!--
Several variables are passed between parent components and their
encapsulated gates.
-->
<connection>
<map_components
component_1="hyperpolarising_activated_current" component_2="hyperpolarising_activated_current_y_gate" />
<map_variables variable_1="y" variable_2="y" />
<map_variables variable_1="time" variable_2="time" />
<map_variables variable_1="V" variable_2="V" />
</connection>
<connection>
<map_components
component_1="time_dependent_potassium_current" component_2="time_dependent_potassium_current_x_gate" />
<map_variables variable_1="x" variable_2="x" />
<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_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" />
<map_variables variable_1="Cai" variable_2="Cai" />
</connection>
<connection>
<map_components
component_1="secondary_inward_current" component_2="secondary_inward_current_f2_gate" />
<map_variables variable_1="f2" variable_2="f2" />
<map_variables variable_1="time" variable_2="time" />
<map_variables variable_1="V" variable_2="V" />
<map_variables variable_1="Cai" variable_2="Cai" />
</connection>
<connection>
<map_components
component_1="transient_outward_current" component_2="transient_outward_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="volumes" component_2="intracellular_sodium_concentration" />
<map_variables variable_1="V_i" variable_2="V_i" />
<map_variables variable_1="Am" variable_2="Am" />
</connection>
<connection>
<map_components
component_1="volumes" component_2="intracellular_calcium_concentration" />
<map_variables variable_1="V_i" variable_2="V_i" />
<map_variables variable_1="V_up" variable_2="V_up" />
<map_variables variable_1="V_rel" variable_2="V_rel" />
<map_variables variable_1="Am" variable_2="Am" />
</connection>
<connection>
<map_components
component_1="volumes" component_2="extracellular_potassium_concentration" />
<map_variables variable_1="V_i" variable_2="V_i" />
<map_variables variable_1="Am" variable_2="Am" />
</connection>
<connection>
<map_components
component_1="volumes" component_2="intracellular_potassium_concentration" />
<map_variables variable_1="V_i" variable_2="V_i" />
<map_variables variable_1="Am" variable_2="Am" />
</connection>
<connection>
<map_components
component_1="extracellular_potassium_concentration" component_2="intracellular_potassium_concentration" />
<map_variables variable_1="i_mK" variable_2="i_mK" />
</connection>
</model>
