- Author:
- David Nickerson <david.nickerson@gmail.com>
- Date:
- 2021-09-17 15:50:49+12:00
- Desc:
- tweak html formatting
- Permanent Source URI:
- https://models.physiomeproject.org/workspace/a1/rawfile/1b3862589abf79ae9119ee0b5e99a8b785d762e1/models/1998_jafri/model.xml
<?xml version="1.0" encoding="iso-8859-1"?>
<!-- FILE : jafri_rice_winslow_model_1998.xml
CREATED : September 2001
LAST MODIFIED : 30th July 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 the mammalian
ventricular action potential based on the Jafri-Rice-Winslow model, 1998. This
model is a development of the LR-II model. In particular, it makes an accurate
model of the membrane currents and adds a more sophisticated model of calcium
ion handling.
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 tau_y_calculation after checking mathml using the
validator.
04/01/2002 - CML - Altered some of the connections.
21/01/2002 - AAC - Updated metadata to conform to the 16/1/02 CellML Metadata
1.0 Specification.
25/02/2002 - CML - Corrected several equations.
28/02/2002 - CML - Corrected several equations, variable units and their
initial values.
06/05/2002 - CML - Added some initial values.
22/07/2002 - CML - Added more metadata.
09/04/2003 - AAC - Added publication date information.
04/06/2003 - CML - Fixed MathML in a few components.
30/07/2003 - CML - Altered a few equations.
-->
<model
name="jafri_rice_winslow_model_1998"
cmeta:id="jafri_rice_winslow_model_1998"
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>2001-09-24</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>
Corrected 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>2003-07-30</dcterms:W3CDTF>
</dcterms:modified>
</cmeta:modification>
<cmeta:modification rdf:parseType="Resource">
<rdf:value>
Corrected equations: alpha_j_calculation and beta_j_calculation in
fast_sodium_current_j_gate, alpha_X_calculation and beta_X_calculation in time_dependent_potassium_current_X_gate, and f_NaK_calculation and
i_NaK_calculation in Ca_release_current_from_JSR.
</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>2003-06-04</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, variable units and their initial values.
</rdf:value>
<cmeta:modifier rdf:parseType="Resource">
<vCard:N rdf:parseType="Resource">
<vCard:Family>Lloyd</vCard:Family>
<vCard:Given>Catherine</vCard:Given>
<vCard:Other>May</vCard:Other>
</vCard:N>
</cmeta:modifier>
<dcterms:modified rdf:parseType="Resource">
<dcterms:W3CDTF>2002-02-28</dcterms:W3CDTF>
</dcterms:modified>
</cmeta:modification>
<cmeta:modification rdf:parseType="Resource">
<rdf:value>
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>
Altered some of the connections.
</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>2002-01-04</dcterms:W3CDTF>
</dcterms:modified>
</cmeta:modification>
<cmeta:modification rdf:parseType="Resource">
<rdf:value>
Changed tau_y_calculation after checking mathml using the 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>
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 "jafri_rice_winslow_model_1998", which is declared on
the <model> element.
-->
<rdf:Description rdf:about="#jafri_rice_winslow_model_1998">
<!-- A human readable name for the model. -->
<dc:title>
The Jafri-Rice-Winslow Model for Calcium Regulation in the Ventricular
Myocyte, 1997
</dc:title>
<!-- A comment regarding the model. -->
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
This is the CellML description of Jafri, Rice and Winslow's
mathematical model for calcium regulation in the ventricular myocyte.
It is based on an accurate model of the membrane currents and adds a
more sophisticated model of calcium handling. The JRW model is based
on the LR-II model for ventricular action potentials, with several
modifications.
</rdf:value>
<!-- The creator of the comment. -->
<dc:creator rdf:parseType="Resource">
<vCard:FN>Catherine Lloyd</vCard:FN>
</dc:creator>
</cmeta:comment>
<!-- The model is relevant to all mammals. -->
<cmeta:species>Mammalia</cmeta:species>
<cmeta:bio_entity>Ventricular Myocyte</cmeta:bio_entity>
<!--
The CellML Metadata Specification recommends that bibliographic metadata
is used to provide information about the original model reference. The
"identifier" attribute on the "BibliographicReference" class provides an
elegant way to identify a cited reference using a database identifier such as Pubmed. All associated data such as author, journal title,
date, etc can be looked up on the database.
-->
<bqs:reference rdf:parseType="Resource">
<bqs:Pubmed_id>9512016</bqs:Pubmed_id>
</bqs:reference>
<cs:simulation>
<rdf:Description rdf:ID="simulation">
<cs:multistepMethod>bdf</cs:multistepMethod>
<cs:iterationMethod>newton</cs:iterationMethod>
<cs:linearSolver>dense</cs:linearSolver>
<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">
700
</cs:endingValue>
</rdf:Description>
</cs:boundIntervals>
</rdf:Description>
</cs:simulation>
</rdf:Description>
</rdf:RDF>
<!--
Below, we define some additional units for association with variables and
constants within the model. The identifiers are fairly self-explanatory.
-->
<units name="ms">
<unit prefix="milli" units="second" />
</units>
<units name="per_ms">
<unit prefix="milli" units="second" exponent="-1" />
</units>
<units name="per_mm">
<unit prefix="milli" units="metre" exponent="-1" />
</units>
<units name="mV">
<unit prefix="milli" units="volt" />
</units>
<units name="per_mV">
<unit prefix="milli" units="volt" exponent="-1" />
</units>
<units name="per_mV_ms">
<unit units="mV" exponent="-1" />
<unit units="ms" exponent="-1" />
</units>
<units name="mS_per_mm2">
<unit prefix="milli" units="siemens" />
<unit prefix="milli" units="metre" exponent="-2" />
</units>
<units name="mm2">
<unit prefix="milli" units="metre" exponent="2" />
</units>
<units name="mM">
<unit prefix="nano" units="mole" />
<unit prefix="milli" units="metre" exponent="-3" />
</units>
<units name="mM_per_ms">
<unit units="mM" />
<unit units="ms" exponent="-1" />
</units>
<units name="per_mM_per_ms">
<unit units="mM" exponent="-1" />
<unit units="ms" exponent="-1" />
</units>
<units name="per_mM3_per_ms">
<unit units="mM" exponent="-3" />
<unit units="ms" exponent="-1" />
</units>
<units name="per_mM4_per_ms">
<unit units="mM" exponent="-4" />
<unit units="ms" exponent="-1" />
</units>
<units name="uF_per_mm2">
<unit prefix="micro" units="farad" />
<unit prefix="milli" units="metre" exponent="-2" />
</units>
<units name="uA_per_mm2">
<unit prefix="micro" units="ampere" />
<unit prefix="milli" units="metre" exponent="-2" />
</units>
<units name="mm_per_ms">
<unit prefix="milli" units="metre" />
<unit units="ms" exponent="-1" />
</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>
<units name="uA_per_mmcu">
<unit prefix="micro" units="ampere" />
<unit prefix="milli" units="metre" exponent="-3"/>
</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">
<variable cmeta:id="time" name="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 main component of the model which defines 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="-84.1638" units="mV" />
<variable
name="R" public_interface="out"
initial_value="8.3145e3" units="gas_constant_units" />
<variable
name="T" public_interface="out"
initial_value="310.0" units="kelvin" />
<variable
name="F" public_interface="out"
initial_value="9.6845e4" units="faradays_constant_units" />
<!-- These variables are imported from other components. -->
<variable name="time" public_interface="in" units="ms" />
<variable name="i_Na" public_interface="in" units="uA_per_mm2" />
<variable name="i_Ca_L_Ca" public_interface="in" units="uA_per_mm2" />
<variable name="i_Ca_L_K" 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_NaCa" public_interface="in" units="uA_per_mm2" />
<variable name="i_Kp" public_interface="in" units="uA_per_mm2" />
<variable name="i_p_Ca" 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_ns_Ca" public_interface="in" units="uA_per_mm2" />
<variable name="Am" public_interface="in" units="per_mm"/>
<!-- These variables is defined here and only used internally. -->
<variable name="Cm" initial_value="0.01" units="uF_per_mm2" />
<variable name="I_stim" units="uA_per_mm2" />
<variable name="stimTime" initial_value="100.0" units="ms"/>
<variable name="stimDuration" initial_value="1.0" units="ms"/>
<variable name="stimCurrent" initial_value="250" units="uA_per_mmcu"/>
<rdf:RDF
xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
xmlns:cmeta="http://www.cellml.org/metadata/1.0#">
<rdf:Description rdf:about="#membrane_voltage_diff_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The kinetics of the transmembrane potential, defined as the sum of
all the sarcolemmal currents and an applied stimulus current.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="membrane_voltage_diff_eq">
<apply id="membrane_voltage_diff_eq"><eq />
<apply><diff />
<bvar><ci> time </ci></bvar>
<ci> V </ci>
</apply>
<apply><divide />
<apply><minus />
<ci>I_stim</ci>
<apply><plus />
<ci> i_Na </ci>
<ci> i_Ca_L_Ca </ci>
<ci> i_Ca_L_K </ci>
<ci> i_K </ci>
<ci> i_NaCa </ci>
<ci> i_K1 </ci>
<ci> i_Kp </ci>
<ci> i_p_Ca </ci>
<ci> i_Na_b </ci>
<ci> i_Ca_b </ci>
<ci> i_NaK </ci>
<ci> i_ns_Ca </ci>
</apply>
</apply>
<ci> Cm </ci>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="IStim_for_cmiss_eq">
<apply id="stimulus_calculation"><eq />
<ci>I_stim</ci>
<piecewise>
<piece>
<apply><divide/>
<ci>stimCurrent</ci>
<ci>Am</ci>
</apply>
<apply><and/>
<apply><geq/>
<ci>time</ci>
<ci>stimTime</ci>
</apply>
<apply><leq/>
<ci>time</ci>
<apply><plus/>
<ci>stimTime</ci>
<ci>stimDuration</ci>
</apply>
</apply>
</apply>
</piece>
<otherwise>
<cn cellml:units="uA_per_mmsq">0.0</cn>
</otherwise>
</piecewise>
</apply>
</math>
</component>
<component name="fast_sodium_current" cmeta:id="fast_sodium_current">
<rdf:RDF
xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
xmlns:cmeta="http://www.cellml.org/metadata/1.0#">
<rdf:Description rdf:about="#fast_sodium_current">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The fast sodium current component contains the differential
equations governing the influx of sodium ions through the cell
surface membrane into the cell.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<!-- These variables are defined here and used in other components. -->
<variable name="i_Na" public_interface="out" units="uA_per_mm2" />
<variable name="E_Na" public_interface="out" units="mV" />
<!-- This variable is defined here and only used internally. -->
<variable name="g_Na" initial_value="0.128" units="mS_per_mm2" />
<!--
Time is imported from the environment, and membrane potential is
imported from the membrane component. These variables are used in the
"sodium_current" parent component, which also acts as an interface,
passing the variables to its encapsulated gate components.
-->
<variable
name="time" public_interface="in"
private_interface="out" units="ms" />
<variable
name="V" public_interface="in"
private_interface="out" units="mV" />
<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="Nai" public_interface="in" units="mM" />
<variable name="Nao" 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" />
<variable name="j" private_interface="in" units="dimensionless" />
<rdf:RDF
xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
xmlns:cmeta="http://www.cellml.org/metadata/1.0#">
<rdf:Description rdf:about="#i_Na_calculation_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
Calculation of the fast sodium current using the three
Hodkin-Huxley type voltage-dependent gating variables m, h, and j.
</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>
<ci> j </ci>
<apply><minus />
<ci> V </ci>
<ci> E_Na </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_Na_calculation_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The sodium reversal potential.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="E_Na_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>
</component>
<!--
The "fast_sodium_current_m_gate" is the m gate encapsulated inside the fast
sodium current.
-->
<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 current -
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="0.0328302" 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"> 0.32 </cn>
<apply><plus />
<ci> V </ci>
<cn cellml:units="mV"> 47.13 </cn>
</apply>
</apply>
<apply><minus />
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply><exp />
<apply><times />
<cn cellml:units="per_mV"> -0.1 </cn>
<apply><plus />
<ci> V </ci>
<cn cellml:units="mV"> 47.13 </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"> 0.08 </cn>
<apply><exp />
<apply><divide />
<apply><minus />
<ci> V </ci>
</apply>
<cn cellml:units="mV"> 11.0 </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="#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="per_mV"> 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 h gate encapsulated in
the fast sodium current.
-->
<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="0.988354" 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>
<piecewise>
<piece>
<apply><times />
<cn cellml:units="per_ms"> 0.135 </cn>
<apply><exp />
<apply><divide />
<apply><plus />
<cn cellml:units="mV"> 80.0 </cn>
<ci> V </ci>
</apply>
<cn cellml:units="mV"> -6.8 </cn>
</apply>
</apply>
</apply>
<apply><lt />
<ci> V </ci>
<cn cellml:units="mV"> -40.0 </cn>
</apply>
</piece>
<otherwise>
<cn cellml:units="per_ms"> 0.0 </cn>
</otherwise>
</piecewise>
</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>
<piecewise>
<piece>
<apply><plus />
<apply><times />
<cn cellml:units="per_ms"> 3.56 </cn>
<apply><exp />
<apply><times />
<cn cellml:units="mV"> 0.079 </cn>
<ci> V </ci>
</apply>
</apply>
</apply>
<apply><times />
<cn cellml:units="per_ms"> 310000.0 </cn>
<apply><exp />
<apply><times />
<cn cellml:units="per_mV"> 0.35 </cn>
<ci> V </ci>
</apply>
</apply>
</apply>
</apply>
<apply><lt />
<ci> V </ci>
<cn cellml:units="mV"> -40.0 </cn>
</apply>
</piece>
<otherwise>
<apply><divide />
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply><times />
<cn cellml:units="ms"> 0.13 </cn>
<apply><plus />
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply><exp />
<apply><divide />
<apply><plus />
<ci> V </ci>
<cn cellml:units="mV"> 10.66 </cn>
</apply>
<cn cellml:units="mV"> -11.1 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</otherwise>
</piecewise>
</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>
<!--
The "fast_sodium_current_j_gate" component is the j gate encapsulated in
the fast sodium current.
-->
<component name="fast_sodium_current_j_gate"
cmeta:id="fast_sodium_current_j_gate">
<rdf:RDF
xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
xmlns:cmeta="http://www.cellml.org/metadata/1.0#">
<rdf:Description rdf:about="#fast_sodium_current_j_gate">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The voltage-dependent slow inactivation gate for the fast sodium
current - the j gate.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<!-- This variable is defined here and used in other components. -->
<variable
name="j" public_interface="out"
initial_value="0.992540" units="dimensionless" />
<!-- These variables are defined here and only used internally. -->
<variable name="alpha_j" units="per_ms" />
<variable name="beta_j" units="per_ms" />
<!--
These variables are imported from 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_j_calculation_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The opening rate of the j gate.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="alpha_j_calculation_eq">
<apply id="alpha_j_calculation"><eq />
<ci> alpha_j </ci>
<piecewise>
<piece>
<apply><times />
<apply><minus />
<apply><times />
<cn cellml:units="per_mV_ms"> -127140.0 </cn>
<apply><exp />
<apply><times />
<cn cellml:units="per_mV"> 0.2444 </cn>
<ci> V </ci>
</apply>
</apply>
</apply>
<apply><times />
<cn cellml:units="per_mV_ms"> 0.00003474 </cn>
<apply><exp />
<apply><times />
<cn cellml:units="per_mV"> -0.04391 </cn>
<ci> V </ci>
</apply>
</apply>
</apply>
</apply>
<apply><divide />
<apply><plus />
<ci> V </ci>
<cn cellml:units="mV"> 37.78 </cn>
</apply>
<apply><plus />
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply><exp />
<apply><times />
<cn cellml:units="per_mV"> 0.311 </cn>
<apply><plus />
<ci> V </ci>
<cn cellml:units="mV"> 79.23 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply><lt />
<ci> V </ci>
<cn cellml:units="mV"> -40.0 </cn>
</apply>
</piece>
<otherwise>
<cn cellml:units="per_ms"> 0.0 </cn>
</otherwise>
</piecewise>
</apply>
</math>
<rdf:RDF
xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
xmlns:cmeta="http://www.cellml.org/metadata/1.0#">
<rdf:Description rdf:about="#beta_j_calculation_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The closing rate of the j gate.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="beta_j_calculation_eq">
<apply id="beta_j_calculation"><eq />
<ci> beta_j </ci>
<piecewise>
<piece>
<apply><times />
<cn cellml:units="per_ms"> 0.1212 </cn>
<apply><divide />
<apply><exp />
<apply><times />
<cn cellml:units="per_mV"> -0.01052 </cn>
<ci> V </ci>
</apply>
</apply>
<apply><plus />
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply><exp />
<apply><times />
<cn cellml:units="per_mV"> -0.1378 </cn>
<apply><plus />
<ci> V </ci>
<cn cellml:units="mV"> 40.14 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply><lt />
<ci> V </ci>
<cn cellml:units="mV"> -40.0 </cn>
</apply>
</piece>
<otherwise>
<apply><times />
<cn cellml:units="per_ms"> 0.3 </cn>
<apply><divide />
<apply><exp />
<apply><times />
<cn cellml:units="per_mV"> -0.0000002535 </cn>
<ci> V </ci>
</apply>
</apply>
<apply><plus />
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply><exp />
<apply><times />
<cn cellml:units="per_mV"> -0.1 </cn>
<apply><plus />
<ci> V </ci>
<cn cellml:units="mV"> 32.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</otherwise>
</piecewise>
</apply>
</math>
<rdf:RDF
xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
xmlns:cmeta="http://www.cellml.org/metadata/1.0#">
<rdf:Description rdf:about="#dj_dt_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The kinetics of the j gate.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="dj_dt_eq">
<apply id="dj_dt"><eq />
<apply><diff />
<bvar><ci> time </ci></bvar>
<ci> j </ci>
</apply>
<apply><minus />
<apply><times />
<ci> alpha_j </ci>
<apply><minus />
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> j </ci>
</apply>
</apply>
<apply><times />
<ci> beta_j </ci>
<ci> j </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="L_type_Ca_channel" cmeta:id="L_type_Ca_channel">
<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="#L_type_Ca_channel">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The JWR model creates a new mathematical model to describe the
L-type calcium channel that is based on the experimentally observed
mode-switching behaviour of the channel. Inactivation occurs as
calcium ion binding induces the channel to switch (from mode normal)
to a mode in which transitions to open states are extremely slow
(mode Ca). The channel has one voltage inactivation gate, y. As well
as Ca, the channel is assumed permeable to K ions also.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<!-- These variables are defined here and used in other components. -->
<variable name="i_Ca_L_Ca" public_interface="out" units="uA_per_mm2" />
<variable name="i_Ca_L_K" public_interface="out" units="uA_per_mm2" />
<!-- These variables are defined here and only used internally. -->
<variable name="P_Ca" initial_value="33.75e-6" units="mm_per_ms" />
<variable name="P_K" initial_value="1.0e-9" units="mm_per_ms" />
<variable name="p_k" units="mm_per_ms" />
<variable name="i_Ca_L_Ca_half" initial_value="-4.58e-3" units="uA_per_mm2" />
<variable name="i_Ca_L_Ca_max" units="uA_per_mm2" />
<variable name="O" initial_value="9.84546e-21" units="dimensionless" />
<variable name="O_Ca" initial_value="0.0" units="dimensionless" />
<variable name="alpha" units="per_ms" />
<variable name="beta" units="per_ms" />
<variable name="gamma" units="per_ms" />
<variable name="alpha_a" units="per_ms" />
<variable name="beta_b" units="per_ms" />
<variable name="a" initial_value="2.0" units="dimensionless" />
<variable name="b" initial_value="2.0" units="dimensionless" />
<variable name="g" initial_value="2.0" units="per_ms" />
<variable name="f" initial_value="0.3" units="per_ms" />
<variable name="g_" initial_value="0.0" units="per_ms" />
<variable name="f_" initial_value="0.0" units="per_ms" />
<variable name="omega" initial_value="0.01" units="per_ms" />
<variable name="C0" initial_value="0.997208" units="dimensionless" />
<variable name="C1" initial_value="6.38897e-5" units="dimensionless" />
<variable name="C2" initial_value="1.535e-9" units="dimensionless" />
<variable name="C3" initial_value="1.63909e-14" units="dimensionless" />
<variable name="C4" initial_value="6.56337e-20" units="dimensionless" />
<variable name="C_Ca0" initial_value="2.72826e-3" units="dimensionless" />
<variable name="C_Ca1" initial_value="6.99215e-7" units="dimensionless" />
<variable name="C_Ca2" initial_value="6.71989e-11" units="dimensionless" />
<variable name="C_Ca3" initial_value="2.87031e-15" units="dimensionless" />
<variable name="C_Ca4" initial_value="4.59752e-20" 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="Ca_SS" public_interface="in" units="mM" />
<variable name="Cao" public_interface="in" units="mM" />
<variable name="Ko" public_interface="in" units="mM" />
<variable name="Ki" 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" />
<!-- 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_Ca_L_Ca_calculation_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
Calculation of the calcium current component of the total channel
current, given as the maximal current multiplied by the
voltage-dependent inactivation gate and the open probability of the
channel based on the mode-switching model.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="i_Ca_L_Ca_calculation_eq">
<apply id="i_Ca_L_Ca_calculation"><eq />
<ci> i_Ca_L_Ca </ci>
<apply><times />
<ci> i_Ca_L_Ca_max </ci>
<ci> y </ci>
<apply><plus />
<ci> O </ci>
<ci> O_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="#i_Ca_L_K_calculation_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
Calculation of the potassium current component of the total channel
current.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="i_Ca_L_K_calculation_eq">
<apply id="i_Ca_L_K_calculation"><eq />
<ci> i_Ca_L_K </ci>
<apply><times />
<ci> p_k </ci>
<ci> y </ci>
<apply><plus />
<ci> O </ci>
<ci> O_Ca </ci>
</apply>
<apply><divide />
<apply><times />
<ci> V </ci>
<apply><power/>
<ci> F </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
</apply>
<apply><times />
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
<apply><divide />
<apply><minus />
<apply><times />
<ci> Ki </ci>
<apply><exp />
<apply><divide />
<apply><times />
<ci> V </ci>
<ci> F </ci>
</apply>
<apply><times />
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
</apply>
<ci> Ko </ci>
</apply>
<apply><minus />
<apply><exp />
<apply><divide />
<apply><times />
<ci> V </ci>
<ci> F </ci>
</apply>
<apply><times />
<ci> R </ci>
<ci> T </ci>
</apply>
</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="#p_K_calculation_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The potassium permeability of the channel, which depends on the
calcium current component.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="p_K_calculation_eq">
<apply id="p_k_calculation"><eq />
<ci> p_k </ci>
<apply><divide />
<ci> P_K </ci>
<apply><plus />
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply><divide />
<ci> i_Ca_L_Ca_max </ci>
<ci> i_Ca_L_Ca_half </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_Ca_L_Ca_max_calculation_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The maximal calcium current through the channel.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="i_Ca_L_Ca_max_calculation_eq">
<apply id="i_Ca_L_Ca_max_calculation"><eq />
<ci> i_Ca_L_Ca_max </ci>
<apply><times />
<ci> P_Ca </ci>
<cn cellml:units="dimensionless"> 4.0 </cn>
<apply><divide />
<apply><times />
<ci> V </ci>
<apply><power/>
<ci> F </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
</apply>
<apply><times />
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
<apply><divide />
<apply><minus />
<apply><times />
<cn cellml:units="dimensionless"> 0.001 </cn>
<apply><exp />
<apply><times />
<cn cellml:units="dimensionless"> 2.0 </cn>
<ci> V </ci>
<apply><divide />
<ci> F </ci>
<apply><times />
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply><times />
<cn cellml:units="dimensionless"> 0.341 </cn>
<ci> Cao </ci>
</apply>
</apply>
<apply><minus />
<apply><exp />
<apply><times />
<cn cellml:units="dimensionless"> 2.0 </cn>
<ci> V </ci>
<apply><divide />
<ci> F </ci>
<apply><times />
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</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="#alpha_calculation_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
Rate constants for state changes in mode normal.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="alpha_calculation_eq">
<apply id="alpha_calculation"><eq />
<ci> alpha </ci>
<apply><times />
<cn cellml:units="per_ms"> 0.4 </cn>
<apply><exp />
<apply><divide />
<apply><plus />
<ci> V </ci>
<cn cellml:units="mV"> 12.0 </cn>
</apply>
<cn cellml:units="mV"> 10.0 </cn>
</apply>
</apply>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="beta_calculation_eq">
<apply id="beta_calculation"><eq />
<ci> beta </ci>
<apply><times />
<cn cellml:units="per_ms"> 0.05 </cn>
<apply><exp />
<apply><divide />
<apply><plus />
<ci> V </ci>
<cn cellml:units="mV"> 12.0 </cn>
</apply>
<cn cellml:units="mV"> -13.0 </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="#alpha_a_calculation_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
Rate constants for state changes in mode Ca (corresponding to
alpha-prime and beta-prime in the JRW paper).
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="alpha_a_calculation_eq">
<apply id="alpha_a_calculation"><eq />
<ci> alpha_a </ci>
<apply><times />
<ci> alpha </ci>
<ci> a </ci>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="beta_a_calculation_eq">
<apply id="beta_b_calculation"><eq />
<ci> beta_b </ci>
<apply><divide />
<ci> beta </ci>
<ci> b </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="#gamma_calculation_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
Rate constant for switching between mode normal and mode Ca.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="gamma_calculation_eq">
<apply id="gamma_calculation"><eq />
<ci> gamma </ci>
<apply><times />
<cn cellml:units="dimensionless"> 0.1875 </cn>
<ci> Ca_SS </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="#C0_diff_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The kinetics of the state transitions in mode normal.
In the normal mode, the calcium channel is able to make the
transition to the open, conducting state (O) from the closed state
(C) at a normal rate.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="C0_diff_eq">
<apply id="C0_diff_eq"><eq />
<apply><diff />
<bvar><ci> time </ci></bvar>
<ci> C0 </ci>
</apply>
<apply><minus />
<apply><plus />
<apply><times />
<ci> beta </ci>
<ci> C1 </ci>
</apply>
<apply><times />
<ci> omega </ci>
<ci> C_Ca0 </ci>
</apply>
</apply>
<apply><times />
<apply><plus />
<apply><times />
<cn cellml:units="dimensionless"> 4.0 </cn>
<ci> alpha </ci>
</apply>
<ci> gamma </ci>
</apply>
<ci> C0 </ci>
</apply>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="C1_diff_eq">
<apply id="C1_diff_eq"><eq />
<apply><diff />
<bvar><ci> time </ci></bvar>
<ci> C1 </ci>
</apply>
<apply><minus />
<apply><plus />
<apply><times />
<cn cellml:units="dimensionless"> 4.0 </cn>
<ci> alpha </ci>
<ci> C0 </ci>
</apply>
<apply><times />
<cn cellml:units="dimensionless"> 2.0 </cn>
<ci> beta </ci>
<ci> C2 </ci>
</apply>
<apply><times />
<apply><divide />
<ci> omega </ci>
<ci> b </ci>
</apply>
<ci> C_Ca1 </ci>
</apply>
</apply>
<apply><times />
<apply><plus />
<ci> beta </ci>
<apply><times />
<cn cellml:units="dimensionless"> 3.0 </cn>
<ci> alpha </ci>
</apply>
<apply><times />
<ci> gamma </ci>
<ci> a </ci>
</apply>
</apply>
<ci> C1 </ci>
</apply>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="C2_diff_eq">
<apply id="C2_diff_eq"><eq />
<apply><diff />
<bvar><ci> time </ci></bvar>
<ci> C2 </ci>
</apply>
<apply><minus />
<apply><plus />
<apply><times />
<cn cellml:units="dimensionless"> 3.0 </cn>
<ci> alpha </ci>
<ci> C1 </ci>
</apply>
<apply><times />
<cn cellml:units="dimensionless"> 3.0 </cn>
<ci> beta </ci>
<ci> C3 </ci>
</apply>
<apply><times />
<apply><divide />
<ci> omega </ci>
<apply><power />
<ci> b </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
</apply>
<ci> C_Ca2 </ci>
</apply>
</apply>
<apply><times />
<apply><plus />
<apply><times />
<ci> beta </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
<apply><times />
<cn cellml:units="dimensionless"> 2.0 </cn>
<ci> alpha </ci>
</apply>
<apply><times />
<ci> gamma </ci>
<apply><power />
<ci> a </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
</apply>
</apply>
<ci> C2 </ci>
</apply>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="C3_diff_eq">
<apply id="C3_diff_eq"><eq />
<apply><diff />
<bvar><ci> time </ci></bvar>
<ci> C3 </ci>
</apply>
<apply><minus />
<apply><plus />
<apply><times />
<cn cellml:units="dimensionless"> 2.0 </cn>
<ci> alpha </ci>
<ci> C2 </ci>
</apply>
<apply><times />
<cn cellml:units="dimensionless"> 4.0 </cn>
<ci> beta </ci>
<ci> C4 </ci>
</apply>
<apply><times />
<apply><divide />
<ci> omega </ci>
<apply><power />
<ci> b </ci>
<cn cellml:units="dimensionless"> 3.0 </cn>
</apply>
</apply>
<ci> C_Ca3 </ci>
</apply>
</apply>
<apply><times />
<apply><plus />
<apply><times />
<ci> beta </ci>
<cn cellml:units="dimensionless"> 3.0 </cn>
</apply>
<ci> alpha </ci>
<apply><times />
<ci> gamma </ci>
<apply><power />
<ci> a </ci>
<cn cellml:units="dimensionless"> 3.0 </cn>
</apply>
</apply>
</apply>
<ci> C3 </ci>
</apply>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="C4_diff_eq">
<apply id="C4_diff_eq"><eq />
<apply><diff />
<bvar><ci> time </ci></bvar>
<ci> C4 </ci>
</apply>
<apply><minus />
<apply><plus />
<apply><times />
<ci> alpha </ci>
<ci> C3 </ci>
</apply>
<apply><times />
<ci> g </ci>
<ci> O </ci>
</apply>
<apply><times />
<apply><divide />
<ci> omega </ci>
<apply><power />
<ci> b </ci>
<cn cellml:units="dimensionless"> 4.0 </cn>
</apply>
</apply>
<ci> C_Ca4 </ci>
</apply>
</apply>
<apply><times />
<apply><plus />
<apply><times />
<ci> beta </ci>
<cn cellml:units="dimensionless"> 4.0 </cn>
</apply>
<ci> f </ci>
<apply><times />
<ci> gamma </ci>
<apply><power />
<ci> a </ci>
<cn cellml:units="dimensionless"> 4.0 </cn>
</apply>
</apply>
</apply>
<ci> C4 </ci>
</apply>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="O_diff_eq">
<apply id="O_diff_eq"><eq />
<apply><diff />
<bvar><ci> time </ci></bvar>
<ci> O </ci>
</apply>
<apply><minus />
<apply><times />
<ci> f </ci>
<ci> C4 </ci>
</apply>
<apply><times />
<ci> g </ci>
<ci> O </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="#C_Ca0_diff_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The kinetics of the state transitions in mode Ca.
Calcium binding to the Ca channel induces a conformational change
from normal mode to mode Ca. This effectively inhibits the
conduction of calcium ions because in mode Ca, the calcium channel
makes the transition to the open, conducting state (O) extremely
slowly.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="C_Ca0_diff_eq">
<apply id="C_Ca0_diff_eq"><eq />
<apply><diff />
<bvar><ci> time </ci></bvar>
<ci> C_Ca0 </ci>
</apply>
<apply><minus />
<apply><plus />
<apply><times />
<ci> beta_b </ci>
<ci> C_Ca1 </ci>
</apply>
<apply><times />
<ci> gamma </ci>
<ci> C_Ca0 </ci>
</apply>
</apply>
<apply><times />
<apply><plus />
<apply><times />
<cn cellml:units="dimensionless"> 4.0 </cn>
<ci> alpha_a </ci>
</apply>
<ci> omega </ci>
</apply>
<ci> C_Ca0 </ci>
</apply>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="C_Ca1_diff_eq">
<apply id="C_Ca1_diff_eq"><eq />
<apply><diff />
<bvar><ci> time </ci></bvar>
<ci> C_Ca1 </ci>
</apply>
<apply><minus />
<apply><plus />
<apply><times />
<cn cellml:units="dimensionless"> 4.0 </cn>
<ci> alpha_a </ci>
<ci> C_Ca0 </ci>
</apply>
<apply><times />
<cn cellml:units="dimensionless"> 2.0 </cn>
<ci> beta_b </ci>
<ci> C_Ca2 </ci>
</apply>
<apply><times />
<ci> gamma </ci>
<ci> a </ci>
<ci> C1 </ci>
</apply>
</apply>
<apply><times />
<apply><plus />
<ci> beta_b </ci>
<apply><times />
<cn cellml:units="dimensionless"> 3.0 </cn>
<ci> alpha_a </ci>
</apply>
<apply><divide />
<ci> omega </ci>
<ci> b </ci>
</apply>
</apply>
<ci> C_Ca1 </ci>
</apply>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="C_Ca2_diff_eq">
<apply id="C_Ca2_diff_eq"><eq />
<apply><diff />
<bvar><ci> time </ci></bvar>
<ci> C_Ca2 </ci>
</apply>
<apply><minus />
<apply><plus />
<apply><times />
<cn cellml:units="dimensionless"> 3.0 </cn>
<ci> alpha_a </ci>
<ci> C_Ca1 </ci>
</apply>
<apply><times />
<cn cellml:units="dimensionless"> 3.0 </cn>
<ci> beta_b </ci>
<ci> C_Ca3 </ci>
</apply>
<apply><times />
<ci> gamma </ci>
<apply><power />
<ci> a </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
<ci> C2 </ci>
</apply>
</apply>
<apply><times />
<apply><plus />
<apply><times />
<ci> beta_b </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
<apply><times />
<cn cellml:units="dimensionless"> 2.0 </cn>
<ci> alpha_a </ci>
</apply>
<apply><divide />
<ci> omega </ci>
<apply><power />
<ci> b </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
</apply>
</apply>
<ci> C_Ca2 </ci>
</apply>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="C_Ca3_diff_eq">
<apply id="C_Ca3_diff_eq"><eq />
<apply><diff />
<bvar><ci> time </ci></bvar>
<ci> C_Ca3 </ci>
</apply>
<apply><minus />
<apply><plus />
<apply><times />
<cn cellml:units="dimensionless"> 2.0 </cn>
<ci> alpha_a </ci>
<ci> C_Ca2 </ci>
</apply>
<apply><times />
<cn cellml:units="dimensionless"> 4.0 </cn>
<ci> beta_b </ci>
<ci> C_Ca4 </ci>
</apply>
<apply><times />
<ci> gamma </ci>
<apply><power />
<ci> a </ci>
<cn cellml:units="dimensionless"> 3.0 </cn>
</apply>
<ci> C3 </ci>
</apply>
</apply>
<apply><times />
<apply><plus />
<apply><times />
<ci> beta_b </ci>
<cn cellml:units="dimensionless"> 3.0 </cn>
</apply>
<ci> alpha_a </ci>
<apply><divide />
<ci> omega </ci>
<apply><power />
<ci> b </ci>
<cn cellml:units="dimensionless"> 3.0 </cn>
</apply>
</apply>
</apply>
<ci> C_Ca3 </ci>
</apply>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="C_Ca4_diff_eq">
<apply id="C_Ca4_diff_eq"><eq />
<apply><diff />
<bvar><ci> time </ci></bvar>
<ci> C_Ca4 </ci>
</apply>
<apply><minus />
<apply><plus />
<apply><times />
<ci> alpha_a </ci>
<ci> C_Ca3 </ci>
</apply>
<apply><times />
<ci> g_ </ci>
<ci> O_Ca </ci>
</apply>
<apply><times />
<ci> gamma </ci>
<apply><power />
<ci> a </ci>
<cn cellml:units="dimensionless"> 4.0 </cn>
</apply>
<ci> C4 </ci>
</apply>
</apply>
<apply><times />
<apply><plus />
<apply><times />
<ci> beta_b </ci>
<cn cellml:units="dimensionless"> 4.0 </cn>
</apply>
<ci> f_ </ci>
<apply><divide />
<ci> omega </ci>
<apply><power />
<ci> b </ci>
<cn cellml:units="dimensionless"> 4.0 </cn>
</apply>
</apply>
</apply>
<ci> C_Ca4 </ci>
</apply>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="O_Ca_diff_eq">
<apply id="O_Ca_diff_eq"><eq />
<apply><diff />
<bvar><ci> time </ci></bvar>
<ci> O_Ca </ci>
</apply>
<apply><minus />
<apply><times />
<ci> f_ </ci>
<ci> C_Ca4 </ci>
</apply>
<apply><times />
<ci> g_ </ci>
<ci> O_Ca </ci>
</apply>
</apply>
</apply>
</math>
</component>
<!--
The "L_type_Ca_channel" component has an encapsulated voltage inactivation
gate, y.
-->
<component name="L_type_Ca_channel_y_gate"
cmeta:id="L_type_Ca_channel_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="#L_type_Ca_channel_y_gate">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The voltage-dependent inactivation gate for the L-type calcium
channel - 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="0.998983" units="dimensionless" />
<!-- These variables are defined here and only used internally. -->
<variable name="y_infinity" units="dimensionless" />
<variable name="tau_y" units="dimensionless" />
<!--
These variables are imported from the environment and the membrane via
the "L_type_Ca_channel" 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="#y_diff_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The kinetics of the y gate.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="y_diff_eq">
<apply id="y_diff_eq"><eq />
<apply><diff />
<bvar><ci> time </ci></bvar>
<ci> y </ci>
</apply>
<apply><divide />
<apply><minus />
<ci> y_infinity </ci>
<ci> y </ci>
</apply>
<ci> tau_y </ci>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="y_infinity_calculation_eq">
<apply id="y_infinity_calculation"><eq />
<ci> y_infinity </ci>
<apply><plus />
<apply><divide />
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply><plus />
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply><exp />
<apply><divide />
<apply><plus />
<ci> V </ci>
<cn cellml:units="mV"> 55.0 </cn>
</apply>
<cn cellml:units="mV"> 7.5 </cn>
</apply>
</apply>
</apply>
</apply>
<apply><divide />
<cn cellml:units="dimensionless"> 0.1 </cn>
<apply><plus />
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply><exp />
<apply><divide />
<apply><plus />
<apply><minus />
<ci> V </ci>
</apply>
<cn cellml:units="mV"> 21.0 </cn>
</apply>
<cn cellml:units="mV"> 6.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="tau_y_calculation_eq">
<apply id="tau_y_calculation"><eq />
<ci> tau_y </ci>
<apply><plus />
<cn cellml:units="dimensionless"> 20.0 </cn>
<apply><divide />
<cn cellml:units="dimensionless"> 600.0 </cn>
<apply><plus />
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply><exp />
<apply><divide />
<apply><plus />
<ci> V </ci>
<cn cellml:units="mV"> 30.0 </cn>
</apply>
<cn cellml:units="mV"> 9.5 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<!--
The time-dependent potassium current has an X^2 dependence on it's
activation gate, and an Xi inactivation gate. These are encapsulated in the
parent "time_dependent_potassium_current" component.
-->
<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 has an X^2 dependence on it's
activation gate, and an Xi inactivation gate. This channel is also
assumed permeable to sodium ions.
</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="g_K" units="mS_per_mm2" />
<variable name="g_K_max" initial_value="0.001128" units="mS_per_mm2" />
<variable name="E_K" units="mV" />
<variable name="P_NaK" initial_value="0.01833" 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="Ko" public_interface="in" units="mM" />
<variable name="Ki" public_interface="in" units="mM" />
<variable name="Nao" public_interface="in" units="mM" />
<variable name="Nai" 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" />
<!-- These variables are imported from encapsulated components. -->
<variable name="X" private_interface="in" units="dimensionless" />
<variable name="Xi" 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="#g_K_calculation_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
Calculation of the maximal channel conductance, dependent on
extracellular potassium concentration.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="g_K_calculation_eq">
<apply id="g_K_calculation"><eq />
<ci> g_K </ci>
<apply><times />
<ci>g_K_max</ci>
<apply><root />
<apply><divide />
<ci> Ko </ci>
<cn cellml:units="mM"> 5.4 </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="#E_K_calculation_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The reversal potential of the channel.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="E_K_calculation_eq">
<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 />
<apply><plus />
<ci> Ko </ci>
<apply><times />
<ci> P_NaK </ci>
<ci> Nao </ci>
</apply>
</apply>
<apply><plus />
<ci> Ki </ci>
<apply><times />
<ci> P_NaK </ci>
<ci> Nai </ci>
</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_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> g_K </ci>
<ci> Xi </ci>
<apply><power />
<ci> X </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
<apply><minus />
<ci> V </ci>
<ci> E_K </ci>
</apply>
</apply>
</apply>
</math>
</component>
<!--
The "time_dependent_potassium_current_X_gate" component is the
time-dependent activation gate encapsulated in the rapid_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- and time-dependent activation gate 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="0.000928836" 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 the environment and the membrane via
the "time_dependent_potassium_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_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_mV_ms"> 0.0000719 </cn>
<apply><divide />
<apply><plus />
<ci> V </ci>
<cn cellml:units="mV"> 30.0 </cn>
</apply>
<apply><minus />
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply><exp />
<apply><times />
<cn cellml:units="per_mV"> -0.148 </cn>
<apply><plus />
<ci> V </ci>
<cn cellml:units="mV"> 30.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
<rdf:RDF
xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
xmlns:cmeta="http://www.cellml.org/metadata/1.0#">
<rdf:Description rdf:about="#beta_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_mV_ms"> 0.000131 </cn>
<apply><divide />
<apply><plus />
<ci> V </ci>
<cn cellml:units="mV"> 30.0 </cn>
</apply>
<apply><plus />
<cn cellml:units="dimensionless"> -1.0 </cn>
<apply><exp />
<apply><times />
<cn cellml:units="per_mV"> 0.0687 </cn>
<apply><plus />
<ci> V </ci>
<cn cellml:units="mV"> 30.0 </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_dependent_potassium_current_Xi_gate" component is the
time-independent inactivation gate encapsulated in the time-dependent
potassium current.
-->
<component name="time_dependent_potassium_current_Xi_gate"
cmeta:id="time_dependent_potassium_current_Xi_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_Xi_gate">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The time-independent inactivation gate for the time-dependent
potassium channel.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<!-- This variable is defined here and used in other components. -->
<variable name="Xi" public_interface="out" units="dimensionless" />
<!--
These variables are imported from the "environment" and the "membrane" via
the "time_dependent_potassium_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="#Xi_calculation_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
Xi is the inward rectification parameter and is given by the
following equation.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="Xi_calculation_eq">
<apply id="Xi_calculation"><eq />
<ci> Xi </ci>
<apply><divide />
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply><plus />
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply><exp />
<apply><divide />
<apply><minus />
<ci> V </ci>
<cn cellml:units="mV"> 56.26 </cn>
</apply>
<cn cellml:units="mV"> 32.1 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<!--
The "time_independent_potassium_current" component contains a single
inactivation gate (K1) whose time constant is small enough that it
can be approximated by its steady-state value K1_infinity.
-->
<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 potassium current.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<!-- These variables are defined here and used in other components. -->
<variable name="i_K1" public_interface="out" units="uA_per_mm2" />
<variable
name="E_K1" public_interface="out"
private_interface="out" units="mV" />
<!-- This variable is defined here and only used internally. -->
<variable name="g_K1" units="mS_per_mm2" />
<variable name="g_K1_max" initial_value="7.5e-3" units="mS_per_mm2" />
<!--
These variables are imported from other components. They are all used in
the parent "time_independent_potassium_current" component and some are
also passed via this interface to the encapsulated gates.
-->
<variable
name="time" public_interface="in"
private_interface="out" units="ms" />
<variable
name="V" public_interface="in"
private_interface="out" units="mV" />
<variable name="Ko" public_interface="in" units="mM" />
<variable name="Ki" 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="K1_infinity" 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="#g_K1_calculation_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
Calculation of the maximal channel conductance, dependent on
extracellular potassium concentration.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="g_K1_calculation_eq">
<apply id="g_K1_calculation"><eq />
<ci> g_K1 </ci>
<apply><times />
<ci>g_K1_max</ci>
<apply><root />
<apply><divide />
<ci> Ko </ci>
<cn cellml:units="mM"> 5.4 </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="#E_K1_calculation_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The following equation calculates the reversal potential of the
time-independent potassium current.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="E_K1_calculation_eq">
<apply id="E_K1_calculation"><eq />
<ci> E_K1 </ci>
<apply><times />
<apply><divide />
<apply><times />
<ci> R </ci>
<ci> T </ci>
</apply>
<ci> F </ci>
</apply>
<apply><ln />
<apply><divide />
<ci> Ko </ci>
<ci> Ki </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_K1_calculation_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
Calculate the 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>
<ci> K1_infinity </ci>
<apply><minus />
<ci> V </ci>
<ci> E_K1 </ci>
</apply>
</apply>
</apply>
</math>
</component>
<!--
The "time_independent_potassium_current_K1_gate" component is the K1 gate
encapsulated in the time-independent potassium current.
-->
<component name="time_independent_potassium_current_K1_gate"
cmeta:id="time_independent_potassium_current_K1_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_independent_potassium_current_K1_gate">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The time constants for the K1 gate are small enough that the gating
variable can be approximated with it's steady-state value.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<!-- This variable is defined here and used in other components. -->
<variable name="K1_infinity" public_interface="out" units="dimensionless" />
<!-- These variables are defined here and only used internally. -->
<variable name="alpha_K1" units="per_ms" />
<variable name="beta_K1" units="per_ms" />
<!--
These variables are imported from the "environment", "membrane" and
"time_independent_potassium_current" components.
-->
<variable name="V" public_interface="in" units="mV" />
<variable name="time" public_interface="in" units="ms" />
<variable name="E_K1" 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_K1_calculation_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The opening rate of the K1 gate.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="alpha_K1_calculation_eq">
<apply id="alpha_K1_calculation"><eq />
<ci> alpha_K1 </ci>
<apply><divide />
<cn cellml:units="per_ms"> 1.02 </cn>
<apply><plus />
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply><exp />
<apply><times />
<cn cellml:units="per_mV"> 0.2385 </cn>
<apply><minus />
<apply><minus />
<ci> V </ci>
<ci> E_K1 </ci>
</apply>
<cn cellml:units="mV"> 59.215 </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_K1_calculation_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The closing rate of the K1 gate.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="beta_K1_calculation_eq">
<apply id="beta_K1_calculation"><eq />
<ci> beta_K1 </ci>
<apply><divide />
<apply><plus />
<apply><times />
<cn cellml:units="per_ms"> 0.49124 </cn>
<apply><exp />
<apply><times />
<cn cellml:units="dimensionless"> 0.08032 </cn>
<apply><minus />
<apply><plus />
<ci> V </ci>
<cn cellml:units="mV"> 5.476 </cn>
</apply>
<ci> E_K1 </ci>
</apply>
</apply>
</apply>
</apply>
<apply><exp />
<apply><times />
<cn cellml:units="dimensionless"> 0.06175 </cn>
<apply><minus />
<ci> V </ci>
<apply><plus />
<ci> E_K1 </ci>
<cn cellml:units="mV"> 594.31 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply><plus />
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply><exp />
<apply><times />
<cn cellml:units="per_mV"> -0.5143 </cn>
<apply><plus />
<apply><minus />
<ci> V </ci>
<ci> E_K1 </ci>
</apply>
<cn cellml:units="mV"> 4.753 </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="#K1_infinity_calculation_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The steady-state approximation for the K1 gating kinetics.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="K1_infinity_calculation_eq">
<apply id="K1_infinity_calculation"><eq />
<ci> K1_infinity </ci>
<apply><divide />
<ci> alpha_K1 </ci>
<apply><plus />
<ci> alpha_K1 </ci>
<ci> beta_K1 </ci>
</apply>
</apply>
</apply>
</math>
</component>
<!--
The "plateau_potassium_current" component contains the equations
which describe the contribution of a time independent
[K]o-insensitive channel at plateau potentials.
-->
<component name="plateau_potassium_current"
cmeta:id="plateau_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="#plateau_potassium_current">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The plateau potassium current component contains the equations which
describe the contribution of a time independent [K]o-insensitive
channel at plateau potentials.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<!-- This variable is defined here and used in other components. -->
<variable name="i_Kp" public_interface="out" units="uA_per_mm2" />
<!-- These variables are defined here and only used internally. -->
<variable name="E_Kp" units="mV" />
<variable name="g_Kp" initial_value="8.28e-5" units="mS_per_mm2" />
<variable name="Kp" units="dimensionless" />
<!-- 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_K1" 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="#E_Kp_calculation_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The channel's reversal potential.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="E_Kp_calculation_eq">
<apply id="E_Kp_calculation"><eq />
<ci> E_Kp </ci>
<ci> E_K1 </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="#Kp_calculation_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The activation variable.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="Kp_calculation_eq">
<apply id="Kp_calculation"><eq />
<ci> Kp </ci>
<apply><divide />
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply><plus />
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply><exp />
<apply><divide />
<apply><minus />
<cn cellml:units="mV"> 7.488 </cn>
<ci> V </ci>
</apply>
<cn cellml:units="mV"> 5.98 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
<rdf:RDF
xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
xmlns:cmeta="http://www.cellml.org/metadata/1.0#">
<rdf:Description rdf:about="#i_Kp_calculation_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
Calculation of the plateau potassium current.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="i_Kp_calculation_eq">
<apply id="i_Kp_calculation"><eq />
<ci> i_Kp </ci>
<apply><times />
<ci> g_Kp </ci>
<ci> Kp </ci>
<apply><minus />
<ci> V </ci>
<ci> E_Kp </ci>
</apply>
</apply>
</apply>
</math>
</component>
<!--
The "Na_Ca_exchanger" component describes how a protein molecule in the cell
surface membrane transports Na ions into the cytosol and exports Ca ions
into the extracellular matrix, in a ratio of 3:1 respectively.
-->
<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 Na/Ca exchanger component describes how a protein molecule in
the cell surface membrane transports Na ions into the cytosol and
exports Ca ions into the extracellular volume, in a ratio of 3:1
respectively.
</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" />
<!-- These variables are defined here and only used internally. -->
<variable name="k_NaCa" initial_value="50.0" units="uA_per_mm2" />
<variable name="K_mNa" initial_value="87.5" units="mM" />
<variable name="K_mCa" initial_value="1.38" units="mM" />
<variable name="k_sat" initial_value="0.1" units="dimensionless" />
<variable name="eta" initial_value="0.35" 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="Nai" public_interface="in" units="mM" />
<variable name="Nao" public_interface="in" units="mM" />
<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="#Na_Ca_exchanger_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
Calculation of the Na/Ca exchanger current.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="Na_Ca_exchanger_eq">
<apply id="Na_Ca_exchanger"><eq />
<ci> i_NaCa </ci>
<apply><times />
<ci> k_NaCa </ci>
<apply><divide />
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply><plus />
<apply><power />
<ci> K_mNa </ci>
<cn cellml:units="dimensionless"> 3.0 </cn>
</apply>
<apply><power />
<ci> Nao </ci>
<cn cellml:units="dimensionless"> 3.0 </cn>
</apply>
</apply>
</apply>
<apply><divide />
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply><plus />
<ci> K_mCa </ci>
<ci> Cao </ci>
</apply>
</apply>
<apply><divide />
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply><plus />
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply><times />
<ci> k_sat </ci>
<apply><exp />
<apply><times />
<apply><minus />
<ci> eta </ci>
<cn cellml:units="dimensionless"> 1.0 </cn>
</apply>
<ci> V </ci>
<apply><divide />
<ci> F </ci>
<apply><times />
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply><minus />
<apply><times />
<apply><exp />
<apply><times />
<ci> eta </ci>
<ci> V </ci>
<apply><divide />
<ci> F </ci>
<apply><times />
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
</apply>
<apply><power />
<ci> Nai </ci>
<cn cellml:units="dimensionless"> 3.0 </cn>
</apply>
<ci> Cao </ci>
</apply>
<apply><times />
<apply><exp />
<apply><times />
<apply><minus />
<ci> eta </ci>
<cn cellml:units="dimensionless"> 1.0 </cn>
</apply>
<ci> V </ci>
<apply><divide />
<ci> F </ci>
<apply><times />
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
</apply>
<apply><power />
<ci> Nao </ci>
<cn cellml:units="dimensionless"> 3.0 </cn>
</apply>
<ci> Cai </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<!--
The "sarcolemmal_calcium_pump" is an additional mechanism for removing Ca
ions from the myoplasm to help maintain a low intracellular calcium
concentration when at rest.
-->
<component name="sarcolemmal_calcium_pump"
cmeta:id="sarcolemmal_calcium_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="#sarcolemmal_calcium_pump">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The sarcolemmal calcium pump is an additional mechanism for removing
Ca ions from the myoplasm to help maintain a low intracellular
calcium concentration when at rest.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<!-- This variable is defined here and used in other components. -->
<variable name="i_p_Ca" public_interface="out" units="uA_per_mm2" />
<!-- These variables are defined here and only used internally. -->
<variable name="K_mpCa" initial_value="0.5e-3" units="mM" />
<variable name="I_pCa" initial_value="1.15e-2" units="uA_per_mm2" />
<!-- These variables are imported from other components. -->
<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="#i_p_Ca_calculation_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The calcium pump current.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="i_p_Ca_calculation_eq">
<apply id="i_p_Ca_calculation"><eq />
<ci> i_p_Ca </ci>
<apply><times />
<ci> I_pCa </ci>
<apply><divide />
<ci> Cai </ci>
<apply><plus />
<ci> K_mpCa </ci>
<ci> Cai </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<!--
The "sodium_background_current" is a time-independent diffusion of Na ions
down their electrochemical gradient, through the cell surface membrane into
the cytosol.
-->
<component name="sodium_background_current"
cmeta:id="sodium_background_current">
<rdf:RDF
xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
xmlns:cmeta="http://www.cellml.org/metadata/1.0#">
<rdf:Description rdf:about="#sodium_background_current">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The sodium background current is a time-independent diffusion of
Na ions down their electrochemical gradient, through the cell
surface membrane into the cytosol.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<!-- This variable is defined here and used in other components. -->
<variable name="i_Na_b" public_interface="out" units="uA_per_mm2" />
<!-- These variables are defined here and only used internally. -->
<variable name="g_Nab" initial_value="1.41e-5" units="mS_per_mm2" />
<variable name="E_NaN" units="mV" />
<!--
Time and membrane potential are imported from the "environment" and the
"membrane" components. The reversal potential is imported from the
"fast_sodium_current" component.
-->
<variable name="time" public_interface="in" units="ms" />
<variable name="V" public_interface="in" units="mV" />
<variable name="E_Na" public_interface="in" units="mV" />
<rdf:RDF
xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
xmlns:cmeta="http://www.cellml.org/metadata/1.0#">
<rdf:Description rdf:about="#E_NaN_calculation_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The reversal potential for the background sodium channel.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="E_NaN_calculation_eq">
<apply id="E_NaN_calculation"><eq />
<ci> E_NaN </ci>
<ci> E_Na </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="#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_NaN </ci>
</apply>
</apply>
</apply>
</math>
</component>
<!--
The "calcium_background_current" describes a time-independent diffusion of
Ca ions down their electrochemical gradient through the cell surface
membrane into the cytosol. However, calcium is not allowed to accumulate to
high intracellular concentrations. This influx is balanced by the Ca ion
extrusion through the Na-Ca exchanger and the sarcolemmal Ca pump.
-->
<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>
The calcium background current describes a time-independent
diffusion of Ca ions down their electrochemical gradient through the
cell surface membrane into the cytosol. However, calcium is not
allowed to accumulate to high intracellular concentrations. This
influx is balanced by the Ca ion extrusion through the Na-Ca
exchanger and the sarcolemmal Ca pump.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<!-- This variable is defined here and used in other components. -->
<variable name="i_Ca_b" public_interface="out" units="uA_per_mm2" />
<!-- These variables are defined here and only used internally. -->
<variable name="g_Cab" initial_value="6.032e-5" units="mS_per_mm2" />
<variable name="E_CaN" units="mV" />
<!-- These variables are imported from other components. -->
<variable name="time" public_interface="in" units="ms" />
<variable name="V" public_interface="in" units="mV" />
<variable name="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="#E_CaN_calculation_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The reversal potential for the background calcium current.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="E_CaN_calculation_eq">
<apply id="E_CaN_calculation"><eq />
<ci> E_CaN </ci>
<apply><times />
<apply><divide />
<apply><times />
<ci> R </ci>
<ci> T </ci>
</apply>
<apply><times />
<cn cellml:units="dimensionless"> 2.0 </cn>
<ci> F </ci>
</apply>
</apply>
<apply><ln />
<apply><divide />
<ci> Cao </ci>
<ci> Cai </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_Ca_b_calculation_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
Calculation of the background calcium 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_CaN </ci>
</apply>
</apply>
</apply>
</math>
</component>
<!--
The "sodium_potassium_pump" is an active protein in the cell membrane which
couples the free energy released by the hydrolysis of ATP to the movement of
Na and K ions against their electrochemical gradients through the cell
surface membrane.
-->
<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 sodium potassium pump is an active protein in the cell membrane
which couples the free energy released by the hydrolysis of ATP to
the movement of Na and K ions against their electrochemical
gradients through the cell membrane.
</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" />
<!-- These variables are defined here and only used internally. -->
<variable name="I_NaK" initial_value="0.013" units="uA_per_mm2" />
<variable name="f_NaK" units="dimensionless" />
<variable name="K_mNai" initial_value="10.0" units="mM" />
<variable name="K_mKo" initial_value="1.5" units="mM" />
<variable name="sigma" units="dimensionless" />
<!-- 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="Nai" public_interface="in" units="mM" />
<variable name="Nao" public_interface="in" units="mM" />
<variable name="Ko" 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="#f_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="f_NaK_calculation_eq">
<apply id="f_NaK_calculation"><eq />
<ci> f_NaK </ci>
<apply><divide />
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply><plus />
<apply><plus />
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply><times />
<cn cellml:units="dimensionless"> 0.1245 </cn>
<apply><exp />
<apply><divide />
<apply><times />
<cn cellml:units="dimensionless"> -0.1 </cn>
<ci> V </ci>
<ci> F </ci>
</apply>
<apply><times />
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply><times />
<cn cellml:units="dimensionless"> 0.0365 </cn>
<ci> sigma </ci>
<apply><exp />
<apply><divide />
<apply><times />
<apply><minus />
<ci> V </ci>
</apply>
<ci> F </ci>
</apply>
<apply><times />
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="sigma_calculation_eq">
<apply id="sigma_calculation"><eq />
<ci> sigma </ci>
<apply><times />
<apply><divide />
<cn cellml:units="dimensionless"> 1.0 </cn>
<cn cellml:units="dimensionless"> 7.0 </cn>
</apply>
<apply><minus />
<apply><exp />
<apply><divide />
<ci> Nao </ci>
<cn cellml:units="dimensionless"> 67.3 </cn>
</apply>
</apply>
<cn cellml:units="dimensionless"> 1.0 </cn>
</apply>
</apply>
</apply>
</math>
<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>
<ci> f_NaK </ci>
<apply><divide />
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply><plus />
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply><power />
<apply><divide />
<ci> K_mNai </ci>
<ci> Nai </ci>
</apply>
<cn cellml:units="dimensionless"> 1.5 </cn>
</apply>
</apply>
</apply>
<apply><divide />
<ci> Ko </ci>
<apply><plus />
<ci> Ko </ci>
<ci> K_mKo </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<!--
The "non_specific_calcium_activated_current" describes a channel which is
activated by calcium ions, but is permeable to only sodium and potassium
ions.
-->
<component name="non_specific_calcium_activated_current"
cmeta:id="non_specific_calcium_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="#non_specific_calcium_activated_current">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The nonspecific calcium activated current describes a channel which
is activated by calcium ions, but is permeable to only sodium and
potassium ions.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<!-- These variables are defined here and used in other components. -->
<variable name="i_ns_Ca" public_interface="out" units="uA_per_mm2" />
<variable name="i_ns_Na" public_interface="out" units="uA_per_mm2" />
<variable name="i_ns_K" public_interface="out" units="uA_per_mm2" />
<!-- These variables are defined here and only used internally. -->
<variable name="I_ns_Na" units="uA_per_mm2" />
<variable name="I_ns_K" units="uA_per_mm2" />
<variable name="K_m_ns_Ca" initial_value="1.2e-3" units="mM" />
<variable name="P_ns_Ca" initial_value="1.75e-9" units="mm_per_ms" />
<variable name="EnsCa" units="mV"/>
<variable name="VnsCa" units="mV"/>
<!--
Time and membrane potential are imported from the "environment" and the
"membrane" components. Intracellular calcium concentration is imported
from the "ionic_concentrations" component.
-->
<variable name="time" public_interface="in" units="ms" />
<variable name="Cai" public_interface="in" units="mM" />
<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="Nao" public_interface="in" units="mM" />
<variable name="Ko" public_interface="in" units="mM" />
<variable name="Nai" public_interface="in" units="mM" />
<variable name="Ki" 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="#EnsCa_calculation_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The reversal potential of the channel.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="EnsCa_calculation_eq">
<apply id="EnsCa_calculation"><eq/>
<ci>EnsCa</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> Ko </ci>
<ci> Nao </ci>
</apply>
<apply><plus/>
<ci> Ki </ci>
<ci> Nai </ci>
</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="#VnsCa_calculation_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The potential offset for the channel.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="VnsCa_calculation_eq">
<apply id="VnsCa_calculation"><eq/>
<ci>VnsCa</ci>
<apply><minus/>
<ci>V</ci>
<ci>EnsCa</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_ns_Na_calculation_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The sodium component of the channel's current.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="i_ns_Na_calculation_eq">
<apply id="i_ns_Na_calculation"><eq />
<ci> i_ns_Na </ci>
<apply><times />
<ci> I_ns_Na </ci>
<apply><divide />
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply><plus />
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply><power />
<apply><divide />
<ci> K_m_ns_Ca </ci>
<ci> Cai </ci>
</apply>
<cn cellml:units="dimensionless"> 3.0 </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="#i_ns_K_calculation_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The potassium component of the channel's current.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="i_ns_K_calculation_eq">
<apply id="i_ns_K_calculation"><eq />
<ci> i_ns_K </ci>
<apply><times />
<ci> I_ns_K </ci>
<apply><divide />
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply><plus />
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply><power />
<apply><divide />
<ci> K_m_ns_Ca </ci>
<ci> Cai </ci>
</apply>
<cn cellml:units="dimensionless"> 3.0 </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="#i_ns_Ca_calculation_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The total nonspecific calcium activated current.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="i_ns_Ca_calculation_eq">
<apply id="i_ns_Ca_calculation"><eq />
<ci> i_ns_Ca </ci>
<apply><plus />
<ci> i_ns_Na </ci>
<ci> i_ns_K </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_ns_Na_max_calculation_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The maximal sodium component current.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="I_ns_Na_max_calculation_eq">
<apply id="I_ns_Na_calculation"><eq />
<ci> I_ns_Na </ci>
<apply><times />
<ci> P_ns_Ca </ci>
<apply><power />
<cn cellml:units="dimensionless"> 1.0 </cn>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
<apply><divide />
<apply><times />
<ci> VnsCa </ci>
<apply><power />
<ci> F </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
</apply>
<apply><times />
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
<apply><divide />
<apply><minus />
<apply><times />
<cn cellml:units="dimensionless"> 0.75 </cn>
<ci> Nai </ci>
<apply><exp />
<apply><divide />
<apply><times />
<ci> VnsCa </ci>
<ci> F </ci>
</apply>
<apply><times />
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
</apply>
<apply><times />
<cn cellml:units="dimensionless"> 0.75 </cn>
<ci> Nao </ci>
</apply>
</apply>
<apply><minus />
<apply><exp />
<apply><divide />
<apply><times />
<ci> VnsCa </ci>
<ci> F </ci>
</apply>
<apply><times />
<ci> R </ci>
<ci> T </ci>
</apply>
</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="#I_ns_K_max_calculation_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The maximal potassium component current.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="I_ns_K_max_calculation_eq">
<apply id="I_ns_K_calculation"><eq />
<ci> I_ns_K </ci>
<apply><times />
<ci> P_ns_Ca </ci>
<apply><power />
<cn cellml:units="dimensionless"> 1.0 </cn>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
<apply><divide />
<apply><times />
<ci> VnsCa </ci>
<apply><power />
<ci> F </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
</apply>
<apply><times />
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
<apply><divide />
<apply><minus />
<apply><times />
<cn cellml:units="dimensionless"> 0.75 </cn>
<ci> Ki </ci>
<apply><exp />
<apply><divide />
<apply><times />
<ci> VnsCa </ci>
<ci> F </ci>
</apply>
<apply><times />
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
</apply>
<apply><times />
<cn cellml:units="dimensionless"> 0.75 </cn>
<ci> Ko </ci>
</apply>
</apply>
<apply><minus />
<apply><exp />
<apply><divide />
<apply><times />
<ci> VnsCa </ci>
<ci> F </ci>
</apply>
<apply><times />
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
<cn cellml:units="dimensionless"> 1.0 </cn>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<!--
In the JRW model, subcellular calcium regulatory mechanisms are described in
detail. There are six calcium fluxes to consider; J_rel, J_leak, J_up,
J_tr, J_xfer and J_trpn. In addition, three membrane current fluxes are
also necessary for the formulation of calcium regulation; i_p_Ca, i_Ca_L_Ca
and i_NaCa. The equations to calculate these fluxes are contained within
the "calcium_subsystem" component.
-->
<component name="calcium_subsystem" cmeta:id="calcium_subsystem">
<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_subsystem">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
In the JRW model, subcellular calcium regulatory mechanisms are
described in detail. There are six calcium fluxes to consider;
J_rel, J_leak, J_up, J_tr, J_xfer and J_trpn. In addition, three
membrane current fluxes are also necessary for the formulation of
calcium regulation; i_p_Ca, i_Ca_L_Ca and i_NaCa.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<!-- These variables are defined here and used in other components. -->
<variable
name="Cai" public_interface="out"
initial_value="9.94893e-11" units="mM" />
<variable
name="Ca_SS" public_interface="out"
initial_value="1.36058e-4" units="mM" />
<variable
name="Am" public_interface="out"
initial_value="546.69" units="per_mm" />
<variable
name="V_myo" public_interface="out"
initial_value="0.92" units="dimensionless" />
<!-- These variables are defined here and only used internally. -->
<variable name="RyR_open" units="dimensionless" />
<variable name="P_O1" initial_value="1.19168e-3" units="dimensionless" />
<variable name="P_O2" initial_value="6.30613e-9" units="dimensionless" />
<variable name="P_C1" initial_value="0.762527" units="dimensionless" />
<variable name="P_C2" initial_value="0.236283" units="dimensionless" />
<variable name="v1" initial_value="1.8" units="per_ms" />
<variable name="v2" initial_value="0.58e-4" units="per_ms" />
<variable name="v3" initial_value="1.8e-3" units="mM_per_ms" />
<variable name="nCa" initial_value="4.0" units="dimensionless" />
<variable name="mCa" initial_value="3.0" units="dimensionless" />
<variable name="k_a_plus" initial_value="1.215e10" units="per_mM4_per_ms" />
<variable name="k_a_minus" initial_value="0.1425" units="per_ms" />
<variable name="k_b_plus" initial_value="4.05e7" units="per_mM3_per_ms" />
<variable name="k_b_minus" initial_value="1.930" units="per_ms" />
<variable name="k_c_plus" initial_value="0.018" units="per_ms" />
<variable name="k_c_minus" initial_value="0.0008" units="per_ms" />
<variable name="k_htrpn_plus" initial_value="20.0" units="per_mM_per_ms" />
<variable name="k_htrpn_minus" initial_value="0.066e-3" units="per_ms" />
<variable name="k_ltrpn_plus" initial_value="40.0" units="per_mM_per_ms" />
<variable name="k_ltrpn_minus" initial_value="0.04" units="per_ms" />
<variable name="tau_tr" initial_value="34.48" units="ms" />
<variable name="Ca_JSR" initial_value="1.17504" units="mM" />
<variable name="Ca_NSR" initial_value="1.243891" units="mM" />
<variable name="V_JSR" units="dimensionless" />
<variable name="V_NSR" units="dimensionless" />
<variable name="V_SS" units="dimensionless" />
<variable name="K_mup" initial_value="0.5e-3" units="mM" />
<variable name="K_mCMDN" initial_value="2.38e-3" units="mM" />
<variable name="K_mCSQN" initial_value="0.8" units="mM" />
<variable name="tau_xfer" initial_value="3.125" units="ms" />
<variable name="HTRPN_tot" initial_value="0.14" units="mM" />
<variable name="LTRPN_tot" initial_value="0.07" units="mM" />
<variable name="HTRPNCa" initial_value="0.13598" units="mM" />
<variable name="LTRPNCa" initial_value="0.00635" units="mM" />
<variable name="CSQN_tot" initial_value="15.0" units="mM" />
<variable name="CMDN_tot" initial_value="0.05" units="mM" />
<variable name="Bi" units="dimensionless" />
<variable name="B_SS" units="dimensionless" />
<variable name="B_JSR" units="dimensionless" />
<variable name="J_rel" units="mM_per_ms" />
<variable name="J_leak" units="mM_per_ms" />
<variable name="J_up" units="mM_per_ms" />
<variable name="J_tr" units="mM_per_ms" />
<variable name="J_xfer" units="mM_per_ms" />
<variable name="J_trpn" units="mM_per_ms" />
<variable name="J_htrpn" units="mM_per_ms" />
<variable name="J_ltrpn" units="mM_per_ms" />
<!-- 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_Ca_b" public_interface="in" units="uA_per_mm2" />
<variable name="i_Ca_L_Ca" public_interface="in" units="uA_per_mm2" />
<variable name="i_NaCa" public_interface="in" units="uA_per_mm2" />
<variable name="i_p_Ca" 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="#V_SS_calculation_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
Calculate some volume fractions as proportions of the total
myoplasmic volume.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="V_SS_calculation_eq">
<apply id="V_SS_calculation"><eq/>
<ci>V_SS</ci>
<apply><times/>
<cn cellml:units="dimensionless">5.828e-5</cn>
<ci>V_myo</ci>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="V_NSR_calculation_eq">
<apply id="V_NSR_calculation"><eq/>
<ci>V_NSR</ci>
<apply><times/>
<cn cellml:units="dimensionless">0.081</cn>
<ci>V_myo</ci>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="V_JSR_calculation_eq">
<apply id="V_JSR_calculation"><eq/>
<ci>V_JSR</ci>
<apply><times/>
<cn cellml:units="dimensionless">0.00464</cn>
<ci>V_myo</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="#J_rel_calculation_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The calcium release flux from the JSR into the restricted subspace
is governed by the fraction of RyR channels in an open state.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="J_rel_calculation_eq">
<apply id="J_rel_calculation"><eq />
<ci> J_rel </ci>
<apply><times />
<ci> v1 </ci>
<ci> RyR_open </ci>
<apply><minus />
<ci> Ca_JSR </ci>
<ci> Ca_SS </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="#RyR_open_calculation_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The "open" RyR's are those P_O1 and P_O2 states.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="RyR_open_calculation_eq">
<apply id="RyR_open_calculation"><eq />
<ci> RyR_open </ci>
<apply><plus />
<ci> P_O1 </ci>
<ci> P_O2 </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="#P_C1_diff_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The kinetic equations governing the transitions between the four
states used to model the RyR's.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="P_C1_diff_eq">
<apply id="P_C1_diff_eq"><eq />
<apply><diff />
<bvar><ci> time </ci></bvar>
<ci> P_C1 </ci>
</apply>
<apply><plus />
<apply><times />
<apply><minus />
<ci> k_a_plus </ci>
</apply>
<apply><power />
<ci> Ca_SS </ci>
<ci> nCa </ci>
</apply>
<ci> P_C1 </ci>
</apply>
<apply><times />
<ci> k_a_minus </ci>
<ci> P_O1 </ci>
</apply>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="P_O1_diff_eq">
<apply id="P_O1_diff_eq"><eq />
<apply><diff />
<bvar><ci> time </ci></bvar>
<ci> P_O1 </ci>
</apply>
<apply><plus />
<apply><minus />
<apply><times />
<ci> k_a_plus </ci>
<apply><power />
<ci> Ca_SS </ci>
<ci> nCa </ci>
</apply>
<ci> P_C1 </ci>
</apply>
<apply><plus />
<apply><times />
<ci> k_a_minus </ci>
<ci> P_O1 </ci>
</apply>
<apply><times />
<ci> k_b_plus </ci>
<apply><power />
<ci> Ca_SS </ci>
<ci> mCa </ci>
</apply>
<ci> P_O1 </ci>
</apply>
<apply><times />
<ci> k_c_plus </ci>
<ci> P_O1 </ci>
</apply>
</apply>
</apply>
<apply><times />
<ci> k_b_minus </ci>
<ci> P_O2 </ci>
</apply>
<apply><times />
<ci> k_c_minus </ci>
<ci> P_C2 </ci>
</apply>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="P_O2_diff_eq">
<apply id="P_O2_diff_eq"><eq />
<apply><diff />
<bvar><ci> time </ci></bvar>
<ci> P_O2 </ci>
</apply>
<apply><minus />
<apply><times />
<ci> k_b_plus </ci>
<apply><power />
<ci> Ca_SS </ci>
<ci> mCa </ci>
</apply>
<ci> P_O1 </ci>
</apply>
<apply><times />
<ci> k_b_minus </ci>
<ci> P_O2 </ci>
</apply>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="P_C2_diff_eq">
<apply id="P_C2_diff_eq"><eq />
<apply><diff />
<bvar><ci> time </ci></bvar>
<ci> P_C2 </ci>
</apply>
<apply><minus />
<apply><times />
<ci> k_c_plus </ci>
<ci> P_O1 </ci>
</apply>
<apply><times />
<ci> k_c_minus </ci>
<ci> P_C2 </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="#J_leak_calculation_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
Calculate the leakage flux from the NSR into the myoplasm.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="J_leak_calculation_eq">
<apply id="J_leak_calculation"><eq />
<ci> J_leak </ci>
<apply><times />
<ci> v2 </ci>
<apply><minus />
<ci> Ca_NSR </ci>
<ci> Cai </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="#J_up_calculation_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
Calculate the uptake flux into the NSR from the myoplasm.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="J_up_calculation_eq">
<apply id="J_up_calculation"><eq />
<ci> J_up </ci>
<apply><times />
<ci> v3 </ci>
<apply><divide />
<apply><power />
<ci> Cai </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
<apply><plus />
<apply><power />
<ci> K_mup </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
<apply><power />
<ci> Cai </ci>
<cn cellml:units="dimensionless"> 2.0 </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="#J_tr_calculation_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
Calculate the translocation flux between the uptake (NSR) and
release (JSR) stores.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="J_tr_calculation_eq">
<apply id="J_tr_calculation"><eq />
<ci> J_tr </ci>
<apply><divide />
<apply><minus />
<ci> Ca_NSR </ci>
<ci> Ca_JSR </ci>
</apply>
<ci> tau_tr </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="#J_xfer_calculation_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
Calculate the calcium flux from the diffusion of calcium out of the
restricted subspace into the myoplasm.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="J_xfer_calculation_eq">
<apply id="J_xfer_calculation"><eq />
<ci> J_xfer </ci>
<apply><divide />
<apply><minus />
<ci> Ca_SS </ci>
<ci> Cai </ci>
</apply>
<ci> tau_xfer </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="#J_htrpn_calculation_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The kinetics of calcium binding to the myoplasm buffer troponin -
both high and low affinity binding sites.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="J_htrpn_calculation_eq">
<apply id="J_htrpn_calculation"><eq />
<ci> J_htrpn </ci>
<apply><minus/>
<apply><times />
<ci> k_htrpn_plus </ci>
<ci> Cai </ci>
<apply><minus />
<ci> HTRPN_tot </ci>
<ci> HTRPNCa </ci>
</apply>
</apply>
<apply><times />
<ci> k_htrpn_minus </ci>
<ci> HTRPNCa </ci>
</apply>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="J_ltrpn_calculation_eq">
<apply id="J_ltrpn_calculation"><eq />
<ci> J_ltrpn </ci>
<apply><minus/>
<apply><times />
<ci> k_ltrpn_plus </ci>
<ci> Cai </ci>
<apply><minus />
<ci> LTRPN_tot </ci>
<ci> LTRPNCa </ci>
</apply>
</apply>
<apply><times />
<ci> k_ltrpn_minus </ci>
<ci> LTRPNCa </ci>
</apply>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="J_trpn_calculation_eq">
<apply id="J_trpn_calculation"><eq />
<ci> J_trpn </ci>
<apply><plus />
<ci>J_htrpn</ci>
<ci>J_ltrpn</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="#HTRPNCa_diff_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
Keep track of the concentration of calcium ions bound to high and
low affinity troponin binding sites.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="HTRPNCa_diff_eq">
<apply id="HTRPNCa_diff_eq"><eq />
<apply><diff />
<bvar><ci> time </ci></bvar>
<ci> HTRPNCa </ci>
</apply>
<ci>J_htrpn</ci>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="LTRPNCa_diff_eq">
<apply id="LTRPNCa_diff_eq"><eq />
<apply><diff />
<bvar><ci> time </ci></bvar>
<ci> LTRPNCa </ci>
</apply>
<ci>J_ltrpn</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="#Bi_calculation_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
Calcium is buffered by calmodulin (CMDN) in the subspace and
myoplasm, and by calsequestrin (CSQN) in the JSR. These are fast
buffers and their effect is modelled using the rapid buffering
approximation.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="Bi_calculation_eq">
<apply id="Bi_calculation"><eq />
<ci> Bi </ci>
<apply><divide />
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply><plus />
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply><divide />
<apply><times />
<ci> CMDN_tot </ci>
<ci> K_mCMDN </ci>
</apply>
<apply><power />
<apply><plus />
<ci> K_mCMDN </ci>
<ci> Cai </ci>
</apply>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="B_SS_calculation_eq">
<apply id="B_SS_calculation"><eq />
<ci> B_SS </ci>
<apply><divide />
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply><plus />
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply><divide />
<apply><times />
<ci> CMDN_tot </ci>
<ci> K_mCMDN </ci>
</apply>
<apply><power />
<apply><plus />
<ci> K_mCMDN </ci>
<ci> Ca_SS </ci>
</apply>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="B_JSR_calculation_eq">
<apply id="B_JSR_calculation"><eq />
<ci> B_JSR </ci>
<apply><divide />
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply><plus />
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply><divide />
<apply><times />
<ci> CSQN_tot </ci>
<ci> K_mCSQN </ci>
</apply>
<apply><power />
<apply><plus />
<ci> K_mCSQN </ci>
<ci> Ca_JSR </ci>
</apply>
<cn cellml:units="dimensionless"> 2.0 </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="#calcium_internal_diff_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The kinetics of the calcium ion concentration changes in the various
compartments of the model.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="calcium_internal_diff_eq">
<apply id="calcium_internal_diff_eq"><eq />
<apply><diff />
<bvar><ci> time </ci></bvar>
<ci> Cai </ci>
</apply>
<apply><times />
<ci> Bi </ci>
<apply><minus />
<apply><plus />
<ci> J_leak </ci>
<ci> J_xfer </ci>
</apply>
<apply><plus />
<ci> J_up </ci>
<ci> J_trpn </ci>
<apply><times />
<apply><plus />
<apply><minus />
<ci> i_Ca_b </ci>
<apply><times />
<cn cellml:units="dimensionless"> 2.0 </cn>
<ci> i_NaCa </ci>
</apply>
</apply>
<ci> i_p_Ca </ci>
</apply>
<apply><divide />
<ci> Am </ci>
<apply><times />
<cn cellml:units="dimensionless"> 2.0 </cn>
<ci> V_myo </ci>
<ci> F </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="calcium_subspace_diff_eq">
<apply id="calcium_subspace_diff_eq"><eq />
<apply><diff />
<bvar><ci> time </ci></bvar>
<ci> Ca_SS </ci>
</apply>
<apply><times />
<ci> B_SS </ci>
<apply><minus />
<apply><minus />
<apply><times />
<ci> J_rel </ci>
<apply><divide />
<ci> V_JSR </ci>
<ci> V_SS </ci>
</apply>
</apply>
<apply><times />
<ci> J_xfer </ci>
<apply><divide />
<ci> V_myo </ci>
<ci> V_SS </ci>
</apply>
</apply>
</apply>
<apply><times />
<ci> i_Ca_L_Ca </ci>
<apply><divide />
<ci> Am </ci>
<apply><times />
<cn cellml:units="dimensionless"> 2.0 </cn>
<ci> V_SS </ci>
<ci> F </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="calcium_JSR_diff_eq">
<apply id="calcium_JSR_diff_eq"><eq />
<apply><diff />
<bvar><ci> time </ci></bvar>
<ci> Ca_JSR </ci>
</apply>
<apply><times />
<ci> B_JSR </ci>
<apply><minus />
<ci> J_tr </ci>
<ci> J_rel </ci>
</apply>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="calcium_NSR_diff_eq">
<apply id="calcium_NSR_diff_eq"><eq />
<apply><diff />
<bvar><ci> time </ci></bvar>
<ci> Ca_NSR </ci>
</apply>
<apply><minus />
<apply><times />
<apply><minus />
<ci> J_up </ci>
<ci> J_leak </ci>
</apply>
<apply><divide />
<ci> V_myo </ci>
<ci> V_NSR </ci>
</apply>
</apply>
<apply><times />
<ci> J_tr </ci>
<apply><divide />
<ci> V_JSR </ci>
<ci> V_NSR </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<!--
The descriptions of the rate of change of [Na]i and [K]i are the same as the
LR-II model. In addition to the LR-II model, both high and low affinity
calcium binding sites are included for troponin (Tn).
-->
<component name="ionic_concentrations" cmeta:id="ionic_concentrations">
<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="#ionic_concentrations">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The descriptions of the rate of change of [Na]i and [K]i are the
same as the LR-II model.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<!-- these variables are defined here and used in other components -->
<variable
name="Nai" public_interface="out"
initial_value="10.2042" units="mM" />
<variable
name="Nao" public_interface="out"
initial_value="140.0" units="mM" />
<variable
name="Ki" public_interface="out"
initial_value="143.727" units="mM" />
<variable
name="Ko" public_interface="out"
initial_value="5.4" units="mM" />
<variable
name="Cao" public_interface="out"
initial_value="1.8" units="mM" />
<!-- 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_Na" public_interface="in" units="uA_per_mm2" />
<variable name="i_Na_b" public_interface="in" units="uA_per_mm2" />
<variable name="i_ns_Na" public_interface="in" units="uA_per_mm2" />
<variable name="i_NaCa" public_interface="in" units="uA_per_mm2" />
<variable name="i_NaK" public_interface="in" units="uA_per_mm2" />
<variable name="i_Ca_L_K" 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_Kp" public_interface="in" units="uA_per_mm2" />
<variable name="i_ns_K" public_interface="in" units="uA_per_mm2" />
<variable name="Am" public_interface="in" units="per_mm" />
<variable name="V_myo" 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 ion concentration.
</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><times />
<apply><minus />
<apply><plus />
<ci> i_Na </ci>
<ci> i_Na_b </ci>
<ci> i_ns_Na </ci>
<apply><times />
<ci> i_NaCa </ci>
<cn cellml:units="dimensionless"> 3.0 </cn>
</apply>
<apply><times />
<ci> i_NaK </ci>
<cn cellml:units="dimensionless"> 3.0 </cn>
</apply>
</apply>
</apply>
<apply><divide />
<ci> Am </ci>
<apply><times />
<ci> V_myo </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="#potassium_internal_diff_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The rate of change of intracellular potassium ion concentration.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="potassium_internal_diff_eq">
<apply id="potassium_internal_diff_eq"><eq />
<apply><diff />
<bvar><ci> time </ci></bvar>
<ci> Ki </ci>
</apply>
<apply><times />
<apply><minus />
<apply><plus />
<ci> i_Ca_L_K </ci>
<ci> i_K </ci>
<ci> i_K1 </ci>
<ci> i_Kp </ci>
<ci> i_ns_K </ci>
<apply><minus />
<apply><times />
<ci> i_NaK </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
</apply>
</apply>
</apply>
<apply><divide />
<ci> Am </ci>
<apply><times />
<ci> V_myo </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="#potassium_external_diff_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The rate of change of extracellular potassium ion concentration.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="potassium_external_diff_eq">
<apply id="potassium_external_diff_eq"><eq />
<apply><diff />
<bvar><ci> time </ci></bvar>
<ci> Ko </ci>
</apply>
<apply><times />
<apply><plus />
<ci> i_Ca_L_K </ci>
<ci> i_K </ci>
<ci> i_K1 </ci>
<ci> i_Kp </ci>
<ci> i_ns_K </ci>
<apply><minus />
<apply><times />
<ci> i_NaK </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
</apply>
</apply>
<apply><divide />
<ci> Am </ci>
<apply><times />
<ci> V_myo </ci>
<ci> F </ci>
</apply>
</apply>
</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. The "containment" relationship is used to
describe geometric hierarchies - or how components are physically arranged
in relation to eachother.
-->
<group>
<relationship_ref relationship="containment" />
<component_ref component="membrane">
<component_ref component="fast_sodium_current">
<component_ref component="fast_sodium_current_m_gate" />
<component_ref component="fast_sodium_current_h_gate" />
<component_ref component="fast_sodium_current_j_gate" />
</component_ref>
<component_ref component="L_type_Ca_channel">
<component_ref component="L_type_Ca_channel_y_gate" />
</component_ref>
<component_ref component="time_dependent_potassium_current">
<component_ref component="time_dependent_potassium_current_X_gate" />
<component_ref component="time_dependent_potassium_current_Xi_gate" />
</component_ref>
<component_ref component="Na_Ca_exchanger" />
<component_ref component="time_independent_potassium_current">
<component_ref component="time_independent_potassium_current_K1_gate" />
</component_ref>
<component_ref component="plateau_potassium_current" />
<component_ref component="sarcolemmal_calcium_pump" />
<component_ref component="sodium_background_current" />
<component_ref component="calcium_background_current" />
<component_ref component="sodium_potassium_pump" />
<component_ref component="non_specific_calcium_activated_current" />
<component_ref component="calcium_subsystem" />
<component_ref component="ionic_concentrations" />
</component_ref>
</group>
<!--
The following <group> element specifies how the components
representing activation and inactivation coefficients are
encapsulated inside the sodium and potassium channel components.
Encapsulation describes the logical hierarchy of components in a network,
and may or may not reflect their physical arrangement.
-->
<group>
<relationship_ref relationship="encapsulation" />
<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="fast_sodium_current_j_gate" />
</component_ref>
<component_ref component="L_type_Ca_channel">
<component_ref component="L_type_Ca_channel_y_gate" />
</component_ref>
<component_ref component="time_dependent_potassium_current">
<component_ref component="time_dependent_potassium_current_X_gate" />
<component_ref component="time_dependent_potassium_current_Xi_gate" />
</component_ref>
<component_ref component="time_independent_potassium_current">
<component_ref component="time_independent_potassium_current_K1_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="fast_sodium_current" component_2="environment" />
<map_variables variable_1="time" variable_2="time" />
</connection>
<connection>
<map_components
component_1="L_type_Ca_channel" 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="Na_Ca_exchanger" 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="plateau_potassium_current" component_2="environment" />
<map_variables variable_1="time" variable_2="time" />
</connection>
<connection>
<map_components
component_1="sarcolemmal_calcium_pump" 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="non_specific_calcium_activated_current" component_2="environment" />
<map_variables variable_1="time" variable_2="time" />
</connection>
<connection>
<map_components
component_1="calcium_subsystem" component_2="environment" />
<map_variables variable_1="time" variable_2="time" />
</connection>
<connection>
<map_components
component_1="ionic_concentrations" 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="membrane" component_2="fast_sodium_current" />
<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="T" variable_2="T" />
<map_variables variable_1="F" variable_2="F" />
</connection>
<connection>
<map_components
component_1="membrane" component_2="L_type_Ca_channel" />
<map_variables variable_1="V" variable_2="V" />
<map_variables variable_1="i_Ca_L_Ca" variable_2="i_Ca_L_Ca" />
<map_variables variable_1="i_Ca_L_K" variable_2="i_Ca_L_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="membrane" component_2="time_dependent_potassium_current" />
<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="membrane" component_2="Na_Ca_exchanger" />
<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="T" variable_2="T" />
<map_variables variable_1="F" variable_2="F" />
</connection>
<connection>
<map_components
component_1="membrane" component_2="time_independent_potassium_current" />
<map_variables variable_1="V" variable_2="V" />
<map_variables variable_1="i_K1" variable_2="i_K1" />
<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="membrane" component_2="plateau_potassium_current" />
<map_variables variable_1="V" variable_2="V" />
<map_variables variable_1="i_Kp" variable_2="i_Kp" />
</connection>
<connection>
<map_components
component_1="membrane" component_2="sarcolemmal_calcium_pump" />
<map_variables variable_1="i_p_Ca" variable_2="i_p_Ca" />
</connection>
<connection>
<map_components
component_1="membrane" component_2="sodium_background_current" />
<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="membrane" component_2="calcium_background_current" />
<map_variables variable_1="V" variable_2="V" />
<map_variables variable_1="i_Ca_b" variable_2="i_Ca_b" />
<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="membrane" component_2="sodium_potassium_pump" />
<map_variables variable_1="V" variable_2="V" />
<map_variables variable_1="i_NaK" variable_2="i_NaK" />
<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="membrane" component_2="non_specific_calcium_activated_current" />
<map_variables variable_1="V" variable_2="V" />
<map_variables variable_1="i_ns_Ca" variable_2="i_ns_Ca" />
<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="membrane" component_2="calcium_subsystem" />
<map_variables variable_1="F" variable_2="F" />
<map_variables variable_1="Am" variable_2="Am" />
</connection>
<connection>
<map_components
component_1="membrane" component_2="ionic_concentrations" />
<map_variables variable_1="F" variable_2="F" />
</connection>
<!-- Several variables are passed between the sibling components. -->
<connection>
<map_components
component_1="fast_sodium_current" component_2="ionic_concentrations" />
<map_variables variable_1="Nai" variable_2="Nai" />
<map_variables variable_1="Nao" variable_2="Nao" />
<map_variables variable_1="i_Na" variable_2="i_Na" />
</connection>
<connection>
<map_components
component_1="fast_sodium_current" component_2="sodium_background_current" />
<map_variables variable_1="E_Na" variable_2="E_Na" />
</connection>
<connection>
<map_components
component_1="L_type_Ca_channel" component_2="calcium_subsystem" />
<map_variables variable_1="Ca_SS" variable_2="Ca_SS" />
<map_variables variable_1="i_Ca_L_Ca" variable_2="i_Ca_L_Ca" />
</connection>
<connection>
<map_components
component_1="L_type_Ca_channel" component_2="ionic_concentrations" />
<map_variables variable_1="i_Ca_L_K" variable_2="i_Ca_L_K" />
<map_variables variable_1="Ki" variable_2="Ki" />
<map_variables variable_1="Ko" variable_2="Ko" />
<map_variables variable_1="Cao" variable_2="Cao" />
</connection>
<connection>
<map_components
component_1="time_dependent_potassium_current" component_2="ionic_concentrations" />
<map_variables variable_1="Ki" variable_2="Ki" />
<map_variables variable_1="Ko" variable_2="Ko" />
<map_variables variable_1="Nao" variable_2="Nao" />
<map_variables variable_1="Nai" variable_2="Nai" />
<map_variables variable_1="i_K" variable_2="i_K" />
</connection>
<connection>
<map_components
component_1="Na_Ca_exchanger" component_2="ionic_concentrations" />
<map_variables variable_1="Cao" variable_2="Cao" />
<map_variables variable_1="Nai" variable_2="Nai" />
<map_variables variable_1="Nao" variable_2="Nao" />
<map_variables variable_1="i_NaCa" variable_2="i_NaCa" />
</connection>
<connection>
<map_components
component_1="Na_Ca_exchanger" component_2="calcium_subsystem" />
<map_variables variable_1="Cai" variable_2="Cai" />
<map_variables variable_1="i_NaCa" variable_2="i_NaCa" />
</connection>
<connection>
<map_components
component_1="time_independent_potassium_current" component_2="ionic_concentrations" />
<map_variables variable_1="Ki" variable_2="Ki" />
<map_variables variable_1="Ko" variable_2="Ko" />
<map_variables variable_1="i_K1" variable_2="i_K1" />
</connection>
<connection>
<map_components
component_1="plateau_potassium_current" component_2="time_independent_potassium_current" />
<map_variables variable_1="E_K1" variable_2="E_K1" />
</connection>
<connection>
<map_components
component_1="plateau_potassium_current" component_2="ionic_concentrations" />
<map_variables variable_1="i_Kp" variable_2="i_Kp" />
</connection>
<connection>
<map_components
component_1="sodium_background_current" component_2="ionic_concentrations" />
<map_variables variable_1="i_Na_b" variable_2="i_Na_b" />
</connection>
<connection>
<map_components
component_1="sarcolemmal_calcium_pump" component_2="calcium_subsystem" />
<map_variables variable_1="i_p_Ca" variable_2="i_p_Ca" />
<map_variables variable_1="Cai" variable_2="Cai" />
</connection>
<connection>
<map_components
component_1="calcium_background_current" component_2="calcium_subsystem" />
<map_variables variable_1="Cai" variable_2="Cai" />
<map_variables variable_1="i_Ca_b" variable_2="i_Ca_b" />
</connection>
<connection>
<map_components
component_1="calcium_background_current" component_2="ionic_concentrations" />
<map_variables variable_1="Cao" variable_2="Cao" />
</connection>
<connection>
<map_components
component_1="sodium_potassium_pump" component_2="ionic_concentrations" />
<map_variables variable_1="Nai" variable_2="Nai" />
<map_variables variable_1="Nao" variable_2="Nao" />
<map_variables variable_1="Ko" variable_2="Ko" />
<map_variables variable_1="i_NaK" variable_2="i_NaK" />
</connection>
<connection>
<map_components
component_1="non_specific_calcium_activated_current" component_2="ionic_concentrations" />
<map_variables variable_1="i_ns_Na" variable_2="i_ns_Na" />
<map_variables variable_1="i_ns_K" variable_2="i_ns_K" />
<map_variables variable_1="Nai" variable_2="Nai" />
<map_variables variable_1="Nao" variable_2="Nao" />
<map_variables variable_1="Ko" variable_2="Ko" />
<map_variables variable_1="Ki" variable_2="Ki" />
</connection>
<connection>
<map_components
component_1="non_specific_calcium_activated_current" component_2="calcium_subsystem" />
<map_variables variable_1="Cai" variable_2="Cai" />
</connection>
<connection>
<map_components
component_1="ionic_concentrations" component_2="calcium_subsystem" />
<map_variables variable_1="Am" variable_2="Am" />
<map_variables variable_1="V_myo" variable_2="V_myo" />
</connection>
<!--
Various variables are passed between parent components and their
encapsulated gates.
-->
<connection>
<map_components
component_1="fast_sodium_current" component_2="fast_sodium_current_m_gate" />
<map_variables variable_1="m" variable_2="m" />
<map_variables variable_1="time" variable_2="time" />
<map_variables variable_1="V" variable_2="V" />
</connection>
<connection>
<map_components
component_1="fast_sodium_current" component_2="fast_sodium_current_h_gate" />
<map_variables variable_1="h" variable_2="h" />
<map_variables variable_1="time" variable_2="time" />
<map_variables variable_1="V" variable_2="V" />
</connection>
<connection>
<map_components
component_1="fast_sodium_current" component_2="fast_sodium_current_j_gate" />
<map_variables variable_1="j" variable_2="j" />
<map_variables variable_1="time" variable_2="time" />
<map_variables variable_1="V" variable_2="V" />
</connection>
<connection>
<map_components
component_1="L_type_Ca_channel" component_2="L_type_Ca_channel_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="time_dependent_potassium_current" component_2="time_dependent_potassium_current_Xi_gate" />
<map_variables variable_1="Xi" variable_2="Xi" />
<map_variables variable_1="time" variable_2="time" />
<map_variables variable_1="V" variable_2="V" />
</connection>
<connection>
<map_components
component_1="time_independent_potassium_current" component_2="time_independent_potassium_current_K1_gate" />
<map_variables variable_1="time" variable_2="time" />
<map_variables variable_1="V" variable_2="V" />
<map_variables variable_1="E_K1" variable_2="E_K1" />
<map_variables variable_1="K1_infinity" variable_2="K1_infinity" />
</connection>
</model>
