- Author:
- David Nickerson <nickerso@users.sourceforge.net>
- Date:
- 2017-07-06 16:36:34+12:00
- Desc:
- adding in simulation and graphing descriptions for the 1962 Noble model.
- Permanent Source URI:
- http://models.cellml.org/workspace/49e/rawfile/fded318b4c2f9f5fe33a27113cde621ce35d4fd8/1962_noble.xml
<?xml version="1.0" encoding="iso-8859-1"?>
<model
name="noble_model_1962"
cmeta:id="noble_model_1962"
xmlns="http://www.cellml.org/cellml/1.0#"
xmlns:cellml="http://www.cellml.org/cellml/1.0#"
xmlns:cmeta="http://www.cellml.org/metadata/1.0#">
<rdf:RDF
xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
xmlns:cmeta="http://www.cellml.org/metadata/1.0#"
xmlns:bqs="http://www.cellml.org/bqs/1.0#"
xmlns:dc="http://purl.org/dc/elements/1.1/"
xmlns:dcterms="http://purl.org/dc/terms/"
xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#">
<!--
The following RDF block contains metadata that applies to this document
as a whole, as indicated by the empty about attribute on the
<rdf:Description> element.
-->
<rdf:Description rdf:about="">
<!--
The Model Builder Metadata. The Dublin Core "creator" element is used
to indicate the person who translated the model into CellML.
-->
<dc:creator rdf:parseType="Resource">
<vCard:N rdf:parseType="Resource">
<vCard:Family>Lloyd</vCard:Family>
<vCard:Given>Catherine</vCard:Given>
<vCard:Other>May</vCard:Other>
</vCard:N>
<vCard:EMAIL rdf:parseType="Resource">
<rdf:value>c.lloyd@auckland.ac.nz</rdf:value>
<rdf:type rdf:resource="http://imc.org/vCard/3.0#internet" />
</vCard:EMAIL>
<vCard:ORG rdf:parseType="Resource">
<vCard:Orgname>The University of Auckland</vCard:Orgname>
<vCard:Orgunit>Bioengineering Institute</vCard:Orgunit>
</vCard:ORG>
</dc:creator>
<!--
The Creation Date metadata. This is the date on which the model
was translated into CellML.
-->
<dcterms:created rdf:parseType="Resource">
<dcterms:W3CDTF>2001-12-18</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>
Encapsulated the model under an interface component for use when
importing the model into a specific experiment or simulation.
</rdf:value>
<cmeta:modifier rdf:parseType="Resource">
<vCard:N rdf:parseType="Resource">
<vCard:Family>Nickerson</vCard:Family>
<vCard:Given>David</vCard:Given>
<vCard:Other>P</vCard:Other>
</vCard:N>
</cmeta:modifier>
<dcterms:modified rdf:parseType="Resource">
<dcterms:W3CDTF>2004-12-21</dcterms:W3CDTF>
</dcterms:modified>
</cmeta:modification>
<cmeta:modification rdf:parseType="Resource">
<rdf:value>
Changed units and added stimulus current.
</rdf:value>
<cmeta:modifier rdf:parseType="Resource">
<vCard:N rdf:parseType="Resource">
<vCard:Family>Nickerson</vCard:Family>
<vCard:Given>David</vCard:Given>
<vCard:Other>P</vCard:Other>
</vCard:N>
</cmeta:modifier>
<dcterms:modified rdf:parseType="Resource">
<dcterms:W3CDTF>2003-04-05</dcterms:W3CDTF>
</dcterms:modified>
</cmeta:modification>
<cmeta:modification rdf:parseType="Resource">
<rdf:value>
Changed the model name so the model loads in the database easier.
</rdf:value>
<cmeta:modifier rdf:parseType="Resource">
<vCard:N rdf:parseType="Resource">
<vCard:Family>Cuellar</vCard:Family>
<vCard:Given>Autumn</vCard:Given>
<vCard:Other>A</vCard:Other>
</vCard:N>
</cmeta:modifier>
<dcterms:modified rdf:parseType="Resource">
<dcterms:W3CDTF>2003-04-05</dcterms:W3CDTF>
</dcterms:modified>
</cmeta:modification>
<cmeta:modification rdf:parseType="Resource">
<rdf:value>
Corrected membrane_voltage_diff_eq.
</rdf:value>
<cmeta:modifier rdf:parseType="Resource">
<vCard:N rdf:parseType="Resource">
<vCard:Family>Lloyd</vCard:Family>
<vCard:Given>Catherine</vCard:Given>
<vCard:Other>May</vCard:Other>
</vCard:N>
</cmeta:modifier>
<dcterms:modified rdf:parseType="Resource">
<dcterms:W3CDTF>2002-02-28</dcterms:W3CDTF>
</dcterms:modified>
</cmeta:modification>
<cmeta:modification rdf:parseType="Resource">
<rdf:value>
Updated metadata to conform to the 16/01/2002 CellML Metadata 1.0
Specification.
</rdf:value>
<cmeta:modifier rdf:parseType="Resource">
<vCard:N rdf:parseType="Resource">
<vCard:Family>Cuellar</vCard:Family>
<vCard:Given>Autumn</vCard:Given>
<vCard:Other>A.</vCard:Other>
</vCard:N>
</cmeta:modifier>
<dcterms:modified rdf:parseType="Resource">
<dcterms:W3CDTF>2002-01-20</dcterms:W3CDTF>
</dcterms:modified>
</cmeta:modification>
<!-- The Publisher metadata. -->
<dc:publisher>
Bioengineering Institute, The University of Auckland.
</dc:publisher>
</rdf:Description>
<!--
The following metadata refers to the model itself, as indicated by the
reference to the ID "noble_model_1962", which is declared on the
<model> element.
-->
<rdf:Description rdf:about="#noble_model_1962">
<!-- A human readable name for the model. -->
<dc:title>
The 1962 Noble Model of Purkinje Fibre Action and Pace-maker Potentials
</dc:title>
<!-- A comment regarding the model. -->
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
This is the CellML description of Noble's 1962 mathematical model of
Purkinje fibre action and pace-maker potentials. The equations
formulated by Hodgkin and Huxley (1952) to describe the electrical
activity of squid nerve have been modified to describe the action
and pace-maker potentials of the Purkinje fibres of the heart.
</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>
<bqs:reference rdf:parseType="Resource">
<bqs:Pubmed_id>14480151</bqs:Pubmed_id>
<bqs:JournalArticle rdf:parseType="Resource">
<dc:creator rdf:parseType="Resource">
<bqs:Person rdf:parseType="Resource">
<vCard:N rdf:parseType="Resource">
<vCard:Family>Noble</vCard:Family>
<vCard:Given>Denis</vCard:Given>
</vCard:N>
</bqs:Person>
</dc:creator>
<dc:title>
A Modification of the Hodgkin-Huxley Equations Applicable to
Purkinje Fibre Action and Pace-maker Potentials
</dc:title>
<dcterms:issued rdf:parseType="Resource">
<dcterms:W3CDTF>1962</dcterms:W3CDTF>
</dcterms:issued>
<bqs:Journal rdf:parseType="Resource">
<dc:title>Journal of Physiology</dc:title>
</bqs:Journal>
<bqs:volume>160</bqs:volume>
<bqs:first_page>317</bqs:first_page>
<bqs:last_page>352</bqs:last_page>
</bqs:JournalArticle>
</bqs:reference>
</rdf:Description>
</rdf:RDF>
<!--
Below, we define some additional units for association with variables and
constants within the model. The identifiers are fairly self-explanatory.
-->
<units name="ms">
<unit prefix="milli" units="second" />
</units>
<units name="per_ms">
<unit prefix="milli" units="second" exponent="-1" />
</units>
<units name="mV">
<unit prefix="milli" units="volt" />
</units>
<units name="per_mV">
<unit prefix="milli" units="volt" exponent="-1" />
</units>
<units name="per_mV_ms">
<unit units="mV" exponent="-1" />
<unit units="ms" exponent="-1" />
</units>
<units name="mS_per_mm2">
<unit prefix="milli" units="siemens" />
<unit prefix="milli" units="metre" exponent="-2" />
</units>
<units name="uF_per_mm2">
<unit prefix="micro" units="farad" />
<unit prefix="milli" units="metre" exponent="-2" />
</units>
<units name="uA_per_mm2">
<unit prefix="micro" units="ampere" />
<unit prefix="milli" units="metre" exponent="-2" />
</units>
<component name="interface" cmeta:id="interface">
<rdf:RDF
xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
xmlns:cmeta="http://www.cellml.org/metadata/1.0#">
<rdf:Description rdf:about="#interface">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
Here we define a component which encapsulates the entire model
and provides the interface to model boundary conditions and
outputs.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<!-- time is always a special case -->
<variable name="time" public_interface="in" private_interface="out" units="ms"/>
<!-- inputs -->
<variable name="I_stim" public_interface="in" private_interface="out" units="uA_per_mm2"/>
<variable name="g_K_add" public_interface="in" private_interface="out" units="mS_per_mm2" />
<!-- outputs -->
</component><!--interface-->
<!--
The "membrane" component is really the `root' node of our model.
It defines the action potential variable "V" among other things.
-->
<component name="membrane" cmeta:id="membrane">
<rdf:RDF
xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
xmlns:cmeta="http://www.cellml.org/metadata/1.0#">
<rdf:Description rdf:about="#membrane">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The main component of the model, containing the membrane currents
and defining the transmembrane potential.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<variable cmeta:id="Vm" name="V" initial_value="-73.8" public_interface="out" units="mV" />
<variable name="Cm" initial_value="0.12" units="uF_per_mm2" />
<variable name="time" public_interface="in" units="ms" />
<variable name="i_Na" public_interface="in" units="uA_per_mm2" />
<variable name="i_K" public_interface="in" units="uA_per_mm2" />
<variable name="i_Leak" public_interface="in" units="uA_per_mm2" />
<variable name="I_stim" public_interface="in" units="uA_per_mm2" />
<!--
The membrane voltage (V) is calculated as an ordinary
differential equation in terms of the currents.
-->
<rdf:RDF
xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
xmlns:cmeta="http://www.cellml.org/metadata/1.0#">
<rdf:Description rdf:about="#membrane_voltage_diff_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The kinetics of the transmembrane potential.
</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_K </ci>
<ci> i_Leak </ci>
</apply>
</apply>
<ci> Cm </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="#IStim_for_cmiss_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
This is a dummy equation that we simply use to make grabbing the
value easier.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<variable name="IStimC" units="uA_per_mm2" public_interface="out"/>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="IStim_for_cmiss_eq">
<apply id="IStim_for_cmiss"><eq/>
<ci>IStimC</ci>
<ci>I_stim</ci>
</apply>
</math>
</component>
<component name="sodium_channel" cmeta:id="sodium_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="#sodium_channel">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The modified sodium current from the 1952 Hodgkin Huxley model.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<variable name="i_Na" public_interface="out" units="uA_per_mm2" />
<variable name="g_Na_max" initial_value="4.0" units="mS_per_mm2" />
<variable name="g_Na" units="mS_per_mm2" />
<variable name="E_Na" initial_value="40.0" units="mV" />
<variable
name="time" public_interface="in"
private_interface="out" units="ms" />
<variable
name="V" public_interface="in"
private_interface="out" units="mV" />
<variable name="m" private_interface="in" units="dimensionless" />
<variable name="h" private_interface="in" units="dimensionless" />
<rdf:RDF
xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
xmlns:cmeta="http://www.cellml.org/metadata/1.0#">
<rdf:Description rdf:about="#g_Na_calculation_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
Calculation of the channel conductance.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="g_Na_calculation_eq">
<apply id="g_Na_calculation"><eq />
<ci> g_Na </ci>
<apply><times />
<apply><power />
<ci> m </ci>
<cn cellml:units="dimensionless"> 3.0 </cn>
</apply>
<ci> h </ci>
<ci> g_Na_max </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_Na_calculation_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
Calculation of the channel current.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="i_Na_calculation_eq">
<apply id="i_Na_calculation"><eq />
<ci> i_Na </ci>
<apply><times />
<apply><plus />
<apply><times />
<ci> g_Na_max </ci>
<apply><power />
<ci> m </ci>
<cn cellml:units="dimensionless"> 3.0 </cn>
</apply>
<ci> h </ci>
</apply>
<cn cellml:units="mS_per_mm2">0.14e-2</cn>
</apply>
<apply><minus />
<ci> V </ci>
<ci> E_Na </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="sodium_channel_m_gate" cmeta:id="sodium_channel_m_gate">
<rdf:RDF
xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
xmlns:cmeta="http://www.cellml.org/metadata/1.0#">
<rdf:Description rdf:about="#sodium_channel_m_gate">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The voltage-dependent activation gate for the sodium channel - the m
gate.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<variable name="m" initial_value="0.05" public_interface="out" units="dimensionless" />
<variable name="alpha_m" units="per_ms" />
<variable name="beta_m" units="per_ms" />
<variable name="V" public_interface="in" units="mV" />
<variable name="time" public_interface="in" units="ms" />
<rdf:RDF
xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
xmlns:cmeta="http://www.cellml.org/metadata/1.0#">
<rdf:Description rdf:about="#alpha_m_calculation_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The opening rate for 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"> 0.1 </cn>
<apply><minus />
<apply><minus />
<ci> V </ci>
</apply>
<cn cellml:units="mV"> 48.0 </cn>
</apply>
</apply>
<apply><minus />
<apply><exp />
<apply><divide />
<apply><minus />
<apply><minus />
<ci> V </ci>
</apply>
<cn cellml:units="mV"> 48.0 </cn>
</apply>
<cn cellml:units="mV"> 15.0 </cn>
</apply>
</apply>
<cn cellml:units="dimensionless"> 1.0 </cn>
</apply>
</apply>
</apply>
</math>
<rdf:RDF
xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
xmlns:cmeta="http://www.cellml.org/metadata/1.0#">
<rdf:Description rdf:about="#beta_m_calculation_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The closing rate for 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><divide />
<apply><times />
<cn cellml:units="per_mV_ms"> 0.12 </cn>
<apply><plus />
<ci> V </ci>
<cn cellml:units="mV"> 8.0 </cn>
</apply>
</apply>
<apply><minus />
<apply><exp />
<apply><divide />
<apply><plus />
<ci> V </ci>
<cn cellml:units="mV"> 8.0 </cn>
</apply>
<cn cellml:units="mV"> 5.0 </cn>
</apply>
</apply>
<cn cellml:units="dimensionless"> 1.0 </cn>
</apply>
</apply>
</apply>
</math>
<rdf:RDF
xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
xmlns:cmeta="http://www.cellml.org/metadata/1.0#">
<rdf:Description rdf:about="#dm_dt_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The kinetics of the m gate.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="dm_dt_eq">
<apply id="dm_dt"><eq />
<apply><diff />
<bvar><ci> time </ci></bvar>
<ci> m </ci>
</apply>
<apply><minus />
<apply><times />
<ci> alpha_m </ci>
<apply><minus />
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> m </ci>
</apply>
</apply>
<apply><times />
<ci> beta_m </ci>
<ci> m </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="sodium_channel_h_gate" cmeta:id="sodium_channel_h_gate">
<rdf:RDF
xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
xmlns:cmeta="http://www.cellml.org/metadata/1.0#">
<rdf:Description rdf:about="#sodium_channel_h_gate">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The voltage-dependent inactivation gate for the sodium channel - the
h gate.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<variable name="h" initial_value="0.785" public_interface="out" units="dimensionless" />
<variable name="alpha_h" units="per_ms" />
<variable name="beta_h" units="per_ms" />
<variable name="V" public_interface="in" units="mV" />
<variable name="time" public_interface="in" units="ms" />
<rdf:RDF
xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
xmlns:cmeta="http://www.cellml.org/metadata/1.0#">
<rdf:Description rdf:about="#alpha_h_calculation_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The opening rate for the h gate.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="alpha_h_calculation_eq">
<apply id="alpha_h_calculation"><eq />
<ci> alpha_h </ci>
<apply><times />
<cn cellml:units="per_ms"> 0.17 </cn>
<apply><exp />
<apply><divide />
<apply><minus />
<apply><minus />
<ci> V </ci>
</apply>
<cn cellml:units="mV"> 90.0 </cn>
</apply>
<cn cellml:units="mV"> 20.0 </cn>
</apply>
</apply>
</apply>
</apply>
</math>
<rdf:RDF
xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
xmlns:cmeta="http://www.cellml.org/metadata/1.0#">
<rdf:Description rdf:about="#beta_h_calculation_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The closing rate for the h gate.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="beta_h_calculation_eq">
<apply id="beta_h_calculation"><eq />
<ci> beta_h </ci>
<apply><divide />
<cn cellml:units="per_ms"> 1.0 </cn>
<apply><plus />
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply><exp />
<apply><divide />
<apply><minus />
<apply><minus />
<ci> V </ci>
</apply>
<cn cellml:units="mV"> 42.0 </cn>
</apply>
<cn cellml:units="mV"> 10.0 </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="#dh_dt_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The kinetics of the h gate.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="dh_dt_eq">
<apply id="dh_dt"><eq />
<apply><diff />
<bvar><ci> time </ci></bvar>
<ci> h </ci>
</apply>
<apply><minus />
<apply><times />
<ci> alpha_h </ci>
<apply><minus />
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> h </ci>
</apply>
</apply>
<apply><times />
<ci> beta_h </ci>
<ci> h </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="potassium_channel" cmeta:id="potassium_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="#potassium_channel">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The modified Hodgkin Huxley 1952 potassium channel.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<variable name="i_K" public_interface="out" units="uA_per_mm2" />
<variable name="g_K1" units="mS_per_mm2" />
<variable name="g_K2" units="mS_per_mm2" />
<variable name="g_K_add" public_interface="in" units="mS_per_mm2" />
<variable
name="time" public_interface="in"
private_interface="out" units="ms" />
<variable
name="V" public_interface="in"
private_interface="out" units="mV" />
<variable name="n" private_interface="in" units="dimensionless" />
<rdf:RDF
xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
xmlns:cmeta="http://www.cellml.org/metadata/1.0#">
<rdf:Description rdf:about="#i_K_calculation_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
Calculation of the potassium current. The g_K_add conductance term
can be used to obtain a quiescent variant of the model by setting
its value to 0.001 mS/mm2.
</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 />
<apply><plus />
<ci> g_K1 </ci>
<ci> g_K2 </ci>
<ci> g_K_add </ci>
</apply>
<apply><plus />
<ci> V </ci>
<cn cellml:units="mV"> 100.0 </cn>
</apply>
</apply>
</apply>
</math>
<rdf:RDF
xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
xmlns:cmeta="http://www.cellml.org/metadata/1.0#">
<rdf:Description rdf:about="#g_K1_calculation_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The conductance of the first "type" of potassium channels present in
this model, using an empirical formaulation.
</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><plus />
<apply><times />
<cn cellml:units="mS_per_mm2"> 1.2e-2 </cn>
<apply><exp />
<apply><divide />
<apply><minus />
<apply><minus />
<ci> V </ci>
</apply>
<cn cellml:units="mV"> 90.0 </cn>
</apply>
<cn cellml:units="mV"> 50.0 </cn>
</apply>
</apply>
</apply>
<apply><times />
<cn cellml:units="mS_per_mm2"> 0.015e-2 </cn>
<apply><exp />
<apply><divide />
<apply><plus />
<ci> V </ci>
<cn cellml:units="mV"> 90.0 </cn>
</apply>
<cn cellml:units="mV"> 60.0 </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="#g_K2_calculation_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The conductance of the second "type" of potassium channels present
in this model, using the Hodgkin Huxley 1952 type kinetics.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="g_K2_calculation_eq">
<apply id="g_K2_calculation"><eq />
<ci> g_K2 </ci>
<apply><times />
<cn cellml:units="mS_per_mm2"> 1.2e-2 </cn>
<apply><power />
<ci> n </ci>
<cn cellml:units="dimensionless"> 4.0 </cn>
</apply>
</apply>
</apply>
</math>
</component>
<component name="potassium_channel_n_gate" cmeta:id="potassium_channel_n_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="#potassium_channel_n_gate">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The voltage-dependent activation gate for the potassium channel -
the n gate.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<variable name="n" initial_value="0.0935" public_interface="out" units="dimensionless" />
<variable name="alpha_n" units="per_ms" />
<variable name="beta_n" units="per_ms" />
<variable name="V" public_interface="in" units="mV" />
<variable name="time" public_interface="in" units="ms" />
<rdf:RDF
xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
xmlns:cmeta="http://www.cellml.org/metadata/1.0#">
<rdf:Description rdf:about="#alpha_n_calculation_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The opening rate for the n gate.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="alpha_n_calculation_eq">
<apply id="alpha_n_calculation"><eq />
<ci> alpha_n </ci>
<apply><divide />
<apply><times />
<cn cellml:units="per_mV_ms"> 0.0001 </cn>
<apply><minus />
<apply><minus />
<ci> V </ci>
</apply>
<cn cellml:units="mV"> 50.0 </cn>
</apply>
</apply>
<apply><minus />
<apply><exp />
<apply><divide />
<apply><minus />
<apply><minus />
<ci> V </ci>
</apply>
<cn cellml:units="mV"> 50.0 </cn>
</apply>
<cn cellml:units="mV"> 10.0 </cn>
</apply>
</apply>
<cn cellml:units="dimensionless"> 1.0 </cn>
</apply>
</apply>
</apply>
</math>
<rdf:RDF
xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
xmlns:cmeta="http://www.cellml.org/metadata/1.0#">
<rdf:Description rdf:about="#beta_n_calculation_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The closing rate for the n gate.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="beta_n_calculation_eq">
<apply id="beta_n_calculation"><eq />
<ci> beta_n </ci>
<apply><times />
<cn cellml:units="per_ms"> 0.002 </cn>
<apply><exp />
<apply><divide />
<apply><minus />
<apply><minus />
<ci> V </ci>
</apply>
<cn cellml:units="mV"> 90.0 </cn>
</apply>
<cn cellml:units="mV"> 80.0 </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="#dn_dt_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The kinetics of the n gate.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="dn_dt_eq">
<apply id="dn_dt"><eq />
<apply><diff />
<bvar><ci> time </ci></bvar>
<ci> n </ci>
</apply>
<apply><minus />
<apply><times />
<ci> alpha_n </ci>
<apply><minus />
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> n </ci>
</apply>
</apply>
<apply><times />
<ci> beta_n </ci>
<ci> n </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="leakage_current" cmeta:id="leakage_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="#leakage_current">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
A non-specific background current attributed in part to chloride
ions. Can be turned on by specifying an appropriate value for the
conductance (~0.00075 mS/mm2).
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<variable name="i_Leak" public_interface="out" units="uA_per_mm2" />
<variable name="g_L" initial_value="0.0" units="mS_per_mm2" />
<variable name="E_L" initial_value="-60.0" units="mV" />
<variable name="time" public_interface="in" units="ms" />
<variable name="V" public_interface="in" units="mV" />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="i_Leak_calculation"><eq />
<ci> i_Leak </ci>
<apply><times />
<ci> g_L </ci>
<apply><minus />
<ci> V </ci>
<ci> E_L </ci>
</apply>
</apply>
</apply>
</math>
</component>
<group>
<relationship_ref relationship="containment" />
<component_ref component="membrane">
<component_ref component="sodium_channel">
<component_ref component="sodium_channel_m_gate" />
<component_ref component="sodium_channel_h_gate" />
</component_ref>
<component_ref component="potassium_channel">
<component_ref component="potassium_channel_n_gate" />
</component_ref>
<component_ref component="leakage_current" />
</component_ref>
</group>
<group>
<relationship_ref relationship="encapsulation" />
<component_ref component="interface">
<component_ref component="membrane"/>
<component_ref component="sodium_channel">
<component_ref component="sodium_channel_m_gate" />
<component_ref component="sodium_channel_h_gate" />
</component_ref>
<component_ref component="potassium_channel">
<component_ref component="potassium_channel_n_gate" />
</component_ref>
<component_ref component="leakage_current" />
</component_ref>
</group>
<connection>
<map_components
component_1="membrane" component_2="interface"/>
<map_variables variable_1="time" variable_2="time"/>
<map_variables variable_1="I_stim" variable_2="I_stim"/>
</connection>
<connection>
<map_components
component_1="sodium_channel" component_2="interface" />
<map_variables variable_1="time" variable_2="time" />
</connection>
<connection>
<map_components
component_1="potassium_channel" component_2="interface"/>
<map_variables variable_1="time" variable_2="time"/>
<map_variables variable_1="g_K_add" variable_2="g_K_add"/>
</connection>
<connection>
<map_components
component_1="leakage_current" component_2="interface" />
<map_variables variable_1="time" variable_2="time" />
</connection>
<connection>
<map_components
component_1="membrane" component_2="sodium_channel" />
<map_variables variable_1="V" variable_2="V" />
<map_variables variable_1="i_Na" variable_2="i_Na" />
</connection>
<connection>
<map_components
component_1="membrane" component_2="potassium_channel" />
<map_variables variable_1="V" variable_2="V" />
<map_variables variable_1="i_K" variable_2="i_K" />
</connection>
<connection>
<map_components
component_1="membrane" component_2="leakage_current" />
<map_variables variable_1="V" variable_2="V" />
<map_variables variable_1="i_Leak" variable_2="i_Leak" />
</connection>
<connection>
<map_components
component_1="sodium_channel" component_2="sodium_channel_m_gate" />
<map_variables variable_1="m" variable_2="m" />
<map_variables variable_1="time" variable_2="time" />
<map_variables variable_1="V" variable_2="V" />
</connection>
<connection>
<map_components
component_1="sodium_channel" component_2="sodium_channel_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="potassium_channel"
component_2="potassium_channel_n_gate" />
<map_variables variable_1="n" variable_2="n" />
<map_variables variable_1="time" variable_2="time" />
<map_variables variable_1="V" variable_2="V" />
</connection>
</model>
