- Author:
- David Nickerson <nickerso@users.sourceforge.net>
- Date:
- 2011-06-21 15:56:12+12:00
- Desc:
- adding a standalone version of the SED-ML document for this example, updating to pass validation using Frank's new web tools
- Permanent Source URI:
- https://models.cellml.org/workspace/a1/rawfile/1e62f9a11a1b467aff7bc1ddd0b4fc8ac3f052c0/models/1977_beeler/experiments/1980_ebihara_johnson.xml
<?xml version="1.0" encoding="iso-8859-1"?>
<model
name="ebihara_johnson_model_1980"
cmeta:id="ebihara_johnson_model_1980"
xmlns="http://www.cellml.org/cellml/1.1#"
xmlns:cellml="http://www.cellml.org/cellml/1.1#"
xmlns:cmeta="http://www.cellml.org/metadata/1.0#">
<rdf:RDF
xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
xmlns:cmeta="http://www.cellml.org/metadata/1.0#"
xmlns:bqs="http://www.cellml.org/bqs/1.0#"
xmlns:dc="http://purl.org/dc/elements/1.1/"
xmlns:dcterms="http://purl.org/dc/terms/"
xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#"
xmlns:cs="http://www.cellml.org/metadata/simulation/1.0#">
<rdf:Description rdf:about="">
<dc:creator rdf:parseType="Resource">
<vCard:N rdf:parseType="Resource">
<vCard:Family>Nickerson</vCard:Family>
<vCard:Given>David</vCard:Given>
</vCard:N>
<vCard:ORG rdf:parseType="Resource">
<vCard:Orgname>The University of Auckland</vCard:Orgname>
<vCard:Orgunit>Auckland BioengineeringInstitute</vCard:Orgunit>
</vCard:ORG>
</dc:creator>
<dcterms:created rdf:parseType="Resource">
<dcterms:W3CDTF>2009-06-23</dcterms:W3CDTF>
</dcterms:created>
</rdf:Description>
<rdf:Description rdf:about="#ebihara_johnson_model_1980">
<dc:title>
The Ebihara-Johnson Model of the Fast Sodium Current in Cardiac Muscle,
1980
</dc:title>
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
This is the CellML description of Ebihara and Johnson's mathematical
model of the fast sodium current in cardiac muscle (1980). It
describes the ionic current with Hodgkin-Huxley formalism. This model
was the first to specifically target a single channel and attempt to
quantify its parameters.
</rdf:value>
<dc:creator rdf:parseType="Resource">
<vCard:FN>Catherine Lloyd</vCard:FN>
</dc:creator>
</cmeta:comment>
<cmeta:species>Mammalia</cmeta:species>
<cmeta:bio_entity>Cardiac Myocyte</cmeta:bio_entity>
<bqs:reference rdf:parseType="Resource">
<bqs:Pubmed_id>7260301</bqs:Pubmed_id>
</bqs:reference>
<cs:simulation>
<rdf:Description rdf:ID="simulation">
<cs:multistepMethod>bdf</cs:multistepMethod>
<cs:iterationMethod>functional</cs:iterationMethod>
<cs:boundIntervals rdf:parseType="Collection">
<rdf:Description>
<cs:boundVariable>
<rdf:Description rdf:about="#time"/>
</cs:boundVariable>
<cs:maximumStepSize rdf:datatype="http://www.w3.org/2001/XMLSchema#double">
0.1
</cs:maximumStepSize>
<cs:tabulationStepSize rdf:datatype="http://www.w3.org/2001/XMLSchema#double">
0.5
</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">
1500
</cs:endingValue>
</rdf:Description>
</cs:boundIntervals>
</rdf:Description>
</cs:simulation>
</rdf:Description>
</rdf:RDF>
<import xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="../model.xml">
<component component_ref="interface" name="model"/>
</import>
<import xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="../../protocols/periodic-IStim.xml">
<component name="stimulus_protocol" component_ref="stimulus_protocol"/>
</import>
<component name="stimulus_parameters" cmeta:id="stimulus_parameters">
<variable name="stimPeriod" public_interface="out" private_interface="out" initial_value="500.0" units="ms"/>
<variable name="stimDuration" public_interface="out" private_interface="out" initial_value="2.0" units="ms"/>
<variable name="stimCurrent" public_interface="out" private_interface="out" initial_value="80" units="uA_per_mmcu"/>
<variable name="Am" public_interface="out" private_interface="out" initial_value="200" units="per_mm"/>
</component>
<connection>
<map_components component_1="stimulus_protocol" component_2="stimulus_parameters"/>
<map_variables variable_1="stimPeriod" variable_2="stimPeriod"/>
<map_variables variable_1="stimDuration" variable_2="stimDuration"/>
<map_variables variable_1="stimCurrent" variable_2="stimCurrent"/>
<map_variables variable_1="Am" variable_2="Am"/>
</connection>
<connection>
<map_components component_1="stimulus_protocol" component_2="time"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="model" component_2="stimulus_protocol"/>
<map_variables variable_1="Istim" variable_2="IStim"/>
</connection>
<component name="time" cmeta:id="time_component">
<rdf:RDF
xmlns: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_component">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The actual definition of the time variable.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<variable name="time" cmeta:id="time" initial_value="0.0" public_interface="out" units="ms"/>
</component>
<connection>
<map_components component_1="model" component_2="time"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<import xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="../model.xml">
<units name="ms" units_ref="ms"/>
<units name="per_ms" units_ref="per_ms"/>
<units name="mV" units_ref="mV"/>
<units name="per_mV" units_ref="per_mV"/>
<units name="per_mV_ms" units_ref="per_mV_ms"/>
<units name="mS_per_mm2" units_ref="mS_per_mm2"/>
<units name="uF_per_mm2" units_ref="uF_per_mm2"/>
<units name="uA_per_mm2" units_ref="uA_per_mm2"/>
<units name="concentration_units" units_ref="concentration_units"/>
</import>
<import xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="../../common/units.xml">
<units name="per_mm" units_ref="per_mm"/>
<units name="uA_per_mmcu" units_ref="uA_per_mmcu"/>
</import>
<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>
In the calculation of the fast sodium current there is no variable
corresponding to the j gate used in the Beeler-Reuter model because
the experimental results showed no need to include a second
deactivation variable.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<variable cmeta:id="INa" name="i_Na" public_interface="out" units="uA_per_mm2" />
<variable name="g_Na" initial_value="23.0e-2" units="mS_per_mm2" />
<variable name="E_Na" initial_value="29.0" units="mV" />
<variable name="m" private_interface="in" units="dimensionless" />
<variable name="h" private_interface="in" units="dimensionless" />
<variable
name="time" public_interface="in"
private_interface="out" units="ms" />
<variable
name="V" public_interface="in"
private_interface="out" units="mV" />
<rdf:RDF
xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
xmlns:cmeta="http://www.cellml.org/metadata/1.0#">
<rdf:Description rdf:about="#i_Na_calculation_eq">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
Calculation of the fast sodium current.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<math xmlns="http://www.w3.org/1998/Math/MathML"
cmeta:id="i_Na_calculation_eq">
<apply id="i_Na_calculation"><eq />
<ci> i_Na </ci>
<apply><times />
<ci> g_Na </ci>
<apply><power />
<ci> m </ci>
<cn cellml:units="dimensionless"> 3.0 </cn>
</apply>
<ci> h </ci>
<apply><minus />
<ci> V </ci>
<ci> E_Na </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="fast_sodium_current_m_gate" cmeta:id="fast_sodium_current_m_gate">
<rdf:RDF
xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
xmlns:cmeta="http://www.cellml.org/metadata/1.0#">
<rdf:Description rdf:about="#fast_sodium_current_m_gate">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
The voltage-dependent activation gate for the fast sodium channel -
the m gate.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<variable
name="m" public_interface="out"
initial_value="0.0" 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. The equation for alpha-m was
incorrectly stated in the original 1980 paper, but it appears as
shown below in Spach and Heidlage (1993), who cite a later paper by
Johnson as their source (Johnson, 1983).
</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 />
<cn cellml:units="mV"> 47.13 </cn>
<ci> V </ci>
</apply>
</apply>
<apply><minus />
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply><exp />
<apply><minus />
<apply><minus />
<ci> V </ci>
</apply>
<cn cellml:units="mV"> 47.13 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
<rdf:RDF
xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
xmlns:cmeta="http://www.cellml.org/metadata/1.0#">
<rdf:Description rdf:about="#beta_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><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 gating 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>
<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 of the fast sodium channel -
the h gate.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<variable
name="h" public_interface="out"
initial_value="0.18" 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 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><minus />
<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"> 3.1e5 </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><minus />
<apply><plus />
<ci> V </ci>
<cn cellml:units="mV"> 10.66 </cn>
</apply>
</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>
<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>
</group>
<connection>
<map_components
component_1="fast_sodium_current" component_2="time" />
<map_variables variable_1="time" variable_2="time" />
</connection>
<connection>
<map_components
component_1="model" component_2="fast_sodium_current" />
<map_variables variable_1="V" variable_2="V" />
</connection>
<connection>
<map_components
component_1="fast_sodium_current" component_2="fast_sodium_current_m_gate" />
<map_variables variable_1="m" variable_2="m" />
<map_variables variable_1="time" variable_2="time" />
<map_variables variable_1="V" variable_2="V" />
</connection>
<connection>
<map_components
component_1="fast_sodium_current" component_2="fast_sodium_current_h_gate" />
<map_variables variable_1="h" variable_2="h" />
<map_variables variable_1="time" variable_2="time" />
<map_variables variable_1="V" variable_2="V" />
</connection>
<component name="Iadd">
<variable name="Iadd" public_interface="out" units="uA_per_mm2"/>
<variable name="INa_EJ" public_interface="in" units="uA_per_mm2"/>
<variable name="INa_original" public_interface="in" units="uA_per_mm2"/>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="Iadd_eq">
<apply id="Iadd_calculate"><eq />
<ci>Iadd</ci>
<apply><minus/>
<ci>INa_EJ</ci>
<ci>INa_original</ci>
</apply>
</apply>
</math>
</component>
<connection>
<map_components component_1="fast_sodium_current" component_2="Iadd" />
<map_variables variable_1="i_Na" variable_2="INa_EJ" />
</connection>
<connection>
<map_components component_1="model" component_2="Iadd" />
<map_variables variable_1="INa" variable_2="INa_original" />
<map_variables variable_1="Iadd" variable_2="Iadd" />
</connection>
</model>
