- Author:
- David Nickerson <david.nickerson@gmail.com>
- Date:
- 2021-09-16 01:07:43+12:00
- Desc:
- adding BR variant comparison to jupyter notebook
- Permanent Source URI:
- https://models.fieldml.org/workspace/a1/rawfile/faebb18f1db53a7d1f8f4e7fc588d660d45744c0/models/1962_noble/1962_noble.xml
<?xml version='1.0' encoding='UTF-8'?>
<model cmeta:id="noble_model_1962" name="noble_model_1962" 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#">
<!--
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 exponent="-1" prefix="milli" units="second"/>
</units>
<units name="mV">
<unit prefix="milli" units="volt"/>
</units>
<units name="per_mV">
<unit exponent="-1" prefix="milli" units="volt"/>
</units>
<units name="per_mV_ms">
<unit exponent="-1" units="mV"/>
<unit exponent="-1" units="ms"/>
</units>
<units name="mS_per_mm2">
<unit prefix="milli" units="siemens"/>
<unit exponent="-2" prefix="milli" units="metre"/>
</units>
<units name="uF_per_mm2">
<unit prefix="micro" units="farad"/>
<unit exponent="-2" prefix="milli" units="metre"/>
</units>
<units name="uA_per_mm2">
<unit prefix="micro" units="ampere"/>
<unit exponent="-2" prefix="milli" units="metre"/>
</units>
<component cmeta:id="interface" name="interface">
<!-- time is always a special case -->
<variable name="time" private_interface="out" public_interface="in" units="ms"/>
<!-- inputs -->
<variable name="I_stim" private_interface="out" public_interface="in" units="uA_per_mm2"/>
<variable name="g_K_add" private_interface="out" public_interface="in" units="mS_per_mm2"/>
<!-- outputs -->
<variable name="V" private_interface="in" public_interface="out" units="mV"/>
</component>
<!--interface-->
<!--
The "membrane" component is really the `root' node of our model.
It defines the action potential variable "V" among other things.
-->
<component cmeta:id="membrane" name="membrane">
<variable cmeta:id="Vm" initial_value="-73.8" name="V" public_interface="out" units="mV"/>
<variable initial_value="0.12" name="Cm" 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.
-->
<math xmlns="http://www.w3.org/1998/Math/MathML">
<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>
<variable name="IStimC" public_interface="out" units="uA_per_mm2"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="IStim_for_cmiss">
<eq/>
<ci>IStimC</ci>
<ci>I_stim</ci>
</apply>
</math>
</component>
<component cmeta:id="sodium_channel" name="sodium_channel">
<variable name="i_Na" public_interface="out" units="uA_per_mm2"/>
<variable initial_value="4.0" name="g_Na_max" units="mS_per_mm2"/>
<variable name="g_Na" units="mS_per_mm2"/>
<variable initial_value="40.0" name="E_Na" units="mV"/>
<variable name="time" private_interface="out" public_interface="in" units="ms"/>
<variable name="V" private_interface="out" public_interface="in" units="mV"/>
<variable name="m" private_interface="in" units="dimensionless"/>
<variable name="h" private_interface="in" units="dimensionless"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<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>
<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" type="e-notation">0.14<sep/>-2</cn>
</apply>
<apply>
<minus/>
<ci>V</ci>
<ci>E_Na</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component cmeta:id="sodium_channel_m_gate" name="sodium_channel_m_gate">
<variable initial_value="0.05" name="m" 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"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<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>
<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>
<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 cmeta:id="sodium_channel_h_gate" name="sodium_channel_h_gate">
<variable initial_value="0.785" name="h" 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"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<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>
<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>
<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 cmeta:id="potassium_channel" name="potassium_channel">
<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" private_interface="out" public_interface="in" units="ms"/>
<variable name="V" private_interface="out" public_interface="in" units="mV"/>
<variable name="n" private_interface="in" units="dimensionless"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<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>
<apply id="g_K1_calculation">
<eq/>
<ci>g_K1</ci>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="mS_per_mm2" type="e-notation">1.2<sep/>-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" type="e-notation">0.015<sep/>-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>
<apply id="g_K2_calculation">
<eq/>
<ci>g_K2</ci>
<apply>
<times/>
<cn cellml:units="mS_per_mm2" type="e-notation">1.2<sep/>-2</cn>
<apply>
<power/>
<ci>n</ci>
<cn cellml:units="dimensionless">4.0</cn>
</apply>
</apply>
</apply>
</math>
</component>
<component cmeta:id="potassium_channel_n_gate" name="potassium_channel_n_gate">
<variable initial_value="0.0935" name="n" 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"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<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>
<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>
<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 cmeta:id="leakage_current" name="leakage_current">
<variable name="i_Leak" public_interface="out" units="uA_per_mm2"/>
<variable initial_value="0.0" name="g_L" units="mS_per_mm2"/>
<variable initial_value="-60.0" name="E_L" 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"/>
<map_variables variable_1="V" variable_2="V"/>
</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>
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<!--
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.
-->
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The Model Builder Metadata. The Dublin Core "creator" element is used
to indicate the person who translated the model into CellML.
-->
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The Creation Date metadata. This is the date on which the model
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The Modification History metadata. This lists the changes that have been
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Encapsulated the model under an interface component for use when
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<rdf:value xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
Changed units and added stimulus current.
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<cmeta:modifier xmlns:cmeta="http://www.cellml.org/metadata/1.0#" rdf:parseType="Resource" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<vCard:N xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" rdf:parseType="Resource" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<vCard:Family xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#">Nickerson</vCard:Family>
<vCard:Given xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#">David</vCard:Given>
<vCard:Other xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#">P</vCard:Other>
</vCard:N>
</cmeta:modifier>
<dcterms:modified xmlns:dcterms="http://purl.org/dc/terms/" rdf:parseType="Resource" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<dcterms:W3CDTF xmlns:dcterms="http://purl.org/dc/terms/">2003-04-05</dcterms:W3CDTF>
</dcterms:modified>
</cmeta:modification>
<cmeta:modification xmlns:cmeta="http://www.cellml.org/metadata/1.0#" rdf:parseType="Resource" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:value xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
Changed the model name so the model loads in the database easier.
</rdf:value>
<cmeta:modifier xmlns:cmeta="http://www.cellml.org/metadata/1.0#" rdf:parseType="Resource" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<vCard:N xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" rdf:parseType="Resource" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<vCard:Family xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#">Cuellar</vCard:Family>
<vCard:Given xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#">Autumn</vCard:Given>
<vCard:Other xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#">A</vCard:Other>
</vCard:N>
</cmeta:modifier>
<dcterms:modified xmlns:dcterms="http://purl.org/dc/terms/" rdf:parseType="Resource" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<dcterms:W3CDTF xmlns:dcterms="http://purl.org/dc/terms/">2003-04-05</dcterms:W3CDTF>
</dcterms:modified>
</cmeta:modification>
<cmeta:modification xmlns:cmeta="http://www.cellml.org/metadata/1.0#" rdf:parseType="Resource" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:value xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
Corrected membrane_voltage_diff_eq.
</rdf:value>
<cmeta:modifier xmlns:cmeta="http://www.cellml.org/metadata/1.0#" rdf:parseType="Resource" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<vCard:N xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" rdf:parseType="Resource" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<vCard:Family xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#">Lloyd</vCard:Family>
<vCard:Given xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#">Catherine</vCard:Given>
<vCard:Other xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#">May</vCard:Other>
</vCard:N>
</cmeta:modifier>
<dcterms:modified xmlns:dcterms="http://purl.org/dc/terms/" rdf:parseType="Resource" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<dcterms:W3CDTF xmlns:dcterms="http://purl.org/dc/terms/">2002-02-28</dcterms:W3CDTF>
</dcterms:modified>
</cmeta:modification>
<cmeta:modification xmlns:cmeta="http://www.cellml.org/metadata/1.0#" rdf:parseType="Resource" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:value xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
Updated metadata to conform to the 16/01/2002 CellML Metadata 1.0 
Specification.
</rdf:value>
<cmeta:modifier xmlns:cmeta="http://www.cellml.org/metadata/1.0#" rdf:parseType="Resource" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<vCard:N xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" rdf:parseType="Resource" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<vCard:Family xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#">Cuellar</vCard:Family>
<vCard:Given xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#">Autumn</vCard:Given>
<vCard:Other xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#">A.</vCard:Other>
</vCard:N>
</cmeta:modifier>
<dcterms:modified xmlns:dcterms="http://purl.org/dc/terms/" rdf:parseType="Resource" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<dcterms:W3CDTF xmlns:dcterms="http://purl.org/dc/terms/">2002-01-20</dcterms:W3CDTF>
</dcterms:modified>
</cmeta:modification>
<!-- The Publisher metadata. -->
<dc:publisher xmlns:dc="http://purl.org/dc/elements/1.1/">
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 xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" rdf:about="#noble_model_1962">
<!-- A human readable name for the model. -->
<dc:title xmlns:dc="http://purl.org/dc/elements/1.1/">
The 1962 Noble Model of Purkinje Fibre Action and Pace-maker Potentials
</dc:title>
<!-- A comment regarding the model. -->
<cmeta:comment xmlns:cmeta="http://www.cellml.org/metadata/1.0#" rdf:parseType="Resource" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:value xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
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 xmlns:dc="http://purl.org/dc/elements/1.1/" rdf:parseType="Resource" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<vCard:FN xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#">Catherine Lloyd</vCard:FN>
</dc:creator>
</cmeta:comment>
<!-- The model is relevant to all mammals. -->
<cmeta:species xmlns:cmeta="http://www.cellml.org/metadata/1.0#">Mammalia</cmeta:species>
<bqs:reference xmlns:bqs="http://www.cellml.org/bqs/1.0#" rdf:parseType="Resource" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<bqs:Pubmed_id xmlns:bqs="http://www.cellml.org/bqs/1.0#">14480151</bqs:Pubmed_id>
<bqs:JournalArticle xmlns:bqs="http://www.cellml.org/bqs/1.0#" rdf:parseType="Resource" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<dc:creator xmlns:dc="http://purl.org/dc/elements/1.1/" rdf:parseType="Resource" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<bqs:Person xmlns:bqs="http://www.cellml.org/bqs/1.0#" rdf:parseType="Resource" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<vCard:N xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" rdf:parseType="Resource" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<vCard:Family xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#">Noble</vCard:Family>
<vCard:Given xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#">Denis</vCard:Given>
</vCard:N>
</bqs:Person>
</dc:creator>
<dc:title xmlns:dc="http://purl.org/dc/elements/1.1/">
A Modification of the Hodgkin-Huxley Equations Applicable to
Purkinje Fibre Action and Pace-maker Potentials
</dc:title>
<dcterms:issued xmlns:dcterms="http://purl.org/dc/terms/" rdf:parseType="Resource" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<dcterms:W3CDTF xmlns:dcterms="http://purl.org/dc/terms/">1962</dcterms:W3CDTF>
</dcterms:issued>
<bqs:Journal xmlns:bqs="http://www.cellml.org/bqs/1.0#" rdf:parseType="Resource" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<dc:title xmlns:dc="http://purl.org/dc/elements/1.1/">Journal of Physiology</dc:title>
</bqs:Journal>
<bqs:volume xmlns:bqs="http://www.cellml.org/bqs/1.0#">160</bqs:volume>
<bqs:first_page xmlns:bqs="http://www.cellml.org/bqs/1.0#">317</bqs:first_page>
<bqs:last_page xmlns:bqs="http://www.cellml.org/bqs/1.0#">352</bqs:last_page>
</bqs:JournalArticle>
</bqs:reference>
</rdf:Description>
</rdf:RDF>
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" rdf:about="#interface">
<cmeta:comment xmlns:cmeta="http://www.cellml.org/metadata/1.0#" rdf:parseType="Resource" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:value xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
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>
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" rdf:about="#membrane">
<cmeta:comment xmlns:cmeta="http://www.cellml.org/metadata/1.0#" rdf:parseType="Resource" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:value xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
The main component of the model, containing the membrane currents
and defining the transmembrane potential.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" rdf:about="#membrane_voltage_diff_eq">
<cmeta:comment xmlns:cmeta="http://www.cellml.org/metadata/1.0#" rdf:parseType="Resource" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:value xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
The kinetics of the transmembrane potential.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" rdf:about="#IStim_for_cmiss_eq">
<cmeta:comment xmlns:cmeta="http://www.cellml.org/metadata/1.0#" rdf:parseType="Resource" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:value xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
This is a dummy equation that we simply use to make grabbing the
value easier.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" rdf:about="#sodium_channel">
<cmeta:comment xmlns:cmeta="http://www.cellml.org/metadata/1.0#" rdf:parseType="Resource" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:value xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
The modified sodium current from the 1952 Hodgkin Huxley model.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" rdf:about="#g_Na_calculation_eq">
<cmeta:comment xmlns:cmeta="http://www.cellml.org/metadata/1.0#" rdf:parseType="Resource" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:value xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
Calculation of the channel conductance.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" rdf:about="#i_Na_calculation_eq">
<cmeta:comment xmlns:cmeta="http://www.cellml.org/metadata/1.0#" rdf:parseType="Resource" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:value xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
Calculation of the channel current.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" rdf:about="#sodium_channel_m_gate">
<cmeta:comment xmlns:cmeta="http://www.cellml.org/metadata/1.0#" rdf:parseType="Resource" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:value xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
The voltage-dependent activation gate for the sodium channel - the m
gate.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" rdf:about="#alpha_m_calculation_eq">
<cmeta:comment xmlns:cmeta="http://www.cellml.org/metadata/1.0#" rdf:parseType="Resource" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:value xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
The opening rate for the m gate.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" rdf:about="#beta_m_calculation_eq">
<cmeta:comment xmlns:cmeta="http://www.cellml.org/metadata/1.0#" rdf:parseType="Resource" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:value xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
The closing rate for the m gate.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" rdf:about="#dm_dt_eq">
<cmeta:comment xmlns:cmeta="http://www.cellml.org/metadata/1.0#" rdf:parseType="Resource" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:value xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
The kinetics of the m gate.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" rdf:about="#sodium_channel_h_gate">
<cmeta:comment xmlns:cmeta="http://www.cellml.org/metadata/1.0#" rdf:parseType="Resource" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:value xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
The voltage-dependent inactivation gate for the sodium channel - the
h gate.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" rdf:about="#alpha_h_calculation_eq">
<cmeta:comment xmlns:cmeta="http://www.cellml.org/metadata/1.0#" rdf:parseType="Resource" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:value xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
The opening rate for the h gate.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" rdf:about="#beta_h_calculation_eq">
<cmeta:comment xmlns:cmeta="http://www.cellml.org/metadata/1.0#" rdf:parseType="Resource" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:value xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
The closing rate for the h gate.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" rdf:about="#dh_dt_eq">
<cmeta:comment xmlns:cmeta="http://www.cellml.org/metadata/1.0#" rdf:parseType="Resource" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:value xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
The kinetics of the h gate.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" rdf:about="#potassium_channel">
<cmeta:comment xmlns:cmeta="http://www.cellml.org/metadata/1.0#" rdf:parseType="Resource" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:value xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
The modified Hodgkin Huxley 1952 potassium channel.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" rdf:about="#i_K_calculation_eq">
<cmeta:comment xmlns:cmeta="http://www.cellml.org/metadata/1.0#" rdf:parseType="Resource" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:value xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
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>
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" rdf:about="#g_K1_calculation_eq">
<cmeta:comment xmlns:cmeta="http://www.cellml.org/metadata/1.0#" rdf:parseType="Resource" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:value xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
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>
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" rdf:about="#g_K2_calculation_eq">
<cmeta:comment xmlns:cmeta="http://www.cellml.org/metadata/1.0#" rdf:parseType="Resource" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:value xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
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>
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" rdf:about="#potassium_channel_n_gate">
<cmeta:comment xmlns:cmeta="http://www.cellml.org/metadata/1.0#" rdf:parseType="Resource" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:value xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
The voltage-dependent activation gate for the potassium channel -
the n gate.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" rdf:about="#alpha_n_calculation_eq">
<cmeta:comment xmlns:cmeta="http://www.cellml.org/metadata/1.0#" rdf:parseType="Resource" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:value xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
The opening rate for the n gate.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" rdf:about="#beta_n_calculation_eq">
<cmeta:comment xmlns:cmeta="http://www.cellml.org/metadata/1.0#" rdf:parseType="Resource" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:value xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
The closing rate for the n gate.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" rdf:about="#dn_dt_eq">
<cmeta:comment xmlns:cmeta="http://www.cellml.org/metadata/1.0#" rdf:parseType="Resource" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:value xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
The kinetics of the n gate.
</rdf:value>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" rdf:about="#leakage_current">
<cmeta:comment xmlns:cmeta="http://www.cellml.org/metadata/1.0#" rdf:parseType="Resource" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:value xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
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>
</model>