- Author:
- Hanne <Hanne@hanne-nielsens-macbook.local>
- Date:
- 2009-12-07 12:36:18+13:00
- Desc:
- Added images in ai and svg format
- Permanent Source URI:
- http://models.cellml.org/workspace/ebihara_johnson_1980/rawfile/c237679e647407c4e8bf8d60d6a40683bc019f93/ebihara_johnson_1980.cellml
<?xml version="1.0" encoding="utf-8"?>
<!-- FILE : ebihara_johnson_model_1980.xml
CREATED : 17th December 2001
LAST MODIFIED : 9th April 2003
AUTHOR : Catherine Lloyd
Department of Engineering Science
The University of Auckland
MODEL STATUS : This model conforms to the CellML 1.0 Specification released on
10th August 2001, and the 16/1/2002 CellML Metadata 1.0 Specification.
DESCRIPTION : This file contains a CellML description of the fast sodium current
in cardiac muscle, based on the Ebihara-johnson model, 1980.
CHANGES:
04/01/2002 - CML - Added the components of the Beeler-Reuter Model.
21/01/2002 - AAC - Updated metadata to conform with the 16/1/02 CellML
Metadata 1.0 Specification.
25/02/2002 - CML - Corrected several equations.
28/02/2002 - CML - Corrected the membrane voltage differential equation.
19/07/2002 - CML - Added more metadata.
09/04/2003 - AAC - Added publication date information.
-->
<model xmlns="http://www.cellml.org/cellml/1.0#" xmlns:cmeta="http://www.cellml.org/metadata/1.0#" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:bqs="http://www.cellml.org/bqs/1.0#" xmlns:cellml="http://www.cellml.org/cellml/1.0#" xmlns:dcterms="http://purl.org/dc/terms/" xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" cmeta:id="ebihara_johnson_1980" name="ebihara_johnson_1980">
<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
<articleinfo>
<title>The Ebihara-Johnson Sodium Current Model (1980)</title>
<author>
<firstname>Catherine</firstname>
<surname>Lloyd</surname>
<affiliation>
<shortaffil>Bioengineering Institute, University of Auckland</shortaffil>
</affiliation>
</author>
</articleinfo>
<section id="sec_status">
<title>Model Status</title>
<para>
This model is valid CellML and contains consistent units but is not fully parameterised.
</para>
</section>
<sect1 id="sec_structure">
<title>Model Structure</title>
<para>
In 1980, Lisa Ebihara and Edward A. Johnson published the first electrophysiological model to specifically target a single ion channel and attempt to quantify its parameters. They used the Hodgkin-Huxley formulation to revise the parameters of the fast sodium current in cardiac muscle. This model exhibits a faster sodium current than the Beeler-Reuter model, and when the two models are coupled, the Ebihara-Johnson can be used as a direct replacement of the sodium kinetics of the Beeler-Reuter.
</para>
<para>
<informalfigure float="0" id="fig_reaction_diagram">
<mediaobject>
<imageobject>
<objectinfo>
<title>model diagram</title>
</objectinfo>
<imagedata fileref="ebihara_1980.png"/>
</imageobject>
</mediaobject>
<caption>Schematic diagram of the Ebihara and Johnson model.</caption>
</informalfigure>
</para>
<para>
The complete original paper reference is cited below:
</para>
<para>
Fast Sodium Current In Cardiac Muscle, Lisa Ebihara and Edward A. Johnson, 1980,
<emphasis>Biophys. J.</emphasis> 32, 779-790. <ulink url="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&list_uids=7260301&dopt=Abstract">PubMed ID: 7260301</ulink>
</para>
</sect1>
</article>
</documentation>
<!--
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 units="second" prefix="milli"/>
</units>
<units name="per_ms">
<unit units="second" prefix="milli" exponent="-1"/>
</units>
<units name="mV">
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</units>
<units name="per_mV">
<unit units="volt" prefix="milli" exponent="-1"/>
</units>
<units name="per_mV_ms">
<unit units="mV" exponent="-1"/>
<unit units="ms" exponent="-1"/>
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<units name="mS_per_mm2">
<unit units="siemens" prefix="milli"/>
<unit units="metre" prefix="milli" exponent="-2"/>
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<units name="uF_per_mm2">
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<units name="concentration_units">
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</units>
<units name="per_concentration_units">
<unit units="concentration_units" exponent="-1"/>
</units>
<!--
The "environment" component is used to declare variables that are used by
all or most of the other components, in this case just "time".
-->
<component cmeta:id="environment" name="environment">
<variable units="ms" public_interface="out" name="time"/>
</component>
<component cmeta:id="membrane" name="membrane">
<variable units="mV" public_interface="out" name="V" initial_value="-87.0"/>
<variable units="uF_per_mm2" name="C" initial_value="0.013"/>
<variable units="ms" public_interface="in" name="time"/>
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<variable units="uA_per_mm2" public_interface="in" name="i_K1"/>
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<ci> i_K1 </ci>
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<ci>C</ci>
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</apply>
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<variable units="uA_per_mm2" public_interface="out" name="IStimC"/>
<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>Istim</ci>
</apply>
</math>
</component>
<component cmeta:id="fast_sodium_current" name="fast_sodium_current">
<variable units="uA_per_mm2" public_interface="out" name="i_Na"/>
<variable units="mS_per_mm2" name="g_Na" initial_value="23.0e-2"/>
<variable units="mV" name="E_Na" initial_value="29.0"/>
<variable units="dimensionless" private_interface="in" name="m"/>
<variable units="dimensionless" private_interface="in" name="h"/>
<variable units="ms" public_interface="in" private_interface="out" name="time"/>
<variable units="mV" public_interface="in" private_interface="out" name="V"/>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="i_Na_calculation_eq">
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<ci> h </ci>
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<ci> E_Na </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component cmeta:id="fast_sodium_current_m_gate" name="fast_sodium_current_m_gate">
<variable units="dimensionless" public_interface="out" name="m" initial_value="0.0"/>
<variable units="per_ms" name="alpha_m"/>
<variable units="per_ms" name="beta_m"/>
<variable units="mV" public_interface="in" name="V"/>
<variable units="ms" public_interface="in" name="time"/>
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<apply id="alpha_m_calculation">
<eq/>
<ci> alpha_m </ci>
<apply>
<divide/>
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<ci> V </ci>
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</apply>
<apply>
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<minus/>
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</apply>
</apply>
</apply>
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</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="beta_m_calculation_eq">
<apply id="beta_m_calculation">
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<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="dm_dt_eq">
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<variable units="per_ms" name="alpha_h"/>
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<variable units="mV" public_interface="in" name="V"/>
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<divide/>
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</apply>
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</apply>
<apply>
<lt/>
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<cn cellml:units="mV"> -40.0 </cn>
</apply>
</piece>
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<cn cellml:units="per_ms"> 0.0 </cn>
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</piecewise>
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<variable units="ms" public_interface="in" private_interface="out" name="time"/>
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<apply>
<ln/>
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<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="mV"> 50.0 </cn>
</apply>
<cn cellml:units="mV"> 17.5 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="beta_x1_calculation">
<eq/>
<ci> beta_x1 </ci>
<apply>
<times/>
<cn cellml:units="per_ms"> 0.0013 </cn>
<apply>
<divide/>
<apply>
<exp/>
<apply>
<minus/>
<apply>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="mV"> 20.0 </cn>
</apply>
<cn cellml:units="mV"> 16.67 </cn>
</apply>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<minus/>
<apply>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="mV"> 20.0 </cn>
</apply>
<cn cellml:units="mV"> 25.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="dx1_dt">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> x1 </ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> alpha_x1 </ci>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> x1 </ci>
</apply>
</apply>
<apply>
<times/>
<ci> beta_x1 </ci>
<ci> x1 </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component cmeta:id="time_independent_outward_current" name="time_independent_outward_current">
<variable units="uA_per_mm2" public_interface="out" name="i_K1"/>
<variable units="ms" public_interface="in" name="time"/>
<variable units="mV" public_interface="in" name="V"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="i_K1_calculation">
<eq/>
<ci> i_K1 </ci>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.0035 </cn>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="per_ms"> 4.0 </cn>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="per_mV"> 0.04 </cn>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="mV"> 85.0 </cn>
</apply>
</apply>
</apply>
<cn cellml:units="dimensionless"> 1.0 </cn>
</apply>
<apply>
<plus/>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="per_mV"> 0.08 </cn>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="mV"> 53 </cn>
</apply>
</apply>
</apply>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="per_mV"> 0.04 </cn>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="mV"> 53.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="per_ms"> 0.2 </cn>
<apply>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="mV"> 23.0 </cn>
</apply>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="per_mV"> -0.04 </cn>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="mV"> 23.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<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_ref component="slow_inward_current">
<component_ref component="slow_inward_current_d_gate"/>
<component_ref component="slow_inward_current_f_gate"/>
</component_ref>
<component_ref component="time_dependent_outward_current">
<component_ref component="time_dependent_outward_current_x1_gate"/>
</component_ref>
<component_ref component="time_independent_outward_current"/>
</component_ref>
</group>
<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_ref component="slow_inward_current">
<component_ref component="slow_inward_current_d_gate"/>
<component_ref component="slow_inward_current_f_gate"/>
</component_ref>
<component_ref component="time_dependent_outward_current">
<component_ref component="time_dependent_outward_current_x1_gate"/>
</component_ref>
</group>
<connection>
<map_components component_2="environment" component_1="membrane"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="fast_sodium_current"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="slow_inward_current"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="time_dependent_outward_current"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="time_independent_outward_current"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="fast_sodium_current" component_1="membrane"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="i_Na" variable_1="i_Na"/>
</connection>
<connection>
<map_components component_2="slow_inward_current" component_1="membrane"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="i_s" variable_1="i_s"/>
</connection>
<connection>
<map_components component_2="time_dependent_outward_current" component_1="membrane"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="i_x1" variable_1="i_x1"/>
</connection>
<connection>
<map_components component_2="time_independent_outward_current" component_1="membrane"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="i_K1" variable_1="i_K1"/>
</connection>
<connection>
<map_components component_2="fast_sodium_current_m_gate" component_1="fast_sodium_current"/>
<map_variables variable_2="m" variable_1="m"/>
<map_variables variable_2="time" variable_1="time"/>
<map_variables variable_2="V" variable_1="V"/>
</connection>
<connection>
<map_components component_2="fast_sodium_current_h_gate" component_1="fast_sodium_current"/>
<map_variables variable_2="h" variable_1="h"/>
<map_variables variable_2="time" variable_1="time"/>
<map_variables variable_2="V" variable_1="V"/>
</connection>
<connection>
<map_components component_2="time_dependent_outward_current_x1_gate" component_1="time_dependent_outward_current"/>
<map_variables variable_2="x1" variable_1="x1"/>
<map_variables variable_2="time" variable_1="time"/>
<map_variables variable_2="V" variable_1="V"/>
</connection>
<connection>
<map_components component_2="slow_inward_current_d_gate" component_1="slow_inward_current"/>
<map_variables variable_2="d" variable_1="d"/>
<map_variables variable_2="time" variable_1="time"/>
<map_variables variable_2="V" variable_1="V"/>
</connection>
<connection>
<map_components component_2="slow_inward_current_f_gate" component_1="slow_inward_current"/>
<map_variables variable_2="f" variable_1="f"/>
<map_variables variable_2="time" variable_1="time"/>
<map_variables variable_2="V" variable_1="V"/>
</connection>
<rdf:RDF>
<rdf:Seq rdf:about="rdf:#citationAuthorsSeq">
<rdf:li rdf:resource="rdf:#author1Vcard"/>
<rdf:li rdf:resource="rdf:#author2Vcard"/>
</rdf:Seq>
<rdf:Description rdf:about="#membrane_voltage_diff_eq">
<cmeta:comment rdf:resource="rdf:#01ce2bc3-4b1b-4cd8-8132-ea8fd74bec04"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#ee288d2a-834d-438d-8313-056b4becbacf">
<rdf:value>
Calculation of the fast sodium current.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#5cc27f0d-03e6-429a-a6e7-50150cc3ade6">
<rdf:value>
In their 1980 paper, Ebihara and Johnson do not include all the
ionic fluxes across the membrane of the cardiac muscle cell, they
only describe the fast sodium current. The Ebihara-Johnson model
can be coupled to the Beeler-Reuter model (1977) as a direct
replacement for the sodium current. The other ionic currents were
very similar to those found using the Beeler-Reuter model. I have
included these equations from the Beeler-Reuter 1977 model in this
CellML description.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="#beta_m_calculation_eq">
<cmeta:comment rdf:resource="rdf:#eadb1115-8ade-4316-bdbd-febac44f269c"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#fb2e8466-2340-493d-8a08-0bd2cff3fc73">
<rdf:value>
The standard Beeler Reuter (1977) activation gate for the slow
inward current.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#1ac263c4-d516-4882-8c09-b73a88f548ce">
<bqs:Pubmed_id>7260301</bqs:Pubmed_id>
<bqs:JournalArticle rdf:resource="rdf:#4f33c5f6-83d3-4ce9-acb0-9ab1053087c9"/>
</rdf:Description>
<rdf:Description rdf:about="#slow_inward_current_d_gate">
<cmeta:comment rdf:resource="rdf:#fb2e8466-2340-493d-8a08-0bd2cff3fc73"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#d3d82ce2-4c1a-4677-96dd-9c8156c31c4c">
<dcterms:modified rdf:resource="rdf:#97c6b53f-6075-4322-9f74-ded798ea53d1"/>
<rdf:value>
Corrected the membrane voltage differential equation.
</rdf:value>
<cmeta:modifier rdf:resource="rdf:#31e76dd7-4d24-47f5-b195-91fba99deea0"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#6a4b539d-ac99-4f56-afd3-bac27c6552f1">
<dcterms:modified rdf:resource="rdf:#abe4ceea-c7b8-4182-b46d-253956884630"/>
<rdf:value>
Corrected several equations.
</rdf:value>
<cmeta:modifier rdf:resource="rdf:#3261da5c-a39f-4b31-8bea-5bcfcc0a4a6f"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#fb27e1b0-f505-4b81-8c51-1468542ddae5">
<dcterms:modified rdf:resource="rdf:#957a00b0-2398-4ae3-995a-a6d007429847"/>
<rdf:value>
Added the components of the Beeler-Reuter Model.
</rdf:value>
<cmeta:modifier rdf:resource="rdf:#8983930a-6651-463f-b4ae-a726a382ec54"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#030183f5-43aa-4f81-aa00-5a9058891496">
<dcterms:W3CDTF>2003-07-22</dcterms:W3CDTF>
</rdf:Description>
<rdf:Description rdf:about="#slow_inward_current">
<cmeta:comment rdf:resource="rdf:#a6c51603-7a67-4a8e-8b43-650cabc68bab"/>
</rdf:Description>
<rdf:Description rdf:about="#dm_dt_eq">
<cmeta:comment rdf:resource="rdf:#576f3fda-98a7-477d-a519-d9c6984b2c37"/>
</rdf:Description>
<rdf:Description rdf:about="#alpha_h_calculation_eq">
<cmeta:comment rdf:resource="rdf:#84728cc5-836c-4cb1-933a-1e59f62d488c"/>
</rdf:Description>
<rdf:Description rdf:about="#ebihara_johnson_1980">
<dc:title>
The Ebihara-Johnson Model of the Fast Sodium Current in Cardiac Muscle,
1980
</dc:title>
<cmeta:bio_entity>Cardiac Myocyte</cmeta:bio_entity>
<cmeta:comment rdf:resource="rdf:#b08fb71e-7d93-43a9-957e-dfcb7212674b"/>
<bqs:reference rdf:resource="rdf:#1ac263c4-d516-4882-8c09-b73a88f548ce"/>
<bqs:reference rdf:parseType="Resource">
<dc:subject rdf:parseType="Resource">
<bqs:subject_type>keyword</bqs:subject_type>
<rdf:value>
<rdf:Bag>
<rdf:li>cardiac</rdf:li>
<rdf:li>electrophysiology</rdf:li>
<rdf:li>channel kinetics</rdf:li>
<rdf:li>fast sodium current</rdf:li>
</rdf:Bag>
</rdf:value>
</dc:subject>
</bqs:reference>
<cmeta:species>Mammalia</cmeta:species>
</rdf:Description>
<rdf:Description rdf:about="rdf:#590f631b-df75-4e74-aed8-ed3781d3d805">
<dcterms:W3CDTF>2003-04-09</dcterms:W3CDTF>
</rdf:Description>
<rdf:Description rdf:about="#fast_sodium_current">
<cmeta:comment rdf:resource="rdf:#db57f440-4dde-4241-a41b-72f02b7daf21"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#3261da5c-a39f-4b31-8bea-5bcfcc0a4a6f">
<vCard:N rdf:resource="rdf:#c905db44-62db-44e3-b99b-afc71f0d5a65"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#576f3fda-98a7-477d-a519-d9c6984b2c37">
<rdf:value>
The gating kinetics of the m gate.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#eadb1115-8ade-4316-bdbd-febac44f269c">
<rdf:value>
The closing rate for the m gate.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#3d6ff7fe-7d60-463b-8474-f1182b075ec0">
<vCard:ORG rdf:resource="rdf:#64aca2e0-9474-4df4-ab17-5d5d84b20622"/>
<vCard:EMAIL rdf:resource="rdf:#f6de55fb-72b1-43fe-98ff-cff13ee5a3ec"/>
<vCard:N rdf:resource="rdf:#0976283e-c5b6-4c35-aef0-c65178e85297"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#c905db44-62db-44e3-b99b-afc71f0d5a65">
<vCard:Given>Catherine</vCard:Given>
<vCard:Family>Lloyd</vCard:Family>
<vCard:Other>May</vCard:Other>
</rdf:Description>
<rdf:Description rdf:about="rdf:#999fe272-8af9-43bc-937e-35b8703cd376">
<dcterms:W3CDTF>2002-07-19</dcterms:W3CDTF>
</rdf:Description>
<rdf:Description rdf:about="rdf:#4fc75d49-fdec-4c58-970a-2f4c306512b6">
<vCard:N rdf:resource="rdf:#e4e609cb-a650-429c-be6e-84c34512c499"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#1775ef0f-301e-4bf4-8865-2941d72b7ee9">
<rdf:value>
This is a dummy equation that we simply use to make grabbing the
value in CMISS much easier.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#abe4ceea-c7b8-4182-b46d-253956884630">
<dcterms:W3CDTF>2002-02-25</dcterms:W3CDTF>
</rdf:Description>
<rdf:Description rdf:about="rdf:#f6de55fb-72b1-43fe-98ff-cff13ee5a3ec">
<rdf:type rdf:resource="http://imc.org/vCard/3.0#internet"/>
<rdf:value>c.lloyd@auckland.ac.nz</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#6f854acd-c72d-431b-9b98-6982e23c5233">
<dcterms:W3CDTF>1980-01-01</dcterms:W3CDTF>
</rdf:Description>
<rdf:Description rdf:about="rdf:#97c6b53f-6075-4322-9f74-ded798ea53d1">
<rdf:type rdf:resource="http://purl.org/dc/terms/W3CDTF"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#9b82fa5c-edb2-49d8-8237-a2438bdf0a38">
<rdf:type rdf:resource="http://purl.org/dc/terms/W3CDTF"/>
</rdf:Description>
<rdf:Description rdf:about="#time_independent_outward_current">
<cmeta:comment rdf:resource="rdf:#c7b9f342-a9db-4929-9f02-69c6900f0e87"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#ee7d7e8a-2227-40e3-8655-a9abc47c4c20">
<vCard:N rdf:resource="rdf:#18ee33d0-2964-4744-9f1f-21a9762aa174"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#0976283e-c5b6-4c35-aef0-c65178e85297">
<vCard:Given>Catherine</vCard:Given>
<vCard:Family>Lloyd</vCard:Family>
<vCard:Other>May</vCard:Other>
</rdf:Description>
<rdf:Description rdf:about="rdf:#7cd6a17f-b952-4d6a-8caa-e3296cf19f34">
<vCard:N rdf:resource="rdf:#92222b87-8be0-463b-9d5d-1ca4192bde54"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#e4e609cb-a650-429c-be6e-84c34512c499">
<vCard:Given>David</vCard:Given>
<vCard:Family>Nickerson</vCard:Family>
<vCard:Other>P</vCard:Other>
</rdf:Description>
<rdf:Description rdf:about="rdf:#c2dd38ca-3802-429a-a960-89f055f705c7">
<vCard:FN>Catherine Lloyd</vCard:FN>
</rdf:Description>
<rdf:Description rdf:about="rdf:#3bf76602-b671-47f0-9947-fec3bed0f386">
<rdf:type rdf:resource="http://www.w3.org/2001/vcard-rdf/3.0#N"/>
<vCard:Given>Autumn</vCard:Given>
<vCard:Family>Cuellar</vCard:Family>
<vCard:Other>A.</vCard:Other>
</rdf:Description>
<rdf:Description rdf:about="rdf:#db57f440-4dde-4241-a41b-72f02b7daf21">
<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>
</rdf:Description>
<rdf:Description rdf:about="rdf:#8983930a-6651-463f-b4ae-a726a382ec54">
<rdf:type rdf:resource="http://www.w3.org/2001/vcard-rdf/3.0#N"/>
<vCard:Given>Catherine</vCard:Given>
<vCard:Family>Lloyd</vCard:Family>
<vCard:Other>May</vCard:Other>
</rdf:Description>
<rdf:Description rdf:about="#time_dependent_outward_current">
<cmeta:comment rdf:resource="rdf:#60cef239-b78f-4f1a-bffe-436e77c9c5c0"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#7cdc05ad-9b3c-4f5a-96c1-ed3e5043f5e0">
<rdf:value>
The voltage-dependent inactivation gate of the fast sodium channel -
the h gate.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#author2VcardN">
<vCard:Given>E</vCard:Given>
<vCard:Family>Johnson</vCard:Family>
<vCard:Other>A</vCard:Other>
</rdf:Description>
<rdf:Description rdf:about="rdf:#957a00b0-2398-4ae3-995a-a6d007429847">
<rdf:type rdf:resource="http://purl.org/dc/terms/W3CDTF"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#aa7cb718-9eb0-4a51-a313-e36082d71045">
<dcterms:modified rdf:resource="rdf:#9b82fa5c-edb2-49d8-8237-a2438bdf0a38"/>
<rdf:value>
Updated metadata to conform to the 16/1/02 CellML Metadata 1.0
Specification.
</rdf:value>
<cmeta:modifier rdf:resource="rdf:#3bf76602-b671-47f0-9947-fec3bed0f386"/>
</rdf:Description>
<rdf:Description rdf:about="#beta_h_calculation_eq">
<cmeta:comment rdf:resource="rdf:#5e910089-77bc-441b-b41e-33be9a0d4f03"/>
</rdf:Description>
<rdf:Description rdf:about="#dh_dt_eq">
<cmeta:comment rdf:resource="rdf:#810d2e14-ca70-47f5-aea8-cc6bf21c9546"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#4f33c5f6-83d3-4ce9-acb0-9ab1053087c9">
<dc:creator rdf:resource="rdf:#citationAuthorsSeq"/>
<dc:title>Fast sodium current in cardiac muscle: A quantitative description</dc:title>
<bqs:volume>32</bqs:volume>
<bqs:first_page>779</bqs:first_page>
<bqs:Journal rdf:resource="rdf:#cd6555f2-87e2-43d7-9aac-aae4892f5712"/>
<dcterms:issued rdf:resource="rdf:#6f854acd-c72d-431b-9b98-6982e23c5233"/>
<bqs:last_page>790</bqs:last_page>
</rdf:Description>
<rdf:Description rdf:about="rdf:#bb615aad-5fac-47b3-b3be-dc17081713ca">
<dcterms:modified rdf:resource="rdf:#030183f5-43aa-4f81-aa00-5a9058891496"/>
<rdf:value>
Modifying units and adding a stimulus current.
</rdf:value>
<cmeta:modifier rdf:resource="rdf:#4fc75d49-fdec-4c58-970a-2f4c306512b6"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#a6c51603-7a67-4a8e-8b43-650cabc68bab">
<rdf:value>
The standard Beeler Reuter (1977) slow inward (calcium) current
formulation.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#31e76dd7-4d24-47f5-b195-91fba99deea0">
<rdf:type rdf:resource="http://www.w3.org/2001/vcard-rdf/3.0#N"/>
<vCard:Given>Catherine</vCard:Given>
<vCard:Family>Lloyd</vCard:Family>
<vCard:Other>May</vCard:Other>
</rdf:Description>
<rdf:Description rdf:about="rdf:#b08fb71e-7d93-43a9-957e-dfcb7212674b">
<dc:creator rdf:resource="rdf:#c2dd38ca-3802-429a-a960-89f055f705c7"/>
<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>
</rdf:Description>
<rdf:Description rdf:about="rdf:#84728cc5-836c-4cb1-933a-1e59f62d488c">
<rdf:value>
The opening rate of the h gate.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#be03ca7a-50b4-414b-b329-3123c3b93114">
<rdf:value>
The standard Beeler Reuter (1977) inactivation gate for the slow
inward current.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#author2Vcard">
<rdf:type rdf:resource="http://www.cellml.org/bqs/1.0#Person"/>
<vCard:N rdf:resource="rdf:#author2VcardN"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#810d2e14-ca70-47f5-aea8-cc6bf21c9546">
<rdf:value>
The kinetics of the h gate.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#c7b9f342-a9db-4929-9f02-69c6900f0e87">
<rdf:value>
The standard Beeler Reuter (1977) time-independent outward
(potassium) current.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#cd6555f2-87e2-43d7-9aac-aae4892f5712">
<dc:title>Biophysical Journal</dc:title>
</rdf:Description>
<rdf:Description rdf:about="">
<dc:publisher>
The University of Auckland, Bioengineering Research Group
</dc:publisher>
<cmeta:modification rdf:resource="rdf:#5402da3f-dcfc-469e-ba89-7b436382f5d0"/>
<cmeta:modification rdf:resource="rdf:#6a4b539d-ac99-4f56-afd3-bac27c6552f1"/>
<cmeta:modification rdf:resource="rdf:#aa7cb718-9eb0-4a51-a313-e36082d71045"/>
<cmeta:modification rdf:resource="rdf:#b0705a4b-f5de-4b90-a39b-b48af2595019"/>
<cmeta:modification rdf:resource="rdf:#bb615aad-5fac-47b3-b3be-dc17081713ca"/>
<cmeta:modification rdf:resource="rdf:#d3d82ce2-4c1a-4677-96dd-9c8156c31c4c"/>
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<dcterms:created rdf:resource="rdf:#97bb2ebc-f171-45c7-8986-a4ca1332b713"/>
<dc:creator rdf:resource="rdf:#3d6ff7fe-7d60-463b-8474-f1182b075ec0"/>
</rdf:Description>
<rdf:Description rdf:about="#slow_inward_current_f_gate">
<cmeta:comment rdf:resource="rdf:#be03ca7a-50b4-414b-b329-3123c3b93114"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#92222b87-8be0-463b-9d5d-1ca4192bde54">
<vCard:Given>Catherine</vCard:Given>
<vCard:Family>Lloyd</vCard:Family>
<vCard:Other>May</vCard:Other>
</rdf:Description>
<rdf:Description rdf:about="rdf:#18ee33d0-2964-4744-9f1f-21a9762aa174">
<vCard:Given>Autumn</vCard:Given>
<vCard:Family>Cuellar</vCard:Family>
<vCard:Other>A</vCard:Other>
</rdf:Description>
<rdf:Description rdf:about="rdf:#5402da3f-dcfc-469e-ba89-7b436382f5d0">
<dcterms:modified rdf:resource="rdf:#999fe272-8af9-43bc-937e-35b8703cd376"/>
<rdf:value>
Added more metadata.
</rdf:value>
<cmeta:modifier rdf:resource="rdf:#7cd6a17f-b952-4d6a-8caa-e3296cf19f34"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#ef13ffa5-1608-4b48-9da5-dba5f8875869">
<rdf:value>
The voltage-dependent activation gate for the fast sodium channel -
the m gate.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#ed6daded-7ab4-4c3a-aa18-37b92c670be2">
<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>
</rdf:Description>
<rdf:Description rdf:about="#fast_sodium_current_h_gate">
<cmeta:comment rdf:resource="rdf:#7cdc05ad-9b3c-4f5a-96c1-ed3e5043f5e0"/>
</rdf:Description>
<rdf:Description rdf:about="#IStim_for_cmiss_eq">
<cmeta:comment rdf:resource="rdf:#1775ef0f-301e-4bf4-8865-2941d72b7ee9"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#author1Vcard">
<rdf:type rdf:resource="http://www.cellml.org/bqs/1.0#Person"/>
<vCard:N rdf:resource="rdf:#author1VcardN"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#4f5fc73d-6169-46d0-9b6e-3d8b2f870dcf">
<rdf:value>
The standard Beeler Reuter (1977) gating variable for the
time-dependent outward potassium current.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#author1VcardN">
<vCard:Given>L</vCard:Given>
<vCard:Family>Ebihara</vCard:Family>
</rdf:Description>
<rdf:Description rdf:about="rdf:#5e910089-77bc-441b-b41e-33be9a0d4f03">
<rdf:value>
The closing rate of the h gate.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#97bb2ebc-f171-45c7-8986-a4ca1332b713">
<dcterms:W3CDTF>2001-12-17</dcterms:W3CDTF>
</rdf:Description>
<rdf:Description rdf:about="rdf:#01ce2bc3-4b1b-4cd8-8132-ea8fd74bec04">
<rdf:value>
The main differential equation for the model specifying the rate of
change of the transmembrane potential as the sum of the ionic
currents and an applied stimulus current.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="#alpha_m_calculation_eq">
<cmeta:comment rdf:resource="rdf:#ed6daded-7ab4-4c3a-aa18-37b92c670be2"/>
</rdf:Description>
<rdf:Description rdf:about="#membrane">
<cmeta:comment rdf:resource="rdf:#5cc27f0d-03e6-429a-a6e7-50150cc3ade6"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#60cef239-b78f-4f1a-bffe-436e77c9c5c0">
<rdf:value>
The standard Beeler Reuter (1977) time-dependent outward (potassium)
current.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#b0705a4b-f5de-4b90-a39b-b48af2595019">
<dcterms:modified rdf:resource="rdf:#590f631b-df75-4e74-aed8-ed3781d3d805"/>
<rdf:value>
Added publication date information.
</rdf:value>
<cmeta:modifier rdf:resource="rdf:#ee7d7e8a-2227-40e3-8655-a9abc47c4c20"/>
</rdf:Description>
<rdf:Description rdf:about="#i_Na_calculation_eq">
<cmeta:comment rdf:resource="rdf:#ee288d2a-834d-438d-8313-056b4becbacf"/>
</rdf:Description>
<rdf:Description rdf:about="#fast_sodium_current_m_gate">
<cmeta:comment rdf:resource="rdf:#ef13ffa5-1608-4b48-9da5-dba5f8875869"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#64aca2e0-9474-4df4-ab17-5d5d84b20622">
<vCard:Orgname>The University of Auckland</vCard:Orgname>
<vCard:Orgunit>The Bioengineering Research Group</vCard:Orgunit>
</rdf:Description>
<rdf:Description rdf:about="#time_dependent_outward_current_x1_gate">
<cmeta:comment rdf:resource="rdf:#4f5fc73d-6169-46d0-9b6e-3d8b2f870dcf"/>
</rdf:Description>
</rdf:RDF>
</model>
