- Author:
- pmr2.import <nobody@models.cellml.org>
- Date:
- 2006-09-04 03:05:05+12:00
- Desc:
- committing version01 of ebihara_johnson_1980
- Permanent Source URI:
- https://staging.physiomeproject.org/workspace/ebihara_johnson_1980/rawfile/a8d17ed22fc2a26d213dfe587599a89bdc2f0353/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_version01" name="ebihara_johnson_1980_version01">
<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 is the original unchecked version of the model imported from the previous
CellML model repository, 24-Jan-2006.
</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 <ulink url="${HTML_EXMPL_HHSA_INTRO}">Hodgkin-Huxley formulation</ulink> to revise the parameters of the fast sodium current in cardiac muscle. This model exhibits a faster sodium current than the <ulink url="${HTML_EXMPL_BR_MODEL}">Beeler-Reuter model</ulink>, 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>
<ulink url="http://www.biophysj.org/cgi/content/abstract/32/2/779">Fast Sodium Current In Cardiac Muscle</ulink>, Lisa Ebihara and Edward A. Johnson, 1980, <ulink url="http://www.biophysj.org/">
<emphasis>Biophys. J.</emphasis>
</ulink> 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>
<para>
The raw CellML description of the Ebihara-Johnson model can be downloaded in various formats as described in <xref linkend="sec_download_this_model"/>. For an example of a more complete documentation for an electrophysiological model, see <ulink url="${HTML_EXMPL_HHSA_INTRO}">The Hodgkin-Huxley Squid Axon Model, 1952</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="millisecond">
<unit units="second" prefix="milli"/>
</units>
<units name="per_millisecond">
<unit units="second" prefix="milli" exponent="-1"/>
</units>
<units name="millivolt">
<unit units="volt" prefix="milli"/>
</units>
<units name="per_millivolt">
<unit units="volt" prefix="milli" exponent="-1"/>
</units>
<units name="per_millivolt_millisecond">
<unit units="millivolt" exponent="-1"/>
<unit units="millisecond" exponent="-1"/>
</units>
<units name="milliS_per_cm2">
<unit units="siemens" prefix="milli"/>
<unit units="metre" prefix="centi" exponent="-2"/>
</units>
<units name="microF_per_cm2">
<unit units="farad" prefix="micro"/>
<unit units="metre" prefix="centi" exponent="-2"/>
</units>
<units name="microA_per_cm2">
<unit units="ampere" prefix="micro"/>
<unit units="metre" prefix="centi" exponent="-2"/>
</units>
<units name="concentration_units">
<unit units="mole" prefix="milli"/>
<unit units="litre" 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 name="environment">
<variable units="millisecond" public_interface="out" name="time"/>
</component>
<component cmeta:id="membrane" name="membrane">
<variable units="millivolt" public_interface="out" name="V"/>
<variable units="microF_per_cm2" name="C" initial_value="1.3"/>
<variable units="millisecond" public_interface="in" name="time"/>
<variable units="microA_per_cm2" public_interface="in" name="i_Na"/>
<variable units="microA_per_cm2" public_interface="in" name="i_s"/>
<variable units="microA_per_cm2" public_interface="in" name="i_x1"/>
<variable units="microA_per_cm2" public_interface="in" name="i_K1"/>
<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>
<times/>
<apply>
<minus/>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> C </ci>
</apply>
</apply>
<apply>
<plus/>
<ci> i_Na </ci>
<ci> i_s </ci>
<ci> i_x1 </ci>
<ci> i_K1 </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component cmeta:id="fast_sodium_current" name="fast_sodium_current">
<variable units="microA_per_cm2" public_interface="out" name="i_Na"/>
<variable units="milliS_per_cm2" name="g_Na" initial_value="23.0"/>
<variable units="millivolt" 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="millisecond" public_interface="in" private_interface="out" name="time"/>
<variable units="millivolt" public_interface="in" private_interface="out" name="V"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<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 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_millisecond" name="alpha_m"/>
<variable units="per_millisecond" name="beta_m"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="millisecond" public_interface="in" name="time"/>
<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_millivolt_millisecond"> 32.0 </cn>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 47.13 </cn>
</apply>
</apply>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<minus/>
<apply>
<minus/>
<ci> V </ci>
</apply>
<cn cellml:units="millivolt"> 47.13 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="beta_m_calculation">
<eq/>
<ci> beta_m </ci>
<apply>
<times/>
<cn cellml:units="per_millisecond"> 0.08 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<ci> V </ci>
</apply>
<cn cellml:units="millivolt"> 11.0 </cn>
</apply>
</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="per_millivolt"> 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">
<variable units="dimensionless" public_interface="out" name="h" initial_value="0.18"/>
<variable units="per_millisecond" name="alpha_h"/>
<variable units="per_millisecond" name="beta_h"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="millisecond" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="alpha_h_calculation">
<eq/>
<ci> alpha_h </ci>
<piecewise>
<piece>
<apply>
<times/>
<cn cellml:units="per_millisecond"> 0.135 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<cn cellml:units="millivolt"> -80.0 </cn>
<ci> V </ci>
</apply>
<cn cellml:units="millivolt"> 6.8 </cn>
</apply>
</apply>
</apply>
<apply>
<lt/>
<ci> V </ci>
<cn cellml:units="millivolt"> -40.0 </cn>
</apply>
</piece>
<otherwise>
<cn cellml:units="per_millisecond"> 0.0 </cn>
</otherwise>
</piecewise>
</apply>
<apply id="beta_h_calculation">
<eq/>
<ci> beta_h </ci>
<piecewise>
<piece>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="per_millisecond"> 3.56 </cn>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="millivolt"> 0.079 </cn>
<ci> V </ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="per_millisecond"> 3.1e5 </cn>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="per_millivolt"> 0.35 </cn>
<ci> V </ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<lt/>
<ci> V </ci>
<cn cellml:units="millivolt"> -40.0 </cn>
</apply>
</piece>
<otherwise>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<times/>
<cn cellml:units="millisecond"> 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="millivolt"> 10.66 </cn>
</apply>
</apply>
<cn cellml:units="millivolt"> 11.1 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</otherwise>
</piecewise>
</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 name="slow_inward_current">
<variable units="microA_per_cm2" public_interface="out" name="i_s"/>
<variable units="milliS_per_cm2" name="g_s" initial_value="0.09"/>
<variable units="millivolt" name="E_s"/>
<variable units="concentration_units" name="Cai" initial_value="0.000000177"/>
<variable units="millisecond" public_interface="in" private_interface="out" name="time"/>
<variable units="millivolt" public_interface="in" private_interface="out" name="V"/>
<variable units="dimensionless" private_interface="in" name="d"/>
<variable units="dimensionless" private_interface="in" name="f"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="E_s_calculation">
<eq/>
<ci> E_s </ci>
<apply>
<minus/>
<cn cellml:units="millivolt"> -82.3 </cn>
<apply>
<times/>
<cn cellml:units="millivolt"> 13.0287 </cn>
<apply>
<ln/>
<ci> Cai </ci>
</apply>
</apply>
</apply>
</apply>
<apply id="i_s_calculation">
<eq/>
<ci> i_s </ci>
<apply>
<times/>
<ci> g_s </ci>
<ci> d </ci>
<ci> f </ci>
<apply>
<minus/>
<ci> V </ci>
<ci> E_s </ci>
</apply>
</apply>
</apply>
<apply id="dCai_dt">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> Cai </ci>
</apply>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="dimensionless"> -0.001 </cn>
<ci> i_s </ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.07 </cn>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 0.001 </cn>
<ci> Cai </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="slow_inward_current_d_gate">
<variable units="dimensionless" public_interface="out" name="d" initial_value="0.003"/>
<variable units="per_millisecond" name="alpha_d"/>
<variable units="per_millisecond" name="beta_d"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="millisecond" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="alpha_d_calculation">
<eq/>
<ci> alpha_d </ci>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="per_millisecond"> 0.095 </cn>
<apply>
<exp/>
<apply>
<minus/>
<apply>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> -5.0 </cn>
</apply>
<cn cellml:units="millivolt"> 100.0 </cn>
</apply>
</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="millivolt"> -5.0 </cn>
</apply>
<cn cellml:units="millivolt"> 13.89 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="beta_d_calculation">
<eq/>
<ci> beta_d </ci>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="per_millisecond"> 0.07 </cn>
<apply>
<exp/>
<apply>
<minus/>
<apply>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 44.0 </cn>
</apply>
<cn cellml:units="millivolt"> 59.0 </cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 44.0 </cn>
</apply>
<cn cellml:units="millivolt"> 20.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="dd_dt">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> d </ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> alpha_d </ci>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> d </ci>
</apply>
</apply>
<apply>
<times/>
<ci> beta_d </ci>
<ci> d </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="slow_inward_current_f_gate">
<variable units="dimensionless" public_interface="out" name="f" initial_value="0.994"/>
<variable units="per_millisecond" name="alpha_f"/>
<variable units="per_millisecond" name="beta_f"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="millisecond" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="alpha_f_calculation">
<eq/>
<ci> alpha_f </ci>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="per_millisecond"> 0.012 </cn>
<apply>
<exp/>
<apply>
<minus/>
<apply>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 28.0 </cn>
</apply>
<cn cellml:units="millivolt"> 125.0 </cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 28.0 </cn>
</apply>
<cn cellml:units="millivolt"> 6.67 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="beta_f_calculation">
<eq/>
<ci> beta_f </ci>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="per_millisecond"> 0.0065 </cn>
<apply>
<exp/>
<apply>
<minus/>
<apply>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 30.0 </cn>
</apply>
<cn cellml:units="millivolt"> 50.0 </cn>
</apply>
</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="millivolt"> 30.0 </cn>
</apply>
<cn cellml:units="millivolt"> 5.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="df_dt">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> f </ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> alpha_f </ci>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> f </ci>
</apply>
</apply>
<apply>
<times/>
<ci> beta_f </ci>
<ci> f </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="time_dependent_outward_current">
<variable units="microA_per_cm2" public_interface="out" name="i_x1"/>
<variable units="per_millisecond" name="alpha_x1"/>
<variable units="per_millisecond" name="beta_x1"/>
<variable units="millisecond" public_interface="in" private_interface="out" name="time"/>
<variable units="millivolt" public_interface="in" private_interface="out" name="V"/>
<variable units="dimensionless" private_interface="in" name="x1"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="i_x1_calculation">
<eq/>
<ci> i_x1 </ci>
<apply>
<times/>
<ci> x1 </ci>
<cn cellml:units="dimensionless"> 0.8 </cn>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="per_millivolt"> 0.04 </cn>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 77.0 </cn>
</apply>
</apply>
</apply>
<cn cellml:units="dimensionless"> 1.0 </cn>
</apply>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="per_millivolt"> 0.04 </cn>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 35.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="time_dependent_outward_current_x1_gate">
<variable units="dimensionless" public_interface="out" name="x1"/>
<variable units="per_millisecond" name="alpha_x1"/>
<variable units="per_millisecond" name="beta_x1"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="millisecond" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="alpha_x1_calculation">
<eq/>
<ci> alpha_x1 </ci>
<apply>
<times/>
<cn cellml:units="per_millisecond"> 0.0005 </cn>
<apply>
<divide/>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 50.0 </cn>
</apply>
<cn cellml:units="millivolt"> 12.1 </cn>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 50.0 </cn>
</apply>
<cn cellml:units="millivolt"> 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_millisecond"> 0.0013 </cn>
<apply>
<divide/>
<apply>
<exp/>
<apply>
<minus/>
<apply>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 20.0 </cn>
</apply>
<cn cellml:units="millivolt"> 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="millivolt"> 20.0 </cn>
</apply>
<cn cellml:units="millivolt"> 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 name="time_independent_outward_current">
<variable units="microA_per_cm2" public_interface="out" name="i_K1"/>
<variable units="millisecond" public_interface="in" name="time"/>
<variable units="millivolt" 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"> 0.35 </cn>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="per_millisecond"> 4.0 </cn>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="per_millivolt"> 0.04 </cn>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 85.0 </cn>
</apply>
</apply>
</apply>
<cn cellml:units="dimensionless"> 1.0 </cn>
</apply>
<apply>
<plus/>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="per_millivolt"> 0.08 </cn>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 53 </cn>
</apply>
</apply>
</apply>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="per_millivolt"> 0.04 </cn>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 53.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="per_millisecond"> 0.2 </cn>
<apply>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 23.0 </cn>
</apply>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="per_millivolt"> -0.04 </cn>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 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:Bag rdf:about="rdf:#4cad624a-59dc-41b7-aa89-d97a3796df5a">
<rdf:li>channel kinetics</rdf:li>
<rdf:li>cardiac</rdf:li>
<rdf:li>electrophysiology</rdf:li>
</rdf:Bag>
<rdf:Seq rdf:about="rdf:#citationAuthorsSeq">
<rdf:li rdf:resource="rdf:#author1Vcard"/>
<rdf:li rdf:resource="rdf:#author2Vcard"/>
</rdf:Seq>
<rdf:Description rdf:about="rdf:#2ee95837-af4a-45f2-90fa-ef002ae8021c">
<rdf:type rdf:resource="http://purl.org/dc/terms/W3CDTF"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#4ab586db-e8b4-476e-8208-47da50876cee">
<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:#2147d6af-9770-4b4e-82c1-3f7edd39a29d">
<bqs:subject_type>keyword</bqs:subject_type>
<rdf:value rdf:resource="rdf:#4cad624a-59dc-41b7-aa89-d97a3796df5a"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#e62f0cc0-d120-47f3-8146-181b40fdf251">
<dcterms:W3CDTF>1980-11-01</dcterms:W3CDTF>
</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:#0f7b9297-0fec-4178-b5f3-3c3681a2c2dd">
<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="rdf:#ff835534-389e-4b02-8ab5-75cb602de884">
<vCard:FN>Catherine Lloyd</vCard:FN>
</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:#3754ca5e-a00b-4c0c-8395-93efaed56da7">
<vCard:Given>Catherine</vCard:Given>
<vCard:Family>Lloyd</vCard:Family>
<vCard:Other>May</vCard:Other>
</rdf:Description>
<rdf:Description rdf:about="rdf:#a9186ea1-4b5b-4b2f-b7d3-09ba7a1a024f">
<vCard:N rdf:resource="rdf:#98a1dce7-a08b-47b5-bafb-12de7d980d26"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#5d976d23-06b2-49bc-b075-e2ed0f6b7b13">
<bqs:Pubmed_id>7260301</bqs:Pubmed_id>
<bqs:JournalArticle rdf:resource="rdf:#3af53cab-80bf-4557-88f8-a2e35a4c8a56"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#81b8cf71-0dba-44c4-97c0-50cd73fb2332">
<vCard:N rdf:resource="rdf:#ff544718-b97b-4b8c-8207-c3589946cf72"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#8ccab341-9cd0-49a6-aa52-311e4ffc9138">
<dcterms:W3CDTF>2003-04-09</dcterms:W3CDTF>
</rdf:Description>
<rdf:Description rdf:about="#fast_sodium_current">
<cmeta:comment rdf:resource="rdf:#8a63f9ad-feee-4315-b12e-380f8a3ecf38"/>
</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:#6805e2ee-01a1-4ba5-b69e-eae77214141f">
<dcterms:modified rdf:resource="rdf:#8ccab341-9cd0-49a6-aa52-311e4ffc9138"/>
<rdf:value>
Added publication date information.
</rdf:value>
<cmeta:modifier rdf:resource="rdf:#114eb577-fe60-470b-b553-cc9fa85c53ef"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#29e6ad25-7434-4879-9e09-9914ae7584a4">
<dcterms:modified rdf:resource="rdf:#8c50ff35-a20a-4107-81a8-e8908ebb353c"/>
<rdf:value>
Added the components of the Beeler-Reuter Model.
</rdf:value>
<cmeta:modifier rdf:resource="rdf:#4ab586db-e8b4-476e-8208-47da50876cee"/>
</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:#a0e124ab-32f0-4e40-917a-448e138bb7ba">
<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:#ff2a5496-c2e7-45cd-a04b-4fbeb2fa6466">
<dc:title>Biophysical Journal</dc:title>
</rdf:Description>
<rdf:Description rdf:about="rdf:#3d2ea7a7-f526-4881-9db1-659430394f2b">
<dcterms:W3CDTF>2002-02-25</dcterms:W3CDTF>
</rdf:Description>
<rdf:Description rdf:about="rdf:#fd65b750-e4a9-4dab-a0e4-8eabb69750f8">
<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="#ebihara_johnson_1980_version01">
<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:#0a4eccce-6fcc-42eb-ab94-5b507e9c5e8e"/>
<bqs:reference rdf:resource="rdf:#46bd7263-7f63-4c5e-844a-dbb564ab2243"/>
<bqs:reference rdf:resource="rdf:#5d976d23-06b2-49bc-b075-e2ed0f6b7b13"/>
<cmeta:species>Mammalia</cmeta:species>
</rdf:Description>
<rdf:Description rdf:about="rdf:#0a4eccce-6fcc-42eb-ab94-5b507e9c5e8e">
<dc:creator rdf:resource="rdf:#ff835534-389e-4b02-8ab5-75cb602de884"/>
<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:#8805e740-393c-4591-bb4f-d915bff3a65c">
<dcterms:modified rdf:resource="rdf:#cbc90361-be10-487b-a59a-d3baafc35805"/>
<rdf:value>
Added more metadata.
</rdf:value>
<cmeta:modifier rdf:resource="rdf:#81b8cf71-0dba-44c4-97c0-50cd73fb2332"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#a619174f-9e8c-418b-b556-a4d1070140e1">
<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:#8a63f9ad-feee-4315-b12e-380f8a3ecf38">
<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:#64721cee-27ad-4237-8a71-c70d956301e2">
<dcterms:modified rdf:resource="rdf:#d1738604-67e9-4641-8c99-438cd10cfa8d"/>
<rdf:value>
Updated metadata to conform to the 16/1/02 CellML Metadata 1.0
Specification.
</rdf:value>
<cmeta:modifier rdf:resource="rdf:#a0e124ab-32f0-4e40-917a-448e138bb7ba"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#98a1dce7-a08b-47b5-bafb-12de7d980d26">
<vCard:Given>Catherine</vCard:Given>
<vCard:Family>Lloyd</vCard:Family>
<vCard:Other>May</vCard:Other>
</rdf:Description>
<rdf:Description rdf:about="rdf:#2312be41-253f-40a7-8938-7a64b4e04bc6">
<vCard:ORG rdf:resource="rdf:#71f172db-88dd-4f25-83f5-a5fcde4272f1"/>
<vCard:EMAIL rdf:resource="rdf:#fd65b750-e4a9-4dab-a0e4-8eabb69750f8"/>
<vCard:N rdf:resource="rdf:#3754ca5e-a00b-4c0c-8395-93efaed56da7"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#91a6ec43-1cd9-42b7-8fe7-a218caa82747">
<vCard:Given>Autumn</vCard:Given>
<vCard:Family>Cuellar</vCard:Family>
<vCard:Other>A</vCard:Other>
</rdf:Description>
<rdf:Description rdf:about="rdf:#d1738604-67e9-4641-8c99-438cd10cfa8d">
<rdf:type rdf:resource="http://purl.org/dc/terms/W3CDTF"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#3af53cab-80bf-4557-88f8-a2e35a4c8a56">
<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:#ff2a5496-c2e7-45cd-a04b-4fbeb2fa6466"/>
<dcterms:issued rdf:resource="rdf:#e62f0cc0-d120-47f3-8146-181b40fdf251"/>
<bqs:last_page>790</bqs:last_page>
</rdf:Description>
<rdf:Description rdf:about="rdf:#02818f8f-fdb8-49d3-8c89-92fd86f7d432">
<dcterms:W3CDTF>2001-12-17</dcterms:W3CDTF>
</rdf:Description>
<rdf:Description rdf:about="rdf:#cbc90361-be10-487b-a59a-d3baafc35805">
<dcterms:W3CDTF>2002-07-19</dcterms:W3CDTF>
</rdf:Description>
<rdf:Description rdf:about="#membrane">
<cmeta:comment rdf:resource="rdf:#0f7b9297-0fec-4178-b5f3-3c3681a2c2dd"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#114eb577-fe60-470b-b553-cc9fa85c53ef">
<vCard:N rdf:resource="rdf:#91a6ec43-1cd9-42b7-8fe7-a218caa82747"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#2146def2-d204-4cb7-97d3-f7048fb7b33f">
<dcterms:modified rdf:resource="rdf:#3d2ea7a7-f526-4881-9db1-659430394f2b"/>
<rdf:value>
Corrected several equations.
</rdf:value>
<cmeta:modifier rdf:resource="rdf:#a9186ea1-4b5b-4b2f-b7d3-09ba7a1a024f"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#985360d9-9e78-44cf-a263-ad8b4db684f2">
<dcterms:modified rdf:resource="rdf:#2ee95837-af4a-45f2-90fa-ef002ae8021c"/>
<rdf:value>
Corrected the membrane voltage differential equation.
</rdf:value>
<cmeta:modifier rdf:resource="rdf:#a619174f-9e8c-418b-b556-a4d1070140e1"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#46bd7263-7f63-4c5e-844a-dbb564ab2243">
<dc:subject rdf:resource="rdf:#2147d6af-9770-4b4e-82c1-3f7edd39a29d"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#ff544718-b97b-4b8c-8207-c3589946cf72">
<vCard:Given>Catherine</vCard:Given>
<vCard:Family>Lloyd</vCard:Family>
<vCard:Other>May</vCard:Other>
</rdf:Description>
<rdf:Description rdf:about="rdf:#71f172db-88dd-4f25-83f5-a5fcde4272f1">
<vCard:Orgname>The University of Auckland</vCard:Orgname>
<vCard:Orgunit>The Bioengineering Research Group</vCard:Orgunit>
</rdf:Description>
<rdf:Description rdf:about="rdf:#34cde6ea-ef39-4354-ae35-61623d89f795">
<rdf:value>
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="">
<dc:publisher>
The University of Auckland, Bioengineering Research Group
</dc:publisher>
<cmeta:modification rdf:resource="rdf:#2146def2-d204-4cb7-97d3-f7048fb7b33f"/>
<cmeta:modification rdf:resource="rdf:#29e6ad25-7434-4879-9e09-9914ae7584a4"/>
<cmeta:modification rdf:resource="rdf:#64721cee-27ad-4237-8a71-c70d956301e2"/>
<cmeta:modification rdf:resource="rdf:#6805e2ee-01a1-4ba5-b69e-eae77214141f"/>
<cmeta:modification rdf:resource="rdf:#8805e740-393c-4591-bb4f-d915bff3a65c"/>
<cmeta:modification rdf:resource="rdf:#985360d9-9e78-44cf-a263-ad8b4db684f2"/>
<dcterms:created rdf:resource="rdf:#02818f8f-fdb8-49d3-8c89-92fd86f7d432"/>
<dc:creator rdf:resource="rdf:#2312be41-253f-40a7-8938-7a64b4e04bc6"/>
</rdf:Description>
<rdf:Description rdf:about="#fast_sodium_current_m_gate">
<cmeta:comment rdf:resource="rdf:#34cde6ea-ef39-4354-ae35-61623d89f795"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#8c50ff35-a20a-4107-81a8-e8908ebb353c">
<rdf:type rdf:resource="http://purl.org/dc/terms/W3CDTF"/>
</rdf:Description>
</rdf:RDF>
</model>
