The Ebihara-Johnson Sodium Current Model (1980)
Catherine
Lloyd
Bioengineering Institute, University of Auckland
Model Status
This model is valid CellML and contains consistent units but is not fully parameterised.
Model Structure
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.
model diagram
Schematic diagram of the Ebihara and Johnson model.
The complete original paper reference is cited below:
Fast Sodium Current In Cardiac Muscle, Lisa Ebihara and Edward A. Johnson, 1980,
Biophys. J. 32, 779-790. PubMed ID: 7260301
Calculation of the fast sodium current.
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.
The standard Beeler Reuter (1977) activation gate for the slow
inward current.
7260301
Corrected the membrane voltage differential equation.
Corrected several equations.
Added the components of the Beeler-Reuter Model.
2003-07-22
The Ebihara-Johnson Model of the Fast Sodium Current in Cardiac Muscle,
1980
Cardiac Myocyte
keyword
cardiac
electrophysiology
channel kinetics
fast sodium current
Mammalia
2003-04-09
The gating kinetics of the m gate.
The closing rate for the m gate.
Catherine
Lloyd
May
2002-07-19
This is a dummy equation that we simply use to make grabbing the
value in CMISS much easier.
2002-02-25
c.lloyd@auckland.ac.nz
1980-01-01
Catherine
Lloyd
May
David
Nickerson
P
Catherine Lloyd
Autumn
Cuellar
A.
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.
Catherine
Lloyd
May
The voltage-dependent inactivation gate of the fast sodium channel -
the h gate.
E
Johnson
A
Updated metadata to conform to the 16/1/02 CellML Metadata 1.0
Specification.
Fast sodium current in cardiac muscle: A quantitative description
32
779
790
Modifying units and adding a stimulus current.
The standard Beeler Reuter (1977) slow inward (calcium) current
formulation.
Catherine
Lloyd
May
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.
The opening rate of the h gate.
The standard Beeler Reuter (1977) inactivation gate for the slow
inward current.
The kinetics of the h gate.
The standard Beeler Reuter (1977) time-independent outward
(potassium) current.
Biophysical Journal
The University of Auckland, Bioengineering Research Group
Catherine
Lloyd
May
Autumn
Cuellar
A
Added more metadata.
The voltage-dependent activation gate for the fast sodium channel -
the m gate.
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).
The standard Beeler Reuter (1977) gating variable for the
time-dependent outward potassium current.
L
Ebihara
The closing rate of the h gate.
2001-12-17
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.
The standard Beeler Reuter (1977) time-dependent outward (potassium)
current.
Added publication date information.
The University of Auckland
The Bioengineering Research Group