The Goldman-Hodgkin-Katz Equation

The Goldman–Hodgkin–Katz voltage equation, used in cell membrane physiology, can be written
E
m
=±
RT
zF
ln
P
K
[
K
o
]+
P
Na
[
Na
o
]+
P
Cl
[
Cl
i
]
P
K
[
K
i
]+
P
Na
[
Na
i
]+
P
Cl
[
Cl
o
]
,
RT
zF
=±0.0000860.
The GHK equation is used to determine the resting membrane potential in real cells. It is a generalization of the Nernst equation. This Demonstration shows the Goldman–Hodgkin–Katz voltage function, plotted in gray, in terms of the argument
x=[
K
o
]
:
E
m
=±
RT
zF
ln
P
K
x+
P
Na
[
Na
o
]+
P
Cl
[
Cl
i
]
P
K
[
K
i
]+
P
Na
[
Na
i
]+
P
Cl
[
Cl
o
]
, where
E
m
is the membrane potential in volts;
R
is the ideal gas constant in joules per kelvin-mol;
T
is the temperature (Kelvin);
F
is Faraday's constant in coulombs/mol;
P
K
,
P
Na
,
P
Cl
are the permeabilities of the potassium, sodium, and chloride ions;
[
K
o
]
,
[
Na
o
]
,
[
Cl
o
]
are the extracellular concentrations of potassium, sodium, and chloride;
[
K
i
]
,
[
Na
i
]
,
[
Cl
i
]
are their intracellular concentrations.
Also shown are the derivatives of the GHK function (red) and the Nernst function (green),
E
m
=±
RT
zF
ln
x
[
K
i
]
. The region between the GHK and Nernst functions is shown filled.

Details

See en.wikipedia.org/wiki/Goldman_equation.

Permanent Citation

Olexandr Eugene Prokopchenko
​
​"The Goldman-Hodgkin-Katz Equation"​
​http://demonstrations.wolfram.com/TheGoldmanHodgkinKatzEquation/​
​Wolfram Demonstrations Project​
​Published: March 7, 2011