Structure of Membranes - Membrane Biophysics, Biological and Medical Physics, Biomedical Engineering - page 19

The Nernst equation determines the equilibrium potential, often called 'the Nernst
potential' for an ion across the membrane. From the equation, it is clear that this
potential depends on the ion concentrations outside (

] in )of
the membrane, the valence of the ionic species, z , and the absolute temperature in
Kelvin T . The constant R is the universal gas constant ( R

[ N ] out ) and inside ( [ N

314 J K − 1 mol − 1 )

= 8 .

485 C mol − 1 ). The development of a Nernst
potential depends on the following two criteria: (i) the concentration gradient of an
ion across the membrane, and (ii) selective ion channels creating a pathway for a
specific type of ion flow across the membrane. It is, therefore, natural to associate
the Nernst potential with an ion type. Nernst or equilibrium potentials V Na , V K , V Cl ,
V Ca , etc. can be found for Na + ,K + ,Cl − ,Ca 2 + , etc. ionic species respectively. In the
case when there exists only one ionic species in the system, and/or channels due to
ion specificity of the channels, the corresponding Nernst or equilibrium potential is
also the membrane potential ( V m ). However, in cases where there exists the flow of
different ions across the membrane, the membrane potential is the sum of all Nernst
potentials referring to ions, normalized with the corresponding conductance. If there
are a number of ions flowing across the membrane, the following relation exists:

and F is the Faraday constant ( F = 96 ,

g i
G

V Nernst , i

V m = (2.8)

i

where V Nernst , i and g i are respectively the Nernst potential and conductance (inverse
Ohmic resistance) through the membrane, corresponding to the ion indexed i . Here,
G = i g i .

In physiology, the most common potentials due to ion flows through a membrane
are V Na , V K , V Cl ,etc.If Na + ,K + ,Cl − flow across a membrane with the correspond-
ing Nernst potentials V Na , V K , V Cl , we find the membrane potential to be represented
by the following equation:

g Na
G

V Na + g K

G

V K + g Cl

G

V Cl

V m = (2.9)

Here, G is the sum of conductances g Na , g K , g Cl , g Ca corresponding to the Na + ,K + ,
Cl − ,Ca 2 + ions across the membrane, respectively.
In the presence of several ions flowing across the real cell membrane, the equi-
librium of the cell depends on the relative membrane permeability for these ions. To
determine the membrane resting potential, the following Goldman-Hodgkin-Katz
(GHK) equation is used:

ln i

] out + j

RT
F

N i N i N j N j P i ( ) [ P j ( ) [ ] in

V m = (2.10)

i

] in + j N i N i N j N j P i ( ) [ P j ( ) [ ] out

Here, the symbols P stand for the respective relative permeabilities of the ions,
the N s in the square brackets stand for the ion concentrations,

+ / − stand for