Information Technology Reference
In-Depth Information
The equilibrium in the inflow or outflow of charges is reached according to
Nernst's conditions [
16
]:
z
F
ln
ŒK
C
in
RT
E
K
D
(1.2)
ŒK
C
out
where E
K
is the K
C
Nernst's potential, ŒK
C
in
is the concentration of the K
C
ions
in the inner part of the membrane, ŒK
C
out
is the concentration of the K
C
ions in the
outer part of the membrane, R is a gas constant, F is the Faraday constant,
z
is the
valence of K
C
, and T is the absolute temperature in Kelvin.
When the neurons are at rest their membrane is permeable to ions of the K
C
,
Na
C
, and Cl
type. In the equilibrium condition the number of open channels for
ions of the K
C
or Cl
type is larger than the number of the open channels for ions
of the Na
C
type. The equilibrium potential of the neuron's membrane depends on
the Nerst potential of the K
C
and Cl
ions.
The exact relation that connects the membrane's potential to ions concentrations
in its inner and outer part results from the Goldman-Hodgkin-Katz equation. The
inflow and outflow of ions continues until the associated voltage gradients become
zero (there is a voltage gradient for the positive ions Na
C
and K
C
and a voltage
gradient for the negative ions Cl
). Voltage gradients are also affected by ion
pumps, that is channels through which an exchange of specific ions takes place.
For example, the Na
C
-K
C
pump is a protein permeable by ions which enables the
exchange of 3Na
C
with 2K
C
. As long as there is a non-zero gradient due to the
concentration of K
C
in the inner and outer part of the membrane the outflow of
these ions continues.
For instance, when the concentration of positive ions K
C
in the outer part of the
membrane raises there is an annihilation of the gradient that forces the K
C
ions to
move outwards. This has as a result, an equilibrium condition to be finally reached.
1.1.1
Nernst's Equation
The following notations are used next: ŒC
x
is the concentration of ions in the
membrane, V.x/is the membrane's potential at point x, along the membrane. Then
according to Fick's diffusion law one has about the diffusive flux J
diff
[
16
,
65
]
J
diff
DD
@ŒC
@x
(1.3)
where D is the diffusion constant (cm
2
/s) and ŒC in the concentration of molecules
(ions) N=cm
3
. Moreover, there is a force that is responsible for the drift motion of
the molecules [
16
,
65
]
J
drift
D
z
ŒC
@
@x
(1.4)
