Neuronal Signaling and the Structure of the Nervous System
147
61 is a constant value that takes into account the universal gas
constant, the temperature (37°C), and the Faraday electrical
constant.
Using the concentration gradients from Table 6–2, the
equilibrium potentials for sodium (
E
Na
) and potassium (
E
K
) are
E
Na
=
61
+
1
log
145
15
=+
60 mV
E
K
=
61
+
1
log
5
150
=−
90 mV
Thus, at these typical concentrations, sodium fl
ux through open
channels will tend to bring the membrane potential toward +60
mV, while potassium fl
ux will bring it toward –90 mV. If the
concentration gradients change, the equilibrium potentials
will change.
When channels for more than one ion species are open
in the membrane at the same time, the permeabilities and con-
centration gradients for all the ions must be considered when
accounting for the membrane potential. For a given concen-
tration gradient, the greater the membrane permeability to
an ion species, the greater the contribution that ion species
will make to the membrane potential. Given the concentra-
tion gradients and relative membrane permeabilities (P
ion
) for
sodium, potassium, and chloride, the potential of a membrane
(V
m
) can be calculated using the
Goldman-Hodgkin-Katz
(GHK) equation:
V
m
= 61 log
P
K
[K
o
] + P
Na
[Na
o
] + P
Cl
[Cl
i
]
P
K
[K
i
] + P
Na
[Na
i
] + P
Cl
[Cl
o
]
The GHK equation is essentially an expanded version of
the Nernst equation that takes into account individual ion per-
meabilities. In fact, setting the permeabilities of any two ions
to zero gives the equilibrium potential for the remaining ion.
Note that the chloride concentrations are reversed as com-
pared to sodium and potassium (the inside concentration is
in the numerator and the outside in the denominator) because
chloride is an anion, and its movement has the opposite effect
on the membrane potential. In an actual nerve cell at rest,
there are many more open potassium channels than sodium
channels; chloride permeability generally falls in between.
Typical values for relative permeabilities are: P
K
= 1, P
Na
= 0.04,
and P
Cl
= 0.45. Inserting those values (along with the con-
centrations in Table 6–2) into the GHK equation allows us to
calculate the resting membrane potential taking all of these
ions into account:
V
m
= 61 log
(1)(5) + (.04)(145) + (.45)(7)
= –70 mV
(1)(150) + (.04)(15) + (.45)(100)
The contributions of sodium and potassium to the overall
membrane potential are a function of their concentration gra-
dients and relative permeabilities. The concentration gradients
determine their equilibrium potentials, and the relative perme-
ability determines how strongly the resting membrane poten-
tial is infl uenced toward those potentials. Potassium has by far
the highest permeability, which explains why a typical neuron’s
resting membrane potential is much closer to the equilibrium
potential for potassium than for sodium (
Figure 6–12
). Based
on its permeability, you might think that chloride would also
have a strong infl uence on the resting membrane potential. This
turns out not to be the case, for reasons that we will return to
shortly.
In other words, the resting potential is generated across
the plasma membrane largely because of the movement of
potassium out of the cell down its concentration gradient
through open or so-called
leak potassium channels,
so that
the inside of the cell becomes negative with respect to the
outside. Even though potassium fl ux has more impact on the
resting membrane potential than does sodium fl ux, the rest-
ing membrane potential is not
equal
to the potassium equilib-
rium potential, because a small number of sodium channels
are open in the resting state. Some sodium ions continu-
ally move into the cell, canceling the effect of an equivalent
number of potassium ions simultaneously moving out. Thus,
ion channels allow net movement of sodium into the cell and
potassium out of the cell.
Over time, the concentration of intracellular sodium
and potassium ions does not change, however, because the
Na
+
/K
+
-ATPase pump maintains the sodium and potassium
concentrations at stable levels. In a resting cell, the number of
ions the pump moves equals the number of ions that move in
0.15 M
(a)
(b)
(c)
NaCl
K
+
Na
+
0.15 M
KCI
Compartment 1
Compartment 2
Na
+
K
+
+
+
+
Na
+
(d)
K
+
+
+
+
Na
+
(e)
Na
+
K
+
+
+
+
+
Na
+
Figure 6–11
Generation of a potential across a membrane due to diffusion of Na
+
through sodium channels (blue). Arrows represent ion movements.
See the text for a fuller explanation.
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