146
Chapter 6
to only one ion (
Figure 6–10
). In this hypothetical situation,
it is assumed that the membrane contains potassium channels
but no sodium or chloride channels. Initially, compartment
1 contains 0.15 M NaCl, compartment 2 contains 0.15 M
KCl, and no ion movement occurs because the channels are
closed (
Figure 6–10a
). There is no potential difference across
the membrane because the two compartments contain equal
numbers of positive and negative ions. The positive ions are
different—sodium versus potassium, but the
total
numbers of
positive ions in the two compartments are the same, and each
positive ion balances a chloride ion.
However, if these potassium channels are opened, potas-
sium will diffuse down its concentration gradient from com-
partment 2 into compartment 1 (
Figure 6–10b
). Sodium ions
will not be able to move across the membrane. After a few potas-
sium ions have moved into compartment 1, that compartment
will have an excess of positive charge, leaving behind an excess
of negative charge in compartment 2 (
Figure 6–10c
). Thus, a
potential difference has been created across the membrane.
This introduces another major factor that can cause net
movement of ions across a membrane: an electrical potential.
As compartment 1 becomes increasingly positive and compart-
ment 2 increasingly negative, the membrane potential differ-
ence begins to infl uence the movement of the potassium ions.
The negative charge of compartment 2 tends to attract them
back into their original compartment and the positive charge
of compartment 1 tends to repulse them (
Figure 6–10d
).
As long as the fl ux or movement of ions due to the potas-
sium concentration gradient is greater than the fl
ux due to the
membrane potential, net movement of potassium will occur
from compartment 2 to compartment 1 (see Figure 6–10d), and
the membrane potential will progressively increase. However,
eventually the membrane potential will become negative
enough to produce a fl ux equal but opposite to the fl
ux pro-
duced by the concentration gradient (
Figure 6–10e
). The
membrane potential at which these two fl uxes become equal in
magnitude but opposite in direction is called the
equilibrium
potential
for that type of ion—in this case, potassium. At the
equilibrium potential for an ion, there is no
net
movement of
the ion because the opposing fl uxes are equal, and the poten-
tial will undergo no further change. It is worth emphasizing
once again that the number of ions crossing the membrane to
establish this equilibrium potential is insignifi cant compared
to the number originally present in compartment 2, so there is
no measurable change in the potassium concentration.
The magnitude of the equilibrium potential (in mV)
for any type of ion depends on the concentration gradient for
that ion across the membrane. If the concentrations on the
two sides were equal, the fl ux due to the concentration gradi-
ent would be zero, and the equilibrium potential would also
be zero. The larger the concentration gradient, the larger
the equilibrium potential because a larger, electrically driven
movement of ions will be required to balance the movement
due to the concentration difference.
Now consider the situation when the membrane separat-
ing the two compartments is replaced with one that contains
only sodium channels. A parallel situation will occur (
Figure
6–11
). Na
+
ions will initially move from compartment 1 to
compartment 2. When compartment 2 is positive with respect
to compartment 1, the difference in electrical charge across
the membrane will begin to drive Na
+
ions from compart-
ment 2 back to compartment 1, and eventually net movement
of sodium will cease. Again, at the equilibrium potential, the
movement of ions due to the concentration gradient is equal
but opposite to the movement due to the electrical gradient.
Thus, the equilibrium potential for one ion species
can be different in magnitude
and
direction from those for
other ion species, depending on the concentration gradients
between the intracellular and extracellular compartments for
each ion. If the concentration gradient for any ion is known,
the equilibrium potential for that ion can be calculated by
means of the Nernst equation.
The
Nernst equation
describes the equilibrium potential
for any ion species—that is, the electrical potential necessary to
balance a given ionic concentration gradient across a membrane
so that the net fl ux of the ion is zero. The Nernst equation is
E
ion
=
61
Z
log
C
o
C
i
where
E
ion
= equilibrium potential for a particular ion, in mV
C
i
= intracellular concentration of the ion
C
o
= extracellular concentration of the ion
Z = the valence of the ion
0.15 M
NaCl
(a)
(b)
(c)
(d)
(e)
K
+
Na
+
K
+
Na
+
K
+
K
+
Na
+
K
+
K
+
K
+
0.15 M
KCI
Compartment 1
Compartment 2
+
+
+
+
+
+
Na
+
+
+
+
+
Figure 6–10
Generation of a potential across a membrane due to diffusion of K
+
through potassium channels (red). Arrows represent ion movements.
See the text for a complete explanation of the steps a–e.
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