Biomedical Engineering Reference
In-Depth Information
[
K
+
Cl
−
]
Channel
[
K
+
Cl
−
]
[
R
+
Cl
−
]
Inside
Outside
FIGURE 12.8
Membrane is permeable to both
K
þ
and
Cl
, but not to a large cation
R
þ
.
R
þ
,as
shown in Figure 12.8. Under steady-state conditions, the Nernst potentials for both
K
þ
and
Cl
but not to a large cation,
Suppose a membrane is permeable to both
K
þ
Cl
must be equal—that is
and
E
K
¼
E
Cl
,or
ln
½
K
þ
o
ln
½
Cl
i
½
Cl
o
E
K
¼
KT
q
½
K
þ
i
¼
E
Cl
¼
KT
ð
12
:
15
Þ
q
After simplifying,
½
K
þ
o
½
K
þ
i
¼
½
Cl
i
ð
12
:
16
Þ
½
Cl
o
Equation (12.16) is known as the
Donnan Equilibrium
. An accompanying principle is
space
charge neutrality
, which states that the number of cations in a given volume is equal to the
number of anions. Thus, at steady-state, ions still diffuse across the membrane, but each
K
þ
that crosses the membrane must be accompanied by a
Cl
for space charge neutrality
R
þ
were not present, then at steady-state, the concentration
to be satisfied. If in Figure 12.8
K
þ
and
Cl
on both sides of the membrane would be equal. With
R
þ
, the concentrations
of
of [
KCl
] on both sides of the membrane are different, as shown in Example Problem 12.1,
R
þ
is now in the intracellular fluid.
where
EXAMPLE PROBLEM 12.1
A membrane is permeable to
R
þ
as shown in the following
figure. Find the steady-state concentration for the following initial conditions.
K
þ
and
Cl
, but not to a large cation
400 mM [
KCl
]
Channel
100 mM [
KCl
]
500 mM [
RCl
]
Inside
Outside
Continued
