Biomedical Engineering Reference
In-Depth Information
Figure 3.2
Space charge neutrality.
Equation (3.7) is a Donnan equilibrium. The rule is important because it con-
tributes to the origin of resting potential. In general, when the cell membrane is at
rest, the active and passive ion flows are balanced and a permanent potential exists
across a membrane only if the membrane is impermeable to some ion(s) and an
active pump is present. The Donnan equilibrium only applies to situations where
ions are passively distributed (i.e., there are no metabolic pumps utilizing energy
regulating ion concentration gradients across the membrane).
EXAMPLE 3.2
A cell contains 100 mM of KCl and 500 mM of protein chloride. The outside of the cell
medium has 400 mM KCl. Assuming that the cell membrane is permeable to Cl
−
and K
+
ions and impermeable to the protein, determine the equilibrium concentrations and the
membrane potential. Also assume that these compounds can completely dissociate.
Solution:
CC
500,
C C
1,000, and
C C
+=
+ =
=
K
,0
K j
,
Cl
,0
Cl i
,
K
,0
Cl
,0
C
1,000
C
−
K,0
Cl,0
From (3.7) we have
=
500
C
C
−
K,0
Cl,0
or
CC
=
=
333 mM,
C
=
167 mM, and
C
=
667 mM
K
,0
Cl
,0
K i
,
Cl i
,
Also,
333
26.71ln
18.4 mV
Φ=Φ =
=
K
Cl
167
The Donnan equilibrium is useful in pH control in red blood cells (RBCs).
When RBCs pass through capillaries in the tissue, CO
2
released from tissues and
water diffuse freely into the red blood cells. They are converted to carbonic acid,
which dissociates into hydrogen and bicarbonate ions, as described in Section 3.2.4.
H
+
ions do not pass through cell membranes but CO
2
passes readily. This situation
cannot be sustained as the osmolarity and cell size will rise with intracellular H
+
and bicarbonate ion concentration, and rupture the cell. To circumvent this situa-
tion, the bicarbonate ion diffuses out to the plasma in exchange for Cl
−
ions due to
