Biomedical Engineering Reference
In-Depth Information
natural logarithm to logarithm of base 10, the constant is 61.5 mV at 37°C or 58
mV at 25°C.
EXAMPLE 3.1
What is the resting
ΔΦ
for Na
+
ions, if the outside concentration is 140 mM and the inside
concentration is 50 mM?
RT
C
50
ΔΦ
=Φ −Φ =−
ln
i
=−
26.17 ln
=
26.95
mV
Solution:
Na
+
i
o
zF
C
140
o
3.2.2 Donnan Equilibrium
Both sides of the cell membrane have two electrolyte solutions and the cell mem-
brane is selectively permeable to some ions but blocks the passage of many ions.
Thus, one charged component is physically restricted to one phase. This restriction
can also result from the inherently immobile nature of one charged component,
such as fixed proteins. In either case, an uneven distribution of the diffusible ions
over the two phases develops, as their concentrations adjust to make their electro-
chemical potentials the same in each phase. In turn, this establishes an osmotic pres-
sure difference and an electric potential difference between the phases. This type of
ionic equilibrium is termed a Donnan equilibrium, named after the Irish physical
chemist Frederick G. Donnan. According to the Donnan equilibrium principle, the
product of the concentrations of diffusible ions on one side of the membrane equals
that product of the concentration of the diffusible ions on the other side. Number of
cations in any given volume must be equal to number of anions in the same volume
(i.e., space charge neutrality—outside of a cell, net charge should be zero). In other
words, to maintain equilibrium, an anion must cross in the same direction for each
cation crossing the membrane in one direction, or vice versa. Assuming that a mem-
brane is permeable to both K
+
and Cl
−
but not to a large cation or anion (Figure
3.2), the Nernst potentials for both K
+
and Cl
−
must be equal at equilibrium, that is,
C
C
RT
RT
Ki
,
Cli
,
−
ln
=
ln
FC
FC
K
,0
Cl
,0
or
CC
CC
K
,0
Cl i
,
=
Ki
,
Cl
,0
(3.7)
