MEMBRANE POTENTIALS
Ion
[X]i
Na+
50mM
Cl-
40
K+
400
Proteins-
400
-70mV
[X]o
c <====
e <====
c <====
e ====>
c ====>
e <====
xxxxxxx
460mM
540
10
0
As you can see, there is a concentration gradient for each ion, as well a -70 mv electrical gradient.
If the concentration gradient for an ion exactly offsets the electrical gradient, then the system is at
equilibrium for that ion. The voltage that exactly offsets a particular concentration gradient is the
equilibrium potential, or reversal potential, for that ion. If the membrane is permeable to a
particular ion, and ONLY that ion, then that ion will flow in (influx) or out (efflux) until the
equilibrium potential is attained. An equation used to calculate equilibrium potential for each ion is
the Nernst equation:
Ei = RT/ZF * ln ([X]o/[X]i) where
R =universal gas constant (8.31 joules/mole-oK )
T = temp in degrees Kelvin
Z = charge on ion
F = faraday constant (96,500 coulombs/mole)
At 293oK (20oC) this simplifies to Ei = 58 log ([X]o/[X]i)
ENa+ = 58 log (460/50) = 58 log 9.2
= 58 (0.964) = +55.9mV
ECl- = -58 log (40/540) = -58 log (13.5) = -58 (1.13) = -65.6mV
EK+ = 58 log (10/400) = 58 log (0.025) = 58 (-1.60) = -92.9mV
However, the membrane is permeable to more than one at a time. Using permeability to potassium
as the reference, typical permeabilities of a membrane at rest are as follows:
At rest: PK+= 1.00
PNa+= .03
PCl- = .10
The Goldman-Katz equation accounts for the contributions of all three ions:
(PNa+[Na+]o + PK+[K+]o + PCl-[Cl-]I)
Em = 58 log ------------------------------------------(PNa+[Na+]i + PK+[K+]i + PCl-[Cl-]o)
(.03(460) + 1.0 (10) + .10 (40))
(13.8 + 10 + 4)
27.8
Erm = 58 log --------------------------------------- = 58 log ------------------- = 58 log -----(.03 (50) + 1.0(400) + .10(540))
(1.5 + 400 + 54)
455.5
= 58 log (.061) = 58 (-1.21) = -70.3mV