Human Physiology, 14th edition (2016)

Interactions Between Cells and the Extracellular Environment 151

cell. The actual voltage, however, has to be calculated, as

described in the next section. This calculation reveals that

an equilibrium potential of 66 mV, with the inside of the cell

the positive pole, maintains the Na^1 concentration of 12 mM

inside and 145 mM outside the cell. The E (^) Na is thus written
as 1 66 mV.
Equilibrium potentials are useful to know because they tell
us what happens to the membrane potential when the plasma
membrane becomes highly permeable to one particular ion.
The resting neuron, for example, has a membrane potential
close to E (^) K because its membrane is most permeable to K^1.
However, when it produces an impulse, it suddenly becomes
highly permeable to Na^1 for a brief time, driving its mem-
brane potential closer to E (^) Na. The resting membrane potential
will be described shortly; the production of nerve impulses is
explained in chapter 7, section 7.2.
Nernst Equation
The diffusion gradient depends on the difference in concen-
tration of the ion. Therefore, the value of the equilibrium
potential must depend on the ratio of the concentrations of the
ion on the two sides of the membrane. The Nernst equation
allows this theoretical equilibrium potential to be calculated
for a particular ion when its concentrations are known. The
following simplified form of the equation is valid at a tem-
perature of 37 8 C:
Ex 5

61

___z log

[Xo]

____

[Xi]

where

E (^) x 5  equilibrium potential in millivolts (mV) for ion x
X (^) o 5  concentration of the ion outside the cell
X (^) i 5  concentration of the ion inside the cell
z 5  valence of the ion ( 1 1 for Na^1 or K^1 )
Note that, using the Nernst equation, the equilibrium
potential for a cation has a negative value when X (^) i is greater
than X (^) o. If we substitute K^1 for X, this is indeed the case. As a
hypothetical example, if the concentration of K^1 were 10 times
higher inside compared to outside the cell, the equilibrium
potential would be 61 mV (log 1/10)  5  61  3  ( 2 1)  5 2 61 mV.
In reality, the concentration of K^1 inside the cell is 30 times
greater than outside (150 mEq/L inside compared to 5 mEq/L
outside). Thus,
EK 5 61 mV log
5 mEq/L

150 mEq/L
5 2 90 mV
This means that a membrane potential of 90 mV, with the
inside of the cell negative, would be required to prevent the dif-
fusion of K^1 out of the cell. This is why the equilibrium poten-
tial for K^1  ( E (^) K ) was given as 2 90 mV in the earlier discussion
of equilibrium potentials.
If we wish to calculate the equilibrium potential for
Na^1 , different values must be used. The concentration of
Na^1 in the extracellular fluid is 145 mEq/L, whereas its
concentration inside cells is 5 to 14 mEq/L. The diffusion
reached where the concentrations of K^1 remained stable. The
membrane potential that would stabilize the K^1 concentra-
tions is known as the K 1 equilibrium potential (abbreviated
E (^) K ). Given the normal K^1 concentration gradient, where the
concentration is 30 times higher inside than outside the cell
( fig.  6.26 ), the value of E (^) K is 2 90 millivolts (mV). A sign
( 1 or 2 ) placed in front of the voltage always indicates the
polarity of the inside of the cell (this is done because when a
neuron produces an impulse, the polarity briefly reverses, as
discussed in chapter 7).
Expressed in a different way, a membrane potential of
2 90 mV is needed to produce an equilibrium in which the K^1
concentrations are 150 mM inside and 5 mM outside the cell
( fig.  6.26 ). At 2 90 mV, these intracellular and extracellular
concentrations are kept stable. If this value were more nega-
tive, it would draw more K^1 into the cell; if it were less nega-
tive, K^1 would diffuse out of the cell.
Now, let’s ask another hypothetical question: What
would the membrane potential be if the membrane were per-
meable only to Na^1? (This is quite different from the usual
situation in which the membrane is less permeable to Na^1
than to K^1 .) What membrane potential would stabilize the
Na^1 concentrations at 12 mM intracellularly and 145 mM
extracellularly ( fig.  6.26 ) if Na^1 were the only ion able to
cross the membrane? This is the  Na 1 equilibrium potential
(abbreviated  E (^) Na ). You could guess that the inside of the cell
would have to be the positive pole, repelling the Na^1 and
causing its concentration to be lower inside than outside the
Figure 6.26 Concentrations of ions in the
intracellular and extracellular fluids. This distribution of
ions, and the different permeabilities of the plasma membrane
to these ions, affects the membrane potential and other
physiological processes.
See the Test Your Quantitative Ability section of the Review
Activities at the end of this chapter.
K+
Cl–
Ca2+
Intracellular fluid
concentrations
Extracellular fluid
concentrations
12 mM
150 mM
9 mM
0.0001 mM
145 mM
5 mM
125 mM
2.5 mM
Na+