198 GROUP I AND II METALS IN BIOLOGICAL SYSTEMS
ψ=[]
[]
=≈−
+
+RT
F
ln. logK
K
out mV
in0 059
10
92
(^57) (5.12)
What we have calculated here is the equilibrium potential — the voltage at
which the inward and outward fl ows of the ion are balanced. This calculation
has not considered other ions that can (Na + ) or cannot (organic phosphates
or ionized proteins) diffuse. In general, one expects that potassium ions can
enter cells due to the negative potentials as calculated above. However, the
same sort of calculation for sodium ions with concentrations of 11 mM inside
red blood cells and 160 mM outside would lead to a large positive potential
of about +70 mV. The concentration gradient for potassium is directed out of
the cell, while the concentration gradient for sodium is directed into the cell.
To pump Na + against a concentration gradient, organisms must utilize active
transport (ion pumps) coupled to energy - yielding reactions such as
ATP H O Na+++→ + 24 ++in Kout ADP PO^3 −()Pi + ++Naout+ +Kin energy (5.13)
The cells we will discuss are those having a known potassium ion resting
potential, although this is only one type of many. Suppose energy input stops.
Sodium ions may still enter cells slowly through diffusion, leaks, and mem-
brane channels. When this happens, Na + must be pumped out of the cell by
active transport. In addition, potassium ions may move out of the cell by dif-
fusion and need to be pumped back in by active transport. In the resting state
for these cells, the Na + channel is closed, the K + channel is open, and the pump
is working. (See Figure 5.3 as adapted from Figure 8.5 of daSilva.) Essentially
the resting cells are impermeable to Na + , Ca 2+ , Cl − , and HPO 42 − but permeable
to K + because the potassium ion channels are open. Specifi cally, for the Na + /K +
ATPase pump, two K + move in for every three Na + that move out, creating an
Figure 5.3 Pumped movement of sodium ions out of and potassium ions into a cell
assisted by ATP hydrolysis. (Adapted by permission of Oxford University Press from
Figure 8.5 of reference 2. Clarendon Press, Oxford and Oxford University Press Inc.,
New York, 1991.)
3 Na +
Inside cell
Outside
cell ATP
ADP
3 Na+ 2 K+
2 K+