and urea from the inside to the outside of a cell (this is not actually found
in nature). The coupled reaction would be written as:
Glucoseout+ureain↔glucosein+ureaout (18.5)
Set the concentrations to 1 mM for both glucose and urea outside and
10 mM inside:
(18.6)
Now set the outside concentrations to 1 mM for glucose and 10 mM for
urea and both inside concentrations at 10 mM:
=58 meV log(0.10) =−58 meV (18.7)
The transport is now energetically favorable. Notice that when the units
are converted to base 10 logarithms, a factor of 10 difference in concen-
tration corresponds to an energy of 58 meV at room temperature.
In the intestines, glucose is cotransported with Na+into epithelial cells
by a symporter, which is a channel that can transport two molecules
in the same direction simultaneously. For the Na+/glucose symporter, two
sodium ions are transported with every glucose molecule:
2Na+out+glucosein→2Na+in+glucoseout (18.8)
The energy to transport the glucose is provided by the simultaneous
transport of the Na+. Consider concentrations of 12 and 145 mM for the
intracellular and extracellular sodium concentrations, respectively, and a
typical membrane potential of −50 mV. For each Na+the change in free
energy is calculated using eqn 18.3:
=−11.0 kJ mol−^1 (18.9)
For every 2 mol of Na+moved, the energy to transport 1 mol of glucose is:
ΔG=2 mol (11.0 kJ mol−^1 ) =22 kJ (18.10)
This energy provides the opportunity to transport glucose against a large
concentration gradient. The glucose does not build up in the epithelial cells
ΔG=×(.23 247. −)log +(
12
145
kJ mol^1196
mM
mM
..) 50 kJ V mol−−^11 (.)− 05 V
ΔGRT
cc
c
ln
((
(
= glucosein ureaout
glucose ou
))
) ttureain)
MM
(
ln
()()
c
=RT
10 10××−−^33 1 10
(()10 10××−−^33 MM()10 10
ΔGRT
cc
c
ln
()()
()
= glucosein ureaout
glucose outtureain)
MM
(
ln
()()
c
=RT
10 10××−−^33 1 10
(()( )110 10 10
330
××
−−=
MM
392 PART 3 UNDERSTANDING BIOLOGICAL SYSTEMS USING PHYSICAL CHEMISTRY
