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:
Glucose out + urea in ↔ glucose in + urea out
(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 concentration 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 + glucose in → 2Na
+
in + glucose out
(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 ( .
.
)log
(
=
×
+
−
2 3 2 47
12
145
196
1
kJ mol
mM
mM
. .
) ( .
)
5
0 0 5
1
1
kJ V mol
V
−
−
−
ΔG RT
c
c
c
ln
(
(
(
=
glucose in urea out
glucose ou
)
)
) t t urea in
)
M
M
(
ln
(
) (
)
c
RT
=
×
×
−
−
10 10
1 10
3
3
( (
) (
)
10 10
10 10
3
3
×
×
−
−
M
M
ΔG RT
c
c
c
ln
(
) ( )
(
)
=
glucose in urea out
glucose out t urea in
)
M
M
(
ln
(
) (
)
c
RT
=
×
×
−
−
10 10
1 10
3
3
( (
) (
)
1 10
10 10
0
3
3
×
×
=
−
−
M
M
392
PART 3
UNDERSTANDING BIOLOGICAL SYSTEMS USING PHYSICAL CHEMISTRY
9781405124362_4_018.qxd 4/29/08 10:47 Page 392
in nature). The coupled reaction would be written as:
Glucose out + urea in ↔ glucose in + urea out
(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 concentration 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 + glucose in → 2Na
+
in + glucose out
(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 ( .
.
)log
(
=
×
+
−
2 3 2 47
12
145
196
1
kJ mol
mM
mM
. .
) ( .
)
5
0 0 5
1
1
kJ V mol
V
−
−
−
ΔG RT
c
c
c
ln
(
(
(
=
glucose in urea out
glucose ou
)
)
) t t urea in
)
M
M
(
ln
(
) (
)
c
RT
=
×
×
−
−
10 10
1 10
3
3
( (
) (
)
10 10
10 10
3
3
×
×
−
−
M
M
ΔG RT
c
c
c
ln
(
) ( )
(
)
=
glucose in urea out
glucose out t urea in
)
M
M
(
ln
(
) (
)
c
RT
=
×
×
−
−
10 10
1 10
3
3
( (
) (
)
1 10
10 10
0
3
3
×
×
=
−
−
M
M
392
PART 3
UNDERSTANDING BIOLOGICAL SYSTEMS USING PHYSICAL CHEMISTRY
9781405124362_4_018.qxd 4/29/08 10:47 Page 392