BioPHYSICAL chemistry

because there is a passive glucose channel that allows the glucose to pass
from the epithelial cells into the bloodstream. In this case, the transporter
serves as a uniporter, which transports a single molecule.
The energy for the Na+/K+pump is driven by the hydrolysis of ATP. As
discussed above, the transport of Na+out of the cell moves the ion from
a low concentration of 10 mM to 140 mM, so this term will be unfavor-
able. Since a charge is being moved, we need to include the contribution
of the membrane potential, which is 70 mV, being more negative in the
inside. Using eqn 18.3 we can calculate the energy change for the Na+as:

=+13.6 kJ mol−^1 (18.11)

The transport of K+is in the opposite direction. The ion moves from a
low concentration of 5 mM to a high concentration of 100 mM, which is
unfavorable, but the contribution of the membrane potential has changed
sign and is favorable and the overall free energy change is nearly zero:

=+1.0 kJ mol−^1 (18.12)

Since 3 mol of Na+ is transported with 2 mol of K+ the net energy
change is:

ΔGtotal=3(+13.6 kJ mol−^1 ) +2(+1.0 kJ mol−^1 ) =+42.8 kJ mol−^1 (18.13)

To estimate the free energy change contributed by converting ATP to ADP,
we must correct the standard free energy difference of −31.3 kJ mol−^1
by the contribution of the high concentration of ATP in the cell. If there
is a thousand-fold greater amount of ATP than ADP, the free energy dif-
ference is estimated to be:

ΔG=−31.3 kJ mol−^1 +(2.3 ×2.47 kJ mol−^1 )log(10^3 )

=−49.1 kJ mol−^1 (18.14)

The dependence of the free energy on concentration quantifies the tendency
of molecules to have equal concentrations on both sides of membranes.
However, if we consider a charged molecule, such as a proton, the free
energy difference is zero when:

(18.15)

ΔV

RT

FZ

c

c

p

p

ln

()

()

=− out

in

ΔG=×(.23 247. −)log +(.

100

5

kJ mol^1196

mM

mM

550 kJ V mol−−^11 )( .− 07 V)

ΔG=×(.23 247. −)log +(

140

10

kJ mol^1196

mM

mM

..) 50 kJ V mol−−^11 (.)+ 07 V

CHAPTER 18 MEMBRANE POTENTIALS 393