Chapter 10, Problem 17P

The ${\text{Na}}^{\text{+}}\text{/}$ glucose symport transports glucose from the lumen of the small intestine into cells lining the lumen. Transport of 1 glucose molecule is directly coupled to the transport of ${\text{1 Na}}^{\text{+}}\text{ion}$ into the cell.

   $1{\text{ Na}}^{+}{}_{\text{out}}+1{\text{ glucose}}_{\text{out}}\to 1{\text{ Na}}^{\text{+}}{}_{\text{in}}+1{\text{ glucose}}_{\text{in}}$

Assume the following conditions at

   ${\text{37}}^{\text{o}}\text{C: }{\left[{\text{Na}}^{\text{+}}\right]}_{\text{in}}\text{=12 Mm, }{\left[{\text{Na}}^{\text{+}}\right]}_{\text{out}}\text{ = 145 mM, }{\left[\text{glucose}\right]}_{\text{out}}\text{ = 28 µM, andΔ= -72 mV}$

(inside negative)
a. What is $\Delta G$ for transport of Na+ from outside to inside under these conditions?
b. What is the upper limit for ${\left[\text{glucose}\right]}_{\text{in}}$ under these conditions?
c. Which of the two hypothetical symports shown below (A or B) would achieve the highest concentration of [glucose]_inunder the conditions described above? Briefly explain your choice.
A: ${\text{1Na}}^{\text{+}}{}_{\text{out}}{\text{+ 2 glucose}}_{\text{out}}\to {\text{ 1Na}}^{\text{+}}{}_{\text{in}}{\text{+ 2 glucose}}_{\text{in}}$

B: ${\text{2 Na}}^{\text{+}}{}_{\text{out}}{\text{+ 1 glucose}}_{\text{out}}\to {\text{ 2 Na}}^{\text{+}}{}_{\text{in}}{\text{+ 1 glucose}}_{\text{in}}$