Chapter 10, Problem 16P

ATP is synthesized from ADP, $\text{Pi }$ , and a proton on the matrix side of the inner mitochondrial membrane. We will refer to the matrix side as the "inside" of the inner mitochondrial membrane (IMM).
a. ${\text{ H}}^{\text{+}}$ transport from the outside of the IMM into the matrix drives this process. The pH inside the matrix is 8.2, and the outside is more acidic by 0.8 pH units. Assuming the IMM membrane potential is 168 mV (inside negative), calculate ?G for the transport of 1 mol of H+ across the IMM into the matrix at
   ${\text{37}}^{\text{O}}{\text{C: H}}^{\text{+}}{}_{\text{(outside)}}\to {\text{ H}}^{\text{+}}{}_{\text{(inside)}}$

b. Assume three mol H+must be translocated to synthesize one mol ATP by coupling of the following reactions.
${\text{ADP + Pi + H}}^{\text{+}}{}_{\text{inside}}\to {\text{ ATP + H}}_{\text{2}}\text{O }\left(\text{ATP synthesis}\right)$ Write the overall reaction for ATP synthesis coupled to ${\text{ H}}^{\text{+}}$ transport [and use this equation for part (c)]:

c. Assume three mol ${\text{ H}}^{\text{+}}$ must be translocated to synthesize one mol ATP as described in part (b) above. Given the following steady-state concentrations:

$\text{ATP = 270 mM}$ and
${\text{P}}_{\text{i}}\text{= 5}\text{.20 mM}$ , the membrane potential
$\text{Δ= 168 mV}$ (inside negative), and the pH values in part (a), calculate the steady-state concentration of ${\text{ADP at 37}}^{\text{o}}\text{C}$ when for the coupled process (ATP synthesis + H+ transport), $\text{ΔG = - 11}\text{.7 kJ / mol}\text{.}$