3. There is a stable pH and electrical potential difference across the mitochond

Question

3. There is a stable pH and electrical potential difference across the mitochondrial membrane in actively respiring cells. The pH of the cytoplasm is 6.8, the pH of the mitochondrial matrix (inside) is 8.3, and the transmembrane potential (Aw) is -150 mV (inside negative). Calculate the free energy of transport (4G.) to move one mole of protons from the cytoplasm (outside) to the matrix (inside) under these conditions and 37'C, Is this direction of proton movement thermodynamically spontaneous? CI Paeaus Given that the free energy of ATP synthesis from ADP and P,is + 57.5 k/mol, is the free energy of transporting one mole of proton from outside the mitochondrion to inside (from question 3) sufficient to drive ATP synthesis? If not, what is the minimum number of moles of protons that would have to move from outside to inside to account for the synthesis of a mole of ATP?

Explanation / Answer

Ans. #3. Note: There is NO need of calcualtion [H+] in the two comprtments. Using dG0' = -2.303 RT (dpH) for the free energy of proton gradient is the same as using dG0' = -RT ln Keq = - 2.303 RT log Keq.

# Free energy change of a proton gradient, when proton moves from its higher to lower concertation, available to ATP synthase is given by-

            dG0’ = -2.303 RT(dpH) + nF(dV)             - equation 1

            where,

R = (0.001987 kcal mol-1K-1 or 0.008314 kJ mol-1 K-1)

                        T = 37.00C = 310.15 K

                      By convention: (dpH) = (pH IN) – (pH OUT) = 8.3 – 6.8 = 1.5

                     By convention:     (dV) = (V IN) – (V OUT) = -150 mV = -0.150 V

Putting the values in equation 1-

dG0’ = [-2.303 (0.008314 kJ mol-1 K-1 x 310.15 K) x 1.5] + [1 x 96.485 kJ V-1 mol-1 x (-0.150V)]

Or, dG0’ = (-8.91 kJ / mol) + (-14.47 kJ / mol)

Hence, dG0’ = -23.38 kJ/ mol

#4. No, transporting 1 mol H+ is NOT sufficient to drive the synthesis of 1 mol ATP because the dG0’ of ATP synthesis is requires 57.5 kJ/mol energy compared to only 23.38 kJ/mol energy released by translocation of 1 mol protons.

# Minimum number of moles of H+ =

            dG0’ of 1 mol ATP synthesis / Energy released by translocation of 1 mol H+

                                                = 57.5 kJ / (23.38 kJ / mol)

                                                = 2.46 mol

Therefore, minimally required number of moles of proton to form 1 mol ATP = 2.46 mol = 2.5 mol

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