Electron transfer translocates protons from the mitochondrial matrix to the inner membrane space, establishing a pH gradient across the inner membrane (outside more acidic than inside). The tendency of protons to diffuse back into the matrix is the driving force for ATP synthesis by ATP synthase. During oxidative phosphorylation by a suspension of mitochondria in a medium of pH 7.4, the pH of the matrix has been measured as 7.7.

(a) Calculate [H+] in the external medium and in the matrix under these conditions.

(b) What is the outside-to-inside ratio of [H+]? Comment on the energy inherent in this concentration difference. (Hint: See Eqn 11-3, p. 409)

(c) Calculate the number of protons in a respiring liver mitochondrion, assuming its inner matrix compartment is a sphere of diameter 1.5 μm.

(d) From these data, is the pH gradient alone sufficient to generate ATP?

(e) If not, suggest how the necessary energy for synthesis of ATP arises.