Final answer:
Protons flow back across the mitochondrial membrane due to chemiosmosis, facilitated by ATP synthase using the energy from the proton gradient to synthesize ATP from ADP and inorganic phosphate.
Step-by-step explanation:
Protons flow back across the mitochondrial membrane through a process called chemiosmosis, which is crucial for ATP synthesis. The ATP synthase acts as a molecular generator, utilizing the potential energy stored in the proton gradient. This gradient is formed by the active transport of protons from the mitochondrial matrix out to the intermembrane space, due to the work of proton pumps within the electron transport chain. When protons flow back into the matrix via ATP synthase, they release this gradient's free energy, which is harnessed to convert ADP to ATP, a process called oxidative phosphorylation.
The movement of these protons back into the matrix is driven by the proton-motive force, which includes both a difference in proton concentration (creating a pH gradient) and an electric potential resulting from the accumulation of positively charged H+ ions on one side of the membrane. The ATP synthase enables protons to flow down this electrochemical gradient and uses the energy released in this process to catalyze the formation of ATP, the energy currency of the cell.