Final answer:
Proton diffusion through the mitochondrial membrane without proteins would eliminate the proton gradient necessary for ATP production, leading to a halt in cellular metabolism.
Step-by-step explanation:
When hydrogen ions (protons) are able to diffuse freely through the mitochondrial membrane without requiring integral membrane proteins, the outcome is significant for cellular respiration. Normally, protons are pumped into the intermembrane space, creating a proton gradient that is critical for the production of ATP through the activity of ATP synthase. If protons could diffuse back into the mitochondria, this would lead to the dissipation of the proton gradient, and ATP production would cease. Consequently, cellular metabolism would be severely impacted as ATP is the primary energy currency of the cell.