Final answer:
Oxidative phosphorylation is the process that involves a membrane, as it occurs in the mitochondria and relies on the electron transport chain and an established proton gradient across the inner mitochondrial membrane to generate ATP.
Step-by-step explanation:
The process that involves a membrane is oxidative phosphorylation.
Oxidative phosphorylation is a critical step in cellular respiration that occurs in the mitochondria. It includes the transfer of electrons through a series of membrane-bound proteins called the electron transport chain, ending with the transfer to oxygen, which forms water. This electron movement powers proton pumps that generate a proton gradient across the inner mitochondrial membrane.
This gradient creates an electrochemical potential used by ATP synthase to synthesize ATP from ADP. This entire process depends intimately on the mitochondrial membrane to function and could not occur without it. In contrast, substrate-level phosphorylation occurs in the cytoplasm during glycolysis and in the mitochondrial matrix during the citric acid cycle, both of which do not directly involve a membrane. The directional movement of motor proteins is also not directly related to membranes but rather to cytoskeletal elements such as microtubules and actin filaments.