Final answer:
ATP hydrolysis inside mitochondria and the membrane potential across the inner membrane are directly involved in the import of proteins into the mitochondrial matrix, utilizing energy generated by the movement of hydrogen ions through ATP synthase.
Step-by-step explanation:
The subset of factors directly involved in driving protein import into the mitochondrial matrix space includes ATP hydrolysis inside mitochondria, as it provides the energy necessary for protein translocation through the mitochondrial membranes. The membrane potential across the inner membrane of the mitochondria is also crucial, as it creates the electrochemical gradient required for chemiosmosis. During chemiosmosis, hydrogen ions (H+) move across the inner membrane through ATP synthase, generating ATP from ADP and inorganic phosphate, thereby providing the energy for various cellular processes, including protein import into the mitochondrial matrix.