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The inner mitochondrial membrane separates mitochondrial matrix from intermembrane space. Its selective permeability permits distinct chemical conditions, while embedded mitochondrial respiratory chain proteins and ATP synthase support oxidative phosphorylation. Cristae increase its surface area.[ref]
Molecular Biology of the Cell, 4th edition by Bruce Alberts and others. Chapter 14, The Mitochondrion Contains an Outer Membrane, an Inner Membrane, and Two Internal Compartments; Figure 14-8
A selective boundary and a productive enzyme have different jobs. Even active respiratory enzymes cannot sustain a useful electrochemical gradient if protons return freely across the boundary. Conversely, an intact boundary without an electron donor does not supply the energy for continued pumping. The isolated mitochondria respiration experiment separates some of these dependencies by additions to the same preparation.