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.
A crista is a fold of the inner mitochondrial membrane into the mitochondrial matrix. Its membrane remains continuous with the surrounding inner mitochondrial membrane; it is not a separately inserted sac like a thylakoid.[ref]
Molecular Biology of the Cell, 4th edition by Bruce Alberts and others. Chapter 12, The Transport of Proteins into Mitochondria and Chloroplasts, Figure 12-22: continuity of cristae and contrast with thylakoids
The diagram idealizes access through the fold's opening. Connectivity alone does not imply instant mixing or identical concentrations throughout the intermembrane space. Narrow geometry and molecular interactions can matter to transport. Increasing surface area also does not, by itself, prove a proportional increase in ATP production: the supply of substrates, available oxygen and the state of the coupling machinery must also support the flux.
