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In a mitochondrion, the intermembrane space lies between the outer mitochondrial membrane and inner mitochondrial membrane, extending into the interiors of cristae. It includes the side of the inner mitochondrial membrane from which protons return through ATP synthase to the mitochondrial matrix.

A useful sidedness check is to follow a single arrow: outward pumping goes from green to yellow in the diagram, while coupled return goes from yellow to green. These are opposing movements of protons, not a circuit in which Electrons return through ATP synthase. The mitochondrial respiratory chain and chemiosmosis articles distinguish the two ledgers.

A mitochondrion is an organelle with an outer mitochondrial membrane and an inner mitochondrial membrane. The latter encloses the mitochondrial matrix and folds into cristae; the intermembrane space lies on its opposite side. This architecture separates a chemical workspace from a membrane that couples Electron transport to ATP formation.^[ref]

For an original location exercise, place soluble label A in the mitochondrial matrix and soluble label B in the interior of a crista. In the depicted geometry, B can reach the peripheral intermembrane space through the fold's opening without crossing a lipid bilayer. A must cross the inner mitochondrial membrane to reach either location. A fold projecting into the mitochondrial matrix therefore does not make its enclosed fluid part of the mitochondrial matrix. Following a continuous path through the colored regions proves the distinction; merely asking whether a label is “inside the mitochondrion” loses it.

The functional connection is equally spatial. The mitochondrial respiratory chain pumps protons from the mitochondrial matrix side across the inner mitochondrial membrane. Their return through ATP synthase can drive ATP formation. Oxidative phosphorylation develops the mechanism and chemiosmosis gives its free energy bookkeeping. Compartmentalization is useful because it lets a shared electrochemical gradient couple different proteins without direct transfer of a chemical intermediate between each pair.

Under aerobic conditions, mitochondria supply much of the ATP in many eukaryotic biological cells; the contribution varies with biological tissue, demand and oxygen supply. Glycolysis also makes ATP in the cytosol. Mature mammalian red blood cells lack mitochondria, and bacteria have no mitochondria at all. Neither all ATP production nor all biological cells fit the familiar mitochondrial picture.^[ref]

Mitochondria descend from a bacterial endosymbiosis and retain a genome and ribosomes, although many required proteins are encoded by nuclear genes. Endosymbiotic theory develops the ancestry argument; organelle protein import explains delivery of nuclear-encoded proteins. A functioning isolated mitochondrion demonstrates biochemical autonomy under supplied conditions, rather than independently establishing that ancestry.

The outer mitochondrial membrane separates the surrounding cytosol from the intermembrane space. Channels permit passage of many small molecules, while the inner mitochondrial membrane supplies the main selective barrier between them and the mitochondrial matrix.^[ref]

Small-solute access does not imply unrestricted access for proteins. The cytochrome c addition in the isolated mitochondria respiration experiment tests a consequence of damage to this boundary. Organelle protein import describes purposeful delivery across mitochondrial boundaries.