In mitochondria, the F0F1 ATP synthase has a long history of scientific study. The F1 portion of the ATP synthase is above the membrane, the F0 portion is within the membrane. It's easy to visualize the F0F1 particle as resembling the fruiting body of a common mushroom, with the head being the F1 particle, the stalk being the gamma subunit of F1, and the base and "roots" being the F0 particle embedded in the membrane. The F1 particle was first isolated by Ephraim Racker in 1961.
The F1 particle is large and can be seen in the transmission electron microscope by negative staining (1962, Fernandez-Moran et al., Journal of Molecular Biology, Vol 22, p 63). These are particles of 90 Å diameter that pepper the inner mitochondrial membrane. They were originally called elementary particles and were thought to contain the entire respiratory apparatus of the mitochondrion, but through a long series of experiments, Ephraim Racker and his colleagues were able to show that this particle is correlated with ATPase activity in uncoupled mitochondria and with the ATPase activity in submitochondrial particles created by exposing mitochondria to ultrasound. This ATPase activity was further associated with the creation of ATP by yet another long series of experiments in many laboratories.
In the 1960s through the 1970s, Paul Boyer developed his binding change, or flip-flop, mechanism, which postulated that ATP synthesis is coupled with a conformational change in the ATP synthase generated by rotation of the gamma subunit. John E. Walker crystallized the ATP synthase and was able to determine that Boyer's conformational model was essentially correct. In the crystal structure, the F1 particle can be seen to be composed of a cylinder of 6 subunits, alternating alpha and beta subunits, that form a ring around an asymmetrical gamma subunit. Facilitated diffusion of protons causes the F0 particle to rotate, rotating the gamma subunit of F1, while the major F1 subunits are fixed in place. This rotation forces a conformational change in the F1 particle, eventually leading to the synthesis of ATP. For elucidating this Boyer and Walker shared in the 1997 Nobel Prize in Chemistry.
The F1 particle is a reversible ATP synthase. Large enough quantities of ATP cause this particle to create a proton gradient. Under physiological conditions, this particle generally runs in the opposite direction, creating ATP while using the protonmotive force created by the electron transport chain as a source of energy. The overall process of creating energy in this fashion is termed oxidative phosphorylation.
A similar particle is found in chloroplasts, the CF1 particle, also a reversible ATP synthase. However, the chloroplast thylakoid membranes are inverted in "F1 topology" relative to mitochondria (the CF1 particles are on the outside) and in this sense chloroplasts more resemble submitochondrial particles.