**4. Overview of the F1FO-ATP Synthase/Hydrolase and Its Supramolecular Structure**

The mitochondrial respiratory chain and its arrangement in SCs, detailed in the previous sections, has the main bioenergetic role to build the electrochemical gradient which allows the F1FO-ATP synthase to build ATP, namely, to accomplish the so-called energy transduction, which converts a transmembrane proton movement into chemical energy, which can be used for all the energy-consuming processes of the cell.

The rotary ATPase family, which embraces structurally similar membrane-bound enzyme complexes working as energy transduction mechanisms, consists of three subfamilies, A-, V- and F-type ATPases, which originate from a common evolutionary ancestor. A-type ATPases occur in Archaea and some bacteria, V-type ATPases are typical of eukaryotic vacuoles, while F-type ATPases occur in eukaryotic mitochondria, tylakoid membranes of chloroplasts and in bacterial cell membranes [122]. In mitochondria, the hydrophilic (F1) and hydrophobic (FO) ATPase domains are joined laterally by a single stalk stator and in the middle by a central stalk. The F-type ATPases can function as ATP synthesis or ion pumps coupled to ATP hydrolysis, a bifunctional mechanism unique in nature [123,124]. The F1FO-ATPase has a mushroom shape, in which F<sup>O</sup> is membrane-embedded and F<sup>1</sup> protrudes outside the mtIM. The enzyme complex is universally known as the nano-machine that produces ATP, the "molecular energy currency" under aerobic conditions [125,126]. The hydrophilic enzyme domain basically consists of a spherical extrinsic hexamer formed by three catalytic β subunits alternated with three non-catalytic α subunits. The (αβ)<sup>3</sup> hexamer contains in the core the asymmetrical central stalk (in turn composed by γ, δ, and ε subunits). The central stalk is joined to the loop of each *c* subunit hairpin. The number of *c* subunits is species dependent: these subunits are arranged as a cylindric palisade to form the *c*-ring. This subunit assembly, namely the *c*-ring and the central stalk, makes up the rotor. The membrane-embedded *a* subunit with unusual "horizontal" hairpin helices named H5–H6 matches the concave barrel-like *c*-ring where the H<sup>+</sup> sites lie and perfectly fits the ring size in order to create the H<sup>+</sup> translocation pathway. A static structure peripheral to the rotor, which spans for the entire enzyme complex length, acts as a stator to prevent the (αβ)<sup>3</sup> rotation torque of the central stalk. The peripheral stalk is composed by various subunits, namely the hydrophilic oligomycin sensitivity-conferring protein (OSCP), F6, *b*, *d*, linked to F1-catalytic domain and embedded in the mtIM by the hydrophobic portion of *b* and A6L subunits. The peripheral stalk is also associated to the supernumerary membrane subunits (*sms*) *e*, *f*, *g*, and 6.8-kDa proteolipid (6.8PL). However, 6.8PL was erroneously believed to be inserted in the central hole of the *c*-ring [127] and another supernumerary subunit, diabetes-associated protein in insulin-sensitive tissue (DAPIT), in the tetrameric F1FO-ATPase porcine model was misassigned, since recently it was reported as localized at the furthest edge of F<sup>O</sup> domain [128] (Figure 3). So, the emerging advances in the enzyme knowledge make researchers continuously re-consider and re-evaluate the F1FO-ATPase structure and function.

In mammalian mitochondria, this astonishing enzyme complex has recently revealed versatile roles, in addressing cells to life or death, in the maintenance of the mitochondrial morphology and raised great expectations as a drug target [129,130]. Accordingly, the modulation of the enzyme functions, often compromised by mitochondrial dysfunctions associated with severe diseases, may contribute to innovative therapeutic strategies at the molecular level.
