In a rotary motor FoF1-ATP synthase that couples H ؉ transport with ATP synthesis͞hydrolysis, it is thought that an Foc subunit oligomer ring (c-ring) in the membrane rotates as protons pass through Fo and a 120°rotation produces one ATP at F1. Despite several structural studies, the copy number of Foc subunits in the c-ring has not been determined for any functional FoF1. Here, we have generated and isolated thermophilic Bacillus FoF1, each containing genetically fused 2-mer-14-mer c (c2-c14). Among them, FoF1 containing c2, c5, or c10 showed ATP-synthesis and other activities. When F1 was removed, Fo containing c10 worked as an H ؉ channel but Fos containing c9, c11 or c12 did not. Thus, the c-ring of functional FoF1 of this organism is a decamer. The inevitable consequence of this finding is noninteger ratios of rotation step sizes of F1͞Fo (120°͞36°) and of H ؉ ͞ATP (10:3). This step-mismatch necessitates elastic twisting of the rotor shaft (and͞or the side stalk) during rotation and permissive coupling between unit rotations by H ؉ transport at Fo and elementary events in catalysis at F1. T he F o F 1 -ATP synthase, often simply called F o F 1 , is composed of two portions: a water-soluble F 1 , which has catalytic sites for ATP synthesis and hydrolysis, and a membrane-integrated F o , which mediates H ϩ (proton) transport (1, 2). When isolated, F 1 has ATP-hydrolyzing activity and F o acts as a proton channel. The bacterial F o F 1 has the simplest subunit structure, ␣ 3  3 ␥␦ for F 1 and ab 2 c n for F o (where n is the copy number of the c subunits), as depicted schematically in Fig. 1A. F 1 and F o are motors that share a common central rotor; a down-hill proton flow through F o drives rotation of the rotor, causing conformational changes in F 1 that result in ATP synthesis. Conversely, ATP hydrolysis in F 1 causes a reverse rotation of the rotor that enforces F o to pump protons to the reverse direction. The ring of F o c subunit oligomer and the ␥-subunits of F 1 comprise the central rotor, and they rotate together as a single body (3). The side stalk made up of ␦-b 2 subunits connects the membranebound F o a subunit with the ␣ 3  3 hexamer ring of F 1 , which prevents the hexameric ring from rotating as ␥ subunit rotates. Rotary motion of F 1 has been analyzed in detail, and it has been established that the ␥ subunit rotates with a discrete 120°step per each consumed ATP (4, 5) (three ATP molecules per revolution). However, little is known about the F o rotation. It has been proposed that each proton is first transported to a glutamic acid of an F o c subunit of the c-ring, which is located at the middle of a transmembrane helix of F o c, through a channel in the periplasmic half of the F o a subunit, and then after one revolution of the c-ring, the proton is released to cytoplasm through another half-channel of F o a (6, 7) (Fig. 1 A). In this mechanism, the copy number of F o c in the c-ring should be equal to the number of transported protons per revolution of the c-ring that directly defines th...