ATP synthase (F(O)F(1)) operates as two rotary motor/generators coupled by a common shaft. Both portions, F(1) and F(O), are rotary steppers. Their symmetries are mismatched (C(3) versus C(10-14)). We used the curvature of fluorescent actin filaments, attached to the rotating c-ring, as a spring balance (flexural rigidity of 8. 10(-26) Nm(2)) to gauge the angular profile of the output torque at F(O) during ATP hydrolysis by F(1) (see theoretical companion article (. Biophys. J. 81:1234-1244.)). The large average output torque (50 +/- 6 pN. nm) proved the absence of any slip. Variations of the torque were small, and the output free energy of the loaded enzyme decayed almost linearly over the angular reaction coordinate. Considering the threefold stepping and high activation barrier of the driving motor proper, the rather constant output torque implied a soft elastic power transmission between F(1) and F(O). It is considered as essential, not only for the robust operation of this ubiquitous enzyme under symmetry mismatch, but also for a high turnover rate of the two counteracting and stepping motor/generators.

The rotary motion in response to ATP hydrolysis of the ring of c subunits of the membrane portion, F o , of ATP synthase, F o F 1 , is still under contention. It was studied with EF o EF 1 (Escherichia coli) using microvideography with a fluorescent actin filament. To overcome the limited specificity of actin attachment through a Cys-maleimide couple which might have hampered the interpretation of previous work, we engineered a`strep-tag' sequence into the C-terminal end of subunit c. It served (a) to purify the holoenzyme and (b) to monospecifically attach a fluorescent actin filament to subunit c. EF o EF 1 was immobilized on a Ni-NTA-coated glass slide by the engineered His-tag at the N-terminus of subunit L L. In the presence of MgATP we observed up to five counterclockwise rotating actin filaments per picture frame of 2000 W Wm 2 size, in some cases yielding a proportion of 5% rotating over total filaments. The rotation was unequivocally attributable to the ring of subunit c. The new, doubly engineered construct serves as a firmer basis for ongoing studies on torque and angular elastic distortions between F 1 and F o .

ATP synthase (F-ATPase) produces ATP at the expense of ion-motive force or vice versa. It is composed from two motor/generators, the ATPase (F1) and the ion translocator (F0), which both are rotary steppers. They are mechanically coupled by 360 degrees rotary motion of subunits against each other. The rotor, subunits gamma(epsilon)C10-14, moves against the stator, (alphabeta)3delta(ab2). The enzyme copes with symmetry mismatch (C3 versus C10-14) between its two motors, and it operates robustly in chimeric constructs or with drastically modified subunits. We scrutinized whether an elastic power transmission accounts for these properties. We used the curvature of fluorescent actin filaments, attached to the rotating c ring, as a spring balance (flexural rigidity of 8.10(-26) N x m2) to gauge the angular profile of the output torque at F0 during ATP hydrolysis by F1. The large average output torque (56 pN nm) proved the absence of any slip. Angular variations of the torque were small, so that the output free energy of the loaded enzyme decayed almost linearly over the angular reaction coordinate. Considering the three-fold stepping and high activation barrier (>40 kJ/mol) of the driving motor (F1) itself, the rather constant output torque seen by F0 implied a soft elastic power transmission between F1 and F0. It is considered as essential, not only for the robust operation of this ubiquitous enzyme under symmetry mismatch, but also for a high turnover rate under load of the two counteracting and stepping motors/generators.

In ATP synthase (F O F 1 -ATPase) ion flow through the membrane-intrinsic portion, F O , drives the central "rotor", subunits c 10 ⑀␥, relative to the "stator" ab 2 ␦(␣␤) 3 . This converts ADP and P i into ATP. Vice versa, ATP hydrolysis drives the rotation backwards. Covalent cross-links between rotor and stator subunits have been shown to inhibit these activities. Aiming at the rotary compliance of subunit ␥ we introduced disulfide bridges between ␥ (rotor) and ␣ or ␤ (stator). We engineered cysteine residues into positions located roughly at the "top," "center," and "bottom" parts of the coiled-coil portion of ␥ and suitable residues on ␣ or ␤. This part of ␥ is located at the center of the (␣␤) 3 domain with its Cterminal part at the top of F 1 and the bottom part close to the F O complex. Disulfide bridge formation under oxidizing conditions was quantitative as shown by SDSpolyacrylamide gel electrophoresis and immunoblotting. As expected both the ATPase activities and the yield of rotating subunits ␥ dropped to zero when the cross-link was formed at the center (␥L262C 7 ␣A334C) and bottom (␥Cys 87 7 ␤D380C) positions. But much to our surprise disulfide bridging impaired neither ATP hydrolysis activity nor the full rotation of ␥ and the enzyme-generated torque of oxidized F 1 , which had been engineered at the top position (␥A285C 7 ␣P280C). Apparently the high torque of this rotary engine uncoiled the ␣-helix and forced amino acids at the C-terminal portion of ␥ into full rotation around their dihedral (Ramachandran) angles.

F‐ATP synthase synthesizes ATP at the expense of ion motive force by a rotary coupling mechanism. A central shaft, subunit γ, functionally connects the ion‐driven rotary motor, FO, with the rotary chemical reactor, F1. Using polarized spectrophotometry we have demonstrated previously the functional rotation of the C‐terminal α‐helical portion of γ in the supposed ‘hydrophobic bearing’ formed by the (αβ)3 hexagon. In apparent contradiction with these spectroscopic results, an engineered disulfide bridge between the α‐helix of γ and subunit α did not impair enzyme activity. Molecular dynamics simulations revealed the possibility of a ‘functional unwinding’ of the α‐helix to form a swivel joint. Furthermore, they suggested a firm clamping of that part of γ even without the engineered cross‐link, i.e. in the wild‐type enzyme. Here, we rechecked the rotational mobility of the C‐terminal portion of γ relative to (αβ)3. Non‐fluorescent, engineered F1 (αP280C/γA285C) was oxidized to form a (nonfluorescent) αγ heterodimer. In a second mutant, containing just the point mutation within α, all subunits were labelled with a fluorescent dye. Following disassembly and reassembly of the combined preparations and cystine reduction, the enzyme was exposed to ATP or 5′‐adenylyl‐imidodiphosphate (AMP‐PNP). After reoxidation, we found fluorescent αγ dimers in all cases in accordance with rotary motion of the entire γ subunit under these conditions. Molecular dynamics simulations covering a time range of nanoseconds therefore do not necessarily account for motional freedom in microseconds. The rotation of γ within hours is compatible with the spectroscopically detected blockade of rotation in the AMP‐PNP‐inhibited enzyme in the time‐range of seconds.