Elasticity, friction, and pathway of γ-subunit rotation in F _o F ₁ -ATP synthase

Abstract

We combine molecular simulations and mechanical modeling to explore the mechanism of energy conversion in the coupled rotary motors of F o F 1 -ATP synthase. A torsional viscoelastic model with frictional dissipation quantitatively reproduces the dynamics and energetics seen in atomistic molecular dynamics simulations of torquedriven γ-subunit rotation in the F 1 -ATPase rotary motor. The torsional elastic coefficients determined from the simulations agree with results from independent single-molecule experiments probing different segments of the γ-subunit, which resolves a long-lasting controversy. At steady rotational speeds of ∼1 kHz corresponding to experimental turnover, the calculated frictional dissipation of less than k B T per rotation is consistent with the high thermodynamic efficiency of the fully reversible motor. Without load, the maximum rotational speed during transitions between dwells is reached at ∼1 MHz. Energetic constraints dictate a unique pathway for the coupled rotations of the F o and F 1 rotary motors in ATP synthase, and explain the need for the finer stepping of the F 1 motor in the mammalian system, as seen in recent experiments. Compensating for incommensurate eightfold and threefold rotational symmetries in F o and F 1 , respectively, a significant fraction of the external mechanical work is transiently stored as elastic energy in the γ-subunit. The general framework developed here should be applicable to other molecular machines.bioenergetics | molecular motor | mechanochemical coupling F o F 1 -ATP synthase is essential for life. From bacteria to human, this protein synthesizes ATP from ADP and inorganic phosphate P i in its F 1 domain, powered by an electrochemical proton gradient that drives the rotation of its membrane-embedded F o domain (1-5). Its two rotary motors, F 1 and F o , are coupled through the γ-subunit forming their central shaft (2). ATP synthase is a fully reversible motor, in which the rotational direction switches according to different sources of energy (2, 6). In hydrolysis mode, the F 1 motor pumps protons against an electrochemical gradient across the membrane-embedded F o part, converting ATP to ADP and P i (7,8).F 1 has a symmetric ring structure composed of three αβ-subunits with the asymmetric γ-subunit sitting inside the ring (9, 10). Each αβ-subunit has a catalytic site located at the αβ-domain interface. The F 1 ring has a pseudothreefold symmetry with the three αβ-subunits taking three different conformations, E (empty), TP (ATP-bound), and DP (ADP bound) (9-11). The F o part is composed of a c ring and an a subunit (3, 12). Driven by protons passing through the interface of the c ring and the a subunit, the c ring rotates together with the γ-subunit (rotor) relative to the a subunit, which is connected to the F 1 ring through the peripheral stalk of the b subunit (stator) (12). Interestingly, in nature, one finds a large variation in the number of subunits in the c ring. In animal mitochondria, one finds c 8 rings, requiring a minimal number of e...

Load-dependent destabilization of the γ-rotor shaft in F O F 1 ATP synthase revealed by hydrogen/deuterium-exchange mass spectrometry

“…Of all the explanations considered above, scenario iv is the most plausible one. It attributes the observed destabilization to rotational resistance, consistent with crystallographically detected contacts between γ and α 3 β 3 (43,44), and with nonspecific friction seen in MD simulations (15).…”

“…Molecular dynamics (MD) simulations (14)(15)(16) can help interpret such data in a dynamic context. However, there is scant information on how the conformation of F o F 1 is affected by internal and external forces while working under physiological conditions, where ATP/ADP interconversion is coupled with transmembrane proton transport in the presence of proton-motive force (PMF).…”

“…iv) Rotational resistance in the apical bearing: The movement of closely spaced protein surfaces relative to each other is accompanied by side-chain clashes and transient binding/ dissociation events (19), likely giving rise to intermittent motion in a stick-slip regime (18). MD simulations indicate that such friction-like effects are also encountered during rotation of the γ C-terminal helix within the α 3 β 3 apical bearing (15). The simulated γ rotation in the study by Okazaki and Hummer (15) is orders of magnitude faster than in our experiments, thereby complicating comparisons of the data obtained.…”

“…5A; it includes the sleeve surrounding the extreme γ C terminus (8), as well as adjacent elements, such as the β-catch loops (42,43). Rotation will be accompanied by steric clashes as γ side chains are forced past the side chains of α 3 β 3 within the tight annular gap of the bearing (15). Intermolecular H-bonds and other noncovalent γ···α 3 β 3 linkages (43, 44) may amplify these resistive effects.…”

Biophysical comparison of ATP synthesis mechanisms shows a kinetic advantage for the rotary process

“…Previous modeling studies of the F-ATPase have addressed structural and mechanistic questions about the rotary mechanism (e.g., refs. [11][12][13][14][15][16][17][18][19][20], but not the metaissue of the mechanism itself compared with alternatives.…”