Dissecting the role of the γ-subunit in the rotary–chemical coupling and torque generation of F 1 -ATPase

A theoretical model of elastically coupled reactions is proposed for single molecule imaging and rotor manipulation experiments on F 1 -ATPase. Stalling experiments are considered in which rates of individual ligand binding, ligand release, and chemical reaction steps have an exponential dependence on rotor angle. These data are treated in terms of the effect of thermodynamic driving forces on reaction rates, and lead to equations relating rate constants and free energies to the stalling angle. These relations, in turn, are modeled using a formalism originally developed to treat electron and other transfer reactions. During stalling the free energy profile of the enzymatic steps is altered by a work term due to elastic structural twisting. Using biochemical and single molecule data, the dependence of the rate constant and equilibrium constant on the stall angle, as well as the Børnsted slope are predicted and compared with experiment. Reasonable agreement is found with stalling experiments for ATP and GTP binding. The model can be applied to other torque-generating steps of reversible ligand binding, such as ADP and P i release, when sufficient data become available. S ingle molecule imaging directly demonstrated a stepping rotation in F 1 -ATPase (1) that was resolved into ∼ 40°and ∼ 80°s ubsteps (initially reported as ∼ 30°and ∼ 90°; cf. refs. 2 and 3), and much information has been extracted by elaborate techniques at the single molecule level (3-6). Complementing experimental tools such as X-ray spectroscopy (7) and ensemble biochemical methods (8), single molecule experiments reveal key details of the coupling between enzymatic processes and rotation (9-12). A detailed picture of highly coordinated substeps has emerged in which the binding of solution ATP to an empty subunit and release of hydrolyzed ADP from the clockwise neighbor (viewed from the rotor side) occur in concert during the ∼ 80°rotation step (13). As depicted in Fig. 1 and Table 1, the subsequent ∼ 40°r otation is coordinated with the hydrolysis of ATP in the third subunit and the release of P i from the subunit that just released ADP (13).Recent stalling (6,13,14) and controlled rotation (15) experiments provide additional insight into the dynamics of the coupling between the rotation of the central shaft and the reaction steps in the stator ring subunits. These experiments yielded the rate constants of various steps, binding and release of ligands, and hydrolysis/synthesis reaction, as a function of the stalled rotor angle θ. The rates show an exponential dependence on θ over a wide range, such as a range of 80°for ATP binding and 40°for hydrolysis. Free energy profiles for the initial and final dwell angles at a specific 40°or 80°step are given in Fig. 2. For intermediate stalling angles, the profile is intermediate between these two limits.In stalling experiments (14) the freely rotating shaft of the ATPase is stalled by magnetic tweezers upon reaching a dwell angle. Rotation experiments have resolved two dwells: the binding dwell (before...

Section: Significancementioning

confidence: 90%

Section: Concluding Discussion and Outlookmentioning

confidence: 99%

Theory for rates, equilibrium constants, and Brønsted slopes in F ₁ -ATPase single molecule imaging experiments

Volkan-Kacso

Marcus

2015

“…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).…”

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confidence: 99%

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

Vahidi

Dunn

et al. 2016

FoF1 is a membrane-bound molecular motor that uses proton-motive force (PMF) to drive the synthesis of ATP from ADP and Pi. Reverse operation generates PMF via ATP hydrolysis. Catalysis in either direction involves rotation of the γε shaft that connects the α3β3 head and the membrane-anchored cn ring. X-ray crystallography and other techniques have provided insights into the structure and function of FoF1 subcomplexes. However, interrogating the conformational dynamics of intact membrane-bound FoF1 during rotational catalysis has proven to be difficult. Here, we use hydrogen/deuterium exchange mass spectrometry to probe the inner workings of FoF1 in its natural membrane-bound state. A pronounced destabilization of the γ C-terminal helix during hydrolysis-driven rotation was observed. This behavior is attributed to torsional stress in γ, arising from γ⋅⋅⋅α3β3 interactions that cause resistance during γ rotation within the apical bearing. Intriguingly, we find that destabilization of γ occurs only when FoF1 operates against a PMF-induced torque; the effect disappears when PMF is eliminated by an uncoupler. This behavior resembles the properties of automotive engines, where bearings inflict greater forces on the crankshaft when operated under load than during idling.

“…Key open questions concern the detailed rotational pathway of the two coupled rotary motors, the impact of the rotational symmetry mismatch between the F o and F 1 motors on the motor mechanics, the resulting need for transient energy storage, the role of frictional dissipation, and the molecular elements associated with stepping of the F 1 motor (18)(19)(20)(21)(22)(23)(24). Here we explore these questions by building a dissipative mechanical model of the F 1 motor on the basis of atomistic molecular dynamics (MD) simulations.…”

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confidence: 99%

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

Okazaki

Hummer

2015

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...