Thermodynamic efficiency and mechanochemical coupling of F ₁ -ATPase

Abstract

F 1 -ATPase is a nanosized biological energy transducer working as part of F o F 1 -ATP synthase. Its rotary machinery transduces energy between chemical free energy and mechanical work and plays a central role in the cellular energy transduction by synthesizing most ATP in virtually all organisms. However, information about its energetics is limited compared to that of the reaction scheme. Actually, fundamental questions such as how efficiently F 1 -ATPase transduces free energy remain unanswered. Here, we demonstrated reversible rotations of isolated F 1 -ATPase in discrete 120°s teps by precisely controlling both the external torque and the chemical potential of ATP hydrolysis as a model system of F o F 1 -ATP synthase. We found that the maximum work performed by F 1 -ATPase per 120°step is nearly equal to the thermodynamical maximum work that can be extracted from a single ATP hydrolysis under a broad range of conditions. Our results suggested a 100% free-energy transduction efficiency and a tight mechanochemical coupling of F 1 -ATPase.electrorotation | molecular motor | nonequilibrium physics A TP synthase F o F 1 plays a central role in the cellular energy transduction by synthesizing most ATP in virtually all organisms, including bacteria, chloroplasts, and mitochondria (1, 2). This enzyme consists of two motors: F o -motor, which is embedded in the membrane, and F 1 -motor (F 1 -ATPase), which protrudes from the membrane (Fig. 1A). F 1 -motor is a reversible motor/generator. As part of F o F 1 -ATP synthase, it acts as a generator. Proton flux through the F o -motor along the transmembrane electrochemical potential drives rotation of the F o -motor's c-ring. Because the rotor subunit (γ-shaft) of F 1 -motor is coupled with the c-ring (3-5), c-ring rotation forces γ-shaft to rotate. Under these conditions, F 1 -motor synthesizes ATP from ADP and phosphate (P i ) (6-8). On the other hand, when isolated, F 1 -motor works as a motor, hydrolyzing ATP to ADP and P i and rotating the γ-shaft counter to the direction it takes during ATP-synthetic rotations (9-12) (Fig. 1B). An ATP hydrolysis makes a 120°rotation of the γ-shaft.Despite the critical role played by F 1 -motor as a mechanochemical energy transducer, information about its energetics remains limited compared to that of the reaction scheme (13-15). In fact, fundamental questions remain unanswered; these questions include how efficiently F 1 -motor can convert energy between the chemical free energy change of an ATP hydrolysis (Δμ) and mechanical work. Previous studies (12, 16) suggested that F 1 -motor works at a high efficiency in the sense that the work against viscous drag during a rotational step in the absence of external torque is nearly equal to Δμ. However, this efficiency should be distinguished from the free-energy transduction efficiency because the work against viscous drag finally dissipates as heat to the surrounding environment and cannot be fully utilized further (17). To evaluate the efficiency of the mechanochemical free-energy trans...

Simple mechanism whereby the F 1 -ATPase motor rotates with near-perfect chemomechanical energy conversion

“…1C are noticeable. First, the magnitude of torque calculated from (θ B − θ TC ) is ∼50 pN nm, on average, throughout six revolutions, consistent with the reported F 1 torque obtained using a conservative force, the same as in this study (10,12). Second, torque oscillates three times during 120°rotation and each oscillation seems to be composed of a jump, followed by a gradual descent (Fig.…”

“…The chemomechanical energy conversion efficiency of F 1 is close to 100% under various ΔG ATP conditions (12). The torque profile found here explains how F 1 achieves this remarkable task.…”

“…Among them, an early study that used counter torque reported the torque was ∼50 pN nm/rad (10), indicating that efficiency in chemomechanical energy conversion by F 1 from chemical energy of ATP hydrolysis (ΔG ATP ) to mechanical work of rotation reaches almost 100%. A recent study, also using counter torque, revealed that this remarkable efficiency holds in a broad range of ΔG ATP (12). However, the underlying mechanism for this highly efficient energy conversion remains unknown because of an elusive relationship between the catalytic scheme and the energetics.…”

“…The torque of this motor has been estimated with various methods (8)(9)(10)(11)(12)(13). Among them, an early study that used counter torque reported the torque was ∼50 pN nm/rad (10), indicating that efficiency in chemomechanical energy conversion by F 1 from chemical energy of ATP hydrolysis (ΔG ATP ) to mechanical work of rotation reaches almost 100%.…”

Enhanced Diffusion of Molecular Motors in the Presence of Adenosine Triphosphate and External Force

“…9, which were obtained by Toyabe et al. 13 Parameters other than K, a, and k are determined as follows. We have l = 2π/3 from the threefold symmetry in the structure of In determining K, a, and k, note that the forward transition rate w + n in the present model represents the following series of events in F 1 -ATPase: 31 (i) the binding of ATP to the motor accompanied by the release of ADP from the motor, (ii) the hydrolysis of ATP catalyzed by the motor, and (iii) the release of Pi from the motor.…”