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...

Swimming speeds and flagellar rotation rates of individual free-swimming Vibrio alginolyticus cells were measured simultaneously by laser dark-field microscopy at 25, 30, and 35 degrees C. A roughly linear relation between swimming speed and flagellar rotation rate was observed. The ratio of swimming speed to flagellar rotation rate was 0.113 microns, which indicated that a cell progressed by 7% of pitch of flagellar helix during one flagellar rotation. At each temperature, however, swimming speed had a tendency to saturate at high flagellar rotation rate. That is, the cell with a faster-rotating flagellum did not always swim faster. To analyze the bacterial motion, we proposed a model in which the torque characteristics of the flagellar motor were considered. The model could be analytically solved, and it qualitatively explained the experimental results. The discrepancy between the experimental and the calculated ratios of swimming speed to flagellar rotation rate was about 20%. The apparent saturation in swimming speed was considered to be caused by shorter flagella that rotated faster but produced less propelling force.

Molecular motors drive mechanical motions utilizing the free energy liberated from chemical reactions such as ATP hydrolysis. Although it is essential to know the efficiency of this free energy transduction, it has been a challenge due to the system's microscopic scale. Here, we evaluate the single-molecule energetics of a rotary molecular motor, F1-ATPase, by applying a recently derived nonequilibrium equality together with an electrorotation method. We show that the sum of the heat flow through the probe's rotational degree of freedom and the work against an external load is almost equal to the free energy change per a single ATP hydrolysis under various conditions. This implies that F1-ATPase works at an efficiency of nearly 100% in a thermally fluctuating environment.

Perineural invasion is an important prognostic factor in pancreatic cancer, increasing as the cancer becomes undifferentiated. Even if there are no cancer cells at the margin of the pancreas at the time of surgery, the cancer cells may spread further to the noncancerous pancreas or retroperitoneum. Sufficient dissection of the neural plexus or intraoperative radiation may be required.