Recover a long-missing thermodynamic limit from experimental trajectories of F1-ATPase molecular motor

In the field of molecular motors, a general thermodynamic limit is widely used in theories but long missing in experiments. By this limit, a motor's forward-to-backward stepping ratio obeys a distinct full-step scaling with an opposing force, and is further related to a thermodynamic force that may inform the motor's stall force and energy efficiency from low-force experiments or even force-independent optical tracking experiments. This limit is now recovered directly from experimental trajectories of F₁-ATPase motor - in a strict 'double-blind' test with the thermodynamic force and the stepping ratio extracted independently from the trajectories by an improved statistical method and a rigorous thermodynamic analysis based on Jarzynski equality. This study thus removes a long-standing controversy in the field of molecular motors, and significantly reduces the difficulty of stall force measurement. Notably, this study also enables experimental access to the elusive stepping ratio, which is essentially a ratio of cycle fluxes and hence difficult to measure so far. Finally, the Jarzynski equality-based thermodynamic analysis is comprehensive, providing a unified conceptual framework to analyze evolutionary optimality of biological molecular motors and guide development of artificial molecular motors.