Fast state detection in F₁-ATPase rotation enhanced by theory of mixed states and external torque

Abstract

During brief 120° transitions between long catalytic dwells, single F₁-ATPase molecules exhibit angular jumps that vary with rotation angles. Using the angular jump profile enables the detection of fast states in the mechano-chemical scheme of the enzyme, states that are difficult to capture from single-molecule trajectories due to the fluctuations of the imaging nanoprobe. In a previous work, a short-lived, three occupancy state was postulated from a multi-state, probabilistic theory to explain the mean angular jump profile. An assumption in the theory was that the 'mixing' of chemical states is negligible during jumps. In a mixing event, two subsequent angular positions recorded by the imaging apparatus belong to two different chemical states of the motor enzyme due to fast reactions within a recording frame. In this paper, we provide an enhanced method for the detection of fast states. On one hand, we show using Langevin simulations that state mixing leads to faster mean angular jump, shifting up the profile. Consequently, the improved method provides a correction to the angular position and lifetime of the postulated three-occupancy metastable state. On the other hand, we show that when F₁-ATPase is subject to torques opposing rotation in hydrolysis direction, the torques shift down the dwell angles without affecting the angle-dependent reaction rates. The torques improve detection capability for the fast state by increasing dwell times which is made evident by the flattening of the mean angular jump profile within 40°–60° from the catalytic dwell. In the three-occupancy state release of ADP occurs in concert with the binding of ATP to a different site in the F₁-ATPase. Similarly, in the full ATP synthase when torques are created by the proton gradient in the F₀ region, the release of the product ATP is presumably accelerated by the binding of ADP to a different site in the F₁ domain.

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