Multi-State Theory of Velocities and Torques in Transitions of Single-Molecule F1-ATPase Rotation

Abstract

Single-molecule spectroscopies revealed some intricate features of the stepping rotation in single F1-ATPase molecules in which a substep have microsecond transition dynamics yet waiting times vary from milliseconds to seconds. Understanding how this complexity leads to functionally useful behavior, requires quantitative predictive modelling. Recently, we proposed method to analyzing fast (10µs timestep) rotation trajectories in F1-ATPase using the distribution rotational velocities in the transitions during the steps between subsequent catalytic dwells. A multi-state theory is used that takes into account a visco-elastic fluctuation of the imaging probe. Using the method we detect the presence of a fast substep previously not detectable. We show that agreement between theory and experiment can be achieved at all angles by assuming a fourth state in the coupling scheme, a state with an ∼10 µs lifetime. This comparison reveals that an 80O substep of the "concerted" ATP binding and ADP release involves an intermediate state reminiscent of a 3-occupancy structure. Its lifetime is about six orders of magnitude smaller than the lifetime for "spontaneous" ADP release from a singly occupied state. The discovery of the metastable state prompted further development of the theory of ATP transfer in F1-ATPase, to now include an intermediate state. We provide relationship between the spring torsional stiffness of the enzyme (∼ 60 pN.nm) estimated from fluctuations and the spring constant (∼ 20 pN.nm) that couples the free energy with mechanical rotation angle. Furthermore, the multi-state model is set up to investigate rotation under opposing torque. Opposing torques offer a way to increase the detection sensitivity for metastable state as dwells are made longer in the presence of load.

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