Torque, chemistry and efficiency in molecular motors: a study of the rotary–chemical coupling in F₁-ATPase

Abstract

Detailed understanding of the action of biological molecular machines must overcome the challenge of gaining a clear knowledge of the corresponding free-energy landscape. An example for this is the elucidation of the nature of converting chemical energy to torque and work in the rotary molecular motor of F1-ATPase. A major part of the challenge involves understanding the rotary–chemical coupling from a non-phenomenological structure/energy description. Here we focused on using a coarse-grained model of F1-ATPase to generate a structure-based free-energy landscape of the rotary–chemical process of the whole system. In particular, we concentrated on exploring the possible impact of the position of the catalytic dwell on the efficiency and torque generation of the molecular machine. It was found that the experimentally observed torque can be reproduced with landscapes that have different positions for the catalytic dwell on the rotary–chemical surface. Thus, although the catalysis is undeniably required for torque generation, the experimentally observed position of the catalytic dwell at 80° might not have a clear advantage for the force generation by F1-ATPase. This further implies that the rotary–chemical couplings in these biological motors are quite robust and their efficiencies do not depend explicitly on the position of the catalytic dwells. Rather, the specific positioning of the dwells with respect to the rotational angle is a characteristic arising due to the structural construct of the molecular machine and might not bear any clear connection to the thermodynamic efficiency for the system.

Theory for rates, equilibrium constants, and Brønsted slopes in F 1 -ATPase single molecule imaging experiments

“…Such model for atom transfer (H + and CH + 3 ) transfer chemical reactions based on the conservation of total bond order has been previously used to describe chemical reactions, and lead to equations similar to those for ATP (16). Atomistic-level treatment permits the detailed exploration of ligand molecule transfer along the path into the pocket (48), and the free energy profile of subunit conformational space coupled to the rotor angle (26,43), and serve to evaluate and correct the model on which Eqs. 6, 13, and 9 or their bond energy-bond order analogs (16) are based.…”

“…Obtaining α via stalling experiments has an advantage over obtaining it via mutations because the latter may also affect λ. A more detailed ab initio theory would also incorporate the structural coupling between the α 3 β 3 ring unit and the rotor, e.g., akin to recent simulations of the electrostatic free energy profile (42,43).…”

“…. .. We note that a mechanism that couples the α 3 β 3 ring to the rotor shaft, including the effective spring constant, has been attributed to an electrostatic energy landscape from simulations (42,43).…”

Simulating the dynamics of the mechanochemical cycle of myosin-V

“…The corresponding energetics were used to generate the free-energy landscape of the motor using a structure-based coarse-grained (CG) model (27,28) that has been used to simulate various biological machines, such as F O F 1 -ATP synthase (29)(30)(31) and other systems (reviewed in ref. 27).…”

Brønsted slopes based on single-molecule imaging data help to unveil the chemically coupled rotation in F 1 -ATPase

“…Here, at least in principle, one can explore the rotary-chemical coupling and its relationships to the dwells from functionally relevant free-energy surfaces calculated from the 3D structure (Fig. 1B) (12)(13)(14). Such an approach can reveal the underlying physical basis of the coupling and also lends theoretical predictions directly comparable to real-time experimental observations.…”