Many active processes in cells are based on the function of molecular motors, which convert chemical (free) energy into work. These molecular motors provide realizations of nanometer-scaled thermodynamic machines and can thereby act as test cases for the recently developed stochastic thermodynamics that applies to such small isothermal systems. The paradigmatic system of this type is a molecular motor working against an external load force or torque, while provided with a given concentration of its fuel (such as ATP). Key questions for understanding the energetics of these motors are the efficiency and reversibility of that energy conversion. In this context, the rotary motor F₁-ATPase has played an important role due to its reversibility. Based on single-molecule observations, the possibility of nearly 100% efficiency has been suggested.

We present a chemomechanical network model of F₁-ATPase that provides a quantitative description of the rotary motor dynamics driven by ATP hydrolysis as well as ATP synthesis caused by forced reverse rotation. The network model exhibits high reversibility, such that the ATP synthesis cycle corresponds to the reversal of ATP-driven motor cycle. However, our quantitative analysis indicates that torque-induced mechanical slip without chemomechanical coupling occurs under high external torque and reduces the maximal efficiency of the free energy conversion from ATP hydrolysis into mechanical work to 40-80% below the optimal efficiency. Heat irreversibly dissipates not only through the viscous friction of the probe, but also directly from the motor due to torque-induced mechanical slip. Such irreversible heat dissipation is a crucial limitation for achieving a 100% free-energy transduction efficiency with biological nanomachines, since biomolecules are easily deformed by external torque. In such imperfect chemomechanical coupling motors, the maximum transduction efficiency is governed by a trade-off between a reduction in heat dissipation through the viscous load and an increase in heat caused by the mechanical slip with increasing external force. This work provides not only crucial insights into understanding the energetics of F₁-ATPase but also useful information on de novo design of artificial nanomachine with high free-energy transduction efficiency.

• Research article
  • Tomonari Sumi, Stefan Klumpp, Is F₁-ATPase a rotary motor with nearly 100% efficiency? Quantitative
    analysis of chemomechanical coupling and mechanical slip, Nano Letters 19, 3370 (2019).
  • DOI: https://doi.org/10.1021/acs.nanolett.9b01181
• Theoretical Physical Chemistry Lab