Startseite Rotational dynamics of ATP synthase: mechanical constraints and energy dissipative channels
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Rotational dynamics of ATP synthase: mechanical constraints and energy dissipative channels

  • Islam K. Matar , Peyman Fahimi EMAIL logo und Chérif F. Matta ORCID logo EMAIL logo
Veröffentlicht/Copyright: 15. Juli 2025
Pure and Applied Chemistry
Aus der Zeitschrift Pure and Applied Chemistry

Abstract

The proton motive force (PMF) across the inner mitochondrial membrane delivers approximately 0.2 eV of energy per proton, powering the FoF1-ATP synthase molecular motor. Here, we provide a detailed accounting of how this energy is utilized: Approximately 75–83 % is transduced into the chemical free energy of ATP synthesis, while the remaining 17–25 % is dissipated through internal friction, viscous drag, proton leakage, electroviscous effects, elastic deformations, and information-theoretic costs. Each dissipation channel is quantitatively evaluated, revealing that internal friction in the F1 motor is the dominant loss mechanism. In this work, we did not account for the possible energy contribution due to the intrinsic electrostatic potential of the enzyme itself. In addition to this energy bookkeeping, we also examine the quantum mechanical constraints on the Fo unit’s rotation. We find that, as can be expected, the energy spacing between quantized rotational states is several orders of magnitude smaller than thermal energies at physiological temperature, and that the tunneling probability through rotational barriers is practically zero. Furthermore, the biological rotation speed (∼100–650 revolutions per second (rps)) is between one and three orders of magnitude below the quantum limit implied by quantization of angular momentum of the c-ring (which would have been ca. 13,000 to 62,000 rps (depending on the size of the c-ring (17–8 subunits, respectively)) in the first rotational energy level of the c-ring). Nevertheless, experimental estimates of the rotation rates in isolated c-rings suggest rates in the vicinity of 43,000 rps, right within our theoretical quantum estimates. However, ATP synthase as a whole operates firmly within the classical regime, despite its nanoscale dimensions, which highlights its evolutionary optimization for robust and efficient energy conversion at the quantum–classical boundary. This is the result of the rotatory coupling between the Fo and the much slower F1 unit. ATP synthase’s purely classical behavior showcases a remarkable evolutionary optimization of one of life’s most essential rotary motor engineered so as to thrive far from the quantum limit, securing its function against the uncertainties of the quantum world. As Schrödinger stated in What is Life? (1944): “The submicroscopic world is full of fluctuations. But in large aggregates of atoms, the law of large numbers ensures that these fluctuations become negligible” a prediction directly confirmed here in the context of the rotational stability of the Fo unit.

Keywords: angular momentum quantization; ATP synthase; molecular motors; quantum biology; quantum mechanical tunneling in biology; quantum science and technology; rotational dynamics
Corresponding authors: Peyman Fahimi, Department of Mathematics and Statistics, Dalhousie University, Halifax, NS, B3H 4R2, Canada, e-mail: ; and Chérif F. Matta, Department of Chemistry and Physics, Mount Saint Vincent University, Halifax, NS, B3M 2J6, Canada; and Department of Chemistry, Saint Mary’s University, Halifax, NS, B3H 3C3, Canada, e-mail:
Special Issue note: A collection of invited papers to celebrate the UN’s proclamation of 2025 as the International Year of Quantum Science and Technology.

  1. Research ethics: Not applicable.

  2. Informed consent: Not applicable.

  3. Author contributions: All authors have accepted responsibility for the entire content of this manuscript and approved its submission.

  4. Use of Large Language Models, AI and Machine Learning Tools: ChatGPT has been used to condense and rephrase certain passages and to assist in the generation of Figure 2.

  5. Conflict of interest: The authors state no conflict of interest.

  6. Research funding: The authors are grateful to the Natural Sciences and Engineering Council of Canada (NSERC), the Canadian Foundation for Innovation (CFI), Saint Mary’s University, Dalhousie University, Mount Saint Vincent University, Digital Research Alliance of Canada, and Research Nova Scotia for their financial support and resources.

  7. Data availability: Not applicable.

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Received: 2025-04-10
Accepted: 2025-06-24
Published Online: 2025-07-15

© 2025 IUPAC & De Gruyter

https://doi.org/10.1515/pac-2025-0477
Schlagwörter für diesen Artikel
angular momentum quantization; ATP synthase; molecular motors; quantum biology; quantum mechanical tunneling in biology; quantum science and technology; rotational dynamics
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