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Reconstruction of the Bacterial Flagellar Motor's Energy Landscape, Viscous Load, and Torque Generation Across Diffusion Regimes

N. J. López-Alamilla1,*, A. L. Nord2, F. Pedaci2, J. Palmeri1, and N.-O. Walliser1,†

  • *Contact author: n.jared.lopezalamilla@gmail.com
  • †Contact author: nils-ole.walliser@umontpellier.fr
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PRX Life 4, 043003 – Published 23 October, 2026

DOI: https://doi.org/10.1103/55kj-nm3g

Abstract

The bacterial flagellar motor (BFM) converts transmembrane ion flux into directed mechanical rotation, driving bacterial motility. Despite extensive study, the frictional forces and energetics governing its torque generation remain poorly understood. Here we combine single-molecule rotation measurements with stochastic thermodynamics to quantitatively estimate its effective torque, viscous drag, and activation energy barriers. We present three complementary methods based on solutions to the Smoluchowski equation for overdamped diffusion in a tilted periodic potential, which use as input the steady-state angular velocity and rotational diffusion data from individual Escherichia coli motors spanning different dynamical regimes. Crucially, these three methods require neither active external torque control, nor prior knowledge of the system's viscous drag or the motor's torque output. The first method assumes as input a model-dependent sinusoidal effective potential (single Fourier mode), albeit with unknown periodicity, yielding closed-form results in the low- and high-tilt limits, whereas the last two methods use a full Fourier-based reconstruction to output the now model-independent effective potential landscape. These approaches yield consistent estimates of the potential periodicity (≈26-fold symmetry), energy barrier height (≈2–4 kBT), and internal friction coefficient (≈0.1 pNnms/rad2). These findings suggest that the reconstructed effective energy landscape is dominated by interactions associated with the LP-ring bearing. Our results reveal that the BFM's torque-velocity relationship deviates significantly from the linear approximation near the critical tilt, where angular diffusion is maximized. More broadly, our framework provides a coherent strategy for reconstructing nanoscale energy landscapes from single-molecule data and is generalizable to other stepping molecular motors operating in cyclic conditions.

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PRX Life 4, 043003– Published 23 October, 2026
  • Received 17 December 2025
  • Accepted 8 September 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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