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  • Featured in Physics
  • Open Access

Thermodynamic Signatures of Sensing and Amplification by Periodically Driven Hair-Cell Bundles

Yanathip Thipmaungprom1,2, Laila Saliekh3,4, Rodrigo Alonso5, Édgar Roldán3,*, Florian Berger1,2,†, and Roman Belousov6,‡

  • *Contact author: edgar@ictp.it
  • †Contact author: f.m.berger@uu.nl
  • ‡Contact author: roman.belousov@embl.de

PRX Life 4, 013039 – Published 31 March, 2026

DOI: https://doi.org/10.1103/6wcm-z333

Abstract

Hair cells actively drive oscillations of their mechanosensitive organelles—the hair bundles that enable hearing and balance sensing in vertebrates. Why and how some hair cells expend energy by sustaining this oscillatory motion in order to fulfill their function as sensors and amplifiers remains unknown. Here, we develop a stochastic thermodynamic theory to describe flows of mechanical energy in a periodically driven hair bundle. Our analysis of thermodynamic fluxes associated with hair-bundle motion and external sinusoidal stimulus reveals that these organelles function as thermodynamic work-to-work machines under different operational modes. One mode allows the cell to harvest energy of the external signal, whereas another channels the power supplied by the cell into the signal. These two regimes might represent thermodynamic signatures of signal sensing and amplification, respectively, which we further connect to the receptor currents through ion channels controlled by the hair bundles. In addition to energy harvesting and work transduction, our model also substantiates the capability of hair cells to operate as heaters and, at the expense of external driving, as active feedback refrigerators. We quantify the performance and robustness of the mechanical work-to-work conversion by hair bundles, whose thermodynamic efficiency in some conditions exceeds 80% of the applied power.

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Research News

How Hair Cells in the Ear Actively Respond to Sound

Published 31 March, 2026

Our ability to hear relies on tiny “hair bundles” in the inner ear. A new thermodynamical model offers an explanation for the different ways that bundles oscillate.

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References (87)

  1. J. Howard, W. M. Roberts, and A. J. Hudspeth, Mechanoelectrical transduction by hair cells, Annu. Rev. Biophys. Biophys. Chem. 17, 99 (1988).
  2. R. Jacobs and A. Hudspeth, Ultrastructural correlates of mechanoelectrical transduction in hair cells of the bullfrog's internal ear, Cold Spring Harbor Symp. Quant. Biol. 55, 547 (1990).
  3. T. Reichenbach and A. J. Hudspeth, The physics of hearing: Fluid mechanics and the active process of the inner ear, Rep. Prog. Phys. 77, 076601 (2014).
  4. P. Martin and A. Hudspeth, Mechanical frequency tuning by sensory hair cells, the receptors and amplifiers of the inner ear, Annu. Rev. Condens. Matter Phys. 12, 29 (2021).
  5. É. Roldán, J. Barral, P. Martin, J. M. R. Parrondo, and F. Jülicher, Quantifying entropy production in active fluctuations of the hair-cell bundle from time irreversibility and uncertainty relations, New J. Phys. 23, 083013 (2021).
  6. Y. Choe, M. O. Magnasco, and A. J. Hudspeth, A model for amplification of hair-bundle motion by cyclical binding of Ca2+ to mechanoelectrical-transduction channels, Proc. Natl. Acad. Sci. USA 95, 15321 (1998).
  7. S. Camalet, T. Duke, F. Jülicher, and J. Prost, Auditory sensitivity provided by self-tuned critical oscillations of hair cells, Proc. Natl. Acad. Sci. 97, 3183 (2000).
  8. P. Martin, D. Bozovic, Y. Choe, and A. J. Hudspeth, Spontaneous oscillation by hair bundles of the bullfrog's sacculus, J. Neurosci. 23, 4533 (2003).
  9. A. Vilfan and T. Duke, Two adaptation processes in auditory hair cells together can provide an active amplifier, Biophys. J. 85, 191 (2003).
  10. B. Nadrowski, P. Martin, and F. Jülicher, Active hair-bundle motility harnesses noise to operate near an optimum of mechanosensitivity, Proc. Natl. Acad. Sci. USA 101, 12195 (2004).
  11. J.-Y. Tinevez, F. Jülicher, and P. Martin, Unifying the various incarnations of active hair-bundle motility by the vertebrate hair cell, Biophys. J. 93, 4053 (2007).
  12. M. Gelfand, O. Piro, M. O. Magnasco, and A. J. Hudspeth, Interactions between hair cells shape spontaneous otoacoustic emissions in a model of the tokay gecko's cochlea, PLoS ONE 5, e11116 (2010).
  13. J. Barral, K. Dierkes, B. Lindner, F. Jülicher, and P. Martin, Coupling a sensory hair-cell bundle to cyber clones enhances nonlinear amplification, Proc. Natl. Acad. Sci. 107, 8079 (2010).
  14. D. Ó. Maoiléidigh, E. M. Nicola, and A. J. Hudspeth, The diverse effects of mechanical loading on active hair bundles, Proc. Natl. Acad. Sci. USA 109, 1943 (2012).
  15. V. Bormuth, J. Barral, J.-F. Joanny, F. Jülicher, and P. Martin, Transduction channels' gating can control friction on vibrating hair-cell bundles in the ear, Proc. Natl. Acad. Sci. USA 111, 7185 (2014).
  16. V. Bormuth, J. Barral, J.-F. Joanny, F. Jülicher, and P. Martin, Hair-bundle friction from transduction channels' gating forces, in AIP Conference Proceedings (AIP Publishing LLC, Melville, NY, 2015).
  17. J. Barral, F. Jülicher, and P. Martin, Friction from transduction channels' gating affects spontaneous hair-bundle oscillations, Biophys. J. 114, 425 (2018).
  18. R. Belousov, F. Berger, and A. J. Hudspeth, Volterra-series approach to stochastic nonlinear dynamics: Linear response of the Van der Pol oscillator driven by white noise, Phys. Rev. E 102, 032209 (2020).
  19. B. Cao, H. Gu, and K. Ma, Complex dynamics of hair bundle of auditory nervous system (i): Spontaneous oscillations and two cases of steady states, Cognit. Neurodyn. 16, 917 (2022).
  20. B. Cao, H. Gu, and R. Wang, Complex dynamics of hair bundle of auditory nervous system (II): Forced oscillations related to two cases of steady state, Cognit. Neurodyn. 16, 1163 (2022).
  21. G. Tucci, É. Roldán, A. Gambassi, R. Belousov, F. Berger, R. Alonso, and A. Hudspeth, Modeling active non-Markovian oscillations, Phys. Rev. Lett. 129, 030603 (2022).
  22. J. M. Marcinik, M. A. Toderi, and D. Bozovic, Comparing parameter-reduction methods on a biophysical model of an auditory hair cell, Phys. Rev. Res. 6, 033121 (2024).
  23. J. Salvi, D. Ó Maoiléidigh, and A. Hudspeth, Identification of bifurcations from observations of noisy biological oscillators, Biophys. J. 111, 798 (2016).
  24. P. Martin and A. J. Hudspeth, Active hair-bundle movements can amplify a hair cell's response to oscillatory mechanical stimuli, Proc. Natl. Acad. Sci. USA 96, 14306 (1999).
  25. F. Berger and A. J. Hudspeth, Violation of the fluctuation response-relation from a linear model of hair bundle oscillations, bioRxiv (2022), DOI: https://doi.org/10.1101/2022.04.15.488459.
  26. M. P. Leighton and D. A. Sivak, Flow of energy and information in molecular machines, Annu. Rev. Phys. Chem. 76, 379 (2025).
  27. C.-Y. Hsieh, Dynamical Landauer principle: Quantifying information transmission by thermodynamics, Phys. Rev. Lett. 134, 050404 (2025).
  28. P. Chattopadhyay, A. Misra, T. Pandit, and G. Paul, Landauer principle and thermodynamics of computation, Rep. Prog. Phys. 88, 086001 (2025).
  29. J. Elliott, H. Shah, R. Belousov, G. Dey, and A. Erzberger, Repulsive particle interactions enable selective information processing at cellular interfaces, Phys. Rev. Lett. 135, 218403 (2025).
  30. I. Haranas, I. Gkigkitzis, K. Cobbett, and R. Gauthier, Landauer's principle of minimum energy might place limits on the detectability of gravitons of certain mass, Eur. J. Appl. Phys. 3, 66 (2021).
  31. J. M. R. Parrondo, J. M. Horowitz, and T. Sagawa, Thermodynamics of information, Nat. Phys. 11, 131 (2015).
  32. S. Ito and T. Sagawa, Maxwell's demon in biochemical signal transduction with feedback loop, Nat. Commun. 6, 7498 (2015).
  33. T. Munakata and M. L. Rosinberg, Entropy production and fluctuation theorems for Langevin processes under continuous non-Markovian feedback control, Phys. Rev. Lett. 112, 180601 (2014).
  34. A. Barato and U. Seifert, Unifying three perspectives on information processing in stochastic thermodynamics, Phys. Rev. Lett. 112, 090601 (2014).
  35. J. M. Horowitz and M. Esposito, Thermodynamics with continuous information flow, Phys. Rev. X 4, 031015 (2014).
  36. P. Sartori, L. Granger, C. F. Lee, and J. M. Horowitz, Thermodynamic costs of information processing in sensory adaptation, PLoS Comput. Biol. 10, e1003974 (2014).
  37. C. C. Govern and P. R. ten Wolde, Optimal resource allocation in cellular sensing systems, Proc. Natl. Acad. Sci. USA 111, 17486 (2014).
  38. G. Lan, P. Sartori, S. Neumann, V. Sourjik, and Y. Tu, The energy–speed–accuracy trade-off in sensory adaptation, Nat. Phys. 8, 422 (2012).
  39. T. Sagawa and M. Ueda, Generalized Jarzynski equality under nonequilibrium feedback control, Phys. Rev. Lett. 104, 090602 (2010).
  40. S. Laughlin, Energy as a constraint on the coding and processing of sensory information, Curr. Opin. Neurobiol. 11, 475 (2001).
  41. M. C. Parker and S. D. Walker, Information transfer and Landauer's principle, Opt. Commun. 229, 23 (2004).
  42. A. Datta, P. Pietzonka, and A. C. Barato, Second law for active heat engines, Phys. Rev. X 12, 031034 (2022).
  43. Y. Zhang and E. Fodor, Pulsating active matter, Phys. Rev. Lett. 131, 238302 (2023).
  44. L. K. Davis, K. Proesmans, and E. Fodor, Active matter under control: Insights from response theory, Phys. Rev. X 14, 011012 (2024).
  45. R. Garcia-Millan, J. Schüttler, M. E. Cates, and S. A. M. Loos, Optimal closed-loop control of active particles and a minimal information engine, Phys. Rev. Lett. 135, 088301 (2025).
  46. K. H. Kim and H. Qian, Fluctuation theorems for a molecular refrigerator, Phys. Rev. E 75, 022102 (2007).
  47. T. Sagawa and M. Ueda, Nonequilibrium thermodynamics of feedback control, Phys. Rev. E 85, 021104 (2012).
  48. M. L. Rosinberg, T. Munakata, and G. Tarjus, Stochastic thermodynamics of Langevin systems under time-delayed feedback control: Second-law-like inequalities, Phys. Rev. E 91, 042114 (2015).
  49. M. L. Rosinberg and J. M. Horowitz, Continuous information flow fluctuations, Europhys. Lett. 116, 10007 (2016).
  50. M. P. Leighton and D. A. Sivak, Inferring subsystem efficiencies in bipartite molecular machines, Phys. Rev. Lett. 130, 178401 (2023).
  51. M. P. Leighton, J. Ehrich, and D. A. Sivak, Information arbitrage in bipartite heat engines, Phys. Rev. X 14, 041038 (2024).
  52. See Supplemental Material at http://link.aps.org/supplemental/10.1103/6wcm-z333 for further theoretical, computational, and experimental details, which also include Refs. [84, 85, 86, 87].
  53. A. Tejero-Cantero, J. Boelts, M. Deistler, J.-M. Lueckmann, C. Durkan, P. J. Gonçalves, D. S. Greenberg, and J. H. Macke, sbi: A toolkit for simulation-based inference, J. Open Source Software 5, 2505 (2020).
  54. K. Cranmer, J. Brehmer, and G. Louppe, The frontier of simulation-based inference, Proc. Natl. Acad. Sci. USA 117, 30055 (2020).
  55. D. Ramunno-Johnson, C. Strimbu, L. Fredrickson, K. Arisaka, and D. Bozovic, Distribution of frequencies of spontaneous oscillations in hair cells of the bullfrog sacculus, Biophys. J. 96, 1159 (2009).
  56. J. B. Azimzadeh and J. D. Salvi, Physiological preparation of hair cells from the sacculus of the american bullfrog (rana catesbeiana), J. Visualized Exp. 121, e55380 (2017).
  57. J. B. Azimzadeh, B. A. Fabella, N. R. Kastan, and A. Hudspeth, Thermal excitation of the mechanotransduction apparatus of hair cells, Neuron 97, 586 (2018).
  58. R. G. Alonso, M. Tobin, P. Martin, and A. J. Hudspeth, Fast recovery of disrupted tip links induced by mechanical displacement of hair bundles, Proc. Natl. Acad. Sci. USA 117, 30722 (2020).
  59. G. Shepherd and D. Corey, The extent of adaptation in bullfrog saccular hair cells, J. Neurosci. 14, 6217 (1994).
  60. U. Seifert, Stochastic thermodynamics, fluctuation theorems and molecular machines, Rep. Prog. Phys. 75, 126001 (2012).
  61. L. Peliti and S. Pigolotti, Stochastic Thermodynamics: An Introduction (Princeton University Press, Princeton, NJ, 2021).
  62. E. Roldán, I. Neri, R. Chetrite, S. Gupta, S. Pigolotti, F. Jülicher, and K. Sekimoto, Martingales for physicists: A treatise on stochastic thermodynamics and beyond, Adv. Phys. 72, 1 (2023).
  63. D. Gupta and S. Sabhapandit, Stochastic efficiency of an isothermal work-to-work converter engine, Phys. Rev. E 96, 042130 (2017).
  64. K. Sekimoto, Langevin equation and thermodynamics, Prog. Theor. Phys. Suppl. 130, 17 (1998).
  65. S. Rana, P. Pal, A. Saha, and A. Jayannavar, Anomalous Brownian refrigerator, Physica A 444, 783 (2016).
  66. M. Baiesi and C. Maes, Life efficiency does not always increase with the dissipation rate, J. Phys. Commun. 2, 045017 (2018).
  67. L. Oberreiter, U. Seifert, and A. C. Barato, Universal minimal cost of coherent biochemical oscillations, Phys. Rev. E 106, 014106 (2022).
  68. D. Santolin and G. Falasco, Dissipation bounds the coherence of stochastic limit cycles, Phys. Rev. Lett. 135, 057101 (2025).
  69. M. Ospeck, V. Eguíluz, and M. Magnasco, Evidence of a hopf bifurcation in frog hair cells, Biophys. J. 80, 2597 (2001).
  70. A. J. Hudspeth, F. Jülicher, and P. Martin, A critique of the critical cochlea: Hopf—a bifurcation—is better than none, J. Neurophysiol. 104, 1219 (2010).
  71. J. D. Salvi, D. Ó Maoiléidigh, B. A. Fabella, M. Tobin, and A. J. Hudspeth, Control of a hair bundle's mechanosensory function by its mechanical load, Proc. Natl. Acad. Sci. USA 112, E1000 (2015).
  72. P. Holmes and D. Rand, Phase portraits and bifurcations of the non-linear oscillator: ẍ+α+γx2+βx+δx3=0, Int. J. Non Linear Mech. 15, 449 (1980).
  73. K. R. Schenk-Hoppé, Bifurcation scenarios of the noisy Duffing–Van der Pol oscillator, Nonlinear Dyn. 11, 255 (1996).
  74. P. Martin and A. J. Hudspeth, Compressive nonlinearity in the hair bundle's active response to mechanical stimulation, Proc. Natl. Acad. Sci. USA 98, 14386 (2001).
  75. P. D. Mitcheson, Energy harvesting for human wearable and implantable bio-sensors, in 2010 Annual International Conference of the IEEE Engineering in Medicine and Biology (IEEE, New York, 2010).
  76. H. Wang, J.-D. Park, and Z. J. Ren, Practical energy harvesting for microbial fuel cells: A review, Environ. Sci. Technol. 49, 3267 (2015).
  77. Q. Shi, T. He, and C. Lee, More than energy harvesting – Combining triboelectric nanogenerator and flexible electronics technology for enabling novel micro-/nano-systems, Nano Energy 57, 851 (2019).
  78. I. R. Graf and B. B. Machta, A bifurcation integrates information from many noisy ion channels and allows for milli-kelvin thermal sensitivity in the snake pit organ, Proc. Natl. Acad. Sci. USA 121, e2308215121 (2024).
  79. R. G. Alonso, F. Gianoli, B. Fabella, and A. J. Hudspeth, Amplification through local critical behavior in the mammalian cochlea, Proc. Natl. Acad. Sci. USA 122, e2503389122 (2025).
  80. M. A. Ruggero, S. S. Narayan, A. N. Temchin, and A. Recio, Mechanical bases of frequency tuning and neural excitation at the base of the cochlea: Comparison of basilar-membrane vibrations and auditory-nerve-fiber responses in chinchilla, Proc. Natl. Acad. Sci. USA 97, 11744 (2000).
  81. J. Fisher, F. Nin, T. Reichenbach, R. Uthaiah, and A. Hudspeth, The spatial pattern of cochlear amplification, Neuron 76, 989 (2012).
  82. H. V. Hulst, C. B. Mercader, F. Jülicher, and P. Martin, Marrying critical oscillators with traveling waves shapes nonlinear sound processing in the cochlea, arXiv:2512.11646.
  83. See Supplemental Material at http://link.aps.org/supplemental/10.1103/6wcm-z333 for original data.
  84. F. Mentré, P. Burtin, Y. Merlé, J. van Bree, A. Mallet, and J.-L. Steimer, Sparse-sampling optimal designs in pharmacokinetics and toxicokinetics, Drug Inf. J. 29, 997 (1995).
  85. D. Jordan and P. Smith, Nonlinear Ordinary Differential Equations: An Introduction for Scientists and Engineers (Oxford University Press, Oxford, England, 2007).
  86. T. H. T. Nguyen, T. T. Nguyen, and F. Mentré, Individual bayesian information matrix for predicting estimation error and shrinkage of individual parameters accounting for data below the limit of quantification, Pharm. Res. 34, 2119 (2017).
  87. R. Belousov, F. Berger, and A. J. Hudspeth, Volterra-series approach to stochastic nonlinear dynamics: The Duffing oscillator driven by white noise, Phys. Rev. E 99, 042204 (2019).

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