- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review Letters

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Featured in Physics
  • Editors' Suggestion
  • Open Access
  • Access by Xinjiang University

Balancing Information and Dissipation with Partially Observed Fluctuating Signals

Giorgio Nicoletti1,*, Ivan Di Terlizzi2,3,†, and Daniel Maria Busiello2,4,‡

  • *Contact author: gnicolet@ictp.it
  • †Contact author: ivandt@pks.mpg.de
  • ‡Contact author: danielmaria.busiello@unipd.it
PDF

Phys. Rev. Lett. 137, 127101 – Published 14 September, 2026

DOI: https://doi.org/10.1103/8gx2-rbns

Abstract

Biological systems sense and extract information from fluctuating signals while operating under energetic constraints and limited resolution. We introduce a general chemical model in which a signaling pathway is activated by hidden signals and produces a readout molecule. A sensor, here modeled as an abstract optimization agent, is coupled to the signaling process and can tune the readout production. We propose viable strategies for the sensor to estimate, and eventually balance, information gathering on the hidden process and the associated dissipative cost relying solely on counting statistics of observed trajectories. We show that these strategies can be successfully implemented to adapt the readout production even with finite-time measurements and limited dynamic resolution, and remain effective in the presence of inhibitory regulatory mechanisms. Our Letter provides a plausible mechanism to actively balance information and dissipation, paving the way for an implementable design principle underpinning biological and biochemical adaptation.

View figure in article

Physics Subject Headings (PhySH)

Viewpoint

Cells Put a Price Tag on Sensing Their World

Published 14 September, 2026

A new model shows how cells could optimize biochemical sensing by balancing information gained against energy spent.

See more in Physics

Article Text

References (70)

  1. C. G. Bowsher and P. S. Swain, Environmental sensing, information transfer, and cellular decision-making, Curr. Opin. Biotechnol. 28, 149 (2014).
  2. G. Reddy, A. Celani, T. J. Sejnowski, and M. Vergassola, Learning to soar in turbulent environments, Proc. Natl. Acad. Sci. U.S.A. 113, E4877 (2016).
  3. G. Balázsi, A. Van Oudenaarden, and J. J. Collins, Cellular decision making and biological noise: From microbes to mammals, Cell 144, 910 (2011).
  4. O. Karin and U. Alon, Temporal fluctuations in chemotaxis gain implement a simulated-tempering strategy for efficient navigation in complex environments, IScience 24 (2021).
  5. T. Nakajima, Biologically inspired information theory: Adaptation through construction of external reality models by living systems, Prog. Biophys. Molec. Biol. 119, 634 (2015).
  6. H.-W. Wang, C. J. Wysocki, and G. H. Gold, Induction of olfactory receptor sensitivity in mice, Science 260, 998 (1993).
  7. V. Sourjik and H. C. Berg, Receptor sensitivity in bacterial chemotaxis, Proc. Natl. Acad. Sci. U.S.A. 99, 123 (2002).
  8. P. R. ten Wolde, N. B. Becker, T. E. Ouldridge, and A. Mugler, Fundamental limits to cellular sensing, J. Stat. Phys. 162, 1395 (2016).
  9. T. Mora and I. Nemenman, Physical limit to concentration sensing in a changing environment, Phys. Rev. Lett. 123, 198101 (2019).
  10. T. Tohme, M. Vergassola, T. Mora, and A. M. Walczak, Fast decisions with biophysically constrained gene promoter architectures, PRX Life 4, 013009 (2026).
  11. C. C. Govern and P. R. ten Wolde, Energy dissipation and noise correlations in biochemical sensing, Phys. Rev. Lett. 113, 258102 (2014).
  12. S. Liang, P. De Los Rios, and D. M. Busiello, Thermodynamic bounds on symmetry breaking in linear and catalytic biochemical systems, Phys. Rev. Lett. 132, 228402 (2024).
  13. T. E. Ouldridge, C. C. Govern, and P. R. ten Wolde, Thermodynamics of computational copying in biochemical systems, Phys. Rev. X 7, 021004 (2017).
  14. J. M. Parrondo, J. M. Horowitz, and T. Sagawa, Thermodynamics of information, Nat. Phys. 11, 131 (2015).
  15. I. Lestas, G. Vinnicombe, and J. Paulsson, Fundamental limits on the suppression of molecular fluctuations, Nature (London) 467, 174 (2010).
  16. A. Solopova, J. Van Gestel, F. J. Weissing, H. Bachmann, B. Teusink, J. Kok, and O. P. Kuipers, Bet-hedging during bacterial diauxic shift, Proc. Natl. Acad. Sci. U.S.A. 111, 7427 (2014).
  17. M. Basan, S. Hui, H. Okano, Z. Zhang, Y. Shen, J. R. Williamson, and T. Hwa, Overflow metabolism in Escherichia coli results from efficient proteome allocation, Nature (London) 528, 99 (2015).
  18. M. J. Falk, J. Wu, A. Matthews, V. Sachdeva, N. Pashine, M. L. Gardel, S. R. Nagel, and A. Murugan, Learning to learn by using nonequilibrium training protocols for adaptable materials, Proc. Natl. Acad. Sci. U.S.A. 120, e2219558120 (2023).
  19. S. Okumura, G. Gines, N. Lobato-Dauzier, A. Baccouche, R. Deteix, T. Fujii, Y. Rondelez, and A. J. Genot, Nonlinear decision-making with enzymatic neural networks, Nature (London) 610, 496 (2022).
  20. 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).
  21. G. Nicoletti and D. M. Busiello, Tuning transduction from hidden observables to optimize information harvesting, Phys. Rev. Lett. 133, 158401 (2024).
  22. G. Nicoletti, M. Bruzzone, S. Suweis, M. Dal Maschio, and D. M. Busiello, Optimal information gain at the onset of habituation to repeated stimuli, eLife 13 (2025).
  23. A. J. Tjalma, V. Galstyan, J. Goedhart, L. Slim, N. B. Becker, and P. R. Ten Wolde, Trade-offs between cost and information in cellular prediction, Proc. Natl. Acad. Sci. U.S.A. 120, e2303078120 (2023).
  24. D. Hartich, A. C. Barato, and U. Seifert, Nonequilibrium sensing and its analogy to kinetic proofreading, New J. Phys. 17, 055026 (2015).
  25. M. Skoge, S. Naqvi, Y. Meir, and N. S. Wingreen, Chemical sensing by nonequilibrium cooperative receptors, Phys. Rev. Lett. 110, 248102 (2013).
  26. H. Chang and A. Levchenko, Adaptive molecular networks controlling chemotactic migration: Dynamic inputs and selection of the network architecture, Phil. Trans. R. Soc. B 368, 20130117 (2013).
  27. A. Levchenko and I. Nemenman, Cellular noise and information transmission, Curr. Opin. Biotechnol. 28, 156 (2014).
  28. R. Fan and A. Hilfinger, Characterizing the nonmonotonic behavior of mutual information along biochemical reaction cascades, Phys. Rev. E 110, 034309 (2024).
  29. M. K. Kajita, K. Aihara, and T. J. Kobayashi, Balancing specificity, sensitivity and speed of ligand discrimination by zero-order ultraspecificity, Phys. Rev. E 96, 012405 (2017).
  30. J. Paulsson, O. G. Berg, and M. Ehrenberg, Stochastic focusing: Fluctuation-enhanced sensitivity of intracellular regulation, Proc. Natl. Acad. Sci. U.S.A. 97, 7148 (2000).
  31. I. Di Terlizzi, Force-free kinetic inference of entropy production, Phys. Rev. Lett. 135, 237101 (2025).
  32. C. Gardiner, Stochastic Methods (Springer, Berlin, Heidelberg, 2009), Vol. 4.
  33. L. Cantini, C. Cianci, D. Fanelli, E. Massi, and L. Barletti, Linear noise approximation for stochastic oscillations of intracellular calcium, J. Theor. Biol. 349, 92 (2014).
  34. R. Grima, Linear-noise approximation and the chemical master equation agree up to second-order moments for a class of chemical systems, Phys. Rev. E 92, 042124 (2015).
  35. R. Cheong, A. Rhee, C. J. Wang, I. Nemenman, and A. Levchenko, Information transduction capacity of noisy biochemical signaling networks, Science 334, 354 (2011).
  36. W. Ma, A. Trusina, H. El-Samad, W. A. Lim, and C. Tang, Defining network topologies that can achieve biochemical adaptation, Cell 138, 760 (2009).
  37. J. Selimkhanov, B. Taylor, J. Yao, A. Pilko, J. Albeck, A. Hoffmann, L. Tsimring, and R. Wollman, Accurate information transmission through dynamic biochemical signaling networks, Science 346, 1370 (2014).
  38. N. Barkai and S. Leibler, Robustness in simple biochemical networks, Nature (London) 387, 913 (1997).
  39. M. Kollmann, L. Løvdok, K. Bartholomé, J. Timmer, and V. Sourjik, Design principles of a bacterial signalling network, Nature (London) 438, 504 (2005).
  40. Y. Tu, Quantitative modeling of bacterial chemotaxis: signal amplification and accurate adaptation, Annu. Rev. Biophys. 42, 337 (2013).
  41. M. Inoue and K. Kaneko, Cooperative adaptive responses in gene regulatory networks with many degrees of freedom, PLoS Comput. Biol. 9, e1003001 (2013).
  42. T. M. Pham and K. Kaneko, Dynamical theory for adaptive systems, J. Stat. Mech. (2024) 113501.
  43. S. Flatt, D. M. Busiello, S. Zamuner, and P. De Los Rios, ABC transporters are billion-year-old Maxwell demons, Commun. Phys. 6, 205 (2023).
  44. J. Agudo-Canalejo and R. Golestanian, Active phase separation in mixtures of chemically interacting particles, Phys. Rev. Lett. 123, 018101 (2019).
  45. S. A. Loos and S. H. Klapp, Irreversibility, heat and information flows induced by non-reciprocal interactions, New J. Phys. 22, 123051 (2020).
  46. T. Suchanek, K. Kroy, and S. A. Loos, Entropy production in the nonreciprocal Cahn-Hilliard model, Phys. Rev. E 108, 064610 (2023).
  47. Z. Zhang and R. Garcia-Millan, Entropy production of nonreciprocal interactions, Phys. Rev. Res. 5, L022033 (2023).
  48. A. Dinelli, J. O’Byrne, A. Curatolo, Y. Zhao, P. Sollich, and J. Tailleur, Non-reciprocity across scales in active mixtures, Nat. Commun. 14, 7035 (2023).
  49. D. M. Busiello, M. Ciarchi, and I. Di Terlizzi, Unraveling active baths through their hidden degrees of freedom, Phys. Rev. Res. 6, 013190 (2024).
  50. T. M. Pham, A. Alonso, and K. Proesmans, Irreversibility in non-reciprocal chaotic systems, New J. Phys. 27, 023003 (2025).
  51. K. Sekimoto, Langevin equation and thermodynamics, Prog. Theor. Phys. Suppl. 130, 17 (1998).
  52. A. Frishman and P. Ronceray, Learning force fields from stochastic trajectories, Phys. Rev. X 10, 021009 (2020).
  53. C. Maes, K. Netočný, and B. Wynants, Steady state statistics of driven diffusions, Physica (Amsterdam) 387A, 2675 (2008).
  54. M. Baiesi and G. Falasco, Inflow rate, a time-symmetric observable obeying fluctuation relations, Phys. Rev. E 92, 042162 (2015).
  55. I. D. Terlizzi, M. Gironella, D. Herraez-Aguilar, T. Betz, F. Monroy, M. Baiesi, and F. Ritort, Variance sum rule for entropy production, Science 383, 971 (2024).
  56. I. Di Terlizzi, M. Baiesi, and F. Ritort, Variance sum rule: Proofs and solvable models, New J. Phys. 26, 063013 (2024).
  57. O. Shoval, H. Sheftel, G. Shinar, Y. Hart, O. Ramote, A. Mayo, E. Dekel, K. Kavanagh, and U. Alon, Evolutionary trade-offs, pareto optimality, and the geometry of phenotype space, Science 336, 1157 (2012).
  58. G. Nicoletti and D. M. Busiello, Information propagation in multilayer systems with higher-order interactions across timescales, Phys. Rev. X 14, 021007 (2024).
  59. G. Nicoletti and D. M. Busiello, Information propagation in Gaussian processes on multilayer networks, J. Phys. Complexity 5, 045004 (2024).
  60. G. Nicoletti and D. M. Busiello, Mutual information disentangles interactions from changing environments, Phys. Rev. Lett. 127, 228301 (2021).
  61. G. Malaguti and P. R. Ten Wolde, Theory for the optimal detection of time-varying signals in cellular sensing systems, eLife 10, e62574 (2021).
  62. M. Baiesi and C. Maes, Life efficiency does not always increase with the dissipation rate, J. Phys. Comm. 2, 045017 (2018).
  63. 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).
  64. H. H. Mattingly, K. Kamino, B. B. Machta, and T. Emonet, Escherichia coli chemotaxis is information limited, Nat. Phys. 17, 1426 (2021).
  65. D. Hathcock, Q. Yu, B. A. Mello, D. N. Amin, G. L. Hazelbauer, and Y. Tu, A nonequilibrium allosteric model for receptor-kinase complexes: The role of energy dissipation in chemotaxis signaling, Proc. Natl. Acad. Sci. U.S.A. 120, e2303115120 (2023).
  66. C. Maes, On the origin and the use of fluctuation relations for the entropy, Sémin. Poincaré 2, 29 (2003).
  67. U. Seifert, Stochastic thermodynamics, fluctuation theorems and molecular machines, Rep. Prog. Phys. 75, 126001 (2012).
  68. L. Peliti and S. Pigolotti, Stochastic Thermodynamics: An Introduction (Princeton University Press, Princeton, NJ, 2021).
  69. G. Gallavotti and E. G. D. Cohen, Dynamical ensembles in nonequilibrium statistical mechanics, Phys. Rev. Lett. 74, 2694 (1995).
  70. G. E. Crooks, Entropy production fluctuation theorem and the nonequilibrium work relation for free energy differences, Phys. Rev. E 60, 2721 (1999).

Outline

Information

Phys. Rev. Lett. 137, 127101– Published 14 September, 2026
  • Received 13 January 2026
  • Accepted 13 July 2026
Crossmark - Check for updates button
Creative Commons Logo

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. Open access publication funded by the Max Planck Society.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation