- Physical Review Journals
All JournalsPhysics Magazine

PRX Life

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
  • Open Access

Beyond Diffusion: Bayesian Learning Strategies in Single-Cell Life

Maor Knafo and Elena Casacuberta

Iñaki Ruiz-Trillo

PDF

PRX Life 4, 023025 – Published 5 June, 2026

DOI: https://doi.org/10.1103/5p5z-t8qy

Abstract

Evolutionary change is shaped not only by genetic variation and selection across generations but also by phenotypic plasticity, niche construction, and nongenetic inheritance. Here we develop a quantitative, falsifiable framework that models individual organisms as learners that infer hidden environmental states from noisy cues and update phenotype strategies within a lifetime. We introduce Markovian, Bayesian Agents (MBAs), which combine regret-gated stochastic exploration with genetic assimilation, and compare them to nonlearning Blind Agents (BAs). Agent-based simulations reveal that MBAs outperform BAs when cue-stress correlations are high, but lose their advantage above a critical environmental stochasticity threshold (ɛ≈0.2). We then test a central prediction in the unicellular holozoan Capsaspora owczarzaki using a smart-incubator conditioning assay: cultures trained with predictive cue-stress pairing show significantly reduced mortality relative to nonpredictive controls (Mann-Whitney U, p=1.07×10−8). Together, model and experiment link within-lifetime inference to cross-generational adaptation in a single-celled system.

View figure in article

Physics Subject Headings (PhySH)

Collections

This article appears in the following collection:

PRX Life Collection on adaptation and learning

PRX Life presents a special collection on ‘Biological systems that learn’, curated by the organizers of the National Institute for Theory and Mathematics in Biology (NITMB) workshop together with early-career researchers. The papers in this collection illustrate how living systems acquire functions, showing it is useful to describe them as tunable matter with many individually adjustable degrees of freedom characterizing microscopic properties. Drawing inspiration from AI and non-biological systems that can acquire desired functions, the featured research highlights the timeliness of the topic and its potential to drive unifying frameworks for emergent collective function in living tunable matter.

Every article in this collection is subject to a rigorous peer review process, upholding the high standards applied to all papers in the journal. The PRX Life editorial team manages peer review and makes all editorial decisions.

Article Text

References (62)

  1. R. G. Shaw and J. R. Etterson, Rapid climate change and the rate of adaptation: Insight from experimental quantitative genetics, New Phytol. 195, 752 (2012).
  2. P. W. Messer, S. P. Ellner, and N. G. Hairston, Can population genetics adapt to rapid evolution? Trends Genet. 32, 408 (2016).
  3. P. W. Messer and D. A. Petrov, Population genomics of rapid adaptation by soft selective sweeps, Trends Ecol. Evol. 28, 659 (2013).
  4. W. J. Blake, M. Kærn, C. R. Cantor, and J. J. Collins, Noise in eukaryotic gene expression, Nature (London) 422, 633 (2003).
  5. M. A. Coomer, L. Ham, and M. P. H. Stumpf, Noise distorts the epigenetic landscape and shapes cell-fate decisions, Cell Syst. 13, 83 (2022).
  6. P. Tataru, M. Simonsen, T. Bataillon, and A. Hobolth, Statistical inference in the Wright–Fisher model using allele frequency data, Syst. Biol. 66, e30 (2017).
  7. M. Kimura, Model of effectively neutral mutations in which selective constraint is incorporated, Proc. Natl. Acad. Sci. USA 76, 3440 (1979).
  8. R. Solé, Revisiting Leigh Van Valen's “A new evolutionary law” (1973), Biol. Theory 17, 120 (2022).
  9. A. I. Khibnik and A. S. Kondrashov, Three mechanisms of Red Queen dynamics, Proc. R. Soc. Lond. B 264, 1049 (1997).
  10. L. Van Valen, A new evolutionary law, Evol. Theory 1, 1 (1973).
  11. M. M. Desai and D. S. Fisher, Beneficial mutation selection balance and the effect of linkage on positive selection, Genetics 176, 1759 (2007).
  12. B. H. Good, M. J. McDonald, J. E. Barrick, R. E. Lenski, and M. M. Desai, The dynamics of molecular evolution over 60,000 generations, Nature (London) 551, 45 (2017).
  13. S. F. Levy, J. R. Blundell, S. Venkataram, D. A. Petrov, D. S. Fisher, and G. Sherlock, Quantitative evolutionary dynamics using high-resolution lineage tracking, Nature (London) 519, 181 (2015).
  14. A. Forsman, Rethinking phenotypic plasticity and its consequences for individuals, populations and species, Heredity 115, 276 (2015).
  15. P. Lyon, F. Keijzer, D. Arendt, and M. Levin, Reframing cognition: Getting down to biological basics, Phil. Trans. R. Soc. B 376, 20190750 (2021).
  16. J. Zheng, J. L. Payne, and A. Wagner, Cryptic genetic variation accelerates evolution by opening access to diverse adaptive peaks, Science 365, 347 (2019).
  17. A. B. Paaby and M. V. Rockman, Cryptic genetic variation: Evolution's hidden substrate, Nat. Rev. Genet. 15, 247 (2014).
  18. J. F. Ayroles, S. M. Buchanan, C. O'Leary, K. Skutt-Kakaria, J. K. Grenier, A. G. Clark, D. L. Hartl, and B. L. de Bivort, Behavioral idiosyncrasy reveals genetic control of phenotypic variability, Proc. Natl. Acad. Sci. USA 112, 6706 (2015).
  19. A. Sebé-Pedrós, M. Irimia, J. del Campo, H. Parra-Acero, C. Russ, C. Nusbaum, B. J. Blencowe, and I. Ruiz-Trillo, Regulated aggregative multicellularity in a close unicellular relative of Metazoa, eLife 2, e01287 (2013).
  20. N. Ros-Rocher, R. Q. Kidner, C. Gerdt, W. S. Davidson, I. Ruiz-Trillo, and J. P. Gerdt, Chemical factors induce aggregative multicellularity in a close unicellular relative of animals, Proc. Natl. Acad. Sci. USA 120, e2216668120 (2023).
  21. J. A. Schwartzman, A. Ebrahimi, G. Chadwick, Y. Sato, B. R. K. Roller, V. J. Orphan, and O. X. Cordero, Bacterial growth in multicellular aggregates leads to the emergence of complex life cycles, Curr. Biol. 32, 3059 (2022).
  22. R. B. Stelkens, M. A. Brockhurst, G. D. D. Hurst, and D. Greig, Hybridization facilitates evolutionary rescue, Evol. Appl. 7, 1209 (2014).
  23. M. J. West-Eberhard, Developmental Plasticity and Evolution (Oxford University Press, New York, 2003).
  24. E. Jablonka and M. J. Lamb, Evolution in Four Dimensions: Genetic, Epigenetic, Behavioral, and Symbolic Variation in the History of Life, revised ed. (MIT Press, Cambridge, MA, 2014).
  25. M. Pigliucci and G. B. Müller, Evolution: The Extended Synthesis (MIT Press, Cambridge, MA, 2010).
  26. K. N. Laland, T. Uller, M. W. Feldman, K. Sterelny, G. B. Müller, A. Moczek, E. Jablonka, and J. Odling-Smee, The extended evolutionary synthesis: Its structure, assumptions and predictions, Proc. R. Soc. B 282, 20151019 (2015).
  27. G. B. Müller, Why an extended evolutionary synthesis is necessary, Interface Focus 7, 20170015 (2017).
  28. D. Noble, A theory of biological relativity: No privileged level of causation, Interface Focus 2, 55 (2012).
  29. A. C. Alarcon Rios, L. B. Zwep, B. Vriesendorp, C. A. J. Knibbe, O. Ciofu, A. Liakopoulos, L. B. S. Aulin, D. E. Rozen, and J. G. C. van Hasselt, Colistin resistance dynamics in Pseudomonas aeruginosa under biofilm and planktonic growth, Antimicrob. Agents Chemother. 69, e00421 (2025).
  30. I. Dagogo-Jack and A. T. Shaw, Tumour heterogeneity and resistance to cancer therapies, Nature Rev. Clin. Oncol. 15, 81 (2018).
  31. G. S. França, M. Baron, B. R. King, J. P. Bossowski, A. Bjornberg, M. Pour, A. Rao, A. S. Patel, S. Misirlioglu, D. Barkley, K. H. Tang, I. Dolgalev, D. A. Liberman, G. Avital, F. Kuperwaser, M. Chiodin, D. A. Levine, T. Papagiannakopoulos, A. Marusyk, T. Lionnet, et al., Cellular adaptation to cancer therapy along a resistance continuum, Nature (London) 631, 876 (2024).
  32. A. Oruni, M. Tchouakui, C. S. D. Tagne, J. Hearn, J. Kayondo, and C. S. Wondji, Temporal evolution of insecticide resistance and bionomics in Anopheles funestus, a key malaria vector in Uganda, Sci. Rep. 14, 32027 (2024).
  33. M. Acar, J. T. Mettetal, and A. van Oudenaarden, Stochastic switching as a survival strategy in fluctuating environments, Nat. Genet. 40, 471 (2008).
  34. H. I. Schreier, Y. Soen, and N. Brenner, Exploratory adaptation in large random networks, Nat. Commun. 8, 14826 (2017).
  35. C. H. Waddington, Genetic assimilation of an acquired character, Evolution 7, 118 (1953).
  36. E. Crispo, The Baldwin effect and genetic assimilation: Revisiting two mechanisms of evolutionary change mediated by phenotypic plasticity, Evolution 61, 2469 (2007).
  37. G. E. Hinton and S. J. Nowlan, How learning can guide evolution, Complex Syst. 1, 495 (1987).
  38. D. H. Ackley and M. L. Littman, Interactions between learning and evolution, in Artificial Life II. SFI Studies in the Sciences of Complexity, edited by C. G. Langton, C. Taylor, J. D. Farmer, and S. Rasmussen (Addison-Wesley, Redwood City, CA, 1991), pp. 487–509.
  39. K. Friston, The free-energy principle: A unified brain theory? Nat. Rev. Neurosci. 11, 127 (2010).
  40. D. V. Tikhonenkov, E. Hehenberger, A. S. Esaulov, O. I. Belyakova, Y. A. Mazei, A. P. Mylnikov, and P. J. Keeling, Insights into the origin of metazoan multicellularity from predatory unicellular relatives of animals, BMC Biol. 18, 39 (2020).
  41. N. Ros-Rocher, A. Pérez-Posada, M. M. Leger, and I. Ruiz-Trillo, The origin of animals: An ancestral reconstruction of the unicellular-to-multicellular transition, Open Biol. 11, 200359 (2021).
  42. J. E. Phillips, M. Santos, M. Konchwala, C. Xing, and D. Pan, Genome editing in the unicellular holozoan Capsaspora owczarzaki suggests a premetazoan role for the Hippo pathway in multicellular morphogenesis, eLife 11, e77598 (2022).
  43. A. Sebé-Pedrós, A. J. Roger, F. B. Lang, N. King, and I. Ruiz-Trillo, Ancient origin of the integrin-mediated adhesion and signaling machinery, Proc. Natl. Acad. Sci. USA 107, 10142 (2010).
  44. H. Suga, Z. Chen, A. de Mendoza, A. Sebé-Pedrós, M. W. Brown, E. Kramer, M. Carr, P. Kerner, M. Vervoort, N. Sánchez-Pons, G. Torruella, R. Derelle, G. Manning, B. F. Lang, C. Russ, B. J. Haas, A. J. Roger, C. Nusbaum, and I. Ruiz-Trillo, The Capsaspora genome reveals a complex unicellular prehistory of animals, Nat. Commun. 4, 2325 (2013).
  45. I. Ruiz-Trillo, K. Kin, and E. Casacuberta, The origin of metazoan multicellularity: A potential microbial black swan event, Annu. Rev. Microbiol. 77, 499 (2023).
  46. H. S. Jennings, Behavior of the Lower Organisms (Columbia University Press, New York, 1906).
  47. P. Lyon, The cognitive cell: Bacterial behavior reconsidered, Front. Microbiol. 6, 264 (2015).
  48. F. Baluška, W. B. Miller, and A. S. Reber, Cellular and organismal agency—Not micromanagement by genes, New Phytol. 232, 1337 (2021).
  49. M. Levin, Collective intelligence of morphogenesis as a teleonomic process (2023), https://doi.org/10.31234/osf.io/5ywqu.
  50. J. Gunawardena, Learning outside the brain: Integrating cognitive science and systems biology, Proc. IEEE 110, 590 (2022).
  51. J. Pla-Mauri and R. Solé, Engineering basal cognition: Minimal genetic circuits for habituation, sensitization, and massed–spaced learning, ACS Synth. Biol. 15, 716 (2026).
  52. C. I. Abramson and M. Levin, Behaviorist approaches to investigating memory and learning: A primer for synthetic biology and bioengineering, Commun. Integr. Biol. 14, 230 (2021).
  53. D. Noble, It's time to admit that genes are not the blueprint for life, Nature (London) 626, 254 (2024).
  54. K. Donohue, R. Rubio de Casas, L. Burghardt, K. Kovach, and C. G. Willis, Germination, postgermination adaptation, and species ecological ranges, Annu. Rev. Ecol. Evol. Syst. 41, 293 (2010).
  55. S. A. Frank and I. Yanai, The origin of novel traits in cancer, Trends Cancer 10, 880 (2024).
  56. A. Mitchell, G. H. Romano, B. Groisman, A. Yona, E. Dekel, M. Kupiec, O. Dahan, and Y. Pilpel, Adaptive prediction of environmental changes by microorganisms, Nature (London) 460, 220 (2009).
  57. S. D. Jamadar, A. Behler, H. Deery, and M. Breakspear, The metabolic costs of cognition, Trends Cognit. Sci. 29, 541 (2025).
  58. C. M. Jakobson and D. F. Jarosz, Metabolites control stress granule disassembly, Nat. Cell Biol. 23, 1053 (2021).
  59. M. Knafo, S. Rezenman, R. Nevo, I. Tsigalnitski, Z. Reich, and R. Kapon, Variability in protein expression and fitness under stress: Distinct modes of early adaptation of populations, PRX Life 3, 013006 (2025).
  60. M. Knafo, E. Casacuberta, and I. Ruiz-Trillo, Code, firmware, simulation scripts, and analysis materials for “Beyond diffusion: Bayesian learning strategies in single-cell life.” Figshare (2026), https://doi.org/10.6084/m9.figshare.32235240.
  61. L. Eckert, M. S. Vidal-Saez, Z. Zhao, J. Garcia-Ojalvo, R. Martinez-Corral, and J. Gunawardena, Biochemically plausible models of habituation for single-cell learning, Curr. Biol. 34, 5646 (2024).
  62. C. Stringer, T. Wang, M. Michaelos, and M. Pachitariu, Cellpose: A generalist algorithm for cellular segmentation, Nat. Methods 18, 100 (2021).

Outline

Information

PRX Life 4, 023025– Published 5 June, 2026
  • Received 19 October 2025
  • Accepted 24 April 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.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation