- Physical Review Journals
All JournalsPhysics Magazine

Physical Review Research

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

Self-balancing of cell populations via martingale turnover with amplification

Tomoyuki Yamaguchi*

  • *Contact author: t.yamaguchi@tokushukai.jp
PDF

Phys. Rev. Research 8, 023085 – Published 29 April, 2026

DOI: https://doi.org/10.1103/l15n-f343

Abstract

Adaptive control in biological systems, such as intestinal immunity, remains poorly understood despite detailed knowledge of underlying regulatory networks. We propose an alternative framework based on stochastic martingale turnover, in which cells proliferate through mutual competition and decay without cell-type-specific regulation. Through stochastic simulations and mathematical analysis, we show that this process autonomously generates balanced population compositions associated with low-decay probabilities. The compositional dynamics can be described as a random walk whose step lengths decrease in low-decay regions. Reduced decay leads to larger total population sizes and an increase in the number of compatible microscopic states, which in turn shapes the distribution of compositions under fluctuating conditions. More generally, the dynamics follow a modified Langevin equation, in which constant mass is replaced by a fitness-dependent effective mass proportional to the total population size. Thus, biological systems regulate resistance to change, not merely direction, in shaping their macroscopic behavior.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (27)

  1. P. Meyer and J. Saez-Rodriguez, Advances in systems biology modeling: 10 years of crowdsourcing DREAM challenges, Cell Syst. 12, 636 (2021).
  2. Z. R. Thornburg et al., Fundamental behaviors emerge from simulations of a living minimal cell, Cell 185, 345 (2022).
  3. N. Eling, M. D. Morgan, and J. C. Marioni, Challenges in measuring and understanding biological noise, Nat. Rev. Genet. 20, 536 (2019).
  4. R. Kedmi and D. R. Littman, Antigen-presenting cells as specialized drivers of intestinal T cell functions, Immunity 57, 2269 (2024).
  5. B. Akagbosu et al., Novel antigen-presenting cell imparts Treg-dependent tolerance to gut microbiota, Nature (London) 610, 752 (2022).
  6. M. Lyu et al., ILC3s select microbiota-specific regulatory T cells to establish tolerance in the gut, Nature (London) 610, 744 (2022).
  7. R. Kedmi et al., A RORγt+ cell instructs gut microbiota-specific Treg cell differentiation, Nature (London) 610, 737 (2022).
  8. P. F. Rodrigues et al., Rorγt-positive dendritic cells are required for the induction of peripheral regulatory T cells in response to oral antigens, Cell 188, 2720 (2025).
  9. L. Fu, R. Upadhyay, M. Pokrovskii, F. M. Chen, G. Romero-Meza, A. Griesemer, and D. R. Littman, PRDM16-dependent antigen-presenting cells induce tolerance to gut antigens, Nature (London) 642, 756 (2025).
  10. M. C. Campos Canesso et al., Identification of antigen-presenting cell–T cell interactions driving immune responses to food, Science 387, eado5088 (2025).
  11. D. Silver et al., Mastering the game of Go with deep neural networks and tree search, Nature (London) 529, 484 (2016).
  12. D. Guo et al., DeepSeek-R1 incentivizes reasoning in LLMs through reinforcement learning, Nature (London) 645, 633 (2025).
  13. G. Pezzulo and M. Levin, Top-down models in biology: Explanation and control of complex living systems above the molecular level, J. R. Soc. Interface 13, 20160555 (2016).
  14. E. O. Neftci and B. B. Averbeck, Reinforcement learning in artificial and biological systems, Nat. Mach. Intell. 1, 133 (2019).
  15. V. Vanchurin, Y. I. Wolf, M. I. Katsnelson, and E. V. Koonin, Toward a theory of evolution as multilevel learning, Proc. Natl. Acad. Sci. USA 119, e2120037119 (2022).
  16. T. Yamaguchi, Learning processes in hierarchical pairs regulate entire gene expression in cells, Sci. Rep. 12, 7549 (2022).
  17. K. B. Athreya and S. Karlin, Embedding of urn schemes into continuous time Markov branching processes and related limit theorems, Ann. Math. Stat. 39, 1801 (1968).
  18. J. L. Doob, Stochastic Processes (Wiley, New York, 1953).
  19. D. T. Gillespie, The chemical Langevin equation, J. Chem. Phys. 113, 297 (2000).
  20. T. Yamaguchi, S. Teraguchi, C. Furusawa, H. Machiyama, T. M. Watanabe, H. Fujita, S. Sakaguchi, and T. Yanagida, Theoretical modeling reveals that regulatory T cells increase T-cell interaction with antigen-presenting cells for stable immune tolerance, Int. Immunol. 31, 743 (2019).
  21. P. W. Reddien, The purpose and ubiquity of turnover, Cell 187, 2657 (2024).
  22. F. Black and M. Scholes, The pricing of options and corporate liabilities, J. Polit. Econ. 81, 637 (1973).
  23. M. Katori, Bessel Processes, Schramm–Loewner Evolution, and the Dyson Model, SpringerBriefs in Mathematical Physics (Springer, Singapore, 2016), Vol. 11, pp. 1–39.
  24. G. Eberl, S. Marmon, M. J. Sunshine, P. D. Rennert, Y. Choi, and D. R. Littman, An essential function for the nuclear receptor RORγt in the generation of fetal lymphoid tissue inducer cells, Nat. Immunol. 5, 64 (2004).
  25. A. Jarade, J. P. Di Santo, and N. Serafini, Group 3 innate lymphoid cells mediate host defense against attaching and effacing pathogens, Curr. Opin. Microbiol. 63, 83 (2021).
  26. S. Whitelam, Generative thermodynamic computing, Phys. Rev. Lett. 136, 037101 (2026).
  27. T. Yamaguchi, GitHub (2025), https://github.com/tyamaguc-tky/Martingale.

Outline

Information

Phys. Rev. Research 8, 023085– Published 29 April, 2026
  • Received 8 August 2025
  • Accepted 2 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