CoChat
Sign Up
Cited by 6Advanced Thermodynamics and Statistical MechanicsComplex Systems and DynamicsGene Regulatory Network Analysis

Theory for optimal estimation and control under resource limitations and its applications to biological information processing and decision-making

Open access
Tottori, Takehiro, Kobayashi, Tetsuya J.·2025·Physical Review Research
DOI 10.1103/gvl6-cvby

Published version of a preprint

Open this paper in CoChat — free account

Abstract

While the information processing of organisms is evolutionarily optimized, it exhibits remarkable diversity in its complexity and capability. One potential source of this diversity is the limitations of resources available for information processing. However, we still lack a theoretical framework that clarifies the relationship between biological information processing and resource limitations and integrates it with downstream decision-making. Together with the accompanying letter [Tottori and Kobayashi, ], this full paper presents an optimal estimation and control framework that explicitly incorporates resource limitations inherent in biological systems. While the accompanying letter focuses on the nontrivial phase transitions induced by resource limitations, the present full paper establishes the theoretical foundation and provides a comprehensive analysis of these transitions. The proposed framework formulates memory that organisms can store and operate, and optimizes it using optimal control theory. This approach accounts for various resource limitations—such as memory capacity, intrinsic noise, and energy cost—and unifies estimation and control. Applying this theory to minimal models of biological information processing and decision-making, we demonstrate that resource limitations can induce discontinuous and nonmonotonic phase transitions between memoryless and memory-based strategies. These results provide a comprehensive theoretical foundation for studying how organisms process information and make decisions under resource limitations, and suggest that the rich diversity observed in biological systems may emerge from such constraints.

The claims and statistics of this paper haven’t been checked yet.

Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.

A few free checks a day · papers already verified open instantly · results are public

Integrity signals

Registry

Crossref · 10.1103/gvl6-cvby

Cites

189 of 189 references verified0 citation errors · 0 not checkable

Statistics

Claims the paper makes

The claims and statistics of this paper haven’t been checked yet.

Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.

A few free checks a day · papers already verified open instantly · results are public

Self-check

Percentages, sums and reported differences re-computed from the paper’s own numbers.

The self-check needs the paper’s full text.

Cites

Flagged first, then by citations

Research works printed but not linked: 75

  1. [5]J. Burge, M. O. Ernst, and M. S. Banks, Journal of Vision 8 , 20 (2008).
  2. [6]W. Bialek and S. Setayeshgar, Proceedings of the National Academy of Sciences 102 , 10040 (2005).
  3. [7]A. Celani and M. Vergassola, Proceedings of the National Academy of Sciences 107 , 1391 (2010).
  4. [8]H. H. Mattingly, K. Kamino, B. B. Machta, and T. Emonet, Nature Physics pp. 1-6 (2021).
  5. [9]K. Nakamura and T. J. Kobayashi, Physical Review Letters 126 , 128102 (2021).
  6. [10]K. Nakamura and T. J. Kobayashi, Physical Review Research 4 , 013120 (2022).
  7. [14]J. E. Niven and S. B. Laughlin, Journal of Experimental Biology 211 , 1792 (2008).
  8. [18]K. Isler and C. P. van Schaik, Biology Letters 2 , 557 (2006).
  9. [19]K. Fonseca-Azevedo and S. Herculano-Houzel, Proceedings of the National Academy of Sciences 109 , 18571 (2012).
  10. [20]V. Balasubramanian, Proceedings of the National Academy of Sciences 118 , e2107022118 (2021).
  11. [22]P. S. Swain, M. B. Elowitz, and E. D. Siggia, Proceedings of the National Academy of Sciences 99 , 12795 (2002).
  12. [26]T. Shibata and K. Fujimoto, Proceedings of the National Academy of Sciences 102 , 331 (2005).
  13. [27]M. Ueda and T. Shibata, Biophysical Journal 93 , 11 (2007).
  14. [29]C. C. Govern and P. R. ten Wolde, Proceedings of the National Academy of Sciences 111 , 17486 (2014).
  15. [30]C. C. Govern and P. R. ten Wolde, Physical Review Letters 113 , 258102 (2014).
  16. [31]A. H. Lang, C. K. Fisher, T. Mora, and P. Mehta, Physical Review Letters 113 , 148103 (2014).
  17. [32]S. J. Bryant and B. B. Machta, Physical Review Letters 131 , 068401 (2023).
  18. [33]S. E. Harvey, S. Lahiri, and S. Ganguli, Physical Review E 108 , 014403 (2023).
  19. [34]N. Ohga, S. Ito, and A. Kolchinsky, Physical Review Letters 131 , 077101 (2023).
  20. [45]R. D. Lange, S. Shivkumar, A. Chattoraj, and R. M. Haefner, Nature Neuroscience pp. 1-10 (2023).
  21. [46]S. Den` eve, J.-R. Duhamel, and A. Pouget, Journal of Neuroscience 27 , 5744 (2007).
  22. [48]N. Hiratani and T. Fukai, Proceedings of the National Academy of Sciences 115 , E6871 (2018).
  23. [51]A. Kutschireiter, M. A. Basnak, R. I. Wilson, and J. Drugowitsch, Proceedings of the National Academy of Sciences 120 , e2210622120 (2023).
  24. [53]T. J. Kobayashi, Physical Review Letters 104 , 228104 (2010).
  25. [54]M. Hinczewski and D. Thirumalai, Physical Review X 4 , 041017 (2014).
  26. [56]T. Mora and I. Nemenman, Physical Review Letters 123 , 198101 (2019).
  27. [58]M. Novak and B. M. Friedrich, New Journal of Physics 23 , 043026 (2021).
  28. [59]A. Auconi, M. Novak, and B. M. Friedrich, Europhysics Letters 138 , 12001 (2022).
  29. [67]R. Dukas, Journal of Theoretical Biology 197 , 41 (1999).
  30. [68]F. Mery and T. J. Kawecki, Proceedings of the Royal Society of London. Series B: Biological Sciences 270 , 2465 (2003).
  31. [72]J. G. Burns, J. Foucaud, and F. Mery, Proceedings of the Royal Society B: Biological Sciences 278 , 923 (2010).
  32. [74]G. Chechik, A. Globerson, N. Tishby, and Y. Weiss, Journal of Machine Learning Research 6 , 165 (2005).
  33. [75]F. Creutzig, A. Globerson, and N. Tishby, Physical Review E 79 , 041925 (2009).
  34. [77]R. Fox and N. Tishby, in 2016 IEEE 55th Conference on Decision and Control (CDC) (2016), pp. 5603-5609.
  35. [79]A. J. Tjalma, V. Galstyan, J. Goedhart, L. Slim, N. B. Becker, and P. R. ten Wolde, Proceedings of the National Academy of Sciences 120 , e2303078120 (2023).
  36. [86]W. M. Wonham, SIAM Journal on Control 6 , 312 (1968).
  37. [87]M. H. A. Davis and P. Varaiya, SIAM Journal on Control 11 , 226 (1973).
  38. [90]M. Nisio, Stochastic Control Theory , vol. 72 of Probability Theory and Stochastic Modelling (Springer Japan, Tokyo, 2015), ISBN 978-4-431-55122-5 978-4-431-551232.
  39. [92]G. Wang, Z. Wu, and J. Xiong, An Introduction to Optimal Control of FBSDE with Incomplete Information , SpringerBriefs in Mathematics (Springer International Publishing, Cham, 2018), ISBN 978-3-319-79038-1 9783-319-79039-8.
  40. [94]W. Li and E. Todorov, International Journal of Control 80 , 1439 (2007).
  41. [95]K. V. B. Verano, E. Panizon, and A. Celani, Proceedings of the National Academy of Sciences 120 , e2304230120 (2023).
  42. [99]A. Bensoussan, J. Frehse, and S. C. P. Yam, Journal de Math´ ematiques Pures et Appliqu´ ees 103 , 1441 (2015).
  43. [101]R. Carmona and F. Delarue, Probabilistic Theory of Mean Field Games with Applications I , no. volume 83 in Probability theory and stochastic modelling (Springer Nature, Cham, 2018), ISBN 978-3-319-56437-1 978-3030-13260-6.
  44. [102]R. Carmona and F. Delarue, Probabilistic Theory of Mean Field Games with Applications II , vol. 84 of Probability Theory and Stochastic Modelling (Springer International Publishing, Cham, 2018), ISBN 978-3-31956435-7 978-3-319-56436-4.
  45. [103]R. E. Kalman, Journal of Basic Engineering 82 , 35 (1960).
  46. [107]R. A. Heinonen, L. Biferale, A. Celani, and M. Vergassola, Physical Review E 107 , 055105 (2023).
  47. [110]O. B´ enichou, M. Coppey, M. Moreau, P.-H. Suet, and R. Voituriez, Physical Review Letters 94 , 198101 (2005).
  48. [113]A. M. Hein, F. Carrara, D. R. Brumley, R. Stocker, and S. A. Levin, Proceedings of the National Academy of Sciences 113 , 9413 (2016).
  49. [115]M. Monti, D. K. Lubensky, and P. R. ten Wolde, Physical Review Letters 121 , 078101 (2018).
  50. [117]M. Seki and H. Ito, Proceedings of the Royal Society B: Biological Sciences 289 , 20220577 (2022).
  51. [119]H. Iwasaki, T. Nishiwaki, Y. Kitayama, M. Nakajima, and T. Kondo, Proceedings of the National Academy of Sciences 99 , 15788 (2002).
  52. [123]V. Dvornyk, O. Vinogradova, and E. Nevo, Proceedings of the National Academy of Sciences 100 , 2495 (2003).
  53. [124]J. Holtzendorff, F. Partensky, D. Mella, J.-F. Lennon, W. R. Hess, and L. Garczarek, Journal of Biological Rhythms 23 , 187 (2008).
  54. [125]I. M. Axmann, U. D¨ uhring, L. Seeliger, A. Arnold, J. T. Vanselow, A. Kramer, and A. Wilde, Journal of Bacteriology 191 , 5342 (2009).
  55. [126]C. W. Mullineaux and R. Stanewsky, Journal of Bacteriology 191 , 5333 (2009).
  56. [129]P. Flombaum, J. L. Gallegos, R. A. Gordillo, J. Rinc´ on, L. L. Zabala, N. Jiao, D. M. Karl, W. K. W. Li, M. W. Lomas, D. Veneziano, et al., Proceedings of the National Academy of Sciences 110 , 9824 (2013).
  57. [131]M. Muraven, D. M. Tice, and R. F. Baumeister, Journal of Personality and Social Psychology 74 , 774 (1998).
  58. Tchou , edited by Y. Achdou, G. Barles, H. Ishii, and G. L. Litvinov (Springer, Berlin, Heidelberg, 2013), Lecture Notes in Mathematics, pp. 1-47, ISBN 978-3-64236433-4.
  59. [138]Y. Achdou and M. Lauri` ere, in Mean Field Games: Cetraro, Italy 2019 , edited by Y. Achdou, P. Cardaliaguet, F. Delarue, A. Porretta, F. Santambrogio, P. Cardaliaguet, and A. Porretta (Springer International Publishing, Cham, 2020), Lecture Notes in Mathematics, pp. 249-307, ISBN 978-3-030-59837-2.
  60. [140]L. Ruthotto, S. J. Osher, W. Li, L. Nurbekyan, and S. W. Fung, Proceedings of the National Academy of Sciences 117 , 9183 (2020).
  61. [141]A. T. Lin, S. W. Fung, W. Li, L. Nurbekyan, and S. J. Osher, Proceedings of the National Academy of Sciences 118 (2021).
  62. [143]H. Cao, X. Guo, and M. Lauri` ere, SIAM Journal on Applied Mathematics pp. 1255-1287 (2024).
  63. [146]Y. Hasegawa, Physical Review E 97 , 022401 (2018).
  64. [147]L. Hahn, A. M. Walczak, and T. Mora, Physical Review Letters 131 , 128401 (2023).
  65. [149]L. van der Maaten, E. Postma, and H. Herik, Journal of Machine Learning Research - JMLR 10 (2007).
  66. [151]S. Fancher and A. Mugler, Physical Review Letters 118 , 078101 (2017).
  67. [152]J. Varennes, S. Fancher, B. Han, and A. Mugler, Physical Review Letters 119 , 188101 (2017).
  68. Physical Review Letters 125 , 048103 (2020).
  69. [154]M. Vennettilli, A. Erez, and A. Mugler, Physical Review E 102 , 052411 (2020).
  70. [156]A. Pezzotta, M. Adorisio, and A. Celani, Physical Review E 98 , 042401 (2018).
  71. [157]M. Durve, L. Piro, M. Cencini, L. Biferale, and A. Celani, Physical Review E 102 , 012402 (2020).
  72. [158]F. Borra, M. Cencini, and A. Celani, Journal of Statistical Mechanics: Theory and Experiment 2021 , 083401 (2021).
  73. [160]H. Kushner, IRE Transactions on Automatic Control 7 , 120 (1962).
  74. [165]J. A. Sharp, K. Burrage, and M. J. Simpson, Journal of The Royal Society Interface 18 , 20210241 (2021).
  75. [167]E. Carlini and F. J. Silva, SIAM Journal on Numerical Analysis 52 , 45 (2014).

Cited by

Sorted by citations

Related

Authors
Tottori, T., & Kobayashi, T. J.
Affiliations
  • RIKEN Center for Brain Science (JP)
  • The University of Tokyo (JP)
Corresponding author
Tottori, Takehiro
ORCID
Venue
Physical Review Research
Publisher
American Physical Society (APS)
Published
2025-10-14
Volume
7
Issue
4
ISSN
2643-1564 (ISSN-L)
DOI
10.1103/gvl6-cvby
OpenAlex
W4415177572
Cited by
6
References
189
Citations by year
2026: 4 · 2025: 2
FWCI
2.47
Type
journal article
Language
en
Open access
Licence
Locations
  • Physical Review Research (publishedVersion, cc-by)
  • arXiv (Cornell University) (submittedVersion, cc-by)
  • DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion, cc-by-sa)
  • arXiv (Cornell University) (cc-by)
Funders
  • Japan Society for the Promotion of Science (22KJ0557, 19H05799, 24H02148, 24H01465, 25H01365)
  • Japan Science and Technology Agency (JPMJAX24LB, JPMJCR2011)
Topics
  • Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Advanced Thermodynamics and Statistical Mechanics
  • Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Complex Systems and Dynamics
  • Life Sciences › Biochemistry, Genetics and Molecular Biology › Molecular Biology › Gene Regulatory Network Analysis
Keywords
resource constraints, biological information processing, decision-making, optimal estimation, optimal control, memory capacity, intrinsic noise, energy costs, phase transitions, minimal models, evolutionary optimization

About these checks

Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.

Statistics and arithmetic are recomputed, not judged.

Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.

What counts as a claim ›How we measure confidence ›How we check this ›

Are you an author, or do you see a problem with this page? Request a review