Implementation of Dynamic Bayesian Decision Making by Intracellular Kinetics
Open accessAbstract
Decision making in a noisy and dynamically changing environment is a fundamental task for a cell. To choose appropriate decisions over time, a cell must be equipped with intracellular kinetics that can conduct dynamic and efficient decision making. By using the theory of sequential inference, I demonstrate that dynamic Bayesian decision making can be implemented by an intracellular kinetics with a dual positive feedback structure. I also show that the combination of linear instantaneous and nonlinear stationary sensitivities to the input dominantly contributes to decision making efficiency, and that the state-dependent sensitivity change further suppresses noisy response. The statistical principles underlying these two factors are further clarified to be a log-likelihood-dependent quantification of the input information and uncertainty-dependent sensitivity control.
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The previous work investigated Eqs. (S5) and (S6) numerically.
“Therefore, the previous work investigated them numerically [1, 2].”
From Theoretical Analysis of Resource-Induced Phase Transitions in Estimation Strategies (2026) · cites this paper as [1]
The paper numerically compares the responses and error rates of several intracellular kinetics (Figs. 1–2, pp. 228104-2–3). Our copy does not identify the citing document’s Eqs. (S5) and (S6), so it cannot establish that those specific equations were investigated. (LLM, conf=0.72)
Experimental — accuracy not yet measuredThe previous work introduced extended state, observation, control, and standard Wiener process variables and transformed the minimal model into a linear-quadratic-Gaussian problem in optimal control theory.
“The previous work introduced the following extended variables: extended state ˜ x t , extended observation ˜ y t , extended control ˜ u t , and extended standard Wiener process ˜ ω t .”
From Theoretical Analysis of Resource-Induced Phase Transitions in Estimation Strategies (2026) · cites this paper as [1]
The paper describes a two-state environmental model, noisy receptor observations, and sequential Bayesian inference (section labeled Abstract), but the passages do not introduce the claimed extended state, observation, control, or Wiener-process variables. Searches for those variables and for a linear-quadratic-Gaussian control formulation found no supporting passage in our copy. (LLM, conf=0.76)
Experimental — accuracy not yet measuredBy employing Pontryagin's minimum principle on the probability density function space, the solution satisfying the optimality condition δJ/δu = 0 is given by Eq. (S4).
“By employing Pontryagin's minimum principle on the probability density function space [1-9], the solution that satisfies the optimality condition δ ˜ J/δ ˜ u = 0 is given by”
From Theoretical Analysis of Resource-Induced Phase Transitions in Estimation Strategies (2026) · cites this paper as [1]
The passage describing the derivation of Bayesian kinetics (section labeled Abstract, page not given) uses sequential Bayesian inference, not Pontryagin’s minimum principle. Searches for Pontryagin’s principle and the stated optimality condition found no passage in our copy addressing the claimed derivation or Eq. (S4). (LLM, conf=0.77)
Experimental — accuracy not yet measuredEq. (S6) is referred to as the observation-based Riccati equation.
“Eq. (S6) is referred to as the observation-based Riccati equation [1, 2].”
From Theoretical Analysis of Resource-Induced Phase Transitions in Estimation Strategies (2026) · cites this paper as [1]
The passage defining the dynamics calls them “Bayesian kinetics” (section labeled Abstract, page not given), and another presents Eq. (2) without calling it a Riccati equation. Searches for “observation-based Riccati equation,” “Riccati,” and “S6” found no passage in our copy that establishes the claimed name for Eq. (S6). (LLM, conf=0.72)
Experimental — accuracy not yet measuredReformulating the control function as a linear function of observation and memory does not degrade performance because the optimal control function is given by a linear function.
“This reformulation does not degrade performance because the optimal control function v ∗ ( y, z ) [Eq. (S10)] is given by the following linear function:”
From Theoretical Analysis of Resource-Induced Phase Transitions in Estimation Strategies (2026) · cites this paper as [1]
The discussion of Eq. (2) describes Bayesian inference kinetics with linear instantaneous sensitivity to receptor input, but it does not give an optimal control function linear in observation and memory. Searches for an optimal control function and for a performance-preserving linear reformulation found no passage addressing that claim. (LLM, conf=0.76)
Experimental — accuracy not yet measured
In the main text, the nonmonotonic phase transition with respect to sensory uncertainty was analytically demonstrated, and it has also been reported numerically in previous work.
“In the main text, we analytically demonstrated the nonmonotonic phase transition with respect to sensory uncertainty, which has also been reported numerically in our previous work [1, 2].”
From Theoretical Analysis of Resource-Induced Phase Transitions in Estimation Strategies (2026) · cites this paper as [1]
The discussion around p. 228104-2 concerns sensitivity to noisy input, and p. 228104-3 concerns how much information receptor signals carry about the environment. Neither passage reports a numerical nonmonotonic phase transition with respect to sensory uncertainty; searches for that phrase and related terms found no such result in our copy. (LLM, conf=0.74)
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- See supplementary material at http://link.aps.org/ supplemental/10.1103/PhysRevLett.104.228104 for the detail of the derivation of the BA kinetics.
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Self-citation
- Authors
- Kobayashi, T. J.
- Affiliations
- Institute of Industrial Science, The University of Tokyo (JP)
- Corresponding author
- Kobayashi, Tetsuya J.
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 2010-06-03
- Volume
- 104
- Issue
- 22
- Pages
- 228104-228104
- ISSN
- 0031-9007 (ISSN-L)
- 1079-7114
- OpenAlex
- W2006510894
- Cited by
- 68
- References
- 31
- Citations by year
- 2026: 2 · 2025: 5 · 2024: 3 · 2023: 1 · 2022: 1 · 2021: 3 · 2020: 4 · 2019: 4 · 2018: 3 · 2017: 9 · 2016: 9 · 2015: 4 · 2014: 4 · 2013: 5 · 2012: 4
- FWCI
- 2.08
- Type
- journal article
- Language
- en
- Open access
- hybrid
- doi.org
- Licence
- Locations
- Physical Review Letters (publishedVersion, cc-by)
- PubMed (publishedVersion)
- Topics
- Life Sciences › Biochemistry, Genetics and Molecular Biology › Molecular Biology › Gene Regulatory Network Analysis
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › stochastic dynamics and bifurcation
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Advanced Thermodynamics and Statistical Mechanics
- Keywords
- sequential inference, noise reduction, cell decision-making, stochastic gene expression
- MeSH terms
- Bayes Theorem, Kinetics, Models, Biological, Feedback, Physiological, Intracellular Space
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