Connection between the Bacterial Chemotactic Network and Optimal Filtering
Open accessAbstract
The chemotactic network of Escherichia coli has been studied extensively both biophysically and information theoretically. Nevertheless, connection between these two aspects is still elusive. In this work, we report such a connection. We derive an optimal filtering dynamics under the assumption that E. coli's sensory system optimally infers the binary information whether it is swimming up or down along an exponential ligand gradient from noisy sensory signals. Then we show that a standard biochemical model of the chemotactic network is mathematically equivalent to this information-theoretically optimal dynamics. Moreover, we demonstrate that an experimentally observed nonlinear response relation can be reproduced from the optimal dynamics. These results suggest that the biochemical network of E. coli chemotaxis is designed to optimally extract the binary information along an exponential gradient in a noisy condition.
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By 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 [5]
The cited paper’s discussion on p. 2 says it derives its dynamics by applying nonlinear filtering theory. Our copy does not mention Pontryagin’s minimum principle or applying it on probability-density-function space; searches for those terms and the stated optimality condition found no supporting passage. The citation is attached to the method, rather than to the citing paper’s Eq. (S4). (LLM, conf=0.73)
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References 60 · Cited by 19
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- Authors
- Nakamura, K., & Kobayashi, T. J.
- Affiliations
- The University of Tokyo (JP)
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 2021-03-23
- Volume
- 126
- Issue
- 12
- Pages
- 128102-128102
- ISSN
- 0031-9007 (ISSN-L)
- 1079-7114
- OpenAlex
- W3031304831
- Cited by
- 19
- References
- 60
- Citations by year
- 2026: 2 · 2025: 3 · 2024: 3 · 2023: 5 · 2022: 3 · 2021: 2 · 2020: 1
- FWCI
- 1.02
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Licence
- Locations
- Physical Review Letters (publishedVersion)
- PubMed (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Funders
- Japan Society for the Promotion of Science (19H05799, 20J21362)
- Japan Science and Technology Agency (JPMJCR2011)
- Topics
- Life Sciences › Biochemistry, Genetics and Molecular Biology › Molecular Biology › Gene Regulatory Network Analysis
- Life Sciences › Biochemistry, Genetics and Molecular Biology › Genetics › Bacterial Genetics and Biotechnology
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Advanced Thermodynamics and Statistical Mechanics
- Keywords
- bacterial chemotaxis, Escherichia coli, optimal filtering, information theory, biochemical network models, signal detection
- MeSH terms
- Chemotaxis, Escherichia coli, Models, Biological
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