Optimal Prediction by Cellular Signaling Networks
Open accessAbstract
Living cells can enhance their fitness by anticipating environmental change. We study how accurately linear signaling networks in cells can predict future signals. We find that maximal predictive power results from a combination of input-noise suppression, linear extrapolation, and selective readout of correlated past signal values. Single-layer networks generate exponential response kernels, which suffice to predict Markovian signals optimally. Multilayer networks allow oscillatory kernels that can optimally predict non-Markovian signals. At low noise, these kernels exploit the signal derivative for extrapolation, while at high noise, they capitalize on signal values in the past that are strongly correlated with the future signal. We show how the common motifs of negative feedback and incoherent feed-forward can implement these optimal response functions. Simulations reveal that E. coli can reliably predict concentration changes for chemotaxis, and that the integration time of its response kernel arises from a trade-off between rapid response and noise suppression.
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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 [3]
The passage labeled Abstract describes optimizing predictive information over response kernels using a mean-squared prediction error, rather than applying Pontryagin’s minimum principle on probability-density-function space. Searches for Pontryagin’s principle, the stated variational condition, and Eq. (S4) found no passage in our copy that addresses the claimed derivation. (LLM, conf=0.76)
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- Authors
- Becker, N. B., Mugler, A., & ten Wolde, P. R.
- Affiliations
- Heidelberg University (DE)
- Purdue University West Lafayette (US)
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 2015-12-17
- Volume
- 115
- Issue
- 25
- Pages
- 258103-258103
- ISSN
- 0031-9007 (ISSN-L)
- 1079-7114
- OpenAlex
- W2195805964
- Cited by
- 63
- References
- 41
- Citations by year
- 2026: 3 · 2025: 9 · 2024: 5 · 2023: 3 · 2022: 1 · 2021: 9 · 2020: 5 · 2019: 12 · 2018: 6 · 2017: 5 · 2016: 5
- FWCI
- 2.31
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Physical Review Letters (publishedVersion)
- PubMed (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- AMOLF Institutional Repository (AMOLF) (submittedVersion)
- arXiv (Cornell University)
- Funders
- Stichting voor Fundamenteel Onderzoek der Materie
- Nederlandse Organisatie voor Wetenschappelijk Onderzoek
- Heidelberg Center for Modeling and Simulation in the Biosciences
- 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
- Life Sciences › Biochemistry, Genetics and Molecular Biology › Genetics › Bacterial Genetics and Biotechnology
- Keywords
- cellular signaling networks, signal prediction, response kernel, noise reduction, linear extrapolation, negative feedback, Escherichia coli chemotaxis
- MeSH terms
- Cell Physiological Phenomena, Chemotaxis, Computer Simulation, Escherichia coli, Markov Chains, Models, Biological, Signal Transduction
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 ›
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