Cellular Signaling Networks Function as Generalized Wiener-Kolmogorov Filters to Suppress Noise
Open accessAbstract
Cellular signaling involves the transmission of environmental information through cascades of stochastic biochemical reactions, inevitably introducing noise that compromises signal fidelity.Each stage of the cascade often takes the form of a kinase-phosphatase push-pull network, a basic unit of signaling pathways whose malfunction is linked with a host of cancers.We show that this ubiquitous enzymatic network motif effectively behaves as a Wiener-Kolmogorov optimal noise filter.Using concepts from umbral calculus, we generalize the linear Wiener-Kolmogorov theory, originally introduced in the context of communication and control engineering, to take nonlinear signal transduction and discrete molecule populations into account.This allows us to derive rigorous constraints for efficient noise reduction in this biochemical system.Our mathematical formalism yields bounds on filter performance in cases important to cellular function-such as ultrasensitive response to stimuli.We highlight features of the system relevant for optimizing filter efficiency, encoded in a single, measurable, dimensionless parameter.Our theory, which describes noise control in a large class of signal transduction networks, is also useful both for the design of synthetic biochemical signaling pathways and the manipulation of pathways through experimental probes such as oscillatory input.
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Reformulating 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 [2]
Section B, “Effects of nonlinearity and discrete populations” (page not provided), finds that the minimum signaling error is attained when the production-rate function R(I) has a linear form, under the stated optimality conditions. This supports the general point that a linear function can attain optimal performance in the paper’s model, but it does not establish that a control function of observation and memory, v*(y,z), is linear or that the citing paper’s reformulation leaves performance unchanged. (LLM, conf=0.78)
Experimental — accuracy not yet measuredThe 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 [2]
The 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 [2]
The theoretical-framework section maps a minimal signaling circuit to a Wiener–Kolmogorov noise filter, but does not introduce the claimed extended state, observation, control, or Wiener-process variables. Searches for those variables and for a linear-quadratic-Gaussian formulation found no supporting passage in our copy; no page numbers were provided. (LLM, conf=0.72)
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 [2]
Appendix B (Eqs. B1–B12; page not provided) derives signaling-error expressions from a stationary probability distribution, while Appendix A (Eqs. A2–A6; page not provided) solves a Wiener–Hopf equation. Searches for Pontryagin’s minimum principle and the claimed δJ/δu optimality condition found no passage addressing that method or Eq. (S4). (LLM, conf=0.76)
Experimental — accuracy not yet measuredIn 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 [2]
The citation is attached to the assertion that previous work numerically reported a nonmonotonic phase transition with respect to sensory uncertainty; the citing authors' analytical demonstration is not attributed to this source. The cited paper's section B, “Effects of nonlinearity and discrete populations” (page unavailable), discusses simulations of noise filtering in a biochemical signaling circuit, but no passage found for “nonmonotonic phase transition” or “sensory uncertainty” reports the cited result. (LLM, conf=0.76)
Experimental — accuracy not yet measured
Eq. (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 [2]
Appendix B discusses an operator equation labeled (B8), but does not identify an observation-based Riccati equation. Searches of our copy for “observation-based Riccati equation,” “Riccati,” and “Eq. (S6)” found no passage addressing the claimed name for Eq. (S6). (LLM, conf=0.75)
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- Authors
- Hinczewski, M., & Thirumalai, D.
- Affiliations
- University of Maryland, College Park (US)
- Venue
- Physical Review X
- Publisher
- American Physical Society (APS)
- Published
- 2014-10-29
- Volume
- 4
- Issue
- 4
- ISSN
- 2160-3308 (ISSN-L)
- OpenAlex
- W3022547592
- Cited by
- 30
- References
- 28
- Citations by year
- 2026: 1 · 2025: 2 · 2024: 1 · 2023: 2 · 2022: 1 · 2021: 4 · 2020: 4 · 2019: 5 · 2018: 3 · 2017: 2 · 2016: 3 · 2015: 2
- FWCI
- 0.96
- Type
- journal article
- Language
- en
- Open access
- gold
- doi.org
- Licence
- Locations
- Physical Review X (publishedVersion, cc-by)
- DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion, cc-by-sa)
- Funders
- National Science Foundation (NSF) (CHE13-61946)
- 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
- signal transduction, noise reduction, umbral calculus, ultrasensitive response, oscillatory input
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