Physical Limit to Concentration Sensing in a Changing Environment
Open accessPublished version of a preprint
Abstract
Cells adapt to changing environments by sensing ligand concentrations using specific receptors. The accuracy of sensing is ultimately limited by the finite number of ligand molecules bound by receptors. Previously derived physical limits to sensing accuracy largely have assumed that the concentration was constant and ignored its temporal fluctuations. We formulate the problem of concentration sensing in a strongly fluctuating environment as a nonlinear field-theoretic problem, for which we find an excellent approximate Gaussian solution. We derive a new physical bound on the relative error in concentration c which scales as δc/c∼(Dacτ)^{-1/4} with ligand diffusivity D, receptor cross section a, and characteristic fluctuation timescale τ, in stark contrast to the usual Berg and Purcell bound δc/c∼(DacT)^{-1/2} for a perfect receptor sensing concentration during time T. We show how the bound can be achieved by a biochemical network downstream of the receptor that adapts the kinetics of signaling as a function of the square root of the sensed concentration.
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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 [4]
The Gaussian solution section derives an approximate posterior using a Gaussian ansatz, and Additional information derives posterior-evolution equations. Searches for Pontryagin’s minimum principle, the optimality condition δJ/δu = 0, and Eq. (S4) found no passage connecting this paper to the attributed method or solution. Page numbers are unavailable in our copy. (LLM, conf=0.73)
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References 28 · Cited by 49
Research works printed but not linked: 20
- H. C. Berg and E. M. Purcell, Biophys. J. 20, 193 (1977).
- W. Bialek and S. Setayeshgar, Proc. Natl. Acad. Sci. U. S. A. 102, 10040 (2005).
- K. Kaizu, W. De Ronde, J. Paijmans, K. Takahashi, F. Tostevin, P. R. T. Wolde, and P. R. ten Wolde, Bio- phys. J. 106, 976 (2014).
- G. Aquino, N. S. Wingreen, and R. G. Endres, J. Stat. Phys. 162, 1353 (2016).
- R. G. Endres and N. S. Wingreen, Phys. Rev. Lett. 103, 158101 (2009).
- E. D. Siggia and M. Vergassola, Proc. Natl. Acad. Sci.
- U. S. A. 110, E3704 (2013).
- J.-B. Lalanne and P. François, Proc. Natl. Acad. Sci. 112, 1898 (2015).
- T. Mora, Phys. Rev. Lett. 115, 038102 (2015).
- V. Singh and I. Nemenman, PLoS Comput. Biol. 13, 1 (2017).
- V. Singh and I. Nemenman, arXiv:1906.08881 (2019). · arXiv
- E. Kussell and S. Leibler, Science 309, 2075 (2005).
- T. Mora and N. S. Wingreen, Phys. Rev. Lett. 104, 1 (2010).
- Z. H. E. Chen, Statistics 182, 1 (2003).
- W. Bialek, C. Callan, and S. Strong, Phys. Rev. Lett. 77, 4693 (1996).
- I. Nemenman and W. Bialek, Phys. Rev. E 65, 2 (2002).
- W. C. Chen, A. Tareen, and J. B. Kinney, Phys. Rev. Lett. 121, 160605 (2018).
- A. Kolmogoroff, C. R. Acad. Sci. Paris 208, 2043 (1939).
- L. Goentoro, O. Shoval, M. W. Kirschner, and U. Alon, Mol. Cell 36, 894 (2009).
- M. D. Lazova, T. Ahmed, D. Bellomo, R. Stocker, and T. S. Shimizu, Proc. Natl. Acad. Sci. U. S. A. 108, 13870 (2011).
- Authors
- Mora, T., & Nemenman, I.
- Affiliations
- Centre National de la Recherche Scientifique (FR)
- Emory University (US)
- Corresponding author
- Mora, Thierry
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 2019-11-05
- Volume
- 123
- Issue
- 19
- Pages
- 198101-198101
- ISSN
- 0031-9007 (ISSN-L)
- 1079-7114
- OpenAlex
- W2967038867
- Cited by
- 49
- References
- 28
- Citations by year
- 2026: 8 · 2025: 5 · 2024: 9 · 2023: 5 · 2022: 6 · 2021: 8 · 2020: 8
- FWCI
- 1.82
- Type
- journal article
- Language
- en
- Open access
- green
- doi.org
- Locations
- Physical Review Letters (publishedVersion)
- bioRxiv (Cold Spring Harbor Laboratory) (acceptedVersion)
- PubMed (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- HAL (submittedVersion)
- arXiv (Cornell University)
- Funders
- Agence Nationale de la Recherche (ANR-17-ERC2-0025-01)
- National Science Foundation (PHY-1410978, IOS-1822677)
- 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
- concentration sensing, ligand-receptor interactions, nonlinear field theory, Gaussian approximation, error scaling
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