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Accuracy of directional chemosensing via signaling cascades
Phys. Rev. E 114, 014402 – Published 6 July, 2026
DOI: https://doi.org/10.1103/wtrw-345p
Abstract
Cells interpret noisy biochemical signals with remarkable precision, raising fundamental questions about the limits of sensing. While receptor-level constraints in chemosensing are well characterized, the role of intracellular signaling remains underexplored. We develop a theoretical framework combining stochastic simulations and analytical methods to quantify the accuracy of spatial gradient detection via readout of the cellular response triggered by a linear signaling cascade. Our analysis reveals striking robustness: directional sensing accuracy is unaffected by cytoplasmic activation rates and remains stable under deactivation rates that are much faster or slower than the rest, a regime frequently observed in natural signaling cascades. This robustness persists under nonlinear output transformations that mimic amplification processes such as actin polymerization. Counterintuitively, under certain conditions, downstream readouts improve directional accuracy by extending the effective integration time set by intracellular dynamics.
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References (70)
- J. E. Segall, Polarization of yeast cells in spatial gradients of alpha mating factor, Proc. Natl. Acad. Sci. USA 90, 8332 (1993).
- T. I. Moore, C.-S. Chou, and T.-M. Yi, Robust spatial sensing of mating pheromone gradients by yeast cells, PLoS ONE 3, e3865 (2008).
- C. Darwin and F. Darwin, The Power of Movement in Plants (William Clowes and Sons, London, 1880).
- L. W. F Muthert, L. G. van Izzo, M. Zanten, and G. Aronne, Root tropisms: Investigations on Earth and in space to unravel plant growth direction, Front Plant Sci. 10, 1807 (2020).
- G. J. Goodhill, Can molecular gradients wire the brain? Trends Neurosci. 39, 202 (2016).
- E. T. Roussos, J. S. Condeelis, and A. Patsialou, Chemotaxis in cancer, Nat. Rev. Cancer 11, 573 (2011).
- M. Ueda and T. Shibata. Stochastic signal processing and transduction in chemotactic response of eukaryotic cells, Biophys. J. 93, 11 (2007).
- M. Ueda, Y. Sako, T. Tanaka, P. Devreotes, and T. Yanagida. Single-molecule analysis of chemotactic signaling in Dictyostelium cells, Science 294, 864 (2001).
- H. Mao, P. S. Cremer, and M. D. Manson, A sensitive, versatile microfluidic assay for bacterial chemotaxis, Proc. Natl. Acad. Sci. USA 100, 5449 (2003).
- R. G. Endres and N. S. Wingreen, Accuracy of direct gradient sensing by single cells, Proc. Natl. Acad. Sci. USA 105, 15749 (2008).
- B. Hu, W. Chen, W.-J. Rappel, and H. Levine, Physical limits on cellular sensing of spatial gradients, Phys. Rev. Lett. 105, 048104 (2010).
- J. Tian, Gradient sensing during chemotaxis, Curr. Opinion Cell Biol. 25, 532 (2013).
- J. Rode, and M. Novak, and B. M. Friedrich, Information theory of chemotactic agents using both spatial and temporal gradient sensing, PRX Life 2, 023012 (2024).
- P. Van Haastert and P. Devreotes, Chemotaxis: Signalling the way forward, Nat. Rev. Mol. Cell. Biol. 5, 626 (2004).
- J. M. Mato, A. Losada, V. Nanjundiah, and T. M. Konijn. Signal input for a chemotactic response in the cellular slime mold Dictyostelium discoideum, Proc. Natl. Acad. Sci. USA 72, 4991 (1975).
- P. J. M. van Haastert and M. Postma, Biased random walk by stochastic fluctuations of chemoattractant-receptor interactions at the lower limit of detection, Biophys. J. 93, 1787 (2007).
- D. Fuller, W. Chen, M. Adler, A. Groisman, H. Levine, W. Rappel, and W. F. Loomis, External and internal constraints on eukaryotic chemotaxis, Proc. Natl. Acad. Sci. USA 107, 9656 (2010).
- H. Berg and E. Purcell, Physics of chemoreception, Biophys. J. 20, 193 (1977).
- R. G. Endres and N. S. Wingreen, Maximum likelihood and the single receptor, Phys. Rev. Lett. 103, 158101 (2009).
- W. Bialek and S. Setayeshgar, Physical limits to biochemical signaling, Proc. Natl. Acad. Sci. USA 102, 10040 (2005).
- K. Kaizu, W. De Ronde, J. Paijmans, K. Takahashi, F. Tostevin, and P. R. Ten Wolde. The Berg-Purcell limit revisited, Biophys. J. 106, 976 (2014).
- K. Wang, W.-J. Rappel, R. Kerr, and H. Levine, Quantifying noise levels of intercellular signals, Phys. Rev. E 75, 061905 (2007).
- W. Bialek and S. Setayeshgar, Cooperativity, sensitivity, and noise in biochemical signaling, Phys. Rev. Lett. 100, 258101 (2008).
- M. Skoge, Y. Meir, and N. S. Wingreen, Dynamics of cooperativity in chemical sensing among cell-surface receptors, Phys. Rev. Lett. 107, 178101 (2011).
- M. Skoge, S. Naqvi, Y. Meir, and N. S. Wingreen, Chemical sensing by nonequilibrium cooperative receptors, Phys. Rev. Lett. 110, 248102 (2013).
- V. Wasnik, Limitations on concentration measurements and gradient discerning times in cellular systems, Phys. Rev. E 105, 034410 (2022).
- R. G. Endres and N. S. Wingreen, Accuracy of direct gradient sensing by cell-surface receptors, Prog. Biophys. Mol. Biol. 100, 33 (2009).
- A. Alonso, R. G. Endres, and J. B. Kirkegaard, Local clustering and global spreading of receptors for optimal spatial gradient sensing, Phys. Rev. Lett. 134, 158401 (2025).
- B. Hu, W. Chen, W.-J. Rappel, and H. Levine, How geometry and internal bias affect the accuracy of eukaryotic gradient sensing, Phys. Rev. E 83, 021917 (2011).
- K. Nakamura and T. J. Kobayashi, Gradient sensing limit of an elongated cell with orientational control, Phys. Rev. E 110, 064407 (2024).
- D. Mou and Y. Cao, Optimal cell shape for accurate chemical gradient sensing in eukaryote chemotaxis, Phys. Rev. Res. 7, 033001 (2025).
- M. Novak and B. M. Friedrich, Bayesian gradient sensing in the presence of rotational diffusion, New J. Phys. 23, 043026 (2021).
- A. J. Bernoff, A. Jilkine, A. N. Hernández, and A. E. Lindsay, Single-cell directional sensing from just a few receptor binding events, Biophys. J. 122, 3108 (2023).
- R. LeFebre, J. A. Landsittel, D. E. Stone, and A. Mugler, Role of signal degradation in directional chemosensing, Phys. Rev. Lett. 133, 138402 (2024).
- D. Ghose, T. Elston, and D. Lew, Orientation of cell polarity by chemical gradients, Annu. Rev. Biophys. 51, 431 (2022).
- R. Seger and E. G. Krebs, The MAPK signaling cascade, FASEB J. 9, 726 (1995).
- A. Munshi and R. Ramesh, Mitogen-activated protein kinases and their role in radiation response, Genes Cancer 4, 401 (2013).
- I. Wortzel and R. Seger, The ERK cascade: Distinct functions within various subcellular organelles, Genes Cancer 2, 195 (2011).
- C. C. Govern and P. R. ten Wolde, Fundamental limits on sensing chemical concentrations with linear biochemical networks, Phys. Rev. Lett. 109, 218103 (2012).
- C. C. Govern and P. R. ten Wolde, Energy dissipation and noise correlations in biochemical sensing, Phys. Rev. Lett. 113, 258102 (2014).
- C. C. Govern and P. R. ten Wolde, Optimal resource allocation in cellular sensing systems, Proc. Natl. Acad. Sci. USA 111, 17486 (2014).
- S. S. Biswal and V. Wasnik, Limitations to extracellular concentration sensing through signaling cascades, J. Stat. Mech. (2024) 073501.
- S. Biswal and V. Wasnik, Accuracy in readout of glutamate concentrations by neuronal cells, Eur. Phys. J. E 46, 30 (2023).
- T. Mora and I. Nemenman, Physical limit to concentration sensing in a changing environment, Phys. Rev. Lett. 123, 198101 (2019).
- G. Malaguti and P. R. ten Wolde, Theory for the optimal detection of time-varying signals in cellular sensing systems, eLife 10, e62574 (2021).
- W. Rappel and H. Levine, Receptor noise limitations on chemotactic sensing, Proc. Natl. Acad. Sci. USA 105, 19270 (2008).
- H. Levine, D. A. Kessler, and W. Rappel, Directional sensing in eukaryotic chemotaxis: A balanced inactivation model, Proc. Natl. Acad. Sci. USA 103, 9761 (2006).
- A. Levchenko and P. A. Iglesias, Models of eukaryotic gradient sensing: Application to chemotaxis of amoebae and neutrophils, Biophys. J. 82, 50 (2002).
- V. H. Wasnik, P. Lipp, and K. Kruse, Positional information readout in signaling, Phys. Rev. Lett. 123, 058102 (2019).
- V. H. Wasnik, P. Lipp, and K. Kruse, Accuracy of position determination in signaling, Phys. Rev. E 100, 022401 (2019).
- A. Alonso, J. B. Kirkegaard, and R. G. Endres, Persistent pseudopod splitting is an effective chemotaxis strategy in shallow gradients, Proc. Natl. Acad. Sci. USA 122, e2502368122 (2025).
- H. Reinhart, B. G. Neel, and T. A. Rapoport, Mathematical models of protein kinase signal transduction, Mol. Cell 9, 957 (2002).
- M. Chaves, E. D. Sontag, and R. J. Dinerstein, Optimal length and signal amplification in weakly activated signal transduction cascades, J. Phys. Chem. B 108, 15311 (2004).
- B.-D. Mariano, D. Radhika, and B. Mauricio. Linear models of activation cascades: Analytical solutions and coarse-graining of delayed signal transduction, J. R. Soc. Interface. 13, 20160409 (2016).
- H. Nunns and L. Goentoro, Signaling pathways as linear transmitters, eLife 7, e33617 (2018).
- D. A. Lauffenburger and J. J. Linderman, Receptors: Models for Binding, Trafficking, and Signaling (Oxford University Press, Oxford, 1992).
- B. Schoeberl, C. Eichler-Jonsson, E. Gilles, and G. Müller Computational modeling of the dynamics of the MAP kinase cascade activated by surface and internalized EGF receptors, Nat. Biotechnol. 20, 370 (2002).
- R. Cheong, A. Rhee, C. J. Wang, I. Nemenman, and A. Levchenko, Information transduction capacity of noisy biochemical signaling networks, Science 334, 354 (2011).
- M. Šoštar, M. Marinović, V. Filić, N. Pavin, and I. Weber, Oscillatory dynamics of Rac1 activity in Dictyostelium discoideum amoebae, PLoS Comput. Biol. 20, e1012025 (2024).
- L. Song, S. M. Nadkarni, H. U. Bödeker, C. Beta, A. Bae, C. Franck, W. J. Rappel, W. F. Loomis, and E. Bodenschatz, Dictyostelium discoideum chemotaxis: Threshold for directed motion, Eur. J. Cell Biol. 85, 981 (2006).
- A. Kortholt, I. Keizer-Gunnink, R. Kataria, and P. J. M. Van Haastert, Ras activation and symmetry breaking during Dictyostelium chemotaxis, J. Cell Sci. 126, 4502 (2013).
- T. M. Cover and J. A. Thomas, Elements of Information Theory, 2nd ed. (Wiley-Interscience, Hoboken, NJ, 2006).
- H. A. El-Masri and C. J. Portier, Replication potential of cells via the protein kinase C-MAPK pathway: Application of a mathematical model, Bull. Math. Biol. 61, 379 (1999).
- W. H. de Ronde, F. Tostevin, and P. R. ten Wolde, Effect of feedback on the fidelity of information transmission of time-varying signals, Phys. Rev. E 82, 031914 (2010).
- C. J. Bashor, A. A. Horwitz, S. G. Peisajovich, and W. A. Lim. Rewiring cells: Synthetic biology as a tool to interrogate the organizational principles of living systems, Annu. Rev. Biophys. 39, 515 (2010).
- J. M. Raser and E. K. O' Shea, Control of stochasticity in eukaryotic gene expression, Science 304, 1811 (2004).
- N. Rosenfeld, J. W. Young, U. Alon, P. S. Swain, and M. B. Elowitz, Gene regulation at the single-cell level, Science 307, 1962 (2005).
- G. B. Arfken and H. J. Weber, Mathematical Methods for Physicists, 6th ed. (Academic Press, Burlington, MA, 2005).
- D. T. Gillespie, Exact stochastic simulation of coupled chemical reactions, J. Phys. Chem. 81, 2340 (1977).
- R. Erban and S. J. Chapman, Stochastic Modelling of Reaction–Diffusion Processes (Cambridge University Press, 2020).