- Physical Review Journals
All JournalsPhysics Magazine

PRX Life

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

You ain't Seen Nothing and Yet: Future Biochemical Concentrations can be Predicted with Surprisingly High Accuracy

Ketevan Danelia1, Sean A. Ridout2, and Ilya Nemenman3

  • 1Department of Physics, Emory University, Atlanta, Georgia 30322, USA
  • 2Department of Physics and Initiative for Theory and Modeling of Living Systems, Emory University, Atlanta, Georgia 30322, USA
  • 3Department of Physics, Department of Biology, and Initiative for Theory and Modeling of Living Systems, Emory University, Atlanta, Georgia 30322, USA

PDF

PRX Life 4, 033008 – Published 29 July, 2026

DOI: https://doi.org/10.1103/b6b7-s4hx

Abstract

Accurate sensing of chemical concentrations is essential for numerous biological processes. The accuracy of this sensing, for small numbers of molecules, is limited by shot noise. Corresponding theoretical limits on sensing precision, as a function of sensing duration, have been well studied in the context of quasistatic and randomly fluctuating concentrations. However, during development and in many other cases, concentration profiles are not random but exhibit predictable spatiotemporal patterns. We propose that leveraging prior knowledge of these structured profiles can improve and accelerate concentration sensing by utilizing information from current molecular binding events to predict future concentrations. By framing the constrained sensing problem as Bayesian inference over an allowed class of spatiotemporal profiles, we derive new theoretical limits on sensing accuracy. Our analysis reveals that maximum a posteriori estimation can outperform the classical Berg-Purcell and maximum-likelihood (Poisson counting) limits, achieving a sensing precision of δc/c=1/a2N, where N is the number of binding events, and a>1 in certain cases. Thus knowledge of the statistical structure of concentration profiles enhances sensing precision, providing a potential explanation for the rapid yet highly accurate cell fate decisions observed during development.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (54)

  1. G. Tkačik and W. Bialek, Information processing in living systems, Annu. Rev. Condens. Matter Phys. 7, 89 (2016).
  2. I. M. De la Fuente, L. Martínez, J. Carrasco-Pujante, M. Fedetz, J. I. López, and I. Malaina, Self-organization and information processing: From basic enzymatic activities to complex adaptive cellular behavior, Front. Genet. 12, 644615 (2021).
  3. A. Levchenko and I. Nemenman, Cellular noise and information transmission, Curr. Opin. Biotechnol. 28, 156 (2014).
  4. W. Driever and C. Nüsslein-Volhard, A gradient of Bicoid protein in Drosophila embryos, Cell 54, 83 (1988).
  5. M. J. Berridge, P. Cobbold, and K. Cuthbertson, Spatial and temporal aspects of cell signalling, Philos. Trans. Roy. Soc. Lond. B, Biol Sci. 320, 325 (1988).
  6. P. Niethammer, C. Grabher, A. T. Look, and T. J. Mitchison, A tissue-scale gradient of hydrogen peroxide mediates rapid wound detection in zebrafish, Nature (London) 459, 996 (2009).
  7. O. Atay and J. M. Skotheim, Spatial and temporal signal processing and decision making by MAPK pathways, J. Cell Biol. 216, 317 (2017).
  8. H. C. Berg and E. M. Purcell, Physics of chemoreception, Biophys. J. 20, 193 (1977).
  9. R. G. Endres and N. S. Wingreen, Maximum likelihood and the single receptor, Phys. Rev. Lett. 103, 158101 (2009).
  10. W. Bialek and S. Setayeshgar, Physical limits to biochemical signaling, Proc. Natl. Acad. Sci. USA 102, 10040 (2005).
  11. 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).
  12. R. G. Endres and N. S. Wingreen, Accuracy of direct gradient sensing by cell-surface receptors, Prog. Biophys. Mol. Biol. 100, 33 (2009).
  13. B. Hu, W. Chen, W.-J. Rappel, and H. Levine, Physical limits on cellular sensing of spatial gradients, Phys. Rev. Lett. 105, 048104 (2010).
  14. D. Ellison, A. Mugler, M. D. Brennan, S. H. Lee, R. J. Huebner, E. R. Shamir, L. A. Woo, J. Kim, P. Amar, I. Nemenman, et al., Cell–cell communication enhances the capacity of cell ensembles to sense shallow gradients during morphogenesis, Proc. Natl. Acad. Sci. USA 113, E679 (2016).
  15. A. Mugler, A. Levchenko, and I. Nemenman, Limits to the precision of gradient sensing with spatial communication and temporal integration, Proc. Natl. Acad. Sci. USA 113, E689 (2016).
  16. T. Mora and N. S. Wingreen, Limits of sensing temporal concentration changes by single cells, Phys. Rev. Lett. 104, 248101 (2010).
  17. T. Mora and I. Nemenman, Physical limit to concentration sensing in a changing environment, Phys. Rev. Lett. 123, 198101 (2019).
  18. V. Singh, M. Tchernookov, and I. Nemenman, Effects of receptor correlations on molecular information transmission, Phys. Rev. E 94, 022425 (2016).
  19. E. D. Siggia and M. Vergassola, Decisions on the fly in cellular sensory systems, Proc. Natl. Acad. Sci. USA 110, E3704 (2013).
  20. J. Desponds, M. Vergassola, and A. M. Walczak, A mechanism for Hunchback promoters to readout morphogenetic positional information in less than a minute, eLife 9, e49758 (2020).
  21. 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).
  22. M. Novak and B. M. Friedrich, Bayesian gradient sensing in the presence of rotational diffusion, New J. Phys. 23, 043026 (2021).
  23. G. Malaguti and P. R. Ten Wolde, Theory for the optimal detection of time-varying signals in cellular sensing systems, eLife 10, e62574 (2021).
  24. P. Sartori and Y. Tu, Noise filtering strategies in adaptive biochemical signaling networks: Application to E. coli chemotaxis, J. Stat. Phys. 142, 1206 (2011).
  25. T. Smith, S. Fancher, A. Levchenko, I. Nemenman, and A. Mugler, Role of spatial averaging in multicellular gradient sensing, Phys. Biol. 13, 035004 (2016).
  26. V. Singh and I. Nemenman, Simple biochemical networks allow accurate sensing of multiple ligands with a single receptor, PLoS Comput. Biol. 13, e1005490 (2017).
  27. M. Carballo-Pacheco, J. Desponds, T. Gavrilchenko, A. Mayer, R. Prizak, G. Reddy, I. Nemenman, and T. Mora, Receptor crosstalk improves concentration sensing of multiple ligands, Phys. Rev. E 99, 022423 (2019).
  28. J. Paulsson, Summing up the noise in gene networks, Nature (London) 427, 415 (2004).
  29. T. E. Saunders and M. Howard, Morphogen profiles can be optimized to buffer against noise, Phys. Rev. E 80, 041902 (2009).
  30. F. Tostevin and P. Reinten Ten Wolde, Mutual information between input and output trajectories of biochemical networks, Phys. Rev. Lett. 102, 218101 (2009).
  31. G. Struhl, K. Struhl, and P. M. Macdonald, The gradient morphogen Bicoid is a concentration-dependent transcriptional activator, Cell 57, 1259 (1989).
  32. T. J. Rink and R. Jacob, Calcium oscillations in non-excitable cells, Trends Neurosci. 12, 43 (1989).
  33. L. Wolpert, Positional information and the spatial pattern of cellular differentiation, J. Theor. Biol. 25, 1 (1969).
  34. J. C. Smith, Forming and interpreting gradients in the early Xenopus embryo, Cold Spring Harbor Perspect. Biol. 1, a002477 (2009).
  35. T. Gregor, E. F. Wieschaus, A. P. McGregor, W. Bialek, and D. W. Tank, Stability and nuclear dynamics of the Bicoid morphogen gradient, Cell 130, 141 (2007).
  36. K. W. Rogers and A. F. Schier, Morphogen gradients: From generation to interpretation, Annu. Rev. Cell Dev. Biol. 27, 377 (2011).
  37. E. Wieschaus, Positional information and cell fate determination in the early Drosophila embryo, Curr. Top. Dev. Biol. 117, 567 (2016).
  38. F. Crick, Diffusion in embryogenesis, Nature (London) 225, 420 (1970).
  39. A. Kicheva, T. Bollenbach, O. Wartlick, F. Jülicher, and M. Gonzalez-Gaitan, Investigating the principles of morphogen gradient formation: From tissues to cells, Curr. Opin. Genet. Dev. 22, 527 (2012).
  40. S. M. Kay, Fundamentals of Statistical Signal Processing: Estimation Theory (Prentice-Hall, Upper Saddle River, NJ, 1993).
  41. S. Bergmann, O. Sandler, H. Sberro, S. Shnider, E. Schejter, B.-Z. Shilo, and N. Barkai, Pre-steady-state decoding of the Bicoid morphogen gradient, PLoS Biol. 5, e46 (2007).
  42. A. Abu-Arish, A. Porcher, A. Czerwonka, N. Dostatni, and C. Fradin, High mobility of Bicoid captured by fluorescence correlation spectroscopy: Implication for the rapid establishment of its gradient, Biophys. J. 99, L33 (2010).
  43. T. Mora, Physical limit to concentration sensing amid spurious ligands, Phys. Rev. Lett. 115, 038102 (2015).
  44. U. Alon, An Introduction to Systems Biology: Design Principles of Biological Circuits (Chapman & Hall/CRC, Boca Raton, FL, 2019).
  45. T. Gregor, D. W. Tank, E. F. Wieschaus, and W. Bialek, Probing the limits to positional information, Cell 130, 153 (2007).
  46. G. Tkačik Jr., C. G. Callan Jr, and W. Bialek, Information flow and optimization in transcriptional regulation, Proc. Natl. Acad. Sci. USA 105, 12265 (2008).
  47. Manu, S. Surkova, A. V. Spirov, V. V. Gursky, H. Janssens, A.-R. Kim, O. Radulescu, C. E. Vanario-Alonso, D. H. Sharp, M. Samsonova et al., Canalization of gene expression in the Drosophila blastoderm by gap gene cross regulation, PLoS Biol. 7, e1000049 (2009).
  48. H. G. Garcia, M. Tikhonov, A. Lin, and T. Gregor, Quantitative imaging of transcription in living Drosophila embryos links polymerase activity to patterning, Curr. Biol. 23, 2140 (2013).
  49. Z. Ali-Murthy and T. B. Kornberg, Bicoid gradient formation and function in the Drosophila pre-syncytial blastoderm, eLife 5, e13222 (2016).
  50. A. Huang, C. Amourda, S. Zhang, N. S. Tolwinski, and T. E. Saunders, Decoding temporal interpretation of the morphogen Bicoid in the early Drosophila embryo, eLife 6, e26258 (2017).
  51. C. Hernández-López, A. Puliafito, Y. Xu, Z. Lu, S. Di Talia, and M. Vergassola, Two-fluid dynamics and micron-thin boundary layers shape cytoplasmic flows in early Drosophila embryos, Proc. Natl. Acad. Sci. USA 120, e2302879120 (2023).
  52. T. R. Sokolowski, T. Gregor, W. Bialek, and G. Tkačik, Deriving a genetic regulatory network from an optimization principle, Proc. Natl. Acad. Sci. USA 122, e2402925121 (2025).
  53. M. B. Elowitz, A. J. Levine, E. D. Siggia, and P. S. Swain, Stochastic gene expression in a single cell, Science 297, 1183 (2002).
  54. J. M. Raser and E. K. O'shea, Noise in gene expression: Origins, consequences, and control, Science 309, 2010 (2005).

Outline

Information

PRX Life 4, 033008– Published 29 July, 2026
  • Received 30 January 2026
  • Accepted 26 June 2026
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation