- 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

Fast Decisions with Biophysically Constrained Gene Promoter Architectures

Tarek Tohme, Massimo Vergassola, and Thierry Mora*

Aleksandra M. Walczak*

  • *These authors contributed equally to this work.
PDF

PRX Life 4, 013009 – Published 21 January, 2026

DOI: https://doi.org/10.1103/sxnt-sbx9

Abstract

Cells integrate signals and make decisions about their future state in short amounts of time. A lot of theoretical effort has gone into asking how to best design gene regulatory circuits that fulfill a given function, yet much less is known about the constraints that performing that function in a small amount of time imposes on circuit architectures. Using an optimization framework, we explore the properties of a class of promoter architectures that distinguish small differences in transcription factor concentrations under time constraints. We show that the full temporal trajectory of gene activity allows for faster decisions than its integrated activity represented by the total number of transcribed mRNA. The topology of promoter architectures that allow for rapidly distinguishing low transcription factor concentrations results in a low, shallow, and noncooperative response, while at high concentrations, the response is high and cooperative. In the presence of noncognate ligands, networks with fast and accurate decision times need not be optimally selective, especially if discrimination is difficult. While optimal networks are generically out of equilibrium, the energy associated with that irreversibility is only modest and negligible at small concentrations. Instead, our results highlight the crucial role of rate-limiting steps imposed by biophysical constraints.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (66)

  1. W. Driever and C. Nüsslein-Volhard, A gradient of bicoid protein in Drosophila embryos, Cell 54, 83 (1988).
  2. L. S. Mosby, A. E. Bowen, and Z. Hadjivasiliou, Morphogens in the evolution of size, shape and patterning, Development 151, dev202412 (2024).
  3. J. L. Christian, Morphogen gradients in development: From form to function, WIREs Dev. Biol. 1, 3 (2012).
  4. J. Briscoe and S. Small, Morphogen rules: Design principles of gradient-mediated embryo patterning, Development 142, 3996 (2015).
  5. O. Feinerman, J. Veiga, J. R. Dorfman, R. N. Germain, and G. Altan-Bonnet, Variability and robustness in T cell activation from regulated heterogeneity in protein levels, Science 321, 1081 (2008).
  6. G. Altan-Bonnet and R. N. Germain, Modeling T cell antigen discrimination based on feedback control of digital ERK responses, PLoS Biol. 3, e356 (2005).
  7. P. Francois, G. Voisinne, E. D. Siggia, G. Altan-Bonnet, and M. Vergassola, Phenotypic model for early T-cell activation displaying sensitivity, specificity, and antagonism, Proc. Natl. Acad. Sci. USA 110, E888 (2013).
  8. S. R. Achar et al., Universal antigen encoding of t cell activation from high-dimensional cytokine dynamics, Science (NY) 376, 880 (2022).
  9. G. Altan-Bonnet, T. Mora, and A. M. Walczak, Quantitative immunology for physicists, Phys. Rep. 849, 1 (2020).
  10. H. Berg and E. Purcell, Physics of chemoreception, Biophys. J. 20, 193 (1977).
  11. R. M. Macnab and D. E. Koshland, The gradient-sensing mechanism in bacterial chemotaxis, Proc. Natl. Acad. Sci. USA 69, 2509 (1972).
  12. V. Sourjik and N. S. Wingreen, Responding to chemical gradients: Bacterial chemotaxis, Curr. Opin. Cell Biol. 24, 262 (2012).
  13. C. Janetopoulos and R. A. Firtel, Directional sensing during chemotaxis, FEBS Lett. 582, 2075 (2008).
  14. Y. Tu, Quantitative modeling of bacterial chemotaxis: Signal amplification and accurate adaptation, Annu. Rev. Biophys. 42, 337 (2013).
  15. M. B. Elowitz, Stochastic gene expression in a single cell, Science 297, 1183 (2002).
  16. G. Tkačik and A. M. Walczak, Information transmission in genetic regulatory networks: A review, J. Phys.: Condens. Matter 23, 153102 (2011).
  17. F. Tostevin, P. R. ten Wolde, and M. Howard, Fundamental limits to position determination by concentration gradients, PLoS Comput. Biol. 3, e78 (2007).
  18. G. Tkacik, C. G. Callan, and W. Bialek, Information flow and optimization in transcriptional regulation, Proc. Natl. Acad. Sci. USA 105, 12265 (2008).
  19. G. Lan, S. Schulmeister, V. Sourjik, and Y. Tu, Adapt locally and act globally: Strategy to maintain high chemoreceptor sensitivity in complex environments, Mol. Syst. Biol. 7, 475 (2011).
  20. G. Lan, P. Sartori, S. Neumann, V. Sourjik, and Y. Tu, The energy–speed–accuracy trade-off in sensory adaptation, Nat. Phys. 8, 422 (2012).
  21. 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).
  22. N. C. Lammers, A. I. Flamholz, and H. G. Garcia, Competing constraints shape the nonequilibrium limits of cellular decision-making, Proc. Natl. Acad. Sci. USA 120, e2211203120 (2023).
  23. W. Bialek and S. Setayeshgar, Physical limits to biochemical signaling, Proc. Natl. Acad. Sci. USA 102, 10040 (2005).
  24. T. Gregor, D. W. Tank, E. F. Wieschaus, and W. Bialek, Probing the limits to positional information, Cell 130, 153 (2007).
  25. T. Mora and I. Nemenman, Physical limit to concentration sensing in a changing environment, Phys. Rev. Lett. 123, 198101 (2019).
  26. M. Carballo-Pacheco et al., Receptor crosstalk improves concentration sensing of multiple ligands, Phys. Rev. E 99, 022423 (2019).
  27. V. Singh and I. Nemenman, Universal properties of concentration sensing in large ligand-receptor networks, Phys. Rev. Lett. 124, 028101 (2020).
  28. V. Singh and I. Nemenman, Simple biochemical networks allow accurate sensing of multiple ligands with a single receptor, PLoS Comput. Biol. 13, e1005490 (2017).
  29. G. Malaguti and P. R. ten Wolde, Theory for the optimal detection of time-varying signals in cellular sensing systems, arXiv:1902.09332.
  30. K. Kaizu et al., The Berg-Purcell limit revisited, Biophys. J. 106, 976 (2014).
  31. P. Sartori and Y. Tu, Free energy cost of reducing noise while maintaining a high sensitivity, Phys. Rev. Lett. 115, 118102 (2015).
  32. P. Sartori and Y. Tu, Noise filtering strategies in adaptive biochemical signaling networks, J. Stat. Phys. 142, 1206 (2011).
  33. A. Eldar, D. Rosin, B. Z. Shilo, and N. Barkai, Self-enhanced ligand degradation underlies robustness of morphogen gradients, Dev. Cell 5, 635 (2003).
  34. R. G. Endres and N. S. Wingreen, Maximum likelihood and the single receptor, Phys. Rev. Lett. 103, 158101 (2009).
  35. R. G. Endres and N. S. Wingreen, Accuracy of direct gradient sensing by cell-surface receptors, Prog. Biophys. Mol. Biol. 100, 33 (2009).
  36. T. Mora and N. S. Wingreen, Limits of sensing temporal concentration changes by single cells, Phys. Rev. Lett. 104, 248101 (2010).
  37. B. Hu, W. Chen, W. J. Rappel, and H. Levine, Physical limits on cellular sensing of spatial gradients, Phys. Rev. Lett. 105, 048104 (2010).
  38. H. Tran et al., Precision in a rush: Trade-offs between reproducibility and steepness of the hunchback expression pattern, PLoS Comput. Biol. 14, e1006513 (2018).
  39. J. Estrada, F. Wong, A. DePace, and J. Gunawardena, Information integration and energy expenditure in gene regulation, Cell 166, 234 (2016).
  40. T. E. Saunders and M. Howard, Morphogen profiles can be optimized to buffer against noise, Phys. Rev. E 80, 041902 (2009).
  41. M. D. Petkova, G. Tkačik, W. Bialek, E. F. Wieschaus, and T. Gregor, Optimal decoding of information from a genetic network, Cell 176, 844 (2019).
  42. Y. Okabe-Oho, H. Murakami, S. Oho, and M. Sasai, Stable, precise, and reproducible patterning of bicoid and hunchback molecules in the early Drosophila embryo, PLoS Comput. Biol. 5, e1000486 (2009).
  43. T. Erdmann, M. Howard, and P. R. ten Wolde, Role of spatial averaging in the precision of gene expression patterns, Phys. Rev. Lett. 103, 258101 (2009).
  44. A. Wald, Sequential tests of statistical hypotheses, Ann. Math. Stat. 16, 117 (1945).
  45. E. D. Siggia and M. Vergassola, Decisions on the fly in cellular sensory systems, Proc. Natl. Acad. Sci. USA 110, E3704 (2013).
  46. W. Whitt, Asymptotic formulas for Markov processes with applications to simulation, Oper. Res. 40, 279 (1992).
  47. 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).
  48. 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).
  49. A. Porcher and N. Dostatni, The bicoid morphogen system, Curr. Biol. 20, R249 (2010).
  50. J. J. Hopfield, Kinetic proofreading: A new mechanism for reducing errors in biosynthetic processes requiring high specificity, Proc. Natl. Acad. Sci. USA 71, 4135 (1974).
  51. J. Ninio, Kinetic amplification of enzyme discrimination, Biochimie 57, 587 (1975).
  52. A. Puglisi, A brief introduction to the inference of entropy production through the fluctuations of currents, Europhys. Lett. 150, 67001 (2025).
  53. S. A. Cepeda-Humerez, G. Rieckh, and G. Tkačik, Stochastic proofreading mechanism alleviates crosstalk in transcriptional regulation, Phys. Rev. Lett. 115, 248101 (2015).
  54. R. Ravasio et al., A minimal scenario for the origin of non-equilibrium order, arXiv:2405.10911.
  55. R. Shelansky et al., Single gene analysis in yeast suggests nonequilibrium regulatory dynamics for transcription, Nat. Commun. 15, 6226 (2024).
  56. F. Mancini, M. Marsili, and A. M. Walczak, Trade-offs in delayed information transmission in biochemical networks, J. Stat. Phys. 162, 1088 (2016).
  57. P. Szymańska-Rożek, D. Villamaina, J. Miekisz, and A. M. Walczak, Dissipation in non-steady state regulatory circuits, Entropy 21, 1212 (2019).
  58. A. Crisanti, A. Puglisi, and D. Villamaina, Nonequilibrium and information: The role of cross correlations, Phys. Rev. E 85, 061127 (2012).
  59. A. Puglisi, S. Pigolotti, L. Rondoni, and A. Vulpiani, Entropy production and coarse graining in Markov processes, J. Stat. Mech. (2010) P05015.
  60. D. M. Busiello, J. Hidalgo, and A. Maritan, Entropy production for coarse-grained dynamics, New J. Phys. 21, 073004 (2019).
  61. T. Lucas et al., Live imaging of bicoid-dependent transcription in Drosophila embryos, Curr. Biol. 23, 2135 (2013).
  62. B. Zoller, S. C. Little, and T. Gregor, Diverse spatial expression patterns emerge from unified kinetics of transcriptional bursting, Cell 175, 835 (2018).
  63. J. O. Dubuis, G. Tkacik, E. F. Wieschaus, T. Gregor, and W. Bialek, Positional information, in bits. Proc. Natl. Acad. Sci. USA 110, 16301 (2013).
  64. P. T. Chen, M. Levo, B. Zoller, and T. Gregor, Gene activity fully predicts transcriptional bursting dynamics, Nat. Struct. Mol. Biol. 32, 1959 (2025).
  65. J. G. Kemeny and J. L. Snell, Finite Markov Chains, Universitiy Series in Undergraduate Mathematics, No. 210 (van Nostrand, Princeton, NJ, 1960).
  66. https://github.com/statbiophys/ConstrainedPromoters.

Outline

Information

PRX Life 4, 013009– Published 21 January, 2026
  • Received 12 July 2025
  • Accepted 4 December 2025
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