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Quantifying second-messenger information transmission in bacteria

Nature Physics volume 21, pages 1009–1018 (2025)Cite this article

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Abstract

Bacterial second messengers are crucial for transmitting environmental information to cells. However, quantifying their information transmission capacity remains challenging. Here we develop a framework for quantifying information processing in cellular signalling systems. We engineer an isolated cyclic adenosine monophosphate (cAMP) signalling channel in Pseudomonas aeruginosa using targeted gene knockouts, optogenetics and a fluorescent cAMP probe. This design enables precise optical control and real-time monitoring of cAMP dynamics. By integrating experimental data with information theory, we reveal the optimal frequency for light-mediated cAMP signalling that maximizes information transmission, reaching about 40 bits per hour. This rate correlates strongly with cAMP degradation kinetics and uses a two-state encoding scheme. Our findings suggest a mechanism for fine-tuned regulation of multiple genes through temporal encoding of second-messenger signals, providing insights into bacterial adaptation strategies.

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Fig. 1: Engineering a synthetic circuit utilizing bPAC and PF2 for measuring information transmission via the cAMP pathway.
Fig. 2: Quantitative analysis of cAMP signalling dynamics under modulated light stimulation at single-cell resolution.
Fig. 3: Relationships and characteristics in transmission rate, optimal frequency and encoding scheme.
Fig. 4: Decoding performance and information transmission of a cAMP communication system using machine learning.

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Data availability

The data supporting this study are available via figshare at https://doi.org/10.6084/m9.figshare.27618465 (ref. 61). Source data are provided with this paper.

References

  1. Perkins, T. J. & Swain, P. S. Strategies for cellular decision-making. Mol. Syst. Biol. 5, 326 (2009).

    Article  Google Scholar 

  2. Balázsi, G., Van Oudenaarden, A. & Collins, J. J. Cellular decision making and biological noise: from microbes to mammals. Cell 144, 910–925 (2011).

    Article  Google Scholar 

  3. Bowsher, C. G. & Swain, P. S. Environmental sensing, information transfer, and cellular decision-making. Curr. Opin. Biotechnol. 28, 149–155 (2014).

    Article  Google Scholar 

  4. Guillemin, A. & Stumpf, M. P. Noise and the molecular processes underlying cell fate decision-making. Phys. Biol. 18, 011002 (2020).

    Article  Google Scholar 

  5. Gomelsky, M. cAMP, c-di-GMP, c-di-AMP and now cGMP: bacteria use them all! Mol. Microbiol. 79, 562–565 (2011).

  6. Newton, A. C., Bootman, M. D. & Scott, J. D. Second messengers. Cold Spring Harb. Perspect. Biol. 8, a005926 (2016).

    Article  Google Scholar 

  7. Friedlander, T., Mayo, A. E., Tlusty, T. & Alon, U. Evolution of bow-tie architectures in biology. PLoS Comput. Biol. 11, e1004055 (2015).

  8. Lee, C. K. et al. Multigenerational memory and adaptive adhesion in early bacterial biofilm communities. Proc. Natl Acad. Sci. USA 115, 4471–4476 (2018).

    Article  ADS  Google Scholar 

  9. Schwaller, B. Cytosolic Ca2+ buffers. Cold Spring Harb. Perspect. Biol. 2, a004051 (2010).

  10. Shannon, C. E. A mathematical theory of communication. Bell Syst. Tech. J. 27, 379–423 (1948).

    Article  MathSciNet  Google Scholar 

  11. Cover, T. & Thomas, J. A. Elements of Information Theory (Wiley, 2006).

  12. Strong, S. P., Koberle, R., Van Steveninck, R. R. D. R. & Bialek, W. Entropy and information in neural spike trains. Phys. Rev. Lett. 80, 197–200 (1998).

    Article  ADS  Google Scholar 

  13. Borst, A. & Theunissen, F. E. Information theory and neural coding. Nat. Neurosci. 2, 947–957 (1999).

    Article  Google Scholar 

  14. Quian Quiroga, R. & Panzeri, S. Extracting information from neuronal populations: information theory and decoding approaches. Nat. Rev. Neurosci. 10, 173–185 (2009).

    Article  Google Scholar 

  15. Tkačik, G., Callan Jr, C. G. & Bialek, W. Information flow and optimization in transcriptional regulation. Proc. Natl Acad. Sci. USA 105, 12265–12270 (2008).

    Article  ADS  Google Scholar 

  16. Cheong, R., Rhee, A., Wang, C. J., Nemenman, I. & Levchenko, A. Information transduction capacity of noisy biochemical signaling networks. Science 334, 354–358 (2011).

    Article  ADS  Google Scholar 

  17. Uda, S. et al. Robustness and compensation of information transmission of signaling pathways. Science 341, 558–561 (2013).

    Article  ADS  Google Scholar 

  18. Selimkhanov, J. et al. Accurate information transmission through dynamic biochemical signaling networks. Science 346, 1370–1373 (2014).

    Article  ADS  Google Scholar 

  19. Uda, S. Application of information theory in systems biology. Biophys. Rev. 12, 377–384 (2020).

    Article  Google Scholar 

  20. Dubuis, J. O., Tkačik, G., Wieschaus, E. F., Gregor, T. & Bialek, W. Positional information, in bits. Proc. Natl Acad. Sci. USA 110, 16301–16308 (2013).

    Article  ADS  MathSciNet  Google Scholar 

  21. McGough, L. et al. Finding the last bits of positional information. PRX Life 2, 013016 (2024).

    Article  Google Scholar 

  22. Tkačik, G., Walczak, A. M. & Bialek, W. Optimizing information flow in small genetic networks. Phys. Rev. E 80, 031920 (2009).

    Article  ADS  Google Scholar 

  23. Tkačik, G. & Walczak, A. M. Information transmission in genetic regulatory networks: a review. J. Phys. Condens. Matter 23, 153102 (2011).

    Article  ADS  Google Scholar 

  24. Wang, Z. J. & Thomson, M. Localization of signaling receptors maximizes cellular information acquisition in spatially structured natural environments. Cell Syst. 13, 530–546.e12 (2022).

  25. Bialek, W., Gregor, T., Sokolowski, T. & Tkačik, G. Deriving a genetic regulatory network from an optimization principle. Proc. Natl Acad. Sci. USA 122, e2402925121 (2024).

    Google Scholar 

  26. Tkačik, G. & Bialek, W. Information processing in living systems. Annu. Rev. Condens. Matter Phys. 7, 89–117 (2016).

    Article  ADS  Google Scholar 

  27. Strateva, T. & Yordanov, D. Pseudomonas aeruginosa—a phenomenon of bacterial resistance. J. Med. Microbiol. 58, 1133–1148 (2009).

    Article  Google Scholar 

  28. Topal, H. et al. Crystal structure and regulation mechanisms of the cyab adenylyl cyclase from the human pathogen Pseudomonas aeruginosa. J. Mol. Biol. 416, 271–286 (2012).

    Article  Google Scholar 

  29. Fuchs, E. L. et al. The Pseudomonas aeruginosa vfr regulator controls global virulence factor expression through cyclic AMP-dependent and -independent mechanisms. J. Bacteriol. 192, 3553–3564 (2010).

    Article  Google Scholar 

  30. Stierl, M. et al. Light modulation of cellular camp by a small bacterial photoactivated adenylyl cyclase, bpac, of the soil bacterium Beggiatoa*. J. Biol. Chem. 286, 1181–1188 (2011).

    Article  Google Scholar 

  31. Harada, K. et al. Red fluorescent protein-based camp indicator applicable to optogenetics and in vivo imaging. Sci. Rep. 7, 7351 (2017).

    Article  ADS  Google Scholar 

  32. Fulcher, N. B., Holliday, P. M., Klem, E., Cann, M. J. & Wolfgang, M. C. The Pseudomonas aeruginosa chp chemosensory system regulates intracellular camp levels by modulating adenylate cyclase activity. Mol. Microbiol. 76, 889–904 (2010).

    Article  Google Scholar 

  33. Tostevin, F. & Ten Wolde, P. R. Mutual information between input and output trajectories of biochemical networks. Phys. Rev. Lett. 102, 218101 (2009).

    Article  ADS  Google Scholar 

  34. Hansen, A. S. & O'Shea, E. K. Limits on information transduction through amplitude and frequency regulation of transcription factor activity. eLife 4, e06559 (2015).

    Article  Google Scholar 

  35. Fuchs, E. L. et al. In vitro and in vivo characterization of the Pseudomonas aeruginosa cyclic AMP (cAMP) phosphodiesterase CpdA, required for camp homeostasis and virulence factor regulation. J. Bacteriol. 192, 2779–2790 (2010).

    Article  Google Scholar 

  36. Unsleber, J. P. & Reiher, M. The exploration of chemical reaction networks. Annu. Rev. Phys. Chem. 71, 121–142 (2020).

    Article  ADS  Google Scholar 

  37. Simpson, M. L. et al. Noise in biological circuits. Wiley Interdisc. Rev. Nanomed. Nanobiotechnol. 1, 214–225 (2009).

    Article  Google Scholar 

  38. Allen, A. O. Probability, Statistics, and Queueing Theory with Computer Science Applications (Academic, 1990).

  39. Cranmer, K., Brehmer, J. & Louppe, G. The frontier of simulation-based inference. Proc. Natl Acad. Sci. USA 117, 30055–30062 (2020).

    Article  ADS  MathSciNet  Google Scholar 

  40. Granados, A. A. et al. Distributed and dynamic intracellular organization of extracellular information. Proc. Natl Acad. Sci. USA 115, 6088–6093 (2018).

    Article  ADS  Google Scholar 

  41. Jetka, T., Nienaltowski, K., Winarski, T., Błoński, S. & Komorowski, M. Information-theoretic analysis of multivariate single-cell signaling responses. PLoS Comput. Biol. 15, e1007132 (2019).

    Article  ADS  Google Scholar 

  42. Tang, Y. et al. Quantifying information accumulation encoded in the dynamics of biochemical signaling. Nat. Commun. 12, 1272 (2021).

    Article  ADS  Google Scholar 

  43. Cepeda-Humerez, S. A., Ruess, J. & Tkačik, G. Estimating information in time-varying signals. PLoS Comput. Biol. 15, e1007290 (2019).

  44. Ying, T. & Alexander, H. Quantifying information of intracellular signaling: progress with machine learning. Rep. Prog. Phys. 85, 086602 (2022).

    Article  MathSciNet  Google Scholar 

  45. Ramirez Sierra, M. A. & Sokolowski, T. R. AI-powered simulation-based inference of a genuinely spatial-stochastic gene regulation model of early mouse embryogenesis. PLoS Comput. Biol. 20, e1012473 (2024).

    Article  Google Scholar 

  46. Gillespie, D. T. A general method for numerically simulating the stochastic time evolution of coupled chemical reactions. J. Comput. Phys. 22, 403–434 (1976).

    Article  ADS  MathSciNet  Google Scholar 

  47. Gillespie, D. T. Exact stochastic simulation of coupled chemical reactions. J. Phys. Chem. 81, 2340–2361 (1977).

    Article  Google Scholar 

  48. Valentini, M. & Filloux, A. Biofilms and cyclic di-GMP (c-di-GMP) signaling: lessons from Pseudomonas aeruginosa and other bacteria. J. Biol. Chem. 291, 12547–12555 (2016).

    Article  Google Scholar 

  49. Klosik, D. F., Grimbs, A., Bornholdt, S. & Hütt, M.-T. The interdependent network of gene regulation and metabolism is robust where it needs to be. Nat. Commun. 8, 534 (2017).

    Article  ADS  Google Scholar 

  50. Veening, J.-W., Smits, W. K. & Kuipers, O. P. Bistability, epigenetics, and bet-hedging in bacteria. Annu. Rev. Microbiol. 62, 193–210 (2008).

    Article  Google Scholar 

  51. Zhou, J., Ma, H. & Zhang, L. Mechanisms of virulence reprogramming in bacterial pathogens. Annu. Rev. Microbiol. 77, 561–581 (2023).

    Article  Google Scholar 

  52. Mattingly, H., Kamino, K., Machta, B. & Emonet, T. Escherichia coli chemotaxis is information limited. Nat. Phys. 17, 1426–1431 (2021).

    Article  Google Scholar 

  53. Huang, W. & Wilks, A. A rapid seamless method for gene knockout in Pseudomonas aeruginosa. BMC Microbiol. 17, 199 (2017).

    Article  Google Scholar 

  54. Grote, A. et al. JCat: a novel tool to adapt codon usage of a target gene to its potential expression host. Nucleic Acids Res. 33, W526–W531 (2005).

    Article  ADS  Google Scholar 

  55. Hoang, T. T., Kutchma, A. J., Becher, A. & Schweizer, H. P. Integration-proficient plasmids for Pseudomonas aeruginosa: site-specific integration and use for engineering of reporter and expression strains. Plasmid 43, 59–72 (2000).

    Article  Google Scholar 

  56. Hoang, T. T., Karkhoff-Schweizer, R. R., Kutchma, A. J. & Schweizer, H. P. A broad-host-range Flp-FRT recombination system for site-specific excision of chromosomally-located DNA sequences: application for isolation of unmarked Pseudomonas aeruginosa mutants. Gene 212, 77–86 (1998).

    Article  Google Scholar 

  57. Gibson, D. G. et al. Enzymatic assembly of DNA molecules up to several hundred kilobases. Nat. Methods 6, 343–345 (2009).

    Article  Google Scholar 

  58. Fu, S. et al. Programming the lifestyles of engineered bacteria for cancer therapy. Natl Sci. Rev. 10, nwad031 (2023).

    Article  Google Scholar 

  59. Chen, W. et al. Genome-wide analysis of gene expression noise brought about by transcriptional regulation in Pseudomonas aeruginosa. mSystems 7, e0096322 (2022).

    Article  Google Scholar 

  60. Taniguchi, Y. et al. Quantifying E. coli proteome and transcriptome with single-molecule sensitivity in single cells. Science 329, 533–538 (2010).

    Article  ADS  Google Scholar 

  61. Xiong, J. et al. Quantifying second messenger information transmission in bacteria. figshare https://doi.org/10.6084/m9.figshare.27618465 (2024).

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Acknowledgements

We thank A. Xia for guidance and assistance with microscope usage; Y. Li, L. Wang and S. Lu for their contributions to the development of the seven-well plate and LED set-up; and S. Wan for valuable suggestions during simulations. This work was supported by the National Key Research and Development Program of China (grant no. 2020YFA0906900, F.J.), the National Natural Science Foundation of China (grant no. 32471489, F.J.; grant no. 32101177, Y.H.; grant no. 32371431, J.C.), Shenzhen Engineering Research Center of Therapeutic Synthetic Microbes (grant no. XMHT20220104015, F.J.) and the Innovation Foundation of National Science Library (Chengdu) (grant no. E3Z0000903, S.Y.).

Author information

Author notes

  1. These authors contributed equally: Jiarui Xiong, Liang Wang, Jialun Lin.

Authors and Affiliations

  1. Hefei National Research Center for Physical Sciences at the Microscale, Department of Polymer Science and Engineering, University of Science and Technology of China, Hefei, China

    Jiarui Xiong

  2. State Key Laboratory of Quantitative Synthetic Biology, Shenzhen Institute of Synthetic Biology, Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences, Shenzhen, China

    Jiarui Xiong, Jialun Lin, Lei Ni, Rongrong Zhang, Yajia Huang & Fan Jin

  3. Research Center for Primate Neuromodulation and Neuroimaging and Research Center for Biomedical Optics and Molecular Imaging, Shenzhen Key Laboratory for Molecular Imaging, Guangdong Provincial Key Laboratory of Biomedical Optical Imaging Technology, Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences, Shenzhen, China

    Liang Wang & Jun Chu

  4. Shenzhen Synthetic Biology Infrastructure, Shenzhen Institute of Synthetic Biology, Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences, Shenzhen, China

    Lei Ni, Rongrong Zhang, Yajia Huang & Fan Jin

  5. National Science Library (Chengdu), Chinese Academy of Sciences, Chengdu, China

    Shuai Yang

  6. Department of Information Resources Management, School of Economics and Management, University of Chinese Academy of Sciences, Beijing, China

    Shuai Yang

  7. Key Laboratory of Biomedical Imaging, Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences, Shenzhen, China

    Jun Chu

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Contributions

Conceptualization: F.J.; development and characterization of the probe: L.W. and J.C.; codon optimization, primer design and strain construction: J.X. and Y.H.; method of utilizing the seven-well plate device and LED lights: L.N. and J.X.; exploration of bacterial culture conditions: J.X. and L.N.; correction of light intensity power between different holes of LED lights: R.Z. and J.X.; optimization of lighting conditions: J.X. and R.Z.; getting data from the periodic light exposure experiment: J.X.; code for analysis of fluorescence intensity in single bacteria: L.N. and S.Y.; method of converting fluorescence intensity into cAMP concentration: F.J.; construction of a CRN model: J.L.; theoretical analysis of cAMP dynamics: F.J. and J.X.; correction of experimental data: J.X.; fitting of experimental data: J.L.; analysis of theoretical noise: F.J. and J.X.; method for converting cAMP concentration to molecule count: L.N. and J.X.; analysis of experimental noise: J.L.; theoretical analysis of SNR: F.J. and J.X.; proposal of the optimal frequency: F.J.; theoretical analysis of the upper limit of information transmission rate: F.J. and J.X.; proposal of the encoding scheme: F.J.; proposal of the random input method: F.J.; acquisition of experimental data on random light exposure: J.X.; training of the classifier: J.L.; assessment of decoding accuracy for experimental and simulated data: J.L.; calculation of BSC capacity: J.X.; manuscript drafting: J.X. (text section) and J.L. (figure and movie section); manuscript revision and review: F.J., J.C., J.X., J.L., L.W., R.Z. and S.Y.

Corresponding authors

Correspondence to Jun Chu or Fan Jin.

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The authors declare no competing interests.

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Nature Physics thanks Shinya Kuroda and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Supplementary information

Supplementary Information

Four main text sections, eight supplementary figures, five supplementary tables and relevant references.

Reporting Summary

Supplementary Data 1

Information on PCR primers used for strain construction and commercial reagents used for bacterial cultivation.

Supplementary Data 2

The raw fluorescence intensity data of cAMP probes under different variants and conditions, corresponding to Supplementary Fig. 1.

Supplementary Data 3

Single-cell volume measurements and noise data corresponding to Supplementary Fig. 6.

Supplementary Data 4

Single-cell CpdA concentrations and the derived cAMP degradation and signal transmission rates corresponding to Supplementary Fig. 7.

Supplementary Video 1

The time-lapse fluorescence microscopy of a single bacterium under periodic illumination with an 840-s cycle.

Supplementary Video 2

The fluorescence intensity changes of a single bacterium under random on/off light stimulation.

Source data

Source Data Fig. 1

This file (.xlsx) provides raw data for the dose–response curve of the cAMP sensor and the temporal changes in fluorescence intensity under light and dark conditions.

Source Data Fig. 2

This file (.xlsx) contains the raw data of two key parameters (k and γ) extracted from individual bacterial cells across all experiments, along with the original measurements of cAMP signal intensity and SNR as a function of reduced frequency. These experimental measurements serve as the foundation for the theoretical analysis and computational modelling shown in Fig. 3.

Source Data Fig. 4

This file (.xlsx) contains raw data of intracellular cAMP dynamics in single bacterial cells under random light stimulation with various code durations and the relationship between decoding accuracy and frequency presented in the main text.

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Xiong, J., Wang, L., Lin, J. et al. Quantifying second-messenger information transmission in bacteria. Nat. Phys. 21, 1009–1018 (2025). https://doi.org/10.1038/s41567-025-02848-2

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