- Physical Review Journals
All JournalsPhysics Magazine

Physical Review Research

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

Structured interactions drive abrupt transitions in the spatial organization of microbial communities

Mattia Mattei1,*, David Soriano-Paños1,2, Mahantesh Halappanavar3, and Alex Arenas1,3

  • *Contact author: mattia.mattei@urv.cat
PDF

Phys. Rev. Research 7, 043210 – Published 24 November, 2025

DOI: https://doi.org/10.1103/g5bm-m9c4

Abstract

Bacteria possess diverse mechanisms to regulate their motility in response to environmental and physiological signals, enabling them to navigate complex habitats and adapt their behavior. Some of these mechanisms are species specific and enable cells to modulate their movement based on the ecological identity of neighboring species. Here, we introduce a model in which bacteria interact via local signals that either enhance or suppress the motility of neighboring cells depending on species type. Through large-scale simulations and a coarse-grained stochastic model, we demonstrate the emergence of a sharp transition driven by nucleation processes: increasing the density of motility-suppressing interactions drives the system from a fully mixed, motile phase to a state characterized by large, stationary bacterial clusters. Remarkably, in systems with a large number of interacting species, this transition can be triggered solely by altering the structure of the motility-regulation interaction matrix while maintaining species and interaction densities constant. In particular, we find that heterogeneous and modular interactions promote the transition more readily than homogeneous random ones. These findings add a dimension to the theory of motility-induced phase separation and contribute to the ongoing effort to understand microbial interactions, suggesting that structured, nonrandom ones may be key to reproducing commonly observed spatial patterns in microbial communities.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (57)

  1. O. X. Cordero and M. S. Datta, Microbial interactions and community assembly at microscales, Curr. Opin. Microbiol. 31, 227 (2016).
  2. J. L. M. Welch, B. J. Rossetti, C. W. Rieken, F. E. Dewhirst, and G. G. Borisy, Biogeography of a human oral microbiome at the micron scale, Proc. Natl. Acad. Sci. USA 113, E791 (2016).
  3. R. Sheth, M. Li, and W. Jiang et al., Spatial metagenomic characterization of microbial biogeography in the gut, Nat. Biotechnol. 37, 877 (2019).
  4. S. L. O’Brien, S. M. Gibbons, S. M. Owens, J. Hampton-Marcell, E. R. Johnston, J. D. Jastrow, J. A. Gilbert, F. Meyer, and D. A. Antonopoulos, Spatial scale drives patterns in soil bacterial diversity, Environ. Microbiol. 18, 2039 (2016).
  5. E. Bar-Zeev, I. Berman-Frank, O. Girshevitz, and T. Berman, Revised paradigm of aquatic biofilm formation facilitated by microgel transparent exopolymer particles, Proc. Natl. Acad. Sci. USA 109, 9119 (2012).
  6. O. Hallatschek, P. Hersen, S. Ramanathan, and D. R. Nelson, Genetic drift at expanding frontiers promotes gene segregation, Proc. Natl. Acad. Sci. USA 104, 19926 (2007).
  7. I. Golding, I. Cohen, and E. Ben-Jacob, Studies of sector formation in expanding bacterial colonies, Europhys. Lett. 48, 587 (1999).
  8. E. Budrene and H. Berg, Complex patterns formed by motile cells of Escherichia coli, Nature (London) 349, 630 (1991).
  9. C. M. Waters and B. L. Bassler, Quorum sensing: Cell-to-cell communication in bacteria, Annu. Rev. Cell Dev. Biol. 21, 319 (2005).
  10. R. Daniels, J. Vanderleyden, and J. Michiels, Quorum sensing and swarming migration in bacteria, FEMS Microbiol. Rev. 28, 261 (2004).
  11. H. H. Hoang, N. Gurich, and J. E. González, Regulation of motility by the ExpR/Sin quorum-sensing system in Sinorhizobium meliloti, J. Bacteriol. 190, 861 (2008).
  12. R. F. Kinsinger, M. C. Shirk, and R. Fall, Rapid surface motility in Bacillus subtilis is dependent on extracellular surfactin and potassium ion, J. Bacteriol. 185, 5627 (2003).
  13. G. Cárcamo-Oyarce, P. Lumjiaktase, R. Kümmerli et al., Quorum sensing triggers the stochastic escape of individual cells from Pseudomonas putida biofilms, Nat. Commun. 6, 5945 (2015).
  14. R. Daniels, S. Reynaert, H. Hoekstra, C. Verreth, J. Janssens, K. Braeken, M. Fauvart, S. Beullens, C. Heusdens, I. Lambrichts, D. E. D. Vos, J. Vanderleyden, J. Vermant, and J. Michiels, Quorum signal molecules as biosurfactants affecting swarming in Rhizobium etli, Proc. Natl. Acad. Sci. USA 103, 14965 (2006).
  15. J. Tailleur and M. E. Cates, Statistical mechanics of interacting run-and-tumble bacteria, Phys. Rev. Lett. 100, 218103 (2008).
  16. M. E. Cates and J. Tailleur, Motility-induced phase separation, Annu. Rev. Condens. Matter Phys. 6, 219 (2015).
  17. Y. Fily and M. C. Marchetti, Athermal phase separation of self-propelled particles with no alignment, Phys. Rev. Lett. 108, 235702 (2012).
  18. G. S. Redner, M. F. Hagan, and A. Baskaran, Structure and dynamics of a phase-separating active colloidal fluid, Phys. Rev. Lett. 110, 055701 (2013).
  19. A. Curatolo, N. Zhou, Y. Zhao et al., Cooperative pattern formation in multi-component bacterial systems through reciprocal motility regulation, Nat. Phys. 16, 1152 (2020).
  20. W. J. M. Ridgway, M. P. Dalwadi, P. Pearce, and S. J. Chapman, Motility-induced phase separation mediated by bacterial quorum sensing, Phys. Rev. Lett. 131, 228302 (2023).
  21. A. Dinelli, J. O’Byrne, A. Curatolo et al., nonreciprocity across scales in active mixtures, Nat. Commun. 14, 7035 (2023).
  22. Y. Duan, J. Agudo-Canalejo, R. Golestanian, and B. Mahault, Dynamical pattern formation without self-attraction in quorum-sensing active matter: The interplay between nonreciprocity and motility, Phys. Rev. Lett. 131, 148301 (2023).
  23. A. Dinelli, A. Altieri, and J. Tailleur, Random motility regulation drives the fragmentation of microbial ecosystems, arXiv:2503.12692.
  24. M. Mattei and A. Arenas, Exploring spatial segregation induced by competition avoidance as driving mechanism for emergent coexistence in microbial communities, Phys. Rev. E 110, 014404 (2024).
  25. See Supplemental Material at http://link.aps.org/supplemental/10.1103/g5bm-m9c4 for spatial organization and cluster size distributions; hysteresis curve and clusters stability; sensitivity analysis; parameters choice and simulation details, which also includes Refs.  [56, 57].
  26. G. J. Tortora, B. R. Funke, and C. L. Case, Microbiology: An Introduction (Benjamin Cummings, Redwood City, CA, 1995), p. 275.
  27. The World Book Encyclopedia (Field Enterprises, Chicago, 1973), p. 18.
  28. K. F. Kelton and A. L. Greer, Nucleation in Condensed Matter: Applications in Materials and Biology, Pergamon Materials Series Vol. 15 (Elsevier, Oxford, UK, 2010).
  29. D. W. Oxtoby, Homogeneous nucleation: Theory and experiment, J. Phys.: Condens. Matter 4, 7627 (1992).
  30. F. Peruani, A. Deutsch, and M. Bär, Nonequilibrium clustering of self-propelled rods, Phys. Rev. E 74, 030904(R) (2006).
  31. D. T. Gillespie, Exact stochastic simulation of coupled chemical reactions, J. Phys. Chem. 81, 2340 (1977).
  32. P. Erdős and A. Rényi, On random graphs. I, Publ. Math. Debrecen 6, 290 (1959).
  33. A.-L. Barabási and R. Albert, Emergence of scaling in random networks, Science 286, 509 (1999).
  34. P. W. Holland, K. B. Laskey, and S. Leinhardt, Stochastic blockmodels: First steps, Social Networks 5, 109 (1983).
  35. V. M. Worlitzer, A. Jose, I. Grinberg, M. Bär, S. Heidenreich, A. Eldar, G. Ariel, and A. Be'er, Biophysical aspects underlying the swarm to biofilm transition, Sci. Adv. 8, eabn8152 (2022).
  36. D. G. Davies, M. R. Parsek, J. P. Pearson, B. H. Iglewski, J. W. Costerton, and E. P. Greenberg, The involvement of cell-to-cell signals in the development of a bacterial biofilm, Science 280, 295 (1998).
  37. D. López, M. A. Fischbach, F. Chu, R. Losick, and R. Kolter, Structurally diverse natural products that cause potassium leakage trigger multicellularity in Bacillus subtilis, Proc. Natl. Acad. Sci. USA 106, 280 (2009).
  38. E. Ben-Jacob, O. Schochet, A. Tenenbaum et al., Generic modeling of cooperative growth patterns in bacterial colonies, Nature (London) 368, 46 (1994).
  39. J. Tyler Bonner and L. J. Savage, Evidence for the formation of cell aggregates by chemotaxis in the development of the slime mold Dictyostelium discoideum, J. Exp. Zool. 106, 1 (1947).
  40. J. Agudo-Canalejo and R. Golestanian, Active phase separation in mixtures of chemically interacting particles, Phys. Rev. Lett. 123, 018101 (2019).
  41. X. Diego, L. Marcon, P. Müller, and J. Sharpe, Key features of Turing systems are determined purely by network topology, Phys. Rev. X 8, 021071 (2018).
  42. R. May, Will a large complex system be stable? Nature (London) 238, 413 (1972).
  43. S. Allesina and S. Tang, Stability criteria for complex ecosystems, Nature (London) 483, 205 (2012).
  44. K. Faust and J. Raes, Microbial interactions: From networks to models, Nat Rev Microbiol 10, 538 (2012).
  45. A. Barberán, S. Bates, E. Casamayor et al., Using network analysis to explore co-occurrence patterns in soil microbial communities, ISME J 6, 343 (2012).
  46. T. P. Peixoto, Network reconstruction via the minimum description length principle, Phys. Rev. X 15, 011065 (2025).
  47. J. E. Goldford, N. Lu, D. Bajić, S. Estrela, M. Tikhonov, A. Sanchez-Gorostiaga, D. Segrè, P. Mehta, and A. Sanchez, Emergent simplicity in microbial community assembly, Science 361, 469 (2018).
  48. A. Zelezniak, S. Andrejev, O. Ponomarova, D. R. Mende, P. Bork, and K. R. Patil, Metabolic dependencies drive species co-occurrence in diverse microbial communities, Proc. Natl. Acad. Sci. USA 112, 6449 (2015).
  49. A. Dal Co, S. van Vliet, D. Kiviet et al., Short-range interactions govern the dynamics and functions of microbial communities, Nat. Ecol. Evol. 4, 366 (2020).
  50. X. Raynaud and N. Nunan, Spatial ecology of bacteria at the microscale in soil, PLOS ONE 9, e87217 (2014).
  51. J. van Gestel, T. Bareia, B. Tenennbaum et al., Short-range quorum sensing controls horizontal gene transfer at micron scale in bacterial communities, Nat. Commun. 12, 2324 (2021).
  52. K. Drescher, J. Dunkel, C. D. Nadell, S. van Teeffelen, I. Grnja, N. S. Wingreen, H. A. Stone, and B. L. Bassler, Architectural transitions in Vibrio cholerae biofilms at single-cell resolution, Proc. Natl. Acad. Sci. USA 113, E2066 (2016).
  53. Z. You, D. J. G. Pearce, A. Sengupta, and L. Giomi, Mono- to multilayer transition in growing bacterial colonies, Phys. Rev. Lett. 123, 178001 (2019).
  54. https://mathworld.wolfram.com/Circle-CircleIntersection.html.
  55. M. Penrose, Random Geometric Graphs, Oxford Studies in Probability (Oxford University Press, Oxford, 2003), Vol. 5.
  56. McGraw-Hill Encyclopedia of Science and Technology (McGraw Hill, New York, 1960), p. 63.
  57. C. Spearman, The proof and measurement of association between two things, Am. J. Psychol. 15, 72 (1904).

Outline

Information

Phys. Rev. Research 7, 043210– Published 24 November, 2025
  • Received 23 July 2025
  • Accepted 31 October 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