- 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

Inhibitory Dynamics in a Two-Population Kuramoto Model Captures Scale-Free Avalanches and Synchronization in Neuronal Cultures

D. Lucente1,*, L. Cerutti2,3,*, M. Brofiga2,3, A. Sarracino4, G. Parodi2,5, S. Martinoia2,6,7, P. Massobrio2,8,†,‡, and L. de Arcangelis1,†,§

  • *These authors contributed equally to this work.
  • †These authors jointly supervised the study.
  • ‡Contact author: Paolo.Massobrio@unige.it
  • §Contact author: lucilla.dearcangelis@unicampania.it
PDF

PRX Life 4, 023031 – Published 23 June, 2026

DOI: https://doi.org/10.1103/j7c1-7yj8

Abstract

Neuronal cultures exhibit a complex activity, bursts, or avalanches, characterized by the coexistence of scale invariance and synchronization, quite stable with the percentage of inhibitory neurons. While this bistable behavior has been already observed in the past, the characterization of the statistical properties of avalanche activity and their temporal organization is still lacking, as well as a model able to reproduce these dynamics. Here we analyze experimental data of human neuronal cultures with controlled percentage of inhibitory neurons and characterize their statistical properties and dynamical organization. In order to model the experimental data, we propose a novel version of the Kuramoto model for two populations of oscillators, excitatory and inhibitory, implementing successfully the inhibition dynamics. The model can fully reproduce the experimental results, confirming the existence of correlations in the temporal organization of avalanche activity and the presence of an amplification-attenuation regime, as found in the human brain.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (48)

  1. J. M. Beggs and D. Plenz, Neuronal avalanches in neocortical circuits, J. Neurosci. 23, 11167 (2003).
  2. V. Pasquale, P. Massobrio, L. Bologna, M. Chiappalone, and S. Martinoia, Self-organization and neuronal avalanches in networks of dissociated cortical neurons, Neuroscience 153, 1354 (2008).
  3. J. M. Beggs and N. Timme, Being critical of criticality in the brain, Front. Physiol. 3, 163 (2012).
  4. M. J. Gutnick, Jr., B. Wolfson, and F. Baldino, Jr., Synchronized neuronal activities in neocortical explant cultures, Exp. Brain Res. 76, 131 (1989).
  5. S. di Santo, R. Burioni, A. Vezzani, and M. A. Muñoz, Self-organized bistability associated with first-order phase transitions, Phys. Rev. Lett. 116, 240601 (2016).
  6. S. di Santo, P. Villegas, R. Burioni, and M. A. Muñoz, Landau–ginzburg theory of cortex dynamics: Scale-free avalanches emerge at the edge of synchronization, Proc. Natl. Acad. Sci. USA 115, E1356 (2018).
  7. V. Buendía, P. Villegas, R. Burioni, and M. A. Muñoz, Hybrid-type synchronization transitions: Where incipient oscillations, scale-free avalanches, and bistability live together, Phys. Rev. Res. 3, 023224 (2021).
  8. V. Buendía, P. Villegas, R. Burioni, and M. A. Muñoz, The broad edge of synchronization: Griffiths effects and collective phenomena in brain networks, Philos. Trans. R. Soc. A 380, 20200424 (2022).
  9. Y. Kuramoto, International symposium on mathematical problems in theoretical physics, Lect. Notes Phys. 39, 420 (1975).
  10. J. A. Acebrón, L. L. Bonilla, C. J. Pérez Vicente, F. Ritort, and R. Spigler, The Kuramoto model: A simple paradigm for synchronization phenomena, Rev. Mod. Phys. 77, 137 (2005).
  11. S. Shinomoto and Y. Kuramoto, Phase transitions in active rotator systems, Prog. Theor. Phys. 75, 1105 (1986).
  12. H. Sakaguchi and Y. Kuramoto, A soluble active rotater model showing phase transitions via mutual entertainment, Prog. Theor. Phys. 76, 576 (1986).
  13. H. Sakaguchi, S. Shinomoto, and Y. Kuramoto, Phase transitions and their bifurcation analysis in a large population of active rotators with mean-field coupling, Prog. Theor. Phys. 79, 600 (1988).
  14. V. Buendía, S. di Santo, P. Villegas, R. Burioni, and M. A. Muñoz, Self-organized bistability and its possible relevance for brain dynamics, Phys. Rev. Res. 2, 013318 (2020).
  15. G. Ódor, I. Papp, S. Deng, and J. Kelling, Synchronization transitions on connectome graphs with external force, Front. Phys. 11, 1150246 (2023).
  16. S. Shinomoto and Y. Kuramoto, Cooperative phenomena in two-dimensional active rotator systems, Prog. Theor. Phys. 75, 1319 (1986).
  17. E. Montbrió, J. Kurths, and B. Blasius, Synchronization of two interacting populations of oscillators, Phys. Rev. E 70, 056125 (2004).
  18. E. Montbrió, D. Pazó, and A. Roxin, Macroscopic description for networks of spiking neurons, Phys. Rev. X 5, 021028 (2015).
  19. E. Montbrió and D. Pazó, Kuramoto model for excitation-inhibition-based oscillations, Phys. Rev. Lett. 120, 244101 (2018).
  20. T. Shimokawa and S. Shinomoto, Inhibitory neurons can facilitate rhythmic activity in a neural network, Phys. Rev. E 73, 066221 (2006).
  21. G. Parodi, M. Brofiga, V. P. Pastore, M. Chiappalone, and S. Martinoia, Deepening the role of excitation/inhibition balance in human iPSCs-derived neuronal networks coupled to MEAs during long-term development, J. Neural Eng. 20, 056011 (2023).
  22. F. Lombardi, H. J. Herrmann, D. Plenz, and L. de Arcangelis, Temporal correlations in neuronal avalanche occurrence, Sci. Rep. 6, 24690 (2016).
  23. F. Lombardi, H. J. Herrmann, L. Parrino, D. Plenz, S. Scarpetta, A. E. Vaudano, L. De Arcangelis, and O. Shriki, Beyond pulsed inhibition: Alpha oscillations modulate attenuation and amplification of neural activity in the awake resting state, Cell Rep. 42, 113162 (2023).
  24. K. Dahmen and J. P. Sethna, Hysteresis, avalanches, and disorder-induced critical scaling: A renormalization-group approach, Phys. Rev. B 53, 14872 (1996).
  25. O. Perković, K. Dahmen, and J. P. Sethna, Avalanches, Barkhausen noise, and plain old criticality, Phys. Rev. Lett. 75, 4528 (1995).
  26. M. C. Kuntz and J. P. Sethna, Noise in disordered systems: The power spectrum and dynamic exponents in avalanche models, Phys. Rev. B 62, 11699 (2000).
  27. A. Maccione, M. Gandolfo, P. Massobrio, A. Novellino, S. Martinoia, and M. Chiappalone, A novel algorithm for precise identification of spikes in extracellularly recorded neuronal signals, J. Neurosci. Methods 177, 241 (2009).
  28. O. Shriki, J. Alstott, F. Carver, T. Holroyd, R. N. Henson, M. L. Smith, R. Coppola, E. Bullmore, and D. Plenz, Neuronal avalanches in the resting MEG of the human brain, J. Neurosci. 33, 7079 (2013).
  29. J. Touboul and A. Destexhe, Can power-law scaling and neuronal avalanches arise from stochastic dynamics? PLoS ONE 5, e8982 (2010).
  30. J. Touboul and A. Destexhe, Power-law statistics and universal scaling in the absence of criticality, Phys. Rev. E 95, 012413 (2017).
  31. V. Priesemann and O. Shriki, Can a time varying external drive give rise to apparent criticality in neural systems? PLoS Comput. Biol. 14, e1006081 (2018).
  32. A. J. Fontenele, N. A. P. de Vasconcelos, T. Feliciano, L. A. Aguiar, C. Soares-Cunha, B. Coimbra, L. Dalla Porta, S. Ribeiro, A. J. Rodrigues, N. Sousa, P. V. Carelli, and M. Copelli, Criticality between cortical states, Phys. Rev. Lett. 122, 208101 (2019).
  33. F. Lombardi, H. J. Herrmann, C. Perrone-Capano, D. Plenz, and L. de Arcangelis, Balance between excitation and inhibition controls the temporal organization of neuronal avalanches, Phys. Rev. Lett. 108, 228703 (2012).
  34. L. de Arcangelis, C. Godano, J. R. Grasso, and E. Lippiello, Statistical physics approach to earthquake occurrence and forecasting, Phys. Rep. 628, 1 (2016).
  35. A. T. Winfree, The Geometry of Biological Time (Springer, Berlin, 1980), Vol. 2.
  36. Y. Kuramoto, Collective synchronization of pulse-coupled oscillators and excitable units, Physica D 50, 15 (1991).
  37. S. H. Strogatz, From Kuramoto to Crawford: Exploring the onset of synchronization in populations of coupled oscillators, Physica D 143, 1 (2000).
  38. F. Lombardi, D. R. Chialvo, H. J. Herrmann, and L. De Arcangelis, Strobing brain thunders: Functional correlation of extreme activity events, Chaos, Solitons, Fract. 55, 102 (2013).
  39. See Supplemental Material at http://link.aps.org/supplemental/10.1103/j7c1-7yj8 for detailed experimental avalanche statistics at the sample level, the methodology for matching model timescales, and extended numerical simulation analyses.
  40. R. Kubo, M. Toda, and N. Hashitsume, Statistical Physics II: Nonequilibrium Statistical Mechanics (Springer Science & Business Media, New York 2012), Vol. 31.
  41. U. M. B. Marconi, A. Puglisi, L. Rondoni, and A. Vulpiani, Fluctuation–dissipation: Response theory in statistical physics, Phys. Rep. 461, 111 (2008).
  42. A. Sarracino and A. Vulpiani, On the fluctuation-dissipation relation in non-equilibrium and non-Hamiltonian systems, Chaos 29, 083132 (2019).
  43. D. Lucente, M. Baldovin, F. Cecconi, M. Cencini, N. Cocciaglia, A. Puglisi, M. Viale, and A. Vulpiani, Conceptual and practical approaches for investigating irreversible processes, New J. Phys. 27, 041201 (2025).
  44. L. de Arcangelis, F. Lombardi, and H. J. Herrmann, Criticality in the brain, J. Stat. Mech. (2014) P03026.
  45. F. Bianchi, M. Thielmann, L. de Arcangelis, and H. J. Herrmann, Critical bursts in filtration, Phys. Rev. Lett. 120, 034503 (2018).
  46. S. Pajevic and D. Plenz, Efficient network reconstruction from dynamical cascades identifies small-world topology of neuronal avalanches, PLoS Comput. Biol. 5, e1000271 (2009).
  47. P. Massobrio, V. Pasquale, and S. Martinoia, Self-organized criticality in cortical assemblies occurs in concurrent scale-free and small-world networks, Sci. Rep. 5, 10578 (2015).
  48. J. P. Neto, F. P. Spitzner, and V. Priesemann, Sampling effects and measurement overlap can bias the inference of neuronal avalanches, PLoS Comput. Biol. 18, e1010678 (2022).

Outline

Information

PRX Life 4, 023031– Published 23 June, 2026
  • Received 11 December 2025
  • Accepted 2 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