The European Physical Journal Special Topics

, Volume 227, Issue 10–11, pp 1015–1028 | Cite as

Neuronal devices: understanding neuronal cultures through percolation helps prepare for the next step

  • Pascal Monceau
  • Stéphane Métens
  • Tanguy Fardet
  • Renaud Renault
  • Samuel BottaniEmail author
Regular Article
Part of the following topical collections:
  1. Advances in Nonlinear Dynamics of Complex Networks: Adaptivity, Stochasticity, Delays


Cultures of dissociated neurons are an invaluable experimental tool in studying neuronal networks at an intermediate scale in an in vitro controlled physico-chemical environment. Moreover, current micro-fabrication techniques allow the design of a custom connectivity between subpopulations, which could make it possible to carry out computations with devices involving living cells. The quorum percolation (QP) model has been designed in the context of neurobiology to describe bursts of activity occurring in neuronal cultures from the point of view of collective phenomena rather than from a dynamical synchronization approach. Such a model is well suited to describe triggered activity in neuronal devices, and its generic character points at the necessity of heavily structured devices to go beyond collective bursting. We derive a continuous extension of the QP model, seen as information propagation on a non-metric directed graph, and discuss how its critical behavior might give insight on the connectivity of neuronal networks. The link with metric graphs, embedded in a two-dimensional space, is tackled by the introduction of a geometrical model based upon a random walk, where axon growth is constrained by obstacles such as walls and channels. This provides a starting point for the construction of neuronal devices in vitro capable of more complex behaviors. Lastly, we show how simulations of bursts with a dynamical adaptive integrate-and-fire model can be interpreted in terms of QP, confirming the robustness of this synchronized behavior.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    J.P. Eckmann, O. Feinerman, L. Gruendlinger, E. Moses, J. Soriano, T. Tlusty, Phys. Rep. 449, 54 (2007) ADSMathSciNetCrossRefGoogle Scholar
  2. 2.
    M.E. Raichle, Trend. Neurosci. 32, 118 (2009) CrossRefGoogle Scholar
  3. 3.
    P. Guevara, D. Duclap, C. Poupon, L. Marrakchi-Kacem, P. Fillard, D. Le Bihan, M. Leboyer, J. Houenou, J.F. Mangin, NeuroImage 61, 1083 (2012) CrossRefGoogle Scholar
  4. 4.
    I. Breskin, J. Soriano, E. Moses, T. Tlusty, Phys. Rev. Lett. 97, 188102 (2006) ADSCrossRefGoogle Scholar
  5. 5.
    G.W. Gross, B.K. Rhoades, H.M.E. Azzazy, W. Ming-Chi, Biosensors, Bioelectronics 10, 553 (1995) CrossRefGoogle Scholar
  6. 6.
    R. Renault, Emergent design of neuronal devices, Ph.D. thesis, Université Paris-Diderot, Paris, 2015 Google Scholar
  7. 7.
    R. Renault, N. Sukenik, S. Descroix, L. Malaquin, J.-L. Viovy, J.-M. Peyrin, S. Bottani, P. Monceau, E. Moses, M. Vignes, PLoS One 10, 1 (2015) Google Scholar
  8. 8.
    J.-M. Peyrin, B. Deleglise, L. Saias, M. Vignes, P. Gougis, S. Magnifico, S. Betuing, M. Pietri, J. Caboche, P. Vanhoutte, J.-L. Viovy, B. Brugg, Lab on a Chip 11, 3663 (2011) CrossRefGoogle Scholar
  9. 9.
    S. Stern, M. Segal, E. Moses, EBioMedicine 2, 1048 (2015) CrossRefGoogle Scholar
  10. 10.
    I. Canals, J. Soriano, G. Orlandi et al., Stem Cell Rep. 5, 546 (2015) CrossRefGoogle Scholar
  11. 11.
    T. DeMarse, K. Dockendorf, in Proceedings 2005 International Joint Conference on Neural Networks (IEEE Montreal, Montreal, Que., Canada, 2005), Vol. 3, pp. 1548–1551. Google Scholar
  12. 12.
    J. Soriano, M. Rodríguez Martínez, T. Tlusty, E. Moses, Proc. Natl. Acad. Sci. U.S.A. 105, 13758 (2008) ADSCrossRefGoogle Scholar
  13. 13.
    Y. Penn, M. Segal, E. Moses, Proc. Natl. Acad. Sci. U.S.A. 12, 3341 (2016) ADSCrossRefGoogle Scholar
  14. 14.
    E.M. Izhikevich, Dynamical systems in neuroscience (MIT Press, Cambridge, Massachusetts, 2007) Google Scholar
  15. 15.
    A. Arenas, J. Kurths, Y. Moreno, Phys. Rep. 469, 1 (2008) CrossRefGoogle Scholar
  16. 16.
    O. Cohen, A. Keselman, E. Moses, J. Soriano, T. Tlusty, Europhys. Lett. 89, 1 (2010) CrossRefGoogle Scholar
  17. 17.
    L. Hernandez-Navarro, J.G. Orlandi, B. Cerruti, E. Vives, J. Soriano, Phys. Rev. Lett. 118, 208101 (2017) ADSCrossRefGoogle Scholar
  18. 18.
    R. Koene, B. Tijms, P. van Hees, F. Postma, A. de Ridder, G.J. Ramakers, J. Van Pelt, A. Van Ooyen, Neuroinformatics 7, 195 (2009) CrossRefGoogle Scholar
  19. 19.
    B. Torben-Nielsen, E. De Schutter, Front. Neuroanat. 8, 92 (2014) CrossRefGoogle Scholar
  20. 20.
    T. Tlusty, J.-P. Eckmann, J. Phys. A 42, 205004 (2009) ADSMathSciNetCrossRefGoogle Scholar
  21. 21.
    S. Métens, P. Monceau, R. Renault, S. Bottani, Phys. Rev. E 93, 032112 (2016) ADSMathSciNetCrossRefGoogle Scholar
  22. 22.
    D. Stauffer, A. Aharony, Introduction to Percolation Theory (Taylor & Francis, London, 1994) Google Scholar
  23. 23.
    R. Renault, P. Monceau, S. Bottani, S. Métens, Physica A 414, 352 (2014) ADSCrossRefGoogle Scholar
  24. 24.
    R. Brette, W. Gerstner, J. Neurophysiol. 94, 3637 (2005) CrossRefGoogle Scholar
  25. 25.
    S. Bottani, Phys. Rev. Lett. 74, 4189 (1995) ADSCrossRefGoogle Scholar

Copyright information

© EDP Sciences, Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Pascal Monceau
    • 1
    • 2
  • Stéphane Métens
    • 1
  • Tanguy Fardet
    • 1
  • Renaud Renault
    • 1
  • Samuel Bottani
    • 1
    • 2
    Email author
  1. 1.Laboratoire Matière et Systèmes Complexes, UMR 7057 CNRSUniversité Denis Diderot-Paris 7Paris CedexFrance
  2. 2.Université d’Evry-Val d’EssonneEvryFrance

Personalised recommendations