Power Laws in Neuronal Culture Activity from Limited Availability of a Shared Resource

  • Damian Berger
  • Sunghoon Joo
  • Tom Lorimer
  • Yoonkey Nam
  • Ruedi StoopEmail author
Conference paper
Part of the Springer Proceedings in Physics book series (SPPHY, volume 191)


We record spontaneous activity from a developing culture of dissociated rat hippocampal neurons in vitro using a multi electrode array. To statistically characterize activity, we look at the time intervals between recorded spikes, which, unlike neuronal avalanche sizes, do not require the selection of a time bin. The distribution of inter event intervals in our data approximate power laws at all recorded stages of development, with exponents that can be used to characterize the development of the culture. Synchronized bursting emerges as the culture matures, and these bursts show activity that decays approximately exponentially. From this, we propose a model for neuronal activity within bursts based on the consumption of a shared resource. Our model produces power law distributed avalanches in simulations, and is analytically demonstrated to produce power law distributed inter event intervals with an exponent close to that observed in our data. This indicates that power law distributions in neuronal avalanche size and other observables, can be also an artefact of exponentially decaying activity within synchronized bursts.



This work was supported by a joint Swiss-South Korea collaboration grant (IZKS2_162190).


  1. 1.
    Stanley, H.E.: Introduction to Phase Transitions and Critical Phenomena. Oxford University Press, Oxford (1987)Google Scholar
  2. 2.
    Beggs, J.M., Plenz, D.: Neuronal avalanches in neocortical circuits. J. Neurosci. 23, 11167–11177 (2003)Google Scholar
  3. 3.
    Beggs, J.M., Plenz, D.: Neuronal avalanches are diverse and precise activity patterns that are stable for many hours in cortical slice cultures. J. Neurosci. 24, 5216–5229 (2004)CrossRefGoogle Scholar
  4. 4.
    Corral, A., Perez, C.J., Diaz-Guilera, A., Arenas, A.: Self-organized criticality and synchronization in a lattice model of integrate-and-fire oscillators. Phys. Rev Lett. 74, 118–121 (1995)ADSCrossRefGoogle Scholar
  5. 5.
    Herz, A.V., Hopfield, J.J.: Earthquake cycles and neural reverberations: collective oscillations in systems with pulse-coupled threshold elements. Phys. Rev. Lett. 96, 1222–1225 (1995)ADSCrossRefGoogle Scholar
  6. 6.
    Orlandi, J.G., Soriano, J., Alvarez-Lacalle, E., Teller, S., Casademunt, J.: Noise focusing and the emergence of coherent activity in neuronal cultures. Nat. Phys. 9, 582–590 (2013)CrossRefGoogle Scholar
  7. 7.
    Pasquale, V., Massobrio, P., Bologna, L.L., Chippalone, M., Martinoia, S.: Self-organization and neuronal avalanches in networks of dissociated cortical neurons. Neuroscience 153, 1354 (2008)CrossRefGoogle Scholar
  8. 8.
    Shew, W.L., Yang, H., Petermann, T., Roy, R., Plenz, D.: Neuronal avalanches imply maximum dynamic range in cortical networks at criticality. J. Neurosci. 29, 15595 (2009)CrossRefGoogle Scholar
  9. 9.
    Lorimer, T., Gomez, F., Stoop, R.: Two universal physical principles shape the power-law statistics of real-world networks. Sci. Rep. 5, 12353 (2015)ADSCrossRefGoogle Scholar
  10. 10.
    Haldeman, C., Beggs, J.M.: Critical branching captures activity in living neural networks and maximizes the number of metastable states. Phys. Rev. Lett. 94, 058101 (2005)ADSCrossRefGoogle Scholar
  11. 11.
    Breskin, I., Soriano, J., Moses, E., Tlusty, T.: Percolation in living neural networks. Phys. Rev. Lett 97, 188102 (2006)ADSCrossRefGoogle Scholar
  12. 12.
    Deluca, A., Corral, A.: Fitting and goodness-of-fit test of non-truncated and truncated power-law distributions. Acta Geophys. 61, 1351–1394 (2013)ADSCrossRefGoogle Scholar
  13. 13.
    Marlinski, V., Beloozerova, I.N.: Burst firing of neurons in the thalamic reticular nucleus during locomotion. J. Neurophysiol. 112, 181–192 (2014)CrossRefGoogle Scholar
  14. 14.
    Reed, W.J., Hughes, B.D.: From gene families and genera to incomes and internet file sizes: Why power laws are so common in nature. Phys. Rev. E 66, 067103 (2002)ADSCrossRefGoogle Scholar
  15. 15.
    Newman, M.E.J.: Power laws, Pareto distributions, and Zipf’s law. Contemp. Phys. 46, 323–351 (2005)ADSCrossRefGoogle Scholar
  16. 16.
    Chialvo, D.: Emergent complex neural dynamics. Nat. Phys. 6, 744–450 (2010)CrossRefGoogle Scholar
  17. 17.
    Friedman, N., Ito, S., Brinkman, B.A.W., Shimono, M., DeVille, R.E.L., Dahmen, K.A., Beggs, J.M., Butler, T.C.: Universal critical dynamics in high resolution neuronal avalanche data. Phys. Rev. Lett. 108, 208102 (2012)ADSCrossRefGoogle Scholar
  18. 18.
    Beggs, J.M., Timme, N.: Being critical of criticality in the brain. Front. Physiol. 3, 163 (2012)CrossRefGoogle Scholar
  19. 19.
    Bak, P., Tang, C., Wiesenfeld, K.: Self-organized criticality: an explanation of the 1/f noise. Phys. Rev. Lett. 59, 381 (1987)ADSCrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Damian Berger
    • 1
    • 3
  • Sunghoon Joo
    • 2
  • Tom Lorimer
    • 1
    • 3
  • Yoonkey Nam
    • 2
  • Ruedi Stoop
    • 1
    • 3
    Email author
  1. 1.Institute of Neuroinformatics and Institute for Computational ScienceUniversity of ZürichZurichSwitzerland
  2. 2.Department of Bio and Brain EngineeringKorea Advanced Institute of Science and Technology (KAIST)Yuseong-gu, DaejeonRepublic of Korea
  3. 3.ETH ZürichZurichSwitzerland

Personalised recommendations