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Generative modelling of regulated dynamical behavior in cultured neuronal networks

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  • Volman, Vladislav
  • Baruchi, Itay
  • Persi, Erez
  • Ben-Jacob, Eshel

Abstract

The spontaneous activity of cultured in vitro neuronal networks exhibits rich dynamical behavior. Despite the artificial manner of their construction, the networks’ activity includes features which seemingly reflect the action of underlying regulating mechanism rather than arbitrary causes and effects. Here, we study the cultured networks dynamical behavior utilizing a generative modelling approach. The idea is to include the minimal required generic mechanisms to capture the non-autonomous features of the behavior, which can be reproduced by computer modelling, and then, to identify the additional features of biotic regulation in the observed behavior which are beyond the scope of the model. Our model neurons are composed of soma described by the two Morris–Lecar dynamical variables (voltage and fraction of open potassium channels), with dynamical synapses described by the Tsodyks–Markram three variables dynamics. The model neuron satisfies our self-consistency test: when fed with data recorded from a real cultured networks, it exhibits dynamical behavior very close to that of the networks’ “representative” neuron. Specifically, it shows similar statistical scaling properties (approximated by similar symmetric Lévy distribution with finite mean). A network of such M–L elements spontaneously generates (when weak “structured noise” is added) synchronized bursting events (SBEs) similar to the observed ones. Both the neuronal statistical scaling properties within the bursts and the properties of the SBEs time series show generative (a new discussed concept) agreement with the recorded data. Yet, the model network exhibits different structure of temporal variations and does not recover the observed hierarchical temporal ordering, unless fed with recorded special neurons (with much higher rates of activity), thus indicating the existence of self-regulation mechanisms. It also implies that the spontaneous activity is not simply noise-induced. Instead, the network seems to possess excitable media like abilities, presumably provided by the underlying glia fabric.

Suggested Citation

  • Volman, Vladislav & Baruchi, Itay & Persi, Erez & Ben-Jacob, Eshel, 2004. "Generative modelling of regulated dynamical behavior in cultured neuronal networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 335(1), pages 249-278.
    • Handle: RePEc:eee:phsmap:v:335:y:2004:i:1:p:249-278
    DOI: 10.1016/j.physa.2003.11.015
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    References listed on IDEAS

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    1. Segev, Ronen & Ben-Jacob, Eshel, 2001. "Spontaneous synchronized bursting in 2D neural networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 302(1), pages 64-69.
    2. Eshel Ben-Jacob, 2002. "When order comes naturally," Nature, Nature, vol. 415(6870), pages 370-370, January.
    3. Benoit Mandelbrot, 2015. "The Variation of Certain Speculative Prices," World Scientific Book Chapters, in: Anastasios G Malliaris & William T Ziemba (ed.), THE WORLD SCIENTIFIC HANDBOOK OF FUTURES MARKETS, chapter 3, pages 39-78, World Scientific Publishing Co. Pte. Ltd..
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    1. di Volo, Matteo & Livi, Roberto, 2013. "The influence of noise on synchronous dynamics in a diluted neural network," Chaos, Solitons & Fractals, Elsevier, vol. 57(C), pages 54-61.
    2. Bonacini, E. & Burioni, R. & di Volo, M. & Groppi, M. & Soresina, C. & Vezzani, A., 2016. "How single node dynamics enhances synchronization in neural networks with electrical coupling," Chaos, Solitons & Fractals, Elsevier, vol. 85(C), pages 32-43.
    3. Leonid A Safonov & Yoshikazu Isomura & Siu Kang & Zbigniew R Struzik & Tomoki Fukai & Hideyuki Câteau, 2010. "Near Scale-Free Dynamics in Neural Population Activity of Waking/Sleeping Rats Revealed by Multiscale Analysis," PLOS ONE, Public Library of Science, vol. 5(9), pages 1-11, September.

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