IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v335y2004i1p249-278.html
   My bibliography  Save this article

Generative modelling of regulated dynamical behavior in cultured neuronal networks

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437103011154
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2003.11.015?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Eshel Ben-Jacob, 2002. "When order comes naturally," Nature, Nature, vol. 415(6870), pages 370-370, January.
    2. 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.
    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..
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Paul Ormerod, 2010. "La crisis actual y la culpabilidad de la teoría macroeconómica," Revista de Economía Institucional, Universidad Externado de Colombia - Facultad de Economía, vol. 12(22), pages 111-128, January-J.
    2. Dominique Guégan & Wayne Tarrant, 2012. "On the necessity of five risk measures," Annals of Finance, Springer, vol. 8(4), pages 533-552, November.
    3. Alagidede, Paul & Panagiotidis, Theodore, 2009. "Modelling stock returns in Africa's emerging equity markets," International Review of Financial Analysis, Elsevier, vol. 18(1-2), pages 1-11, March.
    4. Ben Klemens, 2013. "A Peer-based Model of Fat-tailed Outcomes," Papers 1304.0718, arXiv.org.
    5. Lombardi, Marco J. & Calzolari, Giorgio, 2009. "Indirect estimation of [alpha]-stable stochastic volatility models," Computational Statistics & Data Analysis, Elsevier, vol. 53(6), pages 2298-2308, April.
    6. Geluk, J.L. & De Vries, C.G., 2006. "Weighted sums of subexponential random variables and asymptotic dependence between returns on reinsurance equities," Insurance: Mathematics and Economics, Elsevier, vol. 38(1), pages 39-56, February.
    7. Erie Febrian & Aldrin Herwany, 2009. "Volatility Forecasting Models and Market Co-Integration: A Study on South-East Asian Markets," Working Papers in Economics and Development Studies (WoPEDS) 200911, Department of Economics, Padjadjaran University, revised Sep 2009.
    8. Vianna Franco, Marco P. & Ribeiro, Leonardo Costa & Albuquerque, Eduardo da Motta e, 2022. "Beyond Random Causes: Harmonic Analysis Of Business Cycles At The Moscow Conjuncture Institute," Journal of the History of Economic Thought, Cambridge University Press, vol. 44(3), pages 456-476, September.
    9. de Lima, Pedro J. F., 1997. "On the robustness of nonlinearity tests to moment condition failure," Journal of Econometrics, Elsevier, vol. 76(1-2), pages 251-280.
    10. P. Kearns & A.R. Pagan, 1993. "Australian Stock Market Volatility: 1875–1987," The Economic Record, The Economic Society of Australia, vol. 69(2), pages 163-178, June.
    11. Igor Fedotenkov, 2020. "A Review of More than One Hundred Pareto-Tail Index Estimators," Statistica, Department of Statistics, University of Bologna, vol. 80(3), pages 245-299.
    12. Marco Rocco, 2011. "Extreme value theory for finance: a survey," Questioni di Economia e Finanza (Occasional Papers) 99, Bank of Italy, Economic Research and International Relations Area.
    13. Runde, Ralf & Scheffner, Axel, 1998. "On the existence of moments: With an application to German stock returns," Technical Reports 1998,25, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    14. Chen, Zhimin & Ibragimov, Rustam, 2019. "One country, two systems? The heavy-tailedness of Chinese A- and H- share markets," Emerging Markets Review, Elsevier, vol. 38(C), pages 115-141.
    15. Eleni Constantinou & Robert Georgiades & Avo Kazandjian & George Kouretas, 2005. "Mean and variance causality between the Cyprus Stock Exchange and major equity markets," Working Papers 0501, University of Crete, Department of Economics.
    16. Siddiqi, Hammad, 2007. "Rational Interacting Agents and Volatility Clustering: A New Approach," MPRA Paper 2984, University Library of Munich, Germany.
    17. Ibrahim Ergen, 2014. "Tail dependence and diversification benefits in emerging market stocks: an extreme value theory approach," Applied Economics, Taylor & Francis Journals, vol. 46(19), pages 2215-2227, July.
    18. Fajardo, José & Farias, Aquiles, 2004. "Generalized Hyperbolic Distributions and Brazilian Data," Brazilian Review of Econometrics, Sociedade Brasileira de Econometria - SBE, vol. 24(2), November.
    19. Scheffknecht, Lukas & Geiger, Felix, 2011. "A behavioral macroeconomic model with endogenous boom-bust cycles and leverage dynamcis," FZID Discussion Papers 37-2011, University of Hohenheim, Center for Research on Innovation and Services (FZID).
    20. Bao, Te & Diks, Cees & Li, Hao, 2018. "A generalized CAPM model with asymmetric power distributed errors with an application to portfolio construction," Economic Modelling, Elsevier, vol. 68(C), pages 611-621.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:phsmap:v:335:y:2004:i:1:p:249-278. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.