Skip to main content
SpringerLink
Log in

Dynamical complexity in the C.elegans neural network

  • Regular Article
  • Session C: Papers II
  • Published:
The European Physical Journal Special Topics Aims and scope Submit manuscript

Abstract

We model the neuronal circuit of the C.elegans soil worm in terms of a Hindmarsh-Rose system of ordinary differential equations, dividing its circuit into six communities which are determined via the Walktrap and Louvain methods. Using the numerical solution of these equations, we analyze important measures of dynamical complexity, namely synchronicity, the largest Lyapunov exponent, and the ΦAR auto-regressive integrated information theory measure. We show that ΦAR provides a useful measure of the information contained in the C.elegans brain dynamic network. Our analysis reveals that the C.elegans brain dynamic network generates more information than the sum of its constituent parts, and that attains higher levels of integrated information for couplings for which either all its communities are highly synchronized, or there is a mixed state of highly synchronized and desynchronized communities.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. A. Damasio, Self Comes to Mind: Constructing the Conscious Brain (Vintage, 2012)

  2. S. Dehaene, J.P. Changeux, Neuron. 70, 200 (2011)

    Article  Google Scholar 

  3. G. Tononi, O. Sporns, BMC Neurosci., 31 (2003)

  4. G. Tononi, BMC Neurosci. 5, 42 (2004)

    Article  Google Scholar 

  5. G. Tononi, Prog. Brain Res. 150, 109 (2005)

    Article  Google Scholar 

  6. D. Balduzzi, G. Tononi, PLOS Comput. Biol. 4, e1000091 (2008)

    Article  ADS  Google Scholar 

  7. G. Tononi, Biol. Bull. 215, 216 (2008)

    Article  Google Scholar 

  8. D. Balduzzi, G. Tononi, PLOS Comput Biol. 5, e1000462 (2009)

    Article  ADS  MathSciNet  Google Scholar 

  9. M. Oizumi, L. Albantakis, G. Tononi, PLOS Comput. Biol. 10, e1003588 (2014)

    Article  ADS  Google Scholar 

  10. G. Tononi, Pantheon Books (2012)

  11. 2010–2011 [Online; accessed 27-February-2014]. Connectome File Format – Datasets (Version 2.0). Available: http://cmtk.org/viewer/datasets/

  12. L.R. Varshney, B.L. Chen, E. Paniagua, D.H. Hall, D.B. Chklovskii, PLOS Comput. Biol. 7, e1001066 (2011)

    Article  ADS  Google Scholar 

  13. Y. Bar-yam, Dynamics of Complex Systems (Studies in Nonlinearity) (Westview Press, 2003)

  14. G. Nicolis, C. Nicolis, Foundations of Complex Systems (World Scientific, Singapore, 2007)

  15. A. Fuchs, Nonlinear Dynamics in Complex Systems (Springer-Verlag Berlin Heidelberg, 2013)

  16. G. Tononi, G.M. Edelman, Science, 1846 (1998)

  17. I. Belykh, E. Lange, M. Hasler, Phys. Rev. Lett. 94, 188101 (2005)

    Article  ADS  Google Scholar 

  18. J. Gómez-Gardeñes, G. Zamora-López, Y. Moreno, A. Arenas, PLoS ONE 5, e12313 (2010)

    Article  ADS  Google Scholar 

  19. M.S. Baptista, F.M. Kakmeni, C. Grebogi, Phys. Rev. E 82, 036203 (2010)

    Article  ADS  MathSciNet  Google Scholar 

  20. A. Arenas, A.D. Guilera, J. Kurths, Y. Moreno, C. Zhou, Phys. Rep. 469, 93 (2008)

    Article  ADS  MathSciNet  Google Scholar 

  21. M. Benedek, S. Bergner, T. Könen, A. Fink, A.C. Neubauer, Neuropsychologia 49, 3505 (2011)

    Article  Google Scholar 

  22. G. Benettin, L. Galgani, A. Giorgilli, J.M. Strelcyn, Numer. Appl. Meccanica. 15, 21 (1980)

    Article  Google Scholar 

  23. A.D. Barrett, A.K. Seth, PLOS Comput. Biol. 7, e1001052 (2011)

    Article  ADS  MathSciNet  Google Scholar 

  24. A.L. Hodgkin, A.F. Huxley, J. Physiol. 117, 500 (1952)

    Article  Google Scholar 

  25. C. Gally, J.L. Bessereau, Med. Sci. (Paris) 19, 725 (2003)

    Article  Google Scholar 

  26. C.G. Antonopoulos, S. Srivastava, S.E.D.S. Pinto, M.S. Baptista, PLOS Comput. Biol. 11, e1004372 (2015)

    Article  ADS  Google Scholar 

  27. J.L. Hindmarsh, R.M. Rose, Proc. R. Soc. London Ser. B 221, 87 (1984)

    Article  ADS  Google Scholar 

  28. M.S. Baptista, J. Kurths, Phys. Rev. E 77, 026205 (2008)

    Article  ADS  MathSciNet  Google Scholar 

  29. T. Pereira, M.S. Baptista, J. Kurths, Europhys. Lett. 77, 40006 (2007)

    Article  ADS  Google Scholar 

  30. N. Burić, K. Todorović, N. Vasović, Phys. Rev. E 75, 067204 (2007)

    Article  ADS  Google Scholar 

  31. T.D.L. Prado, S.R. Lopes, C.A.S. Batista, J. Kurths, R.L. Viana, Phys. Rev. E 90, 032818 (2014)

    Article  ADS  Google Scholar 

  32. Y. Kuramoto, D. Battogtokh, Nonlin. Phenom. Complex Syst. 5, 380 (2002)

    Google Scholar 

  33. P. Pons, M. Latapy, Lect. Notes Comput. Sci. 3733, 284 (2005)

    Article  Google Scholar 

  34. V.D. Blondel, J.L. Guillaume, R. Lambiotte, E. Lefebvre, J. Stat. Mech.: Theor. Exper. 2008, P10008 (2008)

    Article  Google Scholar 

  35. 2009 [Online; accessed 4-March-2014]. Community Detection for NetworkX’s Documentation. Available: http://perso.crans.org/aynaud/communities/

  36. J. Hizanidis, V. Kanas, A. Bezerianos, T. Bountis, Int. J. Bif. Chaos. 24, 1450030 (2014)

    Article  MathSciNet  Google Scholar 

  37. J. Hizanidis, N. Kouvaris, G. Zamora-Lopéz, A. Díaz-Guilera, C.G. Antonopoulos, Scientific Reports 6, 19845 (2016)

    Article  ADS  Google Scholar 

  38. R. Srinivasan, D.P. Russell, G.M. Edelman, G. Tononi, J. Neurosc. 19, 5435 (1999)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematical Sciences, University of Essex, Wivenhoe Park, Essex CO4 3SQ, UK

    C.G. Antonopoulos

  2. Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge CB3 0WA, UK

    A.S. Fokas

  3. Center for Research and Applications of Nonlinear Systems, Department of Mathematics, University of Patras, Patras, 26500, Greece

    T.C. Bountis

Authors
  1. C.G. Antonopoulos
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A.S. Fokas
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. T.C. Bountis
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Antonopoulos, C., Fokas, A. & Bountis, T. Dynamical complexity in the C.elegans neural network. Eur. Phys. J. Spec. Top. 225, 1255–1269 (2016). https://doi.org/10.1140/epjst/e2016-02670-3

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1140/epjst/e2016-02670-3

Search

Navigation