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Two-fold effects of inhibitory neurons on the onset of synchronization in Izhikevich neuronal networks

  • Peng-Xiang Lin
  • Chong-Yang Wang
  • Zhi-Xi WuEmail author
Regular Article

Abstract

Synchronization is a widely studied phenomenon in neuroscience. The ever-increasing morbidity of brain diseases makes the investigation on this topic significant in both psychology and medicine. In this paper, we consider an Izhikevich neuronal network composed of both excitatory and inhibitory neurons, and introduce the Tsodyks-Uziel-Markram (TUM) model of neuronal transmission. To study the impact of inhibitory neurons in the synchronization, we make comparative studies by considering the inhibitory neurons could fire either spontaneously or not in the network. Simulation results exemplify that the synchronized system shows different periodic-like oscillatory patterns of multi-stripes. We find that the inhibitory neurons have two-fold impacts on the oscillatory patterns. On the one hand, they can delay the firing of the neurons, deleterious for synchronization. On the other hand, they are able to facilitate the transition of the oscillatory patterns, beneficial for synchronization.

Graphical abstract

Keywords

Statistical and Nonlinear Physics 

References

  1. 1.
    A. Pikovsky, M. Rosenblum, K. Jürgen, Synchronization: A Universal Concept in Nonlinear Sciences (Cambridge University Press, Cambridge, UK, 2001) Google Scholar
  2. 2.
    G. Buzsáki, A. Draguhn, Science 304, 1926 (2004) ADSCrossRefGoogle Scholar
  3. 3.
    M. Bartos, I. Vida, P. Jonas, Nat. Rev. Neurosci. 8, 45 (2007) CrossRefGoogle Scholar
  4. 4.
    P. Fries, Annu. Rev. Neurosci. 32, 209 (2009) CrossRefGoogle Scholar
  5. 5.
    G. Buzsáki, Rhythms of the Brain (Oxford University Press, New York, 2006) Google Scholar
  6. 6.
    X.-J. Wang, Physiol. Rev. 90, 1195 (2010) CrossRefGoogle Scholar
  7. 7.
    M. Steriade, Neuronal Substrates of Sleep and Epilepsy (Cambridge University Press, Cambridge, UK, 2003) Google Scholar
  8. 8.
    J.P. Bolam, C.A. Ingham, P.J. Magill, The Basal Ganglia VIII (Springer Science & Business Media, New York, 2005) Google Scholar
  9. 9.
    P.J. Uhlhaas, W. Singer, Nat. Rev. Neurosci. 11, 100 (2010) CrossRefGoogle Scholar
  10. 10.
    O. Yizhar, L.E. Fenno, M. Prigge, F. Schneider, T.J. Davidson, D.J. OShea, V.S. Sohal, I. Goshen, J. Finkelstein, J.T. Paz, Nature 477, 171 (2011) ADSCrossRefGoogle Scholar
  11. 11.
    W. Gerstner, W.M. Kistler, R. Naud, L. Paninski, Neuronal Dynamics: From single neurons to networks and models of cognition (Cambridge University Press, Cambridge, UK, 2014) Google Scholar
  12. 12.
    A.L. Hodgkin, A.F. Huxley, J. Physiol. 117, 500 (1952) CrossRefGoogle Scholar
  13. 13.
    C. Koch, Biophysics of computation (Oxford University Press, Oxford, 1999) Google Scholar
  14. 14.
    K. Miura, M. Okada, Phys. Rev. E 70, 021914 (2004) ADSMathSciNetCrossRefGoogle Scholar
  15. 15.
    E.M. Izhikevich, IEEE Trans. Neural Networks 14, 1569 (2003) CrossRefGoogle Scholar
  16. 16.
    S.-J. Wang, G. Ouyang, J. Guang, M. Zhang, K.Y. Michael Wong, C. Zhou, Phys. Rev. Lett. 116, 018101 (2016) ADSCrossRefGoogle Scholar
  17. 17.
    C.-Y. Wang, Z.-X. Wu, M.Z.Q. Chen, Phys. Rev. E 95, 012310 (2017) ADSCrossRefGoogle Scholar
  18. 18.
    D. Purves, G.J. Augustine, D. Fitzpatrick, W.C. Hall, A.-S. LaMantia, J.O. McNamara, L.E. White, in Neuroscience, 4th edn. (Sinauer Associates, Sunderland, Massachusetts USA, 2008) Google Scholar
  19. 19.
    R.S. Zucker, W.G. Regehr, Annu. Rev. Physiol. 64, 355 (2002) CrossRefGoogle Scholar
  20. 20.
    M. Tsodyks, A. Uziel, H. Markram, J. Neurosci. 20, RC50 (2000) CrossRefGoogle Scholar
  21. 21.
    H. Markram, M. Tsodyks, Nature 382, 807 (1996) ADSCrossRefGoogle Scholar
  22. 22.
    M.V. Tsodyks, H. Markram, Proc. Natl. Acad. Sci. USA 94, 719 (1997) ADSCrossRefGoogle Scholar
  23. 23.
    P. Scott, A.I. Cowan, C. Stricker, Phys. Rev. E 85, 041921 (2012) ADSCrossRefGoogle Scholar
  24. 24.
    M. di Volo, R. Livi, S. Luccioli, A. Politi, A. Torcini, Phys. Rev. E 87, 032801 (2013) ADSCrossRefGoogle Scholar
  25. 25.
    M. Uzuntarla, J.J. Torres, P. So, M. Ozer, E. Barreto, Phys. Rev. E 95, 012404 (2017) ADSCrossRefGoogle Scholar
  26. 26.
    C. van Vreeswijk, H. Sompolinsky, Science 274, 1724 (1996) ADSCrossRefGoogle Scholar
  27. 27.
    N. Brunel, Neurocomputing 32–33, 307 (2000) CrossRefGoogle Scholar
  28. 28.
    C. Van Vreeswijk, L.F. Abbott, G. Bard Ermentrout, J. Comput. Neurosci. 1, 313 (1994) CrossRefGoogle Scholar
  29. 29.
    T. Shimokawa, S. Shinomoto, Phys. Rev. E 73, 066221 (2006) ADSMathSciNetCrossRefGoogle Scholar
  30. 30.
    M. di Volo, A. Torcini, Phys. Rev. Lett. 121, 128301 (2018) ADSCrossRefGoogle Scholar
  31. 31.
    D. Guo, Q. Wang, M. Perc, Phys. Rev. E 85, 061905 (2012) ADSCrossRefGoogle Scholar
  32. 32.
    H. Hu, J. Gan, P. Jonas, Science 345, 1255263 (2014) CrossRefGoogle Scholar
  33. 33.
    A.K. Vidybida, K.G. Kravchuk, Biosystems 112, 224 (2013) CrossRefGoogle Scholar
  34. 34.
    M. di Volo, R. Burioni, M. Casartelli, R. Livi, A. Vezzani, Phys. Rev. E 93, 012305 (2016) ADSMathSciNetCrossRefGoogle Scholar
  35. 35.
    E. Bertolotti, R. Burioni, M. di Volo, A. Vezzani, Phys. Rev. E 95, 012308 (2017) ADSCrossRefGoogle Scholar
  36. 36.
    F. Pittorino, M.I. Berganza, M. di Volo, A. Vezzani, R. Burioni, Phys. Rev. Lett. 118, 098102 (2017) ADSCrossRefGoogle Scholar
  37. 37.
    E. Fuchs, A. Ayali, E. Ben-Jacob, S. Boccaletti, Phys. Biol. 6, 036018 (2009) ADSCrossRefGoogle Scholar
  38. 38.
    A.L. Hodgkin, J. Physiol. 107, 165 (1948) CrossRefGoogle Scholar
  39. 39.
    L. Neltner, D. Hansel, G. Mato, C. Meunier, Neural Comput. 12, 1607 (2000) CrossRefGoogle Scholar
  40. 40.
    C. Li, Q. Zheng, Phys. Biol. 7, 036010 (2010) ADSCrossRefGoogle Scholar
  41. 41.
    G. Buzski, E. Eidelberg, Brain Res. 230, 346 (1981) CrossRefGoogle Scholar
  42. 42.
    R. Miles, J. Physiol. 428, 61 (1990) CrossRefGoogle Scholar
  43. 43.
    S. Panzeri, E.T. Rolls, F. Battaglia, R. Lavis, Network 12, 423 (2001) CrossRefGoogle Scholar
  44. 44.
    M. Yi, L. Yang, Phys. Rev. E 81, 061924 (2010) ADSCrossRefGoogle Scholar
  45. 45.
    A.A. Farokhniaee, E.W. Large, Phys. Rev. E 95, 062414 (2017) ADSMathSciNetCrossRefGoogle Scholar

Copyright information

© EDP Sciences / Società Italiana di Fisica / Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Institute of Computational Physics and Complex Systems, Lanzhou UniversityLanzhouP.R. China

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