Synaptic Plasticity and Spike Synchronisation in Neuronal Networks

Abstract

Brain plasticity, also known as neuroplasticity, is a fundamental mechanism of neuronal adaptation in response to changes in the environment or due to brain injury. In this review, we show our results about the effects of synaptic plasticity on neuronal networks composed by Hodgkin-Huxley neurons. We show that the final topology of the evolved network depends crucially on the ratio between the strengths of the inhibitory and excitatory synapses. Excitation of the same order of inhibition revels an evolved network that presents the rich-club phenomenon, well known to exist in the brain. For initial networks with considerably larger inhibitory strengths, we observe the emergence of a complex evolved topology, where neurons sparsely connected to other neurons, also a typical topology of the brain. The presence of noise enhances the strength of both types of synapses, but if the initial network has synapses of both natures with similar strengths. Finally, we show how the synchronous behaviour of the evolved network will reflect its evolved topology.

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Notes

  1. 1.

    The Brain is wider than the Sky,

    For, put them side by side,

    The one the other will include

    With ease, and you beside.

    Emily Dickinson, Complete Poems. 1924 (1830-1886).

References

  1. 1.

    W. Gerstner, W. Kistler, Spiking Neuron Models: Single Neurons, Populations, Plasticity (Cambridge University Press, Cambridge, 2002)

    Google Scholar 

  2. 2.

    O. Sporns, G. Tononi, R. Kötter, PLoS Comput. Biol. 1(4), e42 (2005)

    ADS  Article  Google Scholar 

  3. 3.

    R.L. Viana, F.S. Borges, K.C. Iarosz, A.M. Batista, S.R. Lopes, I.L. Caldas, Commun. Nonlinear Sci. Numer. Simul. 19(1), 164 (2014)

    ADS  Article  MathSciNet  Google Scholar 

  4. 4.

    F.S. Borges, E.L. Lameu, A.M. Batista, K.C. Iarosz, M.S. Baptista, R.L. Viana, Phys. A 430, 236 (2015)

    Article  Google Scholar 

  5. 5.

    S. Wolfram, Rev. Mod. Phys. 55(3), 601 (1983)

    ADS  Article  MathSciNet  Google Scholar 

  6. 6.

    C.A.S. Batista, E.L. Lameu, A.M. Batista, S.R. Lopes, T. Pereira, G. Zamora-López, J. Kurths, R.L. Viana, Phys. Rev. E 86, 016211 (2012)

    ADS  Article  Google Scholar 

  7. 7.

    E.L. Lameu, F.S. Borges, R.R. Borges, K.C. Iarosz, I.L. Caldas, A.M. Batista, R.L. Viana, J. Kurths. Chaos. 26, 043107 (2016)

    Article  Google Scholar 

  8. 8.

    E.L. Lameu, F.S. Borges, R.R. Borges, A.M. Batista, M.S. Baptista, R.L. Viana, Commun. Nonlinear Sci. Numer. Simul. 34, 45 (2016)

    ADS  Article  MathSciNet  Google Scholar 

  9. 9.

    M. Girardi-Schappo, M.H.R. Tragtenberg, O. Kinouchi, J. Neurosci. Meth. 220, 116 (2013)

    Article  Google Scholar 

  10. 10.

    M. Girardi-Schappo, G.S. Bortolotto, R.V. Stenzinger, J.J. Gonsalves, M.H.R. Tragtenberg, PLoS ONE 12(3), e0174621 (2017)

    Article  Google Scholar 

  11. 11.

    B. Ibarz, J.M. Casado, M.A.F. Sanjuán, Phys. Rep. 501, 1 (2011)

    ADS  Article  Google Scholar 

  12. 12.

    L.F. Abbott, Brain Res. Bull. 50, 303 (1999)

    Article  Google Scholar 

  13. 13.

    M.I. Rabinovich, P. Varona, A.I. Selverston, H.D.I. Abarbanel, Rev. Mod. Phys. 78, 1213 (2006)

    ADS  Article  Google Scholar 

  14. 14.

    C.A.S. Batista, R.L. Viana, S.R. Lopes, A.M. Batista, Phys. A 410, 628 (2014)

    Article  MathSciNet  Google Scholar 

  15. 15.

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

    ADS  Article  MathSciNet  Google Scholar 

  16. 16.

    L. Lapicque, J. Physiol, Pathol. Gen. 9, 620 (1907)

    Google Scholar 

  17. 17.

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

    Article  Google Scholar 

  18. 18.

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

    ADS  Article  Google Scholar 

  19. 19.

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

    ADS  Article  MathSciNet  Google Scholar 

  20. 20.

    M.S. Baptista, J.X. de Carvalho, M.S. Hussein, PloS ONE 3, e3479 (2008)

    ADS  Article  Google Scholar 

  21. 21.

    C.G. Antonopoulos, S. Srivastava, S.S. Pinto, M.S. Baptista, PLoS Comput. Biol. 11, e1004372 (2015)

    ADS  Article  Google Scholar 

  22. 22.

    P. Uhlhaas, G. Pipa, B. Lima, L. Melloni, S. Neuenschwander, D. Nikolić, W. Singer, Front. Integr. Neurosci. 3, 17 (2009)

    Article  Google Scholar 

  23. 23.

    L. Melloni, C. Molina, M. Pena, D. Torres, W. Singer, E. Rodriguez, J. Neurosci. 27(11), 2858 (2007)

    Article  Google Scholar 

  24. 24.

    F.S. Borges, P.R. Protachevicz, E.L. Lameu, R.C. Bonetti, K.C. Iarosz, I.L. Caldas, M.S. Baptista, A.M. Batista, Neural Netw. 90, 1 (2017)

    Article  Google Scholar 

  25. 25.

    J. Fell, N. Axmacher, Nat Rev. Neurosci. 12, 105 (2011)

    Article  Google Scholar 

  26. 26.

    L.L. Rubchinsky, C. Park, R.M. Worth, Nonlinear Dyn. 68, 329 (2012)

    Article  Google Scholar 

  27. 27.

    E.L. Lameu, F.S. Borges, R.R. Borges, K.C. Iarosz, I.L. Caldas, A.M. Batista, R.L. Viana, J. Kurths. Chaos. 26, 043107 (2016)

    Article  Google Scholar 

  28. 28.

    E.L. Bennett, M.C. Diamond, D. Krech, M.R. Rosenzweig, Science. 146, 610 (1964)

    ADS  Article  Google Scholar 

  29. 29.

    W. James, The Principles of Psychology (Henry Holt and Company, New York, 1890)

    Google Scholar 

  30. 30.

    K.S. Lashley, Psychol. Bull. 30, 237 (1923)

    Google Scholar 

  31. 31.

    E.L. Bennett, M.C. Diamond, D. Krech, M.R. Rosenzweig, Science. 146, 610 (1964)

    ADS  Article  Google Scholar 

  32. 32.

    M.C. Diamond, D. Krech, M.R. Rosenzweig, J. Comp. Neurol. 123, 111 (1964)

    Article  Google Scholar 

  33. 33.

    D.O. Hebb, The Organization of Behavior (Wiley, New York, 1949)

    Google Scholar 

  34. 34.

    W. Gerstner, H. Sprekeler, G. Deco, Science. 338, 60 (2012)

    ADS  Article  Google Scholar 

  35. 35.

    H. Markram, W. Gerstner, P.J. Sjostrom, Front. Synaptic Neurosci. 4, 1 (2012)

    Article  Google Scholar 

  36. 36.

    R.R. Borges, F.S. Borges, E.L. Lameu, A.M. Batista, K.C. Iarosz, I.L. Caldas, R.L. Viana, M.A.F. Sanjuán, Commun. Nonlinear Sci. Numer. Simul. 34, 12 (2016)

    ADS  Article  MathSciNet  Google Scholar 

  37. 37.

    G.-Q. Bi, M.-M. Poo, J. Neurosci. 18(24), 10464 (1998)

    Google Scholar 

  38. 38.

    J.S. Haas, T. Nowotny, H.D.I. Abarbanel, J. Neurophysiol. 96, 3305 (2006)

    Article  Google Scholar 

  39. 39.

    B. Alberts, A. Johnson, J. Lewis, M. Raff, K. Roberts, P. Walter. Molecular Biology of the Cell, 4th ed (Garland Science, New York, 2002)

    Google Scholar 

  40. 40.

    M.A. Arbib, The Handbook of Brain Theory and Neural Networks (The MIT Press, Cambridge, 2002)

    Google Scholar 

  41. 41.

    E. Gouaux, R. Mackinnon, Science. 310(5), 344 (2009)

    Google Scholar 

  42. 42.

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

    ADS  Article  MathSciNet  Google Scholar 

  43. 43.

    G. Deco, A. Buehlmann, T. Masquelier, E. Hugues, Front. Hum. Neurosci. 5, 1 (2011)

    Article  Google Scholar 

  44. 44.

    V.O. Popovych, S. Yanchuk, P.A. Tass, Sci. Rep. 3, 2926 (2013)

    ADS  Article  Google Scholar 

  45. 45.

    Y. Kuramoto, Chemical Oscillations, Waves, and Turbulence (Springer, Berlin, 1984)

    Google Scholar 

  46. 46.

    W. Gerstner, Front. Synaptic Neurosci. 2, 1 (2010)

    Article  Google Scholar 

  47. 47.

    D.E. Feldman, Neuron. 75, 556 (2012)

    Article  Google Scholar 

  48. 48.

    T.V. Bliss, T. Lomo. J. Physiol. 232, 331 (1973)

    Article  Google Scholar 

  49. 49.

    S. Song, K.D. Miller, L.F. Abbott, Nat. Neurosci. 3, 919 (2000)

    Article  Google Scholar 

  50. 50.

    W. Gerstner, R. Kempter, J.L. van Hemmen, Nature 383, 76 (1996)

    ADS  Article  Google Scholar 

  51. 51.

    H. Markram, B. Sakmann, Soc. Neurosci. Abstr. 21, 1 (2007)

    Google Scholar 

  52. 52.

    H. Markram, J. Lübke, M. Frotscher, B. Sakmann, Science 275, 213 (1997)

    Article  Google Scholar 

  53. 53.

    Y. Frégnac, M. Pananceau, A. René, N. Huguet, O. Marre, M. Levy, D.E. Schulz, Front. Synaptic Neurosci. 2, 73 (2010)

    Article  Google Scholar 

  54. 54.

    K.A. Buchanan, J.R. Mellor, Front Synaptic Neurosci. 2, 94 (2010)

    Article  Google Scholar 

  55. 55.

    C.R. Noback, N.L. Strominger, R.J. Demarest, D.A. Ruggiero, The Human Nervous Systems: Structure and Function, 6th ed (Humana Press, Totowa, NJ, 2005)

    Google Scholar 

  56. 56.

    E.K. Towlson, E. Vértes, S.E. Anhert, W.R. Schafer, E.T. Bullmore, J. Neurosc. 33, 6380 (2013)

    Article  Google Scholar 

  57. 57.

    P.E. Vértes, A. Alexander-Bloch, E.T. Bullmore, Philos. Trans. R. Soc. Lond. B Biol. Sci. 369, 20130531 (2014)

    Article  Google Scholar 

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Acknowledgements

This work was possible by partial financial support from the following Brazilian government agencies: CNPq (154705/2016-0, 311467/2014-8), CAPES, Fundação Araucária, and São Paulo Research Foundation (processes FAPESP 2011/19296-1, 2015/07311-7, 2016/16148-5, 2016/23398-8, 2015/50122-0). Research supported by grant 2015/50122-0 São Paulo Research Foundation (FAPESP) and DFG-IRTG 1740/2.

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Correspondence to Kelly C. Iarosz.

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Borges, R.R., Borges, F.S., Lameu, E.L. et al. Synaptic Plasticity and Spike Synchronisation in Neuronal Networks. Braz J Phys 47, 678–688 (2017). https://doi.org/10.1007/s13538-017-0529-5

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Keywords

  • Neuronal network
  • Plasticity
  • Synchronisation