Neuronal Multistability Induced by Delay

  • Cristina Masoller
  • M. C. Torrent
  • Jordi García-Ojalvo
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4668)

Abstract

Feedback circuits are important for understanding the emergence of patterns of neural activity. In this contribution we study how a delayed circuit representing a recurrent synaptic connection interferes with neuronal nonlinear dynamics. The neuron is modeled using a Hodgkin-Huxley type model in which the firing pattern depends on subthreshold oscillations, and the feedback is included as a time delayed linear term in the membrane voltage equation. In the regime of subthreshold oscillations the feedback amplifies the oscillation amplitude, inducing threshold crossings and firing activity that is self regularized by the delay. We also study a small neuron ensemble globally coupled through the delayed mean field. We find that the firing pattern is controlled by the delay. Depending on the delay, either all neurons fire spikes, or they all exhibit subthreshold activity, or the ensemble divides into clusters, with some neurons displaying subthreshold activity while others fire spikes.

Keywords

Oscillation Amplitude Single Neuron Feedback Strength Recurrent Connection Cold Receptor 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, log in to check access.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Suel, G.M., Garcia-Ojalvo, J., Liberman, L.M., Elowitz, M.B.: An excitable gene regulatory circuit induces transient cellular differentiation. Nature 440, 545 (2006)CrossRefGoogle Scholar
  2. 2.
    Stepan, G., Kollar, L.: Math. Comp. Modelling 31, 199 (2000)MATHGoogle Scholar
  3. 3.
    Cabrera, J.L., Milton, J.G.: On-off intermittency in a human balancing task. Phys. Rev. Lett. 89, 158702 (2002)CrossRefGoogle Scholar
  4. 4.
    Moschovakis, A.K., Scudder, C.A., Highstein, S.M.: The microscopic anatomy and physiology of the mammalian saccadic system. Prog. Neurobiol. 50, 133 (1996)CrossRefGoogle Scholar
  5. 5.
    Mergenthaler, K., Engbert, R.: Modeling the control of fixational eye movements with neurophysiological delays. Phys. Rev. Lett. 98, 138104 (2007)CrossRefGoogle Scholar
  6. 6.
    Debanne, D., Gahwiler, B.H., Thompson, S.M.: Long-term synaptic plasticity between pairs of individual CA3 pyramidal cells in rat hippocampal slice cultures. J. of Physiol (London) 507, 237–247 (1998)CrossRefGoogle Scholar
  7. 7.
    Nakazawa, K., Quirk, M.C, Chitwood, R.A., Watanabe, M., Yeckel, M.F., Sun, L.D., Kato, A., Carr, C.A., Johnston, D., Wilson, M.A., Tonegawa, S.: Requirement for hippocampal CA3 NMDA receptors in associative memory recall. Science 297, 211–218 (2002)CrossRefGoogle Scholar
  8. 8.
    Plant, R.E.: A Fitzhugh differential-difference equation modeling recurrent neural feedback. SIAM J. Appl. Math. 40, 150–162 (1981)MATHCrossRefGoogle Scholar
  9. 9.
    Foss, J., Longtin, A., Mensour, B., Milton, J.: Multiestability and delayed recurrent loops. Phys. Rev. Lett. 76, 708–711 (1996)CrossRefGoogle Scholar
  10. 10.
    Foss, J., Milton, J.: Multistability in recurrent neural loops arising from delay. J. Neurophysiol. 84, 975–985 (2000)Google Scholar
  11. 11.
    Martinez, O.D., Segundo, J.P.: Behavior of a single neuron in a recurrent excitatory loop. Biological Cybernetics 47, 33–41 (1983)CrossRefGoogle Scholar
  12. 12.
    Pakdaman, K., Vibert, J.F., Bousssard, E., Azmy, N.: Single neuron with recurrent excitation: Effect of the transmission delay. Neural Networks 9, 797–818 (1996)CrossRefGoogle Scholar
  13. 13.
    Vibert, J.F., Alvarez, F., Pham, J.: Effects of transmission delays and noise in recurrent excitatory neural networks. BioSystems 48, 255–262 (1998)CrossRefGoogle Scholar
  14. 14.
    Rodriguez, E., George, N., Lachaux, J.P., Martinerie, J., Renault, B., Varela, F.J.: Perception’s shadow: long-distance synchronization of human brain activity. Nature 397, 430–433 (1999)CrossRefGoogle Scholar
  15. 15.
    Rosenblum, M.G., Pikovsky, A.S.: Phys. Rev. Lett. 92, 114102 (2004)CrossRefGoogle Scholar
  16. 16.
    Rosenblum, M., Pikovsky, A.: Delayed feedback control of collective synchrony: an approach to suppression of pathological brain rhythms. Phys. Rev. E 70, 041904 (2004)CrossRefGoogle Scholar
  17. 17.
    Rosenblum, M., Tukhlina, N., Pikovsky, A., Cimponeriu, L.: Delayed feedback suppression of collective rhythmic activity in a neuronal ensemble. Int. J. Bif. Chaos 16, 1989 (2006)CrossRefGoogle Scholar
  18. 18.
    Popovych, O.V., Hauptmann, C., Tass, P.A.: Effective desynchronization by nonlinear delayed feedback. Phys. Rev. Lett. 94, 164102 (2005)CrossRefGoogle Scholar
  19. 19.
    Braun, H.A., Huber, M.T., Dewald, M., Schafer, K., Voigt, K.: Int. J. Bif. Chaos Appl. Sci. Eng. 8, 881–889 (1998)MATHCrossRefGoogle Scholar
  20. 20.
    Braun, H.A., Wissing, H., Schafer, K., Hirsch, M.C.: Oscillation and noise determine signal transduction in shark multimodal sensory cells. Nature 367, 270–273 (1994)CrossRefGoogle Scholar
  21. 21.
    Braun, H.A., Bade, H., Hensel, H.: Static and dynamic discharge patterns of bursting cold fibers related to hypothetical receptor mechanisms. Pflügers Arch. 386, 1–9 (1980)CrossRefGoogle Scholar
  22. 22.
    Braun, H.A., Voigt, K., Huber, M.T.: Oscillations, resonances and noise: basis of flexible neuronal pattern generation. Biosystems 71, 39–50 (2003)CrossRefGoogle Scholar
  23. 23.
    Braun, W., Eckhard, B., Braun, H.A., Huber, M.: Phase-space structure of a thermoreceptor. Phys. Rev. E 62, 6352–6360 (2000)CrossRefGoogle Scholar
  24. 24.
    Braun, H.A., Huber, M.T., Anthes, N., Voigt, K., Neiman, A., Pei, X., Moss, F.: Interactions between slow and fast conductances in the Huber/Braun model of cold-receptor discharges. Neurocomputing 32, 51–59 (2000)CrossRefGoogle Scholar
  25. 25.
    Feudel, U., Neiman, A., Pei, X., Wojtenek, W., Braun, H., Huber, M., Moss, F.: Homoclinic bifurcation in a Hodgkin-Huxley model of thermally sensitive neurons. Chaos 10, 231–239 (2000)MATHCrossRefGoogle Scholar
  26. 26.
    Neiman, A., Pei, X., Russell, D., Wojtenek, W., Wilkens, L., Moss, F., Braun, H.A., Huber, M.T., Voigt, K.: Synchronization of the noisy electrosensitive cells in the paddlefish. Phys. Rev. Lett. 82, 660–663 (1999)CrossRefGoogle Scholar
  27. 27.
    Zhou, C.S., Kurths, J.: Noise-induced synchronization and coherence resonance of a Hodgkin-Huxley model of thermally sensitive neurons. Chaos 13, 401–409 (2003)CrossRefGoogle Scholar
  28. 28.
    Ciszak, M., Calvo, O., Masoller, C., Mirasso, C.R., Toral, R.: Anticipating the response of excitable systems driven by random forcing. Phys. Rev. Lett. 90, 204102 (2003)CrossRefGoogle Scholar
  29. 29.
    Sainz-Trapaga, M., Masoller, C., Braun, H.A., Huber, M.T.: Influence of time-delayed feedback in the firing pattern of thermally sensitive neurons. Phys. Rev. E 70, 031904 (2004)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Cristina Masoller
    • 1
  • M. C. Torrent
    • 1
  • Jordi García-Ojalvo
    • 1
  1. 1.Departament de Física i Enginyeria Nuclear, Universitat Politècnica de Catalunya, Colom 11, E-08222 Terrassa, BarcelonaSpain

Personalised recommendations