Journal of Biological Physics

, Volume 37, Issue 3, pp 361–373 | Cite as

Ion concentration dynamics as a mechanism for neuronal bursting

  • Ernest BarretoEmail author
  • John R. Cressman
Original Paper


We describe a simple conductance-based model neuron that includes intra- and extracellular ion concentration dynamics and show that this model exhibits periodic bursting. The bursting arises as the fast-spiking behavior of the neuron is modulated by the slow oscillatory behavior in the ion concentration variables and vice versa. By separating these time scales and studying the bifurcation structure of the neuron, we catalog several qualitatively different bursting profiles that are strikingly similar to those seen in experimental preparations. Our work suggests that ion concentration dynamics may play an important role in modulating neuronal excitability in real biological systems.


Neuron Potassium Sodium Ion concentration Burst Seizure Epilepsy 



The authors would like to acknowledge the assistance of Jeremy Owen in creating Fig. 2. This work was supported by the Collaborative Research in Computational Neuroscience program at National Institutes of Health via grant R01-MH79502 (EB).


  1. 1.
    Hodgkin, A.L., Huxley, A.F.: A quantitative description of membrane current and its application to conduction and excitation in nerve. J. Physiol. 117(4), 500–544 (1952)Google Scholar
  2. 2.
    Frankenhaeuser, B., Hodgkin, A.L.: The after-effects of impulses in the giant nerve fibres of Loligo. J. Physiol. 131, 341–376 (1956)Google Scholar
  3. 3.
    Grafstein, B.: Mechanism of spreading cortical depression. J. Neurophysiol 19, 154–171 (1956)Google Scholar
  4. 4.
    Green, J.D.: The hippocampus. Phys. Rev. 44, 561–608 (1964)Google Scholar
  5. 5.
    Fertziger, A.P., Ranck, J.B., Jr.: Potassium accumulation in interstitial space during epileptiform seizures. Exp. Neurol. 26, 571–585 (1970)CrossRefGoogle Scholar
  6. 6.
    Fröhlich, F., Bazhenov, M., Iragui-Madoz, V., Sejnowski, T.J.: Potassium dynamics in the epileptic cortex: new insights on an old topic. Neurosci. 14(5), 422–433 (2008)Google Scholar
  7. 7.
    Kager, H., Wadman, W.J., Somjen, G.G.: Conditions for the triggering of spreading depression studied with computer simulations. J. Neurophysiol. 88, 2700–2712 (2002)CrossRefGoogle Scholar
  8. 8.
    Somjen, G.G., Kager, H., Wadman, W.J.: Calcium sensitive non-selective cation current promotes seizure-like discharges and spreading depression in a model neuron. J. Comput. Neurosci. 26, 139–147 (2008)CrossRefGoogle Scholar
  9. 9.
    Bazhenov, M., Timofeev, I., Steriade, M., Sejnowski, T.J.: Potassium model for slow (2–3 Hz) in vivo neocortical paroxysmal oscillations. J. Neurophysiol. 92, 1116–1132 (2004)CrossRefGoogle Scholar
  10. 10.
    Fröhlich, F., Bazhenov, M., Timofeev, I., Steriade, M., Sejnowski, T.J.: Slow state transitions of sustained neural oscillations by activity-dependent modulation of intrinsic excitability. J. Neurosci. 26(23), 6153–6162 (2006)CrossRefGoogle Scholar
  11. 11.
    Park, E.H., Durand, D.M.: Role of potassium lateral diffusion in non-synaptic epilepsy: a computational study. J. Theor. Biol. 238, 666–682 (2006)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Kager, H., Wadman, W.J., Somjen, G.G.: Seizure-like afterdischarges simulated in a model neuron. J. Comput. Neurosci. 22, 105–128 (2007)CrossRefGoogle Scholar
  13. 13.
    Somjen, G.G., Kager, H., Wadman, W.J.: Computer simulations of neuron–glia interactions mediated by ion flux. J. Comput. Neurosci. 25, 349–365 (2008)CrossRefGoogle Scholar
  14. 14.
    Postnov, D.E., Müller, F., Schuppner, R.B., Schimansky-Geier, L.: Dynamical structures in binary media of potassium-driven neurons. Phys. Rev. E 80, 031921 (2009)ADSCrossRefGoogle Scholar
  15. 15.
    Fröhlich, F., Sejnowski, T.J., Bazhenov, M.: Network bistability mediates spontaneous transitions between normal and pathological brain states. J. Neurosci. 30(32), 10734–10743 (2010)CrossRefGoogle Scholar
  16. 16.
    Kager, H., Wadman, W.J., Somjen, G.G.: Simulated seizures and spreading depression in a neuron model incorporating interstitial space and ion concentrations. J. Neurophysiol. 84, 495–512 (2000)Google Scholar
  17. 17.
    Somjen, G.G.: Ions in the Brain. Oxford University Press, New York (2004)Google Scholar
  18. 18.
    Cressman, J.R., Ullah, G., Schiff, S.J., Barreto, E.: The influence of sodium and potassium dynamics on excitability, seizures, and the stability of persistent states: I. Single neuron dynamics. J. Comput. Neurosci. 26, 159–170 (2009)MathSciNetCrossRefGoogle Scholar
  19. 19.
    Dayan, P., Abbott, L.F.: Theoretical Neuroscience. MIT, Cambridge (2001)zbMATHGoogle Scholar
  20. 20.
    Bikson, M., Hahn, P.J., Fox, J.E., Jefferys, J.G.R.: Depolarization block of neurons during maintenance of electrographic seizures. J. Neurophysiol. 90, 2402–2408 (2003)CrossRefGoogle Scholar
  21. 21.
    Izhikevich, E.: Dynamical Systems in Neuroscience. MIT, Cambridge (2007)Google Scholar
  22. 22.
    Martens, E., Barreto, E., Strogatz, S.H., Ott, E., So, P., Antonsen, T.M.: Exact results for the Kuramoto model with a bimodal frequency distribution. Phys. Rev. E 79, 026204 (2009)MathSciNetADSCrossRefGoogle Scholar
  23. 23.
    Shilnikov, A.L., Calabrese R., Cymbalyuk, G.S.: Mechanism of bi-stability: tonic spiking and bursting in a neuron model. Phys. Rev. E 71, 056214 (2005)MathSciNetADSCrossRefGoogle Scholar
  24. 24.
    Cymbalyuk, G.S., Calabrese R., Shilnikov, A.L.: How a neuron model can demonstrate co-existence of tonic spiking and bursting? Neurocomputing 6566, 869–875 (2005)CrossRefGoogle Scholar
  25. 25.
    Fröhlich, F., Bazhenov, M.: Coexistence of tonic firing and bursting in cortical neurons. Phys. Rev. E 74, 031922 (2006)ADSCrossRefGoogle Scholar
  26. 26.
    Guckenheimer, J., Holmes, P.: Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields. Springer, New York (1983)zbMATHGoogle Scholar
  27. 27.
    Guckenheimer, J.: Multiple bifurcation problems for chemical reactors. Physica D 20(1), 1–20 (1986)MathSciNetADSzbMATHCrossRefGoogle Scholar
  28. 28.
    Jensen, M.S., Yaari, Y.: Role of intrinsic burst firing, potassium accumulation, and electrical coupling in the elevated potassium model of hippocampal epilepsy. J. Neurophysiol. 77, 1224–1233 (1997)Google Scholar
  29. 29.
    Ziburkus, J., Cressman, J.R., Barreto, E., Schiff, S.J.: Interneuron and pyramidal cell interplay during in vitro seizure-like events. J. Neurophysiol. 95, 3948–3954 (2006)CrossRefGoogle Scholar
  30. 30.
    Connors, B.W., Telfeian, A.E.: Dynamic properties of cells, synapses, circuits and seizures in neocortex. In: Williamson, P.D., et al. (eds.) Neocortical Epilepsies. Advances in Neurology, vol. 84, pp. 141–152 (2000)Google Scholar
  31. 31.
    Pinsky, P.F., Rinzel, J.: Intrinsic and network rhythmogenesis in a reduced Traub model for CA3 neurons. J. Comput. Neurosci. 1, 39–60 (1994)CrossRefGoogle Scholar
  32. 32.
    Marchetti, C., Tabak, J., Chub, N., O’Donovan, M.J., Rinzel, J.: Modeling spontaneous activity in the developing spinal cord using activity-dependent variations of intracellular chloride. J. Neurosci. 25(14), 3601–3612 (2005)CrossRefGoogle Scholar
  33. 33.
    Komendantov, A., Cressman, J.R., Barreto, E.: Ion concentration homeostasis and the regulation of neuronal firing activity: the role of cation-chloride cotransporters. BMC Neurosci. 11(Suppl 1), P27 (2010)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.Center for Neural Dynamics, Department of Physics & Astronomy, and The Krasnow Institute for Advanced StudyGeorge Mason UniversityFairfaxUSA

Personalised recommendations