Skip to main content

Dynamical changes in neurons during seizures determine tonic to clonic shift

Abstract

A tonic-clonic seizure transitions from high frequency asynchronous activity to low frequency coherent oscillations, yet the mechanism of transition remains unknown. We propose a shift in network synchrony due to changes in cellular response. Here we use phase-response curves (PRC) from Morris-Lecar (M-L) model neurons with synaptic depression and gradually decrease input current to cells within a network simulation. This method effectively decreases firing rates resulting in a shift to greater network synchrony illustrating a possible mechanism of the transition phenomenon. PRCs are measured from the M-L conductance based model cell with a range of input currents within the limit cycle. A large network of 3000 excitatory neurons is simulated with a network topology generated from second-order statistics which allows a range of population synchrony. The population synchrony of the oscillating cells is measured with the Kuramoto order parameter, which reveals a transition from tonic to clonic phase exhibited by our model network. The cellular response shift mechanism for the tonic-clonic seizure transition reproduces the population behavior closely when compared to EEG data.

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10

References

  1. Abbott, L. F., Varela, J. A., Sen, K., & Nelson, S. B. (1997). Synaptic depression and cortical gain control [see comments]. Science, 275(5297), 220–224.

    PubMed  Article  CAS  Google Scholar 

  2. Achuthan, S., & Canavier, C. C. (2009). Phase-resetting curves determine synchronization, phase locking, and clustering in networks of neural oscillators. The Journal of Neuroscience: The Official Journal of the Society for Neuroscience, 29(16), 5218–5233.

    Article  CAS  Google Scholar 

  3. Bragin, A., Engel, J., Jr., & Staba, R. J. (2010). High-frequency oscillations in epileptic brain. Current Opinion in Neurology, 23(2), 151–156.

    PubMed  Article  Google Scholar 

  4. Brown, E., Moehlis, J., & Holmes, P. (2004). On the phase reduction and response dynamics of neural oscillator populations. Neural Computation, 16(4), 673–715.

    PubMed  Article  Google Scholar 

  5. Buia, C., & Tiesinga, P. (2006). Attentional modulation of firing rate and synchrony in a model cortical network. Journal of Computational Neuroscience, 20(3), 247–264.

    PubMed  Article  Google Scholar 

  6. Dror, R. O., Canavier, C. C., Butera, R. J., Clark, J. W., & Byrne, J. H. (1999). A mathematical criterion based on phase response curves for stability in a ring of coupled oscillators. Biological Cybernetics, 80(1), 11–23.

    PubMed  Article  CAS  Google Scholar 

  7. Ermentrout, G. B., & Kleinfeld, D. (2001). Traveling electrical waves in cortex: insights from phase dynamics and speculation on a computational role. Neuron, 29(1), 33–44.

    PubMed  Article  CAS  Google Scholar 

  8. Ermentrout, G. B., & Kopell, N. (1998). Fine structure of neural spiking and synchronization in the presence of conduction delays. Proc Natl Acad Sci U S A, 95(3), 1259–164.

    PubMed  Article  CAS  Google Scholar 

  9. Ermentrout, G. B., Beverlin, B. 2nd, Troyer, T., & Netoff, T. I. (2011). The variance of phase-resetting curves. Journal of Computational Neuroscience

  10. Fink, C. G., Booth, V., & Zochowski, M. (2011). Cellularly-driven differences in network synchronization propensity are differentially modulated by firing frequency. PLoS Computational Biology, 7(5), e1002062.

    PubMed  Article  CAS  Google Scholar 

  11. Fisch, J. F., & Olejniczak, P. W. (2006). Generalized-tonic-clonic seizures. In E. Wyllie, A. Gupta, & D. K. Lachhwani (Eds.), The treatment of epilepsy: Principles & practice (p. 279). Philadelphia: Lippincott Williams & Wilkins.

    Google Scholar 

  12. Garcia Dominguez, L., Wennberg, R. A., Gaetz, W., Cheyne, D., Snead, O. C., 3rd, & Perez Velazquez, J. L. (2005). Enhanced synchrony in epileptiform activity? local versus distant phase synchronization in generalized seizures. The Journal of Neuroscience: The Official Journal of the Society for Neuroscience, 25(35), 8077–8084.

    Article  Google Scholar 

  13. Gastaut, H., & Broughton, R. J. (1972). Epileptic seizures; clinical and electrographic features, diagnosis and treatment. Springfield: Thomas.

    Google Scholar 

  14. Glass, L., & Mackey, M. C. (1988). From clocks to chaos: The rhythms of life. Princeton: Princeton University Press.

    Google Scholar 

  15. Goel, P., & Ermentrout, G. B. (2002). Synchrony, stability, and firing patterns in pulse-coupled oscillators. Physica D: Nonlinear Phenomena, 163(3–4), 191.

    Article  Google Scholar 

  16. Hansel, D., Mato, G., & Meunier, C. (1995). Synchrony in excitatory neural networks. Neural Comput, 7(2), 307–37.

    PubMed  Article  CAS  Google Scholar 

  17. Hoppensteadt, F. C., & Izhikevich, E. M. (1997). Weakly connected neural networks. New York: Springer.

    Book  Google Scholar 

  18. Izhikevich, E. M. (2007). Dynamical systems in neuroscience: The geometry of excitability and bursting. Cambridge: MIT.

    Google Scholar 

  19. Kopell, N., & Ermentrout, G. B. (2002). Mechanisms of phase-locking and frequency control in pairs of coupled neural oscillators. In B. Fiedler (Ed.), Handbook on dynamical systems (pp. 3–54). New York: Elsevier.

    Chapter  Google Scholar 

  20. Kuramoto, Y. (1984). Chemical oscillations, waves, and turbulence. Berlin: Springer.

    Book  Google Scholar 

  21. Lewis, T. J., & Rinzel, J. (2003). Dynamics of spiking neurons connected by both inhibitory and electrical coupling. Journal of Computational Neuroscience, 14(3), 283–309.

    PubMed  Article  Google Scholar 

  22. Mancilla, J. G., Lewis, T. J., Pinto, D. J., Rinzel, J., & Connors, B. W. (2007). Synchronization of electrically coupled pairs of inhibitory interneurons in neocortex. The Journal of Neuroscience: The Official Journal of the Society for Neuroscience, 27(8), 2058–2073.

    Article  CAS  Google Scholar 

  23. Manor, Y., & Nadim, F. (2001). Synaptic depression mediates bistability in neuronal networks with recurrent inhibitory connectivity. J Neurosci, 21(23), 9460–9470.

    PubMed  CAS  Google Scholar 

  24. Morris, C., & Lecar, H. (1981). Voltage oscillations in the barnacle giant muscle fiber. Biophysical Journal, 35(1), 193–213.

    PubMed  Article  CAS  Google Scholar 

  25. Neltner, L., Hansel, D., Mato, G., & Meunier, C. (2000). Synchrony in heterogeneous networks of spiking neurons. Neural Comput, 12(7), 1607–41.

    PubMed  Article  CAS  Google Scholar 

  26. Netoff, T. I., & Schiff, S. J. (2002). Decreased neuronal synchronization during experimental seizures. The Journal of Neuroscience: The Official Journal of the Society for Neuroscience, 22(16), 7297–7307.

    CAS  Google Scholar 

  27. Netoff, T. I., Clewley, R., Arno, S., Keck, T., & White, J. A. (2004). Epilepsy in small-world networks. The Journal of Neuroscience: The Official Journal of the Society for Neuroscience, 24(37), 8075–8083.

    Article  CAS  Google Scholar 

  28. Netoff, T. I., et al. (2005). Synchronization in hybrid neuronal networks of the hippocampal formation. Journal of Neurophysiology, 93(3), 1197–1208.

    PubMed  Article  Google Scholar 

  29. Neu, J. (1979). Coupled chemical oscillators. SIAM J. Appl. Math., 37307–315.

  30. Perez Velazquez, J. L., Garcia Dominguez, L., & Wennberg, R. (2007). Complex phase synchronization in epileptic seizures: Evidence for a devil's staircase. Physical Review.E, Statistical, Nonlinear, and Soft Matter Physics, 75(1 Pt 1), 011922.

  31. Quian Quiroga, R., Blanco, S., Rosso, O. A., Garcia, H., & Rabinowicz, A. (1997). Searching for hidden information with gabor transform in generalized tonic-clonic seizures. Electroencephalography and Clinical Neurophysiology, 103(4), 434–439.

    PubMed  Article  CAS  Google Scholar 

  32. Rinzel, J. (1985). Excitation dynamics: Insights from simplified membrane models. Federation Proceedings, 44(15), 2944–2946.

    PubMed  CAS  Google Scholar 

  33. Schindler, K., Elger, C. E., & Lehnertz, K. (2007). Increasing synchronization may promote seizure termination: evidence from status epilepticus. Clinical Neurophysiology: Official Journal of the International Federation of Clinical Neurophysiology, 118(9), 1955–1968.

    Article  Google Scholar 

  34. Schindler, K., Leung, H., Elger, C. E., & Lehnertz, K. (2007). Assessing seizure dynamics by analysing the correlation structure of multichannel intracranial EEG. Brain: A Journal of Neurology, 130(Pt 1), 65–77.

    Google Scholar 

  35. Smeal, R. M., Ermentrout, G. B., & White, J. A. (2010). Phase-response curves and synchronized neural networks. Philosophical Transactions of the Royal Society of London.Series B, Biological Sciences, 365(1551), 2407–2422.

    PubMed  Article  Google Scholar 

  36. Song, S., Sjostrom, P. J., Reigl, M., Nelson, S., & Chklovskii, D. B. (2005). Highly nonrandom features of synaptic connectivity in local cortical circuits. PLoS Biology, 3(3), e68.

    PubMed  Article  Google Scholar 

  37. Strogatz, S. H. (2000). From Kuramoto to Crawford: exploring the onset of synchronization in populations of coupled oscillators. Physica D: Nonlinear Phenomena, 143(1–4), 1.

    Article  Google Scholar 

  38. Tiesinga, P. H., & Sejnowski, T. J. (2004). Rapid temporal modulation of synchrony by competition in cortical interneuron networks. Neural Computation, 16(2), 251–275.

    PubMed  Article  CAS  Google Scholar 

  39. Varela, J. A., Sen, K., Gibson, J., Fost, J., Abbott, L. F., & Nelson, S. B. (1997). A quantitative description of short-term plasticity at excitatory synapses in layer 2/3 of rat primary visual cortex. J Neurosci, 17(20), 7926–740.

    PubMed  CAS  Google Scholar 

  40. Ward, A. A. Jr. (1961). The epileptic neurone. Epilepsia, 270–280.

  41. Watts, D. J., & Strogatz, S. H. (1998). Collective dynamics of 'small-world' networks. Nature, 393(6684), 440–442.

    PubMed  Article  CAS  Google Scholar 

  42. Winfree, A. T. (2001). The geometry of biological time. New York: Springer.

    Google Scholar 

  43. Zhao, L., Beverlin B. 2nd, Netoff, T., & Nykamp D. Q. (2011). Synchronization from second order network connectivity statistics. Frontiers in Computational Neuroscience, 528.

  44. Ziburkus, J., Cressman, J. R., Barreto, E., & Schiff, S. J. (2006). Interneuron and pyramidal cell interplay during in vitro seizure-like events. Journal of Neurophysiology, 95(6), 3948–3954.

    PubMed  Article  Google Scholar 

Download references

Acknowledgments

Thanks to Bard Ermentrout and Chris Warren for helpful discussions. Funding for this work provided by UMN Grant-In-Aid and NSF CAREER award.

Author information

Affiliations

Authors

Corresponding author

Correspondence to Theoden Ivan Netoff.

Additional information

Action Editor: David Terman

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Beverlin, B., Kakalios, J., Nykamp, D. et al. Dynamical changes in neurons during seizures determine tonic to clonic shift. J Comput Neurosci 33, 41–51 (2012). https://doi.org/10.1007/s10827-011-0373-5

Download citation

Keywords

  • Seizure model
  • PRC
  • Tonic clonic
  • Synchrony