Skip to main content
Springer Nature Link
Log in

Dynamical changes in neurons during seizures determine tonic to clonic shift

  • Published:
Journal of Computational Neuroscience Aims and scope Submit manuscript

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, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

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

Similar content being viewed by others

References

  • 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.

    Article  PubMed  CAS  Google Scholar 

  • 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 

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

    Article  PubMed  Google Scholar 

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

    Article  PubMed  Google Scholar 

  • 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.

    Article  PubMed  Google Scholar 

  • 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.

    Article  PubMed  CAS  Google Scholar 

  • 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.

    Article  PubMed  CAS  Google Scholar 

  • 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.

    Article  PubMed  CAS  Google Scholar 

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

  • 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.

    Article  PubMed  CAS  Google Scholar 

  • 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 

  • 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 

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

    Google Scholar 

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

    Google Scholar 

  • 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 

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

    Article  PubMed  CAS  Google Scholar 

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

    Book  Google Scholar 

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

    Google Scholar 

  • 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 

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

    Book  Google Scholar 

  • 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.

    Article  PubMed  Google Scholar 

  • 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 

  • 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 

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

    Article  PubMed  CAS  Google Scholar 

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

    Article  PubMed  CAS  Google Scholar 

  • 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 

  • 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 

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

    Article  PubMed  Google Scholar 

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

  • 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.

  • 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.

    Article  PubMed  CAS  Google Scholar 

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

    PubMed  CAS  Google Scholar 

  • 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 

  • 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 

  • 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.

    Article  PubMed  Google Scholar 

  • 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.

    Article  PubMed  Google Scholar 

  • 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 

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

    Article  PubMed  CAS  Google Scholar 

  • 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 

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

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

    Article  PubMed  CAS  Google Scholar 

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

    Google Scholar 

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

  • 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.

    Article  PubMed  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

Authors and Affiliations

  1. Department of Physics, University of Minnesota, Minneapolis, MN, USA

    Bryce Beverlin II & James Kakalios

  2. Department of Mathematics, University of Minnesota, Minneapolis, MN, USA

    Duane Nykamp

  3. Department of Biomedical Engineering, University of Minnesota, Minneapolis, MN, USA

    Theoden Ivan Netoff

Authors
  1. Bryce Beverlin II
    View author publications

    You can also search for this author inPubMed Google Scholar

  2. James Kakalios
    View author publications

    You can also search for this author inPubMed Google Scholar

  3. Duane Nykamp
    View author publications

    You can also search for this author inPubMed Google Scholar

  4. Theoden Ivan Netoff
    View author publications

    You can also search for this author inPubMed Google Scholar

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

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10827-011-0373-5

Keywords