The influence of depolarization block on seizure-like activity in networks of excitatory and inhibitory neurons
- 455 Downloads
The inhibitory restraint necessary to suppress aberrant activity can fail when inhibitory neurons cease to generate action potentials as they enter depolarization block. We investigate possible bifurcation structures that arise at the onset of seizure-like activity resulting from depolarization block in inhibitory neurons. Networks of conductance-based excitatory and inhibitory neurons are simulated to characterize different types of transitions to the seizure state, and a mean field model is developed to verify the generality of the observed phenomena of excitatory-inhibitory dynamics. Specifically, the inhibitory population’s activation function in the Wilson-Cowan model is modified to be non-monotonic to reflect that inhibitory neurons enter depolarization block given strong input. We find that a physiological state and a seizure state can coexist, where the seizure state is characterized by high excitatory and low inhibitory firing rate. Bifurcation analysis of the mean field model reveals that a transition to the seizure state may occur via a saddle-node bifurcation or a homoclinic bifurcation. We explain the hysteresis observed in network simulations using these two bifurcation types. We also demonstrate that extracellular potassium concentration affects the depolarization block threshold; the consequent changes in bifurcation structure enable the network to produce the tonic to clonic phase transition observed in biological epileptic networks.
KeywordsDepolarization block Seizures Excitatory-inhibitory network Wilson-Cowan model
This research was supported by the National Science Foundation grant DMS-0847749. We thank Tay Netoff for insightful discussions and motivating our investigation. CMK thanks Bernstein Center Freiburg for their support where part of this work was conducted.
Compliance with Ethical Standards
Conflict of interest
The authors declare that they have no conflict of interest.
- Ahmed, O.J., Kramer, M.A., Truccolo, W., Naftulin, J.S., Potter, N.S., Eskandar, E.N., Cosgrove, G.R., Blum, A.S., Hochberg, L.R., & Cash, S.S. (2014). Inhibitory single neuron control of seizures and epileptic traveling waves in humans. BMC Neuroscience, 15(Suppl 1), F3.CrossRefPubMedCentralGoogle Scholar
- Buckmaster, P.S., Zhang, G.F., & Yamawaki, R. (2002). Axon sprouting in a model of temporal lobe epilepsy creates a predominantly excitatory feedback circuit. The Journal of Neuroscience: The Official Journal of the Society for Neuroscience, 22(15), 6650–6658.Google Scholar
- Dzhala, V.I., Kuchibhotla, K.V., Glykys, J.C., Kahle, K.T., Swiercz, W.B., Feng, G., Kuner, T., Augustine, G.J., Bacskai, B.J., & Staley, K.J. (2010). Progressive nkcc1-dependent neuronal chloride accumulation during neonatal seizures. The Journal of Neuroscience, 30(35), 11745–11761.CrossRefPubMedPubMedCentralGoogle Scholar
- Ellender, T.J., Raimondo, J.V., Irkle, A., Lamsa, K.P., & Akerman, C.J. (2014). Excitatory effects of parvalbumin-expressing interneurons maintain hippocampal epileptiform activity via synchronous afterdischarges. The Journal of Neuroscience, 34(46), 15208– 15222.CrossRefPubMedPubMedCentralGoogle Scholar
- Fröhlich, F., Bazhenov, M., Timofeev, I., Steriade, M., & Sejnowski, T.J. (2006). Slow state transitions of sustained neural oscillations by activity-dependent modulation of intrinsic excitability. The Journal of Neuroscience: The Official Journal of the Society for Neuroscience, 26(23), 6153–6162.CrossRefGoogle Scholar
- Gastaut, H., & Broughton, R.J. (1972). Epileptic seizures: clinical and electrographic features, diagnosis and treatment. Springfield: Thomas. https://books.google.de/books/about/Epileptic_Seizures.html?id=Xb1rAAAAMAAJ&pgis=1.Google Scholar
- Goodman, D.F., & Brette, R. (2008). The brian simulator. Frontiers in Neuroscience, 3, 26.Google Scholar
- Gulyás, A.I., Megías, M., Emri, Z., & Freund, T.F. (1999). Total number and ratio of excitatory and inhibitory synapses converging onto single interneurons of different types in the CA1 area of the rat hippocampus. The Journal of Neuroscience: The Official Journal of the Society for Neuroscience, 19(22), 10082– 10097.Google Scholar
- Meijer, H.G.E., Eissa, T.L., Kiewiet, B., Neuman, J.F., Schevon, C.A., Emerson, R.G., Goodman, R.R., McKhann, G.M., Marcuccilli, C.J., Tryba, A.K., Cowan, J.D., van Gils, S.A., & van Drongelen, W. (2015). Modeling focal epileptic activity in the Wilson-cowan model with depolarization block. Journal of Mathematical Neuroscience, 5, 7.CrossRefPubMedPubMedCentralGoogle Scholar
- Zandt, B.J., Visser, S., van Putten, M.J.A.M., & Ten Haken, B. (2014). A neural mass model based on single cell dynamics to model pathophysiology. Journal of Computational Neuroscience.Google Scholar