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Journal of Computational Neuroscience

, Volume 43, Issue 1, pp 65–79 | Cite as

The influence of depolarization block on seizure-like activity in networks of excitatory and inhibitory neurons

  • Christopher M. KimEmail author
  • Duane Q. Nykamp
Article

Abstract

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.

Keywords

Depolarization block Seizures Excitatory-inhibitory network Wilson-Cowan model 

Notes

Acknowledgements

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.

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Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  1. 1.School of MathematicsUniversity of MinnesotaMinneapolisUSA
  2. 2.Laboratory of Biological Modeling, NIDDKNational Institute of HealthBethesdaUSA

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