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

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.

Altered hippocampal interneuron activity precedes ictal onset

“…The earliest preictal change we observed was a loss of the strong spike-field coherence of PV cell spiking to a prominent low-gamma band previously observed in mouse hippocampus ( Chen et al, 2011 ; Cabral et al, 2014 ; Sauer et al, 2015 ). Previous work has suggested that increased inhibitory synaptic activity or the onset of depolarization block in fast-spiking interneurons could precipitate seizure onset ( Velazquez and Carlen, 1999 ; Timofeev et al, 2002 ; Ziburkus et al, 2006 ; Fujiwara-Tsukamoto et al, 2007 ; Gnatkovsky et al, 2008 ; Cammarota et al, 2013 ; Kim and Nykamp, 2017 ), and we found that the onset of ictal spikes occurred immediately after a sharp increase in PV interneuron spiking in both anesthetized and awake animals. However, we found no evidence for decreased interneuron spike amplitude prior to ictal onset, suggesting that these interneurons did not enter depolarization block prior to ictal onset.…”

“…Previous work has also highlighted the potential preictal contribution of excitatory GABAergic effects due to Cl- accumulation ( Cossart et al, 2005 ; Palma et al, 2006 ; Miles et al, 2012 ) or loss of inhibition due to depletion of GABAergic release ( Zhang et al, 2012 ). Interneuron firing may also transiently cease during ictal events as a result of depolarization block ( Ziburkus et al, 2006 ; Cammarota et al, 2013 ; Kim and Nykamp, 2017 ). Developmental dysregulation of inhibitory interneurons causes chronic epileptic disorders ( Lau et al, 2000 ; Cobos et al, 2005 ; Rossignol et al, 2013 ; Tai et al, 2014 ), and interneurons also appear to be particularly sensitive to seizure-related damage ( Sloviter, 1987 ; de Lanerolle et al, 1989 ; Robbins et al, 1991 ; Rice et al, 1996 ; Gibbs et al, 1997 ; Cossart et al, 2001 ).…”

A mean-field approach to the dynamics of networks of complex neurons, from nonlinear Integrate-and-Fire to Hodgkin–Huxley models

“…Notice that the ML model shows a decrease of firing rate at frequencies higher than 8 Hz (i.e. no voltage oscillations and thus no firing activity), as reported previously for this model by Kim and Nykamp (2017). This is a consequence of the depolarization block (DB) observed at high input frequencies (i.e.…”

Minimal model of interictal and ictal discharges “Epileptor-2”

“…Thus such modeling is on the opposite extreme of detail in comparison to the proposed Epileptor-2 model. Another critical point to the fourth assumption is its validity in the case of the depolarization block, which occurs in interneurons during IDs [ 1 , 47 ]. Therefore, the approximation might overestimate the inhibitory currents as well as the potassium accumulation mediated by the accumulation of chloride and the activity of K-Cl-cotransporters during some period within an ID.…”