Spatial propagation of interictal discharges along the cortex

https://doi.org/10.1016/j.bbrc.2018.12.070Get rights and content

Highlights

  • Mathematical model of propagating interictal discharges (IIDs) was developed.

  • IIDs are either GABAergic (IID1s) or GABA-glutamatergic (IID2s).

  • In simulations and in vitro, IIDs propagate along the cortex as waves.

  • Speed of IIDs is several tens of mm/s and is larger for IID2s than for IID1s.

Abstract

Interictal discharges (IIDs) accompany epileptic seizures and highlight the mechanisms of pathological activity. The propagation of IIDs along the neural tissue is not well understood. To simulate IID propagation, this study proposes a new mathematical model that uses the conductance-based refractory density approach for glutamatergic and GABAergic neuronal populations. The mathematical model is found to be consistent with experimental double-patch registrations in the 4-aminopyridine in vitro model of epilepsy. In slices, the spontaneous activity of interneurons leads to their synchronization by means of the depolarizing GABAmediated response, thus initiating IIDs. Modeling reveals a clustering of interneuronal synchronization followed by IIDs with activity fronts that propagate along the cortex. The GABA-mediated depolarization either remains to be subthreshold for the principal neurons and thus results in pure GABAergic IIDs (IID1s) or leads to glutamatergic excitation, thus resulting in another type of IIDs (IID2s). In both the model and experiment, IIDs propagate as waves, with constant activity profiles and velocity. The speed of IIDs is of the order of tens of mm/s and is larger for IID2s than for IID1s (40 and 20 mm/s, respectively). The simulations, consistent with experimental observations, show that the wavelike propagation of IIDs initiated by interneurons is determined by local synaptic connectivity under the conditions of depolarizing GABA.

Introduction

In electrophysiological recordings, interictal discharges (IIDs) are synchronous neuronal discharges with durations in the hundreds of milliseconds, whereas ictal discharges (IDs), or seizure-like events, are patterned discharges that last for tens of seconds and are composed of temporally clustered IID-like events. The spatial propagation of IDs and IIDs has been studied using various experimental approaches, including paired patch-clamp recordings in brain slices [1,2], voltage-sensitive dye imaging in vitro [3], two-photon calcium imaging in vivo [4,5], multielectrode arrays in brain slices [6] and in vivo [7], and nanoparticle-based imaging of potassium ion dynamics in slices [8]. These studies have provided a wide range of data on the properties and mechanisms of epileptic discharges. First, it was revealed that IDs and IIDs have similar profiles at remote sites and can thus be considered propagating waves. Second, in most cases, the speed of IIDs is much higher than that of IDs. For instance, Ridler [6] estimated the velocity of ID propagation at 0.14 mm/s and that of IID propagation at over 4.4 mm/s; Liou et al. [7] estimated ID speed at 0.19–63 mm/s; and Trevelyan [2] estimated IID speed at 29 ± 18 mm/s, in contrast to a broad range of ID velocities, from 0.1 to 10 mm/s [1].

Whereas mechanisms of ID propagation may involve ionic dynamics, and in particular the diffusion of extracellular potassium ions [9,10], the high speed of IIDs suggests a different mechanism. It was supposed that the spiking activity propagating through axonal trees and the postsynaptic currents propagating along dendrites determine the character and limit the speed of the spatial propagation of IIDs along the cortical tissue. Utilizing the 4-aminopyridine (4-AP) in vitro model of temporal lobe epilepsy, previous studies have revealed synaptic mechanisms of local neuronal interactions underlying the generation of IIDs [[11], [12], [13]]. The most important feature of IIDs is that GABAergic interneurons, as opposed to glutamatergic neurons, are preferentially recruited during spontaneous interictal activity. Due to an impaired level of intracellular chloride concentration and thus depolarized reversal potential of the GABA-A receptors, these interneurons are excitatory too. Two types of IIDs have been distinguished: IID1s, which are mediated by pure GABAergic interactions, and IID2s, which are composed of GABA- and glutamate-mediated components [12]. Experimental and modeling results have suggested that switching in regimes is determined by the level of chloride accumulation in neurons [[14], [15], [16], [17], [18]]. The mechanism of IID generation was reproduced in a neuronal population mathematical model based on the conductance-based refractory density (CBRD) approach [14]. However, mathematical modeling is required to answer the question of whether the representation of the mechanisms of IID generation based on local synaptic interactions and axo-dendritic propagation is complete.

Here, we extend our spatially homogeneous mathematical model of IIDs [14] to the spatially extended case of two-dimensional (2-D) propagation along the cortex by taking into consideration the spatial structure of neuronal connections. The extension of the zero-dimensional (0-D) model to a 2-D model shows that the spatially distributed solution shares the properties of the spatially homogeneous solution and is consistent with measurements of the speed of IID propagation.

Section snippets

Modeling

Two coupled neuronal populations of excitatory (pyramidal) neurons (E-population) and interneurons (I-population) were considered. The population dynamics are described in terms of the CBRD approach [19,20], which is a generalization of the original refractory density approach [21,22] for two-compartmental Hodgkin-Huxley-like neurons. The approximations for voltage-gated and synaptic ionic channels were taken from Refs. [[23], [24], [25]], respectively. Lognormal distribution of synaptic

Simulations

In the proepileptic conditions of low magnesium concentration and enhanced GABA reversal potential, two types of spontaneous discharges were simulated, IID1s and IID2s (Fig. 1). I-neurons initiated both types of IIDs. In voltage-clamp recordings with the voltage fixed at −27 mV, IID1s manifested themselves as outward currents in both E-neurons and I-neurons (Fig. 1A). Therefore, only GABAergic synaptic components were present. Due to the enhanced GABA reversal potential, the GABA-mediated

Discussion

Using the 2-D mathematical model, IIDs of the two different types were reproduced. The spatiotemporal patterns of activity revealed that an IID starts from a small initiation site and then spreads across a larger area, which is consistent with the in vivo voltage-sensitive dye imaging data [3]. The initiation was spontaneous in both space and time. The activity propagated as a wave and was determined by local connectivity. The speed of IID1s and IID2s was about 18 and 40 mm/s, respectively.

Acknowledgments

This work was supported by the Russian Science Foundation [grant 16-15-10201]. The authors are grateful to Elena B. Soboleva for her help in the experiments.

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