Seizures occur in a recurrent manner with intermittent states of interictal and ictal discharges (IIDs and IDs). The transitions to and from IDs are determined by a set of processes, including synaptic interaction and ionic dynamics. Although mathematical models of separate types of epileptic discharges have been developed, modeling the transitions between states remains a challenge. A simple generic mathematical model of seizure dynamics (Epileptor) has recently been proposed by Jirsa et al. (2014); however, it is formulated in terms of abstract variables. In this paper, a minimal population-type model of IIDs and IDs is proposed that is as simple to use as the Epileptor, but the suggested model attributes physical meaning to the variables. The model is expressed in ordinary differential equations for extracellular potassium and intracellular sodium concentrations, membrane potential, and short-term synaptic depression variables. A quadratic integrate-and-fire model driven by the population input current is used to reproduce spike trains in a representative neuron. In simulations, potassium accumulation governs the transition from the silent state to the state of an ID. Each ID is composed of clustered IID-like events. The sodium accumulates during discharge and activates the sodium-potassium pump, which terminates the ID by restoring the potassium gradient and thus polarizing the neuronal membranes. The whole-cell and cell-attached recordings of a 4-AP-based in vitro model of epilepsy confirmed the primary model assumptions and predictions. The mathematical analysis revealed that the IID-like events are large-amplitude stochastic oscillations, which in the case of ID generation are controlled by slow oscillations of ionic concentrations. The IDs originate in the conditions of elevated potassium concentrations in a bath solution via a saddle-node-on-invariant-circle-like bifurcation for a non-smooth dynamical system. By providing a minimal biophysical description of ionic dynamics and network interactions, the model may serve as a hierarchical base from a simple to more complex modeling of seizures.

In epilepsy, the balance of excitation and inhibition underlying the basis of neural network activity shifts, resulting in neuronal network hyperexcitability and recurrent seizure-associated discharges. Mechanisms involved in ictal and interictal events are not fully understood, in particular, because of controversial data regarding the dynamics of excitatory and inhibitory synaptic conductances. In the present study, we estimated AMPAR-, NMDAR-, and GABAA R-mediated conductances during two distinct types of interictal discharge (IID) in pyramidal neurons of rat entorhinal cortex in cortico-hippocampal slices. Repetitively emerging seizure-like events and IIDs were recorded in high extracellular potassium, 4-aminopyridine, and reduced magnesium-containing solution. An original procedure for estimating synaptic conductance during IIDs was based on the differences among the current-voltage characteristics of the synaptic components. The synaptic conductance dynamics obtained revealed that the first type of IID is determined by activity of GABAA R channels with depolarized reversal potential. The second type of IID is determined by the interplay between excitation and inhibition, with early AMPAR and prolonged depolarized GABAA R and NMDAR-mediated components. The study then validated the contribution of these components to IIDs by intracellular pharmacological isolation. These data provide new insights into the mechanisms of seizures generation, development, and cessation.

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Interictal discharges (IIDs) are abnormal waveforms registered in the periods before or between seizures. IIDs that are initiated by GABAergic interneurons have not been mathematically modeled yet. In the present study, a mathematical model that describes the mechanisms of these discharges is proposed. The model is based on the experimental recordings of IIDs in pyramidal neurons of the rat entorhinal cortex and estimations of synaptic conductances during IIDs. IIDs were induced in cortico-hippocampal slices by applying an extracellular solution with 4-aminopyridine, high potassium, and low magnesium concentrations. Two different types of IIDs initiated by interneurons were observed. The first type of IID (IID1) was pure GABAergic. The second type of IID (IID2) was induced by GABAergic excitation and maintained by recurrent interactions of both GABA- and glutamatergic neuronal populations. The model employed the conductance-based refractory density (CBRD) approach, which accurately approximates the firing rate of a population of similar Hodgkin-Huxley-like neurons. The model of coupled excitatory and inhibitory populations includes AMPA, NMDA, and GABA-receptor-mediated synapses and gap junctions. These neurons receive both arbitrary deterministic input and individual colored Gaussian noise. Both types of IIDs were successfully reproduced in the model by setting two different depolarized levels for GABA-mediated current reversal potential. It was revealed that short-term synaptic depression is a crucial factor in ceasing each of the discharges, and it also determines their durations and frequencies.

Temporal lobe epilepsy (TLE) is the most common type of focal epilepsy in humans, and is often developed after an initial precipitating brain injury. This form of epilepsy is frequently resistant to pharmacological treatment; therefore, the prevention of TLE is the prospective approach to TLE therapy. The lithium-pilocarpine model in rats replicates some of the main features of TLE in human, including the pathogenic mechanisms of cell damage and epileptogenesis after a primary brain injury. In the present study, we investigated changes in the properties of glutamatergic transmission during the first 3 days after pilocarpine-induced acute seizures in Wistar rats (PILO-rats). Using RT-PCR and electrophysiological techniques, we compared the changes in the temporal cortex (TC) and hippocampus, brain areas differentially affected by seizures. On the first day, we found a transient increase in a ratio of α-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid (AMPA) and N-methyl d-aspartate (NMDA) receptors in the excitatory synaptic response in pyramidal neurons of the CA1 area of the dorsal hippocampus, but not in the TC. This was accompanied by an increase in the slope of input-output (I/O) curves for fEPSPs recorded in CA1, suggesting an enhanced excitability in AMPARs in this brain area. There was no difference in the AMPA/NMDA ratio in control rats on the third day. We also revealed the alterations in NMDA receptor subunit composition in PILO-rats. The GluN2B/GluN2A mRNA expression ratio increased in the dorsal hippocampus but did not change in the ventral hippocampus or the TC. The kinetics of NMDA-mediated evoked EPSCs in hippocampal neurons was slower in PILO-rats compared with control animals. Ifenprodil, a selective antagonist of GluN2B-containing NMDARs, diminished the area and amplitude of evoked EPSCs in CA1 pyramidal cells more efficiently in PILO-rats compared with control animals. These results demonstrate that PILO-induced seizures lead to more severe alterations in excitatory synaptic transmission in the dorsal hippocampus than in the TC. Seizures affect the relative contribution of AMPA and NMDA receptor conductances in the synaptic response and increase the proportion of GluN2B-containing NMDARs in CA1 pyramidal neurons. These alterations disturb normal circuitry functions in the hippocampus, may cause neuron damage, and may be one of the important pathogenic mechanisms of TLE.