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 pathological conditions of epilepsy, the functioning of the neural network crucially depends on the ionic concentrations inside and outside neurons. A number of factors that affect neuronal activity is large. That is why the development of a minimal model that reproduces typical seizures could structure further experimental and analytical studies of the pathological mechanisms. Here, on a base of known biophysical models, we present a simple population-type model that includes only four principal variables, the extracellular potassium concentration, the intracellular sodium concentration, the membrane potential and the synaptic resource diminishing due to short-term synaptic depression. A simple modeled neuron is used as an observer of the population activity. We validate the model assumptions with in vitro experiments. Our model reproduces ictal and interictal events, where the latter result in bursts of spikes in single neurons, and the former represent the cluster of spike bursts. Mathematical analysis reveals that the bursts are spontaneous large-amplitude oscillations, which may cluster after a saddle-node on invariant circle bifurcation in the pro-epileptic conditions. Our consideration has significant bearing in understanding pathological neuronal network dynamics.

Status epilepticus (SE) causes persistent abnormalities in the functioning of neuronal networks, often resulting in worsening epileptic seizures. Many details of cellular and molecular mechanisms of seizure-induced changes are still unknown. The lithium–pilocarpine model of epilepsy in rats reproduces many features of human temporal lobe epilepsy. In this work, using the lithium–pilocarpine model in three-week-old rats, we examined the morphological and electrophysiological changes in the hippocampus within a week following pilocarpine-induced seizures. We found that almost a third of the neurons in the hippocampus and dentate gyrus died on the first day, but this was not accompanied by impaired synaptic plasticity at that time. A diminished long-term potentiation (LTP) was observed following three days, and the negative effect of SE on plasticity increased one week later, being accompanied by astrogliosis. The attenuation of LTP was caused by the weakening of N-methyl-D-aspartate receptor (NMDAR)-dependent signaling. NMDAR-current was more than two-fold weaker during high-frequency stimulation in the post-SE rats than in the control group. Application of glial transmitter D-serine, a coagonist of NMDARs, allows the enhancement of the NMDAR-dependent current and the restoration of LTP. These results suggest that the disorder of neuron–astrocyte interactions plays a critical role in the impairment of synaptic plasticity.

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, 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 three 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 AMPA and 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 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 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 hippocampus, may cause neuron damage, and may be one of the important pathogenic mechanisms of TLE.

Febrile seizures (FSs) in early life are significant risk factors of neurological disorders and cognitive impairment in later life. However, existing data about the impact of FSs on the developing brain are conflicting. We aimed to investigate morphological and functional changes in the hippocampus of young rats exposed to hyperthermia-induced seizures at postnatal day 10. We found that FSs led to a slight morphological disturbance. The cell numbers decreased by 10% in the CA1 and hilus but did not reduce in the CA3 or dentate gyrus areas. In contrast, functional impairments were robust. Long-term potentiation (LTP) in CA3-CA1 synapses was strongly reduced, which we attribute to the insufficient activity of N-methyl-D-aspartate receptors (NMDARs). Using whole-cell recordings, we found higher desensitization of NMDAR currents in the FS group. Since the desensitization of NMDARs depends on subunit composition, we analyzed NMDAR current decays and gene expression of subunits, which revealed no differences between control and FS rats. We suggest that an increased desensitization is due to insufficient activation of the glycine site of NMDARs, as the application of D-serine, the glycine site agonist, allows the restoration of LTP to a control value. Our results reveal a new molecular mechanism of FS impact on the developing brain.