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Mathematical model of Na-K-Cl homeostasis in ictal and interictal discharges.

ABSTRACT: Despite big experimental data on the phenomena and mechanisms of the generation of ictal and interictal discharges (IDs and IIDs), mathematical models that can describe the synaptic interactions of neurons and the ionic dynamics in biophysical detail are not well-established. Based on experimental recordings of combined hippocampal-entorhinal cortex slices from rats in a high-potassium and a low-magnesium solution containing 4-aminopyridine as well as previous observations of similar experimental models, this type of mathematical model has been developed. The model describes neuronal excitation through the application of the conductance-based refractory density approach for three neuronal populations: two populations of glutamatergic neurons with hyperpolarizing and depolarizing GABAergic synapses and one GABAergic population. The ionic dynamics account for the contributions of voltage-gated and synaptic channels, active and passive transporters, and diffusion. The relatively slow dynamics of potassium, chloride, and sodium ion concentrations determine the transitions from pure GABAergic IIDs to IDs and GABA-glutamatergic IIDs. The model reproduces different types of IIDs, including those initiated by interneurons; repetitive IDs; tonic and bursting modes of an ID composed of clustered IID-like events. The simulations revealed contributions from different ionic channels to the ion concentration dynamics before and during ID generation. The proposed model is a step forward to an optimal mathematical description of the mechanisms of epileptic discharges.

SUBMITTER: Chizhov AV

PROVIDER: S-EPMC6420042 | biostudies-literature | 2019

REPOSITORIES: biostudies-literature

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Mathematical model of Na-K-Cl homeostasis in ictal and interictal discharges.

Chizhov Anton V AV Amakhin Dmitry V DV Zaitsev Aleksey V AV

PloS one 20190315 3

Despite big experimental data on the phenomena and mechanisms of the generation of ictal and interictal discharges (IDs and IIDs), mathematical models that can describe the synaptic interactions of neurons and the ionic dynamics in biophysical detail are not well-established. Based on experimental recordings of combined hippocampal-entorhinal cortex slices from rats in a high-potassium and a low-magnesium solution containing 4-aminopyridine as well as previous observations of similar experimenta ...[more]

PMID: 30875397

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Project description: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.

Project description:In organotypic hippocampal slice cultures, principal neurons form aberrant excitatory connections with other principal cells in response to slicing induced deafferentation, similar to mechanisms underlying epileptogenesis in posttraumatic epilepsy. To investigate the consequences of this synaptogenesis, the authors recorded field-potential activity from area CA3 during perfusion with the complete growth medium used during incubation. At 7 days in vitro, slice cultures only displayed multiunit activity. At 14 days in vitro, the majority displayed population bursts reminiscent of interictal-like spikes, but sustained synchronous activity was rare. Band-pass filtering of interictal discharges revealed fast ripple-like complexes, similar to in vivo recordings. Spontaneous ictal-like activity became progressively more prevalent with age: at 21 days in vitro, 50% of organotypic hippocampal slice cultures displayed long-lasting, ictal-like discharges that could be suppressed by phenytoin, whereas interictal activity was not suppressed. The fraction of cultures displaying ictal events continually increased with incubation time. Quantification of population spike activity throughout epileptogenesis using automatic detection and clustering algorithms confirmed the appearance of interictal-like activity before ictal-like discharges and also revealed high-frequency pathologic multiunit activity in slice cultures at 14 to 17 days in vitro. These experiments indicate that interictal-like spikes precede the appearance of ictal-like activity in a reduced in vitro preparation. Epileptiform activity in cultures resembled in vivo epilepsy, including sensitivity to anticonvulsants and steadily increasing seizure incidence over time, although seizure frequency and rate of epileptogenesis were higher in vitro. Organotypic hippocampal slice cultures comprise a useful model system for investigating mechanisms of epileptogenesis as well as developing antiepileptic and antiepileptogenic drugs.

Dataset Information

Mathematical model of Na-K-Cl homeostasis in ictal and interictal discharges.

Publications

Mathematical model of Na-K-Cl homeostasis in ictal and interictal discharges.

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