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

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          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.

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          Neural networks with dynamic synapses.

          Transmission across neocortical synapses depends on the frequency of presynaptic activity (Thomson & Deuchars, 1994). Interpyramidal synapses in layer V exhibit fast depression of synaptic transmission, while other types of synapses exhibit facilitation of transmission. To study the role of dynamic synapses in network computation, we propose a unified phenomenological model that allows computation of the postsynaptic current generated by both types of synapses when driven by an arbitrary pattern of action potential (AP) activity in a presynaptic population. Using this formalism, we analyze different regimes of synaptic transmission and demonstrate that dynamic synapses transmit different aspects of the presynaptic activity depending on the average presynaptic frequency. The model also allows for derivation of mean-field equations, which govern the activity of large, interconnected networks. We show that the dynamics of synaptic transmission results in complex sets of regular and irregular regimes of network activity.
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            Perturbed chloride homeostasis and GABAergic signaling in human temporal lobe epilepsy.

            Changes in chloride (Cl-) homeostasis may be involved in the generation of some epileptic activities. In this study, we asked whether Cl- homeostasis, and thus GABAergic signaling, is altered in tissue from patients with mesial temporal lobe epilepsy associated with hippocampal sclerosis. Slices prepared from this human tissue generated a spontaneous interictal-like activity that was initiated in the subiculum. Records from a minority of subicular pyramidal cells revealed depolarizing GABA(A) receptor-mediated postsynaptic events, indicating a perturbed Cl- homeostasis. We assessed possible contributions of changes in expression of the potassium-chloride cotransporter KCC2. Double in situ hybridization showed that mRNA for KCC2 was absent from approximately 30% of CaMKIIalpha (calcium/calmodulin-dependent protein kinase IIalpha)-positive subicular pyramidal cells. Combining intracellular recordings with biocytin-filled electrodes and KCC2 immunochemistry, we observed that all cells that were hyperpolarized during interictal events were immunopositive for KCC2, whereas the majority of depolarized cells were immunonegative. Bumetanide, at doses that selectively block the chloride-importing potassium-sodium-chloride cotransporter NKCC1, produced a hyperpolarizing shift in GABA(A) reversal potentials and suppressed interictal activity. Changes in Cl- transporter expression thus contribute to human epileptiform activity, and molecules acting on these transporters may be useful antiepileptic drugs.
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              Cation-chloride co-transporters in neuronal communication, development and trauma.

              Electrical signaling in neurons is based on the operation of plasmalemmal ion pumps and carriers that establish transmembrane ion gradients, and on the operation of ion channels that generate current and voltage responses by dissipating these gradients. Although both voltage- and ligand-gated channels are being extensively studied, the central role of ion pumps and carriers is largely ignored in current neuroscience. Such an information gap is particularly evident with regard to neuronal Cl- regulation, despite its immense importance in the generation of inhibitory synaptic responses by GABA- and glycine-gated anion channels. The cation-chloride co-transporters (CCCs) have been identified as important regulators of neuronal Cl- concentration, and recent work indicates that CCCs play a key role in shaping GABA- and glycine-mediated signaling, influencing not only fast cell-to-cell communication but also various aspects of neuronal development, plasticity and trauma.
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                Author and article information

                Contributors
                Role: ConceptualizationRole: Funding acquisitionRole: MethodologyRole: Project administrationRole: SoftwareRole: SupervisionRole: ValidationRole: VisualizationRole: Writing – original draftRole: Writing – review & editing
                Role: ConceptualizationRole: Data curationRole: InvestigationRole: VisualizationRole: Writing – review & editing
                Role: ConceptualizationRole: SupervisionRole: Writing – review & editing
                Role: Editor
                Journal
                PLoS One
                PLoS ONE
                plos
                plosone
                PLoS ONE
                Public Library of Science (San Francisco, CA USA )
                1932-6203
                15 March 2019
                2019
                : 14
                : 3
                : e0213904
                Affiliations
                [1 ] Computational Physics Laboratory, Ioffe Institute, Saint Petersburg, Russia
                [2 ] Laboratory of Molecular Mechanisms of Neural Interactions, Sechenov Institute of Evolutionary Physiology and Biochemistry of the Russian Academy of Sciences, Saint Petersburg, Russia
                Georgia State University, UNITED STATES
                Author notes

                Competing Interests: The authors have declared that no competing interests exist.

                Author information
                http://orcid.org/0000-0002-7993-6770
                http://orcid.org/0000-0002-4503-0647
                Article
                PONE-D-18-27349
                10.1371/journal.pone.0213904
                6420042
                30875397
                fc25b96f-cb11-4ca1-9cce-c5127401347c
                © 2019 Chizhov et al

                This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

                History
                : 19 September 2018
                : 4 March 2019
                Page count
                Figures: 15, Tables: 0, Pages: 31
                Funding
                Funded by: funder-id http://dx.doi.org/10.13039/501100006769, Russian Science Foundation;
                Award ID: 16-15-10201
                Award Recipient :
                This work was supported by the Russian Science Foundation (project 16-15-10201).
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