Ionic dynamics mediate spontaneous termination of seizures and postictal depression state

GABA-Induced Seizure-Like Events Caused by Multi-ionic Interactive Dynamics

Experimental evidence showed that an increase in intracellular chloride concentration [Formula: see text] caused by gamma-aminobutyric acid (GABA) input can promote epileptic firing activity, but the actual mechanisms remain elusive. Here in this theoretical work, we show that influx of chloride and concomitant bicarbonate ion [Formula: see text] efflux upon GABA receptor activation can induce epileptic firing activity by transition of GABA from inhibition to excitation. We analyzed the intrinsic property of neuron firing states as a function of [Formula: see text] We found that as [Formula: see text] increases, the system exhibits a saddle-node bifurcation, above which the neuron exhibits a spectrum of intensive firing, periodic bursting interrupted by depolarization block (DB) state, and eventually a stable DB through a Hopf bifurcation. We demonstrate that only GABA stimuli together with [Formula: see text] efflux can switch GABA's effect to excitation which leads to a series of seizure-like events (SLEs). Exposure to a low [Formula: see text] can drive neurons with high concentrations of [Formula: see text] downward to lower levels of [Formula: see text], during which it could also trigger SLEs depending on the exchange rate with the bath. Our analysis and simulation results show how the competition between GABA stimuli-induced accumulation of [Formula: see text] and [Formula: see text] application-induced decrease of [Formula: see text] regulates the neuron firing activity, which helps to understand the fundamental ionic dynamics of SLE.

Cholinergic modulation supports dynamic switching of resting state networks through selective DMN suppression

Brain activity during the resting state is widely used to examine brain organization, cognition and alterations in disease states. While it is known that neuromodulation and the state of alertness impact resting-state activity, neural mechanisms behind such modulation of resting-state activity are unknown. In this work, we used a computational model to demonstrate that change in excitability and recurrent connections, due to cholinergic modulation, impacts resting-state activity. The results of such modulation in the model match closely with experimental work on direct cholinergic modulation of Default Mode Network (DMN) in rodents. We further extended our study to the human connectome derived from diffusion-weighted MRI. In human resting-state simulations, an increase in cholinergic input resulted in a brain-wide reduction of functional connectivity. Furthermore, selective cholinergic modulation of DMN closely captured experimentally observed transitions between the baseline resting state and states with suppressed DMN fluctuations associated with attention to external tasks. Our study thus provides insight into potential neural mechanisms for the effects of cholinergic neuromodulation on resting-state activity and its dynamics.

Multi-scale modelling of the epileptic brain: advantages of computational therapy exploration

Objective: Epilepsy is a complex disease spanning across multiple scales, from ion channels in neurons to neuronal circuits across the entire brain. Over the past decades, computational models have been used to describe the pathophysiological activity of the epileptic brain from different aspects. Traditionally, each computational model can aid in optimizing therapeutic interventions, therefore, providing a particular view to design strategies for treating epilepsy. As a result, most studies are concerned with generating specific models of the epileptic brain that can help us understand the certain machinery of the pathological state. Those specific models vary in complexity and biological accuracy, with system-level models often lacking biological details.Approach: Here, we review various types of computational model of epilepsy and discuss their potential for different therapeutic approaches and scenarios, including drug discovery, surgical strategies, brain stimulation, and seizure prediction. We propose that we need to consider an integrated approach with a unified modelling framework across multiple scales to understand the epileptic brain. Our proposal is based on the recent increase in computational power, which has opened up the possibility of unifying those specific epileptic models into simulations with an unprecedented level of detail.Main results: A multi-scale epilepsy model can bridge the gap between biologically detailed models, used to address molecular and cellular questions, and brain-wide models based on abstract models which can account for complex neurological and behavioural observations.Significance: With these efforts, we move toward the next generation of epileptic brain models capable of connecting cellular features, such as ion channel properties, with standard clinical measures such as seizure severity.

The role of extracellular glutamate homeostasis dysregulated by astrocyte in epileptic discharges: a model evidence

Glutamate (Glu) is a predominant excitatory neurotransmitter that acts on glutamate receptors to transfer signals in the central nervous system. Abnormally elevated extracellular glutamate levels is closely related to the generation and transition of epileptic seizures. However, there lacks of investigation regarding the role of extracellular glutamate homeostasis dysregulated by astrocyte in neuronal epileptic discharges. According to this, we propose a novel neuron-astrocyte computational model (NAG) by incorporating extracellular Glu concentration dynamics from three aspects of regulatory mechanisms: (1) the Glu uptake through astrocyte EAAT2; (2) the binding and release Glu via activating astrocyte mGluRs; and (3) the Glu free diffusion in the extracellular space. Then the proposed model NAG is analyzed theoretically and numerically to verify the effect of extracellular Glu homeostasis dysregulated by such three regulatory mechanisms on neuronal epileptic discharges. Our results demonstrate that the neuronal epileptic discharges can be aggravated by the downregulation expression of EAAT2, the aberrant activation of mGluRs, and the elevated Glu levels in extracellular micro-environment; as well as various discharge states (including bursting, mixed-mode spiking, and tonic firing) can be transited by their combination. Furthermore, we find that such factors can also alter the bifurcation threshold for the generation and transition of epileptic discharges. The results in this paper can be helpful for researchers to understand the astrocyte role in modulating extracellular Glu homeostasis, and provide theoretical basis for future related experimental studies.

Single closed-loop acoustic stimulation targeting memory consolidation suppressed hippocampal ripple and thalamo-cortical spindle activity in mice

Brain rhythms of sleep reflect neuronal activity underlying sleep-associated memory consolidation. The modulation of brain rhythms, such as the sleep slow oscillation (SO), is used both to investigate neurophysiological mechanisms as well as to measure the impact of sleep on presumed functional correlates. Previously, closed-loop acoustic stimulation in humans targeted to the SO Up-state successfully enhanced the slow oscillation rhythm and phase-dependent spindle activity, although effects on memory retention have varied. Here, we aim to disclose relations between stimulation-induced hippocampo-thalamo-cortical activity and retention performance on a hippocampus-dependent object-place recognition task in mice by applying acoustic stimulation at four estimated SO phases compared to sham condition. Across the 3-h retention interval at the beginning of the light phase closed-loop stimulation failed to improve retention significantly over sham. However, retention during SO Up-state stimulation was significantly higher than for another SO phase. At all SO phases, acoustic stimulation was accompanied by a sharp increase in ripple activity followed by about a second-long suppression of hippocampal sharp wave ripple and longer maintained suppression of thalamo-cortical spindle activity. Importantly, dynamics of SO-coupled hippocampal ripple activity distinguished SOUp-state stimulation. Non-rapid eye movement (NREM) sleep was not impacted by stimulation, yet preREM sleep duration was effected. Results reveal the complex effect of stimulation on the brain dynamics and support the use of closed-loop acoustic stimulation in mice to investigate the inter-regional mechanisms underlying memory consolidation.

A simple, automated method of seizure detection in mouse models of temporal lobe epilepsy

The lack of preventive and disease modifying therapies for temporal lobe epilepsy (TLE) is a major unmet medical need. Search for such therapies utilize mouse models and require detection of seizures in electroencephalography (EEG) recordings. The labor-intensive nature of reviewing EEGs spanning many weeks underscores the need for a method of automated detection. Here we report a simple automated method of detecting seizures in long term EEG recordings from electrodes implanted in the hippocampus in animal models of TLE. We utilize a 2-pronged approach that relies on the increase in power within the gamma band range (20-50hz) during the seizure followed by suppression of activity following the seizure (post-ictal suppression [PIS]). We demonstrate the utility of this method for detecting seizures in hippocampal and amygdala EEG recordings from multiple models of TLE.

Single-compartment model of a pyramidal neuron, fitted to recordings with current and conductance injection

For single neuron models, reproducing characteristics of neuronal activity such as the firing rate, amplitude of spikes, and threshold potentials as functions of both synaptic current and conductance is a challenging task. In the present work, we measure these characteristics of regular spiking cortical neurons using the dynamic patch-clamp technique, compare the data with predictions from the standard Hodgkin-Huxley and Izhikevich models, and propose a relatively simple five-dimensional dynamical system model, based on threshold criteria. The model contains a single sodium channel with slow inactivation, fast activation and moderate deactivation, as well as, two fast repolarizing and slow shunting potassium channels. The model quantitatively reproduces characteristics of steady-state activity that are typical for a cortical pyramidal neuron, namely firing rate not exceeding 30 Hz; critical values of the stimulating current and conductance which induce the depolarization block not exceeding 80 mV and 3, respectively (both values are scaled by the resting input conductance); extremum of hyperpolarization close to the midpoint between spikes. The analysis of the model reveals that the spiking regime appears through a saddle-node-on-invariant-circle bifurcation, and the depolarization block is reached through a saddle-node bifurcation of cycles. The model can be used for realistic network simulations, and it can also be implemented within the so-called mean-field, refractory density framework.

Bursting Dynamics Based on the Persistent Na+ and Na+/K+ Pump Currents: A Dynamic Clamp Approach

Life-supporting rhythmic motor functions like heart-beating in invertebrates and breathing in vertebrates require an indefatigable generation of a robust rhythm by specialized oscillatory circuits, central pattern generators (CPGs). These CPGs should be sufficiently flexible to adjust to environmental changes and behavioral goals. Continuous self-sustained operation of bursting neurons requires intracellular Na+ concentration to remain in a functional range and to have checks and balances of the Na+ fluxes met on a cycle-to-cycle basis during bursting. We hypothesize that at a high excitability state, the interaction of the Na+/K+ pump current, Ipump, and persistent Na+ current, INaP, produces a mechanism supporting functional bursting. INaP is a low voltage-activated inward current that initiates and supports the bursting phase. This current does not inactivate and is a significant source of Na+ influx. Ipump is an outward current activated by [Na+]i and is the major source of Na+ efflux. Both currents are active and counteract each other between and during bursts. We apply a combination of electrophysiology, computational modeling, and dynamic clamp to investigate the role of Ipump and INaP in the leech heartbeat CPG interneurons (HN neurons). Applying dynamic clamp to introduce additional Ipump and INaP into the dynamics of living synaptically isolated HN neurons in real time, we show that their joint increase produces transition into a new bursting regime characterized by higher spike frequency and larger amplitude of the membrane potential oscillations. Further increase of Ipump speeds up this rhythm by shortening burst duration (BD) and interburst interval (IBI).

EEG in neonatal seizures: where to look and what to see

INTRODUCTION

Neonatal seizures are frequent and carry a detrimental prognostic outlook. Diagnosis is based on EEG confirmation. Classification has recently changed.

AREAS COVERED

We consulted original papers, book chapters, atlases, and reviews to provide a narrative overview on EEG characteristics of neonatal seizures. We searched PubMed, without time restrictions (last visited: 31 May 2022). Additional papers were extracted from the references list of selected papers. We describe the typical neonatal ictal EEG discharges morphology, location, and propagation, together with age-dependent features. Etiology-dependent electroclinical features, when identifiable, are presented for both acute symptomatic neonatal seizures and neonatal-onset epilepsies and developmental/epileptic encephalopathies. The few ictal variables known to predict long-term outcome have been discussed.

EXPERT OPINION

Multimodal neuromonitoring in critically ill newborns, high-density EEG, and functional neuroimaging might increase our insight into the neurophysiological bases of seizures in newborns. Increasing availability of long-term monitoring with conventional video-EEG and automated detection methods will allow clinicians and researchers to gather an ever expanding bulk of clinical and neurophysiological data to enhance accuracy with deep phenotyping. The latest classification proposal represents an input for critically revising our diagnostic abilities with respect to seizure definition, duration, and semiology, possibly further promoting clinical research.

Disruption of layer-specific visual processing in a model of focal neocortical epilepsy

The epileptic brain is the result of a sequence of events transforming normal neuronal populations into hyperexcitable networks supporting recurrent seizure generation. These modifications are known to induce fundamental alterations of circuit function and, ultimately, of behavior. However, how hyperexcitability affects information processing in cortical sensory circuits is not yet fully understood. Here, we investigated interlaminar alterations in sensory processing of the visual cortex in a mouse model of focal epilepsy. We found three main circuit dynamics alterations in epileptic mice: (i) a spreading of visual contrast-driven gamma modulation across layers, (ii) an increase in firing rate that is layer-unspecific for excitatory units and localized in infragranular layers for inhibitory neurons, and (iii) a strong and contrast-dependent locking of firing units to network activity. Altogether, our data show that epileptic circuits display a functional disruption of layer-specific organization of visual sensory processing, which could account for visual dysfunction observed in epileptic subjects. Understanding these mechanisms paves the way to circuital therapeutic interventions for epilepsy.

Focal seizures are organized by feedback between neural activity and ion concentration changes

Human and animal EEG data demonstrate that focal seizures start with low-voltage fast activity, evolve into rhythmic burst discharges and are followed by a period of suppressed background activity. This suggests that processes with dynamics in the range of tens of seconds govern focal seizure evolution. We investigate the processes associated with seizure dynamics by complementing the Hodgkin-Huxley mathematical model with the physical laws that dictate ion movement and maintain ionic gradients. Our biophysically realistic computational model closely replicates the electrographic pattern of a typical human focal seizure characterized by low voltage fast activity onset, tonic phase, clonic phase and postictal suppression. Our study demonstrates, for the first time in silico, the potential mechanism of seizure initiation by inhibitory interneurons via the initial build-up of extracellular K+ due to intense interneuronal spiking. The model also identifies ionic mechanisms that may underlie a key feature in seizure dynamics, i.e., progressive slowing down of ictal discharges towards the end of seizure. Our model prediction of specific scaling of inter-burst intervals is confirmed by seizure data recorded in the whole guinea pig brain in vitro and in humans, suggesting that the observed termination pattern may hold across different species. Our results emphasize ionic dynamics as elementary processes behind seizure generation and indicate targets for new therapeutic strategies.

Putrescine Intensifies Glu/GABA Exchange Mechanism and Promotes Early Termination of Seizures

Endogenous anticonvulsant mechanisms represent a reliable and currently underdeveloped strategy against recurrent seizures and may recall novel original therapeutics. Here, we investigated whether the intensification of the astroglial Glu-GABA exchange mechanism by application of the GABA precursor putrescine (PUT) may be effective against convulsive and non-convulsive seizures. We explored the potential of PUT to inhibit spontaneous spike-and-wave discharges (SWDs) in WAG/Rij rats, a genetic model of absence epilepsy. Significant shortening of SWDs in response to intraperitoneally applied PUT has been observed, which could be antagonized by blocking GAT-2/3-mediated astrocytic GABA release with the specific inhibitor SNAP-5114. Direct application of exogenous GABA also reduced SWD duration, suggesting that PUT-triggered astroglial GABA release through GAT-2/3 may be a critical step in limiting seizure duration. PUT application also dose-dependently shortened seizure-like events (SLEs) in the low-[Mg²⁺] in vitro model of temporal lobe epilepsy. SNAP-5114 reversed the antiepileptic effect of PUT in the in vitro model as well, further confirming that PUT reduces seizure duration by triggering glial GABA release. In accordance, we observed that PUT specifically reduces the frequency of excitatory synaptic potentials, suggesting that it specifically acts at excitatory synapses. We also identified that PUT specifically eliminated the tonic depolarization-induced desynchronization of SLEs. Since PUT is an important source of glial GABA and we previously showed significant GABA release, it is suggested that the astroglial Glu-GABA exchange mechanism plays a key role in limiting ictal discharges, potentially opening up novel pathways to control seizure propagation and generalization.

Classification of Seizure Termination Patterns using Deep Learning on intracranial EEG

Seizure termination has received significantly less attention than initiation and propagation and consequently, remains a poorly understood phase of seizure evolution. Yet, its study may have a significant impact on the development of efficient interventional approaches, i.e., it may be critical for the design of treatments that induce or reproduce termination mechanisms that are triggered in self-terminating seizures. In this work, we aim to study temporal and spectral features of intracranial EEG (iEEG) during epileptic seizures to find time-frequency signatures that can predict the termination patterns. We propose a deep learning model for classification of multi channel iEEG epileptic seizure termination pattern into burst suppression and continuous bursting. We decompose the raw time series seizure data into time-frequency maps using Morlet Wavelet Transform. A Convolution Neural Network (CNN) is then trained on cross-patient time-frequency maps to classify the seizure termination patterns. For evaluation of classification performance, we compared the proposed method with k-Nearest Neighbour (k-NN). The CNN is shown to achieve an accuracy of 90 % and precision of 92 % as compared to 70% and 72% accuracy and precision achieved with the k-NN respectively. The proposed model is thus able to capture the temporal and spatial patterns which results in high performance of the classifier. This method of classification can be used to predict how a particular seizure will end and can potentially inform seizure management and treatment. Clinical relevance- This method establishes a model that can be used to classify seizure termination patterns with an accuracy of 90 % which can assist in better treatment of epilepsy patients.

Why won't it stop? The dynamics of benzodiazepine resistance in status epilepticus

Status epilepticus is a life-threatening neurological emergency that affects both adults and children. Approximately 36% of episodes of status epilepticus do not respond to the current preferred first-line treatment, benzodiazepines. The proportion of episodes that are refractory to benzodiazepines is higher in low-income and middle-income countries (LMICs) than in high-income countries (HICs). Evidence suggests that longer episodes of status epilepticus alter brain physiology, thereby contributing to the emergence of benzodiazepine resistance. Such changes include alterations in GABA_A receptor function and in the transmembrane gradient for chloride, both of which erode the ability of benzodiazepines to enhance inhibitory synaptic signalling. Often, current management guidelines for status epilepticus do not account for these duration-related changes in pathophysiology, which might differentially impact individuals in LMICs, where the average time taken to reach medical attention is longer than in HICs. In this Perspective article, we aim to combine clinical insights and the latest evidence from basic science to inspire a new, context-specific approach to efficiently managing status epilepticus.

Ictal wavefront propagation in slices and simulations with conductance-based refractory density model

The mechanisms determining ictal discharge (ID) propagation are still not clear. In the present study, we aimed to examine these mechanisms in animal and mathematical models of epileptiform activity. Using double-patch and extracellular potassium ion concentration recordings in rat hippocampal-cortical slices, we observed that IDs moved at a speed of about 1 mm/s or less. The mechanisms of such slow propagation have been studied with a mathematical, conductance-based refractory density (CBRD) model that describes the GABA- and glutamatergic neuronal populations’ interactions and ion dynamics in brain tissue. The modeling study reveals two main factors triggerring IDs: (i) increased interneuronal activity leading to chloride ion accumulation and a consequent depolarizing GABAergic effect and (ii) the elevation of extracellular potassium ion concentration. The local synaptic transmission followed by local potassium ion extrusion and GABA receptor-mediated chloride ion accumulation underlies the ID wavefront’s propagation. In contrast, potassium ion diffusion in the extracellular space is slower and does not affect ID’s speed. The short discharges, constituting the ID, propagate much faster than the ID front. The accumulation of sodium ions inside neurons due to their hyperactivity and glutamatergic currents boosts the Na⁺/K⁺ pump, which terminates the ID. Knowledge of the mechanism of ID generation and propagation contributes to the development of new treatments against epilepsy.

During an epileptic seizure, neuronal excitation spreads across the brain tissue and is accompanied by significant changes in ionic concentrations. Ictal discharge front spreads at low speeds, less than 1 mm/s. Mechanisms underlying this phenomenon are not yet well understood. We study these mechanisms using electrophysiological recordings in brain slices and computer simulations. Our detailed biophysical model describing neuronal populations’ interaction, spatial propagation, and ionic dynamics reproduces the generation and propagation of spontaneously repeating ictal discharges. The simulations are consistent with our recordings of the electrical activity and the extracellular potassium ion concentration. We distinguished between the two alternative mechanisms of the ictal wavefront propagation: (i) the diffusion of potassium ions released from excited neurons, which depolarizes distant neurons and thus supports excitation, and (ii) the axonal spread of excitation followed by the local extracellular potassium ion accumulation that supports the excitation. Our simulations provide evidence in favor of the latter mechanism. Our experiment-based modeling contributes to a mathematical description of brain tissue functioning and potentially contributes to developing new treatments against epilepsy.

Quantifying seizure termination patterns reveals limited pathways to seizure end

OBJECTIVE

Despite their possible importance in the design of novel neuromodulatory approaches and in understanding status epilepticus, the dynamics and mechanisms of seizure termination are not well studied. We examined intracranial recordings from patients with epilepsy to differentiate seizure termination patterns and investigated whether these patterns are indicative of different underlying mechanisms.

METHODS

Seizures were classified into one of two termination patterns: (a) those that end simultaneously across the brain (synchronous), and (b) those whose termination is piecemeal across the cortex (asynchronous). Both types ended with either a burst suppression pattern, or continuous seizure activity. These patterns were quantified and compared using burst suppression ratio, absolute energy, and network connectivity.

RESULTS

Seizures with electrographic generalization showed burst suppression patterns in 90% of cases, compared with only 60% of seizures which remained focal. Interestingly, we found similar absolute energy and burst suppression ratios in seizures with synchronous and asynchronous termination, while seizures with continuous seizure activity were found to be different from seizures with burst suppression, showing lower energy during seizure and lower burst suppression ratio at the start and end of seizure. Finally, network density was observed to increase with seizure progression, with significantly lower densities in seizures with continuous seizure activity compared to seizures with burst suppression.

SIGNIFICANCE

Based on this spatiotemporal classification scheme, we suggest that there are a limited number of seizure termination patterns and dynamics. If this bears out, it would imply that the number of mechanisms underlying seizure termination is also constrained. Seizures with different termination patterns exhibit different dynamics even before their start. This may provide useful clues about how seizures may be managed, which in turn may lead to more targeted modes of therapy for seizure control.

Comodulation of h- and Na+/K+ Pump Currents Expands the Range of Functional Bursting in a Central Pattern Generator by Navigating between Dysfunctional Regimes

Central pattern generators (CPGs), specialized oscillatory neuronal networks controlling rhythmic motor behaviors such as breathing and locomotion, must adjust their patterns of activity to a variable environment and changing behavioral goals. Neuromodulation adjusts these patterns by orchestrating changes in multiple ionic currents. In the medicinal leech, the endogenous neuromodulator myomodulin speeds up the heartbeat CPG by reducing the electrogenic Na+/K+ pump current and increasing h-current in pairs of mutually inhibitory leech heart interneurons (HNs), which form half-center oscillators (HN HCOs). Here we investigate whether the comodulation of two currents could have advantages over a single current in the control of functional bursting patterns of a CPG. We use a conductance-based biophysical model of an HN HCO to explain the experimental effects of myomodulin. We demonstrate that, in the model, comodulation of the Na+/K+ pump current and h-current expands the range of functional bursting activity by avoiding transitions into nonfunctional regimes, such as asymmetric bursting and plateau-containing seizure-like activity. We validate the model by finding parameters that reproduce temporal bursting characteristics matching experimental recordings from HN HCOs under control, three different myomodulin concentrations, and Cs+ treated conditions. The matching cases are located along the border of an asymmetric regime away from the border with more dangerous seizure-like activity. We found a simple comodulation mechanism with an inverse relation between the pump and h-currents makes a good fit of the matching cases and comprises a general mechanism for the robust and flexible control of oscillatory neuronal networks.SIGNIFICANCE STATEMENT Rhythm-generating neuronal circuits adjust their oscillatory patterns to accommodate a changing environment through neuromodulation. In different species, chemical messengers participating in such processes may target two or more membrane currents. In medicinal leeches, the neuromodulator myomodulin speeds up the heartbeat central pattern generator by reducing Na+/K+ pump current and increasing h-current. In a computational model, we show that this comodulation expands the range of central pattern generator's functional activity by navigating the circuit between dysfunctional regimes resulting in a much wider range of cycle period. This control would not be attainable by modulating only one current, emphasizing the synergy of combined effects. Given the prevalence of h-current and Na+/K+ pump current in neurons, similar comodulation mechanisms may exist across species.

TRESK channel contributes to depolarization-induced shunting inhibition and modulates epileptic seizures

Glutamatergic and GABAergic synaptic transmission controls excitation and inhibition of postsynaptic neurons, whereas activity of ion channels modulates neuronal intrinsic excitability. However, it is unclear how excessive neuronal excitation affects intrinsic inhibition to regain homeostatic stability under physiological or pathophysiological conditions. Here, we report that a seizure-like sustained depolarization can induce short-term inhibition of hippocampal CA3 neurons via a mechanism of membrane shunting. This depolarization-induced shunting inhibition (DShI) mediates a non-synaptic, but neuronal intrinsic, short-term plasticity that is able to suppress action potential generation and postsynaptic responses by activated ionotropic receptors. We demonstrate that the TRESK channel significantly contributes to DShI. Disruption of DShI by genetic knockout of TRESK exacerbates the sensitivity and severity of epileptic seizures of mice, whereas overexpression of TRESK attenuates seizures. In summary, these results uncover a type of homeostatic intrinsic plasticity and its underlying mechanism. TRESK might represent a therapeutic target for antiepileptic drugs.

Unique Actions of GABA Arising from Cytoplasmic Chloride Microdomains

Developmental, cellular, and subcellular variations in the direction of neuronal Cl- currents elicited by GABAA receptor activation have been frequently reported. We found a corresponding variance in the GABAA receptor reversal potential (EGABA) for synapses originating from individual interneurons onto a single pyramidal cell. These findings suggest a similar heterogeneity in the cytoplasmic intracellular concentration of chloride ([Cl-]i) in individual dendrites. We determined [Cl-]i in the murine hippocampus and cerebral cortex of both sexes by (1) two-photon imaging of the Cl--sensitive, ratiometric fluorescent protein SuperClomeleon; (2) Fluorescence Lifetime IMaging (FLIM) of the Cl--sensitive fluorophore MEQ (6-methoxy-N-ethylquinolinium); and (3) electrophysiological measurements of EGABA by pressure application of GABA and RuBi-GABA uncaging. Fluorometric and electrophysiological estimates of local [Cl-]i were highly correlated. [Cl-]i microdomains persisted after pharmacological inhibition of cation-chloride cotransporters, but were progressively modified after inhibiting the polymerization of the anionic biopolymer actin. These methods collectively demonstrated stable [Cl-]i microdomains in individual neurons in vitro and in vivo and the role of immobile anions in its stability. Our results highlight the existence of functionally significant neuronal Cl- microdomains that modify the impact of GABAergic inputs.SIGNIFICANCE STATEMENT Microdomains of varying chloride concentrations in the neuronal cytoplasm are a predictable consequence of the inhomogeneous distribution of anionic polymers such as actin, tubulin, and nucleic acids. Here, we demonstrate the existence and stability of these microdomains, as well as the consequence for GABAergic synaptic signaling: each interneuron produces a postsynaptic GABAA response with a unique reversal potential. In individual hippocampal pyramidal cells, the range of GABAA reversal potentials evoked by stimulating different interneurons was >20 mV. Some interneurons generated postsynaptic responses in pyramidal cells that reversed at potentials beyond what would be considered purely inhibitory. Cytoplasmic chloride microdomains enable each pyramidal cell to maintain a compendium of unique postsynaptic responses to the activity of individual interneurons.

Modeling Neurotransmission: Computational Tools to Investigate Neurological Disorders

The investigation of synaptic functions remains one of the most fascinating challenges in the field of neuroscience and a large number of experimental methods have been tuned to dissect the mechanisms taking part in the neurotransmission process. Furthermore, the understanding of the insights of neurological disorders originating from alterations in neurotransmission often requires the development of (i) animal models of pathologies, (ii) invasive tools and (iii) targeted pharmacological approaches. In the last decades, additional tools to explore neurological diseases have been provided to the scientific community. A wide range of computational models in fact have been developed to explore the alterations of the mechanisms involved in neurotransmission following the emergence of neurological pathologies. Here, we review some of the advancements in the development of computational methods employed to investigate neuronal circuits with a particular focus on the application to the most diffuse neurological disorders.

Analysis of KATP Channels Opening Probability of Hippocampus Cells Treated with Kainic Acid

Background

Kainic acid (KA)-induced seizures may be a valuable tool in the assessment of anti-epileptic drug efficacy in complex partial seizures. This study investigated the effects of KA on ATP-sensitive K⁺ (K_ATP) channels opening probability (NPo), which plays a crucial role in neuronal activities.

Methods

For the optimisation and validation protocol, β-cells were plated onto 35 mm plastic petri dishes and maintained in RPMI-1640 media supplemented with 10 mM glucose, 10% FCS and 25 mM of N-2-hydroxyethylpiperazine-N-ethanesulfonic acid (HEPES). The treatment effects of 10 mM glucose and 30 μM fluoxetine on K_ATP channels NPo of β-cells were assessed via cell-attached patch-clamp recordings. For hippocampus cell experiments, hippocampi were harvested from day 17 of maternal Lister-hooded rat foetus, and then transferred to a Ca²⁺ and Mg²⁺-free HEPES-buffered Hank's salt solution (HHSS). The dissociated cells were cultured and plated onto a 25 mm round cover glasses coated with poly-d-lysine (0.1 mg/mL) in a petri dish. The K_ATP channels NPo of hippocampus cells when perfused with 1 mM and 10 mM of KA were determined.

Results

NPo of β-cells showed significant decreasing patterns (P < 0.001) when treated with 10 mM glucose 0.048 (0.027) as well as 30 μM fluoxetine 0.190 (0.141) as compared to basal counterpart. In hippocampus cell experiment, a significant increase (P < 0.001) in mean NPo 2.148 (0.175) of neurons when applied with 1 mM of KA as compared to basal was observed.

Conclusion

The two concentrations of KA used in the study exerted contrasting effects toward the mean of NPo. It is hypothesised that KA at lower concentration (1 mM) opens more K_ATP channels, leading to hyperpolarisation of the neurons, which may prevent neuronal hyper excitability. No effect was shown in 10 mM KA treatment, suggesting that only lower than 10 mM KA produced significant changes in K_ATP channels. This implies further validation of KA concentration to be used in the future.

On the origin of ultraslow spontaneous Na+ fluctuations in neurons of the neonatal forebrain

Spontaneous neuronal and astrocytic activity in the neonate forebrain is believed to drive the maturation of individual cells and their integration into complex brain-region-specific networks. The previously reported forms include bursts of electrical activity and oscillations in intracellular Ca2+ concentration. Here, we use ratiometric Na+ imaging to demonstrate spontaneous fluctuations in the intracellular Na+ concentration of CA1 pyramidal neurons and astrocytes in tissue slices obtained from the hippocampus of mice at postnatal days 2-4 (P2-4). These occur at very low frequency (∼2/h), can last minutes with amplitudes up to several millimolar, and mostly disappear after the first postnatal week. To further investigate their mechanisms, we model a network consisting of pyramidal neurons and interneurons. Experimentally observed Na+ fluctuations are mimicked when GABAergic inhibition in the simulated network is made depolarizing. Both our experiments and computational model show that blocking voltage-gated Na+ channels or GABAergic signaling significantly diminish the neuronal Na+ fluctuations. On the other hand, blocking a variety of other ion channels, receptors, or transporters including glutamatergic pathways does not have significant effects. Our model also shows that the amplitude and duration of Na+ fluctuations decrease as we increase the strength of glial K+ uptake. Furthermore, neurons with smaller somatic volumes exhibit fluctuations with higher frequency and amplitude. As opposed to this, larger extracellular to intracellular volume ratio observed in neonatal brain exerts a dampening effect. Finally, our model predicts that these periods of spontaneous Na+ influx leave neonatal neuronal networks more vulnerable to seizure-like states when compared with mature brain.NEW & NOTEWORTHY Spontaneous activity in the neonate forebrain plays a key role in cell maturation and brain development. We report spontaneous, ultraslow, asynchronous fluctuations in the intracellular Na+ concentration of neurons and astrocytes. We show that this activity is not correlated with the previously reported synchronous neuronal population bursting or Ca2+ oscillations, both of which occur at much faster timescales. Furthermore, extracellular K+ concentration remains nearly constant. The spontaneous Na+ fluctuations disappear after the first postnatal week.

Dynamics of a neuron-glia system: the occurrence of seizures and the influence of electroconvulsive stimuli : A mathematical and numerical study

In this paper, we investigate the dynamics of a neuron-glia cell system and the underlying mechanism for the occurrence of seizures. For our mathematical and numerical investigation of the cell model we will use bifurcation analysis and some computational methods. It turns out that an increase of the potassium concentration in the reservoir is one trigger for seizures and is related to a torus bifurcation. In addition, we will study potassium dynamics of the model by considering a reduced version and we will show how both mechanisms are linked to each other. Moreover, the reduction of the potassium leak current will also induce seizures. Our study will show that an enhancement of the extracellular potassium concentration, which influences the Nernst potential of the potassium current, may lead to seizures. Furthermore, we will show that an external forcing term (e.g. electroshocks as unidirectional rectangular pulses also known as electroconvulsive therapy) will establish seizures similar to the unforced system with the increased extracellular potassium concentration. To this end, we describe the unidirectional rectangular pulses as an autonomous system of ordinary differential equations. These approaches will explain the appearance of seizures in the cellular model. Moreover, seizures, as they are measured by electroencephalography (EEG), spread on the macro-scale (cm). Therefore, we extend the cell model with a suitable homogenised monodomain model, propose a set of (numerical) experiment to complement the bifurcation analysis performed on the single-cell model. Based on these experiments, we introduce a bidomain model for a more realistic modelling of white and grey matter of the brain. Performing similar (numerical) experiment as for the monodomain model leads to a suitable comparison of both models. The individual cell model, with its seizures explained in terms of a torus bifurcation, extends directly to corresponding results in both the monodomain and bidomain models where the neural firing spreads almost synchronous through the domain as fast traveling waves, for physiologically relevant paramenters.

A simple model of epileptic seizure propagation: Potassium diffusion versus axo-dendritic spread

The mechanisms of epileptic discharge generation and spread are not yet fully known. A recently proposed simple biophysical model of interictal and ictal discharges, Epileptor-2, reproduces well the main features of neuronal excitation and ionic dynamics during discharge generation. In order to distinguish between two hypothesized mechanisms of discharge propagation, we extend the model to the case of two-dimensional propagation along the cortical neural tissue. The first mechanism is based on extracellular potassium diffusion, and the second is the propagation of spikes and postsynaptic signals along axons and dendrites. Our simulations show that potassium diffusion is too slow to reproduce an experimentally observed speed of ictal wavefront propagation (tenths of mm/s). By contrast, the synaptic mechanism predicts well the speed and synchronization of the pre-ictal bursts before the ictal front and the afterdischarges in the ictal core. Though this fact diminishes the role of diffusion and electrodiffusion, the model nevertheless highlights the role of potassium extrusion during neuronal excitation, which provides a positive feedback that changes at the ictal wavefront the balance of excitation versus inhibition in favor of excitation. This finding may help to find a target for a treatment to prevent seizure propagation.

Excitation and Inhibition Balance Underlying Epileptiform Activity

OBJECTIVE

The phenomenon of postictal generalized EEG suppression state (PGES) - a period with suppressed activity following seizure termination and has been found to be associated with sudden unexpected death in epilepsy - remains poorly understood. This article aims to examine the how the balance of excitation and inhibition (E/I balance) affect the dynamics of seizure and PGES.

METHODS

A network of 1000 Izhikevich model neurons was developed and only the strengths of synaptic connections were adjusted to recreate the dynamics observed in recordings of seizure and PGES from human patients.

RESULTS

A rapid rise followed by a slow decay of dominant frequency was observed in iEEG recordings of ictal periods and reproduced in the simulated local field potential by changing the E/I balance of the model network. The rate of this dominant frequency evolution was quantified by a single measure, β, which was found to have a significant rank correlation with the duration of PGES in iEEG data and the rate of E/I balance shift in the model. Significance and Conclusion: (i) highlighting the importance of E/I balance in the dynamics of seizure and PGES; (ii) suggesting the measure, β, as a marker for PGES and the shift in E/I balance as a neural correlate for this marker.

Neuro-Glial Network Model Of Postictal Generalized EEG Suppression (PGES)

Over the past couple of decades, glial cells have been highlighted as active agents in hyperexcitability of neuronal networks, specifically playing key roles in seizure onset and termination. In particular, microglia have been suggested to have both neuroprotective and neurotoxic effects on the brain. Investigation into seizure termination is of particular interest, as it is sometimes followed by a postictal generalized EEG suppression (PGES) - a low activity state that is potentially associated with sudden unexpected death in epilepsy. In this study, we attempt to link glial effects - synaptic pruning and astrocytic potassium clearance - to the duration of spontaneous epileptiform discharges (SEDs) as well as interSED intervals (iSEDs). We build upon an earlier model of a neuroglial network by translating it into the cortical paradigm and including microglial units. Preliminary findings of our model demonstrated that the duration of SEDs is largely determined by the astrocytic potassium clearance, whereas iSEDs significantly increased with microglial-driven synaptic pruning. In our model, astrocytic potassium clearance itself did not bring a PGES-like state, whereas microglial effects did, which suggests a potential biomarker for PGES phenomena.

Modeling cortical spreading depression induced by the hyperactivity of interneurons

Cortical spreading depression (CSD) is a wave of transient intense neuronal firing leading to a long lasting depolarizing block of neuronal activity. It is a proposed pathological mechanism of migraine with aura. Some forms of migraine are associated with a genetic mutation of the Na_v1.1 channel, resulting in its gain of function and implying hyperexcitability of interneurons. This leads to the counterintuitive hypothesis that intense firing of interneurons can cause CSD ignition. To test this hypothesis in silico, we developed a computational model of an E-I pair (a pyramidal cell and an interneuron), in which the coupling between the cells in not just synaptic, but takes into account also the effects of the accumulation of extracellular potassium caused by the activity of the neurons and of the synapses. In the context of this model, we show that the intense firing of the interneuron can lead to CSD. We have investigated the effect of various biophysical parameters on the transition to CSD, including the levels of glutamate or GABA, frequency of the interneuron firing and the efficacy of the KCC2 co-transporter. The key element for CSD ignition in our model was the frequency of interneuron firing and the related accumulation of extracellular potassium, which induced a depolarizing block of the pyramidal cell. This constitutes a new mechanism of CSD ignition.

Mitochondrial dysfunction and role in spreading depolarization and seizure

The effect of pathological phenomena such as epileptic seizures and spreading depolarization (SD) on mitochondria and the potential feedback of mitochondrial dysfunction into the dynamics of those phenomena are complex and difficult to study experimentally due to the simultaneous changes in many variables governing neuronal behavior. By combining a model that accounts for a wide range of neuronal behaviors including seizures, normoxic SD, and hypoxic SD (HSD), together with a detailed model of mitochondrial function and intracellular Ca²⁺ dynamics, we investigate mitochondrial dysfunction and its potential role in recovery of the neuron from seizures, HSD, and SD. Our results demonstrate that HSD leads to the collapse of mitochondrial membrane potential and cellular ATP levels that recover only when normal oxygen supply is restored. Mitochondrial organic phosphate and pH gradients determine the strength of the depolarization block during HSD and SD, how quickly the cell enters the depolarization block when the oxygen supply is disrupted or potassium in the bath solution is raised beyond the physiological value, and how fast the cell recovers from SD and HSD when normal potassium concentration and oxygen supply are restored. Although not as dramatic as phosphate and pH gradients, mitochondrial Ca²⁺ uptake has a similar effect on neuronal behavior during these conditions.

Ionic and synaptic mechanisms of seizure generation and epileptogenesis

The biophysical mechanisms underlying epileptogenesis and the generation of seizures remain to be better understood. Among many factors triggering epileptogenesis are traumatic brain injury breaking normal synaptic homeostasis and genetic mutations disrupting ionic concentration homeostasis. Impairments in these mechanisms, as seen in various brain diseases, may push the brain network to a pathological state characterized by increased susceptibility to unprovoked seizures. Here, we review recent computational studies exploring the roles of ionic concentration dynamics in the generation, maintenance, and termination of seizures. We further discuss how ionic and synaptic homeostatic mechanisms may give rise to conditions which prime brain networks to exhibit recurrent spontaneous seizures and epilepsy.

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

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.

Diagnosis of seizures and encephalopathy using conventional EEG and amplitude integrated EEG

Seizures are more common in the neonatal period than at any other time of life, partly due to the relative hyperexcitability of the neonatal brain. Brain monitoring of sick neonates in the NICU using either conventional electroencephalography or amplitude integrated EEG is essential to accurately detect seizures. Treatment of seizures is important, as evidence increasingly indicates that seizures damage the brain in addition to that caused by the underlying etiology. Prompt treatment has been shown to reduce seizure burden with the potential to ameliorate seizure-mediated damage. Neonatal encephalopathy most commonly caused by a hypoxia-ischemia results in an alteration of mental status and problems such as seizures, hypotonia, apnea, and feeding difficulties. Confirmation of encephalopathy with EEG monitoring can act as an important adjunct to other investigations and the clinical examination, particularly when considering treatment strategies such as therapeutic hypothermia. Brain monitoring also provides useful early prognostic indicators to clinicians. Recent use of machine learning in algorithms to continuously monitor the neonatal EEG, detect seizures, and grade encephalopathy offers the exciting prospect of real-time decision support in the NICU in the very near future.

Biophysical models reveal the relative importance of transporter proteins and impermeant anions in chloride homeostasis

Fast synaptic inhibition in the nervous system depends on the transmembrane flux of Cl^- ions based on the neuronal Cl^- driving force. Established theories regarding the determinants of Cl^- driving force have recently been questioned. Here, we present biophysical models of Cl^- homeostasis using the pump-leak model. Using numerical and novel analytic solutions, we demonstrate that the Na⁺/K⁺-ATPase, ion conductances, impermeant anions, electrodiffusion, water fluxes and cation-chloride cotransporters (CCCs) play roles in setting the Cl^- driving force. Our models, together with experimental validation, show that while impermeant anions can contribute to setting [Cl^-]_i in neurons, they have a negligible effect on the driving force for Cl^- locally and cell-wide. In contrast, we demonstrate that CCCs are well-suited for modulating Cl^- driving force and hence inhibitory signaling in neurons. Our findings reconcile recent experimental findings and provide a framework for understanding the interplay of different chloride regulatory processes in neurons.

Cells called neurons in the brain communicate by triggering or inhibiting electrical activity in other neurons. To inhibit electrical activity, a signal from one neuron usually triggers specific receptors on the second neuron to open, which allows particles called chloride ions to flow into or out of the neuron.

The force that moves chloride ions (the so-called ‘chloride driving force’) depends on two main factors. Firstly, chloride ions, like other particles, tend to move from an area where they are plentiful to areas where they are less abundant. Secondly, chloride ions are negatively charged and are therefore attracted to areas where the net charge (determined by the mix of positively and negatively charged particles) is more positive than their current position.

It was previously believed that a group of proteins known as CCCs, which transport chloride ions and positive ions together across the membranes surrounding cells, sets the chloride driving force. However, it has recently been suggested that negatively charged ions that are unable to cross the membrane (or ‘impermeant anions’ for short) may set the driving force instead by contributing to the net charge across the membrane. Düsterwald et al. used a computational model of the neuron to explore these two possibilities.

In the simulations, altering the activity of the CCCs led to big changes in the chloride driving force. Changing the levels of impermeant anions altered the volume of cells, but did not drive changes in the chloride driving force. This was because the flow of chloride ions across the membrane led to a compensatory change in the net charge across the membrane.

Düsterwald et al. then used an experimental technique called patch-clamping in mice and rats to confirm the model’s predictions. Defects in controlling the chloride driving force in brain cells have been linked with epilepsy, stroke and other neurological diseases. Therefore, a better knowledge of these mechanisms may in future help to identify the best targets for drugs to treat such conditions.

Adaptation and Inhibition Control Pathological Synchronization in a Model of Focal Epileptic Seizure

Pharmacoresistant epilepsy is a common neurological disorder in which increased neuronal intrinsic excitability and synaptic excitation lead to pathologically synchronous behavior in the brain. In the majority of experimental and theoretical epilepsy models, epilepsy is associated with reduced inhibition in the pathological neural circuits, yet effects of intrinsic excitability are usually not explicitly analyzed. Here we present a novel neural mass model that includes intrinsic excitability in the form of spike-frequency adaptation in the excitatory population. We validated our model using local field potential (LFP) data recorded from human hippocampal/subicular slices. We found that synaptic conductances and slow adaptation in the excitatory population both play essential roles for generating seizures and pre-ictal oscillations. Using bifurcation analysis, we found that transitions towards seizure and back to the resting state take place via Andronov-Hopf bifurcations. These simulations therefore suggest that single neuron adaptation as well as synaptic inhibition are responsible for orchestrating seizure dynamics and transition towards the epileptic state.

Using NEURON for Reaction-Diffusion Modeling of Extracellular Dynamics

Development of credible clinically-relevant brain simulations has been slowed due to a focus on electrophysiology in computational neuroscience, neglecting the multiscale whole-tissue modeling approach used for simulation in most other organ systems. We have now begun to extend the NEURON simulation platform in this direction by adding extracellular modeling. The extracellular medium of neural tissue is an active medium of neuromodulators, ions, inflammatory cells, oxygen, NO and other gases, with additional physiological, pharmacological and pathological agents. These extracellular agents influence, and are influenced by, cellular electrophysiology, and cellular chemophysiology-the complex internal cellular milieu of second-messenger signaling and cascades. NEURON's extracellular reaction-diffusion is supported by an intuitive Python-based where/who/what command sequence, derived from that used for intracellular reaction diffusion, to support coarse-grained macroscopic extracellular models. This simulation specification separates the expression of the conceptual model and parameters from the underlying numerical methods. In the volume-averaging approach used, the macroscopic model of tissue is characterized by free volume fraction-the proportion of space in which species are able to diffuse, and tortuosity-the average increase in path length due to obstacles. These tissue characteristics can be defined within particular spatial regions, enabling the modeler to account for regional differences, due either to intrinsic organization, particularly gray vs. white matter, or to pathology such as edema. We illustrate simulation development using spreading depression, a pathological phenomenon thought to play roles in migraine, epilepsy and stroke. Simulation results were verified against analytic results and against the extracellular portion of the simulation run under FiPy. The creation of this NEURON interface provides a pathway for interoperability that can be used to automatically export this class of models into complex intracellular/extracellular simulations and future cross-simulator standardization.

Characterizing Concentration-Dependent Neural Dynamics of 4-Aminopyridine-Induced Epileptiform Activity

Epilepsy remains one of the most common neurological disorders. In patients, it is characterized by unprovoked, spontaneous, and recurrent seizures or ictal events. Typically, inter-ictal events or large bouts of population level activity can be measured between seizures and are generally asymptomatic. Decades of research have focused on understanding the mechanisms leading to the development of seizure-like activity using various pro-convulsive pharmacological agents, including 4-aimnopyridine (4AP).

However, the lack of consistency in the concentrations used for studying 4AP-induced epileptiform activity in animal models may give rise to differences in results and interpretation thereof. Indeed, the range of 4AP concentration in both in vivo and in vitro studies varies from 3 μM to 40 mM. Here, we explored the effects of various 4AP concentrations on the development and characteristics of hippocampal epileptiform activity in acute mouse brain slices of either sex. Using multi-electrode array recordings, we show that 4AP induces hippocampal epileptiform activity for a broad range of concentrations.

The frequency component and the spatiotemporal patterns of the epileptiform activity revealed a dose-dependent response. Finally, in the presence of 4AP, reduction of KCC2 co-transporter activity by KCC2 antagonist VU0240551 prevented the manifestation of the frequency component differences between different concentrations of 4AP. Overall, the study predicts that different concentrations of 4AP can result in the different mechanisms behind hippocampal epileptiform activity, of which some are dependent on the KCC2 co-transporter function.

Origin of slow spontaneous resting-state neuronal fluctuations in brain networks

Resting- or baseline-state low-frequency (0.01-0.2 Hz) brain activity is observed in fMRI, EEG, and local field potential recordings. These fluctuations were found to be correlated across brain regions and are thought to reflect neuronal activity fluctuations between functionally connected areas of the brain. However, the origin of these infra-slow resting-state fluctuations remains unknown. Here, using a detailed computational model of the brain network, we show that spontaneous infra-slow (<0.05 Hz) activity could originate due to the ion concentration dynamics. The computational model implemented dynamics for intra- and extracellular K⁺ and Na⁺ and intracellular Cl^- ions, Na⁺/K⁺ exchange pump, and KCC2 cotransporter. In the network model simulating resting awake-like brain state, we observed infra-slow fluctuations in the extracellular K⁺ concentration, Na⁺/K⁺ pump activation, firing rate of neurons, and local field potentials. Holding K⁺ concentration constant prevented generation of the infra-slow fluctuations. The amplitude and peak frequency of this activity were modulated by the Na⁺/K⁺ pump, AMPA/GABA synaptic currents, and glial properties. Further, in a large-scale network with long-range connections based on CoCoMac connectivity data, the infra-slow fluctuations became synchronized among remote clusters similar to the resting-state activity observed in vivo. Overall, our study proposes that ion concentration dynamics mediated by neuronal and glial activity may contribute to the generation of very slow spontaneous fluctuations of brain activity that are reported as the resting-state fluctuations in fMRI and EEG recordings.

Astroglial role in the pathophysiology of status epilepticus: an overview

Status epilepticus is a medical emergency with elevated morbidity and mortality rates, and represents a leading cause of epilepsy-related deaths. Though status epilepticus can occur at any age, it manifests more likely in children and elderly people. Despite the common prevalence of epileptic disorders, a complete explanation for the mechanisms leading to development of self-limited or long lasting seizures (as in status epilepticus) are still lacking. Apart from neurons, research evidence suggests the involvement of immune and glial cells in epileptogenesis. Among glial cells, astrocytes represent an ideal target for the study of the pathophysiology of status epilepticus, due to their key role in homeostatic balance of the central nervous system. During status epilepticus, astroglial cells are activated by the presence of cytokines, damage associated molecular patterns and reactive oxygen species. The persistent activation of astrocytes leads to a decrease in glutamate clearance with a corresponding accumulation in the synaptic extracellular space, increasing the chance of neuronal excitotoxicity. Moreover, major alterations in astrocytic gap junction coupling, inflammation and receptor expression, facilitate the generation of seizures. Astrocytes are also involved in dysregulation of inhibitory transmission in the central nervous system and directly participate in ionic homeostatic alterations during status epilepticus. In the present review, we focus on the functional and structural changes in astrocytic activity that participate in the development and maintenance of status epilepticus, with special attention on concurrent inflammatory alterations. We also include potential astrocytic treatment targets for status epilepticus.

Minimal model of interictal and ictal discharges "Epileptor-2"

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.

Chloride transporters and GABA polarity in developmental, neurological and psychiatric conditions

Neuronal chloride regulation is a determinant factor for the dynamic tuning of GABAergic inhibition during and beyond brain development. This regulation is mainly dependent on the two co-transporters K⁺/Cl^- co-transporter KCC2 and Na⁺/K⁺/Cl^- co-transporter NKCC1, whose activity can decrease or increase neuronal chloride concentrations respectively. Altered expression and/or activity of either of these co-transporters has been associated with a wide variety of brain disorders including developmental disorders, epilepsy, schizophrenia and stroke. Here, we review current knowledge on chloride transporter expression and activity regulation and highlight the intriguing potential for existing and future interventions to support chloride homeostasis across a wide range of mental disorders and neurological conditions.

Activity-induced spontaneous spikes in GABAergic neurons suppress seizure discharges: an implication of computational modeling

Background

Epilepsy, a prevalent neurological disorder, appears self-termination. The endogenous mechanism for seizure self-termination remains to be addressed in order to develop new strategies for epilepsy treatment. We aim to examine the role of activity-induced spontaneous spikes at GABAergic neurons as an endogenous mechanism in the seizure self-termination.

Methods and Results

Neuronal spikes were induced by depolarization pulses at cortical GABAergic neurons from temporal lobe epilepsy patients and mice, in which some of these neurons fired activity-induced spontaneous spikes. Neural networks including excitatory and inhibitory neurons were computationally constructed, and their functional properties were based on our studies from whole-cell recordings. With the changes in the portion and excitability of inhibitory neurons that generated activity-induced spontaneous spike, the efficacies to suppress synchronous seizure activity were analyzed, such as its onset time, decay slope and spike frequency. The increases in the proportion and excitability of inhibitory neurons that generated activity-induced spontaneous spikes effectively suppressed seizure activity in neural networks. These factors synergistically strengthened the efficacy of seizure activity suppression.

Conclusion

Our study supports a notion that activity-induced spontaneous spikes in GABAergic neurons may be an endogenous mechanism for seizure self-termination. A potential therapeutic strategy for epilepsy is to upregulate the cortical inhibitory neurons that generate activity-induced spontaneous spikes.

Role of KCC2-dependent potassium efflux in 4-Aminopyridine-induced Epileptiform synchronization

A balance between excitation and inhibition is necessary to maintain stable brain network dynamics. Traditionally, seizure activity is believed to arise from the breakdown of this delicate balance in favor of excitation with loss of inhibition. Surprisingly, recent experimental evidence suggests that this conventional view may be limited, and that inhibition plays a prominent role in the development of epileptiform synchronization. Here, we explored the role of the KCC2 co-transporter in the onset of inhibitory network-induced seizures. Our experiments in acute mouse brain slices, of either sex, revealed that optogenetic stimulation of either parvalbumin- or somatostatin-expressing interneurons induced ictal discharges in rodent entorhinal cortex during 4-aminopyridine application. These data point to a proconvulsive role of GABAA receptor signaling that is independent of the inhibitory input location (i.e., dendritic vs. somatic). We developed a biophysically realistic network model implementing dynamics of ion concentrations to explore the mechanisms leading to inhibitory network-induced seizures. In agreement with experimental results, we found that stimulation of the inhibitory interneurons induced seizure-like activity in a network with reduced potassium A-current. Our model predicts that interneuron stimulation triggered an increase of interneuron firing, which was accompanied by an increase in the intracellular chloride concentration and a subsequent KCC2-dependent gradual accumulation of the extracellular potassium promoting epileptiform ictal activity. When the KCC2 activity was reduced, stimulation of the interneurons was no longer able to induce ictal events. Overall, our study provides evidence for a proconvulsive role of GABAA receptor signaling that depends on the involvement of the KCC2 co-transporter.

SK channels participate in the formation of after burst hyperpolarization and partly inhibit the burst strength of epileptic ictal discharges

Epilepsy is a common disease of the central nervous system. Tetanic spasms and convulsions are the key symptoms exhibited during epileptic seizures. However, the majority of patients have a significant post-seizure silence following a serious seizure; the underlying molecular neural mechanisms in this burst interval are unclear. The aim of the present study was to reveal the effect and role of calcium-activated potassium channels during this seizure interval silence period. Cyclothiazide (CTZ) was used to establish the seizure model in rat hippocampal cultured neurons, then the after-burst hyperpolarization (ABH) activities were recorded using the patch clamp technique. By comparing the amplitude and duration of hyperpolarizations, the present study analyzed the association between epileptiform bursts and ABHs when treated with different concentrations of CTZ. In addition, apamin and iberiotoxin were used for pharmacological tests. An intracranial electroencephalogram (EEG) recording was also performed when the CTZ experiments were repeated on animals. The experimental results revealed that treatment with high levels of CTZ induced larger ABHs and was associated with stronger burst activities, which suggested a positive correlation between ABH and epileptiform burst. Apamin, an antagonist of small conductance calcium-activated potassium (SK) channels, decreased the amplitude of ABH; however, reduced ABH was associated with enhanced burst activity, in burst probability and burst strength. These results revealed an important role of SK channels in the formation of ABH and in the inhibition of burst activity. Iberiotoxin, an antagonist of big conductance calcium-activated potassium (BK) channels, had no significant effect on ABH and burst activity. In addition, a positive correlation was identified between burst duration and ABH parameters. An intracellular calcium chelator impaired the amplitude of ABH; however, it did not affect the burst parameters. The rat cortical EEG recordings also exhibited a similar positive correlation between the duration of epileptic burst and after burst depression. Collectively, the results indicate that ABH may serve in the physiological feedback system to reduce the strength of epileptic hyperexcitation, a process in which SK channels are important.

Computational model of interictal discharges triggered by interneurons

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.

Low-to-High Cross-Frequency Coupling in the Electrical Rhythms as Biomarker for Hyperexcitable Neuroglial Networks of the Brain

OBJECTIVE

One of the features used in the study of hyperexcitablility is high-frequency oscillations (HFOs, >80 Hz). HFOs have been reported in the electrical rhythms of the brain's neuroglial networks under physiological and pathological conditions. Cross-frequency coupling (CFC) of HFOs with low-frequency rhythms was used to identify pathologic HFOs in the epileptogenic zones of epileptic patients and as a biomarker for the severity of seizure-like events in genetically modified rodent models. We describe a model to replicate reported CFC features extracted from recorded local field potentials (LFPs) representing network properties.

METHODS

This study deals with a four-unit neuroglial cellular network model where each unit incorporates pyramidal cells, interneurons, and astrocytes. Three different pathways of hyperexcitability generation-Na - ATPase pump, glial potassium clearance, and potassium afterhyperpolarization channel-were used to generate LFPs. Changes in excitability, average spontaneous electrical discharge (SED) duration, and CFC were then measured and analyzed.

RESULTS

Each parameter caused an increase in network excitability and the consequent lengthening of the SED duration. Short SEDs showed CFC between HFOs and theta oscillations (4-8 Hz), but in longer SEDs the low frequency changed to the delta range (1-4 Hz).

CONCLUSION

Longer duration SEDs exhibit CFC features similar to those reported by our team.

SIGNIFICANCE

First, Identifying the exponential relationship between network excitability and SED durations; second, highlighting the importance of glia in hyperexcitability (as they relate to extracellular potassium); and third, elucidation of the biophysical basis for CFC coupling features.

Seizing Control of KCC2: A New Therapeutic Target for Epilepsy

Deficits in GABAergic inhibition result in the abnormal neuronal activation and synchronization that underlies seizures. However, the molecular mechanisms responsible for transforming a normal brain into an epileptic one remain largely unknown. Hyperpolarizing inhibition mediated by type A GABA (GABAA) receptors is dependent on chloride extrusion by the neuron-specific type 2K+-Cl- cotransporter (KCC2). Loss-of-function mutations in KCC2 are a known cause of infantile epilepsy in humans and KCC2 dysfunction is present in patients with both idiopathic and acquired epilepsy. Here we discuss the growing evidence that KCC2 dysfunction has a central role in the development and severity of the epilepsies.

Brain sodium MRI in human epilepsy: Disturbances of ionic homeostasis reflect the organization of pathological regions

In light of technical advancements supporting exploration of MR signals other than ¹H, sodium (²³Na) has received attention as a marker of ionic homeostasis and cell viability. Here, we evaluate for the first time the possibility that ²³Na-MRI is sensitive to pathological processes occurring in human epilepsy. A normative sample of 27 controls was used to normalize regions of interest (ROIs) from 1424 unique brain locales on quantitative ²³Na-MRI and high-resolution ¹H-MPRAGE images. ROIs were based on intracerebral electrodes in ten patients undergoing epileptic network mapping. The stereo-EEG gold standard was used to define regions as belonging to primarily epileptogenic, secondarily irritative and to non-involved regions. Estimates of total sodium concentration (TSC) on ²³Na-MRI and cerebrospinal fluid (CSF) on ¹H imaging were extracted for each patient ROI, and normalized against the same region in controls. ROIs with disproportionate CSF contributions (Z_CSF≥1.96) were excluded. TSC levels were found to be elevated in patients relative to controls except in one patient, who suffered non-convulsive seizures during the scan, in whom we found reduced TSC levels. In the remaining patients, an ANOVA (F₁₁₀₀= 12.37, p<0.0001) revealed a highly significant effect of clinically-defined zones (F₁₁₀₀= 11.13, p<0.0001), with higher normalized TSC in the epileptogenic zone relative to both secondarily irritative (F₁₁₀₀= 11, p=0.0009) and non-involved regions (F₁₁₀₀= 17.8, p<0.0001). We provide the first non-invasive, in vivo evidence of a chronic TSC elevation alongside Z_CSF levels within the normative range, associated with the epileptogenic region even during the interictal period in human epilepsy, and the possibility of reduced TSC levels due to seizure. In line with modified homeostatic mechanisms in epilepsy - including altered mechanisms underlying ionic gating, clearance and exchange - we provide the first indication of ²³Na-MRI as an assay of altered sodium concentrations occurring in epilepsy associated with the organization of clinically relevant divisions of pathological cortex.