Potassium dynamics in the epileptic cortex: new insights on an old topic

Astrocytic Atrophy Following Status Epilepticus Parallels Reduced Ca2+ Activity and Impaired Synaptic Plasticity in the Rat Hippocampus

Epilepsy is a group of neurological disorders commonly associated with the neuronal malfunction leading to generation of seizures. Recent reports point to a possible contribution of astrocytes into this pathology. We used the lithium-pilocarpine model of status epilepticus (SE) in rats to monitor changes in astrocytes. Experiments were performed in acute hippocampal slices 2-4 weeks after SE induction. Nissl staining revealed significant neurodegeneration in the pyramidal cell layers of hippocampal CA1, CA3 areas, and the hilus, but not in the granular cell layer of the dentate gyrus. A significant increase in the density of astrocytes stained with an astrocyte-specific marker, sulforhodamine 101, was observed in CA1 stratum (str.) radiatum. Astrocytes in this area were also whole-cell loaded with a morphological tracer, Alexa Fluor 594, for two-photon excitation imaging. Sholl analyses showed no changes in the size of the astrocytic domain or in the number of primary astrocytic branches, but a significant reduction in the number of distal branches that are resolved with diffraction-limited light microscopy (and are thought to contain Ca2+ stores, such as mitochondria and endoplasmic reticulum). The atrophy of astrocytic branches correlated with the reduced size, but not overall frequency of Ca2+ events. The volume tissue fraction of nanoscopic (beyond the diffraction limit) astrocytic leaflets showed no difference between control and SE animals. The results of spatial entropy-complexity spectrum analysis were also consistent with changes in ratio of astrocytic branches vs. leaflets. In addition, we observed uncoupling of astrocytes through the gap-junctions, which was suggested as a mechanism for reduced K+ buffering. However, no significant difference in time-course of synaptically induced K+ currents in patch-clamped astrocytes argued against possible alterations in K+ clearance by astrocytes. The magnitude of long-term-potentiation (LTP) was reduced after SE. Exogenous D-serine, a co-agonist of NMDA receptors, has rescued the initial phase of LTP. This suggests that the reduced Ca2+-dependent release of D-serine by astrocytes impairs initiation of synaptic plasticity. However, it does not explain the failure of LTP maintenance which may be responsible for cognitive decline associated with epilepsy.

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.

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.

Control of Glutamate Transport by Extracellular Potassium: Basis for a Negative Feedback on Synaptic Transmission

Glutamate and K+, both released during neuronal firing, need to be tightly regulated to ensure accurate synaptic transmission. Extracellular glutamate and K+ ([K+]o) are rapidly taken up by glutamate transporters and K+-transporters or channels, respectively. Glutamate transport includes the exchange of one glutamate, 3 Na+, and one proton, in exchange for one K+. This K+ efflux allows the glutamate binding site to reorient in the outwardly facing position and start a new transport cycle. Here, we demonstrate the sensitivity of the transport process to [K+]o changes. Increasing [K+]o over the physiological range had an immediate and reversible inhibitory action on glutamate transporters. This K+-dependent transporter inhibition was revealed using microspectrofluorimetry in primary astrocytes, and whole-cell patch-clamp in acute brain slices and HEK293 cells expressing glutamate transporters. Previous studies demonstrated that pharmacological inhibition of glutamate transporters decreases neuronal transmission via extrasynaptic glutamate spillover and subsequent activation of metabotropic glutamate receptors (mGluRs). Here, we demonstrate that increasing [K+]o also causes a decrease in neuronal mEPSC frequency, which is prevented by group II mGluR inhibition. These findings highlight a novel, previously unreported physiological negative feedback mechanism in which [K+]o elevations inhibit glutamate transporters, unveiling a new mechanism for activity-dependent modulation of synaptic activity.

Predicting the spatiotemporal diversity of seizure propagation and termination in human focal epilepsy

Recent studies have shown that seizures can spread and terminate across brain areas via a rich diversity of spatiotemporal patterns. In particular, while the location of the seizure onset area is usually invariant across seizures in an individual patient, the source of traveling (2–3 Hz) spike-and-wave discharges during seizures can either move with the slower propagating ictal wavefront or remain stationary at the seizure onset area. Furthermore, although many focal seizures terminate synchronously across brain areas, some evolve into distinct ictal clusters and terminate asynchronously. Here, we introduce a unifying perspective based on a new neural field model of epileptic seizure dynamics. Two main mechanisms, the co-existence of wave propagation in excitable media and coupled-oscillator dynamics, together with the interaction of multiple time scales, account for the reported diversity. We confirm our predictions in seizures and tractography data obtained from patients with pharmacologically resistant epilepsy. Our results contribute toward patient-specific seizure modeling.

A major goal of epilepsy research is understanding the spatiotemporal dynamics of seizure. Here, the authors extend the Epileptor neural mass model into a neural field model, in order to provide a unified and patient-specific model of seizure initiation, propagation, and termination.

Study on the mechanisms of seizure-like events suppression effect by electrical stimulation using a microelectrode array

In this paper, we studied the mechanisms underlying the suppression of seizure-like events (SLEs) by electrical stimulation. We conducted an in-vitro experiment using entorhinal cortex combined hippocampal slices and two convulsant drugs, bicuculline and 4-aminopyridine, to induce spontaneous SLEs. We used a microelectrode array to observe network dynamics over the entire hippocampal area simultaneously, including regions far from the stimulation site. We stimulated the entorhinal cortex region, which has been determined to be a focus of SLEs by Granger causality analysis of multichannel time series data, by an external electrode. In bicuculline application, electrical stimulation showed a marked suppression effect, even though the sizes of the effective region differed. In 4-aminopyridine application, however, stimulation under the same conditions did not suppress the activities in ∼80% of SLEs. The suppression effect was more remarkable in the areas surrounding the stimulation site in both cases. Our experimental results could support the neuronal depolarization blockade mechanism by accumulation of extracellular potassium ions, which is one of the most convincing mechanisms to understand seizure suppression phenomena because of electrical stimulation. Computer simulation using a neuronal network model also confirmed the mechanism.

Neuronal control of astrocytic respiration through a variant of the Crabtree effect

Aerobic glycolysis is a phenomenon that in the long term contributes to synaptic formation and growth, is reduced by normal aging, and correlates with amyloid beta deposition. Aerobic glycolysis starts within seconds of neural activity and it is not obvious why energetic efficiency should be compromised precisely when energy demand is highest. Using genetically encoded FRET nanosensors and real-time oxygen measurements in culture and in hippocampal slices, we show here that astrocytes respond to physiological extracellular K⁺ with an acute rise in cytosolic ATP and a parallel inhibition of oxygen consumption, explained by glycolytic stimulation via the Na⁺-bicarbonate cotransporter NBCe1. This control of mitochondrial respiration via glycolysis modulation is reminiscent of a phenomenon previously described in proliferating cells, known as the Crabtree effect. Fast brain aerobic glycolysis may be interpreted as a strategy whereby neurons manipulate neighboring astrocytes to obtain oxygen, thus maximizing information processing.

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.

Chaotic Dynamics Mediate Brain State Transitions, Driven by Changes in Extracellular Ion Concentrations

Previous studies have suggested that changes in extracellular ion concentrations initiate the transition from an activity state that characterizes sleep in cortical neurons to states that characterize wakefulness. However, because neuronal activity and extracellular ion concentrations are interdependent, isolating their unique roles during sleep-wake transitions is not possible in vivo. Here, we extend the Averaged-Neuron model and demonstrate that, although changes in extracellular ion concentrations occur concurrently, decreasing the conductance of calcium-dependent potassium channels initiates the transition from sleep to wakefulness. We find that sleep is governed by stable, self-sustained oscillations in neuronal firing patterns, whereas the quiet awake state and active awake state are both governed by irregular oscillations and chaotic dynamics; transitions between these separable awake states are prompted by ionic changes. Although waking is indicative of a shift from stable to chaotic neuronal firing patterns, we illustrate that the properties of chaotic dynamics ensure that the transition between states is smooth and robust to noise.

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.

Interneuronal Network Activity at the Onset of Seizure-Like Events in Entorhinal Cortex Slices

The onset of focal seizures in humans and in different animal models of focal epilepsy correlates with reduction of neuronal firing and enhanced interneuronal network activity. Whether this phenomenon contributes to seizure generation is still unclear. We used the in vitro entorhinal cortex slices bathed in 4-aminopirydine (4-AP) as an experimental paradigm model to evaluate the correlation between interneuronal GABAergic network activity and seizure-like events. Epileptiform discharges were recorded in layer V-VI pyramidal neurons and fast-spiking interneurons in slices from male and female mice and in the isolated female guinea pig brain preparation during perfusion with 4-AP. We observed that 90% of seizure-like events recorded in principal cells were preceded by outward currents coupled with extracellular potassium shifts, abolished by pharmacological blockade of GABA_A receptors. Potassium elevations associated to GABA_A receptor-mediated population events were confirmed in the entorhinal cortex of the in vitro isolated whole guinea pig brain. Fast-rising and sustained extracellular potassium increases associated to interneuronal network activity consistently preceded the initiation of seizure-like events. We conclude that in the 4-AP seizure model, interneuronal network activity occurs before 4-AP-induced seizures and therefore supports a role of interneuron activity in focal seizure generation.SIGNIFICANCE STATEMENT The paper focuses on the mechanisms of ictogenesis, a topic that requires a step beyond the simplistic view that seizures, and epilepsy, are due to an increase of excitatory network activity. Focal temporal lobe seizures in humans and in several experimental epilepsies likely correlate with a prevalent activation of interneurons. The potassium channel blocker 4-aminopyridine reliably induces seizure-like events in temporal lobe structures. Herein, we show that a majority of seizures in the entorhinal cortex starts with interneuronal network activity accompanied by a fast and sustained increase in extracellular potassium. Our new findings reinforce and add a new piece of evidence to the proposal that limbic seizures can be supported by GABAergic hyperactivity.

Pannexin-1 channels in epilepsy

Pannexin-1 (Panx1) expression is raised in several animal seizure models and in resected human epileptic brain tissue, suggesting relevance to epilepsy. Multiple factors that are characteristic of seizures are thought to regulate Panx1 channel opening, including elevated levels of extracellular K⁺. Panx1, when open, 1) releases ATP, glutamate, and other metabolites into the extracellular medium, and 2) may depolarize the membrane due to a channel reversal potential around 0mV. Resultant ATP release from stimulated Panx1 can activate purinergic receptors, including P2X7 receptors. Glutamate and other signaling molecules released by Panx1 opening may have both excitatory and inhibitory actions on seizure generation. This review examines the critical and complex roles of Panx1 channels in epilepsy, which could provide a basis for future therapeutics.

A Biophysical Model for Cytotoxic Cell Swelling

We present a dynamic biophysical model to explain neuronal swelling underlying cytotoxic edema in conditions of low energy supply, as observed in cerebral ischemia. Our model contains Hodgkin-Huxley-type ion currents, a recently discovered voltage-gated chloride flux through the ion exchanger SLC26A11, active KCC2-mediated chloride extrusion, and ATP-dependent pumps. The model predicts changes in ion gradients and cell swelling during ischemia of various severity or channel blockage with realistic timescales. We theoretically substantiate experimental observations of chloride influx generating cytotoxic edema, while sodium entry alone does not. We show a tipping point of Na⁺/K⁺-ATPase functioning, where below cell volume rapidly increases as a function of the remaining pump activity, and a Gibbs-Donnan-like equilibrium state is reached. This precludes a return to physiological conditions even when pump strength returns to baseline. However, when voltage-gated sodium channels are temporarily blocked, cell volume and membrane potential normalize, yielding a potential therapeutic strategy.

SIGNIFICANCE STATEMENT

Cytotoxic edema most commonly results from energy shortage, such as in cerebral ischemia, and refers to the swelling of brain cells due to the entry of water from the extracellular space. We show that the principle of electroneutrality explains why chloride influx is essential for the development of cytotoxic edema. With the help of a biophysical model of a single neuron, we show that a tipping point of the energy supply exists, below which the cell volume rapidly increases. We simulate realistic time courses to and reveal critical components of neuronal swelling in conditions of low energy supply. Furthermore, we show that, after transient blockade of the energy supply, cytotoxic edema may be reversed by temporary blockade of Na⁺ channels.

Palladium-Mediated Synthesis of a Near-Infrared Fluorescent K+ Sensor

Potassium (K+) exits electrically excitable cells during normal and pathophysiological activity. Currently, K+-sensitive electrodes and electrical measurements are the primary tools to detect K+ fluxes. Here, we describe the synthesis of a near-IR, oxazine fluorescent K+ sensor (KNIR-1) with a dissociation constant suited for detecting changes in intracellular and extracellular K+ concentrations. KNIR-1 treatment of cells expressing voltage-gated K+ channels enabled the visualization of intracellular K+ depletion upon channel opening and restoration of cytoplasmic K+ after channel closing.

Prediction of the Seizure Suppression Effect by Electrical Stimulation via a Computational Modeling Approach

In this paper, we identified factors that can affect seizure suppression via electrical stimulation by an integrative study based on experimental and computational approach. Preferentially, we analyzed the characteristics of seizure-like events (SLEs) using our previous in vitro experimental data. The results were analyzed in two groups classified according to the size of the effective region, in which the SLE was able to be completely suppressed by local stimulation. However, no significant differences were found between these two groups in terms of signal features or propagation characteristics (i.e., propagation delays, frequency spectrum, and phase synchrony). Thus, we further investigated important factors using a computational model that was capable of evaluating specific influences on effective region size. In the proposed model, signal transmission between neurons was based on two different mechanisms: synaptic transmission and the electrical field effect. We were able to induce SLEs having similar characteristics with differentially weighted adjustments for the two transmission methods in various noise environments. Although the SLEs had similar characteristics, their suppression effects differed. First of all, the suppression effect occurred only locally where directly received the stimulation effect in the high noise environment, but it occurred in the entire network in the low noise environment. Interestingly, in the same noise environment, the suppression effect was different depending on SLE propagation mechanism; only a local suppression effect was observed when the influence of the electrical field transmission was very weak, whereas a global effect was observed with a stronger electrical field effect. These results indicate that neuronal activities synchronized by a strong electrical field effect respond more sensitively to partial changes in the entire network. In addition, the proposed model was able to predict that stimulation of a seizure focus region is more effective for suppression. In conclusion, we confirmed the possibility of a computational model as a simulation tool to analyze the efficacy of deep brain stimulation (DBS) and investigated the key factors that determine the size of an effective region in seizure suppression via electrical stimulation.

Human seizures couple across spatial scales through travelling wave dynamics

Epilepsy—the propensity toward recurrent, unprovoked seizures—is a devastating disease affecting 65 million people worldwide. Understanding and treating this disease remains a challenge, as seizures manifest through mechanisms and features that span spatial and temporal scales. Here we address this challenge through the analysis and modelling of human brain voltage activity recorded simultaneously across microscopic and macroscopic spatial scales. We show that during seizure large-scale neural populations spanning centimetres of cortex coordinate with small neural groups spanning cortical columns, and provide evidence that rapidly propagating waves of activity underlie this increased inter-scale coupling. We develop a corresponding computational model to propose specific mechanisms—namely, the effects of an increased extracellular potassium concentration diffusing in space—that support the observed spatiotemporal dynamics. Understanding the multi-scale, spatiotemporal dynamics of human seizures—and connecting these dynamics to specific biological mechanisms—promises new insights to treat this devastating disease.

The authors record both local and long-range neural activity during human epileptic seizures to study the underlying multi-scale dynamics. They find that coupling of activity across spatial scales increases during seizures through propagating waves that are fit by a model that combines neural activity and potassium concentration dynamics.

Ion diffusion may introduce spurious current sources in current-source density (CSD) analysis

Standard CSD analysis does not account for ionic diffusion. Using biophysically realistic computer simulations, we show that unaccounted-for diffusive currents can lead to the prediction of spurious current sources. This finding may be of strong interest for in vivo electrophysiologists doing extracellular recordings in general, and CSD analysis in particular.

Current-source density (CSD) analysis is a well-established method for analyzing recorded local field potentials (LFPs), that is, the low-frequency part of extracellular potentials. Standard CSD theory is based on the assumption that all extracellular currents are purely ohmic, and thus neglects the possible impact from ionic diffusion on recorded potentials. However, it has previously been shown that in physiological conditions with large ion-concentration gradients, diffusive currents can evoke slow shifts in extracellular potentials. Using computer simulations, we here show that diffusion-evoked potential shifts can introduce errors in standard CSD analysis, and can lead to prediction of spurious current sources. Further, we here show that the diffusion-evoked prediction errors can be removed by using an improved CSD estimator which accounts for concentration-dependent effects.

NEW & NOTEWORTHY Standard CSD analysis does not account for ionic diffusion. Using biophysically realistic computer simulations, we show that unaccounted-for diffusive currents can lead to the prediction of spurious current sources. This finding may be of strong interest for in vivo electrophysiologists doing extracellular recordings in general, and CSD analysis in particular.

Optogenetic activation of VGLUT2-expressing excitatory neurons blocks epileptic seizure-like activity in the mouse entorhinal cortex

We investigated whether an anti-epileptic effect is obtained by selectively activating excitatory neurons expressing ChR2 under the promoter for the synaptic vesicular glutamate transporter 2 (VGLUT2). VGLUT2-expressing cells were optically stimulated while local field potential and whole-cell patch-clamp recordings were performed in mouse entorhinal cortical slices perfused with the proconvulsive compound 4-aminopyridine (4-AP). In control conditions, blue light flashes directly depolarized the majority of putative glutamatergic cells, which in turn synaptically excited GABAergic interneurons. During bath perfusion with 4-AP, photostimuli triggered a fast EPSP-IPSP sequence which was often followed by tonic-clonic seizure-like activity closely resembling spontaneous ictal discharges. The GABAA-receptor antagonist gabazine blocked the progression of both light-induced and spontaneous seizures. Surprisingly, prolonged photostimuli delivered during ongoing seizures caused a robust interruption of synchronous discharges. Such break was correlated with a membrane potential depolarization block in principal cells, while putative GABAergic interneurons changed their firing activity from a burst-like to an irregular single-spike pattern. These data suggest that photostimulation of glutamatergic neurons triggers seizure-like activity only in the presence of an intact GABAergic transmission and that selectively activating the same glutamatergic cells robustly interrupts ongoing seizures by inducing a strong depolarization block, resulting in the disruption of paroxysmal burst-like firing.

Astrocytic gap junction blockade markedly increases extracellular potassium without causing seizures in the mouse neocortex

Extracellular potassium concentration, [K⁺]_o, is a major determinant of neuronal excitability. In the healthy brain, [K⁺]_o levels are tightly controlled. During seizures, [K⁺]_o increases up to 15mM and is thought to cause seizures due to its depolarizing effect. Although astrocytes have been suggested to play a key role in the redistribution (or spatial buffering) of excess K⁺ through Connexin-43 (Cx43)-based Gap Junctions (GJs), the relation between this dynamic regulatory process and seizure generation remains unknown. Here we contrasted the role of astrocytic GJs and hemichannels by studying the effect of GJ and hemichannel blockers on [K⁺]_o regulation in vivo. [K⁺]_o was measured by K⁺-sensitive microelectrodes. Neuronal excitability was estimated by local field potential (LFP) responses to forepaw stimulation and changes in the power of resting state activity. Starting at the baseline [K⁺]_o level of 1.61±0.3mM, cortical microinjection of CBX, a broad spectrum connexin channel blocker, increased [K⁺]_o to 11±3mM, Cx43 GJ/hemichannel blocker Gap27 increased it from 1.9±0.7 to 9±1mM. At these [K⁺]_o levels, no seizures were observed. Cx43 hemichannel blockade with TAT-Gap19 increased [K⁺]_o by only ~1mM. Microinjection of 4-aminopyridine, a known convulsant, increased [K⁺]_o to ~10mM and induced spontaneously recurring seizures, whereas direct application of K⁺ did not trigger seizure activity. These findings are the first in vivo demonstration that astrocytic GJs are major determinants for the spatial buffering of [K⁺]_o and that an increase in [K⁺]_o alone does not trigger seizures in the neocortex.

Reduced Efficacy of the KCC2 Cotransporter Promotes Epileptic Oscillations in a Subiculum Network Model

Pharmacoresistant epilepsy is a chronic neurological condition in which a basal brain hyperexcitability results in paroxysmal hypersynchronous neuronal discharges. Human temporal lobe epilepsy has been associated with dysfunction or loss of the potassium-chloride cotransporter KCC2 in a subset of pyramidal cells in the subiculum, a key structure generating epileptic activities. KCC2 regulates intraneuronal chloride and extracellular potassium levels by extruding both ions. Absence of effective KCC2 may alter the dynamics of chloride and potassium levels during repeated activation of GABAergic synapses due to interneuron activity. In turn, such GABAergic stress may itself affect Cl- regulation. Such changes in ionic homeostasis may switch GABAergic signaling from inhibitory to excitatory in affected pyramidal cells and also increase neuronal excitability. Possibly these changes contribute to periodic bursting in pyramidal cells, an essential component in the onset of ictal epileptic events. We tested this hypothesis with a computational model of a subicular network with realistic connectivity. The pyramidal cell model explicitly incorporated the cotransporter KCC2 and its effects on the internal/external chloride and potassium levels. Our network model suggested the loss of KCC2 in a critical number of pyramidal cells increased external potassium and intracellular chloride concentrations leading to seizure-like field potential oscillations. These oscillations included transient discharges leading to ictal-like field events with frequency spectra as in vitro Restoration of KCC2 function suppressed seizure activity and thus may present a useful therapeutic option. These simulations therefore suggest that reduced KCC2 cotransporter activity alone may underlie the generation of ictal discharges.

SIGNIFICANCE STATEMENT

Ion regulation in the brain is a major determinant of neural excitability. Intracellular chloride in neurons, a partial determinant of the resting potential and the inhibitory reversal potentials, is regulated together with extracellular potassium via kation chloride cotransporters. During temporal lobe epilepsy, the homeostatic regulation of intracellular chloride is impaired in pyramidal cells, yet how this dysregulation may lead to seizures has not been explored. Using a realistic neural network model describing ion mechanisms, we show that chloride homeostasis pathology provokes seizure activity analogous to recordings from epileptogenic brain tissue. We show that there is a critical percentage of pathological cells required for seizure initiation. Our model predicts that restoration of the chloride homeostasis in pyramidal cells could be a viable antiepileptic strategy.

Effect of Ionic Diffusion on Extracellular Potentials in Neural Tissue

Recorded potentials in the extracellular space (ECS) of the brain is a standard measure of population activity in neural tissue. Computational models that simulate the relationship between the ECS potential and its underlying neurophysiological processes are commonly used in the interpretation of such measurements. Standard methods, such as volume-conductor theory and current-source density theory, assume that diffusion has a negligible effect on the ECS potential, at least in the range of frequencies picked up by most recording systems. This assumption remains to be verified. We here present a hybrid simulation framework that accounts for diffusive effects on the ECS potential. The framework uses (1) the NEURON simulator to compute the activity and ionic output currents from multicompartmental neuron models, and (2) the electrodiffusive Kirchhoff-Nernst-Planck framework to simulate the resulting dynamics of the potential and ion concentrations in the ECS, accounting for the effect of electrical migration as well as diffusion. Using this framework, we explore the effect that ECS diffusion has on the electrical potential surrounding a small population of 10 pyramidal neurons. The neural model was tuned so that simulations over ∼100 seconds of biological time led to shifts in ECS concentrations by a few millimolars, similar to what has been seen in experiments. By comparing simulations where ECS diffusion was absent with simulations where ECS diffusion was included, we made the following key findings: (i) ECS diffusion shifted the local potential by up to ∼0.2 mV. (ii) The power spectral density (PSD) of the diffusion-evoked potential shifts followed a 1/f2 power law. (iii) Diffusion effects dominated the PSD of the ECS potential for frequencies up to several hertz. In scenarios with large, but physiologically realistic ECS concentration gradients, diffusion was thus found to affect the ECS potential well within the frequency range picked up in experimental recordings.

Biofouling-Resistant Impedimetric Sensor for Array High-Resolution Extracellular Potassium Monitoring in the Brain

Extracellular potassium concentration, [K⁺]o, plays a fundamental role in the physiological functions of the brain. Studies investigating changes in [K⁺]o have predominantly relied upon glass capillary electrodes with K⁺-sensitive solution gradients for their measurements. However, such electrodes are unsuitable for taking spatio-temporal measurements and are limited by the surface area of their tips. We illustrate seizures invoked chemically and in optogenetically modified mice using blue light exposure while impedimetrically measuring the response. A sharp decrease of 1-2 mM in [K⁺]o before each spike has shown new physiological events not witnessed previously when measuring extracellular potassium concentrations during seizures in mice. We propose a novel approach that uses multichannel monolayer coated gold microelectrodes for in vivo spatio-temporal measurements of [K⁺]o in a mouse brain as an improvement to the conventional glass capillary electrode.

Interaction between synaptic inhibition and glial-potassium dynamics leads to diverse seizure transition modes in biophysical models of human focal seizures

How focal seizures initiate and evolve in human neocortex remains a fundamental problem in neuroscience. Here, we use biophysical neuronal network models of neocortical patches to study how the interaction between inhibition and extracellular potassium ([K (+)] o ) dynamics may contribute to different types of focal seizures. Three main types of propagated focal seizures observed in recent intracortical microelectrode recordings in humans were modelled: seizures characterized by sustained (∼30-60 Hz) gamma local field potential (LFP) oscillations; seizures where the onset in the propagated site consisted of LFP spikes that later evolved into rhythmic (∼2-3 Hz) spike-wave complexes (SWCs); and seizures where a brief stage of low-amplitude fast-oscillation (∼10-20 Hz) LFPs preceded the SWC activity. Our findings are fourfold: (1) The interaction between elevated [K (+)] o (due to abnormal potassium buffering by glial cells) and the strength of synaptic inhibition plays a predominant role in shaping these three types of seizures. (2) Strengthening of inhibition leads to the onset of sustained narrowband gamma seizures. (3) Transition into SWC seizures is obtained either by the weakening of inhibitory synapses, or by a transient strengthening followed by an inhibitory breakdown (e.g. GABA depletion). This reduction or breakdown of inhibition among fast-spiking (FS) inhibitory interneurons increases their spiking activity and leads them eventually into depolarization block. Ictal spike-wave discharges in the model are then sustained solely by pyramidal neurons. (4) FS cell dynamics are also critical for seizures where the evolution into SWC activity is preceded by low-amplitude fast oscillations. Different levels of elevated [K (+)] o were important for transitions into and maintenance of sustained gamma oscillations and SWC discharges. Overall, our modelling study predicts that the interaction between inhibitory interneurons and [K (+)] o glial buffering under abnormal conditions may explain different types of ictal transitions and dynamics during propagated seizures in human focal epilepsy.

Targeting of astrocytic glucose metabolism by beta-hydroxybutyrate

The effectiveness of ketogenic diets and intermittent fasting against neurological disorders has brought interest to the effects of ketone bodies on brain cells. These compounds are known to modify the metabolism of neurons, but little is known about their effect on astrocytes, cells that control the supply of glucose to neurons and also modulate neuronal excitability through the glycolytic production of lactate. Here we have used genetically-encoded Förster Resonance Energy Transfer nanosensors for glucose, pyruvate and ATP to characterize astrocytic energy metabolism at cellular resolution. Our results show that the ketone body beta-hydroxybutyrate strongly inhibited astrocytic glucose consumption in mouse astrocytes in mixed cultures, in organotypic hippocampal slices and in acute hippocampal slices prepared from ketotic mice, while blunting the stimulation of glycolysis by physiological and pathophysiological stimuli. The inhibition of glycolysis was paralleled by an increased ability of astrocytic mitochondria to metabolize pyruvate. These results support the emerging notion that astrocytes contribute to the neuroprotective effect of ketone bodies.

Pubertal Expression of α4βδ GABAA Receptors Reduces Seizure-Like Discharges in CA1 Hippocampus

More than half of children with epilepsy outgrow their seizures, yet the underlying mechanism is unknown. GABAergic inhibition increases at puberty in female mice due to expression of extrasynaptic α4βδ GABAA receptors (GABARs). Therefore, we tested the role of these receptors in regulating seizure-like discharges in CA1 hippocampus using a high K(+) (8.5 mM) seizure model. Spontaneous field potentials were recorded from hippocampus of pre-pubertal (~28-32 PND) and pubertal (~35-44 PND) female wild-type or α4-/- mice. The coastline length, a measure of burst intensity, was assessed. 8.5 mM K(+) induced seizure-like discharges in over 60% of pre-pubertal slices, but only in 7% of pubertal slices, where the coastline length was reduced by 70% (P = 0.04). However, the pubertal decrease in seizure-like discharges was not seen in the α4-/-, implicating α4βδ GABARs as the cause of the decreased seizure-like activity during puberty. Administration of THIP or DS2, to selectively increase α4βδ current, reduced activity in 8.5 mM K(+) at puberty, while blockade of α5-GABARs had no effect. GABAergic current was depolarizing but inhibitory in 8.5 mM K(+), suggesting a mechanism for the effects of α4βδ and α5-GABARs, which exhibit different polarity-dependent desensitization. These data suggest that α4βδ GABARs are anti-convulsant during adolescence.

Effects of astrocytic mechanisms on neuronal hyperexcitability

While originally astrocytes have been thought to only act as support to neurons, recent studies have implicated them in multiple active roles, including the ability to moderate or alter neuronal firing patterns and to possibly be involved in both the prevention and propagation of epileptic seizures. In this study we propose a new model to incorporate pyramidal cells and interneurons (a common neural circuit in CA3 hippocampal slices) as well as a model of astrocyte. As both potassium and calcium ions have been shown to potentially affect neuronal hyperexcitability, the astrocytic model has both mechanisms--the clearance of potassium through potassium channels (such as KIR, KDR and sodium-potassium pump), and the influence of astrocyte in the synapse (forming the tripartite synapse with calcium-glutamate interactions). Preliminary findings of the model results show that when potassium conductances in the astrocyte are decreased, it results in the accumulation of extracellular potassium, leading to both spontaneous discharges and depolarization block, while the alteration of normal calcium response in the astrocyte can lead to just hyperexcitable conditions without the depolarization block.

Modeling of Age-Dependent Epileptogenesis by Differential Homeostatic Synaptic Scaling

Homeostatic synaptic plasticity (HSP) has been implicated in the development of hyperexcitability and epileptic seizures following traumatic brain injury (TBI). Our in vivo experimental studies in cats revealed that the severity of TBI-mediated epileptogenesis depends on the age of the animal. To characterize mechanisms of these differences, we studied the properties of the TBI-induced epileptogenesis in a biophysically realistic cortical network model with dynamic ion concentrations. After deafferentation, which was induced by dissection of the afferent inputs, there was a reduction of the network activity and upregulation of excitatory connections leading to spontaneous spike-and-wave type seizures. When axonal sprouting was implemented, the seizure threshold increased in the model of young but not the older animals, which had slower or unidirectional homeostatic processes. Our study suggests that age-related changes in the HSP mechanisms are sufficient to explain the difference in the likelihood of seizure onset in young versus older animals. Significance statement: Traumatic brain injury (TBI) is one of the leading causes of intractable epilepsy. Likelihood of developing epilepsy and seizures following severe brain trauma has been shown to increase with age. Specific mechanisms of TBI-related epileptogenesis and how these mechanisms are affected by age remain to be understood. We test a hypothesis that the failure of homeostatic synaptic regulation, a slow negative feedback mechanism that maintains neural activity within a physiological range through activity-dependent modulation of synaptic strength, in older animals may augment TBI-induced epileptogenesis. Our results provide new insight into understanding this debilitating disorder and may lead to novel avenues for the development of effective treatments of TBI-induced epilepsy.

Ion dynamics during seizures

Changes in membrane voltage brought about by ion fluxes through voltage and transmitter-gated channels represent the basis of neural activity. As such, electrochemical gradients across the membrane determine the direction and driving force for the flow of ions and are therefore crucial in setting the properties of synaptic transmission and signal propagation. Ion concentration gradients are established by a variety of mechanisms, including specialized transporter proteins. However, transmembrane gradients can be affected by ionic fluxes through channels during periods of elevated neural activity, which in turn are predicted to influence the properties of on-going synaptic transmission. Such activity-induced changes to ion concentration gradients are a feature of both physiological and pathological neural processes. An epileptic seizure is an example of severely perturbed neural activity, which is accompanied by pronounced changes in intracellular and extracellular ion concentrations. Appreciating the factors that contribute to these ion dynamics is critical if we are to understand how a seizure event evolves and is sustained and terminated by neural tissue. Indeed, this issue is of significant clinical importance as status epilepticus—a type of seizure that does not stop of its own accord—is a life-threatening medical emergency. In this review we explore how the transmembrane concentration gradient of the six major ions (K⁺, Na⁺, Cl⁻, Ca²⁺, H⁺and HCO3−) is altered during an epileptic seizure. We will first examine each ion individually, before describing how multiple interacting mechanisms between ions might contribute to concentration changes and whether these act to prolong or terminate epileptic activity. In doing so, we will consider how the availability of experimental techniques has both advanced and restricted our ability to study these phenomena.

Could tuning of the inhibitory tone involve graded changes in neuronal chloride transport?

Hyperpolarizing synaptic inhibition through GABAA and glycine receptors depends on the presence of the neuronal cation-chloride-cotransporter protein, KCC2. Several transcriptional and post-transcriptional mechanisms have been shown to regulate KCC2 and thereby influence the polarity and efficacy of inhibitory synaptic transmission. It is unclear however whether regulation of KCC2 enables the transporter to attain different levels of activity thus allowing a neuron to modulate the strength of inhibitory synaptic transmission to its changing requirements. We therefore investigated whether phosphorylation can allow KCC2 to achieve distinct levels of [Cl(-)]i in neurons. We generated a variety of KCC2 alanine dephosphorylation mimics and used NH4(+)-induced pHi shifts in cultured hippocampal neurons to quantify the rate of KCC2 transport activity exhibited by these mutants. To explore the relationship between KCC2 transport and GABAA receptor-mediated current amplitudes we performed gramicidine perforated-patch recordings. The correlation between EGABA and NH4(+)-induced pHi shifts enabled an estimate of the range of chloride extrusion possible by kinase/phosphatase regulation of KCC2. Our results demonstrate that KCC2 transport can vary considerably in magnitude depending on the combination of alanine mutations present on the protein. Transport can be enhanced to sufficiently high levels that hyperpolarizing GABAA responses may be obtained even in neurons with an extremely negative resting membrane potential and at high extracellular K(+) concentrations. Our findings highlight the significant potential for regulating the inhibitory tone by KCC2-mediated chloride extrusion and suggest that cellular signaling pathways may act combinatorially to alter KCC2 phosphorylation/dephosphorylation and thereby tune the strength of synaptic inhibition.

Interaction of electrically evoked activity with intrinsic dynamics of cultured cortical networks with and without functional fast GABAergic synaptic transmission

The modulation of neuronal activity by means of electrical stimulation is a successful therapeutic approach for patients suffering from a variety of central nervous system disorders. Prototypic networks formed by cultured cortical neurons represent an important model system to gain general insights in the input–output relationships of neuronal tissue. These networks undergo a multitude of developmental changes during their maturation, such as the excitatory–inhibitory shift of the neurotransmitter GABA. Very few studies have addressed how the output properties to a given stimulus change with ongoing development. Here, we investigate input–output relationships of cultured cortical networks by probing cultures with and without functional GABA_Aergic synaptic transmission with a set of stimulation paradigms at various stages of maturation. On the cellular level, low stimulation rates (<15 Hz) led to reliable neuronal responses; higher rates were increasingly ineffective. Similarly, on the network level, lowest stimulation rates (<0.1 Hz) lead to maximal output rates at all ages, indicating a network wide refractory period after each stimulus. In cultures aged 3 weeks and older, a gradual recovery of the network excitability within tens of milliseconds was in contrast to an abrupt recovery after about 5 s in cultures with absent GABA_Aergic synaptic transmission. In these GABA deficient cultures evoked responses were prolonged and had multiple discharges. Furthermore, the network excitability changed periodically, with a very slow spontaneous change of the overall network activity in the minute range, which was not observed in cultures with absent GABA_Aergic synaptic transmission. The electrically evoked activity of cultured cortical networks, therefore, is governed by at least two potentially interacting mechanisms: A refractory period in the order of a few seconds and a very slow GABA dependent oscillation of the network excitability.

Channel-mediated lactate release by K⁺-stimulated astrocytes

Excitatory synaptic transmission is accompanied by a local surge in interstitial lactate that occurs despite adequate oxygen availability, a puzzling phenomenon termed aerobic glycolysis. In addition to its role as an energy substrate, recent studies have shown that lactate modulates neuronal excitability acting through various targets, including NMDA receptors and G-protein-coupled receptors specific for lactate, but little is known about the cellular and molecular mechanisms responsible for the increase in interstitial lactate. Using a panel of genetically encoded fluorescence nanosensors for energy metabolites, we show here that mouse astrocytes in culture, in cortical slices, and in vivo maintain a steady-state reservoir of lactate. The reservoir was released to the extracellular space immediately after exposure of astrocytes to a physiological rise in extracellular K(+) or cell depolarization. Cell-attached patch-clamp analysis of cultured astrocytes revealed a 37 pS lactate-permeable ion channel activated by cell depolarization. The channel was modulated by lactate itself, resulting in a positive feedback loop for lactate release. A rapid fall in intracellular lactate levels was also observed in cortical astrocytes of anesthetized mice in response to local field stimulation. The existence of an astrocytic lactate reservoir and its quick mobilization via an ion channel in response to a neuronal cue provides fresh support to lactate roles in neuronal fueling and in gliotransmission.

A biologically constrained, mathematical model of cortical wave propagation preceding seizure termination

Epilepsy--the condition of recurrent, unprovoked seizures--manifests in brain voltage activity with characteristic spatiotemporal patterns. These patterns include stereotyped semi-rhythmic activity produced by aggregate neuronal populations, and organized spatiotemporal phenomena, including waves. To assess these spatiotemporal patterns, we develop a mathematical model consistent with the observed neuronal population activity and determine analytically the parameter configurations that support traveling wave solutions. We then utilize high-density local field potential data recorded in vivo from human cortex preceding seizure termination from three patients to constrain the model parameters, and propose basic mechanisms that contribute to the observed traveling waves. We conclude that a relatively simple and abstract mathematical model consisting of localized interactions between excitatory cells with slow adaptation captures the quantitative features of wave propagation observed in the human local field potential preceding seizure termination.

Evidence for an excitatory GABAA response in human motor cortex in idiopathic generalised epilepsy

PURPOSE

Impaired GABAergic inhibition has been implicated in the pathophysiology of epilepsy. The possibility of a paradoxical excitatory effect of GABA in epilepsy has been suggested, but has not been investigated in vivo. We investigated pre- and post-synaptic GABAergic mechanisms in patients with idiopathic generalised epilepsy (IGE).

METHOD

In 10 patients and 12 control subjects we explored short- and long-interval intracortical inhibition (SICI, LICI; post-synaptic GABAA and GABAB-mediated respectively) and long-interval intracortical facilitation (LICF; pre-synaptic disinhibition) using transcranial magnetic stimulation.

RESULTS

While post-synaptic GABAB-mediated inhibition was unchanged in IGE (p=0.09), LICF was reduced compared to controls (controls: 141±17% of baseline; untreated patients: 107±12%, p=0.2; treated patients: 79±10%, p=0.003). GABAA-mediated inhibition was reduced in untreated patients (response amplitude 56±4% of baseline vs. 26±6% in controls, p=0.004) and normalised with treatment (37±12%, p=0.5 vs. controls). When measured during LICI, GABAA-mediated inhibition became excitatory in untreated IGE (response amplitude 120±10% of baseline, p=0.017), but not in treated patients.

CONCLUSION

Pre- and post-synaptic GABA-mediated inhibitory mechanisms are altered in IGE. The findings lend in vivo support to evidence from experimental models and in vitro studies of human epileptic brain tissue that GABA may have a paradoxical excitatory role in ictogenesis.

Selective activation of parvalbumin- or somatostatin-expressing interneurons triggers epileptic seizurelike activity in mouse medial entorhinal cortex

GABAergic interneurons are thought to play a critical role in eliciting interictal spikes (IICs) and triggering ictal discharges in temporal lobe epilepsy, yet the contribution of different interneuronal subtypes to seizure initiation is still largely unknown. Here we took advantage of optogenetic techniques combined with patch-clamp and field recordings to selectively stimulate parvalbumin (PV)- or somatostatin (SOM)-positive interneurons expressing channelrhodopsin-2 (CHR-2) in layers II-III of adult mouse medial entorhinal cortical slices during extracellular perfusion with the proconvulsive compound 4-aminopyridine (4-AP, 100-200 μM). In control conditions, blue laser photostimulation selectively activated action potential firing in either PV or SOM interneurons and, in both cases, caused a robust GABAA-receptor-mediated inhibition in pyramidal cells (PCs). During perfusion with 4-AP, brief photostimuli (300 ms) activating either PV or SOM interneurons induced patterns of epileptiform activity that closely replicated spontaneously occurring IICs and tonic-clonic ictal discharges. Laser-induced synchronous firing in both interneuronal types elicited large compound GABAergic inhibitory postsynaptic currents (IPSCs) correlating with IICs and preictal spikes. In addition, spontaneous and laser-induced epileptic events were similarly initiated in concurrence with a large increase in extracellular potassium concentration. Finally, interneuron activation was unable to stop or significantly shorten the progression of seizurelike episodes. These results suggest that entorhinal PV and SOM interneurons are nearly equally effective in triggering interictal and ictal discharges that closely resemble human temporal lobe epileptic activity.

Endogenous and exogenous electric fields as modifiers of brain activity: rational design of noninvasive brain stimulation with transcranial alternating current stimulation

Synchronized neuronal activity in the cortex generates weak electric fields that are routinely measured in humans and animal models by electroencephalography and local field potential recordings. Traditionally, these endogenous electric fields have been considered to be an epiphenomenon of brain activity. Recent work has demonstrated that active cortical networks are surprisingly susceptible to weak perturbations of the membrane voltage of a large number of neurons by electric fields. Simultaneously, noninvasive brain stimulation with weak, exogenous electric fields (transcranial current stimulation, TCS) has undergone a renaissance due to the broad scope of its possible applications in modulating brain activity for cognitive enhancement and treatment of brain disorders. This review aims to interface the recent developments in the study of both endogenous and exogenous electric fields, with a particular focus on rhythmic stimulation for the modulation of cortical oscillations. The main goal is to provide a starting point for the use of rational design for the development of novel mechanism-based TCS therapeutics based on transcranial alternating current stimulation, for the treatment of psychiatric illnesses.

Dynamics from seconds to hours in Hodgkin-Huxley model with time-dependent ion concentrations and buffer reservoirs

The classical Hodgkin-Huxley (HH) model neglects the time-dependence of ion concentrations in spiking dynamics. The dynamics is therefore limited to a time scale of milliseconds, which is determined by the membrane capacitance multiplied by the resistance of the ion channels, and by the gating time constants. We study slow dynamics in an extended HH framework that includes time-dependent ion concentrations, pumps, and buffers. Fluxes across the neuronal membrane change intra- and extracellular ion concentrations, whereby the latter can also change through contact to reservoirs in the surroundings. Ion gain and loss of the system is identified as a bifurcation parameter whose essential importance was not realized in earlier studies. Our systematic study of the bifurcation structure and thus the phase space structure helps to understand activation and inhibition of a new excitability in ion homeostasis which emerges in such extended models. Also modulatory mechanisms that regulate the spiking rate can be explained by bifurcations. The dynamics on three distinct slow times scales is determined by the cell volume-to-surface-area ratio and the membrane permeability (seconds), the buffer time constants (tens of seconds), and the slower backward buffering (minutes to hours). The modulatory dynamics and the newly emerging excitable dynamics corresponds to pathological conditions observed in epileptiform burst activity, and spreading depression in migraine aura and stroke, respectively.

A review of hyperacusis and future directions: part II. Measurement, mechanisms, and treatment

PURPOSE

Hyperacusis can be extremely debilitating, and at present, there is no cure. In this detailed review of the field, we consolidate present knowledge in the hope of facilitating future research.

METHOD

We review and reference the literature on hyperacusis and related areas. This is the 2nd of a 2-part review.

RESULTS

Hyperacusis encompasses a wide range of reactions to sounds, which can be grouped into the categories of excessive loudness, annoyance, fear, and pain. Reasonable approaches to assessing the different forms of hyperacusis are emerging, including brain-imaging studies. Researchers are only beginning to understand the many mechanisms at play, and valid animal models are still evolving. There are many counseling and sound-therapy approaches that some patients find helpful, but well-controlled studies are needed to measure their long-term efficacy and to test new approaches.

CONCLUSIONS

Hyperacusis can make life difficult in this increasingly noisy world, forcing sufferers to dramatically alter their work and social habits. We believe this is an opportune time to explore approaches to better understand and treat hyperacusis.

Permittivity coupling across brain regions determines seizure recruitment in partial epilepsy

Brain regions generating seizures in patients with refractory partial epilepsy are referred to as the epileptogenic zone (EZ). During a seizure, paroxysmal activity is not restricted to the EZ, but may recruit other brain regions and propagate activity through large brain networks, which comprise brain regions that are not necessarily epileptogenic. The identification of the EZ is crucial for candidates for neurosurgery and requires unambiguous criteria that evaluate the degree of epileptogenicity of brain regions. To obtain such criteria and investigate the mechanisms of seizure recruitment and propagation, we develop a mathematical framework of coupled neural populations, which can interact via signaling through a slow permittivity variable. The permittivity variable captures effects evolving on slow timescales, including extracellular ionic concentrations and energy metabolism, with time delays of up to seconds as observed clinically. Our analyses provide a set of indices quantifying the degree of epileptogenicity and predict conditions, under which seizures propagate to nonepileptogenic brain regions, explaining the responses to intracerebral electric stimulation in epileptogenic and nonepileptogenic areas. In conjunction, our results provide guidance in the presurgical evaluation of epileptogenicity based on electrographic signatures in intracerebral electroencephalograms.

Wide field fluorescent imaging of extracellular spatiotemporal potassium dynamics in vivo

Potassium homeostasis is fundamental for the physiological functioning of the brain. Increased [K(+)] in the extracellular fluid has a major impact on neuronal physiology and can lead to ictal events. Compromised regulation of extracellular [K(+)] is involved in generation of seizures in animal models and potentially also in humans. For this reason, the investigation of K(+) spatio-temporal dynamics is of fundamental importance for neuroscientists in the field of epilepsy and other related pathologies. To date, the majority of studies investigating changes in extracellular K(+) have been conducted using a micropipette filled with a K(+) sensitive solution. However, this approach presents a major limitation: the area of the measurement is circumscribed to the tip of the pipette and it is not possible to know the spatiotemporal distribution or origin of the focally measured K(+) signal. Here we propose a novel approach, based on wide field fluorescence, to measure extracellular K(+) dynamics in neural tissue. Recording the local field potential from the somatosensory cortex of the mouse, we compared responses obtained from a K(+)-sensitive microelectrode to the spatiotemporal increases in fluorescence of the fluorophore, Asante Potassium Green-2, in physiological conditions and during 4-AP induced ictal activity. We conclude that wide field imaging is a valuable and versatile tool to measure K(+) dynamics over a large area of the cerebral cortex and is capable of capturing fast dynamics such as during ictal events. Moreover, the present technique is potentially adaptable to address questions regarding spatiotemporal dynamics of other ionic species.

The influence of ion concentrations on the dynamic behavior of the Hodgkin-Huxley model-based cortical network

Action potentials (APs) in the form of very short pulses arise when the cell is excited by any internal or external stimulus exceeding the critical threshold of the membrane. During AP generation, the membrane potential completes its natural cycle through typical phases that can be formatted by ion channels, gates and ion concentrations, as well as the synaptic excitation rate. On the basis of the Hodgkin-Huxley cell model, a cortical network consistent with the real anatomic structure is realized with randomly interrelated small population of neurons to simulate a cerebral cortex segment. Using this model, we investigated the effects of Na(+) and K(+) ion concentrations on the outcome of this network in terms of regularity, phase locking, and synchronization. The results suggested that Na(+) concentration does slightly affect the amplitude but not considerably affects the other parameters specified by depolarization and repolarization. K(+) concentration significantly influences the form, regularity, and synchrony of the network-generated APs. No previous study dealing directly with the effects of both Na(+) and K(+) ion concentrations on regularity and synchronization of the simulated cortical network-generated APs, allowing for the comparison of results obtained using our methods, was encountered in the literature. The results, however, were consistent with those obtained through studies concerning resonance and synchronization from another perspective and with the information revealed through physiological and pharmacological experiments concerning changing ion concentrations or blocking ion channels. Our results demonstrated that the regularity and reliability of brain functions have a strong relationship with cellular ion concentrations, and suggested the management of the dynamic behavior of the cellular network with ion concentrations.

Chaos and commotion in the wake of cortical spreading depression and spreading depolarizations

Punctuated episodes of spreading depolarizations erupt in the brain, encumbering tissue structure and function, and raising fascinating unanswered questions concerning their initiation and propagation. Linked to migraine aura and headache, cortical spreading depression contributes to the morbidity in the world's migraine with aura population. Even more ominously, erupting spreading depolarizations accelerate tissue damage during brain injury. The once-held view that spreading depolarizations may not exist in the human brain has changed, largely because of the discovery of migraine genes that confer cortical spreading depression susceptibility, the application of sophisticated imaging tools and efforts to interrogate their impact in the acutely injured human brain.

On the nature of seizure dynamics

Seizures can occur spontaneously and in a recurrent manner, which defines epilepsy; or they can be induced in a normal brain under a variety of conditions in most neuronal networks and species from flies to humans. Such universality raises the possibility that invariant properties exist that characterize seizures under different physiological and pathological conditions. Here, we analysed seizure dynamics mathematically and established a taxonomy of seizures based on first principles. For the predominant seizure class we developed a generic model called Epileptor. As an experimental model system, we used ictal-like discharges induced in vitro in mouse hippocampi. We show that only five state variables linked by integral-differential equations are sufficient to describe the onset, time course and offset of ictal-like discharges as well as their recurrence. Two state variables are responsible for generating rapid discharges (fast time scale), two for spike and wave events (intermediate time scale) and one for the control of time course, including the alternation between 'normal' and ictal periods (slow time scale). We propose that normal and ictal activities coexist: a separatrix acts as a barrier (or seizure threshold) between these states. Seizure onset is reached upon the collision of normal brain trajectories with the separatrix. We show theoretically and experimentally how a system can be pushed toward seizure under a wide variety of conditions. Within our experimental model, the onset and offset of ictal-like discharges are well-defined mathematical events: a saddle-node and homoclinic bifurcation, respectively. These bifurcations necessitate a baseline shift at onset and a logarithmic scaling of interspike intervals at offset. These predictions were not only confirmed in our in vitro experiments, but also for focal seizures recorded in different syndromes, brain regions and species (humans and zebrafish). Finally, we identified several possible biophysical parameters contributing to the five state variables in our model system. We show that these parameters apply to specific experimental conditions and propose that there exists a wide array of possible biophysical mechanisms for seizure genesis, while preserving central invariant properties. Epileptor and the seizure taxonomy will guide future modeling and translational research by identifying universal rules governing the initiation and termination of seizures and predicting the conditions necessary for those transitions.

Many parameter sets in a multicompartment model oscillator are robust to temperature perturbations

Neurons in cold-blooded animals remarkably maintain their function over a wide range of temperatures, even though the rates of many cellular processes increase twofold, threefold, or many-fold for each 10°C increase in temperature. Moreover, the kinetics of ion channels, maximal conductances, and Ca(2+) buffering each have independent temperature sensitivities, suggesting that the balance of biological parameters can be disturbed by even modest temperature changes. In stomatogastric ganglia of the crab Cancer borealis, the duty cycle of the bursting pacemaker kernel is highly robust between 7 and 23°C (Rinberg et al., 2013). We examined how this might be achieved in a detailed conductance-based model in which exponential temperature sensitivities were given by Q10 parameters. We assessed the temperature robustness of this model across 125,000 random sets of Q10 parameters. To examine how robustness might be achieved across a variable population of animals, we repeated this analysis across six sets of maximal conductance parameters that produced similar activity at 11°C. Many permissible combinations of maximal conductance and Q10 parameters were found over broad regions of parameter space and relatively few correlations among Q10s were observed across successful parameter sets. A significant portion of Q10 sets worked for at least 3 of the 6 maximal conductance sets (∼11.1%). Nonetheless, no Q10 set produced robust function across all six maximal conductance sets, suggesting that maximal conductance parameters critically contribute to temperature robustness. Overall, these results provide insight into principles of temperature robustness in neuronal oscillators.