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

Activity-dependent extracellular potassium changes in unmyelinated versus myelinated areas in olfactory regions of the isolated female guinea-pig brain

The potassium released in the extracellular space during neuronal activity is rapidly removed by glia and neurons to maintain tissue homeostasis. Oligodendrocyte-derived myelin axonal coating contributes to potassium buffering and is therefore crucial to control brain excitability. We studied activity-dependent extracellular potassium ([K+]o) changes in the piriform cortex (PC), a region that features highly segregated bundles of myelinated and unmyelinated fibers. Four-aminopyridine (4AP; 50 μM) treatment or patterned high-frequency stimulations (hfST) were utilized to generate [K+]o changes measured with potassium-sensitive electrodes in the myelinated lateral olfactory tract (LOT), in the unmyelinated PC layer I and in the myelinated deep PC layers in the ex vivo isolated guinea-pig brain. Seizure-like events induced by 4AP are initiated by the abrupt [K+]o rise in the layer I formed by unmyelinated fibers (Uva et al., 2017). Larger [K+]o shifts occurred in unmyelinated layers compared to the myelinated LOT. LOT hfST that mimicks pre-seizure discharges also generated higher [K+]o changes in unmyelinated PC layer I than in LOT and deep PC layers. The treatment with the Kir4.1 potassium channel blocker BaCl2 (100 μM) enhanced the [K+]o changes generated by hfST in myelinated structures. Our data show that activity-dependent [K+]o changes are intrinsically different in myelinated vs unmyelinated cortical regions. The larger [K+]o shifts generated in unmyelinated structures may represent a vehicle for seizure generation.

Uncertainty quantification and sensitivity analysis of neuron models with ion concentration dynamics

This paper provides a comprehensive and computationally efficient case study for uncertainty quantification (UQ) and global sensitivity analysis (GSA) in a neuron model incorporating ion concentration dynamics. We address how challenges with UQ and GSA in this context can be approached and solved, including challenges related to computational cost, parameters affecting the system's resting state, and the presence of both fast and slow dynamics. Specifically, we analyze the electrodiffusive neuron-extracellular-glia (edNEG) model, which captures electrical potentials, ion concentrations (Na+, K+, Ca2+, and Cl-), and volume changes across six compartments. Our methodology includes a UQ procedure assessing the model's reliability and susceptibility to input uncertainty and a variance-based GSA identifying the most influential input parameters. To mitigate computational costs, we employ surrogate modeling techniques, optimized using efficient numerical integration methods. We propose a strategy for isolating parameters affecting the resting state and analyze the edNEG model dynamics under both physiological and pathological conditions. The influence of uncertain parameters on model outputs, particularly during spiking dynamics, is systematically explored. Rapid dynamics of membrane potentials necessitate a focus on informative spiking features, while slower variations in ion concentrations allow a meaningful study at each time point. Our study offers valuable guidelines for future UQ and GSA investigations on neuron models with ion concentration dynamics, contributing to the broader application of such models in computational neuroscience.

Unilateral optogenetic kindling of hippocampus leads to more severe impairments of the inhibitory signaling in the contralateral hippocampus

The kindling model has been used extensively by researchers to study the neurobiology of temporal lobe epilepsy (TLE) due to its capacity to induce intensification of seizures by the progressive recruitment of additional neuronal clusters into epileptogenic networks. We applied repetitive focal optogenetic activation of putative excitatory neurons in the dorsal CA1 area of the hippocampus of mice to investigate the role of inhibitory signaling during this process. This experimental protocol resulted in a kindling phenotype that was maintained for 2 weeks after the animals were fully kindled. As a result of the different phases of optogenetic kindling (OpK), key inhibitory signaling elements, such as KCC2 and NKCC1, exhibited distinct temporal and spatial dynamics of regulation. These alterations in protein expression were related to the distinct pattern of ictal activity propagation through the different hippocampal sublayers. Our results suggest the KCC2 disruption in the contralateral hippocampus of fully kindled animals progressively facilitated the creation of pathological pathways for seizure propagation through the hippocampal network. Upon completion of kindling, we observed animals that were restimulated after a rest period of 14-day showed, besides a persistent KCC2 downregulation, an NKCC1 upregulation in the bilateral dentate gyrus and hippocampus-wide loss of parvalbumin-positive interneurons. These alterations observed in the chronic phase of OpK suggest that the hippocampus of rekindled animals continued to undergo self-modifications during the rest period. The changes resulting from this period suggest the possibility of the development of a mirror focus on the hippocampus contralateral to the site of optical stimulations. Our results offer perspectives for preventing the recruitment and conversion of healthy neuronal networks into epileptogenic ones among patients with epilepsy.

Local extracellular K+ in cortex regulates norepinephrine levels, network state, and behavioral output

Extracellular potassium concentration ([K+]e) is known to increase as a function of arousal. [K+]e is also a potent modulator of transmitter release. Yet, it is not known whether [K+]e is involved in the neuromodulator release associated with behavioral transitions. We here show that manipulating [K+]e controls the local release of monoaminergic neuromodulators, including norepinephrine (NE), serotonin, and dopamine. Imposing a [K+]e increase is adequate to boost local NE levels, and conversely, lowering [K+]e can attenuate local NE. Electroencephalography analysis and behavioral assays revealed that manipulation of cortical [K+]e was sufficient to alter the sleep-wake cycle and behavior of mice. These observations point to the concept that NE levels in the cortex are not solely determined by subcortical release, but that local [K+]e dynamics have a strong impact on cortical NE. Thus, cortical [K+]e is an underappreciated regulator of behavioral transitions.

Metabolic implications of axonal demyelination and its consequences for synchronized network activity: An in silico and in vitro study

Myelination enhances the conduction velocity of action potentials (AP) and increases energy efficiency. Thick myelin sheaths are typically found on large-distance axonal connections or in fast-spiking interneurons, which are critical for synchronizing neuronal networks during gamma-band oscillations. Loss of myelin sheath is associated with multiple alterations in axonal architecture leading to impaired AP propagation. While numerous studies are devoted to the effects of demyelination on conduction velocity, the metabolic effects and the consequences for network synchronization have not been investigated. Here we present a unifying computational model for electrophysiology and metabolism of the myelinated axon. The computational model suggested that demyelination not only decreases the AP speed but AP propagation in demyelinated axons requires compensatory processes like mitochondrial mass increase and a switch from saltatory to continuous propagation to rescue axon functionality at the cost of reduced AP propagation speed and increased energy expenditure. Indeed, these predictions were proven to be true in a culture model of demyelination where the pharmacologically-induced loss of myelin was associated with increased oxygen consumption rates, and a significant broadening of bandwidth as well as a decrease in the power of gamma oscillations.

Slow ion concentration oscillations and multiple states in neuron-glia interaction-insights gained from reduced mathematical models

When potassium in the extracellular space separating neurons and glia reaches sufficient levels, neurons may fire spontaneous action potentials or even become inactivated due to membrane depolarisation, which, in turn, may lead to increased extracellular potassium levels. Under certain circumstances, this chain of events may trigger periodic bursts of neuronal activity. In the present study, reduced neuron-glia models are applied to explore the relationship between bursting behaviour and ion concentration dynamics. These reduced models are built based on a previously developed neuron-glia model, in which channel-mediated neuronal sodium and potassium currents are replaced by a function of neuronal sodium and extracellular potassium concentrations. Simulated dynamics of the resulting two reduced models display features that are qualitatively similar to those of the existing neuron-glia model. Bifurcation analyses of the reduced models show rich and interesting dynamics that include the existence of Hopf bifurcations between which the models exhibit slow ion concentration oscillations for a wide range of parameter values. The study demonstrates that even very simple models can provide insights of possible relevance to complex phenomena.

Degeneracy in epilepsy: multiple routes to hyperexcitable brain circuits and their repair

Due to its complex and multifaceted nature, developing effective treatments for epilepsy is still a major challenge. To deal with this complexity we introduce the concept of degeneracy to the field of epilepsy research: the ability of disparate elements to cause an analogous function or malfunction. Here, we review examples of epilepsy-related degeneracy at multiple levels of brain organisation, ranging from the cellular to the network and systems level. Based on these insights, we outline new multiscale and population modelling approaches to disentangle the complex web of interactions underlying epilepsy and to design personalised multitarget therapies.

Metabolic Recruitment in Brain Tissue

Information processing imposes urgent metabolic demands on neurons, which have negligible energy stores and restricted access to fuel. Here, we discuss metabolic recruitment, the tissue-level phenomenon whereby active neurons harvest resources from their surroundings. The primary event is the neuronal release of K⁺ that mirrors workload. Astrocytes sense K⁺ in exquisite fashion thanks to their unique coexpression of NBCe1 and α2β2 Na⁺/K⁺ ATPase, and within seconds switch to Crabtree metabolism, involving GLUT1, aerobic glycolysis, transient suppression of mitochondrial respiration, and lactate export. The lactate surge serves as a secondary recruiter by inhibiting glucose consumption in distant cells. Additional recruiters are glutamate, nitric oxide, and ammonium, which signal over different spatiotemporal domains. The net outcome of these events is that more glucose, lactate, and oxygen are made available. Metabolic recruitment works alongside neurovascular coupling and various averaging strategies to support the inordinate dynamic range of individual neurons.

SIK3 and Wnk converge on Fray to regulate glial K+ buffering and seizure susceptibility

Glial cells play a critical role in maintaining homeostatic ion concentration gradients. Salt-inducible kinase 3 (SIK3) regulates a gene expression program that controls K+ buffering in glia, and upregulation of this pathway suppresses seizure behavior in the eag, Shaker hyperexcitability mutant. Here we show that boosting the glial SIK3 K+ buffering pathway suppresses seizures in three additional molecularly diverse hyperexcitable mutants, highlighting the therapeutic potential of upregulating glial K+ buffering. We then explore additional mechanisms regulating glial K+ buffering. Fray, a transcriptional target of the SIK3 K+ buffering program, is a kinase that promotes K+ uptake by activating the Na+/K+/Cl- co-transporter, Ncc69. We show that the Wnk kinase phosphorylates Fray in Drosophila glia and that this activity is required to promote K+ buffering. This identifies Fray as a convergence point between the SIK3-dependent transcriptional program and Wnk-dependent post-translational regulation. Bypassing both regulatory mechanisms via overexpression of a constitutively active Fray in glia is sufficient to robustly suppress seizure behavior in multiple Drosophila models of hyperexcitability. Finally, we identify cortex glia as a critical cell type for regulation of seizure susceptibility, as boosting K+ buffering via expression of activated Fray exclusively in these cells is sufficient to suppress seizure behavior. These findings highlight Fray as a key convergence point for distinct K+ buffering regulatory mechanisms and cortex glia as an important locus for control of neuronal excitability.

Activated astrocytes attenuate neocortical seizures in rodent models through driving Na+-K+-ATPase

Epileptic seizures are widely regarded to occur as a result of the excitation-inhibition imbalance from a neuro-centric view. Although astrocyte-neuron interactions are increasingly recognized in seizure, elementary questions about the causal role of astrocytes in seizure remain unanswered. Here we show that optogenetic activation of channelrhodopsin-2-expressing astrocytes effectively attenuates neocortical seizures in rodent models. This anti-seizure effect is independent from classical calcium signaling, and instead related to astrocytic Na+-K+-ATPase-mediated buffering K+, which activity-dependently inhibits firing in highly active pyramidal neurons during seizure. Compared with inhibition of pyramidal neurons, astrocyte stimulation exhibits anti-seizure effects with several advantages, including a wider therapeutic window, large-space efficacy, and minimal side effects. Finally, optogenetic-driven astrocytic Na+-K+-ATPase shows promising therapeutic effects in a chronic focal cortical dysplasia epilepsy model. Together, we uncover a promising anti-seizure strategy with optogenetic control of astrocytic Na+-K+-ATPase activity, providing alternative ideas and a potential target for the treatment of intractable epilepsy.

John EK, Potesta CV, Gallagher MJ, Zhou C. Artificial sleep-like up/down-states induce synaptic plasticity in cortical neurons from mouse brain slices

During non-rapid eye movement (NREM) sleep, cortical neuron activity alternates between a depolarized (firing, up-state) and a hyperpolarized state (down-state) coinciding with delta electroencephalogram (EEG) slow-wave oscillation (SWO, 0. 5-4 Hz) in vivo. Recently, we have found that artificial sleep-like up/down-states can potentiate synaptic strength in layer V cortical neurons ex vivo. Using mouse coronal brain slices, whole cell voltage-clamp recordings were made from layer V cortical pyramidal neurons to record spontaneous excitatory synaptic currents (sEPSCs) and inhibitory synaptic currents (sIPSCs). Artificial sleep-like up/down-states (as SWOs, 0.5 Hz, 10 min, current clamp mode) were induced by injecting sinusoidal currents into layer V cortical neurons. Baseline pre-SWO recordings were recorded for 5 min and post-SWO recordings for at least 25-30 min. Compared to pre-SWO sEPSCs or sIPSCs, post-SWO sEPSCs or sIPSCs in layer V cortical neurons exhibited significantly larger amplitudes and a higher frequency for 30 min. This finding suggests that both sEPSCs and sIPSCs could be potentiated in layer V cortical neurons by the low-level activity of SWOs, and sEPSCs and sIPSCs maintained a balance in layer V cortical neurons during pre- and post-SWO periods. Overall, this study presents an ex vivo method to show SWO's ability to induce synaptic plasticity in layer V cortical neurons, which may underlie sleep-related synaptic potentiation for sleep-related memory consolidation in vivo.

A personalizable autonomous neural mass model of epileptic seizures

Work in the last two decades has shown that neural mass models (NMM) can realistically reproduce and explain epileptic seizure transitions as recorded by electrophysiological methods (EEG, SEEG). In previous work, advances were achieved by increasing excitation and heuristically varying network inhibitory coupling parameters in the models. Based on these early studies, we provide a laminar NMM capable of realistically reproducing the electrical activity recorded by SEEG in the epileptogenic zone during interictal to ictal states. With the exception of the external noise input into the pyramidal cell population, the model dynamics are autonomous. By setting the system at a point close to bifurcation, seizure-like transitions are generated, including pre-ictal spikes, low voltage fast activity, and ictal rhythmic activity. A novel element in the model is a physiologically motivated algorithm for chloride dynamics: the gain of GABAergic post-synaptic potentials is modulated by the pathological accumulation of chloride in pyramidal cells due to high inhibitory input and/or dysfunctional chloride transport. In addition, in order to simulate SEEG signals for comparison with real seizure recordings, the NMM is embedded first in a layered model of the neocortex and then in a realistic physical model. We compare modeling results with data from four epilepsy patient cases. By including key pathophysiological mechanisms, the proposed framework captures succinctly the electrophysiological phenomenology observed in ictal states, paving the way for robust personalization methods based on NMMs.

Repeated applications of high potassium elicit long-term changes in a motor circuit from the crab, Cancer borealis

We examined the effects of altered extracellular potassium concentration on the output of the well-studied pyloric circuit in the crab, Cancer borealis. Pyloric neurons initially become quiescent, then recover spiking and bursting activity in high potassium saline (2.5x[K⁺]). These changes in circuit robustness are maintained after the perturbation is removed; pyloric neurons are more robust to subsequent potassium perturbations even after several hours of wash in control saline. Despite this long-term "memory" of the stimulus history, we found no differences in neuronal activity in control saline. The circuit's adaptation is erased by both low potassium saline (0.4x[K⁺]) and direct hyperpolarizing current. Initial sensitivity of PD neurons to high potassium saline also varies seasonally, indicating that changes in robustness may reflect natural changes in circuit states. Thus, perturbation, followed by recovery of normal activity, can hide cryptic changes in neuronal properties that are only revealed by subsequent challenges.

A mathematical model of neuroimmune interactions in epileptogenesis for discovering treatment strategies

The development of epilepsy (epileptogenesis) involves a complex interplay of neuronal and immune processes. Here, we present a first-of-its-kind mathematical model to better understand the relationships among these processes. Our model describes the interaction between neuroinflammation, blood-brain barrier disruption, neuronal loss, circuit remodeling, and seizures. Formulated as a system of nonlinear differential equations, the model reproduces the available data from three animal models. The model successfully describes characteristic features of epileptogenesis such as its paradoxically long timescales (up to decades) despite short and transient injuries or the existence of qualitatively different outcomes for varying injury intensity. In line with the concept of degeneracy, our simulations reveal multiple routes toward epilepsy with neuronal loss as a sufficient but non-necessary component. Finally, we show that our model allows for in silico predictions of therapeutic strategies, revealing injury-specific therapeutic targets and optimal time windows for intervention.

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A dynamical systems model describes the development of epilepsy after different injuries

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Simulation results are in agreement with data from three animal models

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Model shows degeneracy: multiple distinct but linked mechanisms cause epileptogenesis

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Framework permits studying the effects of therapeutic interventions in silico

Fluid transport in the brain

The brain harbors a unique ability to, figuratively speaking, shift its gears. During wakefulness, the brain is geared fully toward processing information and behaving, while homeostatic functions predominate during sleep. The blood-brain barrier establishes a stable environment that is optimal for neuronal function, yet the barrier imposes a physiological problem; transcapillary filtration that forms extracellular fluid in other organs is reduced to a minimum in brain. Consequently, the brain depends on a special fluid [the cerebrospinal fluid (CSF)] that is flushed into brain along the unique perivascular spaces created by astrocytic vascular endfeet. We describe this pathway, coined the term glymphatic system, based on its dependency on astrocytic vascular endfeet and their adluminal expression of aquaporin-4 water channels facing toward CSF-filled perivascular spaces. Glymphatic clearance of potentially harmful metabolic or protein waste products, such as amyloid-β, is primarily active during sleep, when its physiological drivers, the cardiac cycle, respiration, and slow vasomotion, together efficiently propel CSF inflow along periarterial spaces. The brain's extracellular space contains an abundance of proteoglycans and hyaluronan, which provide a low-resistance hydraulic conduit that rapidly can expand and shrink during the sleep-wake cycle. We describe this unique fluid system of the brain, which meets the brain's requisites to maintain homeostasis similar to peripheral organs, considering the blood-brain-barrier and the paths for formation and egress of the CSF.

Brivaracetam Modulates Short-Term Synaptic Activity and Low-Frequency Spontaneous Brain Activity by Delaying Synaptic Vesicle Recycling in Two Distinct Rodent Models of Epileptic Seizures

Brivaracetam (BRV) is an anti-seizure drug for the treatment of focal and generalized epileptic seizures shown to augment short-term synaptic fatigue by slowing down synaptic vesicle recycling rates in control animals. In this study, we sought to investigate whether altered short-term synaptic activities could be a pathological hallmark during the interictal periods of epileptic seizures in two well-established rodent models, as well as to reveal BRV's therapeutic roles in altered short-term synaptic activities and low-frequency band spontaneous brain hyperactivity in these models. In our study, the electrophysiological field excitatory post-synaptic potential (fEPSP) recordings were performed in rat hippocampal brain slices from the CA1 region by stimulation of the Schaffer collateral/commissural pathway with or without BRV (30 μM for 3 h) in control or epileptic seizure (induced by pilocarpine (PILO) or high potassium (h-K⁺)) models. Short-term synaptic activities were induced by 5, 10, 20, and 40-Hz stimulation sequences. The effects of BRV on pre-synaptic vesicle mobilization were visually assessed by staining the synaptic vesicles with FM1-43 dye followed by imaging with a two-photon microscope. In the fEPSP measurements, short-term synaptic fatigue was found in the control group, while short-term synaptic potentiation (STP) was detected in both PILO and h-K⁺ models. STP was decreased after the slices were treated with BRV (30 μM) for 3 h. BRV also exhibited its therapeutic benefits by decreasing abnormal peak power (frequency range of 8-13 Hz, 31% of variation for PILO model, 25% of variation for h-K⁺ model) and trough power (frequency range of 1-4 Hz, 66% of variation for PILO model, 49% of variation for h-K⁺ model), and FM1-43 stained synaptic vesicle mobility (64% of the variation for PILO model, 45% of the variation for h-K⁺ model) in these epileptic seizure models. To the best of our knowledge, this was the first report that BRV decreased the STP and abnormal low-frequency brain activities during the interictal phase of epileptic seizures by slowing down the mobilization of synaptic vesicles in two rodent models. These mechanistic findings would greatly advance our understanding of BRV's pharmacological role in pathomechanisms of epileptic seizures and its treatment strategy optimization to avoid or minimize BRV-induced possible adverse side reactions.

A unified physiological framework of transitions between seizures, sustained ictal activity and depolarization block at the single neuron level

The majority of seizures recorded in humans and experimental animal models can be described by a generic phenomenological mathematical model, the Epileptor. In this model, seizure-like events (SLEs) are driven by a slow variable and occur via saddle node (SN) and homoclinic bifurcations at seizure onset and offset, respectively. Here we investigated SLEs at the single cell level using a biophysically relevant neuron model including a slow/fast system of four equations. The two equations for the slow subsystem describe ion concentration variations and the two equations of the fast subsystem delineate the electrophysiological activities of the neuron. Using extracellular K⁺ as a slow variable, we report that SLEs with SN/homoclinic bifurcations can readily occur at the single cell level when extracellular K⁺ reaches a critical value. In patients and experimental models, seizures can also evolve into sustained ictal activity (SIA) and depolarization block (DB), activities which are also parts of the dynamic repertoire of the Epileptor. Increasing extracellular concentration of K⁺ in the model to values found during experimental status epilepticus and DB, we show that SIA and DB can also occur at the single cell level. Thus, seizures, SIA, and DB, which have been first identified as network events, can exist in a unified framework of a biophysical model at the single neuron level and exhibit similar dynamics as observed in the Epileptor.Author Summary: Epilepsy is a neurological disorder characterized by the occurrence of seizures. Seizures have been characterized in patients in experimental models at both macroscopic and microscopic scales using electrophysiological recordings. Experimental works allowed the establishment of a detailed taxonomy of seizures, which can be described by mathematical models. We can distinguish two main types of models. Phenomenological (generic) models have few parameters and variables and permit detailed dynamical studies often capturing a majority of activities observed in experimental conditions. But they also have abstract parameters, making biological interpretation difficult. Biophysical models, on the other hand, use a large number of variables and parameters due to the complexity of the biological systems they represent. Because of the multiplicity of solutions, it is difficult to extract general dynamical rules. In the present work, we integrate both approaches and reduce a detailed biophysical model to sufficiently low-dimensional equations, and thus maintaining the advantages of a generic model. We propose, at the single cell level, a unified framework of different pathological activities that are seizures, depolarization block, and sustained ictal activity.

Changes in H+, K+, and Ca2+ Concentrations, as Observed in Seizures, Induce Action Potential Signaling in Cortical Neurons by a Mechanism That Depends Partially on Acid-Sensing Ion Channels

Acid-sensing ion channels (ASICs) are activated by extracellular acidification. Because ASIC currents are transient, these channels appear to be ideal sensors for detecting the onset of rapid pH changes. ASICs are involved in neuronal death after ischemic stroke, and in the sensation of inflammatory pain. Ischemia and inflammation are associated with a slowly developing, long-lasting acidification. Recent studies indicate however that ASICs are unable to induce an electrical signaling activity under standard experimental conditions if pH changes are slow. In situations associated with slow and sustained pH drops such as high neuronal signaling activity and ischemia, the extracellular K⁺ concentration increases, and the Ca²⁺ concentration decreases. We hypothesized that the concomitant changes in H⁺, K⁺, and Ca²⁺ concentrations may allow a long-lasting ASIC-dependent induction of action potential (AP) signaling. We show that for acidification from pH7.4 to pH7.0 or 6.8 on cultured cortical neurons, the number of action potentials and the firing time increased strongly if the acidification was accompanied by a change to higher K⁺ and lower Ca²⁺ concentrations. Under these conditions, APs were also induced in neurons from ASIC1a^-/- mice, in which a pH of ≤ 5.0 would be required to activate ASICs, indicating that ASIC activation was not required for the AP induction. Comparison between neurons of different ASIC genotypes indicated that the ASICs modulate the AP induction under such changed ionic conditions. Voltage-clamp measurements of the Na⁺ and K⁺ currents in cultured cortical neurons showed that the lowering of the pH inhibited Na⁺ and K⁺ currents. In contrast, the lowering of the Ca²⁺ together with the increase in the K⁺ concentration led to a hyperpolarizing shift of the activation voltage dependence of voltage-gated Na⁺ channels. We conclude that the ionic changes observed during high neuronal activity mediate a sustained AP induction caused by the potentiation of Na⁺ currents, a membrane depolarization due to the changed K⁺ reversal potential, the activation of ASICs, and possibly effects on other ion channels. Our study describes therefore conditions under which slow pH changes induce neuronal signaling by a mechanism involving ASICs.

Dynamics of ramping bursts in a respiratory neuron model

Intensive computational and theoretical work has led to the development of multiple mathematical models for bursting in respiratory neurons in the pre-Bötzinger Complex (pre-BötC) of the mammalian brainstem. Nonetheless, these previous models have not captured the pre-inspiratory ramping aspects of these neurons' activity patterns, in which relatively slow tonic spiking gradually progresses to faster spiking and a full-blown burst, with a corresponding gradual development of an underlying plateau potential. In this work, we show that the incorporation of the dynamics of the extracellular potassium ion concentration into an existing model for pre-BötC neuron bursting, along with some parameter adjustments, suffices to induce this ramping behavior. Using fast-slow decomposition, we show that this activity can be considered as a form of parabolic bursting, but with burst termination at a homoclinic bifurcation rather than as a SNIC bifurcation. We also investigate the parameter-dependence of these solutions and show that the proposed model yields a greater dynamic range of burst frequencies, durations, and duty cycles than those produced by other models in the literature.

Brain Stimulation Treatments in Epilepsy: Basic Mechanisms and Clinical Advances

Drug-resistant epilepsy, characterized by ongoing seizures despite appropriate trials of anti-seizure medications, affects approximately one-third of people with epilepsy. Brain stimulation has recently become available as an alternative treatment option to reduce symptomatic seizures in short and long-term follow-up studies. Several questions remain on how to optimally develop patient-specific treatments and manage therapy over the long term. This review aims to discuss the clinical use and mechanisms of action of Responsive Neural Stimulation and Deep Brain Stimulation in the treatment of epilepsy and highlight recent advances that may both improve outcomes and present new challenges. Finally, a rational approach to device selection is presented based on current mechanistic understanding, clinical evidence, and device features.

In Vivo Neocortical [K]o Modulation by Targeted Stimulation of Astrocytes

A normally functioning nervous system requires normal extracellular potassium ion concentration ([K]o). Throughout the nervous system, several processes, including those of an astrocytic nature, are involved in [K]o regulation. In this study we investigated the effect of astrocytic photostimulation on [K]o. We hypothesized that in vivo photostimulation of eNpHR-expressing astrocytes leads to a decreased [K]o. Using optogenetic and electrophysiological techniques we showed that stimulation of eNpHR-expressing astrocytes resulted in a significantly decreased resting [K]o and evoked K responses. The amplitude of the concomitant spreading depolarization-like events also decreased. Our results imply that astrocytic membrane potential modification could be a potential tool for adjusting the [K]o.

Electrophysiological features of sleep in children with Kir4.1 channel mutations and Autism-Epilepsy phenotype: a preliminary study

Study Objectives

Recently, a role for gain-of-function (GoF) mutations of the astrocytic potassium channel Kir4.1 (KCNJ10 gene) has been proposed in subjects with Autism–Epilepsy phenotype (AEP). Epilepsy and autism spectrum disorder (ASD) are common and complexly related to sleep disorders. We tested whether well characterized mutations in KCNJ10 could result in specific sleep electrophysiological features, paving the way to the discovery of a potentially relevant biomarker for Kir4.1-related disorders.

Methods

For this case–control study, we recruited seven children with ASD either comorbid or not with epilepsy and/or EEG paroxysmal abnormalities (AEP) carrying GoF mutations of KCNJ10 and seven children with similar phenotypes but wild-type for the same gene, comparing period-amplitude features of slow waves detected by fronto-central bipolar EEG derivations (F3-C3, F4-C4, and Fz-Cz) during daytime naps.

Results

Children with Kir4.1 mutations displayed longer slow waves periods than controls, in Fz-Cz (mean period = 112,617 ms ± SE = 0.465 in mutated versus mean period = 105,249 ms ± SE = 0.375 in controls, p < 0.001). An analog result was found in F3-C3 (mean period = 125,706 ms ± SE = 0.397 in mutated versus mean period = 120,872 ms ± SE = 0.472 in controls, p < 0.001) and F4-C4 (mean period = 127,914 ms ± SE = 0.557 in mutated versus mean period = 118,174 ms ± SE = 0.442 in controls, p < 0.001).

Conclusion

This preliminary finding suggests that period-amplitude slow wave features are modified in subjects carrying Kir4.1 GoF mutations. Potential clinical applications of this finding are discussed.

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.

Bidirectional astrocytic GLUT1 activation by elevated extracellular K. Glia 2020;69:1012-1021. [PMID: 33277953 DOI: 10.1002/glia.23944]

The acute rise in interstitial K⁺ that accompanies neural activity couples the energy demand of neurons to the metabolism of astrocytes. The effects of elevated K⁺ on astrocytes include activation of aerobic glycolysis, inhibition of mitochondrial respiration and the release of lactate. Using a genetically encoded FRET glucose sensor and a novel protocol based on 3-O-methylglucose trans-acceleration and numerical simulation of glucose dynamics, we report that extracellular K⁺ is also a potent and reversible modulator of the astrocytic glucose transporter GLUT1. In cultured mouse astrocytes, the stimulatory effect developed within seconds, engaged both the influx and efflux modes of the transporter, and was detected even at 1 mM incremental K⁺ . The modulation of GLUT1 explains how astrocytes are able to maintain their glucose pool in the face of strong glycolysis stimulation. We propose that the stimulation of GLUT1 by K⁺ supports the production of lactate by astrocytes and the timely delivery of glucose to active neurons.

Interstitial ions: A key regulator of state-dependent neural activity?

Throughout the nervous system, ion gradients drive fundamental processes. Yet, the roles of interstitial ions in brain functioning is largely forgotten. Emerging literature is now revitalizing this area of neuroscience by showing that interstitial cations (K+, Ca2+ and Mg2+) are not static quantities but change dynamically across states such as sleep and locomotion. In turn, these state-dependent changes are capable of sculpting neuronal activity; for example, changing the local interstitial ion composition in the cortex is sufficient for modulating the prevalence of slow-frequency neuronal oscillations, or potentiating the gain of visually evoked responses. Disturbances in interstitial ionic homeostasis may also play a central role in the pathogenesis of central nervous system diseases. For example, impairments in K+ buffering occur in a number of neurodegenerative diseases, and abnormalities in neuronal activity in disease models disappear when interstitial K+ is normalized. Here we provide an overview of the roles of interstitial ions in physiology and pathology. We propose the brain uses interstitial ion signaling as a global mechanism to coordinate its complex activity patterns, and ion homeostasis failure contributes to central nervous system diseases affecting cognitive functions and behavior.

Impaired State-Dependent Potentiation of GABAergic Synaptic Currents Triggers Seizures in a Genetic Generalized Epilepsy Model

Epileptic activity in genetic generalized epilepsy (GGE) patients preferentially appears during sleep and its mechanism remains unknown. Here, we found that sleep-like slow-wave oscillations (0.5 Hz SWOs) potentiated excitatory and inhibitory synaptic currents in layer V cortical pyramidal neurons from wild-type (wt) mouse brain slices. In contrast, SWOs potentiated excitatory, but not inhibitory, currents in cortical neurons from a heterozygous (het) knock-in (KI) Gabrg2+Q/390X model of Dravet epilepsy syndrome. This created an imbalance between evoked excitatory and inhibitory currents to effectively prompt neuronal action potential firings. Similarly, physiologically similar up-/down-state induction (present during slow-wave sleep) in cortical neurons also potentiated excitatory synaptic currents within brain slices from wt and het KI mice. Moreover, this state-dependent potentiation of excitatory synaptic currents entailed some signaling pathways of homeostatic synaptic plasticity. Consequently, in het KI mice, in vivo SWO induction (using optogenetic methods) triggered generalized epileptic spike-wave discharges (SWDs), being accompanied by sudden immobility, facial myoclonus, and vibrissa twitching. In contrast, in wt littermates, SWO induction did not cause epileptic SWDs and motor behaviors. To our knowledge, this is the first mechanism to explain why epileptic SWDs preferentially happen during non rapid eye-movement sleep and quiet-wakefulness in human GGE patients.

Differential chloride homeostasis in the spinal dorsal horn locally shapes synaptic metaplasticity and modality-specific sensitization

GABAA/glycine-mediated neuronal inhibition critically depends on intracellular chloride (Cl-) concentration which is mainly regulated by the K+-Cl- co-transporter 2 (KCC2) in the adult central nervous system (CNS). KCC2 heterogeneity thus affects information processing across CNS areas. Here, we uncover a gradient in Cl- extrusion capacity across the superficial dorsal horn (SDH) of the spinal cord (laminae I-II: LI-LII), which remains concealed under low Cl- load. Under high Cl- load or heightened synaptic drive, lower Cl- extrusion is unveiled in LI, as expected from the gradient in KCC2 expression found across the SDH. Blocking TrkB receptors increases KCC2 in LI, pointing to differential constitutive TrkB activation across laminae. Higher Cl- lability in LI results in rapidly collapsing inhibition, and a form of activity-dependent synaptic plasticity expressed as a continuous facilitation of excitatory responses. The higher metaplasticity in LI as compared to LII differentially affects sensitization to thermal and mechanical input. Thus, inconspicuous heterogeneity of Cl- extrusion across laminae critically shapes plasticity for selective nociceptive modalities.

An electrodiffusive, ion conserving Pinsky-Rinzel model with homeostatic mechanisms

In most neuronal models, ion concentrations are assumed to be constant, and effects of concentration variations on ionic reversal potentials, or of ionic diffusion on electrical potentials are not accounted for. Here, we present the electrodiffusive Pinsky-Rinzel (edPR) model, which we believe is the first multicompartmental neuron model that accounts for electrodiffusive ion concentration dynamics in a way that ensures a biophysically consistent relationship between ion concentrations, electrical charge, and electrical potentials in both the intra- and extracellular space. The edPR model is an expanded version of the two-compartment Pinsky-Rinzel (PR) model of a hippocampal CA3 neuron. Unlike the PR model, the edPR model includes homeostatic mechanisms and ion-specific leakage currents, and keeps track of all ion concentrations (Na⁺, K⁺, Ca²⁺, and Cl⁻), electrical potentials, and electrical conductivities in the intra- and extracellular space. The edPR model reproduces the membrane potential dynamics of the PR model for moderate firing activity. For higher activity levels, or when homeostatic mechanisms are impaired, the homeostatic mechanisms fail in maintaining ion concentrations close to baseline, and the edPR model diverges from the PR model as it accounts for effects of concentration changes on neuronal firing. We envision that the edPR model will be useful for the field in three main ways. Firstly, as it relaxes commonly made modeling assumptions, the edPR model can be used to test the validity of these assumptions under various firing conditions, as we show here for a few selected cases. Secondly, the edPR model should supplement the PR model when simulating scenarios where ion concentrations are expected to vary over time. Thirdly, being applicable to conditions with failed homeostasis, the edPR model opens up for simulating a range of pathological conditions, such as spreading depression or epilepsy.

Neurons generate their electrical signals by letting ions pass through their membranes. Despite this fact, most models of neurons apply the simplifying assumption that ion concentrations remain effectively constant during neural activity. This assumption is often quite good, as neurons contain a set of homeostatic mechanisms that make sure that ion concentrations vary quite little under normal circumstances. However, under some conditions, these mechanisms can fail, and ion concentrations can vary quite dramatically. Standard models are thus not able to simulate such conditions. Here, we present what to our knowledge is the first multicompartmental neuron model that accounts for ion concentration variations in a way that ensures complete and consistent ion concentration and charge conservation. In this work, we use the model to explore under which activity conditions the ion concentration variations become important for predicting the neurodynamics. We expect the model to be of great value for the field of neuroscience, as it can be used to simulate a range of pathological conditions, such as spreading depression or epilepsy, which are associated with large changes in extracellular ion concentrations.

Rapid adaptation to elevated extracellular potassium in the pyloric circuit of the crab, Cancer borealis

Elevated potassium concentration ([K⁺]) is often used to alter excitability in neurons and networks by shifting the potassium equilibrium potential (E_K) and, consequently, the resting membrane potential. We studied the effects of increased extracellular [K⁺] on the well-described pyloric circuit of the crab Cancer borealis. A 2.5-fold increase in extracellular [K⁺] (2.5×[K⁺]) depolarized pyloric dilator (PD) neurons and resulted in short-term loss of their normal bursting activity. This period of silence was followed within 5-10 min by the recovery of spiking and/or bursting activity during continued superfusion of 2.5×[K⁺] saline. In contrast, when PD neurons were pharmacologically isolated from pyloric presynaptic inputs, they exhibited no transient loss of spiking activity in 2.5×[K⁺], suggesting the presence of an acute inhibitory effect mediated by circuit interactions. Action potential threshold in PD neurons hyperpolarized during an hour-long exposure to 2.5×[K⁺] concurrent with the recovery of spiking and/or bursting activity. Thus the initial loss of activity appears to be mediated by synaptic interactions within the network, but the secondary adaptation depends on changes in the intrinsic excitability of the pacemaker neurons. The complex sequence of events in the responses of pyloric neurons to elevated [K⁺] demonstrates that electrophysiological recordings are necessary to determine both the transient and longer term effects of even modest alterations of K⁺ concentrations on neuronal activity.NEW & NOTEWORTHY Solutions with elevated extracellular potassium are commonly used as a depolarizing stimulus. We studied the effects of high potassium concentration ([K⁺]) on the pyloric circuit of the crab stomatogastric ganglion. A 2.5-fold increase in extracellular [K⁺] caused a transient loss of activity that was not due to depolarization block, followed by a rapid increase in excitability and recovery of spiking within minutes. This suggests that changing extracellular potassium can have complex and nonstationary effects on neuronal circuits.

Caloric restriction triggers morphofunctional remodeling of astrocytes and enhances synaptic plasticity in the mouse hippocampus

Calorie-restricted (CR) diet has multiple beneficial effects on brain function. Here we report morphological and functional changes in hippocampal astrocytes in 3-months-old mice subjected to 1 month of the diet. Whole-cell patch-clamp recordings were performed in the CA1 stratum (str.) radiatum astrocytes of hippocampal slices. The cells were also loaded with fluorescent dye through the patch pipette. CR did not affect the number of astrocytic branches but increased the volume fraction (VF) of distal perisynaptic astrocytic leaflets. The astrocyte growth did not lead to a decrease in the cell input resistance, which may be attributed to a decrease in astrocyte coupling through the gap junctions. Western blotting revealed a decrease in the expression of Cx43 but not Cx30. Immunocytochemical analysis demonstrated a decrease in the density and size of Cx43 clusters. Cx30 cluster density did not change, while their size increased in the vicinity of astrocytic soma. CR shortened K⁺ and glutamate transporter currents in astrocytes in response to 5 × 50 Hz Schaffer collateral stimulation. However, no change in the expression of astrocytic glutamate transporter 1 (GLT-1) was observed, while the level of glutamine synthetase (GS) decreased. These findings suggest that enhanced enwrapping of synapses by the astrocytic leaflets reduces glutamate and K⁺ spillover. Reduced spillover led to a decreased contribution of extrasynaptic N2B containing N-methyl-D-aspartate receptors (NMDARs) to the tail of burst-induced EPSCs. The magnitude of long-term potentiation (LTP) in the glutamatergic CA3–CA1 synapses was significantly enhanced after CR. This enhancement was abolished by N2B-NMDARs antagonist. Our findings suggest that astrocytic morphofunctional remodeling is responsible for enhanced synaptic plasticity, which provides a basis for improved learning and memory reported after CR.

Utilizing Neurons for Digital Logic Circuits: A Molecular Communications Analysis

With the advancement of synthetic biology, several new tools have been conceptualized over the years as alternative treatments for current medical procedures. As part of this work, we investigate how synthetically engineered neurons can operate as digital logic gates that can be used towards bio-computing inside the brain and its impact on epileptic seizure-like behaviour. We quantify the accuracy of logic gates under high firing rates amid a network of neurons and by how much it can smooth out uncontrolled neuronal firings. To test the efficacy of our method, simulations composed of computational models of neurons connected in a structure that represents a logic gate are performed. Our simulations demonstrate the accuracy of performing the correct logic operation, and how specific properties such as the firing rate can play an important role in the accuracy. As part of the analysis, the mean squared error is used to quantify the quality of our proposed model and predict the accurate operation of a gate based on different sampling frequencies. As an application, the logic gates were used to smooth out epileptic seizure-like activity in a biological neuronal network, where the results demonstrated the effectiveness of reducing its mean firing rate. Our proposed system has the potential to be used in future approaches to treating neurological conditions in the brain.

Oligodendrocyte Kir4.1 Channels Clear Out Congested K

Oligodendrocytes Control Potassium Accumulation in White Matter and Seizure Susceptibility.

Larson VA, Mironova Y, Vanderpool KG, Waisman A, Rash JE, Agarwal A, Bergles DE. Elife. 2018 Mar 29;7. pii: e34829. doi:10.7554/eLife.34829.

The inwardly rectifying K⁺ channel K_ir4.1 is broadly expressed by central nervous system glia and deficits in K_ir4.1 lead to seizures and myelin vacuolization. However, the role of oligodendrocyte K_ir4.1 channels in controlling myelination and K⁺ clearance in white matter has not been defined. Here, we show that selective deletion of K_ir4.1 from oligodendrocyte progenitors or mature oligodendrocytes did not impair their development or disrupt the structure of myelin. However, mice lacking oligodendrocyte K_ir4.1 channels exhibited profound functional impairments, including slower clearance of extracellular K⁺ and delayed recovery of axons from repetitive stimulation in white matter, as well as spontaneous seizures, a lower seizure threshold, and activity-dependent motor deficits. These results indicate that K_ir4.1 channels in oligodendrocytes play an important role in extracellular K⁺ homeostasis in white matter and that selective loss of this channel from oligodendrocytes is sufficient to impair K⁺ clearance and promote seizures.

Cortex-wide Changes in Extracellular Potassium Ions Parallel Brain State Transitions in Awake Behaving Mice

Brain state fluctuations modulate sensory processing, but the factors governing state-dependent neural activity remain unclear. Here, we tracked the dynamics of cortical extracellular K+ concentrations ([K+]o) during awake state transitions and manipulated [K+]o in slices, during visual processing, and during skilled motor execution. When mice transitioned from quiescence to locomotion, [K+]o increased by 0.6-1.0 mM in all cortical areas analyzed, and this preceded locomotion by 1 s. Emulating the state-dependent [K+]o increase in cortical slices caused neuronal depolarization and enhanced input-output transformation. In vivo, locomotion increased the gain of visually evoked responses in layer 2/3 of visual cortex; this effect was recreated by imposing a [K+]o increase. Elevating [K+]o in the motor cortex increased movement-induced neuronal spiking in layer 5 and improved motor performance. Thus, [K+]o increases in a cortex-wide state-dependent manner, and this [K+]o increase affects both sensory and motor processing through the dynamic modulation of neural activity.

Role of inhibitory control in modulating focal seizure spread

Focal seizure propagation is classically thought to be spatially contiguous. However, distribution of seizures through a large-scale epileptic network has been theorized. Here, we used a multielectrode array, wide field calcium imaging, and two-photon calcium imaging to study focal seizure propagation pathways in an acute rodent neocortical 4-aminopyridine model. Although ictal neuronal bursts did not propagate beyond a 2-3-mm region, they were associated with hemisphere-wide field potential fluctuations and parvalbumin-positive interneuron activity outside the seizure focus. While bicuculline surface application enhanced contiguous seizure propagation, focal bicuculline microinjection at sites distant to the 4-aminopyridine focus resulted in epileptic network formation with maximal activity at the two foci. Our study suggests that both classical and epileptic network propagation can arise from localized inhibition defects, and that the network appearance can arise in the context of normal brain structure without requirement for pathological connectivity changes between sites.

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.

Biophysical Modeling Suggests Optimal Drug Combinations for Improving the Efficacy of GABA Agonists after Traumatic Brain Injuries

Traumatic brain injuries (TBI) lead to dramatic changes in the surviving brain tissue. Altered ion concentrations, coupled with changes in the expression of membrane-spanning proteins, create a post-TBI brain state that can lead to further neuronal loss caused by secondary excitotoxicity. Several GABA receptor agonists have been tested in the search for neuroprotection immediately after an injury, with paradoxical results. These drugs not only fail to offer neuroprotection, but can also slow down functional recovery after TBI. Here, using computational modeling, we provide a biophysical hypothesis to explain these observations. We show that the accumulation of intracellular chloride ions caused by a transient upregulation of Na+-K+-2Cl- (NKCC1) co-transporters as observed following TBI, causes GABA receptor agonists to lead to excitation and depolarization block, rather than the expected hyperpolarization. The likelihood of prolonged, excitotoxic depolarization block is further exacerbated by the extremely high levels of extracellular potassium seen after TBI. Our modeling results predict that the neuroprotective efficacy of GABA receptor agonists can be substantially enhanced when they are combined with NKCC1 co-transporter inhibitors. This suggests a rational, biophysically principled method for identifying drug combinations for neuroprotection after TBI.

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.

Small changes in synaptic gain lead to seizure-like activity in neuronal network at criticality

Epilepsy is a neurological disorder characterised by spontaneous recurrent seizures. The mechanisms by which multiple molecular and cellular changes lead to seizures is not well understood. Here, we study cortical seizure generation by simulating the activity of neuron groups in a network using the laminar cortex model. We identified a clear boundary between low-amplitude, asynchronous activity and high-amplitude, rhythmic activity, around which small changes in excitatory synaptic gain led to strong oscillatory activity. Neuron groups only responded significantly to stimulation around the boundary. The consequences of biophysical changes induced by epilepsy-related SCN1A mutations were also examined. Marked reduction in neuronal inhibition, as caused by mutations underlying Dravet syndrome, invariably led to strong neuronal firing, whereas small reductions in inhibition could cause significant changes when the network was poised close to the boundary. The study highlights the critical role of network dynamics in seizure genesis.

First Insights Into Within Host Translocation of the Bacillus cereus Toxin Cereulide Using a Porcine Model

Bacillus cereus is a gram-positive pathogen mainly known to evoke two types of foodborne poisonings. The diarrheal syndrome is caused by enterotoxins produced during growth in the intestine. In contrast, the emetic type is caused by the dodecadepsipeptide cereulide pre-formed in food. Usually, both diseases are self-limiting but occasionally more severe forms, including fatal ones, are reported. Since the mechanisms of cereulide toxin uptake and translocation within the body as well as the mechanism of its toxic action are still unknown, we used a porcine model to investigate the uptake, routes of excretion and distribution of cereulide within the host. Pigs were orally challenged with cereulide using single doses of 10-150 μg cereulide kg^-1 body weight to study acute effects or using daily doses of 10 μg cereulide kg^-1 body weight administered for 7 days to investigate effects of longtime, chronic exposure. Our study showed that part of cereulide ingested with food is rapidly excreted with feces while part of the cereulide toxin is absorbed, passes through membranes and is distributed within the body. Results from the chronic trial indicate bioaccumulation of cereulide in certain tissues and organs, such as kidney, liver, muscles and fat tissues. Beside its detection in various tissues and organs, our study also demonstrated that cereulide is able to cross the blood-brain-barrier, which may partially explain the cerebral effects reported from human intoxication cases. The neurobehavioral symptoms, such as seizures and lethargy, observed in our porcine model resemble those reported from human food borne intoxications. The rapid onset of these symptoms indicates direct effects of cereulide on the central nervous system (CNS), which warrant further research. The porcine model presented here might be useful to study the specific neurobiological effect in detail. Furthermore, our study revealed that typical diagnostic specimens used in human medicine, such as blood samples and urine, are not suitable for diagnostics of food borne cereulide intoxications. Instead, screening of fecal samples by SIDA-LC-MS may represent a simple and non-invasive method for detection of cereulide intoxications in clinical settings as well as in foodborne outbreak situations.

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.

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.