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

Transplantation of GABAergic Interneurons into the Neonatal Primary Visual Cortex Reduces Absence Seizures in Stargazer Mice

Epilepsies are debilitating neurological disorders characterized by repeated episodes of pathological seizure activity. Absence epilepsy (AE) is a poorly understood type of seizure with an estimated 30% of affected patients failing to respond to antiepileptic drugs. Thus, novel therapies are needed for the treatment of AE. A promising cell-based therapeutic strategy is centered on transplantation of embryonic neural stem cells from the medial ganglionic eminence (MGE), which give rise to gamma-aminobutyric acidergic (GABAergic) interneurons during embyronic development. Here, we used the Stargazer (Stg) mouse model of AE to map affected loci using c-Fos immunohistochemistry, which revealed intense seizure-induce activity in visual and somatosensory cortices. We report that transplantation of MGE cells into the primary visual cortex (V1) of Stg mice significantly reduces AE episodes and lowers mortality. Electrophysiological analysis in acute cortical slices of visual cortex demonstrated that Stg V1 neurons exhibit more pronounced increases in activity in response to a potassium-mediated excitability challenge than wildtypes (WT). The defective network activity in V1 was significantly altered following WT MGE transplantation, associating it with behavioral rescue of seizures in Stgs. Taken together, these findings present MGE grafting in the V1 as a possible clinical approach in the treatment of AE.

Bistable dynamics underlying excitability of ion homeostasis in neuron models

When neurons fire action potentials, dissipation of free energy is usually not directly considered, because the change in free energy is often negligible compared to the immense reservoir stored in neural transmembrane ion gradients and the long-term energy requirements are met through chemical energy, i.e., metabolism. However, these gradients can temporarily nearly vanish in neurological diseases, such as migraine and stroke, and in traumatic brain injury from concussions to severe injuries. We study biophysical neuron models based on the Hodgkin-Huxley (HH) formalism extended to include time-dependent ion concentrations inside and outside the cell and metabolic energy-driven pumps. We reveal the basic mechanism of a state of free energy-starvation (FES) with bifurcation analyses showing that ion dynamics is for a large range of pump rates bistable without contact to an ion bath. This is interpreted as a threshold reduction of a new fundamental mechanism of ionic excitability that causes a long-lasting but transient FES as observed in pathological states. We can in particular conclude that a coupling of extracellular ion concentrations to a large glial-vascular bath can take a role as an inhibitory mechanism crucial in ion homeostasis, while the Na⁺/K⁺ pumps alone are insufficient to recover from FES. Our results provide the missing link between the HH formalism and activator-inhibitor models that have been successfully used for modeling migraine phenotypes, and therefore will allow us to validate the hypothesis that migraine symptoms are explained by disturbed function in ion channel subunits, Na⁺/K⁺ pumps, and other proteins that regulate ion homeostasis.

Event-triggered feedback in noise-driven phase oscillators

Using a stochastic nonlinear phase oscillator model, we study the effect of event-triggered feedback on the statistics of interevent intervals. Events are associated with the entering of a new cycle. The feedback is modeled by an instantaneous increase (positive feedback) or decrease (negative feedback) of the oscillator frequency whenever an event occurs followed by an exponential decay on a slow time scale. In addition to the known excitable and oscillatory regimes, which are separated by a saddle node on invariant circle bifurcation, positive feedback can lead to bistable dynamics and a change of the system's excitability. The feedback has also a strong effect on noise-induced phenomena like coherence resonance or anticoherence resonance. Both positive and negative feedback can lead to more regular output for particular noise strengths. Finally, we investigate serial correlations in the sequence of interevent intervals that occur due to the additional slow dynamics. We derive approximations for the serial correlation coefficient and show that positive feedback results in extended positive interval correlations, whereas negative feedback yields short-ranging negative correlations. Investigating the interplay of feedback and the nonlinear phase dynamics close to the bifurcation, we find that correlations are most pronounced for optimal feedback strengths.

The pannexins: past and present

The pannexins (Panxs) are a family of chordate proteins homologous to the invertebrate gap junction forming proteins named innexins. Three distinct Panx paralogs (Panx1, Panx2, and Panx3) are shared among the major vertebrate phyla, but they appear to have suppressed (or even lost) their ability to directly couple adjacent cells. Connecting the intracellular and extracellular compartments is now widely accepted as Panx's primary function, facilitating the passive movement of ions and small molecules along electrochemical gradients. The tissue distribution of the Panxs ranges from pervasive to very restricted, depending on the paralog, and are often cell type-specific and/or developmentally regulated within any given tissue. In recent years, Panxs have been implicated in an assortment of physiological and pathophysiological processes, particularly with respect to ATP signaling and inflammation, and they are now considered to be a major player in extracellular purinergic communication. The following is a comprehensive review of the Panx literature, exploring the historical events leading up to their discovery, outlining our current understanding of their biochemistry, and describing the importance of these proteins in health and disease.

Physiological sharp wave-ripples and interictal events in vitro: what's the difference?

Sharp wave-ripples and interictal events are physiological and pathological forms of transient high activity in the hippocampus with similar features. Sharp wave-ripples have been shown to be essential in memory consolidation, whereas epileptiform (interictal) events are thought to be damaging. It is essential to grasp the difference between physiological sharp wave-ripples and pathological interictal events to understand the failure of control mechanisms in the latter case. We investigated the dynamics of activity generated intrinsically in the Cornu Ammonis region 3 of the mouse hippocampus in vitro, using four different types of intervention to induce epileptiform activity. As a result, sharp wave-ripples spontaneously occurring in Cornu Ammonis region 3 disappeared, and following an asynchronous transitory phase, activity reorganized into a new form of pathological synchrony. During epileptiform events, all neurons increased their firing rate compared to sharp wave-ripples. Different cell types showed complementary firing: parvalbumin-positive basket cells and some axo-axonic cells stopped firing as a result of a depolarization block at the climax of the events in high potassium, 4-aminopyridine and zero magnesium models, but not in the gabazine model. In contrast, pyramidal cells began firing maximally at this stage. To understand the underlying mechanism we measured changes of intrinsic neuronal and transmission parameters in the high potassium model. We found that the cellular excitability increased and excitatory transmission was enhanced, whereas inhibitory transmission was compromised. We observed a strong short-term depression in parvalbumin-positive basket cell to pyramidal cell transmission. Thus, the collapse of pyramidal cell perisomatic inhibition appears to be a crucial factor in the emergence of epileptiform events.

Rational design of transcranial current stimulation (TCS) through mechanistic insights into cortical network dynamics

Transcranial current stimulation (TCS) is a promising method of non-invasive brain stimulation to modulate cortical network dynamics. Preliminary studies have demonstrated the ability of TCS to enhance cognition and reduce symptoms in both neurological and psychiatric illnesses. Despite the encouraging results of these studies, the mechanisms by which TCS and endogenous network dynamics interact remain poorly understood. Here, we propose that the development of the next generation of TCS paradigms with increased efficacy requires such mechanistic understanding of how weak electric fields (EFs) imposed by TCS interact with the nonlinear dynamics of large-scale cortical networks. We highlight key recent advances in the study of the interaction dynamics between TCS and cortical network activity. In particular, we illustrate an interdisciplinary approach that bridges neurobiology and electrical engineering. We discuss the use of (1) hybrid biological-electronic experimental approaches to disentangle feedback interactions; (2) large-scale computer simulations for the study of weak global perturbations imposed by TCS; and (3) optogenetic manipulations informed by dynamic systems theory to probe network dynamics. Together, we here provide the foundation for the use of rational design for the development of the next generation of TCS neurotherapeutics.

Inhibitory synaptic plasticity: spike timing-dependence and putative network function

While the plasticity of excitatory synaptic connections in the brain has been widely studied, the plasticity of inhibitory connections is much less understood. Here, we present recent experimental and theoretical findings concerning the rules of spike timing-dependent inhibitory plasticity and their putative network function. This is a summary of a workshop at the COSYNE conference 2012.

Single neuron dynamics during experimentally induced anoxic depolarization

We studied single neuron dynamics during anoxic depolarizations, which are often observed in cases of neuronal energy depletion. Anoxic and similar depolarizations play an important role in several pathologies, notably stroke, migraine, and epilepsy. One of the effects of energy depletion was experimentally simulated in slices of rat cortex by blocking the sodium-potassium pumps with ouabain. The membrane voltage of pyramidal cells was measured. Five different kinds of dynamical behavior of the membrane voltage were observed during the resulting depolarizations. Using bifurcation analysis of a single cell model, we show that these voltage dynamics all are responses of the same cell, with normally functioning ion channels, to particular courses of the intra- and extracellular concentrations of sodium and potassium.

Analysis of synchronization in a slowly changing environment: how slow coupling becomes fast weak coupling

Many physical and biological oscillators are coupled indirectly through a slowly evolving dynamic medium. We present a perturbation method that shows that slow dynamics of a coupling medium is effectively equivalent to weak coupling of oscillators. Our methods first apply the theory of averaging to obtain a periodic solution to a single system and then exploit small fluctuations around the mean to analyze coupling between systems. We use this method to explain the spike-to-spike asynchrony seen in a model for bursting neurons coupled through extracellular potassium and to explore synchronization in a model for quorum sensing.

Computational models of neuron-astrocyte interaction in epilepsy

Astrocytes actively shape the dynamics of neurons and neuronal ensembles by affecting several aspects critical to neuronal function, such as regulating synaptic plasticity, modulating neuronal excitability, and maintaining extracellular ion balance. These pathways for astrocyte-neuron interaction can also enhance the information-processing capabilities of brains, but in other circumstances may lead the brain on the road to pathological ruin. In this article, we review the existing computational models of astrocytic involvement in epileptogenesis, focusing on their relevance to existing physiological data.

Curious and contradictory roles of glial connexins and pannexins in epilepsy

Glia play an under-recognized role in epilepsy. This review examines the involvement of glial connexins (Cxs) and pannexins (Panxs), proteins which form gap junctions and membrane hemichannels (connexins) and hemichannels (pannexins), in epilepsy. These proteins, particularly glial Cx43, have been shown to be upregulated in epileptic brain tissue. In a cobalt model of in vitro seizures, seizures increased Panxs1 and 2 and Cx43 expression, and remarkably reorganized the interrelationships between their mRNA levels (transcriptome) which then became statistically significant. Gap junctions are highly implicated in synchronous seizure activity. Blocking gap junctional communication (GJC) is often anticonvulsant, and assumed to be due to blocking gap junctionally-medicated electrotonic coupling between neurons. However, in organotypic hippocampal slice cultures, connexin43 specific peptides, which attenuate GJC possibly by blocking connexon docking, diminished spontaneous seizures. Glia have many functions including extracellular potassium redistribution, in part via gap junctions, which if blocked, can be seizuregenic. Glial gap junctions are critical for the delivery of nutrients to neurons, which if interrupted, can depress seizure activity. Other functions of glia possibly related to epileptogenesis are mentioned including anatomic reorganization in chronic seizure models greatly increasing the overlapping domains of glial processes, changes in neurotransmitter re-uptake, and possible glial generation of currents and fields during seizure activity. Finally there is recent evidence for Cx43 hemichannels and Panx1 channels in glial membranes which could play a role in brain damage and seizure activity. Although glial Cxs and Panxs are increasingly recognized as contributing to fundamental mechanisms of epilepsy, the data are often contradictory and controversial, requiring much more research. This article is part of a Special Issue entitled Electrical Synapses.

Phase space approach for modeling of epileptic dynamics

Epileptic electroencephalography recordings can be described in terms of four prototypic wave forms: fast sinusoidal oscillations, large slow waves, fast spiking, and spike waves. On the macroscopic level, these wave forms have been modeled by different mechanistic models which share canonical features. Here we derive a minimal model of excitatory and inhibitory processes with features common to all previous models. We can infer that at least three interacting processes are required to support the prototypic epileptic dynamics. Based on a separation of time scales we analyze the model in terms of interacting manifolds in phase space. This allows qualitative reverse engineering of all epileptic wave forms and transitions between them. We propose this method as a complement to traditional approaches to modeling epileptiform rhythms.

Acute feedback control of astrocytic glycolysis by lactate

Neuronal activity is accompanied by a rapid increase in interstitial lactate, which is hypothesized to serve as a fuel for neurons and a signal for local vasodilation. Using FRET microscopy, we report here that the rate of glycolysis in cultured mice astrocytes can be acutely modulated by physiological changes in extracellular lactate. Glycolytic inhibition by lactate was not accompanied by detectable variations in intracellular pH or intracellular ATP and was not dependent of mitochondrial function. Pyruvate was also inhibitory, suggesting that the effect of lactate is not mediated by the NADH/NAD(+) ratio. We propose that lactate serves as a fast negative feedback signal limiting its own production by astrocytes and therefore the amplitude of the lactate surge. The inhibition of glucose usage by lactate was much stronger in resting astrocytes than in K(+)-stimulated astrocytes, which suggests that lactate may also help diverting glucose from resting to active zones.

NBCe1 mediates the acute stimulation of astrocytic glycolysis by extracellular K+

Excitatory synaptic transmission stimulates brain tissue glycolysis. This phenomenon is the signal detected in FDG-PET imaging and, through enhanced lactate production, is also thought to contribute to the fMRI signal. Using a method based on Förster resonance energy transfer in mouse astrocytes, we have recently observed that a small rise in extracellular K(+) can stimulate glycolysis by >300% within seconds. The K(+) response was blocked by ouabain, but intracellular engagement of the Na(+)/K(+) ATPase pump with Na(+) was ineffective, suggesting that the canonical feedback regulatory pathway involving the Na(+) pump and ATP depletion is only permissive and that a second mechanism is involved. Because of their predominant K(+) permeability and high expression of the electrogenic Na(+)/HCO(3)(-) cotransporter NBCe1, astrocytes respond to a rise in extracellular K(+) with plasma membrane depolarization and intracellular alkalinization. In the present article, we show that a fast glycolytic response can be elicited independently of K(+) by plasma membrane depolarization or by intracellular alkalinization. The glycolytic response to K(+) was absent in astrocytes from NBCe1 null mice (Slc4a4) and was blocked by functional or pharmacological inhibition of the NBCe1. Hippocampal neurons acquired K(+)-sensitive glycolysis upon heterologous NBCe1 expression. The phenomenon could also be reconstituted in HEK293 cells by coexpression of the NBCe1 and a constitutively open K(+) channel. We conclude that the NBCe1 is a key element in a feedforward mechanism linking excitatory synaptic transmission to fast modulation of glycolysis in astrocytes.

Self-terminating wave patterns and self-organized pacemakers in a phenomenological model of spreading depression

A simple reaction-diffusion model of spreading depression (SD) is presented. Its local dynamics are governed by two activator and two inhibitor variables that provide an extremely simplified description of the mutual interaction between the neurons and extracellular space. This interaction is realized by the substances in the extracellular space that are increasing excitability of the neurons that have released them and are diffusing to the neighboring neurons, thereby spreading this excitation. Typical dynamic patterns of simulated activity are presented. The focus is laid on the case where response of the extracellular medium is relatively fast, and retracting waves, spiral-shaped waves, and autonomous pacemakers are observed, which is in good agreement with experimental observations. The underlying mechanisms are found to be related to switching between the local bi-stable, excitable, and self-sustained dynamics in the simulated medium. This article is part of a Special Issue entitled: Neural Coding.

Efficacy of synaptic inhibition depends on multiple, dynamically interacting mechanisms implicated in chloride homeostasis

Chloride homeostasis is a critical determinant of the strength and robustness of inhibition mediated by GABA(A) receptors (GABA(A)Rs). The impact of changes in steady state Cl(-) gradient is relatively straightforward to understand, but how dynamic interplay between Cl(-) influx, diffusion, extrusion and interaction with other ion species affects synaptic signaling remains uncertain. Here we used electrodiffusion modeling to investigate the nonlinear interactions between these processes. Results demonstrate that diffusion is crucial for redistributing intracellular Cl(-) load on a fast time scale, whereas Cl(-)extrusion controls steady state levels. Interaction between diffusion and extrusion can result in a somato-dendritic Cl(-) gradient even when KCC2 is distributed uniformly across the cell. Reducing KCC2 activity led to decreased efficacy of GABA(A)R-mediated inhibition, but increasing GABA(A)R input failed to fully compensate for this form of disinhibition because of activity-dependent accumulation of Cl(-). Furthermore, if spiking persisted despite the presence of GABA(A)R input, Cl(-) accumulation became accelerated because of the large Cl(-) driving force that occurs during spikes. The resulting positive feedback loop caused catastrophic failure of inhibition. Simulations also revealed other feedback loops, such as competition between Cl(-) and pH regulation. Several model predictions were tested and confirmed by [Cl(-)](i) imaging experiments. Our study has thus uncovered how Cl(-) regulation depends on a multiplicity of dynamically interacting mechanisms. Furthermore, the model revealed that enhancing KCC2 activity beyond normal levels did not negatively impact firing frequency or cause overt extracellular K(-) accumulation, demonstrating that enhancing KCC2 activity is a valid strategy for therapeutic intervention.

Ionic dynamics mediate spontaneous termination of seizures and postictal depression state

Epileptic seizures are characterized by periods of recurrent, highly synchronized activity that spontaneously terminates, followed by postictal state when neuronal activity is generally depressed. The mechanisms for spontaneous seizure termination and postictal depression remain poorly understood. Using a realistic computational model, we demonstrate that termination of seizure and postictal depression state may be mediated by dynamics of the intracellular and extracellular ion concentrations. Spontaneous termination was linked to progressive increase of intracellular sodium concentration mediated by activation of sodium channels during highly active epileptic state. In contrast, an increase of intracellular chloride concentration extended seizure duration making possible long-lasting epileptic activity characterized by multiple transitions between tonic and clonic states. After seizure termination, the extracellular potassium was reduced below baseline, resulting in postictal depression. Our study suggests that the coupled dynamics of sodium, potassium, and chloride ions play a critical role in the development and termination of seizures. Findings from this study could help identify novel therapeutics for seizure disorder.

Dependence of spontaneous neuronal firing and depolarisation block on astroglial membrane transport mechanisms

Exposed to a sufficiently high extracellular potassium concentration ([K( + )]₀), the neuron can fire spontaneous discharges or even become inactivated due to membrane depolarisation ('depolarisation block'). Since these phenomena likely are related to the maintenance and propagation of seizure discharges, it is of considerable importance to understand the conditions under which excess [K( + )]₀ causes them. To address the putative effect of glial buffering on neuronal activity under elevated [K( + )](o) conditions, we combined a recently developed dynamical model of glial membrane ion and water transport with a Hodgkin-Huxley type neuron model. In this interconnected glia-neuron model we investigated the effects of natural heterogeneity or pathological changes in glial membrane transporter density by considering a large set of models with different, yet empirically plausible, sets of model parameters. We observed both the high [K( + )]₀-induced duration of spontaneous neuronal firing and the prevalence of depolarisation block to increase when reducing the magnitudes of the glial transport mechanisms. Further, in some parameter regions an oscillatory bursting spiking pattern due to the dynamical coupling of neurons and glia was observed. Bifurcation analyses of the neuron model and of a simplified version of the neuron-glia model revealed further insights about the underlying mechanism behind these phenomena. The above insights emphasise the importance of combining neuron models with detailed astroglial models when addressing phenomena suspected to be influenced by the astroglia-neuron interaction. To facilitate the use of our neuron-glia model, a CellML version of it is made publicly available.

Fast and reversible stimulation of astrocytic glycolysis by K+ and a delayed and persistent effect of glutamate

Synaptic activity is followed within seconds by a local surge in lactate concentration, a phenomenon that underlies functional magnetic resonance imaging and whose causal mechanisms are unclear, partly because of the limited spatiotemporal resolution of standard measurement techniques. Using a novel Förster resonance energy transfer-based method that allows real-time measurement of the glycolytic rate in single cells, we have studied mouse astrocytes in search for the mechanisms responsible for the lactate surge. Consistent with previous measurements with isotopic 2-deoxyglucose, glutamate was observed to stimulate glycolysis in cultured astrocytes, but the response appeared only after a lag period of several minutes. Na(+) overloads elicited by engagement of the Na(+)-glutamate cotransporter with d-aspartate or application of the Na(+) ionophore gramicidin also failed to stimulate glycolysis in the short term. In marked contrast, K(+) stimulated astrocytic glycolysis by fourfold within seconds, an effect that was observed at low millimolar concentrations and was also present in organotypic hippocampal slices. After removal of the agonists, the stimulation by K(+) ended immediately but the stimulation by glutamate persisted unabated for >20 min. Both stimulations required an active Na(+)/K(+) ATPase pump. By showing that small rises in extracellular K(+) mediate short-term, reversible modulation of astrocytic glycolysis and that glutamate plays a long-term effect and leaves a metabolic trace, these results support the view that astrocytes contribute to the lactate surge that accompanies synaptic activity and underscore the role of these cells in neurometabolic and neurovascular coupling.

Potassium accumulation between type I hair cells and calyx terminals in mouse crista

The mode of synaptic transmission in the vestibular periphery, between type I hair cells and their associated calyx terminal, has been the subject of much debate. The close and extensive apposition of pre- and post-synaptic elements has led some to suggest potassium (K(+)) accumulates in the intercellular space and even plays a role in synaptic transmission. During patch clamp recordings from isolated and embedded hair cells in a semi-intact preparation of the mouse cristae, we noted marked differences in whole-cell currents. Embedded type I hair cells show a prominent droop during steady-state activation as well as a dramatic collapse in tail currents. Responses to a depolarizing voltage step (-124 to +16 mV) in embedded, but not isolated, hair cells resulted in a >40 mV shift of the K(+) equilibrium potential and a rise in effective K(+) concentration (>50 mM) in the intercellular space. Together these data suggest K(+) accumulation in the intercellular space accounts for the different responses in isolated and embedded type I hair cells. To test this notion, we exposed the preparation to hyperosmotic solutions to enlarge the intercellular space. As predicted, the K(+) accumulation effects were reduced; however, a fit of our data with a classic diffusion model suggested K(+) permeability, rather than the intercellular space, had been altered by the hyperosmotic change. These results support the notion that under depolarizing conditions substantial K(+) accumulation occurs in the space between type I hair cells and calyx. The extent of K(+) accumulation during normal synaptic transmission, however, remains to be determined.

The influence of the chloride currents on action potential firing and volume regulation of excitable cells studied by a kinetic model

In excitable cells, the generation of an action potential (AP) is associated with transient changes of the intra- and extracellular concentrations of small ions such as Na(+), K(+) and Cl(-). If these changes cannot be fully reversed between successive APs cumulative changes of trans-membrane ion gradients will occur, impinging on the cell volume and the duration, amplitude and frequency of APs. Previous computational studies focused on effects associated with excitation-induced changes of potassium and sodium. Here we present a model based study on the influence of chloride on the fidelity of AP firing and cellular volume regulation during excitation. Our simulations show that depending on the magnitude of the basal chloride permeability two complementary types of responsiveness and volume variability exist: (i) At high chloride permeability (typical for muscle cells), large excitatory stimuli are required to elicit APs; repetitive stimuli of equal strength result in almost identical spike train patterns (Markovian behavior), however, long excitation may lead to after discharges due to an outward directed current of intracellular chloride ions which accumulate during excitation; cell volume changes are large. (ii) At low chloride permeability (e.g., neurons), small excitatory stimuli are sufficient to elicit APs, repetitive stimuli of equal strength produce spike trains with progressively changing amplitude, frequency and duration (short-term memory effects or non-Markovian behavior); cell volume changes are small. We hypothesize that variation of the basal chloride permeability could be an important mechanism of neuronal cells to adapt their responsiveness to external stimuli during learning and memory processes.

Dynamics of epileptiform activity in mouse hippocampal slices

Increase of the extracellular K⁺ concentration mediates seizure-like synchronized activities in vitro and was proposed to be one of the main factors underlying epileptogenesis in some types of seizures in vivo. While underlying biophysical mechanisms clearly involve cell depolarization and overall increase in excitability, it remains unknown what qualitative changes of the spatio-temporal network dynamics occur after extracellular K⁺ increase. In this study, we used multi-electrode recordings from mouse hippocampal slices to explore changes of the network activity during progressive increase of the extracellular K⁺ concentration. Our analysis revealed complex spatio-temporal evolution of epileptiform activity and demonstrated a sequence of state transitions from relatively simple network bursts into complex bursting, with multiple synchronized events within each burst. We describe these transitions as qualitative changes of the state attractors, constructed from experimental data, mediated by elevation of extracellular K⁺ concentration.

Chronic deficit in the expression of voltage-gated potassium channel Kv3.4 subunit in the hippocampus of pilocarpine-treated epileptic rats

Voltage gated K(+) channels (Kv) are a highly diverse group of channels critical in determining neuronal excitability. Deficits of Kv channel subunit expression and function have been implicated in the pathogenesis of epilepsy. In this study, we investigate whether the expression of the specific subunit Kv3.4 is affected during epileptogenesis following pilocarpine-induced status epilepticus. For this purpose, we used immunohistochemistry, Western blotting assays and comparative analysis of gene expression using TaqMan-based probes and delta-delta cycle threshold (ΔΔCT) method of quantitative real-time polymerase chain reaction (qPCR) technique in samples obtained from age-matched control and epileptic rats. A marked down-regulation of Kv3.4 immunoreactivity was detected in the stratum lucidum and hilus of dentate gyrus in areas corresponding to the mossy fiber system of chronically epileptic rats. Correspondingly, a 20% reduction of Kv3.4 protein levels was detected in the hippocampus of chronic epileptic rats. Real-time quantitative PCR analysis of gene expression revealed that a significant 33% reduction of transcripts for Kv3.4 (gene Kcnc4) occurred after 1 month of pilocarpine-induced status epilepticus and persisted during the chronic phase of the model. These data indicate a reduced expression of Kv3.4 channels at protein and transcript levels in the epileptic hippocampus. Down-regulation of Kv3.4 in mossy fibers may contribute to enhanced presynaptic excitability leading to recurrent seizures in the pilocarpine model of temporal lobe epilepsy.

Ion concentration dynamics as a mechanism for neuronal bursting

We describe a simple conductance-based model neuron that includes intra- and extracellular ion concentration dynamics and show that this model exhibits periodic bursting. The bursting arises as the fast-spiking behavior of the neuron is modulated by the slow oscillatory behavior in the ion concentration variables and vice versa. By separating these time scales and studying the bifurcation structure of the neuron, we catalog several qualitatively different bursting profiles that are strikingly similar to those seen in experimental preparations. Our work suggests that ion concentration dynamics may play an important role in modulating neuronal excitability in real biological systems.

Ensembles of excitable two-state units with delayed feedback

A two-state unit is considered as an abstract modification for an excitable system. Each state is characterized by a different waiting time distribution. This non-Markovian approach allows for a renewal process description of the system dynamics. Exact formulas for the interspike interval distribution and power spectral density are found. In the limit of an infinity ensemble of globally coupled units the mean-field equations for the populations of both states are derived. Depending on the coupling strength and on the noise intensity the ensemble undergoes saddle-node bifurcations and demonstrates bistability, while a pitchfork bifurcation emerges on a cusp point. The ensemble undergoes Hopf bifurcations and bulk oscillations emerge, in the onset of coherent activation events, only when the feedback affects individual units with a certain time delay.

Network bistability mediates spontaneous transitions between normal and pathological brain states

Little is known about how cortical networks support the emergence of remarkably different activity patterns. Physiological activity interspersed with epochs of pathological hyperactivity in the epileptic brain represents a clinically relevant yet poorly understood case of such rich dynamic repertoire. Using a realistic computational model, we demonstrate that physiological sparse and pathological tonic-clonic activity may coexist in the same cortical network for identical afferent input level. Transient perturbations in the afferent input were sufficient to switch the network between these two stable states. The effectiveness of the potassium regulatory apparatus determined the stability of the physiological state and the threshold for seizure initiation. Our findings contrast with the common notions of (1) pathological brain activity representing dynamic instabilities and (2) necessary adjustments of experimental conditions to elicit different network states. Rather, we propose that the rich dynamic repertoire of cortical networks may be based on multistabilities intrinsic to the network.

The K+-Cl cotransporter KCC2 promotes GABAergic excitation in the mature rat hippocampus

GABAergic excitatory [K(+)](o) transients can be readily evoked in the mature rat hippocampus by intense activation of GABA(A) receptors (GABA(A)Rs). Here we show that these [K(+)](o) responses induced by high-frequency stimulation or GABA(A) agonist application are generated by the neuronal K(+)-Cl() cotransporter KCC2 and that the transporter-mediated KCl extrusion is critically dependent on the bicarbonate-driven accumulation of Cl() in pyramidal neurons. The mechanism underlying GABAergic [K(+)](o) transients was studied in CA1 stratum pyramidale using intracellular sharp microelectrodes and extracellular ion-sensitive microelectrodes. The evoked [K(+)](o) transients, as well as the associated afterdischarges, were strongly suppressed by 0.5-1 mm furosemide, a KCl cotransport inhibitor. Importantly, the GABA(A)R-mediated intrapyramidal accumulation of Cl(), as measured by monitoring the reversal potential of fused IPSPs, was unaffected by the drug. It was further confirmed that the reduction in the [K(+)](o) transients was not due to effects of furosemide on the Na(+)-dependent K(+)-Cl() cotransporter NKCC1 or on intraneuronal carbonic anhydrase activity. Blocking potassium channels by Ba(2+) enhanced [K(+)](o) transients whereas pyramidal cell depolarizations were attenuated in further agreement with a lack of contribution by channel-mediated K(+) efflux. The key role of the GABA(A)R channel-mediated anion fluxes in the generation of the [K(+)](o) transients was examined in experiments where bicarbonate was replaced with formate. This anion substitution had no significant effect on the rate of Cl() accumulation, [K(+)](o) response or afterdischarges. Our findings reveal a novel excitatory mode of action of KCC2 that can have substantial implications for the role of GABAergic transmission during ictal epileptiform activity.

Potassium accumulation as dynamic modulator of neurohypophysial excitability

Activity-dependent modulation of excitable responses from neurohypophysial axons and their secretory swellings has long been recognized as an important regulator of arginine vasopressin and oxytocin release during patterned stimulation. Various activity-dependent mechanisms, including action potential broadening, potassium accumulation, and autocrine or paracrine feedback, have been proposed as underlying mechanisms. However, the relevance of any specific mechanism on net excitability in the intact preparation, during different levels of overall activation, and during realistic stimulation with trains of action potentials has remained largely undetermined. Using high-speed optical recordings and potentiometric dyes, we have quantified the dynamics of global excitability under physiologically more realistic conditions, that is in the intact neurohypophysis during trains of stimuli at varying frequencies and levels of overall activity. Net excitability facilitated during stimulation at low frequencies or at low activity. During persistent high-intensity or high-frequency stimulation, net excitability became severely depressed. Depression of excitable responses was strongly affected by manipulations of extracellular potassium levels, including changes to resting [K(+)](out), increases of interstitial spaces with hypertonic solutions and inhibition of Na(+)/K(+) ATPase activity. Application of the GABA(A) receptor blocker bicuculline or manipulations of Ca(2+) influx showed little effect. Numerical simulation of K(+) accumulation on action potentials of individual axons reproduced optically recorded population responses, including the overall depression of action potential (AP) amplitudes, modest AP broadening and the prominent loss of hyperpolarizing undershoots. Hence, extracellular potassium accumulation dominates activity-dependent depression of neurohypophysial excitability under elevated stimulation conditions. The intricate dependence on the short-term stimulation history and its resulting feedback on neurohypophysial excitability renders [K(+)](out) accumulation a surprisingly complex mechanism for regulating axonal excitability and subsequent neuroendocrine release.

Non-junction functions of pannexin-1 channels

Pannexins are large-pore ion channels with broad expression in the central nervous system (CNS). The channels function by releasing large signaling molecules, such ATP and arachidonic acid derivatives, from neurons and possibly astrocytes. They might also contribute to novel forms of non-synaptic communication in the CNS, thereby affecting synaptic function, astrocytic Ca(2+) wave propagation and possibly regulation of vascular tone in the brain. Panx1 activation in various in vitro pathological conditions implicates these channels in ischemic, excitotoxic and ATP-dependent cell death, whereas Panx coupling with purinergic receptors triggers the inflammasome. Novel functions for the pannexin channels are likely to be discovered as current understanding of how they are regulated in physiological and pathological situations improves.

Firing patterns and synchronization in nonsynaptic epileptiform activity: the effect of gap junctions modulated by potassium accumulation

Several lines of evidence point to the modification of firing patterns and of synchronization due to gap junctions (GJs) as having a role in the establishment of epileptiform activity (EA). However, previous studies consider GJs as ohmic resistors, ignoring the effects of intense variations in ionic concentration known to occur during seizures. In addition to GJs, extracellular potassium is regarded as a further important factor involved in seizure initiation and sustainment. To analyze how these two mechanisms act together to shape firing and synchronization, we use a detailed computational model for in vitro high-K(+) and low-Ca(2+) nonsynaptic EA. The model permits us to explore the modulation of electrotonic interactions under ionic concentration changes caused by electrodiffusion in the extracellular space, altered by tortuosity. In addition, we investigate the special case of null GJ current. Increased electrotonic interaction alters bursts and action potential frequencies, favoring synchronization. The particularities of pattern changes depend on the tortuosity and array size. Extracellular potassium accumulation alone modifies firing and synchronization when the GJ coupling is null.

Gene expression analysis of tuberous sclerosis complex cortical tubers reveals increased expression of adhesion and inflammatory factors

Cortical tubers in patients with tuberous sclerosis complex are associated with disabling neurological manifestations, including intractable epilepsy. While these malformations are believed to result from the effects of TSC1 or TSC2 gene mutations, the molecular mechanisms leading to tuber formation, as well as the onset of seizures, remain largely unknown. We used the Affymetrix Gene Chip platform to provide the first genome-wide investigation of gene expression in surgically resected tubers, compared with histological normal perituberal tissue from the same patients or autopsy control tissue. We identified 2501 differentially expressed genes in cortical tubers compared with autopsy controls. Expression of genes associated with cell adhesion, for example, VCAM1, integrins and CD44, or with the inflammatory response, including complement factors, serpinA3, CCL2 and several cytokines, was increased in cortical tubers, whereas genes related to synaptic transmission, for example, the glial glutamate transporter GLT-1, and voltage-gated channel activity, exhibited lower expression. Gene expression in perituberal cortex was distinct from autopsy control cortex suggesting that even in the absence of tissue pathology the transcriptome is altered in TSC. Changes in gene expression yield insights into new candidate genes that may contribute to tuber formation or seizure onset, representing new targets for potential therapeutic development.

The cortical innate immune response increases local neuronal excitability leading to seizures

Brain glial cells, five times more prevalent than neurons, have recently received attention for their potential involvement in epileptic seizures. Microglia and astrocytes, associated with inflammatory innate immune responses, are responsible for surveillance of brain damage that frequently results in seizures. Thus, an intriguing suggestion has been put forward that seizures may be facilitated and perhaps triggered by brain immune responses. Indeed, recent evidence strongly implicates innate immune responses in lowering seizure threshold in experimental models of epilepsy, yet, there is no proof that they can play an independent role in initiating seizures in vivo. Here, we show that cortical innate immune responses alone produce profound increases of brain excitability resulting in focal seizures. We found that cortical application of lipopolysaccharide, binding to toll-like receptor 4 (TLR4), triples evoked field potential amplitudes and produces focal epileptiform discharges. These effects are prevented by pre-application of interleukin-1 receptor antagonist. Our results demonstrate how the innate immune response may participate in acute seizures, increasing neuronal excitability through interleukin-1 release in response to TLR4 detection of the danger signals associated with infections of the central nervous system and with brain injury. These results suggest an important role of innate immunity in epileptogenesis and focus on glial inhibition, through pharmacological blockade of TLR4 and the pro-inflammatory mediators released by activated glia, in the study and treatment of seizure disorders in humans.

Dynamical structures in binary media of potassium-driven neurons

According to the conventional approach neural ensembles are modeled with fixed ionic concentrations in the extracellular environment. However, in some cases the extracellular concentration of potassium ions cannot be regarded as constant. Such cases represent specific chemical pathway for neurons to interact and can influence strongly the behavior of single neurons and of large ensembles. The released chemical agent diffuses in the external medium and lowers thresholds of individual excitable units. We address this problem by studying simplified excitable units given by a modified FitzHugh-Nagumo dynamics. In our model the neurons interact only chemically via the released and diffusing potassium in the surrounding nonactive medium and are permanently affected by noise. First, we study the dynamics of a single excitable unit embedded in the extracellular matter. That leads to a number of noise-induced effects such as self-modulation of firing rate in an individual neuron. After the consideration of two coupled neurons we consider the spatially extended situation. By holding parameters of the neuron fixed, various patterns appear ranging from spirals and traveling waves to oscillons and inverted structures depending on the parameters of the medium.

Cellular and network mechanisms of electrographic seizures

Epileptic seizures constitute a complex multiscale phenomenon that is characterized by synchronized hyperexcitation of neurons in neuronal networks. Recent progress in understanding pathological seizure dynamics provides crucial insights into underlying mechanisms and possible new avenues for the development of novel treatment modalities. Here we review some recent work that combines in vivo experiments and computational modeling to unravel the pathophysiology of seizures of cortical origin. We particularly focus on how activity-dependent changes in extracellular potassium concentration affects the intrinsic dynamics of neurons involved in cortical seizures characterized by spike/wave complexes and fast runs.