Mechanistic hypotheses for nonsynaptic epileptiform activity induction and its transition from the interictal to ictal state-Computational simulation

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

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

Deciphering the role of metal and non-metals in the treatment of epilepsy

Metals and non-metals have known to play a significant role in various physiological roles in the body including the central nervous system (CNS). The alterations in their concentration in the CNS leads to abnormalities in the normal functions which may lead to various neurological conditions including epilepsy. Manganese is a cofactor required for antioxidant enzymes such as Superoxide dismutase, Glutamine synthetase, etc. The accumulation of iron leads to formation of reactive oxygen species (ROS) and reactive nitrogen species (RNS) which have the potential to cause ferroptosis, one of the reasons for epileptogenesis. Zinc has biphasic response, both neurotoxic and neuroprotective, based on concentration levels in the CNS. Selenium is a main element for selenoproteins which is responsible for the regulation of oxidative state and antioxidant defence mechanism. The reduction in the phosphorous levels in the CNS is widely observed after generalised tonic clonic seizures (GTC), which can be a potential diagnostic biomarker. Copper acts in the CNS in an identical manner, i.e., by blocking both AMPA mediated and GABA mediated neuronal transmission. Magnesium blocks calcium channels in the NMDA receptor and prevents glutamatergic transmission, thus inhibiting excitotoxicity. Lithium acts as a proconvulsive agent and is used in combination with pilocarpine to induce seizures. The identified potential of metals and non-metals in epilepsy can be utilised in order to devise new adjuvant therapies for the management of epilepsy. The article summaries in depth the role of metals and non-metals in the treatment of epilepsy supported with special paragraph on author perspective on to the topic. Furthermore, an update of preclinical and clinical evidences are discussed in the review to give evidence on metal and non-metal based therapies in epilepsy.

From phenomenological to biophysical models of seizures

Epilepsy is a complex disease that requires various approaches for its study. In this short review, we discuss the contribution of theoretical and computational models. The review presents theoretical frameworks that underlie the understanding of certain seizure properties and their classification based on their dynamical properties at the onset and offset of seizures. Dynamical system tools are valuable resources in the study of seizures. By analyzing the complex, dynamic behavior of seizures, these tools can provide insights into seizure mechanisms and offer a framework for their classification. Additionally, computational models have high potential for clinical applications, as they can be used to develop more accurate diagnostic and personalized medicine tools. We discuss various modeling approaches that span different scales and levels, while also questioning the neurocentric view, and emphasize the importance of considering glial cells. Finally, we explore the epistemic value provided by this type of approach.

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.

Modeling seizures: From single neurons to networks

Dynamical system tools offer a complementary approach to detailed biophysical seizure modeling, with a high potential for clinical applications. This review describes the theoretical framework that provides a basis for theorizing certain properties of seizures and for their classification according to their dynamical properties at onset and offset. We describe various modeling approaches spanning different scales, from single neurons to large-scale networks. This narrative review provides an accessible overview of this field, including non-exhaustive examples of key recent works.

The Effect of Low Magnesium Concentration on Ictal Discharges In A Non-Synaptic Model

Magnesium (Mg[Formula: see text] is an essential mineral for several cellular functions. The concentration of this ion below the physiological concentration induces recurrent neuronal discharges both in slices of the hippocampus and in neuronal cultures. These epileptiform discharges are initially sensitive to the application of [Formula: see text]-methyl-D-aspartate (NMDA) receptor antagonists, but these antagonists may lose their effectiveness with prolonged exposure to low [Mg[Formula: see text]], when extracellular Ca[Formula: see text] reduction occurs, typical of ictal periods, indicating the absence of synaptic connections. The study herein presented aimed at investigating the effect of reducing the [Mg[Formula: see text]] during the induction of Nonsynaptic Epileptiform Activities (NSEA). As an experimental protocol, NSEA were induced in rat hippocampal dentate gyrus (DG), using a bath solution containing high-K[Formula: see text] and zero-added-Ca[Formula: see text]. Additionally, computer simulations were performed using a mathematical model that represents electrochemical characteristics of the tissue of the DG granular layer. The experimental results show that the reduction of [Mg[Formula: see text]] causes an increase in the duration of the ictal period and a reduction in the interictal period, intensifying epileptiform discharges. The computer simulations suggest that the reduction of the Mg[Formula: see text] level intensifies the epileptiform discharges by a joint effect of reducing the surface charge screening and reducing the activity of the Na/K pump.

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

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

Realistic spiking neural network: Non-synaptic mechanisms improve convergence in cell assembly

Learning in neural networks inspired by brain tissue has been studied for machine learning applications. However, existing works primarily focused on the concept of synaptic weight modulation, and other aspects of neuronal interactions, such as non-synaptic mechanisms, have been neglected. Non-synaptic interaction mechanisms have been shown to play significant roles in the brain, and four classes of these mechanisms can be highlighted: (i) electrotonic coupling; (ii) ephaptic interactions; (iii) electric field effects; and iv) extracellular ionic fluctuations. In this work, we proposed simple rules for learning inspired by recent findings in machine learning adapted to a realistic spiking neural network. We show that the inclusion of non-synaptic interaction mechanisms improves cell assembly convergence. By including extracellular ionic fluctuation represented by the extracellular electrodiffusion in the network, we showed the importance of these mechanisms to improve cell assembly convergence. Additionally, we observed a variety of electrophysiological patterns of neuronal activity, particularly bursting and synchronism when the convergence is improved.

GABAa excitation and synaptogenesis after Status Epilepticus - A computational study

The role of GABAergic neurotransmission on epileptogenesis has been the subject of speculation according to different approaches. However, it is a very complex task to specifically consider the action of the GABAa neurotransmitter, which, in its dependence on the intracellular level of Cl-, can change its effect from inhibitory to excitatory. We have developed a computational model that represents the dentate gyrus and is composed of three different populations of neurons (granule cells, interneurons and mossy cells) that are mutually interconnected. The interconnections of the neurons were based on compensation theory with Hebbian and anti-Hebbian rules. The model also incorporates non-synaptic mechanisms to control the ionic homeostasis and was able to reproduce ictal discharges. The goal of the work was to investigate the hypothesis that the observed aberrant sprouting is promoted by GABAa excitatory action. Conjointly with the abnormal sprouting of the mossy fibres, the simulations show a reduction of the mossy cells connections in the network and an increased inhibition of the interneurons as a response of the neuronal network to control the activity. This finding contributes to increasing the changes in the connectivity of the neuronal circuitry and to increasing the epileptiform activity occurrences.

Changes of Ionic Concentrations During Seizure Transitions - A Modeling Study

Traditionally, it is considered that neuronal synchronization in epilepsy is caused by a chain reaction of synaptic excitation. However, it has been shown that synchronous epileptiform activity may also arise without synaptic transmission. In order to investigate the respective roles of synaptic interactions and nonsynaptic mechanisms in seizure transitions, we developed a computational model of hippocampal cells, involving the extracellular space, realistic dynamics of [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] ions, glial uptake and extracellular diffusion mechanisms. We show that the network behavior with fixed ionic concentrations may be quite different from the neurons' behavior when more detailed modeling of ionic dynamics is included. In particular, we show that in the extended model strong discharge of inhibitory interneurons may result in long lasting accumulation of extracellular [Formula: see text], which sustains the depolarization of the principal cells and causes their pathological discharges. This effect is not present in a reduced, purely synaptic network. These results point to the importance of nonsynaptic mechanisms in the transition to seizure.

Long-term alcohol exposure elicits hippocampal nonsynaptic epileptiform activity changes associated with expression and functional changes in NKCC1, KCC2 co-transporters and Na+/K+-ATPase

Nonsynaptic mechanism changes, particularly the enhancement of NKCC1 expression in the dentate gyrus (DG) after 4weeks of ethanol consumption, motivate the present work, in which rats were submitted to a period of chronic consumption (12weeks). Four groups of six animals (6-week-old male Wistar rats) were formed, including the control (C), ethanol 1 (E1), ethanol 2 (E2) and ethanol 3 (E3) groups. The rats in the E1, E2 and E3 groups were treated daily with a 30% v/v solution of ethanol, administered via oral gavage (1.0, 2.0 and 3.0g/kg, respectively). Nonsynaptic epileptiform activities (NEA) were induced by means of the zero-Ca2+ and high-K+ model using hippocampal slices and were recorded in the DG. The presence of NKCC1, KCC2, α1-Na+/K+-ATPase and GFAP immunoreactivity was analyzed. The results demonstrate that alcohol consumption changes NEA, and these changes are more prominent at the lower dosage. An increase in the DC shifts associated with epileptiform discharges was present with the low dose. This increase was correlated with the increment of NKCC1 expression. Confocal microscopy images indicate the NKCC1 increase was pronounced in the initial axonal segment of granule cells. The blockage of these cotransporters during NEA induction with bumetanide suppressed the DC shift increase and diminished all parameters of NEA that were quantified for all groups treated with ethanol. Therefore, the increase in NKCC1 expression and the effective activity of this cotransporter, which were observed in the treated groups, suggest that drugs that act for block NKCC1 represent promising strategies for diminishing the effects of alcohol damage on the brain.

Effects of A1 receptor agonist/antagonist on spontaneous seizures in pilocarpine-induced epileptic rats

Adenosine is an endogenous anticonvulsant that activates pre- and postsynaptic adenosine A1 receptors. A1 receptor agonists increase the latency for the development of seizures and status epilepticus following pilocarpine administration. Although hippocampal adenosine is increased in the chronic phase of the pilocarpine model, it is not known whether the modulation of A1 receptors may influence the frequency of spontaneous recurrent seizures (SRS). Here, we tested the hypothesis that the A1 receptor agonist RPia ([R]-N-phenylisopropyladenosine) and the A1 antagonist DPCPX (8-Cyclopentyl-1,3-dipropylxanthine) administered to chronic pilocarpine epileptic rats would respectively decrease and increase the frequency of SRS and hippocampal excitability. Four months after Pilo-induced SE, chronic epileptic rats were video-monitored for the recording of SRS before (basal) and after a 2-week treatment with RPia (25μg/kg) or DPCPX (50μg/kg). Following sacrifice, brain slices were studied with electrophysiology. We found that rats given RPia had a 93% nonsignificant reduction in the frequency of seizures compared with their own pretreatment baseline. In contrast, the administration of DPCPX resulted in an 87% significant increase in seizure rate. Nontreated epileptic rats had a similar frequency of seizures along the study. Corroborating our behavioral data, in vitro recordings showed that slices from animals previously given DPCPX had a shorter latency to develop epileptiform activity, longer and higher DC shifts, and higher spike amplitude compared with slices from nontreated Pilo controls. In contrast, smaller spike amplitude was recorded in slices from animals given RPia. In summary, the administration of A1 agonists reduced hippocampal excitability but not the frequency of spontaneous recurrent seizures in chronic epileptic rats, whereas A1 receptor antagonists increased both.

Enhanced nonsynaptic epileptiform activity in the dentate gyrus after kainate-induced status epilepticus

Understanding the mechanisms that influence brain excitability and synchronization provides hope that epileptic seizures can be controlled. In this scenario, non-synaptic mechanisms have a critical role in seizure activity. The contribution of ion transporters to the regulation of seizure-like activity has not been extensively studied. Here, we examined how non-synaptic epileptiform activity (NEA) in the CA1 and dentate gyrus (DG) regions of the hippocampal formation were affected by kainic acid (KA) administration. NEA enhancement in the DG and suppression in area CA1 were associated with increased NKCC1 expression in neurons and severe neuronal loss accompanied by marked glial proliferation, respectively. Twenty-four hours after KA, the DG exhibited intense microglial activation that was associated with reduced cell density in the infra-pyramidal lamina; however, cellular density recovered 7 days after KA. Intense Ki67 immunoreactivity was observed in the subgranular proliferative zone of the DG, which indicates new neuron incorporation into the granule layer. In addition, bumetanide, a selective inhibitor of neuronal Cl(-) uptake mediated by NKCC1, was used to confirm that the NKCC1 increase effectively contributed to NEA changes in the DG. Furthermore, 7 days after KA, prominent NKCC1 staining was identified in the axon initial segments of granule cells, at the exact site where action potentials are preferentially initiated, which endowed these neurons with increased excitability. Taken together, our data suggest a key role of NKCC1 in NEA in the DG.

Role of adenosine in the antiepileptic effects of deep brain stimulation

Despite the effectiveness of anterior thalamic nucleus (AN) deep brain stimulation (DBS) for the treatment of epilepsy, mechanisms responsible for the antiepileptic effects of this therapy remain elusive. As adenosine modulates neuronal excitability and seizure activity in animal models, we hypothesized that this nucleoside could be one of the substrates involved in the effects of AN DBS. We applied 5 days of stimulation to rats rendered chronically epileptic by pilocarpine injections and recorded epileptiform activity in hippocampal slices. We found that slices from animals given DBS had reduced hippocampal excitability and were less susceptible to develop ictal activity. In live animals, AN DBS significantly increased adenosine levels in the hippocampus as measured by microdialysis. The reduced excitability of DBS in vitro was completely abolished in animals pre-treated with A1 receptor antagonists and was strongly potentiated by A1 receptor agonists. We conclude that some of the antiepileptic effects of DBS may be mediated by adenosine.

Effects of anterior thalamic nucleus deep brain stimulation in chronic epileptic rats

Deep brain stimulation (DBS) has been investigated for the treatment of epilepsy. In rodents, an increase in the latency for the development of seizures and status epilepticus (SE) has been reported in different animal models but the consequences of delivering stimulation to chronic epileptic animals have not been extensively addressed. We study the effects of anterior thalamic nucleus (AN) stimulation at different current intensities in rats rendered epileptic following pilocarpine (Pilo) administration. Four months after Pilo-induced SE, chronic epileptic rats were bilaterally implanted with AN electrodes or had sham-surgery. Stimulation was delivered for 6 h/day, 5 days/week at 130 Hz, 90 µsec. and either 100 µA or 500 µA. The frequency of spontaneous recurrent seizures in animals receiving stimulation was compared to that recorded in the preoperative period and in rats given sham treatment. To investigate the effects of DBS on hippocampal excitability, brain slices from animals receiving AN DBS or sham surgery were studied with electrophysiology. We found that rats treated with AN DBS at 100 µA had a 52% non-significant reduction in the frequency of seizures as compared to sham-treated controls and 61% less seizures than at baseline. Animals given DBS at 500 µA had 5.1 times more seizures than controls and a 2.8 fold increase in seizure rate as compared to preoperative values. In non-stimulated controls, the average frequency of seizures before and after surgery remained unaltered. In vitro recordings have shown that slices from animals previously given DBS at 100 µA had a longer latency for the development of epileptiform activity, shorter and smaller DC shifts, and a smaller spike amplitude compared to non-stimulated controls. In contrast, a higher spike amplitude was recorded in slices from animals given AN DBS at 500 µA.

Alcohol abuse promotes changes in non-synaptic epileptiform activity with concomitant expression changes in cotransporters and glial cells

Non-synaptic mechanisms are being considered the common factor of brain damage in status epilepticus and alcohol intoxication. The present work reports the influence of the chronic use of ethanol on epileptic processes sustained by non-synaptic mechanisms. Adult male Wistar rats administered with ethanol (1, 2 e 3 g/kg/d) during 28 days were compared with Control. Non-synaptic epileptiform activities (NEAs) were induced by means of the zero-calcium and high-potassium model using hippocampal slices. The observed involvement of the dentate gyrus (DG) on the neurodegeneration promoted by ethanol motivated the monitoring of the electrophysiological activity in this region. The DG regions were analyzed for the presence of NKCC1, KCC2, GFAP and CD11b immunoreactivity and cell density. The treated groups showed extracellular potential measured at the granular layer with increased DC shift and population spikes (PS), which was remarkable for the group E1. The latencies to the NEAs onset were more prominent also for the treated groups, being correlated with the neuronal loss. In line with these findings were the predispositions of the treated slices for neuronal edema after NEAs induction, suggesting that restrict inter-cell space counteracts the neuronal loss and subsists the hyper-synchronism. The significant increase of the expressions of NKCC1 and CD11b for the treated groups confirms the existence of conditions favorable to the observed edematous necrosis. The data suggest that the ethanol consumption promotes changes on the non-synaptic mechanisms modulating the NEAs. For the lower ethanol dosage the neurophysiological changes were more effective suggesting to be due to the less intense neurodegenertation.

Effect of co-transporter blockers on non-synaptic epileptiform activity-computational simulation

The important role of cation-chloride co-transporters in epilepsy is being supported by an increasing number of investigations. However, enormous complexity is involved since the action of these co-transporters has effects on the ionic homeostasis influencing directly the neuronal excitability and the tissue propensity to sustain seizure. To unravel the complex mechanisms involving the co-transporters action during seizure, this paper shows simulations of non-synaptic epileptiform activity and the effect of the blockage of the two different types of cation-chloride co-transporters present in the brain: Na, K and 2Cl co-transporter (NKCC) and K and Cl co-transporter (KCC). The simulations were performed with an electrochemical model representing the non-synaptic structure of the granule cell layer of the dentate gyrus (DG) of the rat hippocampus. The simulations suggest: (i) the potassium clearance is based on the systemic interplay between the Na/K pump and the NKCC co-transporters; (ii) the simultaneous blockage of the NKCC of the neurons and KCC of glial cells acts efficiently suppressing the epileptiform activities; and (iii) the simulations show that depending on the combined blockage of the co-transporters, the epileptiform activities may be suppressed or enhanced.

Enhanced synaptic connectivity in the dentate gyrus during epileptiform activity: network simulation

Structural rearrangement of the dentate gyrus has been described as the underlying cause of many types of epilepsies, particularly temporal lobe epilepsy. It is said to occur when aberrant connections are established in the damaged hippocampus, as described in human epilepsy and experimental models. Computer modelling of the dentate gyrus circuitry and the corresponding structural changes has been used to understand how abnormal mossy fibre sprouting can subserve seizure generation observed in experimental models when epileptogenesis is induced by status epilepticus. The model follows the McCulloch-Pitts formalism including the representation of the nonsynaptic mechanisms. The neuronal network comprised granule cells, mossy cells, and interneurons. The compensation theory and the Hebbian and anti-Hebbian rules were used to describe the structural rearrangement including the effects of the nonsynaptic mechanisms on the neuronal activity. The simulations were based on neuroanatomic data and on the connectivity pattern between the cells represented. The results suggest that there is a joint action of the compensation theory and Hebbian rules during the inflammatory process that accompanies the status epilepticus. The structural rearrangement simulated for the dentate gyrus circuitry promotes speculation about the formation of the abnormal mossy fiber sprouting and its role in epileptic seizures.

Changes of paired-pulse evoked responses during the development of epileptic activity in the hippocampus

Dysfunction of inhibitory synaptic transmission can destroy the balance between excitatory and inhibitory synaptic inputs in neurons, thereby inducing epileptic activity. The aim of the paper is to investigate the effects of successive excitatory inputs on the epileptic activity induced in the absence of inhibitions. Paired-pulse orthodromic and antidromic stimulations were used to test the changes in the evoked responses in the hippocampus. Picrotoxin (PTX), γ-aminobutyric acid (GABA) type A (GABA(A)) receptor antagonist, was added to block the inhibitory synaptic transmission and to establish the epileptic model. Extracellular evoked population spike (PS) was recorded in the CA1 region of the hippocampus. The results showed that the application of PTX induced a biphasic change in the paired-pulse ratio of PS amplitude. A short latency increase of the second PS (PS2) was later followed by a reappearance of PS2 depression. This type of depression was observed in both orthodromic and antidromic paired-pulse responses, whereas the GABAergic PS2 depression [called paired-pulse depression (PPD)] during baseline recordings only appeared in orthodromic-evoked responses. In addition, the depression duration at approximately 100 ms was consistent with a relative silent period observed within spontaneous burst discharges induced by prolonged application of PTX. In conclusion, the neurons may ignore the excitatory inputs and intrinsically generate bursts during epileptic activity. The depolarization block could be the mechanisms underlying the PPD in the absence of GABA(A) inhibitions. The distinct neuronal responses to stimulations during different epileptic stages may implicate the different antiepileptic effects of electrical stimulation.

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.

The role of extracellular potassium dynamics in the different stages of ictal bursting and spreading depression: a computational study

Experimental evidences point out the participation of nonsynaptic mechanisms (e.g., fluctuations in extracellular ions) in epileptiform bursting and spreading depression (SD). During these abnormal oscillatory patterns, it is observed an increase of extracellular potassium concentration [K(+)](o) and a decrease of extracellular calcium concentration [Ca(2+)](o) which raises the neuronal excitability. However, whether the high [K(+)](o) triggers and propagates these abnormal neuronal activities or plays a secondary role into this process is unclear. To better understand the influence of extracellular potassium dynamics in these oscillatory patterns, the experimental conditions of high [K(+)](o) and zero [Ca(2+)](o) were replicated in an extended Golomb model where we added important regulatory mechanisms of ion concentration as Na(+)-K(+) pump, ion diffusion and glial buffering. Within these conditions, simulations of the cell model exhibit seizure-like discharges (ictal bursting). The SD was elicited by the interruption of the Na(+)-K(+) pump activity, mimicking the effect of cellular hypoxia (an experimental protocol to elicit SD, the hypoxia-induced SD). We used the bifurcation theory and the fast-slow method to analyze the interference of K(+) dynamics in the cellular excitability. This analysis indicates that the system loses its stability at a high [K(+)](o), transiting to an elevated state of neuronal excitability. Effects of high [K(+)](o) are observed in different stages of ictal bursting and SD. In the initial stage, the increase of [K(+)](o) creates favorable conditions to trigger both oscillatory patterns. During the neuronal activity, a continuous growth of [K(+)](o) by outward K(+) flow depresses K(+) currents in a positive feedback way. At the last stage, due to the depression of K(+) currents, the Na(+)-K(+) pump is the main mechanism in the end of neuronal activity. Thus, this work suggests that [K(+)](o) dynamics may play a fundamental role in these abnormal oscillatory patterns.