The influence of potassium concentration on epileptic seizures in a coupled neuronal model in the hippocampus

The neuronal and synaptic dynamics underlying post-inhibitory rebound burst related to major depressive disorder in the lateral habenula neuron model

A burst behavior observed in the lateral habenula (LHb) neuron related to major depressive disorder has attracted much attention. The burst is induced from silence by the excitatory N-methyl-D-aspartate (NMDA) synapse or by the inhibitory stimulation, i.e., a post-inhibitory rebound (PIR) burst, which has not been explained clearly. In the present paper, the neuronal and synaptic dynamics for the PIR burst are acquired in a theoretical neuron model. At first, dynamic cooperations between the fast rise of inhibitory γ-aminobutyric acid (GABA) synapse, slow rise of NMDA synapse, and T-type calcium current to evoke the PIR burst are obtained. Similar to the inhibitory pulse stimulation, fast rising GABA current can reduce the membrane potential to a level low enough to de-inactivate the low threshold T-type calcium current to evoke a PIR spike, which can enhance the slow rising NMDA current activated at a time before or after the PIR spike. The NMDA current following the PIR spike exhibits slow decay to induce multiple spikes to form the PIR burst. Such results present a theoretical explanation and a candidate for the PIR burst in real LHb neurons. Then, the dynamical mechanism for the PIR spike mediated by the T-type calcium channel is obtained. At large conductance of T-type calcium channel, the resting state corresponds to a stable focus near Hopf bifurcation and exhibits an "uncommon" threshold curve with membrane potential much lower than the resting membrane potential. Inhibitory modulation induces membrane potential decreased to run across the threshold curve to evoke the PIR spike. At small conductance of the T-type calcium channel, a stable node appears and manifests a common threshold curve with higher membrane potential, resulting in non-PIR phenomenon. The results present the dynamic cooperations between neuronal dynamics and fast/slow dynamics of different synapses for the PIR burst observed in the LHb neuron, which is helpful for the modulations to major depressive disorder.

The effect of ferroptosis-related mitochondrial dysfunction in the development of temporal lobe epilepsy

Temporal lobe epilepsy (TLE) is the most common form of epileptic syndrome. It has been established that due to its complex pathogenesis, a considerable proportion of TLE patients often progress to drug-resistant epilepsy. Ferroptosis has emerged as an important neuronal death mechanism in TLE, which is primarily influenced by lipid accumulation and oxidative stress. In previous studies of ferroptosis, more attention has been focused on the impact of changes in the levels of proteins related to the redox equilibrium and signaling pathways on epileptic seizures. However, it is worth noting that the oxidative-reduction changes in different organelles may have different pathophysiological significance in the process of ferroptosis-related diseases. Mitochondria, as a key organelle involved in ferroptosis, its structural damage and functional impairment can lead to energy metabolism disorders and disruption of the excitatory inhibitory balance, significantly increasing the susceptibility to epileptic seizures. Therefore, secondary mitochondrial dysfunction in the process of ferroptosis could play a crucial role in TLE pathogenesis. This review focuses on ferroptosis and mitochondria, discussing the pathogenic role of ferroptosis-related mitochondrial dysfunction in TLE, thus aiming to provide novel insights and potential implications of ferroptosis-related secondary mitochondrial dysfunction in epileptic seizures and to offer new insights for the precise exploration of ferroptosis-related therapeutic targets for TLE patients.

Examining the low-voltage fast seizure-onset and its response to optogenetic stimulation in a biophysical network model of the hippocampus

Low-voltage fast (LVF) seizure-onset is one of the two frequently observed temporal lobe seizure-onset patterns. Depth electroencephalogram profile analysis illustrated that the peak amplitude of LVF onset was deep temporal areas, e.g., hippocampus. However, the specific dynamic transition mechanisms between normal hippocampal rhythmic activity and LVF seizure-onset remain unclear. Recently, the optogenetic approach to gain control over epileptic hyper-excitability both in vitro and in vivo has become a novel noninvasive modulation strategy. Here, we combined biophysical modeling to study LVF dynamics following changes in crucial physiological parameters, and investigated the potential optogenetic intervention mechanism for both excitatory and inhibitory control. In an Ammon's horn 3 (CA3) biophysical model with light-sensitive protein channelrhodopsin 2 (ChR2), we found that the cooperative effects of excessive extracellular potassium concentration of parvalbumin-positive (PV+) inhibitory interneurons and synaptic links could induce abundant types of discharges of the hippocampus, and lead to transitions from gamma oscillations to LVF seizure-onset. Simulations of optogenetic stimulation revealed that the LVF seizure-onset and morbid fast spiking could not be eliminated by targeting PV+ neurons, whereas the epileptic network was more sensitive to the excitatory control of principal neurons with strong optogenetic currents. We illustrate that in the epileptic hippocampal network, the trajectories of the normal and the seizure state are in close vicinity and optogenetic perturbations therefore may result in transitions. The network model system developed in this study represents a scientific instrument to disclose the underlying principles of LVF, to characterize the effects of optogenetic neuromodulation, and to guide future treatment for specific types of seizures.

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.

Complex spiking neural networks with synaptic time-delay based on anti-interference function

The research on a brain-like model with bio-interpretability is conductive to promoting its information processing ability in the field of artificial intelligence. Biological results show that the synaptic time-delay can improve the information processing abilities of the nervous system, which are an important factor related to the formation of brain cognitive functions. However, the synaptic plasticity with time-delay of a brain-like model still lacks bio-interpretability. In this study, combining excitatory and inhibitory synapses, we construct the complex spiking neural networks (CSNNs) with synaptic time-delay that more conforms biological characteristics, in which the topology has scale-free property and small-world property, and the nodes are represented by an Izhikevich neuron model. Then, the information processing abilities of CSNNs with different types of synaptic time-delay are comparatively evaluated based on the anti-interference function, and the mechanism of this function is discussed. Using two indicators of the anti-interference function and three kinds of noise, our simulation results consistently verify that: (i) From the perspective of anti-interference function, an CSNN with synaptic random time-delay outperforms an CSNN with synaptic fixed time-delay, which in turn outperforms an CSNN with synaptic none time-delay. The results imply that brain-like networks with more bio-interpretable synaptic time-delay have stronger information processing abilities. (ii) The synaptic plasticity is the intrinsic factor of the anti-interference function of CSNNs with different types of synaptic time-delay. (iii) The synaptic random time-delay makes an CSNN present better topological characteristics, which can improve the information processing ability of a brain-like network. It implies that synaptic time-delay is a factor that affects the anti-interference function at the level of performance.

Adiabatic dynamic causal modelling

This technical note introduces adiabatic dynamic causal modelling, a method for inferring slow changes in biophysical parameters that control fluctuations of fast neuronal states. The application domain we have in mind is inferring slow changes in variables (e.g., extracellular ion concentrations or synaptic efficacy) that underlie phase transitions in brain activity (e.g., paroxysmal seizure activity). The scheme is efficient and yet retains a biophysical interpretation, in virtue of being based on established neural mass models that are equipped with a slow dynamic on the parameters (such as synaptic rate constants or effective connectivity). In brief, we use an adiabatic approximation to summarise fast fluctuations in hidden neuronal states (and their expression in sensors) in terms of their second order statistics; namely, their complex cross spectra. This allows one to specify and compare models of slowly changing parameters (using Bayesian model reduction) that generate a sequence of empirical cross spectra of electrophysiological recordings. Crucially, we use the slow fluctuations in the spectral power of neuronal activity as empirical priors on changes in synaptic parameters. This introduces a circular causality, in which synaptic parameters underwrite fast neuronal activity that, in turn, induces activity-dependent plasticity in synaptic parameters. In this foundational paper, we describe the underlying model, establish its face validity using simulations and provide an illustrative application to a chemoconvulsant animal model of seizure activity.

Dynamic Transitions in Neuronal Network Firing Sustained by Abnormal Astrocyte Feedback

Astrocytes play a crucial role in neuronal firing activity. Their abnormal state may lead to the pathological transition of neuronal firing patterns and even induce seizures. However, there is still little evidence explaining how the astrocyte network modulates seizures caused by structural abnormalities, such as gliosis. To explore the role of gliosis of the astrocyte network in epileptic seizures, we first established a direct astrocyte feedback neuronal network model on the basis of the hippocampal CA3 neuron-astrocyte model to simulate the condition of gliosis when astrocyte processes swell and the feedback to neurons increases in an abnormal state. We analyzed the firing pattern transitions of the neuronal network when astrocyte feedback starts to change via increases in both astrocyte feedback intensity and the connection probability of astrocytes to neurons in the network. The results show that as the connection probability and astrocyte feedback intensity increase, neuronal firing transforms from a nonepileptic synchronous firing state to an asynchronous firing state, and when astrocyte feedback starts to become abnormal, seizure-like firing becomes more severe and synchronized; meanwhile, the synchronization area continues to expand and eventually transforms into long-term seizure-like synchronous firing. Therefore, our results prove that astrocyte feedback can regulate the firing of the neuronal network, and when the astrocyte network develops gliosis, there will be an increase in the induction rate of epileptic seizures.

Temporal phenotyping for transitional disease progress: An application to epilepsy and Alzheimer's disease

Complicated multifactorial diseases deteriorate from one disease to other diseases. For example, existing studies consider Alzheimer's disease (AD) a comorbidity of epilepsy, but also recognize epilepsy to occur more frequently in patients with AD than those without. It is important to understand the progress of disease that deteriorates to severe diseases. To this end, we develop a transitional phenotyping method based on both longitudinal and cross-sectional relationships between diseases and/or medications. For a cross-sectional approach, we utilized a skip-gram model to represent co-occurred disease or medication. For a longitudinal approach, we represented each patient as a transition probability between medical events and used supervised tensor factorization to decompose into groups of medical events that develop together. Then we harmonized both information to derive high-risk transitional patterns. We applied our method to disease progress from epilepsy to AD. An epilepsy-AD cohort of 600,000 patients were extracted from Cerner Health Facts data. Our experimental results suggested a causal relationship between epilepsy and later onset of AD, and also identified five epilepsy subgroups with distinct phenotypic patterns leading to AD. While such findings are preliminary, the proposed method combining representation learning with tensor factorization seems to be an effective approach for risk factor analysis.

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

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

Candidate Genes Associated with Delayed Neuropsychomotor Development and Seizures in a Patient with Ring Chromosome 20

Ring chromosome 20 (r20) is characterized by intellectual impairment, behavioral disorders, and refractory epilepsy. We report a patient presenting nonmosaic ring chromosome 20 followed by duplication and deletion in 20q13.33 with seizures, delayed neuropsychomotor development and language, mild hypotonia, low weight gain, and cognitive deficit. Chromosomal microarray analysis (CMA) enabled us to restrict a chromosomal segment and thus integrate clinical and molecular data with systems biology. With this approach, we were able to identify candidate genes that may help to explain the consequences of deletions in 20q13.33. In our analysis, we observed five hubs (ARFGAP1, HELZ2, COL9A3, PTK6, and EEF1A2), seven bottlenecks (CHRNA4, ARFRP1, GID8, COL9A3, PTK6, ZBTB46, and SRMS), and two H-B nodes (PTK6 and COL9A3). The candidate genes may play an important role in the developmental delay and seizures observed in r20 patients. Gene ontology included microtubule-based movement, nucleosome assembly, DNA repair, and cholinergic synaptic transmission. Defects in these bioprocesses are associated with the development of neurological diseases, intellectual disability, neuropathies, and seizures. Therefore, in this study, we can explore molecular cytogenetic data, identify proteins through network analysis of protein-protein interactions, and identify new candidate genes associated with the main clinical findings in patients with 20q13.33 deletions.

Astrocytic modulation of potassium under seizures

The contribution of an impaired astrocytic K⁺ regulation system to epileptic neuronal hyperexcitability has been increasingly recognized in the last decade. A defective K⁺ regulation leads to an elevated extracellular K⁺ concentration ([K⁺]_o). When [K⁺]_o reaches peaks of 10-12 mM, it is strongly associated with seizure initiation during hypersynchronous neuronal activities. On the other hand, reactive astrocytes during a seizure attack restrict influx of K⁺ across the membrane both passively and actively. In addition to decreased K⁺ buffering, aberrant Ca²⁺ signaling and declined glutamate transport have also been observed in astrogliosis in epileptic specimens, precipitating an increased neuronal discharge and induction of seizures. This review aims to provide an overview of experimental findings that implicated astrocytic modulation of extracellular K⁺ in the mechanism of epileptogenesis.

Nucleic Acid Aptamers for Molecular Therapy of Epilepsy and Blood-Brain Barrier Damages

Epilepsy is the fourth most prevalent brain disorder affecting millions of people of all ages. Epilepsy is divided into six categories different in etiology and molecular mechanisms; however, their common denominator is the inability to maintain ionic homeostasis. Antiepileptic drugs have a broad spectrum of action and high toxicity to the whole organism. In many cases, they could not penetrate the blood-brain barrier (BBB) and reach corresponding targets. Nucleic acid aptamers are a new and promising class of antiepileptic drugs as they are non-toxic, specific, and able to regulate the permeability of ion channels or inhibit inflammatory proteins. In this review, we summarize the mechanisms of epileptogenesis and its interconnection with the BBB and show the potential of aptamers for antiepileptic treatment.

Astrocytic Kir4.1 channels and gap junctions account for spontaneous epileptic seizure

Experimental recordings in hippocampal slices indicate that astrocytic dysfunction may cause neuronal hyper-excitation or seizures. Considering that astrocytes play important roles in mediating local uptake and spatial buffering of K⁺ in the extracellular space of the cortical circuit, we constructed a novel model of an astrocyte-neuron network module consisting of a single compartment neuron and 4 surrounding connected astrocytes and including extracellular potassium dynamics. Next, we developed a new model function for the astrocyte gap junctions, connecting two astrocyte-neuron network modules. The function form and parameters of the gap junction were based on nonlinear regression fitting of a set of experimental data published in previous studies. Moreover, we have created numerical simulations using the above single astrocyte-neuron network module and the coupled astrocyte-neuron network modules. Our model validates previous experimental observations that both Kir4.1 channels and gap junctions play important roles in regulating the concentration of extracellular potassium. In addition, we also observe that changes in Kir4.1 channel conductance and gap junction strength induce spontaneous epileptic activity in the absence of external stimuli.

Astrocytes are critical regulators of normal physiological activity in the central nervous system, and one of their key functions is removing extracellular K⁺. In recent years, numerous biological studies have shown that astrocytic Kir4.1 channels and gap junctions between astrocytes act as major K⁺ clearance mechanisms. Dysfunction of either of these regulatory mechanisms may cause generation of K⁺-induced seizures. However, it is unclear how and to what extent these two K⁺-regulating processes lead to spontaneous epileptic activity. These questions were addressed in the present study by constructing novel single astrocyte-neuron network models and a coupled astrocyte-neuron module network connected by an astrocyte gap junction based on existing experimental observations and previous theoretical reports. Simulation results first verified that either down-regulation of astrocytic Kir4.1 channels or a decrease of the gap junction strength between astrocytes causes neuropathological hyper-excitability and spontaneous epileptic activity. These results imply that dysfunctional astrocytes should be considered as targets for therapeutic strategies in epilepsy.

The Energy Coding of a Structural Neural Network Based on the Hodgkin-Huxley Model

Based on the Hodgkin-Huxley model, the present study established a fully connected structural neural network to simulate the neural activity and energy consumption of the network by neural energy coding theory. The numerical simulation result showed that the periodicity of the network energy distribution was positively correlated to the number of neurons and coupling strength, but negatively correlated to signal transmitting delay. Moreover, a relationship was established between the energy distribution feature and the synchronous oscillation of the neural network, which showed that when the proportion of negative energy in power consumption curve was high, the synchronous oscillation of the neural network was apparent. In addition, comparison with the simulation result of structural neural network based on the Wang-Zhang biophysical model of neurons showed that both models were essentially consistent.

Severe Convulsions and Dysmyelination in Both Jimpy and Cx32/47 -/- Mice may Associate Astrocytic L-Channel Function with Myelination and Oligodendrocytic Connexins with Internodal Kv Channels

The Jimpy mouse illustrates the importance of interactions between astrocytes and oligodendrocytes. It has a mutation in Plp coding for proteolipid protein and DM20. Its behavior is normal at birth but from the age of ~2 weeks it shows severe convulsions associated with oligodendrocyte/myelination deficits and early death. A normally occurring increase in oxygen consumption by highly elevated K+ concentrations is absent in Jimpy brain slices and cultured astrocytes, reflecting that Plp at early embryonic stages affects common precursors as also shown by the ability of conditioned medium from normal astrocytes to counteract histological abnormalities. This metabolic response is now known to reflect opening of L-channels for Ca2+. The resulting deficiency in Ca2+ entry has many consequences, including lack of K+-stimulated glycogenolysis and release of gliotransmitter ATP. Lack of purinergic stimulation compromises oligodendrocyte survival and myelination and affects connexins and K+ channels. Mice lacking the oligodendrocytic connexins Cx32 and 47 show similar neurological dysfunction as Jimpy. This possibly reflects that K+ released by intermodal axonal Kv channels is transported underneath a loosened myelin sheath instead of reaching the extracellular space via connexin-mediated transport to oligodendrocytes, followed by release and astrocytic Na+,K+-ATPase-driven uptake with subsequent Kir4.1-facilitated release and neuronal uptake.

Down-regulated expression of aquaporin-4 in the cerebellum after status epilepticus

Status epilepticus (SE) is a common neurological condition associated with high rates of mortality and permanent brain injury. SE usually leads to neuronal death which may be accompanied by edema, epileptogenesis and learning impairment. Aquaporin-4 (AQP4), is a transmembrane water channel protein in the neuropil of the central nervous system that has an important role in water transport in the brain; AQP4 expression is altered in many pathological conditions such as changes in the blood- brain barrier and/or astrocytic activation, including seizures. AQP4 was shown to be downregulated in the piriform cortex and the hippocampus after SE. Although it is normally expressed at a high level in the cerebellum, little is known about AQP4 levels in the cerebellum following SE. We addressed this in the present study in a mouse model of pilocarpine-induced SE. We found that AQP4 expression was reduced from 3 h to 3 days after SE, with the levels recovering on day 7. Moreover, mice in the acute post-SE stages exhibited impaired motor coordination and learning. These results indicate that cerebellar damage following SE involves changes in AQP4 expression.

Classification of epileptic seizures using wavelet packet log energy and norm entropies with recurrent Elman neural network classifier

Electroencephalogram shortly termed as EEG is considered as the fundamental segment for the assessment of the neural activities in the brain. In cognitive neuroscience domain, EEG-based assessment method is found to be superior due to its non-invasive ability to detect deep brain structure while exhibiting superior spatial resolutions. Especially for studying the neurodynamic behavior of epileptic seizures, EEG recordings reflect the neuronal activity of the brain and thus provide required clinical diagnostic information for the neurologist. This specific proposed study makes use of wavelet packet based log and norm entropies with a recurrent Elman neural network (REN) for the automated detection of epileptic seizures. Three conditions, normal, pre-ictal and epileptic EEG recordings were considered for the proposed study. An adaptive Weiner filter was initially applied to remove the power line noise of 50 Hz from raw EEG recordings. Raw EEGs were segmented into 1 s patterns to ensure stationarity of the signal. Then wavelet packet using Haar wavelet with a five level decomposition was introduced and two entropies, log and norm were estimated and were applied to REN classifier to perform binary classification. The non-linear Wilcoxon statistical test was applied to observe the variation in the features under these conditions. The effect of log energy entropy (without wavelets) was also studied. It was found from the simulation results that the wavelet packet log entropy with REN classifier yielded a classification accuracy of 99.70 % for normal-pre-ictal, 99.70 % for normal-epileptic and 99.85 % for pre-ictal-epileptic.