The influence of depolarization block on seizure-like activity in networks of excitatory and inhibitory neurons

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.

Parvalbumin Interneuron Impairment Leads to Synaptic Transmission Deficits and Seizures in SCN8A Epileptic Encephalopathy

SCN8A epileptic encephalopathy (EE) is a severe epilepsy syndrome resulting from de novo mutations in the voltage-gated sodium channel Na v 1.6, encoded by the gene SCN8A . Na v 1.6 is expressed in both excitatory and inhibitory neurons, yet previous studies have primarily focused on the impact SCN8A mutations have on excitatory neuron function, with limited studies on the importance of inhibitory interneurons to seizure onset and progression. Inhibitory interneurons are critical in balancing network excitability and are known to contribute to the pathophysiology of other epilepsies. Parvalbumin (PV) interneurons are the most prominent inhibitory neuron subtype in the brain, making up about 40% of inhibitory interneurons. Notably, PV interneurons express high levels of Na v 1.6. To assess the role of PV interneurons within SCN8A EE, we used two mouse models harboring patient-derived SCN8A gain-of-function mutations, Scn8a D/+ , where the SCN8A mutation N1768D is expressed globally, and Scn8a W/+ -PV, where the SCN8A mutation R1872W is selectively expressed in PV interneurons. Expression of the R1872W SCN8A mutation selectively in PV interneurons led to the development of spontaneous seizures in Scn8a W/+ -PV mice and seizure-induced death, decreasing survival compared to wild-type. Electrophysiology studies showed that PV interneurons in Scn8a D/+ and Scn8a W/+ -PV mice were susceptible to depolarization block, a state of action potential failure. Scn8a D/+ and Scn8a W/+ -PV interneurons also exhibited increased persistent sodium current, a hallmark of SCN8A gain-of-function mutations that contributes to depolarization block. Evaluation of synaptic connections between PV interneurons and pyramidal cells showed an increase in synaptic transmission failure at high frequencies (80-120Hz) as well as an increase in synaptic latency in Scn8a D/+ and Scn8a W/+ -PV interneurons. These data indicate a distinct impairment of synaptic transmission in SCN8A EE, potentially decreasing overall cortical network inhibition. Together, our novel findings indicate that failure of PV interneuron spiking via depolarization block along with frequency-dependent inhibitory synaptic impairment likely elicits an overall reduction in the inhibitory drive in SCN8A EE, leading to unchecked excitation and ultimately resulting in seizures and seizure-induced death.

Idealized multiple-timescale model of cortical spreading depolarization initiation and pre-epileptic hyperexcitability caused by NaV1.1/SCN1A mutations

Na_V1.1 (SCN1A) is a voltage-gated sodium channel mainly expressed in GABAergic neurons. Loss of function mutations of Na_V1.1 lead to epileptic disorders, while gain of function mutations cause a migraine in which cortical spreading depolarizations (CSDs) are involved. It is still debated how these opposite effects initiate two different manifestations of neuronal hyperactivity: epileptic seizures and CSD. To investigate this question, we previously built a conductance-based model of two neurons (GABAergic and pyramidal), with dynamic ion concentrations (Lemaire et al. in PLoS Comput Biol 17(7):e1009239, 2021. https://doi.org/10.1371/journal.pcbi.1009239 ). When implementing either Na_V1.1 migraine or epileptogenic mutations, ion concentration modifications acted as slow processes driving the system to the corresponding pathological firing regime. However, the large dimensionality of the model complicated the exploitation of its implicit multi-timescale structure. Here, we substantially simplify our biophysical model to a minimal version more suitable for bifurcation analysis. The explicit timescale separation allows us to apply slow-fast theory, where slow variables are treated as parameters in the fast singular limit. In this setting, we reproduce both pathological transitions as dynamic bifurcations in the full system. In the epilepsy condition, we shift the spike-terminating bifurcation to lower inputs for the GABAergic neuron, to model an increased susceptibility to depolarization block. The resulting failure of synaptic inhibition triggers hyperactivity of the pyramidal neuron. In the migraine scenario, spiking-induced release of potassium leads to the abrupt increase of the extracellular potassium concentration. This causes a dynamic spike-terminating bifurcation of both neurons, which we interpret as CSD initiation.

Modeling NaV1.1/SCN1A sodium channel mutations in a microcircuit with realistic ion concentration dynamics suggests differential GABAergic mechanisms leading to hyperexcitability in epilepsy and hemiplegic migraine

Loss of function mutations of SCN1A, the gene coding for the voltage-gated sodium channel Na_V1.1, cause different types of epilepsy, whereas gain of function mutations cause sporadic and familial hemiplegic migraine type 3 (FHM-3). However, it is not clear yet how these opposite effects can induce paroxysmal pathological activities involving neuronal networks’ hyperexcitability that are specific of epilepsy (seizures) or migraine (cortical spreading depolarization, CSD). To better understand differential mechanisms leading to the initiation of these pathological activities, we used a two-neuron conductance-based model of interconnected GABAergic and pyramidal glutamatergic neurons, in which we incorporated ionic concentration dynamics in both neurons. We modeled FHM-3 mutations by increasing the persistent sodium current in the interneuron and epileptogenic mutations by decreasing the sodium conductance in the interneuron. Therefore, we studied both FHM-3 and epileptogenic mutations within the same framework, modifying only two parameters. In our model, the key effect of gain of function FHM-3 mutations is ion fluxes modification at each action potential (in particular the larger activation of voltage-gated potassium channels induced by the Na_V1.1 gain of function), and the resulting CSD-triggering extracellular potassium accumulation, which is not caused only by modifications of firing frequency. Loss of function epileptogenic mutations, on the other hand, increase GABAergic neurons’ susceptibility to depolarization block, without major modifications of firing frequency before it. Our modeling results connect qualitatively to experimental data: potassium accumulation in the case of FHM-3 mutations and facilitated depolarization block of the GABAergic neuron in the case of epileptogenic mutations. Both these effects can lead to pyramidal neuron hyperexcitability, inducing in the migraine condition depolarization block of both the GABAergic and the pyramidal neuron. Overall, our findings suggest different mechanisms of network hyperexcitability for migraine and epileptogenic Na_V1.1 mutations, implying that the modifications of firing frequency may not be the only relevant pathological mechanism.

The voltage-gated sodium channel Na_V1.1 is a major target of human mutations implicated in different pathologies. In particular, mutations identified in certain types of epilepsy cause loss of function of the channel, whereas mutations identified in certain types of migraine (in which spreading depolarizations of the cortical circuits of the brain are involved) cause instead gain of function. Here, we study dysfunctions induced by these differential effects in a two-neuron (GABAergic and pyramidal) conductance-based model with dynamic ion concentrations. We obtain results that can be related to experimental findings in both situations. Namely, extracellular potassium accumulation induced by the activity of the GABAergic neuron in the case of CSD, and higher propensity of the GABAergic neuron to depolarization block in the epileptogenic scenario, without significant modifications of its firing frequency prior to it. Both scenarios can induce hyperexcitability of the pyramidal neuron, leading in the migraine condition to depolarization block of both the GABAergic and the pyramidal neuron. Our results are successfully confronted to experimental data and suggest that modification of firing frequency is not the only key mechanism in these pathologies of neuronal excitability.

Gut metabolite S-equol ameliorates hyperexcitability in entorhinal cortex neurons following Theiler murine encephalomyelitis virus-induced acute seizures

Objective

A growing body of evidence indicates a potential role for the gut–brain axis as a novel therapeutic target in treating seizures. The present study sought to characterize the gut microbiome in Theiler murine encephalomyelitis virus (TMEV)‐induced seizures, and to evaluate the effect of microbial metabolite S‐equol on neuronal physiology as well as TMEV‐induced neuronal hyperexcitability ex vivo.

Methods

We infected C57BL/6J mice with TMEV and monitored the development of acute behavioral seizures 0–7 days postinfection (dpi). Fecal samples were collected at 5–7 dpi and processed for 16S sequencing, and bioinformatics were performed with QIIME2. Finally, we conducted whole‐cell patch‐clamp recordings in cortical neurons to investigate the effect of exogenous S‐equol on cell intrinsic properties and neuronal hyperexcitability.

Results

We demonstrated that gut microbiota diversity is significantly altered in TMEV‐infected mice at 5–7 dpi, exhibiting separation in beta diversity in TMEV‐infected mice dependent on seizure phenotype, and lower abundance of genus Allobaculum in TMEV‐infected mice regardless of seizure phenotype. In contrast, we identified specific loss of S‐equol‐producing genus Adlercreutzia as a microbial hallmark of seizure phenotype following TMEV infection. Electrophysiological recordings indicated that exogenous S‐equol alters cortical neuronal physiology. We found that entorhinal cortex neurons are hyperexcitable in TMEV‐infected mice, and exogenous application of microbial‐derived S‐equol ameliorated this TMEV‐induced hyperexcitability.

Significance

Our study presents the first evidence of microbial‐derived metabolite S‐equol as a potential mechanism for alteration of TMEV‐induced neuronal excitability. These findings provide new insight for the novel role of S‐equol and the gut–brain axis in epilepsy treatment.

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.

Glioma-induced peritumoral hyperexcitability in a pediatric glioma model

Epileptic seizures are among the most common presenting symptom in patients with glioma. The etiology of glioma-related seizures is complex and not completely understood. Studies using adult glioma patient tissue and adult glioma mouse models, show that neurons adjacent to the tumor mass, peritumoral neurons, are hyperexcitable and contribute to seizures. Although it is established that there are phenotypic and genotypic distinctions in gliomas from adult and pediatric patients, it is unknown whether these established differences in pediatric glioma biology and the microenvironment in which these glioma cells harbor, the developing brain, differentially impacts surrounding neurons. In the present study, we examine the effect of patient-derived pediatric glioma cells on the function of peritumoral neurons using two pediatric glioma models. Pediatric glioma cells were intracranially injected into the cerebrum of postnatal days 2 and 3 (p2/3) mouse pups for 7 days. Electrophysiological recordings showed that cortical layer 2/3 peritumoral neurons exhibited significant differences in their intrinsic properties compared to those of sham control neurons. Peritumoral neurons fired significantly more action potentials in response to smaller current injection and exhibited a depolarization block in response to higher current injection. The threshold for eliciting an action potential and pharmacologically induced epileptiform activity was lower in peritumoral neurons compared to sham. Our findings suggest that pediatric glioma cells increase excitability in the developing peritumoral neurons by exhibiting early onset of depolarization block, which was not previously observed in adult glioma peritumoral neurons.

Dynamical mesoscale model of absence seizures in genetic models

A mesoscale network model is proposed for the development of spike and wave discharges (SWDs) in the cortico-thalamo-cortical (C-T-C) circuit. It is based on experimental findings in two genetic models of childhood absence epilepsy–rats of WAG/Rij and GAERS strains. The model is organized hierarchically into two levels (brain structures and individual neurons) and composed of compartments for representation of somatosensory cortex, reticular and ventroposteriomedial thalamic nuclei. The cortex and the two thalamic compartments contain excitatory and inhibitory connections between four populations of neurons. Two connected subnetworks both including relevant parts of a C-T-C network responsible for SWD generation are modelled: a smaller subnetwork for the focal area in which the SWD generation can take place, and a larger subnetwork for surrounding areas which can be only passively involved into SWDs, but which is mostly responsible for normal brain activity. This assumption allows modeling of both normal and SWD activity as a dynamical system (no noise is necessary), providing reproducibility of results and allowing future analysis by means of theory of dynamical system theories. The model is able to reproduce most time-frequency changes in EEG activity accompanying the transition from normal to epileptiform activity and back. Three different mechanisms of SWD initiation reported previously in experimental studies were successfully reproduced in the model. The model incorporates also a separate mechanism for the maintenance of SWDs based on coupling analysis from experimental data. Finally, the model reproduces the possibility to stop ongoing SWDs with high frequency electrical stimulation, as described in the literature.

A mean-field approach to the dynamics of networks of complex neurons, from nonlinear Integrate-and-Fire to Hodgkin-Huxley models

We present a mean-field formalism able to predict the collective dynamics of large networks of conductance-based interacting spiking neurons. We apply this formalism to several neuronal models, from the simplest Adaptive Exponential Integrate-and-Fire model to the more complex Hodgkin-Huxley and Morris-Lecar models. We show that the resulting mean-field models are capable of predicting the correct spontaneous activity of both excitatory and inhibitory neurons in asynchronous irregular regimes, typical of cortical dynamics. Moreover, it is possible to quantitatively predict the population response to external stimuli in the form of external spike trains. This mean-field formalism therefore provides a paradigm to bridge the scale between population dynamics and the microscopic complexity of the individual cells physiology.NEW & NOTEWORTHY Population models are a powerful mathematical tool to study the dynamics of neuronal networks and to simulate the brain at macroscopic scales. We present a mean-field model capable of quantitatively predicting the temporal dynamics of a network of complex spiking neuronal models, from Integrate-and-Fire to Hodgkin-Huxley, thus linking population models to neurons electrophysiology. This opens a perspective on generating biologically realistic mean-field models from electrophysiological recordings.

Altered hippocampal interneuron activity precedes ictal onset

Although failure of GABAergic inhibition is a commonly hypothesized mechanism underlying seizure disorders, the series of events that precipitate a rapid shift from healthy to ictal activity remain unclear. Furthermore, the diversity of inhibitory interneuron populations poses a challenge for understanding local circuit interactions during seizure initiation. Using a combined optogenetic and electrophysiological approach, we examined the activity of identified mouse hippocampal interneuron classes during chemoconvulsant seizure induction in vivo. Surprisingly, synaptic inhibition from parvalbumin- (PV) and somatostatin-expressing (SST) interneurons remained intact throughout the preictal period and early ictal phase. However, these two sources of inhibition exhibited cell-type-specific differences in their preictal firing patterns and sensitivity to input. Our findings suggest that the onset of ictal activity is not associated with loss of firing by these interneurons or a failure of synaptic inhibition but is instead linked with disruptions of the respective roles these interneurons play in the hippocampal circuit.

Minimal model of interictal and ictal discharges "Epileptor-2"

Seizures occur in a recurrent manner with intermittent states of interictal and ictal discharges (IIDs and IDs). The transitions to and from IDs are determined by a set of processes, including synaptic interaction and ionic dynamics. Although mathematical models of separate types of epileptic discharges have been developed, modeling the transitions between states remains a challenge. A simple generic mathematical model of seizure dynamics (Epileptor) has recently been proposed by Jirsa et al. (2014); however, it is formulated in terms of abstract variables. In this paper, a minimal population-type model of IIDs and IDs is proposed that is as simple to use as the Epileptor, but the suggested model attributes physical meaning to the variables. The model is expressed in ordinary differential equations for extracellular potassium and intracellular sodium concentrations, membrane potential, and short-term synaptic depression variables. A quadratic integrate-and-fire model driven by the population input current is used to reproduce spike trains in a representative neuron. In simulations, potassium accumulation governs the transition from the silent state to the state of an ID. Each ID is composed of clustered IID-like events. The sodium accumulates during discharge and activates the sodium-potassium pump, which terminates the ID by restoring the potassium gradient and thus polarizing the neuronal membranes. The whole-cell and cell-attached recordings of a 4-AP-based in vitro model of epilepsy confirmed the primary model assumptions and predictions. The mathematical analysis revealed that the IID-like events are large-amplitude stochastic oscillations, which in the case of ID generation are controlled by slow oscillations of ionic concentrations. The IDs originate in the conditions of elevated potassium concentrations in a bath solution via a saddle-node-on-invariant-circle-like bifurcation for a non-smooth dynamical system. By providing a minimal biophysical description of ionic dynamics and network interactions, the model may serve as a hierarchical base from a simple to more complex modeling of seizures.

In pathological conditions of epilepsy, the functioning of the neural network crucially depends on the ionic concentrations inside and outside neurons. A number of factors that affect neuronal activity is large. That is why the development of a minimal model that reproduces typical seizures could structure further experimental and analytical studies of the pathological mechanisms. Here, on a base of known biophysical models, we present a simple population-type model that includes only four principal variables, the extracellular potassium concentration, the intracellular sodium concentration, the membrane potential and the synaptic resource diminishing due to short-term synaptic depression. A simple modeled neuron is used as an observer of the population activity. We validate the model assumptions with in vitro experiments. Our model reproduces ictal and interictal events, where the latter result in bursts of spikes in single neurons, and the former represent the cluster of spike bursts. Mathematical analysis reveals that the bursts are spontaneous large-amplitude oscillations, which may cluster after a saddle-node on invariant circle bifurcation in the pro-epileptic conditions. Our consideration has significant bearing in understanding pathological neuronal network dynamics.