Computer model of ethosuximide's effect on a thalamic neuron

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.

Modeling Neurotransmission: Computational Tools to Investigate Neurological Disorders

The investigation of synaptic functions remains one of the most fascinating challenges in the field of neuroscience and a large number of experimental methods have been tuned to dissect the mechanisms taking part in the neurotransmission process. Furthermore, the understanding of the insights of neurological disorders originating from alterations in neurotransmission often requires the development of (i) animal models of pathologies, (ii) invasive tools and (iii) targeted pharmacological approaches. In the last decades, additional tools to explore neurological diseases have been provided to the scientific community. A wide range of computational models in fact have been developed to explore the alterations of the mechanisms involved in neurotransmission following the emergence of neurological pathologies. Here, we review some of the advancements in the development of computational methods employed to investigate neuronal circuits with a particular focus on the application to the most diffuse neurological disorders.

Modeling pathogenesis and treatment response in childhood absence epilepsy

OBJECTIVE

Childhood absence epilepsy (CAE) is a genetic generalized epilepsy syndrome with polygenic inheritance, with genes for γ-aminobutyric acid (GABA) receptors and T-type calcium channels implicated in the disorder. Previous studies of T-type calcium channel electrophysiology have shown genetic changes and medications have multiple effects. The aim of this study was to use an established thalamocortical computer model to determine how T-type calcium channels work in concert with cortical excitability to contribute to pathogenesis and treatment response in CAE.

METHODS

The model is comprised of cortical pyramidal, cortical inhibitory, thalamocortical relay, and thalamic reticular single-compartment neurons, implemented with Hodgkin-Huxley model ion channels and connected by AMPA, GABA_A , and GABA_B synapses. Network behavior was simulated for different combinations of T-type calcium channel conductance, inactivation time, steady state activation/inactivation shift, and cortical GABA_A conductance.

RESULTS

Decreasing cortical GABA_A conductance and increasing T-type calcium channel conductance converted spindle to spike and wave oscillations; smaller changes were required if both were changed in concert. In contrast, left shift of steady state voltage activation/inactivation did not lead to spike and wave oscillations, whereas right shift reduced network propensity for oscillations of any type.

SIGNIFICANCE

These results provide a window into mechanisms underlying polygenic inheritance in CAE, as well as a mechanism for treatment effects and failures mediated by these channels. Although the model is a simplification of the human thalamocortical network, it serves as a useful starting point for predicting the implications of ion channel electrophysiology in polygenic epilepsy such as CAE.

Computational modeling of epilepsy for an experimental neurologist

Computational modeling can be a powerful tool for an experimentalist, providing a rigorous mathematical model of the system you are studying. This can be valuable in testing your hypotheses and developing experimental protocols prior to experimenting. This paper reviews models of seizures and epilepsy at different scales, including cellular, network, cortical region, and brain scales by looking at how they have been used in conjunction with experimental data. At each scale, models with different levels of abstraction, the extraction of physiological detail, are presented. Varying levels of detail are necessary in different situations. Physiologically realistic models are valuable surrogates for experimental systems because, unlike in an experiment, every parameter can be changed and every variable can be observed. Abstract models are useful in determining essential parameters of a system, allowing the experimentalist to extract principles that explain the relationship between mechanisms and the behavior of the system. Modeling is becoming easier with the emergence of platforms dedicated to neuronal modeling and databases of models that can be downloaded. Modeling will never be a replacement for animal and clinical experiments, but it should be a starting point in designing experiments and understanding their results.

Computer modelling of epilepsy

Epilepsy is a complex set of disorders that can involve many areas of the cortex, as well as underlying deep-brain systems. The myriad manifestations of seizures, which can be as varied as déjà vu and olfactory hallucination, can therefore give researchers insights into regional functions and relations. Epilepsy is also complex genetically and pathophysiologically: it involves microscopic (on the scale of ion channels and synaptic proteins), macroscopic (on the scale of brain trauma and rewiring) and intermediate changes in a complex interplay of causality. It has long been recognized that computer modelling will be required to disentangle causality, to better understand seizure spread and to understand and eventually predict treatment efficacy. Over the past few years, substantial progress has been made in modelling epilepsy at levels ranging from the molecular to the socioeconomic. We review these efforts and connect them to the medical goals of understanding and treating the disorder.

Interactions between membrane conductances underlying thalamocortical slow-wave oscillations

Neurons of the central nervous system display a broad spectrum of intrinsic electrophysiological properties that are absent in the traditional "integrate-and-fire" model. A network of neurons with these properties interacting through synaptic receptors with many time scales can produce complex patterns of activity that cannot be intuitively predicted. Computational methods, tightly linked to experimental data, provide insights into the dynamics of neural networks. We review this approach for the case of bursting neurons of the thalamus, with a focus on thalamic and thalamocortical slow-wave oscillations. At the single-cell level, intrinsic bursting or oscillations can be explained by interactions between calcium- and voltage-dependent channels. At the network level, the genesis of oscillations, their initiation, propagation, termination, and large-scale synchrony can be explained by interactions between neurons with a variety of intrinsic cellular properties through different types of synaptic receptors. These interactions can be altered by neuromodulators, which can dramatically shift the large-scale behavior of the network, and can also be disrupted in many ways, resulting in pathological patterns of activity, such as seizures. We suggest a coherent framework that accounts for a large body of experimental data at the ion-channel, single-cell, and network levels. This framework suggests physiological roles for the highly synchronized oscillations of slow-wave sleep.

Treatment of typical absence seizures and related epileptic syndromes

Typical absences are brief (seconds) generalised seizures of sudden onset and termination. They have 2 essential components: clinically, the impairment of consciousness (absence) and, generalised 3 to 4Hz spike/polyspike and slow wave discharges on electroencephalogram (EEG). They differ fundamentally from other seizures and are pharmacologically unique. Their clinical and EEG manifestations are syndrome-related. Impairment of consciousness may be severe, moderate, mild or inconspicuous. This is often associated with motor manifestations, automatisms and autonomic disturbances. Clonic, tonic and atonic components alone or in combination are motor symptoms; myoclonia, mainly of facial muscles, is the most common. The ictal EEG discharge may be consistently brief (2 to 5 seconds) or long (15 to 30 seconds), continuous or fragmented, with single or multiple spikes associated with the slow wave. The intradischarge frequency may be constant or may vary (2.5 to 5Hz). Typical absences are easily precipitated by hyperventilation in about 90% of untreated patients. They are usually spontaneous, but can be triggered by photic, pattern, video games stimuli, and mental or emotional factors. Typical absences usually start in childhood or adolescence. They occur in around 10 to 15% of adults with epilepsies, often combined with other generalised seizures. They may remit with age or be lifelong. Syndromic diagnosis is important for treatment strategies and prognosis. Absences may be severe and the only seizure type, as in childhood absence epilepsy. They may predominate in other syndromes or be mild and nonpredominant in syndromes such as juvenile myoclonic epilepsy where myoclonic jerks and generalised tonic clonic seizures are the main concern. Typical absence status epilepticus occurs in about 30% of patients and is more common in certain syndromes, e.g. idiopathic generalised epilepsy with perioral myoclonia or phantom absences. Typical absence seizures are often easy to diagnose and treat. Valproic acid, ethosuximide and lamotrigine, alone or in combination, are first-line therapy. Valproic acid controls absences in 75% of patients and also GTCS (70%) and myoclonic jerks (75%); however, it may be undesirable for some women. Similarly, lamotrigine may control absences and GTCS in possibly 50 to 60% of patients, but may worsen myoclonic jerks; skin rashes are common. Ethosuximide controls 70% of absences, but it is unsuitable as monotherapy if other generalised seizures coexist. A combination of any of these 3 drugs may be needed for resistant cases. Low dosages of lamotrigine added to valproic acid may have a dramatic beneficial effect. Clonazepam, particularly in absences with myoclonic components, and acetazolamide may be useful adjunctive drugs.

Why do we sleep?

Slow-wave sleep consists in slowly recurring waves that are associated with a large-scale spatio-temporal synchrony across neocortex. These slow-wave complexes alternate with brief episodes of fast oscillations, similar to the sustained fast oscillations that occur during the wake state. We propose that alternating fast and slow waves consolidate information acquired previously during wakefulness. Slow-wave sleep would thus begin with spindle oscillations that open molecular gates to plasticity, then proceed by iteratively 'recalling' and 'storing' information primed in neural assemblies. This scenario provides a biophysical mechanism consistent with the growing evidence that sleep serves to consolidate memories.

The NEURON simulation environment

The moment-to-moment processing of information by the nervous system involves the propagation and interaction of electrical and chemical signals that are distributed in space and time. Biologically realistic modeling is needed to test hypotheses about the mechanisms that govern these signals and how nervous system function emerges from the operation of these mechanisms. The NEURON simulation program provides a powerful and flexible environment for implementing such models of individual neurons and small networks of neurons. It is particularly useful when membrane potential is nonuniform and membrane currents are complex. We present the basic ideas that would help informed users make the most efficient use of NEURON.

Inhibition can disrupt hypersynchrony in model neuronal networks

1. Model neuronal network simulations were performed using a reduced Traub neuronal network model. In the absence of inhibition the network produced synchronous population bursting. 2. Bursting of individual neurons was dependent on 1 or more of the following: build-up of charge in the dendritic compartment, prolonged current flow through simulated NMDA associated channels, current flow through T channels. Interburst interval duration and consequent burst frequency was dependent on the density of slow after-hyperpolarizing potassium channels. 3. Addition of an inhibitory interneuron population projecting to GABAA receptors resulted in rapid desynchronization of the population, generally after only 1-2 cycles. This effect was found to be due to reduced participation in the individual population burst and to the need for multi-synaptic activation of the individual neuron in the presence of inhibition. 4. This desynchronizing effect could be offset by increasing the strength of interburst hyperpolarization either through increased density of IAHP, or through the addition of a separate inhibitory interneuron pool projected to GABAB receptors. 5. These data suggest that the synchronizing effects of inhibition may vary depending on circumstances-with desynchronization being dominant in cases characterized by large population bursts such as those seen in epilepsy.

Control of slow oscillations in the thalamocortical neuron: a computer model

We investigated computer models of a single thalamocortical neuron to assess the interaction of intrinsic voltage-sensitive channels and cortical synaptic input in producing the range of oscillation frequencies observed in these cells in vivo. A morphologically detailed model with Hodgkin-Huxley-like ion channels demonstrated that intrinsic properties would be sufficient to readily produce 3 to 6 Hz oscillations. Hyperpolarization of the model cell reduced its oscillation frequency monotonically whether through current injection or modulation of a potassium conductance, simulating the response to a neuromodulatory input. We performed detailed analysis of highly reduced models to determine the mechanism of this frequency control. The interburst interval was controlled by two different mechanisms depending on whether or not the pacemaker current, IH, was present. In the absence of IH, depolarization during the interburst interval occurred at the same rate with different current injections. The voltage difference from the nadir to threshold for the low-threshold calcium current, IT, determined the interburst interval. In contrast, with IH present, the rate of depolarization depended on injected current. With the full model, simulated repetitive cortical synaptic input entrained oscillations up to approximately double the natural frequency. Cortical input readily produced phase resetting as well. Our findings suggest that neither ascending brainstem control altering underlying hyperpolarization, nor descending drive by repetitive cortical inputs, would alone be sufficient to produce the range of oscillation frequencies seen in thalamocortical neurons. Instead, intrinsic neuronal mechanisms would dominate for generating the delta range (0.5-4 Hz) oscillations seen during slow wave sleep, whereas synaptic interactions with cortex and the thalamic reticular nucleus would be required for faster oscillations in the frequency range of spindling (7-14 Hz).

Multiple dynamical modes of thalamic relay neurons: rhythmic bursting and intermittent phase-locking

A model of thalamocortical relay neuron is studied to assess whether a 7-14 Hz (spindle) oscillation and a 0.5-4 Hz (delta) oscillation may result from the interplay between a T-type calcium current and a non-specific cation sag current. With moderate change of membrane parameter values, the model neuron can exhibit both the spindle and delta rhythms, at different levels of hyperpolarization; only the slower (delta) one or none. In the case when the model neuron is not intrinsically oscillatory, its response to rhythmic hyperpolarization is complex, and displays the "intermittent phase-locking" phenomenon where bursts of Na+ action potentials occur infrequently but their occurrence is phase-locked to the rhythmic input. The rhythmic bursting, whenever possible, is shown to emerge (bifurcate) from a subthreshold oscillation. Near the bifurcation chaotic discharge patterns are observed, where spikes occur intermittently at randomly chosen cycles of a mostly subthreshold slow oscillation. Furthermore, when both the spindle and delta modes can be realized, the transition between the two appears as a sudden drop of the rhythmic frequency with increased hyperpolarization. The T-type calcium current and the sag current may explain the "intermittent phase-locking" phenomenon that is characteristic to thalamic relay neurons during spindle oscillation and provide a cellular basis for the 7-14 Hz rhythm and the slower 0.5-4 Hz rhythm.

Analysis of bursting in a thalamic neuron model

We extend a quantitative model for low-voltage, slow-wave excitability based on the T-type calcium current (Wang et al. 1991) by juxtaposing it with a Hodgkin-Huxley-like model for fast sodium spiking in the high voltage regime to account for the distinct firing modes of thalamic neurons. We employ bifurcation analysis to illustrate the stimulus-response behavior of the full model under both voltage regimes. The model neuron shows continuous sodium spiking when depolarized sufficiently from rest. Depending on the parameters of calcium current inactivation, there are two types of low-voltage responses to a hyperpolarizing current step: a single rebound low threshold spike (LTS) upon release of the step and periodic LTSs. Bursting is seen as sodium spikes ride the LTS crest. In both cases, we analyze the LTS burst response by projecting its trajectory into a fast/slow phase plane. We also use phase plane methods to show that a potassium A-current shifts the threshold for sodium spikes, reducing the number of fast sodium spikes in an LTS burst. It can also annihilate periodic bursting. We extend the previous work of Rose and Hindmarsh (1989a-c) for a thalamic neuron and propose a simpler model for thalamic activity. We consider burst modulation by using a neuromodulator-dependent potassium leakage conductance as a control parameter. These results correspond with experiments showing that the application of certain neurotransmitters can switch firing modes.

Thalamocortical oscillations in the sleeping and aroused brain

Sleep is characterized by synchronized events in billions of synaptically coupled neurons in thalamocortical systems. The activation of a series of neuromodulatory transmitter systems during awakening blocks low-frequency oscillations, induces fast rhythms, and allows the brain to recover full responsiveness. Analysis of cortical and thalamic networks at many levels, from molecules to single neurons to large neuronal assemblies, with a variety of techniques, ranging from intracellular recordings in vivo and in vitro to computer simulations, is beginning to yield insights into the mechanisms of the generation, modulation, and function of brain oscillations.

Ionic mechanisms for intrinsic slow oscillations in thalamic relay neurons

The oscillatory properties of single thalamocortical neurons were investigated by using a Hodgkin-Huxley-like model that included Ca2+ diffusion, the low-threshold Ca2+ current (lT) and the hyperpolarization-activated inward current (lh). lh was modeled by double activation kinetics regulated by intracellular Ca2+. The model exhibited waxing and waning oscillations consisting of 1-25-s bursts of slow oscillations (3.5-4 Hz) separated by long silent periods (4-20 s). During the oscillatory phase, the entry of Ca2+ progressively shifted the activation function of lh, terminating the oscillations. A similar type of waxing and waning oscillation was also observed, in the absence of Ca2+ regulation of lh, from the combination of lT, lh, and a slow K+ current. Singular approximation showed that for both models, the activation variables of lh controlled the dynamics of thalamocortical cells. Dynamical analysis of the system in a phase plane diagram showed that waxing and waning oscillations arose when lh entrained the system alternately between stationary and oscillating branches.