Mathematical model of Na-K-Cl homeostasis in ictal and interictal discharges

Chizhov, Anton V.; Amakhin, Dmitry V.; Zaitsev, Aleksey V.

doi:10.1371/journal.pone.0213904

Cited by 16 publications

(19 citation statements)

References 60 publications

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“…Indeed, while changes in the GABA reversal potential are seen during seizure propagation (Ellender et al, 2014), the changes in chloride concentrations necessary to elicit this feature do not exist prior to or during seizure initiation (Ellender et al, 2010;, which is the focus of this research. Moreover, the mechanisms proposed in the work of Chizhov et al (2017Chizhov et al ( , 2019 that investigate the potential causal role of GABA in seizure initiation do not focus on the capacity of excitatory cells for PIR, in contrast to the "GABAergic initiation hypothesis" discussed here.…”

Section: Discussionmentioning

confidence: 93%

“…We also highlight an important distinction between this work and other computational work investigating the role of GABAergic signaling in epileptiform activity and inter-ictal discharges (IID): while recent literature investigating this topic makes use of the potential depolarizing capacity of GABA (Chizhov et al, 2017(Chizhov et al, , 2019, the work presented here uses purely inhibitory GABAergic synapses. Indeed, while changes in the GABA reversal potential are seen during seizure propagation (Ellender et al, 2014), the changes in chloride concentrations necessary to elicit this feature do not exist prior to or during seizure initiation (Ellender et al, 2010;, which is the focus of this research.…”

Section: Discussionmentioning

confidence: 99%

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Inhibitory Network Bistability Explains Increased Interneuronal Activity Prior to Seizure Onset

Rich

Chameh

Rafiee

et al. 2020

Front. Neural Circuits

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Recent experimental literature has revealed that GABAergic interneurons exhibit increased activity prior to seizure onset, alongside additional evidence that such activity is synchronous and may arise abruptly. These findings have led some to hypothesize that this interneuronal activity may serve a causal role in driving the sudden change in brain activity that heralds seizure onset. However, the mechanisms predisposing an inhibitory network toward increased activity, specifically prior to ictogenesis, without a permanent change to inputs to the system remain unknown. We address this question by comparing simulated inhibitory networks containing control interneurons and networks containing hyperexcitable interneurons modeled to mimic treatment with 4-Aminopyridine (4-AP), an agent commonly used to model seizures in vivo and in vitro. Our in silico study demonstrates that model inhibitory networks with 4-AP interneurons are more prone than their control counterparts to exist in a bistable state in which asynchronously firing networks can abruptly transition into synchrony driven by a brief perturbation. This transition into synchrony brings about a corresponding increase in overall firing rate. We further show that perturbations driving this transition could arise in vivo from background excitatory synaptic activity in the cortex. Thus, we propose that bistability explains the increase in interneuron activity observed experimentally prior to seizure via a transition from incoherent to coherent dynamics. Moreover, bistability explains why inhibitory networks containing hyperexcitable interneurons are more vulnerable to this change in dynamics, and how such networks can undergo a transition without a permanent change in the drive. We note that while our comparisons are between networks of control and ictogenic neurons, the conclusions drawn specifically relate to the unusual dynamics that arise prior to seizure, and not seizure onset itself. However, providing a mechanistic explanation for this phenomenon specifically in a pro-ictogenic setting generates experimentally testable hypotheses regarding the role of inhibitory neurons in pre-ictal neural dynamics, and motivates further computational research into mechanisms underlying a newly hypothesized multi-step pathway to seizure initiated by inhibition.

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Section: Discussionmentioning

confidence: 93%

Section: Discussionmentioning

confidence: 99%

Inhibitory Network Bistability Explains Increased Interneuronal Activity Prior to Seizure Onset

Rich

Chameh

Rafiee

et al. 2020

Front. Neural Circuits

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“…al. [56,57] do not focus on the capacity of excitatory 576 cells for PIR, in contrast to the "GABAergic initiation hypothesis" discussed here.…”

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confidence: 92%

“…In contrast, in this study bistability is analyzed solely in an inhibitory network, and the 564 bistability does not in itself represent the transition into seizure, but rather a dynamical 565 change that might precipitate seizure onset due to its downstream effects (as illustrated 566 by a "GABAergic initiation hypothesis" schematized in Fig 1). 567 We also highlight an important distinction between this work and other makes use of the potential depolarizing capacity of GABA [56,57], the work presented 571 here uses purely inhibitory GABAergic synapses. Indeed, while changes in the GABA 572 reversal potential are seen during seizure propagation [3], the changes in chloride 573 concentrations necessary to elicit this feature are unlikely to exist prior to or during 574 seizure initiation, which is the focus of this research.…”

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confidence: 96%

Modeling implicates inhibitory network bistability as an underpinning of seizure initiation

Rich

Rafiee

et al. 2019

Preprint

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A plethora of recent experimental literature implicates the abrupt, synchronous activation of GABAergic interneurons in driving the sudden change in brain activity that heralds seizure initiation. However, the mechanisms predisposing an inhibitory network toward sudden coherence specifically during ictogenesis remain unknown. We address this question by comparing simulated inhibitory networks containing control interneurons and networks containing hyper-excitable interneurons modeled to mimic treatment with 4-Aminopyridine (4-AP), an agent commonly used to model seizures in vivo and in vitro. Our in silico study demonstrates that model inhibitory networks with 4-AP interneurons are more prone than their control counterparts to exist in a bistable state in which asynchronously firing networks can abruptly transition into synchrony due to a brief perturbation. We further show that perturbations driving this transition could reasonably arise in vivo based on models of background excitatory synaptic activity in the cortex. Thus, these results propose a mechanism by which an inhibitory network can transition from incoherent to coherent dynamics in a fashion that may precipitate seizure as a downstream effect. Moreover, this mechanism specifically April 11, 2019 1/36Recently, some studies of seizure initiation have shifted focus to over-activity of 25 inhibitory interneurons. This literature has yielded convincing evidence that 26 interneurons serve a causal role in seizure initiation [1,[8][9][10][11][12][13], laying the groundwork for 27 a novel hypothesis for seizure initiation (a "GABAergic initiation hypothesis") in which 28 synchronous activation of inhibitory interneurons precipitates the onset of a seizure, as 29 diagrammed in Fig 1 [12]. Given the contemporaneous nature of this hypothesis it is an 30ideal target for rigorous computational study; here, such research aims to unearth a 31 mechanism explaining the predisposition of inhibitory interneurons in a hyper-excitable 32April 11, 2019 2/36 environment to suddenly transition into synchrony, the necessary initial step in this 33 hypothesis. We thus focus on the earliest time in the transition to seizure and not 34 aspects of propagation and termination. 35The study of inhibitory network synchrony is decades old, dating back to the work of 36 Wang and Rinzel [14]. Various mechanisms have been proposed to explain the 37 generation of oscillations in purely inhibitory networks, the most prominent of which 38 may be the Interneuron Network Gamma (ING) mechanism [15-20]. Previous work has 39 shown that inhibitory networks built to examine population activity in an in vitro 40 hippocampal preparation manifest "sharp transitions" into coherent population activity 41 caused by a small, permanent increase to the external drive to the network [21]. 42 Additional studies have explored the effect of connection probabilities and cell 43 characteristics manifested by classifications of cell excitability on inhibitory network 44 synchrony [22, 23], and have noted that bist...

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“…Some mathematical models that consider spatial propagation suggest that the excitability of the tissue surrounding the seizure core may play a determining role in the seizure onset pattern [17]. Whereas the generation of interictal discharges is modeled in the conditions of impaired-but-fixed ionic concentrations [18], the dynamics of ictal discharges and the excitability of the cortical tissue is hypothesized to be governed by the ionic dynamics [19], [20], [21]. Generally, a computational approach to this issue requires a biophysical consideration of the neuronal population interactions in the conditions of changing ionic concentrations of sodium, potassium, chloride, and calcium ions inside and outside the neurons and glial cells.…”

Section: Introductionmentioning

confidence: 99%

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

Chizhov

Sanin

2020

PLoS ONE

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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.

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Mathematical model of Na-K-Cl homeostasis in ictal and interictal discharges

Cited by 16 publications

References 60 publications

Inhibitory Network Bistability Explains Increased Interneuronal Activity Prior to Seizure Onset

Inhibitory Network Bistability Explains Increased Interneuronal Activity Prior to Seizure Onset

Modeling implicates inhibitory network bistability as an underpinning of seizure initiation

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

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