Damien Depannemaecker, Anton Ivanov, Davide Lillo, Len Spek, Christophe Bernard, Viktor Jirsa
{"title":"A unified physiological framework of transitions between seizures, sustained ictal activity and depolarization block at the single neuron level.","authors":"Damien Depannemaecker, Anton Ivanov, Davide Lillo, Len Spek, Christophe Bernard, Viktor Jirsa","doi":"10.1007/s10827-022-00811-1","DOIUrl":null,"url":null,"abstract":"<p><p>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<sup>+</sup> as a slow variable, we report that SLEs with SN/homoclinic bifurcations can readily occur at the single cell level when extracellular K<sup>+</sup> 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<sup>+</sup> 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.</p>","PeriodicalId":54857,"journal":{"name":"Journal of Computational Neuroscience","volume":null,"pages":null},"PeriodicalIF":1.5000,"publicationDate":"2022-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8818009/pdf/","citationCount":"15","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Computational Neuroscience","FirstCategoryId":"3","ListUrlMain":"https://doi.org/10.1007/s10827-022-00811-1","RegionNum":4,"RegionCategory":"医学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2022/1/15 0:00:00","PubModel":"Epub","JCR":"Q3","JCRName":"MATHEMATICAL & COMPUTATIONAL BIOLOGY","Score":null,"Total":0}
引用次数: 15
Abstract
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.
期刊介绍:
The Journal of Computational Neuroscience provides a forum for papers that fit the interface between computational and experimental work in the neurosciences. The Journal of Computational Neuroscience publishes full length original papers, rapid communications and review articles describing theoretical and experimental work relevant to computations in the brain and nervous system. Papers that combine theoretical and experimental work are especially encouraged. Primarily theoretical papers should deal with issues of obvious relevance to biological nervous systems. Experimental papers should have implications for the computational function of the nervous system, and may report results using any of a variety of approaches including anatomy, electrophysiology, biophysics, imaging, and molecular biology. Papers investigating the physiological mechanisms underlying pathologies of the nervous system, or papers that report novel technologies of interest to researchers in computational neuroscience, including advances in neural data analysis methods yielding insights into the function of the nervous system, are also welcomed (in this case, methodological papers should include an application of the new method, exemplifying the insights that it yields).It is anticipated that all levels of analysis from cognitive to cellular will be represented in the Journal of Computational Neuroscience.