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Byvaltcev E, Behbood M, Schleimer JH, Gensch T, Semyanov A, Schreiber S, Strauss U. KCC2 reverse mode helps to clear postsynaptically released potassium at glutamatergic synapses. Cell Rep 2023; 42:112934. [PMID: 37537840 PMCID: PMC10480490 DOI: 10.1016/j.celrep.2023.112934] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/21/2023] [Revised: 07/09/2023] [Accepted: 07/18/2023] [Indexed: 08/05/2023] Open
Abstract
Extracellular potassium [K+]o elevation during synaptic activity retrogradely modifies presynaptic release and astrocytic uptake of glutamate. Hence, local K+ clearance and replenishment mechanisms are crucial regulators of glutamatergic transmission and plasticity. Based on recordings of astrocytic inward rectifier potassium current IKir and K+-sensitive electrodes as sensors of [K+]o as well as on in silico modeling, we demonstrate that the neuronal K+-Cl- co-transporter KCC2 clears local perisynaptic [K+]o during synaptic excitation by operating in an activity-dependent reversed mode. In reverse mode, KCC2 replenishes K+ in dendritic spines and complements clearance of [K+]o, therewith attenuating presynaptic glutamate release and shortening LTP. We thus demonstrate a physiological role of KCC2 in neuron-glial interactions and regulation of synaptic signaling and plasticity through the uptake of postsynaptically released K+.
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Affiliation(s)
- Egor Byvaltcev
- Charité - Universitätsmedizin Berlin, Institute of Cell- and Neurobiology, Charitéplatz 1, 10117 Berlin, Germany
| | - Mahraz Behbood
- Institute for Theoretical Biology, Department of Biology, Humboldt-Universität zu Berlin, 10115 Berlin, Germany; Bernstein Center for Computational Neuroscience Berlin, 10115 Berlin, Germany
| | - Jan-Hendrik Schleimer
- Institute for Theoretical Biology, Department of Biology, Humboldt-Universität zu Berlin, 10115 Berlin, Germany; Bernstein Center for Computational Neuroscience Berlin, 10115 Berlin, Germany
| | - Thomas Gensch
- Institute of Biological Information Processing 1 (IBI-1, Molecular and Cellular Physiology), Forschungszentrum Jülich, Wilhem-Jonen Straße, 52428 Jülich, Germany
| | - Alexey Semyanov
- Department of Physiology, Jiaxing University College of Medicine, Zhejiang Pro, Jiaxing 314033, China
| | - Susanne Schreiber
- Institute for Theoretical Biology, Department of Biology, Humboldt-Universität zu Berlin, 10115 Berlin, Germany; Bernstein Center for Computational Neuroscience Berlin, 10115 Berlin, Germany
| | - Ulf Strauss
- Charité - Universitätsmedizin Berlin, Institute of Cell- and Neurobiology, Charitéplatz 1, 10117 Berlin, Germany.
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2
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Øyehaug L. Slow ion concentration oscillations and multiple states in neuron-glia interaction-insights gained from reduced mathematical models. FRONTIERS IN NETWORK PHYSIOLOGY 2023; 3:1189118. [PMID: 37284003 PMCID: PMC10241345 DOI: 10.3389/fnetp.2023.1189118] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 03/18/2023] [Accepted: 04/28/2023] [Indexed: 06/08/2023]
Abstract
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.
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3
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Depannemaecker D, Ezzati A, Wang H, Jirsa V, Bernard C. From phenomenological to biophysical models of seizures. Neurobiol Dis 2023; 182:106131. [PMID: 37086755 DOI: 10.1016/j.nbd.2023.106131] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/17/2023] [Revised: 04/12/2023] [Accepted: 04/14/2023] [Indexed: 04/24/2023] Open
Abstract
Epilepsy is a complex disease that requires various approaches for its study. In this short review, we discuss the contribution of theoretical and computational models. The review presents theoretical frameworks that underlie the understanding of certain seizure properties and their classification based on their dynamical properties at the onset and offset of seizures. Dynamical system tools are valuable resources in the study of seizures. By analyzing the complex, dynamic behavior of seizures, these tools can provide insights into seizure mechanisms and offer a framework for their classification. Additionally, computational models have high potential for clinical applications, as they can be used to develop more accurate diagnostic and personalized medicine tools. We discuss various modeling approaches that span different scales and levels, while also questioning the neurocentric view, and emphasize the importance of considering glial cells. Finally, we explore the epistemic value provided by this type of approach.
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Affiliation(s)
- Damien Depannemaecker
- Institut de Neurosciences des Syst' emes, Aix-Marseille University, INSERM, Marseille, France.
| | - Aitakin Ezzati
- Institut de Neurosciences des Syst' emes, Aix-Marseille University, INSERM, Marseille, France
| | - Huifang Wang
- Institut de Neurosciences des Syst' emes, Aix-Marseille University, INSERM, Marseille, France
| | - Viktor Jirsa
- Institut de Neurosciences des Syst' emes, Aix-Marseille University, INSERM, Marseille, France
| | - Christophe Bernard
- Institut de Neurosciences des Syst' emes, Aix-Marseille University, INSERM, Marseille, France.
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4
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Recruitment of interictal- and ictal-like discharges in posterior piriform cortex by delta-rate (1–4 Hz) focal bursts in anterior piriform cortex in vivo. Epilepsy Res 2022; 187:107032. [DOI: 10.1016/j.eplepsyres.2022.107032] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/29/2022] [Revised: 09/10/2022] [Accepted: 10/06/2022] [Indexed: 11/23/2022]
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5
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Liou JY, Ma H, Wenzel M, Zhao M, Baird-Daniel E, Smith EH, Daniel A, Emerson R, Yuste R, Schwartz TH, Schevon CA. Role of inhibitory control in modulating focal seizure spread. Brain 2019; 141:2083-2097. [PMID: 29757347 DOI: 10.1093/brain/awy116] [Citation(s) in RCA: 61] [Impact Index Per Article: 12.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/02/2017] [Accepted: 03/04/2018] [Indexed: 11/12/2022] Open
Abstract
Focal seizure propagation is classically thought to be spatially contiguous. However, distribution of seizures through a large-scale epileptic network has been theorized. Here, we used a multielectrode array, wide field calcium imaging, and two-photon calcium imaging to study focal seizure propagation pathways in an acute rodent neocortical 4-aminopyridine model. Although ictal neuronal bursts did not propagate beyond a 2-3-mm region, they were associated with hemisphere-wide field potential fluctuations and parvalbumin-positive interneuron activity outside the seizure focus. While bicuculline surface application enhanced contiguous seizure propagation, focal bicuculline microinjection at sites distant to the 4-aminopyridine focus resulted in epileptic network formation with maximal activity at the two foci. Our study suggests that both classical and epileptic network propagation can arise from localized inhibition defects, and that the network appearance can arise in the context of normal brain structure without requirement for pathological connectivity changes between sites.
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Affiliation(s)
- Jyun-You Liou
- Department of Physiology and Cellular Biophysics, Columbia University, New York, NY, USA
| | - Hongtao Ma
- Department of Neurological Surgery, Feil Family Brain and Mind Research Institute, Sackler Brain and Spine Institute, Weill Cornell Medical College, New York, NY, USA
| | - Michael Wenzel
- Neurotechnology Center, Department of Biological Sciences, Columbia University, New York, NY, USA; Department of Neuroscience, Columbia University, New York, NY, USA
| | - Mingrui Zhao
- Department of Neurological Surgery, Feil Family Brain and Mind Research Institute, Sackler Brain and Spine Institute, Weill Cornell Medical College, New York, NY, USA
| | - Eliza Baird-Daniel
- Department of Neurological Surgery, Feil Family Brain and Mind Research Institute, Sackler Brain and Spine Institute, Weill Cornell Medical College, New York, NY, USA
| | - Elliot H Smith
- Department of Neurological Surgery, Columbia University Medical Center, New York, NY, USA
| | - Andy Daniel
- Department of Neurological Surgery, Feil Family Brain and Mind Research Institute, Sackler Brain and Spine Institute, Weill Cornell Medical College, New York, NY, USA
| | - Ronald Emerson
- Hospital for Special Surgery, Weill Cornell Medical College, 535 East 70th Street, New York, NY, USA
| | - Rafael Yuste
- Neurotechnology Center, Department of Biological Sciences, Columbia University, New York, NY, USA; Department of Neuroscience, Columbia University, New York, NY, USA
| | - Theodore H Schwartz
- Department of Neurological Surgery, Feil Family Brain and Mind Research Institute, Sackler Brain and Spine Institute, Weill Cornell Medical College, New York, NY, USA
| | - Catherine A Schevon
- Department of Neurology, Columbia University Medical Center, New York, New York, USA
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6
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Solbrå A, Bergersen AW, van den Brink J, Malthe-Sørenssen A, Einevoll GT, Halnes G. A Kirchhoff-Nernst-Planck framework for modeling large scale extracellular electrodiffusion surrounding morphologically detailed neurons. PLoS Comput Biol 2018; 14:e1006510. [PMID: 30286073 PMCID: PMC6191143 DOI: 10.1371/journal.pcbi.1006510] [Citation(s) in RCA: 20] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/06/2018] [Revised: 10/16/2018] [Accepted: 09/12/2018] [Indexed: 11/30/2022] Open
Abstract
Many pathological conditions, such as seizures, stroke, and spreading depression, are associated with substantial changes in ion concentrations in the extracellular space (ECS) of the brain. An understanding of the mechanisms that govern ECS concentration dynamics may be a prerequisite for understanding such pathologies. To estimate the transport of ions due to electrodiffusive effects, one must keep track of both the ion concentrations and the electric potential simultaneously in the relevant regions of the brain. Although this is currently unfeasible experimentally, it is in principle achievable with computational models based on biophysical principles and constraints. Previous computational models of extracellular ion-concentration dynamics have required extensive computing power, and therefore have been limited to either phenomena on very small spatiotemporal scales (micrometers and milliseconds), or simplified and idealized 1-dimensional (1-D) transport processes on a larger scale. Here, we present the 3-D Kirchhoff-Nernst-Planck (KNP) framework, tailored to explore electrodiffusive effects on large spatiotemporal scales. By assuming electroneutrality, the KNP-framework circumvents charge-relaxation processes on the spatiotemporal scales of nanometers and nanoseconds, and makes it feasible to run simulations on the spatiotemporal scales of millimeters and seconds on a standard desktop computer. In the present work, we use the 3-D KNP framework to simulate the dynamics of ion concentrations and the electrical potential surrounding a morphologically detailed pyramidal cell. In addition to elucidating the single neuron contribution to electrodiffusive effects in the ECS, the simulation demonstrates the efficiency of the 3-D KNP framework. We envision that future applications of the framework to more complex and biologically realistic systems will be useful in exploring pathological conditions associated with large concentration variations in the ECS.
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Affiliation(s)
- Andreas Solbrå
- Center for Integrative Neuroplasticity, University of Oslo, Oslo, Norway
- Department of Physics, University of Oslo, Oslo, Norway
| | | | | | - Anders Malthe-Sørenssen
- Center for Integrative Neuroplasticity, University of Oslo, Oslo, Norway
- Department of Physics, University of Oslo, Oslo, Norway
| | - Gaute T. Einevoll
- Center for Integrative Neuroplasticity, University of Oslo, Oslo, Norway
- Department of Physics, University of Oslo, Oslo, Norway
- Department of Mathematical Sciences and Technology, Norwegian University of Life Sciences, Ås, Norway
| | - Geir Halnes
- Department of Mathematical Sciences and Technology, Norwegian University of Life Sciences, Ås, Norway
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7
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Gentiletti D, Suffczynski P, Gnatkovsky V, de Curtis M. Changes of Ionic Concentrations During Seizure Transitions - A Modeling Study. Int J Neural Syst 2017; 27:1750004. [PMID: 27802792 DOI: 10.1142/s0129065717500046] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
Traditionally, it is considered that neuronal synchronization in epilepsy is caused by a chain reaction of synaptic excitation. However, it has been shown that synchronous epileptiform activity may also arise without synaptic transmission. In order to investigate the respective roles of synaptic interactions and nonsynaptic mechanisms in seizure transitions, we developed a computational model of hippocampal cells, involving the extracellular space, realistic dynamics of [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] ions, glial uptake and extracellular diffusion mechanisms. We show that the network behavior with fixed ionic concentrations may be quite different from the neurons' behavior when more detailed modeling of ionic dynamics is included. In particular, we show that in the extended model strong discharge of inhibitory interneurons may result in long lasting accumulation of extracellular [Formula: see text], which sustains the depolarization of the principal cells and causes their pathological discharges. This effect is not present in a reduced, purely synaptic network. These results point to the importance of nonsynaptic mechanisms in the transition to seizure.
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Affiliation(s)
- Damiano Gentiletti
- 1 Department of Biomedical Physics, Faculty of Physics, University of Warsaw, ul. Pasteura 5, Warsaw, Poland
| | - Piotr Suffczynski
- 1 Department of Biomedical Physics, Faculty of Physics, University of Warsaw, ul. Pasteura 5, Warsaw, Poland
| | - Vadym Gnatkovsky
- 2 Unit of Epileptology and Experimental Neurophysiology, Fondazione IRCCS Istituto Neurologico Carlo Besta, Via Giovanni Celoria 11, Milan, Italy
| | - Marco de Curtis
- 2 Unit of Epileptology and Experimental Neurophysiology, Fondazione IRCCS Istituto Neurologico Carlo Besta, Via Giovanni Celoria 11, Milan, Italy
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8
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Halnes G, Mäki-Marttunen T, Keller D, Pettersen KH, Andreassen OA, Einevoll GT. Effect of Ionic Diffusion on Extracellular Potentials in Neural Tissue. PLoS Comput Biol 2016; 12:e1005193. [PMID: 27820827 PMCID: PMC5098741 DOI: 10.1371/journal.pcbi.1005193] [Citation(s) in RCA: 37] [Impact Index Per Article: 4.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/19/2016] [Accepted: 10/11/2016] [Indexed: 01/06/2023] Open
Abstract
Recorded potentials in the extracellular space (ECS) of the brain is a standard measure of population activity in neural tissue. Computational models that simulate the relationship between the ECS potential and its underlying neurophysiological processes are commonly used in the interpretation of such measurements. Standard methods, such as volume-conductor theory and current-source density theory, assume that diffusion has a negligible effect on the ECS potential, at least in the range of frequencies picked up by most recording systems. This assumption remains to be verified. We here present a hybrid simulation framework that accounts for diffusive effects on the ECS potential. The framework uses (1) the NEURON simulator to compute the activity and ionic output currents from multicompartmental neuron models, and (2) the electrodiffusive Kirchhoff-Nernst-Planck framework to simulate the resulting dynamics of the potential and ion concentrations in the ECS, accounting for the effect of electrical migration as well as diffusion. Using this framework, we explore the effect that ECS diffusion has on the electrical potential surrounding a small population of 10 pyramidal neurons. The neural model was tuned so that simulations over ∼100 seconds of biological time led to shifts in ECS concentrations by a few millimolars, similar to what has been seen in experiments. By comparing simulations where ECS diffusion was absent with simulations where ECS diffusion was included, we made the following key findings: (i) ECS diffusion shifted the local potential by up to ∼0.2 mV. (ii) The power spectral density (PSD) of the diffusion-evoked potential shifts followed a 1/f2 power law. (iii) Diffusion effects dominated the PSD of the ECS potential for frequencies up to several hertz. In scenarios with large, but physiologically realistic ECS concentration gradients, diffusion was thus found to affect the ECS potential well within the frequency range picked up in experimental recordings.
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Affiliation(s)
- Geir Halnes
- Department of Mathematical Sciences and Technology, Norwegian University of Life Sciences, Ås, Norway
| | - Tuomo Mäki-Marttunen
- NORMENT, KG Jebsen Centre for Psychosis Research, Institute of Clinical Medicine, University of Oslo, Oslo, Norway
| | - Daniel Keller
- Blue Brain Project, École Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland
| | - Klas H. Pettersen
- Letten Centre and GliaLab, Institute of Basic Medical Sciences, University of Oslo, Oslo, Norway
- Centre for Molecular Medicine Norway, University of Oslo, Oslo, Norway
| | - Ole A. Andreassen
- NORMENT, KG Jebsen Centre for Psychosis Research, Institute of Clinical Medicine, University of Oslo, Oslo, Norway
| | - Gaute T. Einevoll
- Department of Mathematical Sciences and Technology, Norwegian University of Life Sciences, Ås, Norway
- Department of Physics, University of Oslo, Oslo, Norway
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9
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Y Ho EC, Truccolo W. Interaction between synaptic inhibition and glial-potassium dynamics leads to diverse seizure transition modes in biophysical models of human focal seizures. J Comput Neurosci 2016; 41:225-44. [PMID: 27488433 PMCID: PMC5002283 DOI: 10.1007/s10827-016-0615-7] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/07/2015] [Revised: 06/18/2016] [Accepted: 07/06/2016] [Indexed: 11/10/2022]
Abstract
How focal seizures initiate and evolve in human neocortex remains a fundamental problem in neuroscience. Here, we use biophysical neuronal network models of neocortical patches to study how the interaction between inhibition and extracellular potassium ([K (+)] o ) dynamics may contribute to different types of focal seizures. Three main types of propagated focal seizures observed in recent intracortical microelectrode recordings in humans were modelled: seizures characterized by sustained (∼30-60 Hz) gamma local field potential (LFP) oscillations; seizures where the onset in the propagated site consisted of LFP spikes that later evolved into rhythmic (∼2-3 Hz) spike-wave complexes (SWCs); and seizures where a brief stage of low-amplitude fast-oscillation (∼10-20 Hz) LFPs preceded the SWC activity. Our findings are fourfold: (1) The interaction between elevated [K (+)] o (due to abnormal potassium buffering by glial cells) and the strength of synaptic inhibition plays a predominant role in shaping these three types of seizures. (2) Strengthening of inhibition leads to the onset of sustained narrowband gamma seizures. (3) Transition into SWC seizures is obtained either by the weakening of inhibitory synapses, or by a transient strengthening followed by an inhibitory breakdown (e.g. GABA depletion). This reduction or breakdown of inhibition among fast-spiking (FS) inhibitory interneurons increases their spiking activity and leads them eventually into depolarization block. Ictal spike-wave discharges in the model are then sustained solely by pyramidal neurons. (4) FS cell dynamics are also critical for seizures where the evolution into SWC activity is preceded by low-amplitude fast oscillations. Different levels of elevated [K (+)] o were important for transitions into and maintenance of sustained gamma oscillations and SWC discharges. Overall, our modelling study predicts that the interaction between inhibitory interneurons and [K (+)] o glial buffering under abnormal conditions may explain different types of ictal transitions and dynamics during propagated seizures in human focal epilepsy.
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Affiliation(s)
- E C Y Ho
- Department of Neuroscience & Institute for Brain Science, Brown University, Providence, RI, USA.
- U.S. Department of Veterans Affairs, Center for Neurorestoration and Neurotechnology, Providence, RI, USA.
| | - Wilson Truccolo
- Department of Neuroscience & Institute for Brain Science, Brown University, Providence, RI, USA.
- U.S. Department of Veterans Affairs, Center for Neurorestoration and Neurotechnology, Providence, RI, USA.
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10
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Du M, Li J, Wang R, Wu Y. The influence of potassium concentration on epileptic seizures in a coupled neuronal model in the hippocampus. Cogn Neurodyn 2016; 10:405-14. [PMID: 27668019 PMCID: PMC5018011 DOI: 10.1007/s11571-016-9390-4] [Citation(s) in RCA: 19] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/20/2015] [Revised: 03/14/2016] [Accepted: 05/19/2016] [Indexed: 10/21/2022] Open
Abstract
Experiments on hippocampal slices have recorded that a novel pattern of epileptic seizures with alternating excitatory and inhibitory activities in the CA1 region can be induced by an elevated potassium ion (K(+)) concentration in the extracellular space between neurons and astrocytes (ECS-NA). To explore the intrinsic effects of the factors (such as glial K(+) uptake, Na(+)-K(+)-ATPase, the K(+) concentration of the bath solution, and K(+) lateral diffusion) influencing K(+) concentration in the ECS-NA on the epileptic seizures recorded in previous experiments, we present a coupled model composed of excitatory and inhibitory neurons and glia in the CA1 region. Bifurcation diagrams showing the glial K(+) uptake strength with either the Na(+)-K(+)-ATPase pump strength or the bath solution K(+) concentration are obtained for neural epileptic seizures. The K(+) lateral diffusion leads to epileptic seizure in neurons only when the synaptic conductance values of the excitatory and inhibitory neurons are within an appropriate range. Finally, we propose an energy factor to measure the metabolic demand during neuron firing, and the results show that different energy demands for the normal discharges and the pathological epileptic seizures of the coupled neurons.
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Affiliation(s)
- Mengmeng Du
- State Key Laboratory for Strength and Vibration of Mechanical Structures, School of Aerospace, Xi’an Jiaotong University, Xi’an, China
| | - Jiajia Li
- State Key Laboratory for Strength and Vibration of Mechanical Structures, School of Aerospace, Xi’an Jiaotong University, Xi’an, China
| | - Rong Wang
- State Key Laboratory for Strength and Vibration of Mechanical Structures, School of Aerospace, Xi’an Jiaotong University, Xi’an, China
| | - Ying Wu
- State Key Laboratory for Strength and Vibration of Mechanical Structures, School of Aerospace, Xi’an Jiaotong University, Xi’an, China
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11
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Wu XX, Shuai J. Effects of extracellular potassium diffusion on electrically coupled neuron networks. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 91:022712. [PMID: 25768536 DOI: 10.1103/physreve.91.022712] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/31/2014] [Indexed: 06/04/2023]
Abstract
Potassium accumulation and diffusion during neuronal epileptiform activity have been observed experimentally, and potassium lateral diffusion has been suggested to play an important role in nonsynaptic neuron networks. We adopt a hippocampal CA1 pyramidal neuron network in a zero-calcium condition to better understand the influence of extracellular potassium dynamics on the stimulus-induced activity. The potassium concentration in the interstitial space for each neuron is regulated by potassium currents, Na(+)-K(+) pumps, glial buffering, and ion diffusion. In addition to potassium diffusion, nearby neurons are also coupled through gap junctions. Our results reveal that the latency of the first spike responding to stimulus monotonically decreases with increasing gap-junction conductance but is insensitive to potassium diffusive coupling. The duration of network oscillations shows a bell-like shape with increasing potassium diffusive coupling at weak gap-junction coupling. For modest electrical coupling, there is an optimal K(+) diffusion strength, at which the flow of potassium ions among the network neurons appropriately modulates interstitial potassium concentrations in a degree that provides the most favorable environment for the generation and continuance of the action potential waves in the network.
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Affiliation(s)
- Xing-Xing Wu
- Department of Physics, Xiamen University, Xiamen 361005, P. R. China
| | - Jianwei Shuai
- Department of Physics, State Key Lab of Cellular Stress Biology, Innovation Center for Cell Signaling Network, and Fujian Provincial Key Laboratory of Theoretical and Computational Chemistry, Xiamen University; Xiamen 361005, P. R. China
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12
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Enhanced multiple vibrational resonances by Na+ and K+ dynamics in a neuron model. Sci Rep 2015; 5:7684. [PMID: 25567752 PMCID: PMC4286765 DOI: 10.1038/srep07684] [Citation(s) in RCA: 18] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/07/2014] [Accepted: 12/08/2014] [Indexed: 12/13/2022] Open
Abstract
Some neuronal receptors perceive external input in the form of hybrid periodic signals. The signal detection may be based on the mechanism of vibrational resonance, in which a system's response to the low frequency signal can become optimal by an appropriate choice of the vibration amplitude of HFS. The vibrational resonance effect is investigated in a neuron model in which the intra- and extra-cellular potassium and sodium concentrations are allowed to evolve temporally, depending on ion currents, Na+-K+ pumps, glial buffering, and ion diffusion. Our results reveal that, compared to the vibrational resonances in the model with constant ion concentrations, the significantly enhanced vibrational multi-resonances can be observed for the single neuron system where the potassium and sodium ion concentrations vary temporally. Thus, in contradiction to a popular view that ion concentrations dynamics play little role in signal detection, we indicate that the neuron's response to an external subthreshold signal can be largely improved by sodium and potassium dynamics.
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13
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Wilson D, Moehlis J. A Hamilton-Jacobi-Bellman approach for termination of seizure-like bursting. J Comput Neurosci 2014; 37:345-55. [PMID: 24965911 PMCID: PMC4159579 DOI: 10.1007/s10827-014-0507-7] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/29/2013] [Revised: 02/19/2014] [Accepted: 05/26/2014] [Indexed: 11/23/2022]
Abstract
We use Hamilton-Jacobi-Bellman methods to find minimum-time and energy-optimal control strategies to terminate seizure-like bursting behavior in a conductance-based neural model. Averaging is used to eliminate fast variables from the model, and a target set is defined through bifurcation analysis of the slow variables of the model. This method is illustrated for a single neuron model and for a network model to illustrate its efficacy in terminating bursting once it begins. This work represents a numerical proof-of-concept that a new class of control strategies can be employed to mitigate bursting, and could ultimately be adapted to treat medically intractible epilepsy in patient-specific models.
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Affiliation(s)
- Dan Wilson
- Department of Mechanical Engineering, University of California, Santa Barbara, CA, 93106, USA,
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14
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Chang WP, Shyu BC. Anterior Cingulate epilepsy: mechanisms and modulation. Front Integr Neurosci 2014; 7:104. [PMID: 24427123 PMCID: PMC3879463 DOI: 10.3389/fnint.2013.00104] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/25/2013] [Accepted: 12/16/2013] [Indexed: 11/13/2022] Open
Abstract
Epilepsy is a common neurological disorder, about 1% population worldwide suffered from this disease. In 1989, the International League Against Epilepsy (ILAE) classified anterior cingulate epilepsy as a form of frontal lobe epilepsy (FLE). FLE is the second most common type of epilepsy. Previous clinical studies showed that FLE account an important cause in refractory epilepsy, therefore to find alternative approach to modulate FLE is very important. Basic research using animal models and brain slice have revealed some insights on the epileptogenesis and modulation of seizure in anterior cingulate cortex (ACC). Interneurons play an important role in the synchronization of cingulate epilepsy. Research has shown that the epileptogenesis of seizure originated from mesial frontal lobe might be caused by a selective increase in nicotine-evoked γ-aminobutyric acid (GABA) inhibition, because the application of the GABAA receptor antagonist picrotoxin inhibited epileptic discharges. Gap junctions are also involved in the regulation of cingulate epilepsy. Previous studies have shown that the application of gap junction blockers could attenuate ACC seizures, while gap junction opener could enhance them in an in vitro preparation. μ-Opioid receptors have been shown to be involved in the epileptic synchronization mechanism in ACC seizures in a brain slice preparation. Application of the μ-opioid agonist DAMGO significantly abolished the ictal discharges in a 4-aminopyridine induced electrographic seizure model in ACC. Basic research has also found that thalamic modulation has an inhibitory effect on ACC seizures. Studies have shown that the medial thalamus may be a target for deep brain stimulation to cure ACC seizures.
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Affiliation(s)
- Wei-Pang Chang
- Graduate Institute of Life Science, National Defense Medical Center Taipei, Taiwan ; Institute of Biomedical Science, Academia Sinica Taipei, Taiwan
| | - Bai-Chuang Shyu
- Graduate Institute of Life Science, National Defense Medical Center Taipei, Taiwan ; Institute of Biomedical Science, Academia Sinica Taipei, Taiwan
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15
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Halnes G, Østby I, Pettersen KH, Omholt SW, Einevoll GT. Electrodiffusive model for astrocytic and neuronal ion concentration dynamics. PLoS Comput Biol 2013; 9:e1003386. [PMID: 24367247 PMCID: PMC3868551 DOI: 10.1371/journal.pcbi.1003386] [Citation(s) in RCA: 35] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/24/2013] [Accepted: 10/24/2013] [Indexed: 11/24/2022] Open
Abstract
The cable equation is a proper framework for modeling electrical neural signalling that takes place at a timescale at which the ionic concentrations vary little. However, in neural tissue there are also key dynamic processes that occur at longer timescales. For example, endured periods of intense neural signaling may cause the local extracellular K+-concentration to increase by several millimolars. The clearance of this excess K+ depends partly on diffusion in the extracellular space, partly on local uptake by astrocytes, and partly on intracellular transport (spatial buffering) within astrocytes. These processes, that take place at the time scale of seconds, demand a mathematical description able to account for the spatiotemporal variations in ion concentrations as well as the subsequent effects of these variations on the membrane potential. Here, we present a general electrodiffusive formalism for modeling of ion concentration dynamics in a one-dimensional geometry, including both the intra- and extracellular domains. Based on the Nernst-Planck equations, this formalism ensures that the membrane potential and ion concentrations are in consistency, it ensures global particle/charge conservation and it accounts for diffusion and concentration dependent variations in resistivity. We apply the formalism to a model of astrocytes exchanging ions with the extracellular space. The simulations show that K+-removal from high-concentration regions is driven by a local depolarization of the astrocyte membrane, which concertedly (i) increases the local astrocytic uptake of K+, (ii) suppresses extracellular transport of K+, (iii) increases axial transport of K+ within astrocytes, and (iv) facilitates astrocytic relase of K+ in regions where the extracellular concentration is low. Together, these mechanisms seem to provide a robust regulatory scheme for shielding the extracellular space from excess K+. When neurons generate electrical signals they release potassium ions (K+) into the extracellular space. During periods of intense neural activity, the local extracellular K+ may increase drastically. If it becomes too high, it can lead to neural dysfunction. Astrocytes (a kind of glial cells) are involved in preventing this from happening. Astrocytes can take up excess K+, transport it intracellularly, and release it in regions where the concentration is lower. This process is called spatial buffering, and a full mechanistic understanding of it is currently lacking. The aim of this work is twofold: First, we develop a formalism for modeling ion concentration dynamics in the intra- and extracellular space. The formalism is general, and could be used to simulate many cellular processes. It accounts for ion transports due to diffusion (along concentration gradients) as well as electrical migration (along voltage gradients). It extends previous, related formalisms, which have focused only on intracellular dynamics. Secondly, we apply the formalism to model how astrocytes exchange ions with the extracellular space. We conclude that the membrane mechanisms possessed by astrocytes seem optimal for shielding the extracellular space from excess K+, and provide a full mechanistic description of the spatial (K+) buffering process.
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Affiliation(s)
- Geir Halnes
- Department of Mathematical Sciences and Technology, Norwegian University of Life Sciences, Ås, Norway
- * E-mail:
| | - Ivar Østby
- Department of Mathematical Sciences and Technology, Norwegian University of Life Sciences, Ås, Norway
| | - Klas H. Pettersen
- Centre for Integrative Genetics, Department of Mathematical Sciences and Technology, Norwegian University of Life Sciences, Ås, Norway
| | - Stig W. Omholt
- Centre for Integrative Genetics, Department of Animal and Aqucultural Sciences, Norwegian University of Life Sciences, Ås, Norway
| | - Gaute T. Einevoll
- Department of Mathematical Sciences and Technology, Norwegian University of Life Sciences, Ås, Norway
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16
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Chang WP, Wu JJS, Shyu BC. Thalamic modulation of cingulate seizure activity via the regulation of gap junctions in mice thalamocingulate slice. PLoS One 2013; 8:e62952. [PMID: 23690968 PMCID: PMC3653920 DOI: 10.1371/journal.pone.0062952] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/22/2013] [Accepted: 03/26/2013] [Indexed: 11/19/2022] Open
Abstract
The thalamus is an important target for deep brain stimulation in the treatment of seizures. However, whether the modulatory effect of thalamic inputs on cortical seizures occurs through the modulation of gap junctions has not been previously studied. Therefore, we tested the effects of different gap junction blockers and couplers in a drug-resistant seizure model and studied the role of gap junctions in the thalamic modulation on cortical seizures. Multielectrode array and calcium imaging were used to record the cortical seizures induced by 4-aminopyridine (250 µM) and bicuculline (5-50 µM) in a novel thalamocingulate slice preparation. Seizure-like activity was significantly attenuated by the pan-gap junction blockers carbenoxolone and octanol and specific neuronal gap junction blocker mefloquine. The gap junction coupler trimethylamine significantly enhanced seizure-like activity. Gap junction blockers did not influence the initial phase of seizure-like activity, but they significantly decreased the amplitude and duration of the maintenance phase. The development of seizures is regulated by extracellular potassium concentration. Carbenoxolone partially restored the amplitude and duration after removing the thalamic inputs. A two-dimensional current source density analysis showed that the sink and source signals shifted to deeper layers after removing the thalamic inputs during the clonic phase. These results indicate that the regulatory mechanism of deep brain stimulation in the thalamus occurs partially though gap junctions.
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Affiliation(s)
- Wei-Pang Chang
- Graduate Institute of Life Sciences, National Defense Medical Center, Taipei, Taiwan, Republic of China
| | - José Jiun-Shian Wu
- Institute of Zoology, National Taiwan University, Taipei, Taiwan, Republic of China
| | - Bai-Chuang Shyu
- Graduate Institute of Life Sciences, National Defense Medical Center, Taipei, Taiwan, Republic of China
- Institute of Biomedical Science, Academia Sinica, Taipei, Taiwan, Republic of China
- * E-mail:
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17
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Lewin N, Aksay E, Clancy CE. Computational modeling reveals dendritic origins of GABA(A)-mediated excitation in CA1 pyramidal neurons. PLoS One 2012; 7:e47250. [PMID: 23071770 PMCID: PMC3470566 DOI: 10.1371/journal.pone.0047250] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/24/2012] [Accepted: 09/11/2012] [Indexed: 12/16/2022] Open
Abstract
GABA is the key inhibitory neurotransmitter in the adult central nervous system, but in some circumstances can lead to a paradoxical excitation that has been causally implicated in diverse pathologies from endocrine stress responses to diseases of excitability including neuropathic pain and temporal lobe epilepsy. We undertook a computational modeling approach to determine plausible ionic mechanisms of GABA(A)-dependent excitation in isolated post-synaptic CA1 hippocampal neurons because it may constitute a trigger for pathological synchronous epileptiform discharge. In particular, the interplay intracellular chloride accumulation via the GABA(A) receptor and extracellular potassium accumulation via the K/Cl co-transporter KCC2 in promoting GABA(A)-mediated excitation is complex. Experimentally it is difficult to determine the ionic mechanisms of depolarizing current since potassium transients are challenging to isolate pharmacologically and much GABA signaling occurs in small, difficult to measure, dendritic compartments. To address this problem and determine plausible ionic mechanisms of GABA(A)-mediated excitation, we built a detailed biophysically realistic model of the CA1 pyramidal neuron that includes processes critical for ion homeostasis. Our results suggest that in dendritic compartments, but not in the somatic compartments, chloride buildup is sufficient to cause dramatic depolarization of the GABA(A) reversal potential and dominating bicarbonate currents that provide a substantial current source to drive whole-cell depolarization. The model simulations predict that extracellular K(+) transients can augment GABA(A)-mediated excitation, but not cause it. Our model also suggests the potential for GABA(A)-mediated excitation to promote network synchrony depending on interneuron synapse location - excitatory positive-feedback can occur when interneurons synapse onto distal dendritic compartments, while interneurons projecting to the perisomatic region will cause inhibition.
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Affiliation(s)
- Naomi Lewin
- Department of Physiology and Biophysics, Weill Medical College of Cornell University, New York, New York, United States of America
- Tri-Institutional MD-PhD Program, Physiology, Biophysics and Systems Biology Graduate Program, Department of Pharmacology, University of California Davis, Davis, California, United States of America
| | - Emre Aksay
- Department of Physiology and Biophysics, Weill Medical College of Cornell University, New York, New York, United States of America
| | - Colleen E. Clancy
- Tri-Institutional MD-PhD Program, Physiology, Biophysics and Systems Biology Graduate Program, Department of Pharmacology, University of California Davis, Davis, California, United States of America
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18
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19
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Wu XX, Shuai JW. Multistability in a neuron model with extracellular potassium dynamics. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 85:061911. [PMID: 23005131 DOI: 10.1103/physreve.85.061911] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/27/2012] [Revised: 04/24/2012] [Indexed: 06/01/2023]
Abstract
Experiments show a primary role of extracellular potassium concentrations in neuronal hyperexcitability and in the generation of epileptiform bursting and depolarization blocks without synaptic mechanisms. We adopt a physiologically relevant hippocampal CA1 neuron model in a zero-calcium condition to better understand the function of extracellular potassium in neuronal seizurelike activities. The model neuron is surrounded by interstitial space in which potassium ions are able to accumulate. Potassium currents, Na{+}-K{+} pumps, glial buffering, and ion diffusion are regulatory mechanisms of extracellular potassium. We also consider a reduced model with a fixed potassium concentration. The bifurcation structure and spiking frequency of the two models are studied. We show that, besides hyperexcitability and bursting pattern modulation, the potassium dynamics can induce not only bistability but also tristability of different firing patterns. Our results reveal the emergence of the complex behavior of multistability due to the dynamical [K{+}]{o} modulation on neuronal activities.
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Affiliation(s)
- Xing-Xing Wu
- Department of Physics and Institute of Theoretical Physics and Astrophysics, Xiamen University, Xiamen 361005, People's Republic of China
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20
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BENTZEN NCK, ZHABOTINSKY AM, LAUGESEN JL. MODELING OF GLUTAMATE-INDUCED DYNAMICAL PATTERNS. Int J Neural Syst 2011; 19:395-407. [DOI: 10.1142/s0129065709002105] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
Based on established physiological mechanisms, the paper presents a detailed computer model, which supports the hypothesis that temporal lobe epilepsy may be caused by failure of glutamate reuptake from the extracellular space. The elevated glutamate concentration causes an increased activation of NMDA receptors in pyramidal neurons, which in turn leads to neuronal dynamics that is qualitatively identical to epileptiform activity. We identify by chaos analysis a surprising possibility that muscarinergic receptors can help the system out of a chaotic regime.
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Affiliation(s)
- N. C. K. BENTZEN
- Department of Physics, The Technical University of Denmark, Fysikvej 309, 2800 Lyngby, Denmark
| | - A. M. ZHABOTINSKY
- Department of Chemistry, MS015, Brandeis University, Waltham, MA 02254-9110, USA
| | - J. L. LAUGESEN
- Department of Physics, The Technical University of Denmark, Fysikvej 309, 2800 Lyngby, Denmark
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21
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Aur D. Understanding the physical mechanism of transition to epileptic seizures. J Neurosci Methods 2011; 200:80-5. [PMID: 21679727 DOI: 10.1016/j.jneumeth.2011.05.028] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/10/2011] [Revised: 05/11/2011] [Accepted: 05/27/2011] [Indexed: 10/18/2022]
Abstract
The mechanisms of generating epileptic seizures are still unknown. To identify the mechanisms that underlie the transition to seizure a combination of features that include firing rate, power spectrum and complexity measures were simultaneously analyzed. Pre-ictal periods are characterized by large fluctuations of firing rate which reflect local dysfunctional regulation of neuronal activity. This local dysfunction in neuronal activity is translated in changes of endogenous electric field within clustered regions with high frequency oscillations (HFO) that act at fundamental level of charge dynamics and lead to chaotic dynamics followed by electrical resonances. Right before the onset of seizures the presence of chaotic behavior becomes persistent and leads all types of cells to fire simultaneously and generate the transition to ictal state. The alteration in neuronal regulation and the nature of physical phenomena involved in this transition supports some models of seizure generation and rules out others.
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Affiliation(s)
- Dorian Aur
- Dept of Comparative Medicine, Stanford University, Palo Alto, CA, United States.
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22
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Igelström KM, Shirley CH, Heyward PM. Low-magnesium medium induces epileptiform activity in mouse olfactory bulb slices. J Neurophysiol 2011; 106:2593-605. [PMID: 21832029 DOI: 10.1152/jn.00601.2011] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/18/2022] Open
Abstract
Magnesium-free medium can be used in brain slice studies to enhance glutamate receptor function, but this manipulation causes seizure-like activity in many cortical areas. The rodent olfactory bulb (OB) slice is a popular preparation, and potentially ictogenic ionic conditions have often been used to study odor processing. We studied low Mg(2+)-induced epileptiform discharges in mouse OB slices using extracellular and whole cell electrophysiological recordings. Low-Mg(2+) medium induced two distinct types of epileptiform activity: an intraglomerular delta-frequency oscillation resembling slow sniff-induced activity and minute-long seizure-like events (SLEs) consisting of large negative-going field potentials accompanied by sustained depolarization of output neurons. SLEs were dependent on N-methyl-D-aspartate receptors and sodium currents and were facilitated by α-amino-3-hydroxy-5-methyl-4-isoxazole propionate receptors. The events were initiated in the glomerular layer and propagated laterally through the external plexiform layer at a slow time scale. Our findings confirm that low-Mg(2+) medium should be used with caution in OB slices. Furthermore, the SLEs resembled the so-called slow direct current (DC) shift of clinical and experimental seizures, which has recently been recognized as being of great clinical importance. The OB slice may therefore provide a robust and unique in vitro model of acute seizures in which mechanisms of epileptiform DC shifts can be studied in isolation from fast oscillations.
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Affiliation(s)
- Kajsa M Igelström
- Dept. of Physiology, Univ. of Otago, PO Box 913, Dunedin 9054, New Zealand.
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23
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The impact of the glial spatial buffering on the K(+) Nernst potential. Cogn Neurodyn 2011; 5:285-91. [PMID: 22942917 DOI: 10.1007/s11571-011-9165-x] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/11/2011] [Revised: 06/28/2011] [Accepted: 07/07/2011] [Indexed: 10/18/2022] Open
Abstract
Astrocytes play a critical role in CNS metabolism, regulation of volume and ion homeostasis of the interstitial space. Of special relevance is their clearance of K(+) that is released by active neurons into the extracellular space. Mathematical analysis of a modified Nernst equation for the electrochemical equilibrium of neuronal plasma membranes, suggests that K(+) uptake by glial cells is not only relevant during neuronal activity but also has a non-neglectable impact on the basic electrical membrane properties, specifically the resting membrane potential, of neurons and might be clinically valuable as a factor in the genetics and epigenetics of the epilepsy and tuberous sclerosis complex.
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24
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Øyehaug L, Østby I, Lloyd CM, Omholt SW, Einevoll GT. Dependence of spontaneous neuronal firing and depolarisation block on astroglial membrane transport mechanisms. J Comput Neurosci 2011; 32:147-65. [PMID: 21667153 DOI: 10.1007/s10827-011-0345-9] [Citation(s) in RCA: 53] [Impact Index Per Article: 4.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/16/2009] [Revised: 04/01/2011] [Accepted: 05/24/2011] [Indexed: 11/25/2022]
Abstract
Exposed to a sufficiently high extracellular potassium concentration ([K( + )]₀), the neuron can fire spontaneous discharges or even become inactivated due to membrane depolarisation ('depolarisation block'). Since these phenomena likely are related to the maintenance and propagation of seizure discharges, it is of considerable importance to understand the conditions under which excess [K( + )]₀ causes them. To address the putative effect of glial buffering on neuronal activity under elevated [K( + )](o) conditions, we combined a recently developed dynamical model of glial membrane ion and water transport with a Hodgkin-Huxley type neuron model. In this interconnected glia-neuron model we investigated the effects of natural heterogeneity or pathological changes in glial membrane transporter density by considering a large set of models with different, yet empirically plausible, sets of model parameters. We observed both the high [K( + )]₀-induced duration of spontaneous neuronal firing and the prevalence of depolarisation block to increase when reducing the magnitudes of the glial transport mechanisms. Further, in some parameter regions an oscillatory bursting spiking pattern due to the dynamical coupling of neurons and glia was observed. Bifurcation analyses of the neuron model and of a simplified version of the neuron-glia model revealed further insights about the underlying mechanism behind these phenomena. The above insights emphasise the importance of combining neuron models with detailed astroglial models when addressing phenomena suspected to be influenced by the astroglia-neuron interaction. To facilitate the use of our neuron-glia model, a CellML version of it is made publicly available.
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Affiliation(s)
- Leiv Øyehaug
- Centre for Integrative Genetics (CIGENE), Department of Mathematical Sciences and Technology, Norwegian University of Life Sciences, 1430 Ås, Norway.
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25
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Barreto E, Cressman JR. Ion concentration dynamics as a mechanism for neuronal bursting. J Biol Phys 2011; 37:361-73. [PMID: 22654181 DOI: 10.1007/s10867-010-9212-6] [Citation(s) in RCA: 88] [Impact Index Per Article: 6.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/26/2010] [Accepted: 12/13/2010] [Indexed: 11/25/2022] Open
Abstract
We describe a simple conductance-based model neuron that includes intra- and extracellular ion concentration dynamics and show that this model exhibits periodic bursting. The bursting arises as the fast-spiking behavior of the neuron is modulated by the slow oscillatory behavior in the ion concentration variables and vice versa. By separating these time scales and studying the bifurcation structure of the neuron, we catalog several qualitatively different bursting profiles that are strikingly similar to those seen in experimental preparations. Our work suggests that ion concentration dynamics may play an important role in modulating neuronal excitability in real biological systems.
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Affiliation(s)
- Ernest Barreto
- Center for Neural Dynamics, Department of Physics & Astronomy, and The Krasnow Institute for Advanced Study, George Mason University, Fairfax, VA 22030 USA
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26
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Durand DM, Park EH, Jensen AL. Potassium diffusive coupling in neural networks. Philos Trans R Soc Lond B Biol Sci 2010; 365:2347-62. [PMID: 20603356 DOI: 10.1098/rstb.2010.0050] [Citation(s) in RCA: 65] [Impact Index Per Article: 4.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Abstract
Conventional neural networks are characterized by many neurons coupled together through synapses. The activity, synchronization, plasticity and excitability of the network are then controlled by its synaptic connectivity. Neurons are surrounded by an extracellular space whereby fluctuations in specific ionic concentration can modulate neuronal excitability. Extracellular concentrations of potassium ([K(+)](o)) can generate neuronal hyperexcitability. Yet, after many years of research, it is still unknown whether an elevation of potassium is the cause or the result of the generation, propagation and synchronization of epileptiform activity. An elevation of potassium in neural tissue can be characterized by dispersion (global elevation of potassium) and lateral diffusion (local spatial gradients). Both experimental and computational studies have shown that lateral diffusion is involved in the generation and the propagation of neural activity in diffusively coupled networks. Therefore, diffusion-based coupling by potassium can play an important role in neural networks and it is reviewed in four sections. Section 2 shows that potassium diffusion is responsible for the synchronization of activity across a mechanical cut in the tissue. A computer model of diffusive coupling shows that potassium diffusion can mediate communication between cells and generate abnormal and/or periodic activity in small (section sign 3) and in large networks of cells (section sign 4). Finally, in section sign 5, a study of the role of extracellular potassium in the propagation of axonal signals shows that elevated potassium concentration can block the propagation of neural activity in axonal pathways. Taken together, these results indicate that potassium accumulation and diffusion can interfere with normal activity and generate abnormal activity in neural networks.
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Affiliation(s)
- Dominique M Durand
- Department of Biomedical Engineering, Neural Engineering Center, Case Western Reserve University, Cleveland, OH 44106, USA.
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27
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Network bistability mediates spontaneous transitions between normal and pathological brain states. J Neurosci 2010; 30:10734-43. [PMID: 20702704 DOI: 10.1523/jneurosci.1239-10.2010] [Citation(s) in RCA: 89] [Impact Index Per Article: 6.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022] Open
Abstract
Little is known about how cortical networks support the emergence of remarkably different activity patterns. Physiological activity interspersed with epochs of pathological hyperactivity in the epileptic brain represents a clinically relevant yet poorly understood case of such rich dynamic repertoire. Using a realistic computational model, we demonstrate that physiological sparse and pathological tonic-clonic activity may coexist in the same cortical network for identical afferent input level. Transient perturbations in the afferent input were sufficient to switch the network between these two stable states. The effectiveness of the potassium regulatory apparatus determined the stability of the physiological state and the threshold for seizure initiation. Our findings contrast with the common notions of (1) pathological brain activity representing dynamic instabilities and (2) necessary adjustments of experimental conditions to elicit different network states. Rather, we propose that the rich dynamic repertoire of cortical networks may be based on multistabilities intrinsic to the network.
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28
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Zalay OC, Serletis D, Carlen PL, Bardakjian BL. System characterization of neuronal excitability in the hippocampus and its relevance to observed dynamics of spontaneous seizure-like transitions. J Neural Eng 2010; 7:036002. [DOI: 10.1088/1741-2560/7/3/036002] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
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29
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Postnov DE, Müller F, Schuppner RB, Schimansky-Geier L. Dynamical structures in binary media of potassium-driven neurons. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2009; 80:031921. [PMID: 19905160 DOI: 10.1103/physreve.80.031921] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/18/2009] [Revised: 08/03/2009] [Indexed: 05/28/2023]
Abstract
According to the conventional approach neural ensembles are modeled with fixed ionic concentrations in the extracellular environment. However, in some cases the extracellular concentration of potassium ions cannot be regarded as constant. Such cases represent specific chemical pathway for neurons to interact and can influence strongly the behavior of single neurons and of large ensembles. The released chemical agent diffuses in the external medium and lowers thresholds of individual excitable units. We address this problem by studying simplified excitable units given by a modified FitzHugh-Nagumo dynamics. In our model the neurons interact only chemically via the released and diffusing potassium in the surrounding nonactive medium and are permanently affected by noise. First, we study the dynamics of a single excitable unit embedded in the extracellular matter. That leads to a number of noise-induced effects such as self-modulation of firing rate in an individual neuron. After the consideration of two coupled neurons we consider the spatially extended situation. By holding parameters of the neuron fixed, various patterns appear ranging from spirals and traveling waves to oscillons and inverted structures depending on the parameters of the medium.
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Affiliation(s)
- D E Postnov
- Department of Physics, Saratov State University, Astrakhanskaya ul 83, Saratov 410012, Russia
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30
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Shahar E, Derchansky M, Carlen P. The role of altered tissue osmolality on the characteristics and propagation of seizure activity in the intact isolated mouse hippocampus. Clin Neurophysiol 2009; 120:673-8. [DOI: 10.1016/j.clinph.2009.01.014] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/06/2008] [Revised: 12/28/2008] [Accepted: 01/19/2009] [Indexed: 10/21/2022]
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31
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The role of extracellular potassium dynamics in the different stages of ictal bursting and spreading depression: a computational study. J Theor Biol 2009; 258:219-28. [PMID: 19490858 DOI: 10.1016/j.jtbi.2009.01.032] [Citation(s) in RCA: 38] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/08/2008] [Revised: 01/24/2009] [Accepted: 01/30/2009] [Indexed: 11/22/2022]
Abstract
Experimental evidences point out the participation of nonsynaptic mechanisms (e.g., fluctuations in extracellular ions) in epileptiform bursting and spreading depression (SD). During these abnormal oscillatory patterns, it is observed an increase of extracellular potassium concentration [K(+)](o) and a decrease of extracellular calcium concentration [Ca(2+)](o) which raises the neuronal excitability. However, whether the high [K(+)](o) triggers and propagates these abnormal neuronal activities or plays a secondary role into this process is unclear. To better understand the influence of extracellular potassium dynamics in these oscillatory patterns, the experimental conditions of high [K(+)](o) and zero [Ca(2+)](o) were replicated in an extended Golomb model where we added important regulatory mechanisms of ion concentration as Na(+)-K(+) pump, ion diffusion and glial buffering. Within these conditions, simulations of the cell model exhibit seizure-like discharges (ictal bursting). The SD was elicited by the interruption of the Na(+)-K(+) pump activity, mimicking the effect of cellular hypoxia (an experimental protocol to elicit SD, the hypoxia-induced SD). We used the bifurcation theory and the fast-slow method to analyze the interference of K(+) dynamics in the cellular excitability. This analysis indicates that the system loses its stability at a high [K(+)](o), transiting to an elevated state of neuronal excitability. Effects of high [K(+)](o) are observed in different stages of ictal bursting and SD. In the initial stage, the increase of [K(+)](o) creates favorable conditions to trigger both oscillatory patterns. During the neuronal activity, a continuous growth of [K(+)](o) by outward K(+) flow depresses K(+) currents in a positive feedback way. At the last stage, due to the depression of K(+) currents, the Na(+)-K(+) pump is the main mechanism in the end of neuronal activity. Thus, this work suggests that [K(+)](o) dynamics may play a fundamental role in these abnormal oscillatory patterns.
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32
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Fröhlich F, Bazhenov M, Iragui-Madoz V, Sejnowski TJ. Potassium dynamics in the epileptic cortex: new insights on an old topic. Neuroscientist 2009; 14:422-33. [PMID: 18997121 PMCID: PMC2854295 DOI: 10.1177/1073858408317955] [Citation(s) in RCA: 145] [Impact Index Per Article: 9.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/12/2023]
Abstract
The role of changes in the extracellular potassium concentration [K(+)](o) in epilepsy has remained unclear. Historically, it was hypothesized that [K(+)]( o) is the causal factor for epileptic seizures. This so-called potassium accumulation hypothesis led to substantial debate but subsequently failed to find wide acceptance. However, recent studies on the pathophysiology of tissue from epileptic human patients and animal epilepsy models revealed aberrations in [K(+)](o) regulation. Computational models of cortical circuits that include ion concentration dynamics have catalyzed a renewed interest in the role of [K(+)](o) in epilepsy. The authors here connect classical and more recent insights on [K(+)]( o) dynamics in the cortex with the goal of providing starting points for a next generation of [K(+)](o) research. Such research may ultimately lead to an entirely new class of antiepileptic drugs that act on the [K(+)](o) regulation system.
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Affiliation(s)
- Flavio Fröhlich
- Salk Institute for Biological Studies, Computational Neurobiology Laboratory, La Jolla, CA, USA
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33
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Cressman JR, Ullah G, Ziburkus J, Schiff SJ, Barreto E. The influence of sodium and potassium dynamics on excitability, seizures, and the stability of persistent states: I. Single neuron dynamics. J Comput Neurosci 2009; 26:159-70. [PMID: 19169801 DOI: 10.1007/s10827-008-0132-4] [Citation(s) in RCA: 197] [Impact Index Per Article: 13.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/20/2008] [Revised: 10/17/2008] [Accepted: 11/25/2008] [Indexed: 11/29/2022]
Abstract
In these companion papers, we study how the interrelated dynamics of sodium and potassium affect the excitability of neurons, the occurrence of seizures, and the stability of persistent states of activity. In this first paper, we construct a mathematical model consisting of a single conductance-based neuron together with intra- and extracellular ion concentration dynamics. We formulate a reduction of this model that permits a detailed bifurcation analysis, and show that the reduced model is a reasonable approximation of the full model. We find that competition between intrinsic neuronal currents, sodium-potassium pumps, glia, and diffusion can produce very slow and large-amplitude oscillations in ion concentrations similar to what is seen physiologically in seizures. Using the reduced model, we identify the dynamical mechanisms that give rise to these phenomena. These models reveal several experimentally testable predictions. Our work emphasizes the critical role of ion concentration homeostasis in the proper functioning of neurons, and points to important fundamental processes that may underlie pathological states such as epilepsy.
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Affiliation(s)
- John R Cressman
- Department of Physics and Astronomy, The Center for Neural Dynamics, and The Krasnow Institute for Advanced Study, George Mason University, Fairfax, VA 22030, USA.
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Durand DM, Park EY. Diffusive coupling can induce synchronized periodic activity in neural networks. ANNUAL INTERNATIONAL CONFERENCE OF THE IEEE ENGINEERING IN MEDICINE AND BIOLOGY SOCIETY. IEEE ENGINEERING IN MEDICINE AND BIOLOGY SOCIETY. ANNUAL INTERNATIONAL CONFERENCE 2009; 2008:3677-8. [PMID: 19163508 DOI: 10.1109/iembs.2008.4650005] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
Abstract
Diffusive coupling also known as nearest-neighbor coupling is a common form of coupling but its role in the behavior of neural circuits is unclear. Previous experimental and theoretical studies have shown that potassium lateral diffusion coupling (i.e., diffusive coupling) was responsible for synchronization of neuronal activity. We tested the hypothesis that potassium lateral diffusion coupling is required to generate periodic epileptiform activity in a zero-Ca(2+) CA1 pyramidal neuron network model. The simulation results show that potassium lateral diffusion coupling is crucial for establishing a periodic synchronized epileptiform activity similar to that observed in experimental preparations. This results suggest that potassium lateral diffusion coupling - a physiological realization of the concept of diffusive coupling - can play a role in network behavior.
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Affiliation(s)
- D M Durand
- Neural Engineering Center, Department of Biomedical Engineering, Case Western Reserve University, OH, USA
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Abstract
Diffusive coupling (nearest-neighbor coupling) is the most common type of coupling present in many systems. Previous experimental and theoretical studies have shown that potassium lateral diffusion coupling (i.e., diffusive coupling) can be responsible for synchronization of neuronal activity. Recent in vivo experiments carried out with anesthetized rat hippocampus suggested that the extracellular potassium could play an important role in the generation of a novel type of epileptiform nonsynaptic activity. Yet, the role of potassium in the generation of seizures remains controversial. We tested the hypothesis that potassium lateral diffusion coupling is responsible for the coupling mechanisms for network periodicity in a nonsynaptic model of epilepsy in vivo using a CA1 pyramidal neuron network model The simulation results show that 1), potassium lateral diffusion coupling is crucial for establishing epileptiform activity similar to that generated experimentally; and 2), there exists a scaling relation between the critical coupling strength and the number of cells in the network. The results not only agree with the theoretical prediction, but strongly suggest that potassium lateral diffusion coupling, a physiological realization of the concept of diffusive coupling, can play an important role in entraining periodicity in a nonsynaptic neural network.
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Takeshita D, Sato YD, Bahar S. Transitions between multistable states as a model of epileptic seizure dynamics. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2007; 75:051925. [PMID: 17677116 DOI: 10.1103/physreve.75.051925] [Citation(s) in RCA: 28] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/03/2006] [Revised: 03/26/2007] [Indexed: 05/16/2023]
Abstract
Epileptic seizures are generally considered to result from excess and synchronized neural activity. Additionally, changes in amplitude and frequency are often seen in local field potential or electroencephalogram recordings during a seizure event. To investigate how seizures initiate, and how dynamical changes occur during seizure progression, we develop a neocortical network model based on a model suggested by Wilson [J. Theor. Biol. 200, 375 (1999)]. We propose a possible mechanism for seizure initiation as a bifurcation, and suggest that experimentally observed changes in field potential amplitude and frequency during the course of a seizure may be explained by noise-induced transitions among multistable states.
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Affiliation(s)
- Daisuke Takeshita
- Center for Neurodynamics and Department of Physics and Astronomy, University of Missouri at St Louis, St Louis, MO 63121, USA
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