51
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Toglia P, Ullah G. Mitochondrial dysfunction and role in spreading depolarization and seizure. J Comput Neurosci 2019; 47:91-108. [PMID: 31506806 DOI: 10.1007/s10827-019-00724-6] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/13/2018] [Revised: 03/12/2019] [Accepted: 07/26/2019] [Indexed: 11/24/2022]
Abstract
The effect of pathological phenomena such as epileptic seizures and spreading depolarization (SD) on mitochondria and the potential feedback of mitochondrial dysfunction into the dynamics of those phenomena are complex and difficult to study experimentally due to the simultaneous changes in many variables governing neuronal behavior. By combining a model that accounts for a wide range of neuronal behaviors including seizures, normoxic SD, and hypoxic SD (HSD), together with a detailed model of mitochondrial function and intracellular Ca2+ dynamics, we investigate mitochondrial dysfunction and its potential role in recovery of the neuron from seizures, HSD, and SD. Our results demonstrate that HSD leads to the collapse of mitochondrial membrane potential and cellular ATP levels that recover only when normal oxygen supply is restored. Mitochondrial organic phosphate and pH gradients determine the strength of the depolarization block during HSD and SD, how quickly the cell enters the depolarization block when the oxygen supply is disrupted or potassium in the bath solution is raised beyond the physiological value, and how fast the cell recovers from SD and HSD when normal potassium concentration and oxygen supply are restored. Although not as dramatic as phosphate and pH gradients, mitochondrial Ca2+ uptake has a similar effect on neuronal behavior during these conditions.
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Affiliation(s)
- Patrick Toglia
- Department of Physics, University of South Florida, 4202 E. Fowler Ave., Tampa, FL, 33620, USA
| | - Ghanim Ullah
- Department of Physics, University of South Florida, 4202 E. Fowler Ave., Tampa, FL, 33620, USA.
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52
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González OC, Krishnan GP, Timofeev I, Bazhenov M. Ionic and synaptic mechanisms of seizure generation and epileptogenesis. Neurobiol Dis 2019; 130:104485. [PMID: 31150792 DOI: 10.1016/j.nbd.2019.104485] [Citation(s) in RCA: 17] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/12/2019] [Revised: 05/23/2019] [Accepted: 05/27/2019] [Indexed: 01/09/2023] Open
Abstract
The biophysical mechanisms underlying epileptogenesis and the generation of seizures remain to be better understood. Among many factors triggering epileptogenesis are traumatic brain injury breaking normal synaptic homeostasis and genetic mutations disrupting ionic concentration homeostasis. Impairments in these mechanisms, as seen in various brain diseases, may push the brain network to a pathological state characterized by increased susceptibility to unprovoked seizures. Here, we review recent computational studies exploring the roles of ionic concentration dynamics in the generation, maintenance, and termination of seizures. We further discuss how ionic and synaptic homeostatic mechanisms may give rise to conditions which prime brain networks to exhibit recurrent spontaneous seizures and epilepsy.
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Affiliation(s)
- Oscar C González
- Neurosciences Graduate Program, University of California, San Diego, CA 92093, United States of America; Department of Medicine, University of California, San Diego, CA 92093, United States of America
| | - Giri P Krishnan
- Department of Medicine, University of California, San Diego, CA 92093, United States of America
| | - Igor Timofeev
- Centre de recherche de l'Institut universitaire en santé mentale de Québec (CRIUSMQ), 2601 de la Canardière, Québec, QC, Canada; Department of Psychiatry and Neuroscience, Université Laval, Québec, QC, Canada
| | - Maxim Bazhenov
- Neurosciences Graduate Program, University of California, San Diego, CA 92093, United States of America; Department of Medicine, University of California, San Diego, CA 92093, United States of America.
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53
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Sudhakar SK, Choi TJ, Ahmed OJ. Biophysical Modeling Suggests Optimal Drug Combinations for Improving the Efficacy of GABA Agonists after Traumatic Brain Injuries. J Neurotrauma 2019; 36:1632-1645. [PMID: 30484362 PMCID: PMC6531909 DOI: 10.1089/neu.2018.6065] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/09/2023] Open
Abstract
Traumatic brain injuries (TBI) lead to dramatic changes in the surviving brain tissue. Altered ion concentrations, coupled with changes in the expression of membrane-spanning proteins, create a post-TBI brain state that can lead to further neuronal loss caused by secondary excitotoxicity. Several GABA receptor agonists have been tested in the search for neuroprotection immediately after an injury, with paradoxical results. These drugs not only fail to offer neuroprotection, but can also slow down functional recovery after TBI. Here, using computational modeling, we provide a biophysical hypothesis to explain these observations. We show that the accumulation of intracellular chloride ions caused by a transient upregulation of Na+-K+-2Cl- (NKCC1) co-transporters as observed following TBI, causes GABA receptor agonists to lead to excitation and depolarization block, rather than the expected hyperpolarization. The likelihood of prolonged, excitotoxic depolarization block is further exacerbated by the extremely high levels of extracellular potassium seen after TBI. Our modeling results predict that the neuroprotective efficacy of GABA receptor agonists can be substantially enhanced when they are combined with NKCC1 co-transporter inhibitors. This suggests a rational, biophysically principled method for identifying drug combinations for neuroprotection after TBI.
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Affiliation(s)
| | - Thomas J. Choi
- Department of Psychology, University of Michigan, Ann Arbor, Michigan
| | - Omar J. Ahmed
- Department of Psychology, University of Michigan, Ann Arbor, Michigan
- Department of Biomedical Engineering, University of Michigan, Ann Arbor, Michigan
- Department of Neuroscience Graduate Program, University of Michigan, Ann Arbor, Michigan
- Department of Kresge Hearing Research Institute, University of Michigan, Ann Arbor, Michigan
- Department of Michigan Center for Integrative Research in Critical Care, University of Michigan, Ann Arbor, Michigan
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54
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Chizhov AV, Amakhin DV, Zaitsev AV. Mathematical model of Na-K-Cl homeostasis in ictal and interictal discharges. PLoS One 2019; 14:e0213904. [PMID: 30875397 PMCID: PMC6420042 DOI: 10.1371/journal.pone.0213904] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/19/2018] [Accepted: 03/04/2019] [Indexed: 12/22/2022] Open
Abstract
Despite big experimental data on the phenomena and mechanisms of the generation of ictal and interictal discharges (IDs and IIDs), mathematical models that can describe the synaptic interactions of neurons and the ionic dynamics in biophysical detail are not well-established. Based on experimental recordings of combined hippocampal-entorhinal cortex slices from rats in a high-potassium and a low-magnesium solution containing 4-aminopyridine as well as previous observations of similar experimental models, this type of mathematical model has been developed. The model describes neuronal excitation through the application of the conductance-based refractory density approach for three neuronal populations: two populations of glutamatergic neurons with hyperpolarizing and depolarizing GABAergic synapses and one GABAergic population. The ionic dynamics account for the contributions of voltage-gated and synaptic channels, active and passive transporters, and diffusion. The relatively slow dynamics of potassium, chloride, and sodium ion concentrations determine the transitions from pure GABAergic IIDs to IDs and GABA-glutamatergic IIDs. The model reproduces different types of IIDs, including those initiated by interneurons; repetitive IDs; tonic and bursting modes of an ID composed of clustered IID-like events. The simulations revealed contributions from different ionic channels to the ion concentration dynamics before and during ID generation. The proposed model is a step forward to an optimal mathematical description of the mechanisms of epileptic discharges.
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Affiliation(s)
- Anton V. Chizhov
- Computational Physics Laboratory, Ioffe Institute, Saint Petersburg, Russia
- Laboratory of Molecular Mechanisms of Neural Interactions, Sechenov Institute of Evolutionary Physiology and Biochemistry of the Russian Academy of Sciences, Saint Petersburg, Russia
- * E-mail:
| | - Dmitry V. Amakhin
- Laboratory of Molecular Mechanisms of Neural Interactions, Sechenov Institute of Evolutionary Physiology and Biochemistry of the Russian Academy of Sciences, Saint Petersburg, Russia
| | - Aleksey V. Zaitsev
- Laboratory of Molecular Mechanisms of Neural Interactions, Sechenov Institute of Evolutionary Physiology and Biochemistry of the Russian Academy of Sciences, Saint Petersburg, Russia
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55
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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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56
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Buchin A, Kerr CC, Huberfeld G, Miles R, Gutkin B. Adaptation and Inhibition Control Pathological Synchronization in a Model of Focal Epileptic Seizure. eNeuro 2018; 5:ENEURO.0019-18.2018. [PMID: 30302390 PMCID: PMC6173584 DOI: 10.1523/eneuro.0019-18.2018] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/10/2018] [Revised: 06/07/2018] [Accepted: 06/07/2018] [Indexed: 01/12/2023] Open
Abstract
Pharmacoresistant epilepsy is a common neurological disorder in which increased neuronal intrinsic excitability and synaptic excitation lead to pathologically synchronous behavior in the brain. In the majority of experimental and theoretical epilepsy models, epilepsy is associated with reduced inhibition in the pathological neural circuits, yet effects of intrinsic excitability are usually not explicitly analyzed. Here we present a novel neural mass model that includes intrinsic excitability in the form of spike-frequency adaptation in the excitatory population. We validated our model using local field potential (LFP) data recorded from human hippocampal/subicular slices. We found that synaptic conductances and slow adaptation in the excitatory population both play essential roles for generating seizures and pre-ictal oscillations. Using bifurcation analysis, we found that transitions towards seizure and back to the resting state take place via Andronov-Hopf bifurcations. These simulations therefore suggest that single neuron adaptation as well as synaptic inhibition are responsible for orchestrating seizure dynamics and transition towards the epileptic state.
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Affiliation(s)
- Anatoly Buchin
- University of Washington, Department of Physiology and Biophysics (United States, Seattle), 1959 NE Pacific St, 98195
| | - Cliff C. Kerr
- University of Sydney, School of Physics (Australia, Sydney), Physics Rd, NSW 2006
| | - Gilles Huberfeld
- Sorbonne Université-UPMC, Pitié-Salpêtrière Hô, Neurophysiology Department (France, Paris), 47-83 Boulevard de l’Hôpital, 75013
- Institut national de la santé et de la recherche médicale Unit 1129 “Infantile Epilepsies and Brain Plasticity”, Paris Descartes University, Sorbonne Paris Cité University group, (France, Paris), 149 rue de Sévres 75015
| | - Richard Miles
- Brain and Spine Institute, Cortex and Epilepsie Group (France, Paris), 47 Boulevard Hôpital, 75013
| | - Boris Gutkin
- Paris Sciences & Lettres Research University, Laboratoire des Neurosciences Cognitives, Group for Neural Theory (France, Paris), 29, rue d'Ulm, 75005 France
- National Research University Higher School of Economics, Center for Cognition and Decision Making (Russia, Moscow), 20 Myasnitskaya, 109316
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57
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Yao C, He Z, Nakano T, Shuai J. Spiking patterns of a neuron model to stimulus: Rich dynamics and oxygen's role. CHAOS (WOODBURY, N.Y.) 2018; 28:083112. [PMID: 30180647 DOI: 10.1063/1.5018707] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/08/2017] [Accepted: 07/23/2018] [Indexed: 06/08/2023]
Abstract
Neuronal spiking patterns, which are of fundamental importance for the understanding of information processing in neural systems, can be generated in response to different stimuli. We here investigate in detail the stimulus-induced spiking patterns in a biologically plausible neuron model in which the oxygen concentration and the dynamical concentrations of potassium, sodium, and chloride are considered. Various types of spiking patterns can be induced by the different external potassium accumulations in response to the stimulus, including two different types of epileptic seizure (SZ) and spreading depression (SD) states, two different mixed states of SD and SZ, SZ state with multi-burst, and tonic firing behaviors. Interestingly, we show that these rich spiking patterns can also be induced by the current stimulus with a low oxygen concentration. Furthermore, we reveal that the stimulus can induce two different phase transitions from the SD state to the SZ state according to the phase transition theory, which results in the different electrical activities. All these findings may provide insight into information processing in neural systems.
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Affiliation(s)
- Chenggui Yao
- Department of Mathematics, Shaoxing University, Shaoxing 312000, China
| | - Zhiwei He
- Department of Mathematics, Shaoxing University, Shaoxing 312000, China
| | - Tadashi Nakano
- Graduate School of Frontier Biosciences, Osaka University, 1-1 Yamadaoka, Suita, Osaka 565-0871, Japan
| | - Jianwei Shuai
- Department of Physics, Xiamen University, Xiamen 361005, People's Republic of China
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58
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Chizhov AV, Zefirov AV, Amakhin DV, Smirnova EY, Zaitsev AV. Minimal model of interictal and ictal discharges "Epileptor-2". PLoS Comput Biol 2018; 14:e1006186. [PMID: 29851959 PMCID: PMC6005638 DOI: 10.1371/journal.pcbi.1006186] [Citation(s) in RCA: 35] [Impact Index Per Article: 5.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/28/2017] [Revised: 06/18/2018] [Accepted: 05/09/2018] [Indexed: 12/01/2022] Open
Abstract
Seizures occur in a recurrent manner with intermittent states of interictal and ictal discharges (IIDs and IDs). The transitions to and from IDs are determined by a set of processes, including synaptic interaction and ionic dynamics. Although mathematical models of separate types of epileptic discharges have been developed, modeling the transitions between states remains a challenge. A simple generic mathematical model of seizure dynamics (Epileptor) has recently been proposed by Jirsa et al. (2014); however, it is formulated in terms of abstract variables. In this paper, a minimal population-type model of IIDs and IDs is proposed that is as simple to use as the Epileptor, but the suggested model attributes physical meaning to the variables. The model is expressed in ordinary differential equations for extracellular potassium and intracellular sodium concentrations, membrane potential, and short-term synaptic depression variables. A quadratic integrate-and-fire model driven by the population input current is used to reproduce spike trains in a representative neuron. In simulations, potassium accumulation governs the transition from the silent state to the state of an ID. Each ID is composed of clustered IID-like events. The sodium accumulates during discharge and activates the sodium-potassium pump, which terminates the ID by restoring the potassium gradient and thus polarizing the neuronal membranes. The whole-cell and cell-attached recordings of a 4-AP-based in vitro model of epilepsy confirmed the primary model assumptions and predictions. The mathematical analysis revealed that the IID-like events are large-amplitude stochastic oscillations, which in the case of ID generation are controlled by slow oscillations of ionic concentrations. The IDs originate in the conditions of elevated potassium concentrations in a bath solution via a saddle-node-on-invariant-circle-like bifurcation for a non-smooth dynamical system. By providing a minimal biophysical description of ionic dynamics and network interactions, the model may serve as a hierarchical base from a simple to more complex modeling of seizures. In pathological conditions of epilepsy, the functioning of the neural network crucially depends on the ionic concentrations inside and outside neurons. A number of factors that affect neuronal activity is large. That is why the development of a minimal model that reproduces typical seizures could structure further experimental and analytical studies of the pathological mechanisms. Here, on a base of known biophysical models, we present a simple population-type model that includes only four principal variables, the extracellular potassium concentration, the intracellular sodium concentration, the membrane potential and the synaptic resource diminishing due to short-term synaptic depression. A simple modeled neuron is used as an observer of the population activity. We validate the model assumptions with in vitro experiments. Our model reproduces ictal and interictal events, where the latter result in bursts of spikes in single neurons, and the former represent the cluster of spike bursts. Mathematical analysis reveals that the bursts are spontaneous large-amplitude oscillations, which may cluster after a saddle-node on invariant circle bifurcation in the pro-epileptic conditions. Our consideration has significant bearing in understanding pathological neuronal network dynamics.
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Affiliation(s)
- Anton V. Chizhov
- Laboratory of Molecular Mechanisms of Neural Interactions, Sechenov Institute of Evolutionary Physiology and Biochemistry of the Russian Academy of Sciences, Saint Petersburg, Russia
- Computational Physics Laboratory, Ioffe Institute, Saint Petersburg, Russia
- * E-mail:
| | - Artyom V. Zefirov
- Laboratory of Molecular Mechanisms of Neural Interactions, Sechenov Institute of Evolutionary Physiology and Biochemistry of the Russian Academy of Sciences, Saint Petersburg, Russia
- Computational Physics Laboratory, Ioffe Institute, Saint Petersburg, Russia
| | - Dmitry V. Amakhin
- Laboratory of Molecular Mechanisms of Neural Interactions, Sechenov Institute of Evolutionary Physiology and Biochemistry of the Russian Academy of Sciences, Saint Petersburg, Russia
| | - Elena Yu. Smirnova
- Laboratory of Molecular Mechanisms of Neural Interactions, Sechenov Institute of Evolutionary Physiology and Biochemistry of the Russian Academy of Sciences, Saint Petersburg, Russia
- Computational Physics Laboratory, Ioffe Institute, Saint Petersburg, Russia
| | - Aleksey V. Zaitsev
- Laboratory of Molecular Mechanisms of Neural Interactions, Sechenov Institute of Evolutionary Physiology and Biochemistry of the Russian Academy of Sciences, Saint Petersburg, Russia
- Institute of Experimental Medicine, Almazov National Medical Research Centre, Saint Petersburg, Russia
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59
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Naji M, Komarov M, Krishnan GP, Malhotra A, Powell FL, Rukhadze I, Fenik VB, Bazhenov M. Computational model of brain-stem circuit for state-dependent control of hypoglossal motoneurons. J Neurophysiol 2018; 120:296-305. [PMID: 29617218 DOI: 10.1152/jn.00728.2017] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/28/2022] Open
Abstract
In patients with obstructive sleep apnea (OSA), the pharyngeal muscles become relaxed during sleep, which leads to a partial or complete closure of upper airway. Experimental studies suggest that withdrawal of noradrenergic and serotonergic drives importantly contributes to depression of hypoglossal motoneurons and, therefore, may contribute to OSA pathophysiology; however, specific cellular and synaptic mechanisms remain unknown. In this new study, we developed a biophysical network model to test the hypothesis that, to explain experimental observations, the neuronal network for monoaminergic control of excitability of hypoglossal motoneurons needs to include excitatory and inhibitory perihypoglossal interneurons that mediate noradrenergic and serotonergic drives to hypoglossal motoneurons. In the model, the state-dependent activation of the hypoglossal motoneurons was in qualitative agreement with in vivo data during simulated rapid eye movement (REM) and non-REM sleep. The model was applied to test the mechanisms of action of noradrenergic and serotonergic drugs during REM sleep as observed in vivo. We conclude that the proposed minimal neuronal circuit is sufficient to explain in vivo data and supports the hypothesis that perihypoglossal interneurons may mediate state-dependent monoaminergic drive to hypoglossal motoneurons. The population of the hypothesized perihypoglossal interneurons may serve as novel targets for pharmacological treatment of OSA. NEW & NOTEWORTHY In vivo studies suggest that during rapid eye movement sleep, withdrawal of noradrenergic and serotonergic drives critically contributes to depression of hypoglossal motoneurons (HMs), which innervate the tongue muscles. By means of a biophysical model, which is consistent with a broad range of empirical data, we demonstrate that the neuronal network controlling the excitability of HMs needs to include excitatory and inhibitory interneurons that mediate noradrenergic and serotonergic drives to HMs.
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Affiliation(s)
- Mohsen Naji
- Department of Medicine, Division of Pulmonary, Critical Care & Sleep Medicine, University of California, San Diego, La Jolla, California
| | - Maxim Komarov
- Department of Medicine, Division of Pulmonary, Critical Care & Sleep Medicine, University of California, San Diego, La Jolla, California
| | - Giri P Krishnan
- Department of Medicine, Division of Pulmonary, Critical Care & Sleep Medicine, University of California, San Diego, La Jolla, California
| | - Atul Malhotra
- Department of Medicine, Division of Pulmonary, Critical Care & Sleep Medicine, University of California, San Diego, La Jolla, California
| | - Frank L Powell
- Department of Medicine, Division of Pulmonary, Critical Care & Sleep Medicine, University of California, San Diego, La Jolla, California
| | - Irma Rukhadze
- Veterans Affairs Greater Los Angeles Healthcare System, Los Angeles, California.,Department of Medicine, University of California, Los Angeles School of Medicine , Los Angeles, California
| | - Victor B Fenik
- Veterans Affairs Greater Los Angeles Healthcare System, Los Angeles, California.,WebSciences International, Los Angeles, California
| | - Maxim Bazhenov
- Department of Medicine, Division of Pulmonary, Critical Care & Sleep Medicine, University of California, San Diego, La Jolla, California
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60
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Du M, Li J, Chen L, Yu Y, Wu Y. Astrocytic Kir4.1 channels and gap junctions account for spontaneous epileptic seizure. PLoS Comput Biol 2018; 14:e1005877. [PMID: 29590095 PMCID: PMC5891073 DOI: 10.1371/journal.pcbi.1005877] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/24/2017] [Revised: 04/09/2018] [Accepted: 11/06/2017] [Indexed: 01/30/2023] Open
Abstract
Experimental recordings in hippocampal slices indicate that astrocytic dysfunction may cause neuronal hyper-excitation or seizures. Considering that astrocytes play important roles in mediating local uptake and spatial buffering of K+ in the extracellular space of the cortical circuit, we constructed a novel model of an astrocyte-neuron network module consisting of a single compartment neuron and 4 surrounding connected astrocytes and including extracellular potassium dynamics. Next, we developed a new model function for the astrocyte gap junctions, connecting two astrocyte-neuron network modules. The function form and parameters of the gap junction were based on nonlinear regression fitting of a set of experimental data published in previous studies. Moreover, we have created numerical simulations using the above single astrocyte-neuron network module and the coupled astrocyte-neuron network modules. Our model validates previous experimental observations that both Kir4.1 channels and gap junctions play important roles in regulating the concentration of extracellular potassium. In addition, we also observe that changes in Kir4.1 channel conductance and gap junction strength induce spontaneous epileptic activity in the absence of external stimuli. Astrocytes are critical regulators of normal physiological activity in the central nervous system, and one of their key functions is removing extracellular K+. In recent years, numerous biological studies have shown that astrocytic Kir4.1 channels and gap junctions between astrocytes act as major K+ clearance mechanisms. Dysfunction of either of these regulatory mechanisms may cause generation of K+-induced seizures. However, it is unclear how and to what extent these two K+-regulating processes lead to spontaneous epileptic activity. These questions were addressed in the present study by constructing novel single astrocyte-neuron network models and a coupled astrocyte-neuron module network connected by an astrocyte gap junction based on existing experimental observations and previous theoretical reports. Simulation results first verified that either down-regulation of astrocytic Kir4.1 channels or a decrease of the gap junction strength between astrocytes causes neuropathological hyper-excitability and spontaneous epileptic activity. These results imply that dysfunctional astrocytes should be considered as targets for therapeutic strategies in epilepsy.
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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
- State Key Laboratory of Medical Neurobiology, School of Life Science and Human Phenome Institute, Institutes of Brain Science, Institute of Science and Technology for Brain-Inspired Intelligence, Fudan University, Shanghai, China
| | - Jiajia Li
- State Key Laboratory for Strength and Vibration of Mechanical Structures, School of Aerospace, Xi’an Jiaotong University, Xi’an, China
| | - Liang Chen
- Department of Neurosurgery, Huashan Hospital, Shanghai Medical College, Fudan University, Shanghai, China
| | - Yuguo Yu
- State Key Laboratory of Medical Neurobiology, School of Life Science and Human Phenome Institute, Institutes of Brain Science, Institute of Science and Technology for Brain-Inspired Intelligence, Fudan University, Shanghai, China
- * E-mail: (YY); (YW)
| | - Ying Wu
- State Key Laboratory for Strength and Vibration of Mechanical Structures, School of Aerospace, Xi’an Jiaotong University, Xi’an, China
- Key Laboratory for NeuroInformation of Ministry of Education, University of Electronic Science and Technology of China, Chengdu, China
- * E-mail: (YY); (YW)
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61
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Calvetti D, Capo Rangel G, Gerardo Giorda L, Somersalo E. A computational model integrating brain electrophysiology and metabolism highlights the key role of extracellular potassium and oxygen. J Theor Biol 2018. [PMID: 29530764 DOI: 10.1016/j.jtbi.2018.02.029] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/11/2022]
Abstract
The human brain is a small organ which uses a disproportionate amount of the total metabolic energy production in the body. While it is well understood that the most significant energy sink is the maintenance of the neuronal membrane potential during the brain signaling activity, the role of astrocytes in the energy balance continues to be the topic of a lot of research. A key function of astrocytes, besides clearing glutamate from the synaptic clefts, is the potassium clearing after neuronal activation. Extracellular potassium plays a significant role in triggering neuronal firing, and elevated concentration of potassium may lead to abnormal firing patterns, e.g., seizures, thus emphasizing the importance of the glial K+ buffering role. The predictive mathematical model proposed in this paper elucidates the role of glial potassium clearing in brain energy metabolism, integrating a detailed model of the ion dynamics which regulates neuronal firing with a four compartment metabolic model. Because of the very different characteristic time scales of electrophysiology and metabolism, care must be taken when coupling the two models to ensure that the predictions, e.g., neuronal firing frequencies and the oxygen-glucose index (OGI) of the brain during activation and rest, are in agreement with empirical observations. The temporal multi-scale nature of the problem requires the design of new computational tools to ensure a stable and accurate numerical treatment. The model predictions for different protocols, including combinations of elevated activation and ischemic episodes, are in good agreement with experimental observations reported in the literature.
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Affiliation(s)
- D Calvetti
- Department of Mathematics, Applied Mathematics and Statistics, Case Western Reserve University, USA
| | | | | | - E Somersalo
- Department of Mathematics, Applied Mathematics and Statistics, Case Western Reserve University, USA; Basque Center for Applied Mathematics, Spain.
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62
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Study on the mechanisms of seizure-like events suppression effect by electrical stimulation using a microelectrode array. Neuroreport 2018; 28:471-478. [PMID: 28445249 DOI: 10.1097/wnr.0000000000000786] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
Abstract
In this paper, we studied the mechanisms underlying the suppression of seizure-like events (SLEs) by electrical stimulation. We conducted an in-vitro experiment using entorhinal cortex combined hippocampal slices and two convulsant drugs, bicuculline and 4-aminopyridine, to induce spontaneous SLEs. We used a microelectrode array to observe network dynamics over the entire hippocampal area simultaneously, including regions far from the stimulation site. We stimulated the entorhinal cortex region, which has been determined to be a focus of SLEs by Granger causality analysis of multichannel time series data, by an external electrode. In bicuculline application, electrical stimulation showed a marked suppression effect, even though the sizes of the effective region differed. In 4-aminopyridine application, however, stimulation under the same conditions did not suppress the activities in ∼80% of SLEs. The suppression effect was more remarkable in the areas surrounding the stimulation site in both cases. Our experimental results could support the neuronal depolarization blockade mechanism by accumulation of extracellular potassium ions, which is one of the most convincing mechanisms to understand seizure suppression phenomena because of electrical stimulation. Computer simulation using a neuronal network model also confirmed the mechanism.
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Kroos JM, Marinelli I, Diez I, Cortes JM, Stramaglia S, Gerardo-Giorda L. Patient-specific computational modeling of cortical spreading depression via diffusion tensor imaging. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING 2017; 33:e2874. [PMID: 28226410 DOI: 10.1002/cnm.2874] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/06/2016] [Revised: 02/15/2017] [Accepted: 02/19/2017] [Indexed: 06/06/2023]
Abstract
Cortical spreading depression, a depolarization wave originating in the visual cortex and traveling towards the frontal lobe, is commonly accepted as a correlate of migraine visual aura. As of today, little is known about the mechanisms that can trigger or stop such phenomenon. However, the complex and highly individual characteristics of the brain cortex suggest that the geometry might have a significant impact in supporting or contrasting the propagation of cortical spreading depression. Accurate patient-specific computational models are fundamental to cope with the high variability in cortical geometries among individuals, but also with the conduction anisotropy induced in a given cortex by the complex neuronal organisation in the grey matter. In this paper, we integrate a distributed model for extracellular potassium concentration with patient-specific diffusivity tensors derived locally from diffusion tensor imaging data.
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Affiliation(s)
- Julia M Kroos
- Basque Center for Applied Mathematics, Bilbao, Spain
| | | | - Ibai Diez
- Comp. Neuroimaging Lab, BioCruces Health Research Institute, Cruces University Hospital, Barakaldo, Spain
| | - Jesus M Cortes
- Comp. Neuroimaging Lab, BioCruces Health Research Institute, Cruces University Hospital, Barakaldo, Spain
- Ikerbasque: The Basque Foundation for Science, Bilbao, Spain
- Department of Cell Biology and Histology, University of the Basque Country (UPV/EHU), Leioa, Spain
| | - Sebastiano Stramaglia
- Basque Center for Applied Mathematics, Bilbao, Spain
- Dipartimento di Fisica, Universita di Bari, Italy
- INFN, Sezione di Bari, Italy
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64
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Hübel N, Hosseini-Zare MS, Žiburkus J, Ullah G. The role of glutamate in neuronal ion homeostasis: A case study of spreading depolarization. PLoS Comput Biol 2017; 13:e1005804. [PMID: 29023523 PMCID: PMC5655358 DOI: 10.1371/journal.pcbi.1005804] [Citation(s) in RCA: 21] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/10/2016] [Revised: 10/24/2017] [Accepted: 09/30/2017] [Indexed: 01/30/2023] Open
Abstract
Simultaneous changes in ion concentrations, glutamate, and cell volume together with exchange of matter between cell network and vasculature are ubiquitous in numerous brain pathologies. A complete understanding of pathological conditions as well as normal brain function, therefore, hinges on elucidating the molecular and cellular pathways involved in these mostly interdependent variations. In this paper, we develop the first computational framework that combines the Hodgkin-Huxley type spiking dynamics, dynamic ion concentrations and glutamate homeostasis, neuronal and astroglial volume changes, and ion exchange with vasculature into a comprehensive model to elucidate the role of glutamate uptake in the dynamics of spreading depolarization (SD)-the electrophysiological event underlying numerous pathologies including migraine, ischemic stroke, aneurysmal subarachnoid hemorrhage, intracerebral hematoma, and trauma. We are particularly interested in investigating the role of glutamate in the duration and termination of SD caused by K+ perfusion and oxygen-glucose deprivation. Our results demonstrate that glutamate signaling plays a key role in the dynamics of SD, and that impaired glutamate uptake leads to recovery failure of neurons from SD. We confirm predictions from our model experimentally by showing that inhibiting astrocytic glutamate uptake using TFB-TBOA nearly quadruples the duration of SD in layers 2-3 of visual cortical slices from juvenile rats. The model equations are either derived purely from first physical principles of electroneutrality, osmosis, and conservation of particles or a combination of these principles and known physiological facts. Accordingly, we claim that our approach can be used as a future guide to investigate the role of glutamate, ion concentrations, and dynamics cell volume in other brain pathologies and normal brain function.
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Affiliation(s)
- Niklas Hübel
- Department of Physics, University of South Florida, Tampa, Florida, United States of America
| | - Mahshid S. Hosseini-Zare
- Department of Biology and Biochemistry, University of Houston, Houston, Texas, United States of America
| | - Jokūbas Žiburkus
- Department of Biology and Biochemistry, University of Houston, Houston, Texas, United States of America
| | - Ghanim Ullah
- Department of Physics, University of South Florida, Tampa, Florida, United States of America
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Grigorovsky V, Bardakjian BL. Low-to-High Cross-Frequency Coupling in the Electrical Rhythms as Biomarker for Hyperexcitable Neuroglial Networks of the Brain. IEEE Trans Biomed Eng 2017; 65:1504-1515. [PMID: 28961101 DOI: 10.1109/tbme.2017.2757878] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/05/2022]
Abstract
OBJECTIVE One of the features used in the study of hyperexcitablility is high-frequency oscillations (HFOs, >80 Hz). HFOs have been reported in the electrical rhythms of the brain's neuroglial networks under physiological and pathological conditions. Cross-frequency coupling (CFC) of HFOs with low-frequency rhythms was used to identify pathologic HFOs in the epileptogenic zones of epileptic patients and as a biomarker for the severity of seizure-like events in genetically modified rodent models. We describe a model to replicate reported CFC features extracted from recorded local field potentials (LFPs) representing network properties. METHODS This study deals with a four-unit neuroglial cellular network model where each unit incorporates pyramidal cells, interneurons, and astrocytes. Three different pathways of hyperexcitability generation-Na - ATPase pump, glial potassium clearance, and potassium afterhyperpolarization channel-were used to generate LFPs. Changes in excitability, average spontaneous electrical discharge (SED) duration, and CFC were then measured and analyzed. RESULTS Each parameter caused an increase in network excitability and the consequent lengthening of the SED duration. Short SEDs showed CFC between HFOs and theta oscillations (4-8 Hz), but in longer SEDs the low frequency changed to the delta range (1-4 Hz). CONCLUSION Longer duration SEDs exhibit CFC features similar to those reported by our team. SIGNIFICANCE First, Identifying the exponential relationship between network excitability and SED durations; second, highlighting the importance of glia in hyperexcitability (as they relate to extracellular potassium); and third, elucidation of the biophysical basis for CFC coupling features.
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Zylbertal A, Yarom Y, Wagner S. The Slow Dynamics of Intracellular Sodium Concentration Increase the Time Window of Neuronal Integration: A Simulation Study. Front Comput Neurosci 2017; 11:85. [PMID: 28970791 PMCID: PMC5609115 DOI: 10.3389/fncom.2017.00085] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/27/2017] [Accepted: 09/04/2017] [Indexed: 12/02/2022] Open
Abstract
Changes in intracellular Na+ concentration ([Na+]i) are rarely taken into account when neuronal activity is examined. As opposed to Ca2+, [Na+]i dynamics are strongly affected by longitudinal diffusion, and therefore they are governed by the morphological structure of the neurons, in addition to the localization of influx and efflux mechanisms. Here, we examined [Na+]i dynamics and their effects on neuronal computation in three multi-compartmental neuronal models, representing three distinct cell types: accessory olfactory bulb (AOB) mitral cells, cortical layer V pyramidal cells, and cerebellar Purkinje cells. We added [Na+]i as a state variable to these models, and allowed it to modulate the Na+ Nernst potential, the Na+-K+ pump current, and the Na+-Ca2+ exchanger rate. Our results indicate that in most cases [Na+]i dynamics are significantly slower than [Ca2+]i dynamics, and thus may exert a prolonged influence on neuronal computation in a neuronal type specific manner. We show that [Na+]i dynamics affect neuronal activity via three main processes: reduction of EPSP amplitude in repeatedly active synapses due to reduction of the Na+ Nernst potential; activity-dependent hyperpolarization due to increased activity of the Na+-K+ pump; specific tagging of active synapses by extended Ca2+ elevation, intensified by concurrent back-propagating action potentials or complex spikes. Thus, we conclude that [Na+]i dynamics should be considered whenever synaptic plasticity, extensive synaptic input, or bursting activity are examined.
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Affiliation(s)
- Asaph Zylbertal
- Department of Neurobiology, Institute of Life Sciences, The Hebrew University and the Edmond and Lily Safra Center for Brain SciencesJerusalem, Israel
| | - Yosef Yarom
- Department of Neurobiology, Institute of Life Sciences, The Hebrew University and the Edmond and Lily Safra Center for Brain SciencesJerusalem, Israel
| | - Shlomo Wagner
- Sagol Department of Neurobiology, University of HaifaHaifa, Israel
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67
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Madi MK, Karameh FN. Hybrid Cubature Kalman filtering for identifying nonlinear models from sampled recording: Estimation of neuronal dynamics. PLoS One 2017; 12:e0181513. [PMID: 28727850 PMCID: PMC5519212 DOI: 10.1371/journal.pone.0181513] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/06/2016] [Accepted: 07/03/2017] [Indexed: 11/18/2022] Open
Abstract
Kalman filtering methods have long been regarded as efficient adaptive Bayesian techniques for estimating hidden states in models of linear dynamical systems under Gaussian uncertainty. Recent advents of the Cubature Kalman filter (CKF) have extended this efficient estimation property to nonlinear systems, and also to hybrid nonlinear problems where by the processes are continuous and the observations are discrete (continuous-discrete CD-CKF). Employing CKF techniques, therefore, carries high promise for modeling many biological phenomena where the underlying processes exhibit inherently nonlinear, continuous, and noisy dynamics and the associated measurements are uncertain and time-sampled. This paper investigates the performance of cubature filtering (CKF and CD-CKF) in two flagship problems arising in the field of neuroscience upon relating brain functionality to aggregate neurophysiological recordings: (i) estimation of the firing dynamics and the neural circuit model parameters from electric potentials (EP) observations, and (ii) estimation of the hemodynamic model parameters and the underlying neural drive from BOLD (fMRI) signals. First, in simulated neural circuit models, estimation accuracy was investigated under varying levels of observation noise (SNR), process noise structures, and observation sampling intervals (dt). When compared to the CKF, the CD-CKF consistently exhibited better accuracy for a given SNR, sharp accuracy increase with higher SNR, and persistent error reduction with smaller dt. Remarkably, CD-CKF accuracy shows only a mild deterioration for non-Gaussian process noise, specifically with Poisson noise, a commonly assumed form of background fluctuations in neuronal systems. Second, in simulated hemodynamic models, parametric estimates were consistently improved under CD-CKF. Critically, time-localization of the underlying neural drive, a determinant factor in fMRI-based functional connectivity studies, was significantly more accurate under CD-CKF. In conclusion, and with the CKF recently benchmarked against other advanced Bayesian techniques, the CD-CKF framework could provide significant gains in robustness and accuracy when estimating a variety of biological phenomena models where the underlying process dynamics unfold at time scales faster than those seen in collected measurements.
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Affiliation(s)
- Mahmoud K. Madi
- Department of Electrical and Computer Engineering, American University of Beirut, Beirut, Lebanon
| | - Fadi N. Karameh
- Department of Electrical and Computer Engineering, American University of Beirut, Beirut, Lebanon
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68
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Zhang Y, Bucher D, Nadim F. Ionic mechanisms underlying history-dependence of conduction delay in an unmyelinated axon. eLife 2017; 6. [PMID: 28691900 PMCID: PMC5519330 DOI: 10.7554/elife.25382] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/23/2017] [Accepted: 07/06/2017] [Indexed: 11/13/2022] Open
Abstract
Axonal conduction velocity can change substantially during ongoing activity, thus modifying spike interval structures and, potentially, temporal coding. We used a biophysical model to unmask mechanisms underlying the history-dependence of conduction. The model replicates activity in the unmyelinated axon of the crustacean stomatogastric pyloric dilator neuron. At the timescale of a single burst, conduction delay has a non-monotonic relationship with instantaneous frequency, which depends on the gating rates of the fast voltage-gated Na+ current. At the slower timescale of minutes, the mean value and variability of conduction delay increase. These effects are because of hyperpolarization of the baseline membrane potential by the Na+/K+ pump, balanced by an h-current, both of which affect the gating of the Na+ current. We explore the mechanisms of history-dependence of conduction delay in axons and develop an empirical equation that accurately predicts this history-dependence, both in the model and in experimental measurements.
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Affiliation(s)
- Yang Zhang
- Department of Mathematical Sciences, New Jersey Institute of Technology, Newark, United States
| | - Dirk Bucher
- Federated Department of Biological Sciences, NJIT and Rutgers University, Newark, United States
| | - Farzan Nadim
- Department of Mathematical Sciences, New Jersey Institute of Technology, Newark, United States.,Federated Department of Biological Sciences, NJIT and Rutgers University, Newark, United States
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Ridley B, Marchi A, Wirsich J, Soulier E, Confort-Gouny S, Schad L, Bartolomei F, Ranjeva JP, Guye M, Zaaraoui W. Brain sodium MRI in human epilepsy: Disturbances of ionic homeostasis reflect the organization of pathological regions. Neuroimage 2017; 157:173-183. [PMID: 28602596 DOI: 10.1016/j.neuroimage.2017.06.011] [Citation(s) in RCA: 24] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/17/2017] [Revised: 06/01/2017] [Accepted: 06/03/2017] [Indexed: 12/15/2022] Open
Abstract
In light of technical advancements supporting exploration of MR signals other than 1H, sodium (23Na) has received attention as a marker of ionic homeostasis and cell viability. Here, we evaluate for the first time the possibility that 23Na-MRI is sensitive to pathological processes occurring in human epilepsy. A normative sample of 27 controls was used to normalize regions of interest (ROIs) from 1424 unique brain locales on quantitative 23Na-MRI and high-resolution 1H-MPRAGE images. ROIs were based on intracerebral electrodes in ten patients undergoing epileptic network mapping. The stereo-EEG gold standard was used to define regions as belonging to primarily epileptogenic, secondarily irritative and to non-involved regions. Estimates of total sodium concentration (TSC) on 23Na-MRI and cerebrospinal fluid (CSF) on 1H imaging were extracted for each patient ROI, and normalized against the same region in controls. ROIs with disproportionate CSF contributions (ZCSF≥1.96) were excluded. TSC levels were found to be elevated in patients relative to controls except in one patient, who suffered non-convulsive seizures during the scan, in whom we found reduced TSC levels. In the remaining patients, an ANOVA (F1100= 12.37, p<0.0001) revealed a highly significant effect of clinically-defined zones (F1100= 11.13, p<0.0001), with higher normalized TSC in the epileptogenic zone relative to both secondarily irritative (F1100= 11, p=0.0009) and non-involved regions (F1100= 17.8, p<0.0001). We provide the first non-invasive, in vivo evidence of a chronic TSC elevation alongside ZCSF levels within the normative range, associated with the epileptogenic region even during the interictal period in human epilepsy, and the possibility of reduced TSC levels due to seizure. In line with modified homeostatic mechanisms in epilepsy - including altered mechanisms underlying ionic gating, clearance and exchange - we provide the first indication of 23Na-MRI as an assay of altered sodium concentrations occurring in epilepsy associated with the organization of clinically relevant divisions of pathological cortex.
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Affiliation(s)
- Ben Ridley
- Aix-Marseille Univ, CNRS, CRMBM UMR 7339, Marseille, France; APHM, Hôpital de la Timone, Pôle d'Imagerie Médicale, CEMEREM, Marseille, France
| | - Angela Marchi
- APHM, Hôpital de la Timone, Clinical Neurophysiology and Epileptology Department, Marseille, France; Aix Marseille Univ, Inserm, INS, Institut de Neurosciences des Systèmes, Marseille, France
| | - Jonathan Wirsich
- Aix-Marseille Univ, CNRS, CRMBM UMR 7339, Marseille, France; APHM, Hôpital de la Timone, Pôle d'Imagerie Médicale, CEMEREM, Marseille, France; Aix Marseille Univ, Inserm, INS, Institut de Neurosciences des Systèmes, Marseille, France
| | - Elisabeth Soulier
- Aix-Marseille Univ, CNRS, CRMBM UMR 7339, Marseille, France; APHM, Hôpital de la Timone, Pôle d'Imagerie Médicale, CEMEREM, Marseille, France
| | - Sylviane Confort-Gouny
- Aix-Marseille Univ, CNRS, CRMBM UMR 7339, Marseille, France; APHM, Hôpital de la Timone, Pôle d'Imagerie Médicale, CEMEREM, Marseille, France
| | - Lothar Schad
- Computer Assisted Clinical Medicine, Heidelberg University, Mannheim, Germany
| | - Fabrice Bartolomei
- Aix Marseille Univ, Inserm, INS, Institut de Neurosciences des Systèmes, Marseille, France; APHM, Hôpitaux de la Timone, Service de Neurophysiologie Clinique, Marseille, France
| | - Jean-Philippe Ranjeva
- Aix-Marseille Univ, CNRS, CRMBM UMR 7339, Marseille, France; APHM, Hôpital de la Timone, Pôle d'Imagerie Médicale, CEMEREM, Marseille, France
| | - Maxime Guye
- Aix-Marseille Univ, CNRS, CRMBM UMR 7339, Marseille, France; APHM, Hôpital de la Timone, Pôle d'Imagerie Médicale, CEMEREM, Marseille, France.
| | - Wafaa Zaaraoui
- Aix-Marseille Univ, CNRS, CRMBM UMR 7339, Marseille, France; APHM, Hôpital de la Timone, Pôle d'Imagerie Médicale, CEMEREM, Marseille, France
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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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71
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Synchronous Infra-Slow Bursting in the Mouse Accessory Olfactory Bulb Emerge from Interplay between Intrinsic Neuronal Dynamics and Network Connectivity. J Neurosci 2017; 37:2656-2672. [PMID: 28148726 DOI: 10.1523/jneurosci.3107-16.2017] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/06/2016] [Revised: 01/12/2017] [Accepted: 01/16/2017] [Indexed: 11/21/2022] Open
Abstract
Rhythmic neuronal activity of multiple frequency bands has been described in many brain areas and attributed to numerous brain functions. Among these, little is known about the mechanism and role of infra-slow oscillations, which have been demonstrated recently in the mouse accessory olfactory bulb (AOB). Along with prolonged responses to stimuli and distinct network connectivity, they inexplicably affect the AOB processing of social relevant stimuli. Here, we show that assemblies of AOB mitral cells are synchronized by lateral interactions through chemical and electrical synapses. Using a network model, we demonstrate that the synchronous oscillations in these assemblies emerge from interplay between intrinsic membrane properties and network connectivity. As a consequence, the AOB network topology, in which each mitral cell receives input from multiple glomeruli, enables integration of chemosensory stimuli over extended time scales by interglomerular synchrony of infra-slow bursting. These results provide a possible functional significance for the distinct AOB physiology and topology. Beyond the AOB, this study presents a general model for synchronous infra-slow bursting in neuronal networks.SIGNIFICANCE STATEMENT Infra-slow rhythmic neuronal activity with a very long (>10 s) duration has been described in many brain areas, but little is known about the role of this activity and the mechanisms that produce it. Here, we combine experimental and computational methods to show that synchronous infra-slow bursting activity in mitral cells of the mouse accessory olfactory bulb (AOB) emerges from interplay between intracellular dynamics and network connectivity. In this novel mechanism, slow intracellular Na+ dynamics endow AOB mitral cells with a weak tendency to burst, which is further enhanced and stabilized by chemical and electrical synapses between them. Combined with the unique topology of the AOB network, infra-slow bursting enables integration and binding of multiple chemosensory stimuli over a prolonged time scale.
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72
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Joos B, Barlow BM, Morris CE. Calculating the Consequences of Left-Shifted Nav Channel Activity in Sick Excitable Cells. Handb Exp Pharmacol 2017; 246:401-422. [PMID: 29030712 DOI: 10.1007/164_2017_63] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/29/2022]
Abstract
Two features common to diverse sick excitable cells are "leaky" Nav channels and bleb damage-damaged membranes. The bleb damage, we have argued, causes a channel kinetics based "leakiness." Recombinant (node of Ranvier type) Nav1.6 channels voltage-clamped in mechanically-blebbed cell-attached patches undergo a damage intensity dependent kinetic change. Specifically, they experience a coupled hyperpolarizing (left) shift of the activation and inactivation processes. The biophysical observations on Nav1.6 currents formed the basis of Nav-Coupled Left Shift (Nav-CLS) theory. Node of Ranvier excitability can be modeled with Nav-CLS imposed at varying LS intensities and with varying fractions of total nodal membrane affected. Mild damage from which sick excitable cells might recover is of most interest pathologically. Accordingly, Na+/K+ ATPase (pump) activity was included in the modeling. As we described more fully in our other recent reviews, Nav-CLS in nodes with pumps proves sufficient to predict many of the pathological excitability phenomena reported for sick excitable cells. This review explains how the model came about and outlines how we have used it. Briefly, we direct the reader to studies in which Nav-CLS is being implemented in larger scale models of damaged excitable tissue. For those who might find it useful for teaching or research purposes, we coded the Nav-CLS/node of Ranvier model (with pumps) in NEURON. We include, here, the resulting "Regimes" plot of classes of excitability dysfunction.
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Affiliation(s)
- Bela Joos
- Department of Physics, University of Ottawa, Ottawa, ON, Canada.
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73
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Perez C, Ziburkus J, Ullah G. Analyzing and Modeling the Dysfunction of Inhibitory Neurons in Alzheimer's Disease. PLoS One 2016; 11:e0168800. [PMID: 28036398 PMCID: PMC5201300 DOI: 10.1371/journal.pone.0168800] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/03/2016] [Accepted: 12/05/2016] [Indexed: 12/15/2022] Open
Abstract
Alzheimer's disease (AD) is characterized by the abnormal proteolytic processing of amyloid precursor protein, resulting in increased production of a self-aggregating form of beta amyloid (Aβ). Several lines of work on AD patients and transgenic mice with high Aβ levels exhibit altered rhythmicity, aberrant neuronal network activity and hyperexcitability reflected in clusters of hyperactive neurons, and spontaneous epileptic activity. Recent studies highlight that abnormal accumulation of Aβ changes intrinsic properties of inhibitory neurons, which is one of the main reasons underlying the impaired network activity. However, specific cellular mechanisms leading to interneuronal dysfunction are not completely understood. Using extended Hodgkin-Huxley (HH) formalism in conjunction with patch-clamp experiments, we investigate the mechanisms leading to the impaired activity of interneurons. Our detailed analysis indicates that increased Na+ leak explains several observations in inhibitory neurons, including their failure to reliably produce action potentials, smaller action potential amplitude, increased resting membrane potential, and higher membrane depolarization in response to a range of stimuli in a model of APPSWE/PSEN1DeltaE9 (APdE9) AD mice as compared to age-matched control mice. While increasing the conductance of hyperpolarization activated cyclic nucleotide-gated (HCN) ion channel could account for most of the observations, the extent of increase required to reproduce these observations render such changes unrealistic. Furthermore, increasing the conductance of HCN does not account for the observed changes in depolarizability of interneurons from APdE9 mice as compared to those from NTG mice. None of the other pathways tested could lead to all observations about interneuronal dysfunction. Thus we conclude that upregulated sodium leak is the most likely source of impaired interneuronal function.
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Affiliation(s)
- Carlos Perez
- Department of Physics, University of South Florida, Tampa, FL 33620, United States of America
| | - Jokubas Ziburkus
- Department of Biology and Biochemistry, University of Houston, Houston, TX 77204, United States of America
| | - Ghanim Ullah
- Department of Physics, University of South Florida, Tampa, FL 33620, United States of America
- * E-mail:
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Meier SR, Lancaster JL, Fetterhoff D, Kraft RA, Hampson RE, Starobin JM. The relationship between nernst equilibrium variability and the multifractality of interspike intervals in the hippocampus. J Comput Neurosci 2016; 42:167-175. [PMID: 27909842 DOI: 10.1007/s10827-016-0633-5] [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: 05/18/2016] [Revised: 11/14/2016] [Accepted: 11/21/2016] [Indexed: 11/26/2022]
Abstract
Spatiotemporal patterns of action potentials are considered to be closely related to information processing in the brain. Auto-generating neurons contributing to these processing tasks are known to cause multifractal behavior in the inter-spike intervals of the output action potentials. In this paper we define a novel relationship between this multifractality and the adaptive Nernst equilibrium in hippocampal neurons. Using this relationship we are able to differentiate between various drugs at varying dosages. Conventional methods limit their ability to account for cellular charge depletion by not including these adaptive Nernst equilibria. Our results provide a new theoretical approach for measuring the effects which drugs have on single-cell dynamics.
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Affiliation(s)
- Stephen R Meier
- Department of Applied Mathematics and Statistics, State University of New York, Stony Brook, NY, 11794, USA.
| | | | - Dustin Fetterhoff
- Department of Biology II, Ludwig Maximilian University of Munich, Munich, Germany
| | - Robert A Kraft
- Department of Biomedical Engineering, Wake Forest School of Medicine, Winston-Salem, NC, 27109, USA
| | - Robert E Hampson
- Department of Physiology & Pharmacology, Wake Forest School of Medicine, Winston-Salem, NC, 27109, USA
| | - Joseph M Starobin
- Department of Nanoscience, The University of North Carolina, Greensboro, NC, 27401, USA
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Buchin A, Chizhov A, Huberfeld G, Miles R, Gutkin BS. Reduced Efficacy of the KCC2 Cotransporter Promotes Epileptic Oscillations in a Subiculum Network Model. J Neurosci 2016; 36:11619-11633. [PMID: 27852771 PMCID: PMC6231544 DOI: 10.1523/jneurosci.4228-15.2016] [Citation(s) in RCA: 45] [Impact Index Per Article: 5.6] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/24/2015] [Revised: 08/04/2016] [Accepted: 08/07/2016] [Indexed: 12/17/2022] Open
Abstract
Pharmacoresistant epilepsy is a chronic neurological condition in which a basal brain hyperexcitability results in paroxysmal hypersynchronous neuronal discharges. Human temporal lobe epilepsy has been associated with dysfunction or loss of the potassium-chloride cotransporter KCC2 in a subset of pyramidal cells in the subiculum, a key structure generating epileptic activities. KCC2 regulates intraneuronal chloride and extracellular potassium levels by extruding both ions. Absence of effective KCC2 may alter the dynamics of chloride and potassium levels during repeated activation of GABAergic synapses due to interneuron activity. In turn, such GABAergic stress may itself affect Cl- regulation. Such changes in ionic homeostasis may switch GABAergic signaling from inhibitory to excitatory in affected pyramidal cells and also increase neuronal excitability. Possibly these changes contribute to periodic bursting in pyramidal cells, an essential component in the onset of ictal epileptic events. We tested this hypothesis with a computational model of a subicular network with realistic connectivity. The pyramidal cell model explicitly incorporated the cotransporter KCC2 and its effects on the internal/external chloride and potassium levels. Our network model suggested the loss of KCC2 in a critical number of pyramidal cells increased external potassium and intracellular chloride concentrations leading to seizure-like field potential oscillations. These oscillations included transient discharges leading to ictal-like field events with frequency spectra as in vitro Restoration of KCC2 function suppressed seizure activity and thus may present a useful therapeutic option. These simulations therefore suggest that reduced KCC2 cotransporter activity alone may underlie the generation of ictal discharges. SIGNIFICANCE STATEMENT Ion regulation in the brain is a major determinant of neural excitability. Intracellular chloride in neurons, a partial determinant of the resting potential and the inhibitory reversal potentials, is regulated together with extracellular potassium via kation chloride cotransporters. During temporal lobe epilepsy, the homeostatic regulation of intracellular chloride is impaired in pyramidal cells, yet how this dysregulation may lead to seizures has not been explored. Using a realistic neural network model describing ion mechanisms, we show that chloride homeostasis pathology provokes seizure activity analogous to recordings from epileptogenic brain tissue. We show that there is a critical percentage of pathological cells required for seizure initiation. Our model predicts that restoration of the chloride homeostasis in pyramidal cells could be a viable antiepileptic strategy.
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Affiliation(s)
- Anatoly Buchin
- École normale supérieure, Paris Sciences et Lettres University, Laboratoire de Neurosciences Cognitives, Institute national de la santé et de la recherche médicale U960, Group for Neural Theory, 75005 Paris, France,
- Peter the Great St. Petersburg Polytechnic University, St. Petersburg 195251, Russia
- National Research University Higher School of Economics, Center for Cognition and Decision Making, Moscow 109316, Russia
| | - Anton Chizhov
- Ioffe Institute, Computational Physics Laboratory, St. Petersburg 194021, Russia
- Sechenov Institute of Evolutionary Physiology and Biochemistry of the Russian Academy of Sciences, St. Petersburg 194223, Russia
| | - Gilles Huberfeld
- Université Pierre et Marie Curie, Pitié-Salpêtrière Hôpital, Assistance Publique-Hôpitaux de Paris, Neurophysiology Department, 75013 Paris, France
- Institute national de la santé et de la recherche médicale U1129 "Infantile Epilepsies and Brain Plasticity," Paris Descartes University, Pôle de recherche et d'enseignement supérieur Sorbonne Paris Cité, 75015 Paris, France, and
| | - Richard Miles
- Institut du Cerveau et de la Moelle Epinière, Cortex et Epilepsie Group, 75013 Paris, France
| | - Boris S Gutkin
- École normale supérieure, Paris Sciences et Lettres University, Laboratoire de Neurosciences Cognitives, Institute national de la santé et de la recherche médicale U960, Group for Neural Theory, 75005 Paris, France
- National Research University Higher School of Economics, Center for Cognition and Decision Making, Moscow 109316, Russia
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77
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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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78
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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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79
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Zandt BJ, ten Haken B, van Putten MJAM, Dahlem MA. How does spreading depression spread? Physiology and modeling. Rev Neurosci 2016; 26:183-98. [PMID: 25719306 DOI: 10.1515/revneuro-2014-0069] [Citation(s) in RCA: 26] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/06/2014] [Accepted: 10/31/2014] [Indexed: 11/15/2022]
Abstract
Spreading depression (SD) is a wave phenomenon in gray matter tissue. Locally, it is characterized by massive redistribution of ions across cell membranes. As a consequence, there is sustained membrane depolarization and tissue polarization that depress any normal electrical activity. Despite these dramatic events, SD remains difficult to observe in humans noninvasively, which, for long, has slowed advances in this field. The growing appreciation of its clinical importance in migraine and stroke is therefore consistent with an increasing need for computational methods that tackle the complexity of the problem at multiple levels. In this review, we focus on mathematical tools to investigate the question of spread and its two complementary aspects: What are the physiological mechanisms and what is the spatial extent of SD in the cortex? This review discusses two types of models used to study these two questions, namely, Hodgkin-Huxley type and generic activator-inhibitor models, and the recent advances in techniques to link them.
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80
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Ahn S, Jun SB, Lee HW, Lee S. Computational modeling of epileptiform activities in medial temporal lobe epilepsy combined with in vitro experiments. J Comput Neurosci 2016; 41:207-23. [PMID: 27416961 DOI: 10.1007/s10827-016-0614-8] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/06/2015] [Revised: 04/20/2016] [Accepted: 06/28/2016] [Indexed: 10/21/2022]
Abstract
In this paper, we propose a comprehensive computational model that is able to reproduce three epileptiform activities. The model targets a hippocampal formation that is known to be an important lesion in medial temporal lobe epilepsy. It consists of four sub-networks consisting of excitatory and inhibitory neurons and well-known signal pathways, with consideration of propagation delay. The three epileptiform activities involve fast and slow interictal discharge and ictal discharge, and those activities can be induced in vitro by application of 4-Aminopyridine in entorhinal cortex combined hippocampal slices. We model the three epileptiform activities upon previously reported biological mechanisms and verify the simulation results by comparing them with in vitro experimental data obtained using a microelectrode array. We use the results of Granger causality analysis of recorded data to set input gains of signal pathways in the model, so that the compatibility between the computational and experimental models can be improved. The proposed model can be expanded to evaluate the suppression effect of epileptiform activities due to new treatment methods.
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Affiliation(s)
- Sora Ahn
- Department of Electronics Engineering, Ewha Womans University, Seoul, 120-750, South Korea
| | - Sang Beom Jun
- Department of Electronics Engineering, Ewha Womans University, Seoul, 120-750, South Korea
| | - Hyang Woon Lee
- Department of Neurology, Ewha Medical Research Institute, Ewha Womans University School of Medicine, Seoul, 158-710, South Korea
| | - Seungjun Lee
- Department of Electronics Engineering, Ewha Womans University, Seoul, 120-750, South Korea.
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81
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Friedrich T, Tavraz NN, Junghans C. ATP1A2 Mutations in Migraine: Seeing through the Facets of an Ion Pump onto the Neurobiology of Disease. Front Physiol 2016; 7:239. [PMID: 27445835 PMCID: PMC4914835 DOI: 10.3389/fphys.2016.00239] [Citation(s) in RCA: 57] [Impact Index Per Article: 7.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/31/2016] [Accepted: 06/03/2016] [Indexed: 12/31/2022] Open
Abstract
Mutations in four genes have been identified in familial hemiplegic migraine (FHM), from which CACNA1A (FHM type 1) and SCN1A (FHM type 3) code for neuronal voltage-gated calcium or sodium channels, respectively, while ATP1A2 (FHM type 2) encodes the α2 isoform of the Na(+),K(+)-ATPase's catalytic subunit, thus classifying FHM primarily as an ion channel/ion transporter pathology. FHM type 4 is attributed to mutations in the PRRT2 gene, which encodes a proline-rich transmembrane protein of as yet unknown function. The Na(+),K(+)-ATPase maintains the physiological gradients for Na(+) and K(+) ions and is, therefore, critical for the activity of ion channels and transporters involved neuronal excitability, neurotransmitter uptake or Ca(2+) signaling. Strikingly diverse functional abnormalities have been identified for disease-linked ATP1A2 mutations which frequently lead to changes in the enzyme's voltage-dependent properties, kinetics, or apparent cation affinities, but some mutations are truly deleterious for enzyme function and thus cause full haploinsufficiency. Here, we summarize structural and functional data about the Na(+),K(+)-ATPase available to date and an overview is provided about the particular properties of the α2 isoform that explain its physiological relevance in electrically excitable tissues. In addition, current concepts about the neurobiology of migraine, the correlations between primary brain dysfunction and mechanisms of headache pain generation are described, together with insights gained recently from modeling approaches in computational neuroscience. Then, a survey is given about ATP1A2 mutations implicated in migraine cases as documented in the literature with focus on mutations that were described to completely destroy enzyme function, or lead to misfolded or mistargeted protein in particular model cell lines. We also discuss whether or not there are correlations between these most severe mutational effects and clinical phenotypes. Finally, perspectives for future research on the implications of Na(+),K(+)-ATPase mutations in human pathologies are presented.
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Affiliation(s)
- Thomas Friedrich
- Department of Physical Chemistry/Bioenergetics, Institute of Chemistry, Technical University of BerlinBerlin, Germany
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82
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Anions Govern Cell Volume: A Case Study of Relative Astrocytic and Neuronal Swelling in Spreading Depolarization. PLoS One 2016; 11:e0147060. [PMID: 26974767 PMCID: PMC4790933 DOI: 10.1371/journal.pone.0147060] [Citation(s) in RCA: 34] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/22/2015] [Accepted: 12/27/2015] [Indexed: 11/30/2022] Open
Abstract
Cell volume changes are ubiquitous in normal and pathological activity of the brain. Nevertheless, we know little about the dynamics of cell and tissue swelling, and the differential changes in the volumes of neurons and glia during pathological states such as spreading depolarizations (SD) under ischemic and non–ischemic conditions, and epileptic seizures. By combining the Hodgkin–Huxley type spiking dynamics, dynamic ion concentrations, and simultaneous neuronal and astroglial volume changes into a comprehensive model, we elucidate why glial cells swell more than neurons in SD and the special case of anoxic depolarization (AD), and explore the relative contributions of the two cell types to tissue swelling. Our results demonstrate that anion channels, particularly Cl−, are intrinsically connected to cell swelling and blocking these currents prevents changes in cell volume. The model is based on a simple and physiologically realistic description. We introduce model extensions that are either derived purely from first physical principles of electroneutrality, osmosis, and conservation of particles, or by a phenomenological combination of these principles and known physiological facts. This work provides insights into numerous studies related to neuronal and glial volume changes in SD that otherwise seem contradictory, and is broadly applicable to swelling in other cell types and conditions.
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83
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Park Y, Ermentrout B. Weakly coupled oscillators in a slowly varying world. J Comput Neurosci 2016; 40:269-81. [DOI: 10.1007/s10827-016-0596-6] [Citation(s) in RCA: 19] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/29/2015] [Revised: 02/17/2016] [Accepted: 02/22/2016] [Indexed: 10/22/2022]
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84
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Hübel N, Andrew RD, Ullah G. Large extracellular space leads to neuronal susceptibility to ischemic injury in a Na+/K+ pumps-dependent manner. J Comput Neurosci 2016; 40:177-92. [PMID: 26852334 DOI: 10.1007/s10827-016-0591-y] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/10/2015] [Revised: 01/17/2016] [Accepted: 01/21/2016] [Indexed: 11/29/2022]
Abstract
The extent of anoxic depolarization (AD), the initial electrophysiological event during ischemia, determines the degree of brain region-specific neuronal damage. Neurons in higher brain regions exhibiting nonreversible, strong AD are more susceptible to ischemic injury as compared to cells in lower brain regions that exhibit reversible, weak AD. While the contrasting ADs in different brain regions in response to oxygen-glucose deprivation (OGD) is well established, the mechanism leading to such differences is not clear. Here we use computational modeling to elucidate the mechanism behind the brain region-specific recovery from AD. Our extended Hodgkin-Huxley (HH) framework consisting of neural spiking dynamics, processes of ion accumulation, and ion homeostatic mechanisms unveils that glial-vascular K(+) clearance and Na(+)/K(+)-exchange pumps are key to the cell's recovery from AD. Our phase space analysis reveals that the large extracellular space in the upper brain regions leads to impaired Na(+)/K(+)-exchange pumps so that they function at lower than normal capacity and are unable to bring the cell out of AD after oxygen and glucose is restored.
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Affiliation(s)
- Niklas Hübel
- Department of Physics, University of South Florida, Tampa, FL, 33620, USA.
| | - R David Andrew
- Department of Biomedical and Molecular Sciences, Queen's University, Kingston, ON, Canada
| | - Ghanim Ullah
- Department of Physics, University of South Florida, Tampa, FL, 33620, USA
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85
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Kroos JM, Diez I, Cortes JM, Stramaglia S, Gerardo-Giorda L. Geometry Shapes Propagation: Assessing the Presence and Absence of Cortical Symmetries through a Computational Model of Cortical Spreading Depression. Front Comput Neurosci 2016; 10:6. [PMID: 26869913 PMCID: PMC4735361 DOI: 10.3389/fncom.2016.00006] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/14/2015] [Accepted: 01/12/2016] [Indexed: 01/27/2023] Open
Abstract
Cortical spreading depression (CSD), a depolarization wave which originates in the visual cortex and travels toward the frontal lobe, has been suggested to be one neural correlate of aura migraine. To the date, little is known about the mechanisms which can trigger or stop aura migraine. Here, to shed some light on this problem and, under the hypothesis that CSD might mediate aura migraine, we aim to study different aspects favoring or disfavoring the propagation of CSD. In particular, by using a computational neuronal model distributed throughout a realistic cortical mesh, we study the role that the geometry has in shaping CSD. Our results are two-fold: first, we found significant differences in the propagation traveling patterns of CSD, both intra and inter-hemispherically, revealing important asymmetries in the propagation profile. Second, we developed methods able to identify brain regions featuring a peculiar behavior during CSD propagation. Our study reveals dynamical aspects of CSD, which, if applied to subject-specific cortical geometry, might shed some light on how to differentiate between healthy subjects and those suffering migraine.
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Affiliation(s)
- Julia M. Kroos
- BCAM – Basque Center for Applied MathematicsBilbao, Spain,*Correspondence: Julia M. Kroos
| | - Ibai Diez
- Computational Neuroimaging Group, Quantitative Biomedicine Unit, Biocruces Health Research Institute, Cruces University HospitalBarakaldo, Spain
| | - Jesus M. Cortes
- Computational Neuroimaging Group, Quantitative Biomedicine Unit, Biocruces Health Research Institute, Cruces University HospitalBarakaldo, Spain,Ikerbasque, The Basque Foundation for ScienceBilbao, Spain,Department of Cell Biology and Histology, University of the Basque CountryLeioa, Spain
| | - Sebastiano Stramaglia
- BCAM – Basque Center for Applied MathematicsBilbao, Spain,Dipartimento di Fisica, Center of Innovative Technologies for Signal Detection and Processing, Istituto Nazionale di Fisica Nucleare Sezione di Bari, Università di BariBari, Italy
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86
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Volman V, Ng LJ. Perinodal glial swelling mitigates axonal degradation in a model of axonal injury. J Neurophysiol 2015; 115:1003-17. [PMID: 26683073 DOI: 10.1152/jn.00912.2015] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/28/2015] [Accepted: 12/13/2015] [Indexed: 12/15/2022] Open
Abstract
Mild traumatic brain injury (mTBI) has been associated with the damage to myelinated axons in white matter tracts. Animal models and in vitro studies suggest that axonal degradation develops during a latent period following a traumatic event. This delay has been attributed to slowly developing axonal membrane depolarization that is initiated by injury-induced ionic imbalance and in turn, leads to the activation of Ca(2+) proteases via pathological accumulation of Ca(2+). However, the mechanisms mitigating the transition to axonal degradation after injury remain elusive. We addressed this question in a detailed biophysical model of axonal injury that incorporated ion exchange and glial swelling mechanisms. We show that glial swelling, which often co-occurs with mTBI, promotes axonal survival by regulating extracellular K(+) dynamics, extending the range of injury parameters in which axons exhibit stable membrane potential postinjury. In addition, glial swelling was instrumental in reducing axonal sensitivity to repetitive stretch injury that occurred several minutes following the first one. Results of this study suggest that acute post-traumatic swelling of perinodal astrocytes helps prevent or postpone axonal degradation by maintaining physiologically relevant levels of extracellular K(+).
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Affiliation(s)
- Vladislav Volman
- Simulation, Engineering, and Testing, L-3 Applied Technologies Incorporated, San Diego, California
| | - Laurel J Ng
- Simulation, Engineering, and Testing, L-3 Applied Technologies Incorporated, San Diego, California
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87
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Zylbertal A, Kahan A, Ben-Shaul Y, Yarom Y, Wagner S. Prolonged Intracellular Na+ Dynamics Govern Electrical Activity in Accessory Olfactory Bulb Mitral Cells. PLoS Biol 2015; 13:e1002319. [PMID: 26674618 PMCID: PMC4684409 DOI: 10.1371/journal.pbio.1002319] [Citation(s) in RCA: 19] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/07/2015] [Accepted: 11/05/2015] [Indexed: 11/21/2022] Open
Abstract
Persistent activity has been reported in many brain areas and is hypothesized to mediate working memory and emotional brain states and to rely upon network or biophysical feedback. Here, we demonstrate a novel mechanism by which persistent neuronal activity can be generated without feedback, relying instead on the slow removal of Na+ from neurons following bursts of activity. We show that mitral cells in the accessory olfactory bulb (AOB), which plays a major role in mammalian social behavior, may respond to a brief sensory stimulation with persistent firing. By combining electrical recordings, Ca2+ and Na+ imaging, and realistic computational modeling, we explored the mechanisms underlying the persistent activity in AOB mitral cells. We found that the exceptionally slow inward current that underlies this activity is governed by prolonged dynamics of intracellular Na+ ([Na+]i), which affects neuronal electrical activity via several pathways. Specifically, elevated dendritic [Na+]i reverses the Na+-Ca2+ exchanger activity, thus modifying the [Ca2+]i set-point. This process, which relies on ubiquitous membrane mechanisms, is likely to play a role in other neuronal types in various brain regions. An experimental and computational study reveals a novel mechanism for persistent activity of neurons in response to transient stimulation. Instead of involving feedback mechanisms, it relies on slow changes in intracellular sodium ion concentration, leading to prolonged calcium-dependent inward current. The accessory olfactory system is essential for chemical communication in animals during social interactions. During this process, the principle cells of the accessory olfactory bulb (AOB) may respond to transient stimulation with prolonged activity, sometimes lasting for minutes—a property known as persistent activity. This property, which has been observed in other brain areas, is usually attributed to positive feedback mechanisms either at the cellular or the network level. Here, we show how persistent activity can emerge without feedback, relying on slow changes in internal ionic concentrations, which keep a record of past neuronal activity for long periods of time. We used a combined computational and experimental approach to show that the complex interaction between various ions, their extrusion mechanisms, and the membrane potential leads to stimulus-dependent persistent activity in the AOB. The same mechanism may apply to other neuronal types in various brain regions.
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Affiliation(s)
- Asaph Zylbertal
- Department of Neurobiology, Institute of Life Sciences, Hebrew University and the Edmond and Lily Safra Center for Brain Sciences, Jerusalem, Israel
- * E-mail:
| | - Anat Kahan
- School of Medicine, Department of Medical Neurobiology, Hebrew University, Jerusalem, Israel
| | - Yoram Ben-Shaul
- School of Medicine, Department of Medical Neurobiology, Hebrew University, Jerusalem, Israel
| | - Yosef Yarom
- Department of Neurobiology, Institute of Life Sciences, Hebrew University and the Edmond and Lily Safra Center for Brain Sciences, Jerusalem, Israel
| | - Shlomo Wagner
- Sagol Department of Neurobiology, University of Haifa, Haifa, Israel
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88
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Reznik RI, Barreto E, Sander E, So P. Effects of polarization induced by non-weak electric fields on the excitability of elongated neurons with active dendrites. J Comput Neurosci 2015; 40:27-50. [PMID: 26560333 DOI: 10.1007/s10827-015-0582-4] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/25/2015] [Revised: 10/17/2015] [Accepted: 10/22/2015] [Indexed: 10/22/2022]
Abstract
An externally-applied electric field can polarize a neuron, especially a neuron with elongated dendrites, and thus modify its excitability. Here we use a computational model to examine, predict, and explain these effects. We use a two-compartment Pinsky-Rinzel model neuron polarized by an electric potential difference imposed between its compartments, and we apply an injected ramp current. We vary three model parameters: the magnitude of the applied potential difference, the extracellular potassium concentration, and the rate of current injection. A study of the Time-To-First-Spike (TTFS) as a function of polarization leads to the identification of three regions of polarization strength that have different effects. In the weak region, the TTFS increases linearly with polarization. In the intermediate region, the TTFS increases either sub- or super-linearly, depending on the current injection rate and the extracellular potassium concentration. In the strong region, the TTFS decreases. Our results in the weak and strong region are consistent with experimental observations, and in the intermediate region, we predict novel effects that depend on experimentally-accessible parameters. We find that active channels in the dendrite play a key role in these effects. Our qualitative results were found to be robust over a wide range of inter-compartment conductances and the ratio of somatic to dendritic membrane areas. In addition, we discuss preliminary results where synaptic inputs replace the ramp injection protocol. The insights and conclusions were found to extend from our polarized PR model to a polarized PR model with I h dendritic currents. Finally, we discuss the degree to which our results may be generalized.
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Affiliation(s)
- Robert I Reznik
- School of Physics, Astronomy, and Computational Sciences and The Krasnow Institute for Advanced Study, George Mason University, Fairfax, VA, 22030, USA.
| | - Ernest Barreto
- School of Physics, Astronomy, and Computational Sciences and The Krasnow Institute for Advanced Study, George Mason University, Fairfax, VA, 22030, USA.
| | - Evelyn Sander
- Department of Mathematical Sciences, George Mason University, Fairfax, VA, 22030, USA.
| | - Paul So
- School of Physics, Astronomy, and Computational Sciences and The Krasnow Institute for Advanced Study, George Mason University, Fairfax, VA, 22030, USA.
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89
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Adebimpe A, Aarabi A, Bourel-Ponchel E, Mahmoudzadeh M, Wallois F. Functional Brain Dysfunction in Patients with Benign Childhood Epilepsy as Revealed by Graph Theory. PLoS One 2015; 10:e0139228. [PMID: 26431333 PMCID: PMC4592214 DOI: 10.1371/journal.pone.0139228] [Citation(s) in RCA: 30] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/08/2015] [Accepted: 09/10/2015] [Indexed: 11/24/2022] Open
Abstract
There is growing evidence that brain networks are altered in epileptic subjects. In this study, we investigated the functional connectivity and brain network properties of benign childhood epilepsy with centrotemporal spikes using graph theory. Benign childhood epilepsy with centrotemporal spikes is the most common form of idiopathic epilepsy in young children under the age of 16 years. High-density EEG data were recorded from patients and controls in resting state with eyes closed. Data were preprocessed and spike and spike-free segments were selected for analysis. Phase locking value was calculated for all paired combinations of channels and for five frequency bands (δ, θ, α, β1 and β2). We computed the degree and small-world parameters—clustering coefficient (C) and path length (L)—and compared the two patient conditions to controls. A higher degree at epileptic zones during interictal epileptic spikes (IES) was observed in all frequency bands. Both patient conditions reduced connection at the occipital and right frontal regions close to the epileptic zone in the α band. The “small-world” features (high C and short L) were deviated in patients compared to controls. A changed from an ordered network in the δ band to a more randomly organized network in the α band was observed in patients compared to healthy controls. These findings show that the benign epileptic brain network is disrupted not only at the epileptic zone, but also in other brain regions especially frontal regions.
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Affiliation(s)
- Azeez Adebimpe
- Institut National de la Santé et de la Recherche Médicale (INSERM U1105), Centre Universitaire de Recheche en Santé (CURS), University Hospital, Amiens, France
| | - Ardalan Aarabi
- Institut National de la Santé et de la Recherche Médicale (INSERM U1105), Centre Universitaire de Recheche en Santé (CURS), University Hospital, Amiens, France
- * E-mail:
| | - Emilie Bourel-Ponchel
- Institut National de la Santé et de la Recherche Médicale (INSERM U1105), Centre Universitaire de Recheche en Santé (CURS), University Hospital, Amiens, France
- Explorations Fonctionnelles du Système Nerveux (EFSN) pédiatrique, University Hospital, Amiens, France
| | - Mahdi Mahmoudzadeh
- Institut National de la Santé et de la Recherche Médicale (INSERM U1105), Centre Universitaire de Recheche en Santé (CURS), University Hospital, Amiens, France
- Explorations Fonctionnelles du Système Nerveux (EFSN) pédiatrique, University Hospital, Amiens, France
| | - Fabrice Wallois
- Institut National de la Santé et de la Recherche Médicale (INSERM U1105), Centre Universitaire de Recheche en Santé (CURS), University Hospital, Amiens, France
- Explorations Fonctionnelles du Système Nerveux (EFSN) pédiatrique, University Hospital, Amiens, France
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90
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Ullah G, Wei Y, Dahlem MA, Wechselberger M, Schiff SJ. The Role of Cell Volume in the Dynamics of Seizure, Spreading Depression, and Anoxic Depolarization. PLoS Comput Biol 2015; 11:e1004414. [PMID: 26273829 PMCID: PMC4537206 DOI: 10.1371/journal.pcbi.1004414] [Citation(s) in RCA: 63] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/09/2014] [Accepted: 06/24/2015] [Indexed: 11/19/2022] Open
Abstract
Cell volume changes are ubiquitous in normal and pathological activity of the brain. Nevertheless, we know little of how cell volume affects neuronal dynamics. We here performed the first detailed study of the effects of cell volume on neuronal dynamics. By incorporating cell swelling together with dynamic ion concentrations and oxygen supply into Hodgkin-Huxley type spiking dynamics, we demonstrate the spontaneous transition between epileptic seizure and spreading depression states as the cell swells and contracts in response to changes in osmotic pressure. Our use of volume as an order parameter further revealed a dynamical definition for the experimentally described physiological ceiling that separates seizure from spreading depression, as well as predicted a second ceiling that demarcates spreading depression from anoxic depolarization. Our model highlights the neuroprotective role of glial K buffering against seizures and spreading depression, and provides novel insights into anoxic depolarization and the relevant cell swelling during ischemia. We argue that the dynamics of seizures, spreading depression, and anoxic depolarization lie along a continuum of the repertoire of the neuron membrane that can be understood only when the dynamic ion concentrations, oxygen homeostasis,and cell swelling in response to osmotic pressure are taken into consideration. Our results demonstrate the feasibility of a unified framework for a wide range of neuronal behaviors that may be of substantial importance in the understanding of and potentially developing universal intervention strategies for these pathological states.
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Affiliation(s)
- Ghanim Ullah
- Department of Physics, University of South Florida, Tampa, Florida 33620, United States of America
| | - Yina Wei
- Department of Cell Biology and Neuroscience, University of California, Riverside, California 92501 United States of America
| | | | - Martin Wechselberger
- School of Mathematics and Statistics, University of Sydney, New South Wales, 2006, Australia
| | - Steven J Schiff
- Center for Neural Engineering, Departments of Engineering Science and Mechanics, Neurosurgery, and Physics, The Pennsylvania State University, University Park, Pennsylvania 16802, United States of America
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91
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Naze S, Bernard C, Jirsa V. Computational modeling of seizure dynamics using coupled neuronal networks: factors shaping epileptiform activity. PLoS Comput Biol 2015; 11:e1004209. [PMID: 25970348 PMCID: PMC4430284 DOI: 10.1371/journal.pcbi.1004209] [Citation(s) in RCA: 45] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/30/2014] [Accepted: 02/24/2015] [Indexed: 11/21/2022] Open
Abstract
Epileptic seizure dynamics span multiple scales in space and time. Understanding seizure mechanisms requires identifying the relations between seizure components within and across these scales, together with the analysis of their dynamical repertoire. Mathematical models have been developed to reproduce seizure dynamics across scales ranging from the single neuron to the neural population. In this study, we develop a network model of spiking neurons and systematically investigate the conditions, under which the network displays the emergent dynamic behaviors known from the Epileptor, which is a well-investigated abstract model of epileptic neural activity. This approach allows us to study the biophysical parameters and variables leading to epileptiform discharges at cellular and network levels. Our network model is composed of two neuronal populations, characterized by fast excitatory bursting neurons and regular spiking inhibitory neurons, embedded in a common extracellular environment represented by a slow variable. By systematically analyzing the parameter landscape offered by the simulation framework, we reproduce typical sequences of neural activity observed during status epilepticus. We find that exogenous fluctuations from extracellular environment and electro-tonic couplings play a major role in the progression of the seizure, which supports previous studies and further validates our model. We also investigate the influence of chemical synaptic coupling in the generation of spontaneous seizure-like events. Our results argue towards a temporal shift of typical spike waves with fast discharges as synaptic strengths are varied. We demonstrate that spike waves, including interictal spikes, are generated primarily by inhibitory neurons, whereas fast discharges during the wave part are due to excitatory neurons. Simulated traces are compared with in vivo experimental data from rodents at different stages of the disorder. We draw the conclusion that slow variations of global excitability, due to exogenous fluctuations from extracellular environment, and gap junction communication push the system into paroxysmal regimes. We discuss potential mechanisms underlying such machinery and the relevance of our approach, supporting previous detailed modeling studies and reflecting on the limitations of our methodology. Neurons communicate via different types of synapses on very fast time scales. The combination of hundred thousand of such interconnected cells within a fluctuating extracellular environment forms a complex network that gives rise to function and behavior via the formation of dynamical patterns of activity. In the context of epilepsy, the functional properties of the network at the source of a seizure are disrupted by a possibly large set of factors at the cellular and molecular levels. It is therefore needed to sacrifice some biological accuracy to model seizure dynamics in favor of macroscopic realizations. Here, we present a neuronal network model that convenes both neuronal and network representations with the goal to describe brain dynamics involved in the development of epilepsy. We compare our modeling results with animal in vivo recordings to validate our approach in the context of seizures. Such system-level methodology has significant bearing in understanding neuronal network dynamics that entangle multiple synaptic and extracellular modalities.
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Affiliation(s)
- Sebastien Naze
- UMR1106 Inserm, Institut de Neurosciences des Systèmes, Marseille, France
- Aix-Marseille University, Marseille, France
- * E-mail: (SN); (VJ)
| | - Christophe Bernard
- UMR1106 Inserm, Institut de Neurosciences des Systèmes, Marseille, France
- Aix-Marseille University, Marseille, France
| | - Viktor Jirsa
- UMR1106 Inserm, Institut de Neurosciences des Systèmes, Marseille, France
- Aix-Marseille University, Marseille, France
- * E-mail: (SN); (VJ)
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92
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Sibille J, Dao Duc K, Holcman D, Rouach N. The neuroglial potassium cycle during neurotransmission: role of Kir4.1 channels. PLoS Comput Biol 2015; 11:e1004137. [PMID: 25826753 PMCID: PMC4380507 DOI: 10.1371/journal.pcbi.1004137] [Citation(s) in RCA: 58] [Impact Index Per Article: 6.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/09/2014] [Accepted: 01/18/2015] [Indexed: 12/14/2022] Open
Abstract
Neuronal excitability relies on inward sodium and outward potassium fluxes during action potentials. To prevent neuronal hyperexcitability, potassium ions have to be taken up quickly. However, the dynamics of the activity-dependent potassium fluxes and the molecular pathways underlying extracellular potassium homeostasis remain elusive. To decipher the specific and acute contribution of astroglial Kir4.1 channels in controlling potassium homeostasis and the moment to moment neurotransmission, we built a tri-compartment model accounting for potassium dynamics between neurons, astrocytes and the extracellular space. We here demonstrate that astroglial Kir4.1 channels are sufficient to account for the slow membrane depolarization of hippocampal astrocytes and crucially contribute to extracellular potassium clearance during basal and high activity. By quantifying the dynamics of potassium levels in neuron-glia-extracellular space compartments, we show that astrocytes buffer within 6 to 9 seconds more than 80% of the potassium released by neurons in response to basal, repetitive and tetanic stimulations. Astroglial Kir4.1 channels directly lead to recovery of basal extracellular potassium levels and neuronal excitability, especially during repetitive stimulation, thereby preventing the generation of epileptiform activity. Remarkably, we also show that Kir4.1 channels strongly regulate neuronal excitability for slow 3 to 10 Hz rhythmic activity resulting from probabilistic firing activity induced by sub-firing stimulation coupled to Brownian noise. Altogether, these data suggest that astroglial Kir4.1 channels are crucially involved in extracellular potassium homeostasis regulating theta rhythmic activity.
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Affiliation(s)
- Jérémie Sibille
- Neuroglial Interactions in Cerebral Physiopathology, Center for Interdisciplinary Research in Biology, Collège de France, INSERM U1050, CNRS UMR 7241, Labex Memolife, PSL Research University, Paris, France
- Université Paris Diderot, Sorbonne Paris Cité, Paris, France
| | - Khanh Dao Duc
- IBENS, Ecole Normale Supérieure, INSERM U1024, CNRS UMR 8197, Paris, France
- Université Paris 6, Paris, France
| | - David Holcman
- IBENS, Ecole Normale Supérieure, INSERM U1024, CNRS UMR 8197, Paris, France
- * E-mail: (DH); (NR)
| | - Nathalie Rouach
- Neuroglial Interactions in Cerebral Physiopathology, Center for Interdisciplinary Research in Biology, Collège de France, INSERM U1050, CNRS UMR 7241, Labex Memolife, PSL Research University, Paris, France
- * E-mail: (DH); (NR)
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93
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Bursting regimes in a reaction-diffusion system with action potential-dependent equilibrium. PLoS One 2015; 10:e0122401. [PMID: 25823018 PMCID: PMC4379183 DOI: 10.1371/journal.pone.0122401] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/04/2014] [Accepted: 02/14/2015] [Indexed: 11/30/2022] Open
Abstract
The equilibrium Nernst potential plays a critical role in neural cell dynamics. A common approximation used in studying electrical dynamics of excitable cells is that the ionic concentrations inside and outside the cell membranes act as charge reservoirs and remain effectively constant during excitation events. Research into brain electrical activity suggests that relaxing this assumption may provide a better understanding of normal and pathophysiological functioning of the brain. In this paper we explore time-dependent ionic concentrations by allowing the ion-specific Nernst potentials to vary with developing transmembrane potential. As a specific implementation, we incorporate the potential-dependent Nernst shift into a one-dimensional Morris-Lecar reaction-diffusion model. Our main findings result from a region in parameter space where self-sustaining oscillations occur without external forcing. Studying the system close to the bifurcation boundary, we explore the vulnerability of the system with respect to external stimulations which disrupt these oscillations and send the system to a stable equilibrium. We also present results for an extended, one-dimensional cable of excitable tissue tuned to this parameter regime and stimulated, giving rise to complex spatiotemporal pattern formation. Potential applications to the emergence of neuronal bursting in similar two-variable systems and to pathophysiological seizure-like activity are discussed.
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94
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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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95
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Krishnan GP, Filatov G, Shilnikov A, Bazhenov M. Electrogenic properties of the Na⁺/K⁺ ATPase control transitions between normal and pathological brain states. J Neurophysiol 2015; 113:3356-74. [PMID: 25589588 DOI: 10.1152/jn.00460.2014] [Citation(s) in RCA: 42] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/23/2014] [Accepted: 01/09/2015] [Indexed: 11/22/2022] Open
Abstract
Ionic concentrations fluctuate significantly during epileptic seizures. In this study, using a combination of in vitro electrophysiology, computer modeling, and dynamical systems analysis, we demonstrate that changes in the potassium and sodium intra- and extracellular ion concentrations ([K(+)] and [Na(+)], respectively) during seizure affect the neuron dynamics by modulating the outward Na(+)/K(+) pump current. First, we show that an increase of the outward Na(+)/K(+) pump current mediates termination of seizures when there is a progressive increase in the intracellular [Na(+)]. Second, we show that the Na(+)/K(+) pump current is crucial in maintaining the stability of the physiological network state; a reduction of this current leads to the onset of seizures via a positive-feedback loop. We then present a novel dynamical mechanism for bursting in neurons with a reduced Na(+)/K(+) pump. Overall, our study demonstrates the profound role of the current mediated by Na(+)/K(+) ATPase on the stability of neuronal dynamics that was previously unknown.
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Affiliation(s)
- Giri P Krishnan
- Department of Cell Biology and Neuroscience, University of California, Riverside, California
| | - Gregory Filatov
- Department of Cell Biology and Neuroscience, University of California, Riverside, California
| | - Andrey Shilnikov
- Neuroscience Institute and Department of Mathematics and Statistics, Georgia State University, Atlanta, Georgia; and Institute for Information Technology, Mathematics and Mechanics, Lobachevsky State University of Nizhni Novgorod, Nizhni Novgorod, Russia
| | - Maxim Bazhenov
- Department of Cell Biology and Neuroscience, University of California, Riverside, California;
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96
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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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97
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El Houssaini K, Ivanov AI, Bernard C, Jirsa VK. Seizures, refractory status epilepticus, and depolarization block as endogenous brain activities. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 91:010701. [PMID: 25679555 DOI: 10.1103/physreve.91.010701] [Citation(s) in RCA: 31] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/11/2014] [Indexed: 06/04/2023]
Abstract
Epilepsy, refractory status epilepticus, and depolarization block are pathological brain activities whose mechanisms are poorly understood. Using a generic mathematical model of seizure activity, we show that these activities coexist under certain conditions spanning the range of possible brain activities. We perform a detailed bifurcation analysis and predict strategies to escape from some of the pathological states. Experimental results using rodent data provide support of the model, highlighting the concept that these pathological activities belong to the endogenous repertoire of brain activities.
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Affiliation(s)
- Kenza El Houssaini
- Aix Marseille Université, Inserm, INS UMR_S 1106, 13005, Marseille, France
| | - Anton I Ivanov
- Aix Marseille Université, Inserm, INS UMR_S 1106, 13005, Marseille, France
| | - Christophe Bernard
- Aix Marseille Université, Inserm, INS UMR_S 1106, 13005, Marseille, France
| | - Viktor K Jirsa
- Aix Marseille Université, Inserm, INS UMR_S 1106, 13005, Marseille, France
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98
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Hübel N, Dahlem MA. Dynamics from seconds to hours in Hodgkin-Huxley model with time-dependent ion concentrations and buffer reservoirs. PLoS Comput Biol 2014; 10:e1003941. [PMID: 25474648 PMCID: PMC4256015 DOI: 10.1371/journal.pcbi.1003941] [Citation(s) in RCA: 43] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/22/2014] [Accepted: 09/26/2014] [Indexed: 11/19/2022] Open
Abstract
The classical Hodgkin-Huxley (HH) model neglects the time-dependence of ion concentrations in spiking dynamics. The dynamics is therefore limited to a time scale of milliseconds, which is determined by the membrane capacitance multiplied by the resistance of the ion channels, and by the gating time constants. We study slow dynamics in an extended HH framework that includes time-dependent ion concentrations, pumps, and buffers. Fluxes across the neuronal membrane change intra- and extracellular ion concentrations, whereby the latter can also change through contact to reservoirs in the surroundings. Ion gain and loss of the system is identified as a bifurcation parameter whose essential importance was not realized in earlier studies. Our systematic study of the bifurcation structure and thus the phase space structure helps to understand activation and inhibition of a new excitability in ion homeostasis which emerges in such extended models. Also modulatory mechanisms that regulate the spiking rate can be explained by bifurcations. The dynamics on three distinct slow times scales is determined by the cell volume-to-surface-area ratio and the membrane permeability (seconds), the buffer time constants (tens of seconds), and the slower backward buffering (minutes to hours). The modulatory dynamics and the newly emerging excitable dynamics corresponds to pathological conditions observed in epileptiform burst activity, and spreading depression in migraine aura and stroke, respectively.
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Affiliation(s)
- Niklas Hübel
- Department of Theoretical Physics, Technische Universität Berlin, Berlin, Germany
| | - Markus A. Dahlem
- Department of Physics, Humboldt Universität zu Berlin, Berlin, Germany
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99
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Luke TB, Barreto E, So P. Macroscopic complexity from an autonomous network of networks of theta neurons. Front Comput Neurosci 2014; 8:145. [PMID: 25477811 PMCID: PMC4235384 DOI: 10.3389/fncom.2014.00145] [Citation(s) in RCA: 20] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/31/2014] [Accepted: 10/27/2014] [Indexed: 11/13/2022] Open
Abstract
We examine the emergence of collective dynamical structures and complexity in a network of interacting populations of neuronal oscillators. Each population consists of a heterogeneous collection of globally-coupled theta neurons, which are a canonical representation of Type-1 neurons. For simplicity, the populations are arranged in a fully autonomous driver-response configuration, and we obtain a full description of the asymptotic macroscopic dynamics of this network. We find that the collective macroscopic behavior of the response population can exhibit equilibrium and limit cycle states, multistability, quasiperiodicity, and chaos, and we obtain detailed bifurcation diagrams that clarify the transitions between these macrostates. Furthermore, we show that despite the complexity that emerges, it is possible to understand the complicated dynamical structure of this system by building on the understanding of the collective behavior of a single population of theta neurons. This work is a first step in the construction of a mathematically-tractable network-of-networks representation of neuronal network dynamics.
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Affiliation(s)
- Tanushree B Luke
- School of Physics, Astronomy, and Computational Sciences and The Krasnow Institute for Advanced Study, George Mason University Fairfax, VA, USA
| | - Ernest Barreto
- School of Physics, Astronomy, and Computational Sciences and The Krasnow Institute for Advanced Study, George Mason University Fairfax, VA, USA
| | - Paul So
- School of Physics, Astronomy, and Computational Sciences and The Krasnow Institute for Advanced Study, George Mason University Fairfax, VA, USA
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100
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Chen P, Wang L, Deng Q, Ruan H, Cai W. Alteration in rectification of potassium channels in perinatal hypoxia ischemia brain damage. J Neurophysiol 2014; 113:592-600. [PMID: 25355958 DOI: 10.1152/jn.00144.2014] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/22/2022] Open
Abstract
Oligodendrocyte progenitor cells (OPCs) are susceptible to perinatal hypoxia ischemia brain damage (HIBD), which results in infant cerebral palsy due to the effects on myelination. The origin of OPC vulnerability in HIBD, however, remains controversial. In this study, we defined the HIBD punctate lesions by MRI diffuse excessive high signal intensity (DEHSI) in postnatal 7-day-old rats. The electrophysiological functional properties of OPCs in HIBD were recorded by patch-clamp in acute cerebral cortex slices. The slices were intracellularly injected with Lucifer yellow and immunohistochemically labeled with NG2 antibody to identify local OPCs. Passive membrane properties and K(+) channel functions in OPCs were analyzed to estimate the onset of vulnerability in HIBD. The resting membrane potential, membrane resistance, and membrane capacitance of OPCs were increased in both the gray and white matter of the cerebral cortex. OPCs in both the gray and white matter exhibited voltage-dependent K(+) currents, which consisted of the initiated rectified potassium currents (IA) and the sustained rectified currents (IK). The significant alternation in membrane resistance was influenced by the diversity of potassium channel kinetics. These findings suggest that the rectification of IA and IK channels may play a significant role in OPC vulnerability in HIBD.
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Affiliation(s)
- Penghui Chen
- Department of Neurobiology, The Third Military Medical University, Chongqing, China; and
| | - Liyan Wang
- Department of Pediatrics, Xinqiao Hospital, The Third Military Medical University, Chongqing, China
| | - Qiyue Deng
- Department of Neurobiology, The Third Military Medical University, Chongqing, China; and
| | - Huaizhen Ruan
- Department of Neurobiology, The Third Military Medical University, Chongqing, China; and
| | - Wenqin Cai
- Department of Neurobiology, The Third Military Medical University, Chongqing, China; and
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