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Al Harrach M, Yochum M, Ruffini G, Bartolomei F, Wendling F, Benquet P. NeoCoMM: A neocortical neuroinspired computational model for the reconstruction and simulation of epileptiform events. Comput Biol Med 2024; 180:108934. [PMID: 39079417 DOI: 10.1016/j.compbiomed.2024.108934] [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: 01/18/2024] [Revised: 06/13/2024] [Accepted: 07/20/2024] [Indexed: 08/29/2024]
Abstract
BACKGROUND Understanding the pathophysiological dynamics that underline Interictal Epileptiform Events (IEEs) such as epileptic spikes, spike-and-waves or High-Frequency Oscillations (HFOs) is of major importance in the context of neocortical refractory epilepsy, as it paves the way for the development of novel therapies. Typically, these events are detected in Local Field Potential (LFP) recordings obtained through depth electrodes during pre-surgical investigations. Although essential, the underlying pathophysiological mechanisms for the generation of these epileptic neuromarkers remain unclear. The aim of this paper is to propose a novel neurophysiologically relevant reconstruction of the neocortical microcircuitry in the context of epilepsy. This reconstruction intends to facilitate the analysis of a comprehensive set of parameters encompassing physiological, morphological, and biophysical aspects that directly impact the generation and recording of different IEEs. METHOD a novel microscale computational model of an epileptic neocortical column was introduced. This model incorporates the intricate multilayered structure of the cortex and allows for the simulation of realistic interictal epileptic signals. The proposed model was validated through comparisons with real IEEs recorded using intracranial stereo-electroencephalography (SEEG) signals from both humans and animals. Using the model, the user can recreate epileptiform patterns observed in different species (human, rodent, and mouse) and study the intracellular activity associated with these patterns. RESULTS Our model allowed us to unravel the relationship between glutamatergic and GABAergic synaptic transmission of the epileptic neural network and the type of generated IEE. Moreover, sensitivity analyses allowed for the exploration of the pathophysiological parameters responsible for the transitions between these events. Finally, the presented modeling framework also provides an Electrode Tissue Model (ETI) that adds realism to the simulated signals and offers the possibility of studying their sensitivity to the electrode characteristics. CONCLUSION The model (NeoCoMM) presented in this work can be of great use in different applications since it offers an in silico framework for sensitivity analysis and hypothesis testing. It can also be used as a starting point for more complex studies.
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Affiliation(s)
- M Al Harrach
- University of Rennes, INSERM, LTSI-U1099, 35000 Rennes, France.
| | - M Yochum
- Neuroelectrics, Av. Tibidabo 47b, 08035 Barcelona, Spain
| | - G Ruffini
- Neuroelectrics, Av. Tibidabo 47b, 08035 Barcelona, Spain
| | - F Bartolomei
- Hopitaux de Marseille, Service d'Epileptologie et de Rythmologie Cerebrale, Hopital La Timone, Marseille, France
| | - F Wendling
- University of Rennes, INSERM, LTSI-U1099, 35000 Rennes, France
| | - P Benquet
- University of Rennes, INSERM, LTSI-U1099, 35000 Rennes, France
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2
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Behbood M, Lemaire L, Schleimer JH, Schreiber S. The Na+/K+-ATPase generically enables deterministic bursting in class I neurons by shearing the spike-onset bifurcation structure. PLoS Comput Biol 2024; 20:e1011751. [PMID: 39133755 PMCID: PMC11383233 DOI: 10.1371/journal.pcbi.1011751] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/11/2023] [Revised: 09/09/2024] [Accepted: 08/02/2024] [Indexed: 09/10/2024] Open
Abstract
Slow brain rhythms, for example during slow-wave sleep or pathological conditions like seizures and spreading depolarization, can be accompanied by oscillations in extracellular potassium concentration. Such slow brain rhythms typically have a lower frequency than tonic action-potential firing. They are assumed to arise from network-level mechanisms, involving synaptic interactions and delays, or from intrinsically bursting neurons. Neuronal burst generation is commonly attributed to ion channels with slow kinetics. Here, we explore an alternative mechanism generically available to all neurons with class I excitability. It is based on the interplay of fast-spiking voltage dynamics with a one-dimensional slow dynamics of the extracellular potassium concentration, mediated by the activity of the Na+/K+-ATPase. We use bifurcation analysis of the complete system as well as the slow-fast method to reveal that this coupling suffices to generate a hysteresis loop organized around a bistable region that emerges from a saddle-node loop bifurcation-a common feature of class I excitable neurons. Depending on the strength of the Na+/K+-ATPase, bursts are generated from pump-induced shearing the bifurcation structure, spiking is tonic, or cells are silenced via depolarization block. We suggest that transitions between these dynamics can result from disturbances in extracellular potassium regulation, such as glial malfunction or hypoxia affecting the Na+/K+-ATPase activity. The identified minimal mechanistic model outlining the sodium-potassium pump's generic contribution to burst dynamics can, therefore, contribute to a better mechanistic understanding of pathologies such as epilepsy syndromes and, potentially, inform therapeutic strategies.
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Affiliation(s)
- Mahraz Behbood
- Institute for Theoretical Biology, Department of Biology, Humboldt-Universität zu Berlin, Berlin, Germany
- Bernstein Center for Computational Neuroscience, Berlin, Germany
| | - Louisiane Lemaire
- Institute for Theoretical Biology, Department of Biology, Humboldt-Universität zu Berlin, Berlin, Germany
- Bernstein Center for Computational Neuroscience, Berlin, Germany
| | - Jan-Hendrik Schleimer
- Institute for Theoretical Biology, Department of Biology, Humboldt-Universität zu Berlin, Berlin, Germany
- Bernstein Center for Computational Neuroscience, Berlin, Germany
| | - Susanne Schreiber
- Institute for Theoretical Biology, Department of Biology, Humboldt-Universität zu Berlin, Berlin, Germany
- Bernstein Center for Computational Neuroscience, Berlin, Germany
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3
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Signorelli L, Manzoni A, Sætra MJ. Uncertainty quantification and sensitivity analysis of neuron models with ion concentration dynamics. PLoS One 2024; 19:e0303822. [PMID: 38771746 PMCID: PMC11108148 DOI: 10.1371/journal.pone.0303822] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/05/2024] [Accepted: 05/01/2024] [Indexed: 05/23/2024] Open
Abstract
This paper provides a comprehensive and computationally efficient case study for uncertainty quantification (UQ) and global sensitivity analysis (GSA) in a neuron model incorporating ion concentration dynamics. We address how challenges with UQ and GSA in this context can be approached and solved, including challenges related to computational cost, parameters affecting the system's resting state, and the presence of both fast and slow dynamics. Specifically, we analyze the electrodiffusive neuron-extracellular-glia (edNEG) model, which captures electrical potentials, ion concentrations (Na+, K+, Ca2+, and Cl-), and volume changes across six compartments. Our methodology includes a UQ procedure assessing the model's reliability and susceptibility to input uncertainty and a variance-based GSA identifying the most influential input parameters. To mitigate computational costs, we employ surrogate modeling techniques, optimized using efficient numerical integration methods. We propose a strategy for isolating parameters affecting the resting state and analyze the edNEG model dynamics under both physiological and pathological conditions. The influence of uncertain parameters on model outputs, particularly during spiking dynamics, is systematically explored. Rapid dynamics of membrane potentials necessitate a focus on informative spiking features, while slower variations in ion concentrations allow a meaningful study at each time point. Our study offers valuable guidelines for future UQ and GSA investigations on neuron models with ion concentration dynamics, contributing to the broader application of such models in computational neuroscience.
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Affiliation(s)
- Letizia Signorelli
- Department of Mathematics, Politecnico di Milano, Milano, Italy
- Department of Numerical Analysis and Scientific Computing, Simula Research Laboratory, Oslo, Norway
| | - Andrea Manzoni
- MOX, Department of Mathematics, Politecnico di Milano, Milano, Italy
| | - Marte J. Sætra
- Department of Numerical Analysis and Scientific Computing, Simula Research Laboratory, Oslo, Norway
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4
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Gong L, Pasqualetti F, Papouin T, Ching S. Astrocytes as a mechanism for contextually-guided network dynamics and function. PLoS Comput Biol 2024; 20:e1012186. [PMID: 38820533 PMCID: PMC11168681 DOI: 10.1371/journal.pcbi.1012186] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/18/2023] [Revised: 06/12/2024] [Accepted: 05/21/2024] [Indexed: 06/02/2024] Open
Abstract
Astrocytes are a ubiquitous and enigmatic type of non-neuronal cell and are found in the brain of all vertebrates. While traditionally viewed as being supportive of neurons, it is increasingly recognized that astrocytes play a more direct and active role in brain function and neural computation. On account of their sensitivity to a host of physiological covariates and ability to modulate neuronal activity and connectivity on slower time scales, astrocytes may be particularly well poised to modulate the dynamics of neural circuits in functionally salient ways. In the current paper, we seek to capture these features via actionable abstractions within computational models of neuron-astrocyte interaction. Specifically, we engage how nested feedback loops of neuron-astrocyte interaction, acting over separated time-scales, may endow astrocytes with the capability to enable learning in context-dependent settings, where fluctuations in task parameters may occur much more slowly than within-task requirements. We pose a general model of neuron-synapse-astrocyte interaction and use formal analysis to characterize how astrocytic modulation may constitute a form of meta-plasticity, altering the ways in which synapses and neurons adapt as a function of time. We then embed this model in a bandit-based reinforcement learning task environment, and show how the presence of time-scale separated astrocytic modulation enables learning over multiple fluctuating contexts. Indeed, these networks learn far more reliably compared to dynamically homogeneous networks and conventional non-network-based bandit algorithms. Our results fuel the notion that neuron-astrocyte interactions in the brain benefit learning over different time-scales and the conveyance of task-relevant contextual information onto circuit dynamics.
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Affiliation(s)
- Lulu Gong
- Department of Electrical and Systems Engineering, Washington University, St. Louis, Missouri, United States of America
| | - Fabio Pasqualetti
- Department of Mechanical Engineering, University of California, Riverside, California, United States of America
| | - Thomas Papouin
- Department of Neuroscience, Washington University School of Medicine, St. Louis, Missouri, United States of America
| | - ShiNung Ching
- Department of Electrical and Systems Engineering, Washington University, St. Louis, Missouri, United States of America
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5
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Hong R, Zheng T, Marra V, Yang D, Liu JK. Multi-scale modelling of the epileptic brain: advantages of computational therapy exploration. J Neural Eng 2024; 21:021002. [PMID: 38621378 DOI: 10.1088/1741-2552/ad3eb4] [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: 08/29/2023] [Accepted: 04/15/2024] [Indexed: 04/17/2024]
Abstract
Objective: Epilepsy is a complex disease spanning across multiple scales, from ion channels in neurons to neuronal circuits across the entire brain. Over the past decades, computational models have been used to describe the pathophysiological activity of the epileptic brain from different aspects. Traditionally, each computational model can aid in optimizing therapeutic interventions, therefore, providing a particular view to design strategies for treating epilepsy. As a result, most studies are concerned with generating specific models of the epileptic brain that can help us understand the certain machinery of the pathological state. Those specific models vary in complexity and biological accuracy, with system-level models often lacking biological details.Approach: Here, we review various types of computational model of epilepsy and discuss their potential for different therapeutic approaches and scenarios, including drug discovery, surgical strategies, brain stimulation, and seizure prediction. We propose that we need to consider an integrated approach with a unified modelling framework across multiple scales to understand the epileptic brain. Our proposal is based on the recent increase in computational power, which has opened up the possibility of unifying those specific epileptic models into simulations with an unprecedented level of detail.Main results: A multi-scale epilepsy model can bridge the gap between biologically detailed models, used to address molecular and cellular questions, and brain-wide models based on abstract models which can account for complex neurological and behavioural observations.Significance: With these efforts, we move toward the next generation of epileptic brain models capable of connecting cellular features, such as ion channel properties, with standard clinical measures such as seizure severity.
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Affiliation(s)
- Rongqi Hong
- School of Computer Science, Centre for Human Brain Health, University of Birmingham, Birmingham, United Kingdom
| | - Tingting Zheng
- School of Computer Science, Centre for Human Brain Health, University of Birmingham, Birmingham, United Kingdom
| | | | - Dongping Yang
- Research Centre for Frontier Fundamental Studies, Zhejiang Lab, Hangzhou, People's Republic of China
| | - Jian K Liu
- School of Computer Science, Centre for Human Brain Health, University of Birmingham, Birmingham, United Kingdom
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6
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Ma Z, Xu Y, Baier G, Liu Y, Li B, Zhang L. Dynamical modulation of hypersynchronous seizure onset with transcranial magneto-acoustic stimulation in a hippocampal computational model. CHAOS (WOODBURY, N.Y.) 2024; 34:043107. [PMID: 38558041 DOI: 10.1063/5.0181510] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/17/2023] [Accepted: 03/09/2024] [Indexed: 04/04/2024]
Abstract
Hypersynchronous (HYP) seizure onset is one of the frequently observed seizure-onset patterns in temporal lobe epileptic animals and patients, often accompanied by hippocampal sclerosis. However, the exact mechanisms and ion dynamics of the transition to HYP seizures remain unclear. Transcranial magneto-acoustic stimulation (TMAS) has recently been proposed as a novel non-invasive brain therapy method to modulate neurological disorders. Therefore, we propose a biophysical computational hippocampal network model to explore the evolution of HYP seizure caused by changes in crucial physiological parameters and design an effective TMAS strategy to modulate HYP seizure onset. We find that the cooperative effects of abnormal glial uptake strength of potassium and excessive bath potassium concentration could produce multiple discharge patterns and result in transitions from the normal state to the HYP seizure state and ultimately to the depolarization block state. Moreover, we find that the pyramidal neuron and the PV+ interneuron in HYP seizure-onset state exhibit saddle-node-on-invariant-circle/saddle homoclinic (SH) and saddle-node/SH at onset/offset bifurcation pairs, respectively. Furthermore, the response of neuronal activities to TMAS of different ultrasonic waveforms revealed that lower sine wave stimulation can increase the latency of HYP seizures and even completely suppress seizures. More importantly, we propose an ultrasonic parameter area that not only effectively regulates epileptic rhythms but also is within the safety limits of ultrasound neuromodulation therapy. Our results may offer a more comprehensive understanding of the mechanisms of HYP seizure and provide a theoretical basis for the application of TMAS in treating specific types of seizures.
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Affiliation(s)
- Zhiyuan Ma
- Department of Biomedical Engineering, College of Chemistry and Life Science, Beijing University of Technology, Beijing 100124, China
| | - Yuejuan Xu
- Department of Biomedical Engineering, College of Chemistry and Life Science, Beijing University of Technology, Beijing 100124, China
| | - Gerold Baier
- Cell and Developmental Biology, Faculty of Life Sciences, University College London, London WC1E 6BT, United Kingdom
| | - Youjun Liu
- Department of Biomedical Engineering, College of Chemistry and Life Science, Beijing University of Technology, Beijing 100124, China
| | - Bao Li
- Department of Biomedical Engineering, College of Chemistry and Life Science, Beijing University of Technology, Beijing 100124, China
| | - Liyuan Zhang
- Department of Biomedical Engineering, College of Chemistry and Life Science, Beijing University of Technology, Beijing 100124, China
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7
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Li D, Li S, Pan M, Li Q, Song J, Zhang R. The role of extracellular glutamate homeostasis dysregulated by astrocyte in epileptic discharges: a model evidence. Cogn Neurodyn 2024; 18:485-502. [PMID: 38699615 PMCID: PMC11061099 DOI: 10.1007/s11571-023-10001-z] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/18/2023] [Revised: 07/26/2023] [Accepted: 08/13/2023] [Indexed: 05/05/2024] Open
Abstract
Glutamate (Glu) is a predominant excitatory neurotransmitter that acts on glutamate receptors to transfer signals in the central nervous system. Abnormally elevated extracellular glutamate levels is closely related to the generation and transition of epileptic seizures. However, there lacks of investigation regarding the role of extracellular glutamate homeostasis dysregulated by astrocyte in neuronal epileptic discharges. According to this, we propose a novel neuron-astrocyte computational model (NAG) by incorporating extracellular Glu concentration dynamics from three aspects of regulatory mechanisms: (1) the Glu uptake through astrocyte EAAT2; (2) the binding and release Glu via activating astrocyte mGluRs; and (3) the Glu free diffusion in the extracellular space. Then the proposed model NAG is analyzed theoretically and numerically to verify the effect of extracellular Glu homeostasis dysregulated by such three regulatory mechanisms on neuronal epileptic discharges. Our results demonstrate that the neuronal epileptic discharges can be aggravated by the downregulation expression of EAAT2, the aberrant activation of mGluRs, and the elevated Glu levels in extracellular micro-environment; as well as various discharge states (including bursting, mixed-mode spiking, and tonic firing) can be transited by their combination. Furthermore, we find that such factors can also alter the bifurcation threshold for the generation and transition of epileptic discharges. The results in this paper can be helpful for researchers to understand the astrocyte role in modulating extracellular Glu homeostasis, and provide theoretical basis for future related experimental studies.
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Affiliation(s)
- Duo Li
- The Medical Big Data Research Center and The School of Mathematics, Northwest University, Xi’an, 710127 China
| | - Sihui Li
- The Medical Big Data Research Center and The School of Mathematics, Northwest University, Xi’an, 710127 China
| | - Min Pan
- The Medical Big Data Research Center and The School of Mathematics, Northwest University, Xi’an, 710127 China
| | - Qiang Li
- The Medical Big Data Research Center and The School of Mathematics, Northwest University, Xi’an, 710127 China
| | - Jiangling Song
- The Medical Big Data Research Center and The School of Mathematics, Northwest University, Xi’an, 710127 China
| | - Rui Zhang
- The Medical Big Data Research Center and The School of Mathematics, Northwest University, Xi’an, 710127 China
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Forouzandehmehr M, Paci M, Hyttinen J, Koivumäki JT. In silico study of the mechanisms of hypoxia and contractile dysfunction during ischemia and reperfusion of hiPSC cardiomyocytes. Dis Model Mech 2024; 17:dmm050365. [PMID: 38516812 PMCID: PMC11073514 DOI: 10.1242/dmm.050365] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/21/2023] [Accepted: 03/15/2024] [Indexed: 03/23/2024] Open
Abstract
Interconnected mechanisms of ischemia and reperfusion (IR) has increased the interest in IR in vitro experiments using human induced pluripotent stem cell-derived cardiomyocytes (hiPSC-CMs). We developed a whole-cell computational model of hiPSC-CMs including the electromechanics, a metabolite-sensitive sarcoplasmic reticulum Ca2+-ATPase (SERCA) and an oxygen dynamics formulation to investigate IR mechanisms. Moreover, we simulated the effect and action mechanism of levosimendan, which recently showed promising anti-arrhythmic effects in hiPSC-CMs in hypoxia. The model was validated using hiPSC-CM and in vitro animal data. The role of SERCA in causing relaxation dysfunction in IR was anticipated to be comparable to its function in sepsis-induced heart failure. Drug simulations showed that levosimendan counteracts the relaxation dysfunction by utilizing a particular Ca2+-sensitizing mechanism involving Ca2+-bound troponin C and Ca2+ flux to the myofilament, rather than inhibiting SERCA phosphorylation. The model demonstrates extensive characterization and promise for drug development, making it suitable for evaluating IR therapy strategies based on the changing levels of cardiac metabolites, oxygen and molecular pathways.
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Affiliation(s)
| | - Michelangelo Paci
- Department of Electrical, Electronic, and Information Engineering ‘Guglielmo Marconi’, University of Bologna, 47522 Cesena, Italy
| | - Jari Hyttinen
- Faculty of Medicine and Health Technology, Tampere University, 33520 Tampere, Finland
| | - Jussi T. Koivumäki
- Faculty of Medicine and Health Technology, Tampere University, 33520 Tampere, Finland
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Khamis H, Cohen O. Coupled action potential and calcium dynamics underlie robust spontaneous firing in dopaminergic neurons. Phys Biol 2024; 21:026005. [PMID: 38382117 DOI: 10.1088/1478-3975/ad2bd4] [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: 08/16/2023] [Accepted: 02/21/2024] [Indexed: 02/23/2024]
Abstract
Dopaminergic neurons are specialized cells in the substantia nigra, tasked with dopamine secretion. This secretion relies on intracellular calcium signaling coupled to neuronal electrical activity. These neurons are known to display spontaneous calcium oscillationsin-vitroandin-vivo, even in synaptic isolation, controlling the basal dopamine levels. Here we outline a kinetic model for the ion exchange across the neuronal plasma membrane. Crucially, we relax the assumption of constant, cytoplasmic sodium and potassium concentration. We show that sodium-potassium dynamics are strongly coupled to calcium dynamics and are essential for the robustness of spontaneous firing frequency. The model predicts several regimes of electrical activity, including tonic and 'burst' oscillations, and predicts the switch between those in response to perturbations. 'Bursting' correlates with increased calcium amplitudes, while maintaining constant average, allowing for a vast change in the calcium signal responsible for dopamine secretion. All the above traits provide the flexibility to create rich action potential dynamics that are crucial for cellular function.
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Affiliation(s)
- Hadeel Khamis
- Gateway Institute for Brain Research, Fort Lauderdale, FL 33314, United States of America
| | - Ohad Cohen
- Gateway Institute for Brain Research, Fort Lauderdale, FL 33314, United States of America
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Verardo C, Mele LJ, Selmi L, Palestri P. Finite-element modeling of neuromodulation via controlled delivery of potassium ions using conductive polymer-coated microelectrodes. J Neural Eng 2024; 21:026002. [PMID: 38306702 DOI: 10.1088/1741-2552/ad2581] [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: 04/25/2023] [Accepted: 02/02/2024] [Indexed: 02/04/2024]
Abstract
Objective. The controlled delivery of potassium is an interesting neuromodulation modality, being potassium ions involved in shaping neuron excitability, synaptic transmission, network synchronization, and playing a key role in pathological conditions like epilepsy and spreading depression. Despite many successful examples of pre-clinical devices able to influence the extracellular potassium concentration, computational frameworks capturing the corresponding impact on neuronal activity are still missing.Approach. We present a finite-element model describing a PEDOT:PSS-coated microelectrode (herein, simplyionic actuator) able to release potassium and thus modulate the activity of a cortical neuron in anin-vitro-like setting. The dynamics of ions in the ionic actuator, the neural membrane, and the cellular fluids are solved self-consistently.Main results. We showcase the capability of the model to describe on a physical basis the modulation of the intrinsic excitability of the cell and of the synaptic transmission following the electro-ionic stimulation produced by the actuator. We consider three case studies for the ionic actuator with different levels of selectivity to potassium: ideal selectivity, no selectivity, and selectivity achieved by embedding ionophores in the polymer.Significance. This work is the first step toward a comprehensive computational framework aimed to investigate novel neuromodulation devices targeting specific ionic species, as well as to optimize their design and performance, in terms of the induced modulation of neural activity.
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Affiliation(s)
- Claudio Verardo
- Polytechnic Department of Engineering and Architecture, Università degli Studi di Udine, Udine, Italy
- BioRobotics Institute and Department of Excellence in Robotics and AI, Scuola Superiore Sant'Anna, Pisa, Italy
| | - Leandro Julian Mele
- Polytechnic Department of Engineering and Architecture, Università degli Studi di Udine, Udine, Italy
- Department of Materials Science and Engineering, Stanford University, Stanford, CA, United States of America
| | - Luca Selmi
- Department of Engineering "Enzo Ferrari", Università degli Studi di Modena e Reggio Emilia, Modena, Italy
| | - Pierpaolo Palestri
- Polytechnic Department of Engineering and Architecture, Università degli Studi di Udine, Udine, Italy
- Department of Engineering "Enzo Ferrari", Università degli Studi di Modena e Reggio Emilia, Modena, Italy
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Zhang L, Ma Z, Yu Y, Li B, Wu S, Liu Y, Baier G. Examining the low-voltage fast seizure-onset and its response to optogenetic stimulation in a biophysical network model of the hippocampus. Cogn Neurodyn 2024; 18:265-282. [PMID: 38406204 PMCID: PMC10881931 DOI: 10.1007/s11571-023-09935-1] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/30/2022] [Revised: 11/07/2022] [Accepted: 01/24/2023] [Indexed: 02/12/2023] Open
Abstract
Low-voltage fast (LVF) seizure-onset is one of the two frequently observed temporal lobe seizure-onset patterns. Depth electroencephalogram profile analysis illustrated that the peak amplitude of LVF onset was deep temporal areas, e.g., hippocampus. However, the specific dynamic transition mechanisms between normal hippocampal rhythmic activity and LVF seizure-onset remain unclear. Recently, the optogenetic approach to gain control over epileptic hyper-excitability both in vitro and in vivo has become a novel noninvasive modulation strategy. Here, we combined biophysical modeling to study LVF dynamics following changes in crucial physiological parameters, and investigated the potential optogenetic intervention mechanism for both excitatory and inhibitory control. In an Ammon's horn 3 (CA3) biophysical model with light-sensitive protein channelrhodopsin 2 (ChR2), we found that the cooperative effects of excessive extracellular potassium concentration of parvalbumin-positive (PV+) inhibitory interneurons and synaptic links could induce abundant types of discharges of the hippocampus, and lead to transitions from gamma oscillations to LVF seizure-onset. Simulations of optogenetic stimulation revealed that the LVF seizure-onset and morbid fast spiking could not be eliminated by targeting PV+ neurons, whereas the epileptic network was more sensitive to the excitatory control of principal neurons with strong optogenetic currents. We illustrate that in the epileptic hippocampal network, the trajectories of the normal and the seizure state are in close vicinity and optogenetic perturbations therefore may result in transitions. The network model system developed in this study represents a scientific instrument to disclose the underlying principles of LVF, to characterize the effects of optogenetic neuromodulation, and to guide future treatment for specific types of seizures.
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Affiliation(s)
- Liyuan Zhang
- Department of Biomedical Engineering, Faculty of Environment and Life, Beijing University of Technology, Beijing, 100124 China
| | - Zhiyuan Ma
- Department of Biomedical Engineering, Faculty of Environment and Life, Beijing University of Technology, Beijing, 100124 China
| | - Ying Yu
- School of Engineering Medicine, Beihang University, Beijing, 100191 China
| | - Bao Li
- Department of Biomedical Engineering, Faculty of Environment and Life, Beijing University of Technology, Beijing, 100124 China
| | - Shuicai Wu
- Department of Biomedical Engineering, Faculty of Environment and Life, Beijing University of Technology, Beijing, 100124 China
| | - Youjun Liu
- Department of Biomedical Engineering, Faculty of Environment and Life, Beijing University of Technology, Beijing, 100124 China
| | - Gerold Baier
- Cell and Developmental Biology, University College London, London, WC1E 6BT UK
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12
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Chizhov AV, Amakhin DV, Sagtekin AE, Desroches M. Single-compartment model of a pyramidal neuron, fitted to recordings with current and conductance injection. BIOLOGICAL CYBERNETICS 2023; 117:433-451. [PMID: 37755465 DOI: 10.1007/s00422-023-00976-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/06/2023] [Accepted: 09/07/2023] [Indexed: 09/28/2023]
Abstract
For single neuron models, reproducing characteristics of neuronal activity such as the firing rate, amplitude of spikes, and threshold potentials as functions of both synaptic current and conductance is a challenging task. In the present work, we measure these characteristics of regular spiking cortical neurons using the dynamic patch-clamp technique, compare the data with predictions from the standard Hodgkin-Huxley and Izhikevich models, and propose a relatively simple five-dimensional dynamical system model, based on threshold criteria. The model contains a single sodium channel with slow inactivation, fast activation and moderate deactivation, as well as, two fast repolarizing and slow shunting potassium channels. The model quantitatively reproduces characteristics of steady-state activity that are typical for a cortical pyramidal neuron, namely firing rate not exceeding 30 Hz; critical values of the stimulating current and conductance which induce the depolarization block not exceeding 80 mV and 3, respectively (both values are scaled by the resting input conductance); extremum of hyperpolarization close to the midpoint between spikes. The analysis of the model reveals that the spiking regime appears through a saddle-node-on-invariant-circle bifurcation, and the depolarization block is reached through a saddle-node bifurcation of cycles. The model can be used for realistic network simulations, and it can also be implemented within the so-called mean-field, refractory density framework.
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Affiliation(s)
- Anton V Chizhov
- MathNeuro Team, Inria Centre at Universite Cote d'Azur, Sophia Antipolis, France.
- 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
| | - A Erdem Sagtekin
- Istanbul Technical University, Istanbul, Turkey
- University of Tuebingen, Tuebingen, Germany
| | - Mathieu Desroches
- MathNeuro Team, Inria Centre at Universite Cote d'Azur, Sophia Antipolis, France
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13
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Dutta S, Iyer KK, Vanhatalo S, Breakspear M, Roberts JA. Mechanisms underlying pathological cortical bursts during metabolic depletion. Nat Commun 2023; 14:4792. [PMID: 37553358 PMCID: PMC10409751 DOI: 10.1038/s41467-023-40437-0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/08/2022] [Accepted: 07/27/2023] [Indexed: 08/10/2023] Open
Abstract
Cortical activity depends upon a continuous supply of oxygen and other metabolic resources. Perinatal disruption of oxygen availability is a common clinical scenario in neonatal intensive care units, and a leading cause of lifelong disability. Pathological patterns of brain activity including burst suppression and seizures are a hallmark of the recovery period, yet the mechanisms by which these patterns arise remain poorly understood. Here, we use computational modeling of coupled metabolic-neuronal activity to explore the mechanisms by which oxygen depletion generates pathological brain activity. We find that restricting oxygen supply drives transitions from normal activity to several pathological activity patterns (isoelectric, burst suppression, and seizures), depending on the potassium supply. Trajectories through parameter space track key features of clinical electrophysiology recordings and reveal how infants with good recovery outcomes track toward normal parameter values, whereas the parameter values for infants with poor outcomes dwell around the pathological values. These findings open avenues for studying and monitoring the metabolically challenged infant brain, and deepen our understanding of the link between neuronal and metabolic activity.
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Affiliation(s)
- Shrey Dutta
- Brain Modelling Group, QIMR Berghofer Medical Research Institute, Brisbane, QLD, Australia.
- Faculty of Medicine, University of Queensland, Brisbane, QLD, Australia.
- School of Psychological Sciences, College of Engineering, Science and Environment, University of Newcastle, Callaghan, NSW, Australia.
| | - Kartik K Iyer
- Brain Modelling Group, QIMR Berghofer Medical Research Institute, Brisbane, QLD, Australia
| | - Sampsa Vanhatalo
- Pediatric Research Center, Department of Physiology, Helsinki University Hospital, University of Helsinki, Helsinki, Finland
| | - Michael Breakspear
- School of Psychological Sciences, College of Engineering, Science and Environment, University of Newcastle, Callaghan, NSW, Australia
- School of Medicine and Public Health, College of Health and Medicine, University of Newcastle, Callaghan, NSW, Australia
| | - James A Roberts
- Brain Modelling Group, QIMR Berghofer Medical Research Institute, Brisbane, QLD, Australia
- Faculty of Medicine, University of Queensland, Brisbane, QLD, Australia
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14
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Erazo-Toscano R, Fomenko M, Core S, Calabrese RL, Cymbalyuk G. Bursting Dynamics Based on the Persistent Na + and Na +/K + Pump Currents: A Dynamic Clamp Approach. eNeuro 2023; 10:ENEURO.0331-22.2023. [PMID: 37433684 PMCID: PMC10444573 DOI: 10.1523/eneuro.0331-22.2023] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/20/2022] [Revised: 06/04/2023] [Accepted: 06/16/2023] [Indexed: 07/13/2023] Open
Abstract
Life-supporting rhythmic motor functions like heart-beating in invertebrates and breathing in vertebrates require an indefatigable generation of a robust rhythm by specialized oscillatory circuits, central pattern generators (CPGs). These CPGs should be sufficiently flexible to adjust to environmental changes and behavioral goals. Continuous self-sustained operation of bursting neurons requires intracellular Na+ concentration to remain in a functional range and to have checks and balances of the Na+ fluxes met on a cycle-to-cycle basis during bursting. We hypothesize that at a high excitability state, the interaction of the Na+/K+ pump current, Ipump, and persistent Na+ current, INaP, produces a mechanism supporting functional bursting. INaP is a low voltage-activated inward current that initiates and supports the bursting phase. This current does not inactivate and is a significant source of Na+ influx. Ipump is an outward current activated by [Na+]i and is the major source of Na+ efflux. Both currents are active and counteract each other between and during bursts. We apply a combination of electrophysiology, computational modeling, and dynamic clamp to investigate the role of Ipump and INaP in the leech heartbeat CPG interneurons (HN neurons). Applying dynamic clamp to introduce additional Ipump and INaP into the dynamics of living synaptically isolated HN neurons in real time, we show that their joint increase produces transition into a new bursting regime characterized by higher spike frequency and larger amplitude of the membrane potential oscillations. Further increase of Ipump speeds up this rhythm by shortening burst duration (BD) and interburst interval (IBI).
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Affiliation(s)
- Ricardo Erazo-Toscano
- Neuroscience Institute, Georgia State University, Atlanta, 30302 GA
- Department of Biology, Emory University, Atlanta, 30322 GA
| | - Mykhailo Fomenko
- Neuroscience Institute, Georgia State University, Atlanta, 30302 GA
| | - Samuel Core
- Neuroscience Institute, Georgia State University, Atlanta, 30302 GA
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15
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Øyehaug L. Slow ion concentration oscillations and multiple states in neuron-glia interaction-insights gained from reduced mathematical models. FRONTIERS IN NETWORK PHYSIOLOGY 2023; 3:1189118. [PMID: 37284003 PMCID: PMC10241345 DOI: 10.3389/fnetp.2023.1189118] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 03/18/2023] [Accepted: 04/28/2023] [Indexed: 06/08/2023]
Abstract
When potassium in the extracellular space separating neurons and glia reaches sufficient levels, neurons may fire spontaneous action potentials or even become inactivated due to membrane depolarisation, which, in turn, may lead to increased extracellular potassium levels. Under certain circumstances, this chain of events may trigger periodic bursts of neuronal activity. In the present study, reduced neuron-glia models are applied to explore the relationship between bursting behaviour and ion concentration dynamics. These reduced models are built based on a previously developed neuron-glia model, in which channel-mediated neuronal sodium and potassium currents are replaced by a function of neuronal sodium and extracellular potassium concentrations. Simulated dynamics of the resulting two reduced models display features that are qualitatively similar to those of the existing neuron-glia model. Bifurcation analyses of the reduced models show rich and interesting dynamics that include the existence of Hopf bifurcations between which the models exhibit slow ion concentration oscillations for a wide range of parameter values. The study demonstrates that even very simple models can provide insights of possible relevance to complex phenomena.
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16
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Lemaire L, Desroches M, Krupa M, Mantegazza M. Idealized multiple-timescale model of cortical spreading depolarization initiation and pre-epileptic hyperexcitability caused by Na V1.1/SCN1A mutations. J Math Biol 2023; 86:92. [PMID: 37171678 DOI: 10.1007/s00285-023-01917-5] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/12/2022] [Revised: 01/30/2023] [Accepted: 03/28/2023] [Indexed: 05/13/2023]
Abstract
NaV1.1 (SCN1A) is a voltage-gated sodium channel mainly expressed in GABAergic neurons. Loss of function mutations of NaV1.1 lead to epileptic disorders, while gain of function mutations cause a migraine in which cortical spreading depolarizations (CSDs) are involved. It is still debated how these opposite effects initiate two different manifestations of neuronal hyperactivity: epileptic seizures and CSD. To investigate this question, we previously built a conductance-based model of two neurons (GABAergic and pyramidal), with dynamic ion concentrations (Lemaire et al. in PLoS Comput Biol 17(7):e1009239, 2021. https://doi.org/10.1371/journal.pcbi.1009239 ). When implementing either NaV1.1 migraine or epileptogenic mutations, ion concentration modifications acted as slow processes driving the system to the corresponding pathological firing regime. However, the large dimensionality of the model complicated the exploitation of its implicit multi-timescale structure. Here, we substantially simplify our biophysical model to a minimal version more suitable for bifurcation analysis. The explicit timescale separation allows us to apply slow-fast theory, where slow variables are treated as parameters in the fast singular limit. In this setting, we reproduce both pathological transitions as dynamic bifurcations in the full system. In the epilepsy condition, we shift the spike-terminating bifurcation to lower inputs for the GABAergic neuron, to model an increased susceptibility to depolarization block. The resulting failure of synaptic inhibition triggers hyperactivity of the pyramidal neuron. In the migraine scenario, spiking-induced release of potassium leads to the abrupt increase of the extracellular potassium concentration. This causes a dynamic spike-terminating bifurcation of both neurons, which we interpret as CSD initiation.
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Affiliation(s)
- Louisiane Lemaire
- Inria at Université Côte d'Azur, MathNeuro Project-Team, Valbonne-Sophia Antipolis, France.
- Institute for Theoretical Biology, Humboldt-University of Berlin, Berlin, Germany.
- Bernstein Center for Computational Neuroscience, Berlin, Germany.
| | - Mathieu Desroches
- Inria at Université Côte d'Azur, MathNeuro Project-Team, Valbonne-Sophia Antipolis, France
| | - Martin Krupa
- Inria at Université Côte d'Azur, MathNeuro Project-Team, Valbonne-Sophia Antipolis, France
- Laboratoire Jean-Alexandre Dieudonné, Université Côte d'Azur, Nice, France
| | - Massimo Mantegazza
- Institute of Molecular and Cellular Pharmacology (IPMC), Université Côte d'Azur, Valbonne-Sophia Antipolis, France
- CNRS UMR7275, Institute of Molecular and Cellular Pharmacology (IPMC), Valbonne-Sophia Antipolis, France
- INSERM, Valbonne-Sophia Antipolis, France
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17
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Depannemaecker D, Ezzati A, Wang H, Jirsa V, Bernard C. From phenomenological to biophysical models of seizures. Neurobiol Dis 2023; 182:106131. [PMID: 37086755 DOI: 10.1016/j.nbd.2023.106131] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/17/2023] [Revised: 04/12/2023] [Accepted: 04/14/2023] [Indexed: 04/24/2023] Open
Abstract
Epilepsy is a complex disease that requires various approaches for its study. In this short review, we discuss the contribution of theoretical and computational models. The review presents theoretical frameworks that underlie the understanding of certain seizure properties and their classification based on their dynamical properties at the onset and offset of seizures. Dynamical system tools are valuable resources in the study of seizures. By analyzing the complex, dynamic behavior of seizures, these tools can provide insights into seizure mechanisms and offer a framework for their classification. Additionally, computational models have high potential for clinical applications, as they can be used to develop more accurate diagnostic and personalized medicine tools. We discuss various modeling approaches that span different scales and levels, while also questioning the neurocentric view, and emphasize the importance of considering glial cells. Finally, we explore the epistemic value provided by this type of approach.
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Affiliation(s)
- Damien Depannemaecker
- Institut de Neurosciences des Syst' emes, Aix-Marseille University, INSERM, Marseille, France.
| | - Aitakin Ezzati
- Institut de Neurosciences des Syst' emes, Aix-Marseille University, INSERM, Marseille, France
| | - Huifang Wang
- Institut de Neurosciences des Syst' emes, Aix-Marseille University, INSERM, Marseille, France
| | - Viktor Jirsa
- Institut de Neurosciences des Syst' emes, Aix-Marseille University, INSERM, Marseille, France
| | - Christophe Bernard
- Institut de Neurosciences des Syst' emes, Aix-Marseille University, INSERM, Marseille, France.
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18
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Janjic P, Solev D, Kocarev L. Non-trivial dynamics in a model of glial membrane voltage driven by open potassium pores. Biophys J 2023; 122:1470-1490. [PMID: 36919241 PMCID: PMC10147837 DOI: 10.1016/j.bpj.2023.03.013] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/12/2022] [Revised: 02/01/2023] [Accepted: 03/07/2023] [Indexed: 03/16/2023] Open
Abstract
Despite the molecular evidence that a nearly linear steady-state current-voltage relationship in mammalian astrocytes reflects a total current resulting from more than one differentially regulated K+ conductance, detailed ordinary differential equation (ODE) models of membrane voltage Vm are still lacking. Various experimental results reporting altered rectification of the major Kir currents in glia, dominated by Kir4.1, have motivated us to develop a detailed model of Vm dynamics incorporating the weaker potassium K2P-TREK1 current in addition to Kir4.1, and study the stability of the resting state Vr. The main question is whether, with the loss of monotonicity in glial I-V curve resulting from altered Kir rectification, the nominal resting state Vr remains stable, and the cell retains the trivial, potassium electrode behavior with Vm after EK. The minimal two-dimensional model of Vm near Vr showed that an N-shape deformed Kir I-V curve induces multistability of Vm in a model that incorporates K2P activation kinetics, and nonspecific K+ leak currents. More specifically, an asymmetrical, nonlinear decrease of outward Kir4.1 conductance, turning the channels into inward rectifiers, introduces instability of Vr. That happens through a robust bifurcation giving birth to a second, more depolarized stable resting state Vdr > -10 mV. Realistic recordings from electrographic seizures were used to perturb the model. Simulations of the model perturbed by constant current through gap junctions and seizure-like discharges as local field potentials led to depolarization and switching of Vm between the two stable states, in a downstate-upstate manner. In the event of prolonged depolarizations near Vdr, such catastrophic instability would affect all aspects of the glial function, from metabolic support to membrane transport, and practically all neuromodulatory roles assigned to glia.
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Affiliation(s)
- Predrag Janjic
- Laboratory for Complex Systems and Networks, Research Centre for Computer Science and Information Technologies, Macedonian Academy of Sciences and Arts, Skopje, North Macedonia.
| | - Dimitar Solev
- Laboratory for Complex Systems and Networks, Research Centre for Computer Science and Information Technologies, Macedonian Academy of Sciences and Arts, Skopje, North Macedonia
| | - Ljupco Kocarev
- Laboratory for Complex Systems and Networks, Research Centre for Computer Science and Information Technologies, Macedonian Academy of Sciences and Arts, Skopje, North Macedonia
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19
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Cooray GK, Rosch RE, Friston KJ. Global dynamics of neural mass models. PLoS Comput Biol 2023; 19:e1010915. [PMID: 36763644 PMCID: PMC9949652 DOI: 10.1371/journal.pcbi.1010915] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/28/2022] [Revised: 02/23/2023] [Accepted: 02/03/2023] [Indexed: 02/12/2023] Open
Abstract
Neural mass models are used to simulate cortical dynamics and to explain the electrical and magnetic fields measured using electro- and magnetoencephalography. Simulations evince a complex phase-space structure for these kinds of models; including stationary points and limit cycles and the possibility for bifurcations and transitions among different modes of activity. This complexity allows neural mass models to describe the itinerant features of brain dynamics. However, expressive, nonlinear neural mass models are often difficult to fit to empirical data without additional simplifying assumptions: e.g., that the system can be modelled as linear perturbations around a fixed point. In this study we offer a mathematical analysis of neural mass models, specifically the canonical microcircuit model, providing analytical solutions describing slow changes in the type of cortical activity, i.e. dynamical itinerancy. We derive a perturbation analysis up to second order of the phase flow, together with adiabatic approximations. This allows us to describe amplitude modulations in a relatively simple mathematical format providing analytic proof-of-principle for the existence of semi-stable states of cortical dynamics at the scale of a cortical column. This work allows for model inversion of neural mass models, not only around fixed points, but over regions of phase space that encompass transitions among semi or multi-stable states of oscillatory activity. Crucially, these theoretical results speak to model inversion in the context of multiple semi-stable brain states, such as the transition between interictal, pre-ictal and ictal activity in epilepsy.
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Affiliation(s)
- Gerald Kaushallye Cooray
- GOS-UCL Institute of Child Health, University College London, London, United Kingdom
- Great Ormond Street Hospital NHS Foundation Trust, London, United Kingdom
- Karolinska Institutet, Stockholm, Sweden
- * E-mail:
| | - Richard Ewald Rosch
- Great Ormond Street Hospital NHS Foundation Trust, London, United Kingdom
- The Wellcome Centre for Human Neuroimaging, Queen Square Institute of Neurology, University College London, London, United Kingdom
- MRC Centre for Neurodevelopmental Disorders, Institute of Psychiatry, Psychology and Neuroscience, King’s College London, United Kingdom
| | - Karl John Friston
- The Wellcome Centre for Human Neuroimaging, Queen Square Institute of Neurology, University College London, London, United Kingdom
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20
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Zhuang D, Riera M, Zhou R, Deary A, Paesani F. Hydration Structure of Na + and K + Ions in Solution Predicted by Data-Driven Many-Body Potentials. J Phys Chem B 2022; 126:9349-9360. [PMID: 36326071 DOI: 10.1021/acs.jpcb.2c05674] [Citation(s) in RCA: 7] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/05/2022]
Abstract
The hydration structure of Na+ and K+ ions in solution is systematically investigated using a hierarchy of molecular models that progressively include more accurate representations of many-body interactions. We found that a conventional empirical pairwise additive force field that is commonly used in biomolecular simulations is unable to reproduce the extended X-ray absorption fine structure (EXAFS) spectra for both ions. In contrast, progressive inclusion of many-body effects rigorously derived from the many-body expansion of the energy allows the MB-nrg potential energy functions (PEFs) to achieve nearly quantitative agreement with the experimental EXAFS spectra, thus enabling the development of a molecular-level picture of the hydration structure of both Na+ and K+ in solution. Since the MB-nrg PEFs have already been shown to accurately describe isomeric equilibria and vibrational spectra of small ion-water clusters in the gas phase, the present study demonstrates that the MB-nrg PEFs effectively represent the long-sought-after models able to correctly predict the properties of ionic aqueous systems from the gas to the liquid phase, which has so far remained elusive.
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Affiliation(s)
- Debbie Zhuang
- Department of Chemistry and Biochemistry, University of California San Diego, La Jolla, California92093, United States
| | - Marc Riera
- Department of Chemistry and Biochemistry, University of California San Diego, La Jolla, California92093, United States
| | - Ruihan Zhou
- Department of Chemistry and Biochemistry, University of California San Diego, La Jolla, California92093, United States
| | - Alexander Deary
- Department of Chemistry and Biochemistry, University of California San Diego, La Jolla, California92093, United States
| | - Francesco Paesani
- Department of Chemistry and Biochemistry, University of California San Diego, La Jolla, California92093, United States.,Materials Science and Engineering, University of California San Diego, La Jolla, California92093, United States.,San Diego Supercomputer Center, University of California San Diego, La Jolla, California92093, United States
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21
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Aussel A, Ranta R, Aron O, Colnat-Coulbois S, Maillard L, Buhry L. Cell to network computational model of the epileptic human hippocampus suggests specific roles of network and channel dysfunctions in the ictal and interictal oscillations. J Comput Neurosci 2022; 50:519-535. [PMID: 35971033 DOI: 10.1007/s10827-022-00829-5] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/16/2020] [Revised: 07/03/2022] [Accepted: 07/12/2022] [Indexed: 10/15/2022]
Abstract
The mechanisms underlying the generation of hippocampal epileptic seizures and interictal events and their interactions with the sleep-wake cycle are not yet fully understood. Indeed, medial temporal lobe epilepsy is associated with hippocampal abnormalities both at the neuronal (channelopathies, impaired potassium and chloride dynamics) and network level (neuronal and axonal loss, mossy fiber sprouting), with more frequent seizures during wakefulness compared with slow-wave sleep. In this article, starting from our previous computational modeling work of the hippocampal formation based on realistic topology and synaptic connectivity, we study the role of micro- and mesoscale pathological conditions of the epileptic hippocampus in the generation and maintenance of seizure-like theta and interictal oscillations. We show, through the simulations of hippocampal activity during slow-wave sleep and wakefulness that: (i) both mossy fiber sprouting and sclerosis account for seizure-like theta activity, (ii) but they have antagonist effects (seizure-like activity occurrence increases with sprouting but decreases with sclerosis), (iii) though impaired potassium and chloride dynamics have little influence on the generation of seizure-like activity, they do play a role on the generation of interictal patterns, and (iv) seizure-like activity and fast ripples are more likely to occur during wakefulness and interictal spikes during sleep.
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Affiliation(s)
- Amélie Aussel
- Laboratoire Lorrain de Recherche en Informatique et ses applications (LORIA UMR 7503), University of Lorraine, 54506, Nancy, France. .,Centre de Recherche en Automatique de Nancy, University of Lorraine, CRAN-CNRS UMR 7039, Nancy, France.
| | - Radu Ranta
- Centre de Recherche en Automatique de Nancy, University of Lorraine, CRAN-CNRS UMR 7039, Nancy, France
| | - Olivier Aron
- Centre de Recherche en Automatique de Nancy, University of Lorraine, CRAN-CNRS UMR 7039, Nancy, France.,Department of Neurology, CHU de Nancy, Nancy, France
| | - Sophie Colnat-Coulbois
- Centre de Recherche en Automatique de Nancy, University of Lorraine, CRAN-CNRS UMR 7039, Nancy, France.,Department of Neurology, CHU de Nancy, Nancy, France
| | - Louise Maillard
- Centre de Recherche en Automatique de Nancy, University of Lorraine, CRAN-CNRS UMR 7039, Nancy, France.,Department of Neurology, CHU de Nancy, Nancy, France
| | - Laure Buhry
- Laboratoire Lorrain de Recherche en Informatique et ses applications (LORIA UMR 7503), University of Lorraine, 54506, Nancy, France
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22
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Kelley C, Newton AJH, Hrabetova S, McDougal RA, Lytton WW. Multiscale Computer Modeling of Spreading Depolarization in Brain Slices. eNeuro 2022; 9:ENEURO.0082-22.2022. [PMID: 35927026 PMCID: PMC9410770 DOI: 10.1523/eneuro.0082-22.2022] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/21/2022] [Revised: 06/28/2022] [Accepted: 07/11/2022] [Indexed: 11/21/2022] Open
Abstract
Spreading depolarization (SD) is a slow-moving wave of neuronal depolarization accompanied by a breakdown of ion concentration homeostasis, followed by long periods of neuronal silence (spreading depression), and is associated with several neurologic conditions. We developed multiscale (ions to tissue slice) computer models of SD in brain slices using the NEURON simulator: 36,000 neurons (two voltage-gated ion channels; three leak channels; three ion exchangers/pumps) in the extracellular space (ECS) of a slice (1 mm sides, varying thicknesses) with ion (K+, Cl-, Na+) and O2 diffusion and equilibration with a surrounding bath. Glia and neurons cleared K+ from the ECS via Na+/K+ pumps. SD propagated through the slices at realistic speeds of 2-4 mm/min, which increased by as much as 50% in models incorporating the effects of hypoxia or propionate. In both cases, the speedup was mediated principally by ECS shrinkage. Our model allows us to make testable predictions, including the following: (1) SD can be inhibited by enlarging ECS volume; (2) SD velocity will be greater in areas with greater neuronal density, total neuronal volume, or larger/more dendrites; (3) SD is all-or-none: initiating K+ bolus properties have little impact on SD speed; (4) Slice thickness influences SD because of relative hypoxia in the slice core, exacerbated by SD in a pathologic cycle; and (5) SD and high neuronal spike rates will be observed in the core of the slice. Cells in the periphery of the slice near an oxygenated bath will resist SD.
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Affiliation(s)
- Craig Kelley
- Program in Biomedical Engineering, SUNY Downstate Health Sciences University & NYU Tandon School of Engineering, Brooklyn, NY, 11203
| | - Adam J H Newton
- Department of Physiology and Pharmacology, SUNY Downstate Health Sciences University, Brooklyn, New York 11203
| | - Sabina Hrabetova
- Department of Cell Biology, SUNY Downstate Health Sciences University, Brooklyn, New York 11203
- Robert F. Furchgott Center for Neural and Behavioral Science, SUNY Downstate Health Sciences University, Brooklyn, New York 11203
| | - Robert A McDougal
- Department of Biostatistics, Yale University, New Haven, Connecticut 06513
- Yale Center for Medical Informatics, Yale University, New Haven, Connecticut 06513
- Program in Computational Biology and Bioinformatics, Yale University, New Haven, Connecticut 06513
| | - William W Lytton
- Department of Physiology and Pharmacology, SUNY Downstate Health Sciences University, Brooklyn, New York 11203
- Robert F. Furchgott Center for Neural and Behavioral Science, SUNY Downstate Health Sciences University, Brooklyn, New York 11203
- Department of Neurology, SUNY Downstate Health Sciences University, Brooklyn, New York 11203
- Department of Neurology, Kings County Hospital Center, Brooklyn, New York 11203
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23
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Schreiner J, Mardal KA. Simulating epileptic seizures using the bidomain model. Sci Rep 2022; 12:10065. [PMID: 35710825 PMCID: PMC9203799 DOI: 10.1038/s41598-022-12101-y] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/05/2021] [Accepted: 04/28/2022] [Indexed: 11/10/2022] Open
Abstract
Epileptic seizures are due to excessive and synchronous neural activity. Extensive modelling of seizures has been done on the neuronal level, but it remains a challenge to scale these models up to whole brain models. Measurements of the brain's activity over several spatiotemporal scales follow a power-law distribution in terms of frequency. During normal brain activity, the power-law exponent is often found to be around 2 for frequencies between a few Hz and up to 150 Hz, but is higher during seizures and for higher frequencies. The Bidomain model has been used with success in modelling the electrical activity of the heart, but has been explored far less in the context of the brain. This study extends previous models of epileptic seizures on the neuronal level to the whole brain using the Bidomain model. Our approach is evaluated in terms of power-law distributions. The electric potentials were simulated in 7 idealized two-dimensional models and 3 three-dimensional patient-specific models derived from magnetic resonance images (MRI). Computed electric potentials were found to follow power-law distributions with slopes ranging from 2 to 5 for frequencies greater than 10-30 Hz.
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Affiliation(s)
- Jakob Schreiner
- Simula Research Laboratory, Oslo, 0164, Norway.
- Expert Analytics AS, Oslo, 0179, Norway.
| | - Kent-Andre Mardal
- Simula Research Laboratory, Oslo, 0164, Norway
- Expert Analytics AS, Oslo, 0179, Norway
- Department of Mathematics, University of Oslo, Oslo, 0851, Norway
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24
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Interneuronal dynamics facilitate the initiation of spike block in cortical microcircuits. J Comput Neurosci 2022; 50:275-298. [PMID: 35441302 DOI: 10.1007/s10827-022-00815-x] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/28/2021] [Revised: 02/09/2022] [Accepted: 03/09/2022] [Indexed: 10/18/2022]
Abstract
Pyramidal cell spike block is a common occurrence in migraine with aura and epileptic seizures. In both cases, pyramidal cells experience hyperexcitation with rapidly increasing firing rates, major changes in electrochemistry, and ultimately spike block that temporarily terminates neuronal activity. In cortical spreading depression (CSD), spike block propagates as a slowly traveling wave of inactivity through cortical pyramidal cells, which is thought to precede migraine attacks with aura. In seizures, highly synchronized cortical activity can be interspersed with, or terminated by, spike block. While the identifying characteristic of CSD and seizures is the pyramidal cell hyperexcitation, it is currently unknown how the dynamics of the cortical microcircuits and inhibitory interneurons affect the initiation of hyperexcitation and subsequent spike block.We tested the contribution of cortical inhibitory interneurons to the initiation of spike block using a cortical microcircuit model that takes into account changes in ion concentrations that result from neuronal firing. Our results show that interneuronal inhibition provides a wider dynamic range to the circuit and generally improves stability against spike block. Despite these beneficial effects, strong interneuronal firing contributed to rapidly changing extracellular ion concentrations, which facilitated hyperexcitation and led to spike block first in the interneuron and then in the pyramidal cell. In all cases, a loss of interneuronal firing triggered pyramidal cell spike block. However, preventing interneuronal spike block was insufficient to rescue the pyramidal cell from spike block. Our data thus demonstrate that while the role of interneurons in cortical microcircuits is complex, they are critical to the initiation of pyramidal cell spike block. We discuss the implications that localized effects on cortical interneurons have beyond the isolated microcircuit and their contribution to CSD and epileptic seizures.
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25
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Sharples SA, Parker J, Vargas A, Milla-Cruz JJ, Lognon AP, Cheng N, Young L, Shonak A, Cymbalyuk GS, Whelan PJ. Contributions of h- and Na+/K+ Pump Currents to the Generation of Episodic and Continuous Rhythmic Activities. Front Cell Neurosci 2022; 15:715427. [PMID: 35185470 PMCID: PMC8855656 DOI: 10.3389/fncel.2021.715427] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/26/2021] [Accepted: 12/29/2021] [Indexed: 12/31/2022] Open
Abstract
Developing spinal motor networks produce a diverse array of outputs, including episodic and continuous patterns of rhythmic activity. Variation in excitability state and neuromodulatory tone can facilitate transitions between episodic and continuous rhythms; however, the intrinsic mechanisms that govern these rhythms and their transitions are poorly understood. Here, we tested the capacity of a single central pattern generator (CPG) circuit with tunable properties to generate multiple outputs. To address this, we deployed a computational model composed of an inhibitory half-center oscillator (HCO). Following predictions of our computational model, we tested the contributions of key properties to the generation of an episodic rhythm produced by isolated spinal cords of the newborn mouse. The model recapitulates the diverse state-dependent rhythms evoked by dopamine. In the model, episodic bursting depended predominantly on the endogenous oscillatory properties of neurons, with Na+/K+ ATPase pump (IPump) and hyperpolarization-activated currents (Ih) playing key roles. Modulation of either IPump or Ih produced transitions between episodic and continuous rhythms and silence. As maximal activity of IPump decreased, the interepisode interval and period increased along with a reduction in episode duration. Decreasing maximal conductance of Ih decreased episode duration and increased interepisode interval. Pharmacological manipulations of Ih with ivabradine, and IPump with ouabain or monensin in isolated spinal cords produced findings consistent with the model. Our modeling and experimental results highlight key roles of Ih and IPump in producing episodic rhythms and provide insight into mechanisms that permit a single CPG to produce multiple patterns of rhythmicity.
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Affiliation(s)
- Simon A. Sharples
- School of Psychology and Neuroscience, University of St Andrews, St Andrews, United Kingdom
- Hotchkiss Brain Institute, University of Calgary, Calgary, AB, Canada
- Department of Neuroscience, University of Calgary, Calgary, AB, Canada
| | - Jessica Parker
- Neuroscience Institute, Georgia State University, Atlanta, GA, United States
| | - Alex Vargas
- Neuroscience Institute, Georgia State University, Atlanta, GA, United States
| | - Jonathan J. Milla-Cruz
- Hotchkiss Brain Institute, University of Calgary, Calgary, AB, Canada
- Department of Comparative Biology and Experimental Medicine, University of Calgary, Calgary, AB, Canada
| | - Adam P. Lognon
- Hotchkiss Brain Institute, University of Calgary, Calgary, AB, Canada
- Department of Neuroscience, University of Calgary, Calgary, AB, Canada
| | - Ning Cheng
- Hotchkiss Brain Institute, University of Calgary, Calgary, AB, Canada
- Department of Comparative Biology and Experimental Medicine, University of Calgary, Calgary, AB, Canada
| | - Leanne Young
- Department of Comparative Biology and Experimental Medicine, University of Calgary, Calgary, AB, Canada
| | - Anchita Shonak
- Hotchkiss Brain Institute, University of Calgary, Calgary, AB, Canada
- Department of Neuroscience, University of Calgary, Calgary, AB, Canada
| | - Gennady S. Cymbalyuk
- Neuroscience Institute, Georgia State University, Atlanta, GA, United States
- Department of Physics and Astronomy, Georgia State University, Atlanta, GA, United States
- Gennady S. Cymbalyuk,
| | - Patrick J. Whelan
- Hotchkiss Brain Institute, University of Calgary, Calgary, AB, Canada
- Department of Neuroscience, University of Calgary, Calgary, AB, Canada
- Department of Comparative Biology and Experimental Medicine, University of Calgary, Calgary, AB, Canada
- *Correspondence: Patrick J. Whelan,
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26
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A unified physiological framework of transitions between seizures, sustained ictal activity and depolarization block at the single neuron level. J Comput Neurosci 2022; 50:33-49. [PMID: 35031915 PMCID: PMC8818009 DOI: 10.1007/s10827-022-00811-1] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/21/2021] [Revised: 11/10/2021] [Accepted: 01/03/2022] [Indexed: 10/29/2022]
Abstract
The majority of seizures recorded in humans and experimental animal models can be described by a generic phenomenological mathematical model, the Epileptor. In this model, seizure-like events (SLEs) are driven by a slow variable and occur via saddle node (SN) and homoclinic bifurcations at seizure onset and offset, respectively. Here we investigated SLEs at the single cell level using a biophysically relevant neuron model including a slow/fast system of four equations. The two equations for the slow subsystem describe ion concentration variations and the two equations of the fast subsystem delineate the electrophysiological activities of the neuron. Using extracellular K+ as a slow variable, we report that SLEs with SN/homoclinic bifurcations can readily occur at the single cell level when extracellular K+ reaches a critical value. In patients and experimental models, seizures can also evolve into sustained ictal activity (SIA) and depolarization block (DB), activities which are also parts of the dynamic repertoire of the Epileptor. Increasing extracellular concentration of K+ in the model to values found during experimental status epilepticus and DB, we show that SIA and DB can also occur at the single cell level. Thus, seizures, SIA, and DB, which have been first identified as network events, can exist in a unified framework of a biophysical model at the single neuron level and exhibit similar dynamics as observed in the Epileptor.Author Summary: Epilepsy is a neurological disorder characterized by the occurrence of seizures. Seizures have been characterized in patients in experimental models at both macroscopic and microscopic scales using electrophysiological recordings. Experimental works allowed the establishment of a detailed taxonomy of seizures, which can be described by mathematical models. We can distinguish two main types of models. Phenomenological (generic) models have few parameters and variables and permit detailed dynamical studies often capturing a majority of activities observed in experimental conditions. But they also have abstract parameters, making biological interpretation difficult. Biophysical models, on the other hand, use a large number of variables and parameters due to the complexity of the biological systems they represent. Because of the multiplicity of solutions, it is difficult to extract general dynamical rules. In the present work, we integrate both approaches and reduce a detailed biophysical model to sufficiently low-dimensional equations, and thus maintaining the advantages of a generic model. We propose, at the single cell level, a unified framework of different pathological activities that are seizures, depolarization block, and sustained ictal activity.
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27
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Ellingsrud AJ, Boullé N, Farrell PE, Rognes ME. Accurate numerical simulation of electrodiffusion and water movement in brain tissue. MATHEMATICAL MEDICINE AND BIOLOGY-A JOURNAL OF THE IMA 2021; 38:516-551. [PMID: 34791309 DOI: 10.1093/imammb/dqab016] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/12/2021] [Revised: 08/09/2021] [Accepted: 10/19/2021] [Indexed: 12/19/2022]
Abstract
Mathematical modelling of ionic electrodiffusion and water movement is emerging as a powerful avenue of investigation to provide a new physiological insight into brain homeostasis. However, in order to provide solid answers and resolve controversies, the accuracy of the predictions is essential. Ionic electrodiffusion models typically comprise non-trivial systems of non-linear and highly coupled partial and ordinary differential equations that govern phenomena on disparate time scales. Here, we study numerical challenges related to approximating these systems. We consider a homogenized model for electrodiffusion and osmosis in brain tissue and present and evaluate different associated finite element-based splitting schemes in terms of their numerical properties, including accuracy, convergence and computational efficiency for both idealized scenarios and for the physiologically relevant setting of cortical spreading depression (CSD). We find that the schemes display optimal convergence rates in space for problems with smooth manufactured solutions. However, the physiological CSD setting is challenging: we find that the accurate computation of CSD wave characteristics (wave speed and wave width) requires a very fine spatial and fine temporal resolution.
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Affiliation(s)
| | - Nicolas Boullé
- Mathematical Institute, University of Oxford, Oxford, UK
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28
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Amakhin DV, Soboleva EB, Chizhov AV, Zaitsev AV. Insertion of Calcium-Permeable AMPA Receptors during Epileptiform Activity In Vitro Modulates Excitability of Principal Neurons in the Rat Entorhinal Cortex. Int J Mol Sci 2021; 22:12174. [PMID: 34830051 PMCID: PMC8621524 DOI: 10.3390/ijms222212174] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/13/2021] [Revised: 11/05/2021] [Accepted: 11/07/2021] [Indexed: 12/19/2022] Open
Abstract
Epileptic activity leads to rapid insertion of calcium-permeable α-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid receptors (CP-AMPARs) into the synapses of cortical and hippocampal glutamatergic neurons, which generally do not express them. The physiological significance of this process is not yet fully understood; however, it is usually assumed to be a pathological process that augments epileptic activity. Using whole-cell patch-clamp recordings in rat entorhinal cortex slices, we demonstrate that the timing of epileptiform discharges, induced by 4-aminopyridine and gabazine, is determined by the shunting effect of Ca2+-dependent slow conductance, mediated predominantly by K+-channels. The blockade of CP-AMPARs by IEM-1460 eliminates this extra conductance and consequently increases the rate of discharge generation. The blockade of NMDARs reduced the additional conductance to a lesser extent than the blockade of CP-AMPARs, indicating that CP-AMPARs are a more significant source of intracellular Ca2+. The study's main findings were implemented in a mathematical model, which reproduces the shunting effect of activity-dependent conductance on the generation of discharges. The obtained results suggest that the expression of CP-AMPARs in principal neurons reduces the discharge generation rate and may be considered as a protective mechanism.
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Affiliation(s)
- Dmitry V. Amakhin
- Sechenov Institute of Evolutionary Physiology and Biochemistry, Toreza Prospekt 44, 194223 Saint Petersburg, Russia; (D.V.A.); (E.B.S.); (A.V.C.)
| | - Elena B. Soboleva
- Sechenov Institute of Evolutionary Physiology and Biochemistry, Toreza Prospekt 44, 194223 Saint Petersburg, Russia; (D.V.A.); (E.B.S.); (A.V.C.)
| | - Anton V. Chizhov
- Sechenov Institute of Evolutionary Physiology and Biochemistry, Toreza Prospekt 44, 194223 Saint Petersburg, Russia; (D.V.A.); (E.B.S.); (A.V.C.)
- Ioffe Institute, Russian Academy of Sciences, Polytekhnicheskaya 26, 194021 Saint Petersburg, Russia
| | - Aleksey V. Zaitsev
- Sechenov Institute of Evolutionary Physiology and Biochemistry, Toreza Prospekt 44, 194223 Saint Petersburg, Russia; (D.V.A.); (E.B.S.); (A.V.C.)
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29
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Hagiwara A, Bydder M, Oughourlian TC, Yao J, Salamon N, Jahan R, Villablanca JP, Enzmann DR, Ellingson BM. Sodium MR Neuroimaging. AJNR Am J Neuroradiol 2021; 42:1920-1926. [PMID: 34446457 PMCID: PMC8583254 DOI: 10.3174/ajnr.a7261] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/12/2021] [Accepted: 05/28/2021] [Indexed: 12/26/2022]
Abstract
Sodium MR imaging has the potential to complement routine proton MR imaging examinations with the goal of improving diagnosis, disease characterization, and clinical monitoring in neurologic diseases. In the past, the utility and exploration of sodium MR imaging as a valuable clinical tool have been limited due to the extremely low MR signal, but with recent improvements in imaging techniques and hardware, sodium MR imaging is on the verge of becoming clinically realistic for conditions that include brain tumors, ischemic stroke, and epilepsy. In this review, we briefly describe the fundamental physics of sodium MR imaging tailored to the neuroradiologist, focusing on the basics necessary to understand factors that play into making sodium MR imaging feasible for clinical settings and describing current controversies in the field. We will also discuss the current state of the field and the potential future clinical uses of sodium MR imaging in the diagnosis, phenotyping, and therapeutic monitoring in neurologic diseases.
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Affiliation(s)
- A Hagiwara
- From the UCLA Brain Tumor Imaging Laboratory (A.H., M.B., T.C.O., J.Y., B.M.E.), Center for Computer Vision and Imaging Biomarkers
- Department of Radiological Sciences (A.H., M.B., J.Y., N.S., R.J., J.P.V., D.R.E., B.M.E.)
| | - M Bydder
- From the UCLA Brain Tumor Imaging Laboratory (A.H., M.B., T.C.O., J.Y., B.M.E.), Center for Computer Vision and Imaging Biomarkers
- Department of Radiological Sciences (A.H., M.B., J.Y., N.S., R.J., J.P.V., D.R.E., B.M.E.)
| | - T C Oughourlian
- From the UCLA Brain Tumor Imaging Laboratory (A.H., M.B., T.C.O., J.Y., B.M.E.), Center for Computer Vision and Imaging Biomarkers
- Neuroscience Interdepartmental Program (T.C.O., B.M.E.)
| | - J Yao
- From the UCLA Brain Tumor Imaging Laboratory (A.H., M.B., T.C.O., J.Y., B.M.E.), Center for Computer Vision and Imaging Biomarkers
- Department of Bioengineering (J.Y., B.M.E.), Henry Samueli School of Engineering and Applied Science, University of California Los Angeles, Los Angeles, California
- Department of Radiological Sciences (A.H., M.B., J.Y., N.S., R.J., J.P.V., D.R.E., B.M.E.)
| | - N Salamon
- Department of Radiological Sciences (A.H., M.B., J.Y., N.S., R.J., J.P.V., D.R.E., B.M.E.)
| | - R Jahan
- Department of Radiological Sciences (A.H., M.B., J.Y., N.S., R.J., J.P.V., D.R.E., B.M.E.)
| | - J P Villablanca
- Department of Radiological Sciences (A.H., M.B., J.Y., N.S., R.J., J.P.V., D.R.E., B.M.E.)
| | - D R Enzmann
- Department of Radiological Sciences (A.H., M.B., J.Y., N.S., R.J., J.P.V., D.R.E., B.M.E.)
| | - B M Ellingson
- From the UCLA Brain Tumor Imaging Laboratory (A.H., M.B., T.C.O., J.Y., B.M.E.), Center for Computer Vision and Imaging Biomarkers
- Department of Bioengineering (J.Y., B.M.E.), Henry Samueli School of Engineering and Applied Science, University of California Los Angeles, Los Angeles, California
- Department of Radiological Sciences (A.H., M.B., J.Y., N.S., R.J., J.P.V., D.R.E., B.M.E.)
- Neuroscience Interdepartmental Program (T.C.O., B.M.E.)
- Department of Psychiatry and Biobehavioral Sciences (B.M.E.), David Geffen School of Medicine, University of California, Los Angeles, Los Angeles, California
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30
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A dynamics model of neuron-astrocyte network accounting for febrile seizures. Cogn Neurodyn 2021; 16:411-423. [PMID: 35401866 PMCID: PMC8934847 DOI: 10.1007/s11571-021-09706-w] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/31/2020] [Revised: 06/03/2021] [Accepted: 07/17/2021] [Indexed: 10/20/2022] Open
Abstract
Febrile seizure (FS) is a full-body convulsion caused by a high body temperature that affect young kids, however, how these most common of human seizures are generated by fever has not been known. One common observation is that cortical neurons become overexcited with abnormal running of sodium and potassium ions cross membrane in raised body temperature condition, Considering that astrocyte Kir4.1 channel play a critical role in maintaining extracellular homeostasis of ionic concentrations and electrochemical potentials of neurons by fast depletion of extracellular potassium ions, we examined here the potential role of temperature-dependent Kir4.1 channel in astrocytes in causing FS. We first built up a temperature-dependent computational model of the Kir4.1 channel in astrocytes and validated with experiments. We have then built up a neuron-astrocyte network and examine the role of the Kir4.1 channel in modulating neuronal firing dynamics as temperature increase. The numerical experiment demonstrated that the Kir4.1 channel function optimally in the body temperature around 37 °C in cleaning 'excessive' extracellular potassium ions during neuronal firing process, however, higher temperature deteriorates its cleaning function, while lower temperature slows down its cleaning efficiency. With the increase of temperature, neurons go through different stages of spiking dynamics from spontaneous slow oscillations, to tonic spiking, fast bursting oscillations, and eventually epileptic bursting. Thus, our study may provide a potential new mechanism that febrile seizures may be happened due to temperature-dependent functional disorders of Kir4.1 channel in astrocytes. Supplementary Information The online version contains supplementary material available at 10.1007/s11571-021-09706-w.
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31
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Gerster M, Taher H, Škoch A, Hlinka J, Guye M, Bartolomei F, Jirsa V, Zakharova A, Olmi S. Patient-Specific Network Connectivity Combined With a Next Generation Neural Mass Model to Test Clinical Hypothesis of Seizure Propagation. Front Syst Neurosci 2021; 15:675272. [PMID: 34539355 PMCID: PMC8440880 DOI: 10.3389/fnsys.2021.675272] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/02/2021] [Accepted: 07/07/2021] [Indexed: 11/13/2022] Open
Abstract
Dynamics underlying epileptic seizures span multiple scales in space and time, therefore, understanding seizure mechanisms requires identifying the relations between seizure components within and across these scales, together with the analysis of their dynamical repertoire. In this view, mathematical models have been developed, ranging from single neuron to neural population. In this study, we consider a neural mass model able to exactly reproduce the dynamics of heterogeneous spiking neural networks. We combine mathematical modeling with structural information from non invasive brain imaging, thus building large-scale brain network models to explore emergent dynamics and test the clinical hypothesis. We provide a comprehensive study on the effect of external drives on neuronal networks exhibiting multistability, in order to investigate the role played by the neuroanatomical connectivity matrices in shaping the emergent dynamics. In particular, we systematically investigate the conditions under which the network displays a transition from a low activity regime to a high activity state, which we identify with a seizure-like event. This approach allows us to study the biophysical parameters and variables leading to multiple recruitment events at the network level. We further exploit topological network measures in order to explain the differences and the analogies among the subjects and their brain regions, in showing recruitment events at different parameter values. We demonstrate, along with the example of diffusion-weighted magnetic resonance imaging (dMRI) connectomes of 20 healthy subjects and 15 epileptic patients, that individual variations in structural connectivity, when linked with mathematical dynamic models, have the capacity to explain changes in spatiotemporal organization of brain dynamics, as observed in network-based brain disorders. In particular, for epileptic patients, by means of the integration of the clinical hypotheses on the epileptogenic zone (EZ), i.e., the local network where highly synchronous seizures originate, we have identified the sequence of recruitment events and discussed their links with the topological properties of the specific connectomes. The predictions made on the basis of the implemented set of exact mean-field equations turn out to be in line with the clinical pre-surgical evaluation on recruited secondary networks.
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Affiliation(s)
- Moritz Gerster
- Institut für Theoretische Physik, Technische Universität Berlin, Berlin, Germany
| | - Halgurd Taher
- Inria Sophia Antipolis Méditerranée Research Centre, MathNeuro Team, Valbonne, France
| | - Antonín Škoch
- National Institute of Mental Health, Klecany, Czechia
- MR Unit, Department of Diagnostic and Interventional Radiology, Institute for Clinical and Experimental Medicine, Prague, Czechia
| | - Jaroslav Hlinka
- National Institute of Mental Health, Klecany, Czechia
- Institute of Computer Science of the Czech Academy of Sciences, Prague, Czechia
| | - Maxime Guye
- Faculté de Médecine de la Timone, Centre de Résonance Magnétique et Biologique et Médicale (CRMBM, UMR CNRS-AMU 7339), Medical School of Marseille, Aix-Marseille Université, Marseille, France
- Assistance Publique -Hôpitaux de Marseille, Hôpital de la Timone, Pôle d'Imagerie, Marseille, France
| | - Fabrice Bartolomei
- Assistance Publique - Hôpitaux de Marseille, Hôpital de la Timone, Service de Neurophysiologie Clinique, Marseille, France
| | - Viktor Jirsa
- Aix Marseille Université, Inserm, Institut de Neurosciences des Systèmes, UMRS 1106, Marseille, France
| | - Anna Zakharova
- Institut für Theoretische Physik, Technische Universität Berlin, Berlin, Germany
| | - Simona Olmi
- Inria Sophia Antipolis Méditerranée Research Centre, MathNeuro Team, Valbonne, France
- Consiglio Nazionale delle Ricerche, Istituto dei Sistemi Complessi, Sesto Fiorentino, Italy
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32
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Song JL, Kim JA, Struck AF, Zhang R, Westover MB. A model of metabolic supply-demand mismatch leading to secondary brain injury. J Neurophysiol 2021; 126:653-667. [PMID: 34232754 DOI: 10.1152/jn.00674.2020] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/10/2023] Open
Abstract
Secondary brain injury (SBI) is defined as new or worsening injury to the brain after an initial neurologic insult, such as hemorrhage, trauma, ischemic stroke, or infection. It is a common and potentially preventable complication following many types of primary brain injury (PBI). However, mechanistic details about how PBI leads to additional brain injury and evolves into SBI are poorly characterized. In this work, we propose a mechanistic model for the metabolic supply demand mismatch hypothesis (MSDMH) of SBI. Our model, based on the Hodgkin-Huxley model, supplemented with additional dynamics for extracellular potassium, oxygen concentration, and excitotoxity, provides a high-level unified explanation for why patients with acute brain injury frequently develop SBI. We investigate how decreased oxygen, increased extracellular potassium, excitotoxicity, and seizures can induce SBI and suggest three underlying paths for how events following PBI may lead to SBI. The proposed model also helps explain several important empirical observations, including the common association of acute brain injury with seizures, the association of seizures with tissue hypoxia and so on. In contrast to current practices which assume that ischemia plays the predominant role in SBI, our model suggests that metabolic crisis involved in SBI can also be nonischemic. Our findings offer a more comprehensive understanding of the complex interrelationship among potassium, oxygen, excitotoxicity, seizures, and SBI.NEW & NOTEWORTHY We present a novel mechanistic model for the metabolic supply demand mismatch hypothesis (MSDMH), which attempts to explain why patients with acute brain injury frequently develop seizure activity and secondary brain injury (SBI). Specifically, we investigate how decreased oxygen, increased extracellular potassium, excitotoxicity, seizures, all common sequalae of primary brain injury (PBI), can induce SBI and suggest three underlying paths for how events following PBI may lead to SBI.
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Affiliation(s)
- Jiang-Ling Song
- The Medical Big Data Research Center, Northwest University, Xi'an, China.,Department of Neurology, Massachusetts General Hospital, Harvard Medical School, Boston, Massachusetts
| | - Jennifer A Kim
- Department of Neurology, Yale New Haven Hospital, New Haven, Connecticut
| | - Aaron F Struck
- Departments of Neurology, University of Wisconsin-Madison, Madison, Wisconsin.,William S Middleton Veterans Administration Hospital, Madison, Wisconsin
| | - Rui Zhang
- The Medical Big Data Research Center, Northwest University, Xi'an, China
| | - M Brandon Westover
- Department of Neurology, Massachusetts General Hospital, Harvard Medical School, Boston, Massachusetts
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33
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Sætra MJ, Einevoll GT, Halnes G. An electrodiffusive neuron-extracellular-glia model for exploring the genesis of slow potentials in the brain. PLoS Comput Biol 2021; 17:e1008143. [PMID: 34270543 PMCID: PMC8318289 DOI: 10.1371/journal.pcbi.1008143] [Citation(s) in RCA: 12] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/07/2020] [Revised: 07/28/2021] [Accepted: 06/28/2021] [Indexed: 11/29/2022] Open
Abstract
Within the computational neuroscience community, there has been a focus on simulating the electrical activity of neurons, while other components of brain tissue, such as glia cells and the extracellular space, are often neglected. Standard models of extracellular potentials are based on a combination of multicompartmental models describing neural electrodynamics and volume conductor theory. Such models cannot be used to simulate the slow components of extracellular potentials, which depend on ion concentration dynamics, and the effect that this has on extracellular diffusion potentials and glial buffering currents. We here present the electrodiffusive neuron-extracellular-glia (edNEG) model, which we believe is the first model to combine compartmental neuron modeling with an electrodiffusive framework for intra- and extracellular ion concentration dynamics in a local piece of neuro-glial brain tissue. The edNEG model (i) keeps track of all intraneuronal, intraglial, and extracellular ion concentrations and electrical potentials, (ii) accounts for action potentials and dendritic calcium spikes in neurons, (iii) contains a neuronal and glial homeostatic machinery that gives physiologically realistic ion concentration dynamics, (iv) accounts for electrodiffusive transmembrane, intracellular, and extracellular ionic movements, and (v) accounts for glial and neuronal swelling caused by osmotic transmembrane pressure gradients. The edNEG model accounts for the concentration-dependent effects on ECS potentials that the standard models neglect. Using the edNEG model, we analyze these effects by splitting the extracellular potential into three components: one due to neural sink/source configurations, one due to glial sink/source configurations, and one due to extracellular diffusive currents. Through a series of simulations, we analyze the roles played by the various components and how they interact in generating the total slow potential. We conclude that the three components are of comparable magnitude and that the stimulus conditions determine which of the components that dominate.
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Affiliation(s)
- Marte J. Sætra
- Department of Numerical Analysis and Scientific Computing, Simula Research Laboratory, Oslo, Norway
| | - Gaute T. Einevoll
- Centre for Integrative Neuroplasticity, University of Oslo, Oslo, Norway
- Department of Physics, University of Oslo, Oslo, Norway
- Department of Physics, Norwegian University of Life Sciences, Ås, Norway
| | - Geir Halnes
- Centre for Integrative Neuroplasticity, University of Oslo, Oslo, Norway
- Department of Physics, Norwegian University of Life Sciences, Ås, Norway
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34
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Depannemaecker D, Destexhe A, Jirsa V, Bernard C. Modeling seizures: From single neurons to networks. Seizure 2021; 90:4-8. [PMID: 34219016 DOI: 10.1016/j.seizure.2021.06.015] [Citation(s) in RCA: 13] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/18/2021] [Revised: 06/11/2021] [Accepted: 06/11/2021] [Indexed: 11/26/2022] Open
Abstract
Dynamical system tools offer a complementary approach to detailed biophysical seizure modeling, with a high potential for clinical applications. This review describes the theoretical framework that provides a basis for theorizing certain properties of seizures and for their classification according to their dynamical properties at onset and offset. We describe various modeling approaches spanning different scales, from single neurons to large-scale networks. This narrative review provides an accessible overview of this field, including non-exhaustive examples of key recent works.
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Affiliation(s)
- Damien Depannemaecker
- Paris-Saclay University, French National Centre for Scientific Research (CNRS), Institute of Neuroscience (NeuroPSI), 91198 Gif sur Yvette, France.
| | - Alain Destexhe
- Paris-Saclay University, French National Centre for Scientific Research (CNRS), Institute of Neuroscience (NeuroPSI), 91198 Gif sur Yvette, France.
| | - Viktor Jirsa
- Aix Marseille Univ, INSERM, INS, Institut des Neurosciences des Systèmes, Marseille, France.
| | - Christophe Bernard
- Aix Marseille Univ, INSERM, INS, Institut des Neurosciences des Systèmes, Marseille, France.
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35
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Contreras SA, Schleimer JH, Gulledge AT, Schreiber S. Activity-mediated accumulation of potassium induces a switch in firing pattern and neuronal excitability type. PLoS Comput Biol 2021; 17:e1008510. [PMID: 34043638 PMCID: PMC8205125 DOI: 10.1371/journal.pcbi.1008510] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/06/2020] [Revised: 06/15/2021] [Accepted: 04/16/2021] [Indexed: 01/30/2023] Open
Abstract
During normal neuronal activity, ionic concentration gradients across a neuron’s membrane are often assumed to be stable. Prolonged spiking activity, however, can reduce transmembrane gradients and affect voltage dynamics. Based on mathematical modeling, we investigated the impact of neuronal activity on ionic concentrations and, consequently, the dynamics of action potential generation. We find that intense spiking activity on the order of a second suffices to induce changes in ionic reversal potentials and to consistently induce a switch from a regular to an intermittent firing mode. This transition is caused by a qualitative alteration in the system’s voltage dynamics, mathematically corresponding to a co-dimension-two bifurcation from a saddle-node on invariant cycle (SNIC) to a homoclinic orbit bifurcation (HOM). Our electrophysiological recordings in mouse cortical pyramidal neurons confirm the changes in action potential dynamics predicted by the models: (i) activity-dependent increases in intracellular sodium concentration directly reduce action potential amplitudes, an effect typically attributed solely to sodium channel inactivation; (ii) extracellular potassium accumulation switches action potential generation from tonic firing to intermittently interrupted output. Thus, individual neurons may respond very differently to the same input stimuli, depending on their recent patterns of activity and/or the current brain-state. Ionic concentrations in the brain are not constant. We show that during intense neuronal activity, they can change on the order of seconds and even switch neuronal spiking patterns under identical stimulation from a regular firing mode to an intermittently interrupted one. Triggered by an accumulation of extracellular potassium, such a transition is caused by a specific, qualitative change in of the neuronal voltage dynamics—a so-called bifurcation—which affects crucial features of action-potential generation and bears consequences for how information is encoded and how neurons behave together in the network. Also, changes in intracellular sodium can induce measurable effects, like a reduction of spike amplitude that occurs independently of the fast amplitude effects attributed to sodium channel inactivation. Taken together, our results demonstrate that a neuron can respond very differently to the same stimulus, depending on its previous activity or the current brain state. This finding may be particularly relevant when other regulatory mechanisms of ionic homeostasis are challenged, for example, during pathological states of glial impairment or oxygen deprivation. Finally, categorization of cortical neurons as intrinsically bursting or regular spiking may be biased by the ionic concentrations at the time of the observation, highlighting the non-static nature of neuronal dynamics.
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Affiliation(s)
- Susana Andrea Contreras
- Institute for Theoretical Biology, Humboldt-University of Berlin, Berlin, Germany
- Bernstein Center for Computational Neuroscience Berlin, Berlin, Germany
| | - Jan-Hendrik Schleimer
- Institute for Theoretical Biology, Humboldt-University of Berlin, Berlin, Germany
- Bernstein Center for Computational Neuroscience Berlin, Berlin, Germany
| | - Allan T. Gulledge
- Molecular and Systems Biology, Geisel School of Medicine at Dartmouth College, Hanover, New Hampshire, United States of America
| | - Susanne Schreiber
- Institute for Theoretical Biology, Humboldt-University of Berlin, Berlin, Germany
- Bernstein Center for Computational Neuroscience Berlin, Berlin, Germany
- * E-mail:
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36
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Eelkman Rooda OHJ, Kros L, Faneyte SJ, Holland PJ, Gornati SV, Poelman HJ, Jansen NA, Tolner EA, van den Maagdenberg AMJM, De Zeeuw CI, Hoebeek FE. Single-pulse stimulation of cerebellar nuclei stops epileptic thalamic activity. Brain Stimul 2021; 14:861-872. [PMID: 34022430 DOI: 10.1016/j.brs.2021.05.002] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/20/2020] [Revised: 04/05/2021] [Accepted: 05/03/2021] [Indexed: 01/24/2023] Open
Abstract
BACKGROUND Epileptic (absence) seizures in the cerebral cortex can be stopped by pharmacological and optogenetic stimulation of the cerebellar nuclei (CN) neurons that innervate the thalamus. However, it is unclear how such stimulation can modify underlying thalamo-cortical oscillations. HYPOTHESIS Here we tested whether rhythmic synchronized thalamo-cortical activity during absence seizures can be desynchronized by single-pulse optogenetic stimulation of CN neurons to stop seizure activity. METHODS We performed simultaneous thalamic single-cell and electrocorticographical recordings in awake tottering mice, a genetic model of absence epilepsy, to investigate the rhythmicity and synchronicity. Furthermore, we tested interictally the impact of single-pulse optogenetic CN stimulation on thalamic and cortical recordings. RESULTS We show that thalamic firing is highly rhythmic and synchronized with cortical spike-and-wave discharges during absence seizures and that this phase-locked activity can be desynchronized upon single-pulse optogenetic stimulation of CN neurons. Notably, this stimulation of CN neurons was more effective in stopping seizures than direct, focal stimulation of groups of afferents innervating the thalamus. During interictal periods, CN stimulation evoked reliable but heterogeneous responses in thalamic cells in that they could show an increase or decrease in firing rate at various latencies, bi-phasic responses with an initial excitatory and subsequent inhibitory response, or no response at all. CONCLUSION Our data indicate that stimulation of CN neurons and their fibers in thalamus evokes differential effects in its downstream pathways and desynchronizes phase-locked thalamic neuronal firing during seizures, revealing a neurobiological mechanism that may explain how cerebellar stimulation can stop seizures.
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Affiliation(s)
- Oscar H J Eelkman Rooda
- Department of Neuroscience, Erasmus Medical Center, 3015, AA Rotterdam, the Netherlands; Department of Neurosurgery, Erasmus Medical Center, 3015, AA Rotterdam, the Netherlands
| | - Lieke Kros
- Department of Neuroscience, Erasmus Medical Center, 3015, AA Rotterdam, the Netherlands
| | - Sade J Faneyte
- Department of Neuroscience, Erasmus Medical Center, 3015, AA Rotterdam, the Netherlands
| | - Peter J Holland
- School of Psychology, University of Birmingham, Birmingham, United Kingdom
| | - Simona V Gornati
- Department of Neuroscience, Erasmus Medical Center, 3015, AA Rotterdam, the Netherlands
| | - Huub J Poelman
- Department of Neuroscience, Erasmus Medical Center, 3015, AA Rotterdam, the Netherlands
| | - Nico A Jansen
- Department of Neurology, Leiden University Medical Center, 2300, RC Leiden, the Netherlands; Department of Human Genetics, Leiden University Medical Center, 2300, RC Leiden, the Netherlands
| | - Else A Tolner
- Department of Neurology, Leiden University Medical Center, 2300, RC Leiden, the Netherlands; Department of Human Genetics, Leiden University Medical Center, 2300, RC Leiden, the Netherlands
| | - Arn M J M van den Maagdenberg
- Department of Neurology, Leiden University Medical Center, 2300, RC Leiden, the Netherlands; Department of Human Genetics, Leiden University Medical Center, 2300, RC Leiden, the Netherlands
| | - Chris I De Zeeuw
- Department of Neuroscience, Erasmus Medical Center, 3015, AA Rotterdam, the Netherlands; Netherlands Institute for Neuroscience, Royal Dutch Academy for Arts and Sciences, 1105, BA Amsterdam, the Netherlands
| | - Freek E Hoebeek
- Department of Neuroscience, Erasmus Medical Center, 3015, AA Rotterdam, the Netherlands; Department for Developmental Origins of Disease, University Medical Center Utrecht Brain Center and Wilhelmina Children's Hospital, Utrecht Medical Center, 3508, AB Utrecht, the Netherlands.
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Gandolfi D, Boiani GM, Bigiani A, Mapelli J. Modeling Neurotransmission: Computational Tools to Investigate Neurological Disorders. Int J Mol Sci 2021; 22:4565. [PMID: 33925434 PMCID: PMC8123833 DOI: 10.3390/ijms22094565] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/15/2021] [Revised: 04/22/2021] [Accepted: 04/25/2021] [Indexed: 02/06/2023] Open
Abstract
The investigation of synaptic functions remains one of the most fascinating challenges in the field of neuroscience and a large number of experimental methods have been tuned to dissect the mechanisms taking part in the neurotransmission process. Furthermore, the understanding of the insights of neurological disorders originating from alterations in neurotransmission often requires the development of (i) animal models of pathologies, (ii) invasive tools and (iii) targeted pharmacological approaches. In the last decades, additional tools to explore neurological diseases have been provided to the scientific community. A wide range of computational models in fact have been developed to explore the alterations of the mechanisms involved in neurotransmission following the emergence of neurological pathologies. Here, we review some of the advancements in the development of computational methods employed to investigate neuronal circuits with a particular focus on the application to the most diffuse neurological disorders.
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Affiliation(s)
- Daniela Gandolfi
- Department of Biomedical, Metabolic and Neural Sciences, University of Modena and Reggio Emilia, Via Campi 287, 41125 Modena, Italy; (D.G.); (G.M.B.); (A.B.)
| | - Giulia Maria Boiani
- Department of Biomedical, Metabolic and Neural Sciences, University of Modena and Reggio Emilia, Via Campi 287, 41125 Modena, Italy; (D.G.); (G.M.B.); (A.B.)
| | - Albertino Bigiani
- Department of Biomedical, Metabolic and Neural Sciences, University of Modena and Reggio Emilia, Via Campi 287, 41125 Modena, Italy; (D.G.); (G.M.B.); (A.B.)
- Center for Neuroscience and Neurotechnology, University of Modena and Reggio Emilia, Via Campi 287, 41125 Modena, Italy
| | - Jonathan Mapelli
- Department of Biomedical, Metabolic and Neural Sciences, University of Modena and Reggio Emilia, Via Campi 287, 41125 Modena, Italy; (D.G.); (G.M.B.); (A.B.)
- Center for Neuroscience and Neurotechnology, University of Modena and Reggio Emilia, Via Campi 287, 41125 Modena, Italy
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38
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Chang J, Paydarfar D. Falling off a limit cycle using phase-agnostic stimuli: Applications to clinical oscillopathies. CHAOS (WOODBURY, N.Y.) 2021; 31:023134. [PMID: 33653068 DOI: 10.1063/5.0032974] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/15/2020] [Accepted: 01/29/2021] [Indexed: 06/12/2023]
Abstract
For over a century, physiological studies have shown that precisely timed pulses can switch off a biological oscillator. This empiric finding has shaped our mechanistic understanding of how perturbations start, stop, and reset biological oscillators and has led to treatments that suppress pathological oscillations using electrical pulses given within specified therapeutic phase windows. Here, we present evidence, using numerical simulations of models of epileptic seizures and reentrant tachycardia, that the phase window can be opened to the entire cycle using novel complex stimulus waveforms. Our results reveal that the trajectories are displaced by such phase-agnostic stimuli off the oscillator's limit cycle and corralled into a region where oscillation is suppressed, irrespective of the phase at which the stimulus was applied. Our findings suggest the need for broadening theoretical understanding of how complex perturbing waveforms interact with biological oscillators to access their arrhythmic states. In clinical practice, oscillopathies may be treated more effectively with non-traditional stimulus waveforms that obviate the need for phase specificity.
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Affiliation(s)
- Joshua Chang
- Department of Neurology, Dell Medical School, The University of Texas at Austin, Austin, Texas 78712, USA
| | - David Paydarfar
- Department of Neurology, Dell Medical School, The University of Texas at Austin, Austin, Texas 78712, USA
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Perez C, Felix L, Durry S, Rose CR, Ullah G. On the origin of ultraslow spontaneous Na + fluctuations in neurons of the neonatal forebrain. J Neurophysiol 2021; 125:408-425. [PMID: 33236936 PMCID: PMC7948148 DOI: 10.1152/jn.00373.2020] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/22/2020] [Revised: 11/19/2020] [Accepted: 11/19/2020] [Indexed: 11/22/2022] Open
Abstract
Spontaneous neuronal and astrocytic activity in the neonate forebrain is believed to drive the maturation of individual cells and their integration into complex brain-region-specific networks. The previously reported forms include bursts of electrical activity and oscillations in intracellular Ca2+ concentration. Here, we use ratiometric Na+ imaging to demonstrate spontaneous fluctuations in the intracellular Na+ concentration of CA1 pyramidal neurons and astrocytes in tissue slices obtained from the hippocampus of mice at postnatal days 2-4 (P2-4). These occur at very low frequency (∼2/h), can last minutes with amplitudes up to several millimolar, and mostly disappear after the first postnatal week. To further investigate their mechanisms, we model a network consisting of pyramidal neurons and interneurons. Experimentally observed Na+ fluctuations are mimicked when GABAergic inhibition in the simulated network is made depolarizing. Both our experiments and computational model show that blocking voltage-gated Na+ channels or GABAergic signaling significantly diminish the neuronal Na+ fluctuations. On the other hand, blocking a variety of other ion channels, receptors, or transporters including glutamatergic pathways does not have significant effects. Our model also shows that the amplitude and duration of Na+ fluctuations decrease as we increase the strength of glial K+ uptake. Furthermore, neurons with smaller somatic volumes exhibit fluctuations with higher frequency and amplitude. As opposed to this, larger extracellular to intracellular volume ratio observed in neonatal brain exerts a dampening effect. Finally, our model predicts that these periods of spontaneous Na+ influx leave neonatal neuronal networks more vulnerable to seizure-like states when compared with mature brain.NEW & NOTEWORTHY Spontaneous activity in the neonate forebrain plays a key role in cell maturation and brain development. We report spontaneous, ultraslow, asynchronous fluctuations in the intracellular Na+ concentration of neurons and astrocytes. We show that this activity is not correlated with the previously reported synchronous neuronal population bursting or Ca2+ oscillations, both of which occur at much faster timescales. Furthermore, extracellular K+ concentration remains nearly constant. The spontaneous Na+ fluctuations disappear after the first postnatal week.
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Affiliation(s)
- Carlos Perez
- Department of Physics, University of South Florida, Tampa, Florida
| | - Lisa Felix
- Faculty of Mathematics and Natural Sciences, Institute of Neurobiology, Heinrich Heine University Düsseldorf, Düsseldorf, Germany
| | - Simone Durry
- Faculty of Mathematics and Natural Sciences, Institute of Neurobiology, Heinrich Heine University Düsseldorf, Düsseldorf, Germany
| | - Christine R Rose
- Faculty of Mathematics and Natural Sciences, Institute of Neurobiology, Heinrich Heine University Düsseldorf, Düsseldorf, Germany
| | - Ghanim Ullah
- Department of Physics, University of South Florida, Tampa, Florida
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40
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Impaired θ-γ Coupling Indicates Inhibitory Dysfunction and Seizure Risk in a Dravet Syndrome Mouse Model. J Neurosci 2020; 41:524-537. [PMID: 33234612 DOI: 10.1523/jneurosci.2132-20.2020] [Citation(s) in RCA: 20] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/13/2020] [Revised: 10/02/2020] [Accepted: 11/12/2020] [Indexed: 01/24/2023] Open
Abstract
Dravet syndrome (DS) is an epileptic encephalopathy that still lacks biomarkers for epileptogenesis and its treatment. Dysfunction of NaV1.1 sodium channels, which are chiefly expressed in inhibitory interneurons, explains the epileptic phenotype. Understanding the network effects of these cellular deficits may help predict epileptogenesis. Here, we studied θ-γ coupling as a potential marker for altered inhibitory functioning and epileptogenesis in a DS mouse model. We found that cortical θ-γ coupling was reduced in both male and female juvenile DS mice and persisted only if spontaneous seizures occurred. θ-γ Coupling was partly restored by cannabidiol (CBD). Locally disrupting NaV1.1 expression in the hippocampus or cortex yielded early attenuation of θ-γ coupling, which in the hippocampus associated with fast ripples, and which was replicated in a computational model when voltage-gated sodium currents were impaired in basket cells (BCs). Our results indicate attenuated θ-γ coupling as a promising early indicator of inhibitory dysfunction and seizure risk in DS.
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41
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Erhardt AH, Mardal KA, Schreiner JE. Dynamics of a neuron-glia system: the occurrence of seizures and the influence of electroconvulsive stimuli : A mathematical and numerical study. J Comput Neurosci 2020; 48:229-251. [PMID: 32399790 PMCID: PMC7242278 DOI: 10.1007/s10827-020-00746-5] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/27/2019] [Revised: 02/28/2020] [Accepted: 04/04/2020] [Indexed: 10/25/2022]
Abstract
In this paper, we investigate the dynamics of a neuron-glia cell system and the underlying mechanism for the occurrence of seizures. For our mathematical and numerical investigation of the cell model we will use bifurcation analysis and some computational methods. It turns out that an increase of the potassium concentration in the reservoir is one trigger for seizures and is related to a torus bifurcation. In addition, we will study potassium dynamics of the model by considering a reduced version and we will show how both mechanisms are linked to each other. Moreover, the reduction of the potassium leak current will also induce seizures. Our study will show that an enhancement of the extracellular potassium concentration, which influences the Nernst potential of the potassium current, may lead to seizures. Furthermore, we will show that an external forcing term (e.g. electroshocks as unidirectional rectangular pulses also known as electroconvulsive therapy) will establish seizures similar to the unforced system with the increased extracellular potassium concentration. To this end, we describe the unidirectional rectangular pulses as an autonomous system of ordinary differential equations. These approaches will explain the appearance of seizures in the cellular model. Moreover, seizures, as they are measured by electroencephalography (EEG), spread on the macro-scale (cm). Therefore, we extend the cell model with a suitable homogenised monodomain model, propose a set of (numerical) experiment to complement the bifurcation analysis performed on the single-cell model. Based on these experiments, we introduce a bidomain model for a more realistic modelling of white and grey matter of the brain. Performing similar (numerical) experiment as for the monodomain model leads to a suitable comparison of both models. The individual cell model, with its seizures explained in terms of a torus bifurcation, extends directly to corresponding results in both the monodomain and bidomain models where the neural firing spreads almost synchronous through the domain as fast traveling waves, for physiologically relevant paramenters.
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Affiliation(s)
- André H Erhardt
- Department of Mathematics, University of Oslo, P.O.Box 1053 Blindern, 0316, Oslo, Norway.
| | - Kent-Andre Mardal
- Department of Mathematics, University of Oslo, P.O.Box 1053 Blindern, 0316, Oslo, Norway.,Department of Computational Physiology, Simula Research Laboratory, 1325, Lysaker, Norway
| | - Jakob E Schreiner
- Department of Computational Physiology, Simula Research Laboratory, 1325, Lysaker, Norway.,Expert Analytics AS, Tordenskiolds gate 3, 0160, Oslo, Norway
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42
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Nguyen QA, Moolchand P, Soltesz I. Connecting Pathological Cellular Mechanisms to Large-Scale Seizure Structures. Trends Neurosci 2020; 43:547-549. [PMID: 32376035 DOI: 10.1016/j.tins.2020.04.006] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/15/2020] [Accepted: 04/21/2020] [Indexed: 10/24/2022]
Abstract
Epilepsy is a neurological disorder characterized by recurrent seizures, where abnormal electrical activity begins in a local brain area and propagates before terminating. In a recent study, Liou and colleagues used multiscale computational modeling to gain mechanistic insights into clinical seizure dynamics based on cellular-level biophysical properties.
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Affiliation(s)
- Quynh-Anh Nguyen
- Department of Neurosurgery, Stanford University, Stanford, CA 94305, USA
| | - Prannath Moolchand
- Department of Neurosurgery, Stanford University, Stanford, CA 94305, USA
| | - Ivan Soltesz
- Department of Neurosurgery, Stanford University, Stanford, CA 94305, USA.
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43
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An electrodiffusive, ion conserving Pinsky-Rinzel model with homeostatic mechanisms. PLoS Comput Biol 2020; 16:e1007661. [PMID: 32348299 PMCID: PMC7213750 DOI: 10.1371/journal.pcbi.1007661] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/15/2020] [Revised: 05/11/2020] [Accepted: 04/07/2020] [Indexed: 02/05/2023] Open
Abstract
In most neuronal models, ion concentrations are assumed to be constant, and effects of concentration variations on ionic reversal potentials, or of ionic diffusion on electrical potentials are not accounted for. Here, we present the electrodiffusive Pinsky-Rinzel (edPR) model, which we believe is the first multicompartmental neuron model that accounts for electrodiffusive ion concentration dynamics in a way that ensures a biophysically consistent relationship between ion concentrations, electrical charge, and electrical potentials in both the intra- and extracellular space. The edPR model is an expanded version of the two-compartment Pinsky-Rinzel (PR) model of a hippocampal CA3 neuron. Unlike the PR model, the edPR model includes homeostatic mechanisms and ion-specific leakage currents, and keeps track of all ion concentrations (Na+, K+, Ca2+, and Cl−), electrical potentials, and electrical conductivities in the intra- and extracellular space. The edPR model reproduces the membrane potential dynamics of the PR model for moderate firing activity. For higher activity levels, or when homeostatic mechanisms are impaired, the homeostatic mechanisms fail in maintaining ion concentrations close to baseline, and the edPR model diverges from the PR model as it accounts for effects of concentration changes on neuronal firing. We envision that the edPR model will be useful for the field in three main ways. Firstly, as it relaxes commonly made modeling assumptions, the edPR model can be used to test the validity of these assumptions under various firing conditions, as we show here for a few selected cases. Secondly, the edPR model should supplement the PR model when simulating scenarios where ion concentrations are expected to vary over time. Thirdly, being applicable to conditions with failed homeostasis, the edPR model opens up for simulating a range of pathological conditions, such as spreading depression or epilepsy. Neurons generate their electrical signals by letting ions pass through their membranes. Despite this fact, most models of neurons apply the simplifying assumption that ion concentrations remain effectively constant during neural activity. This assumption is often quite good, as neurons contain a set of homeostatic mechanisms that make sure that ion concentrations vary quite little under normal circumstances. However, under some conditions, these mechanisms can fail, and ion concentrations can vary quite dramatically. Standard models are thus not able to simulate such conditions. Here, we present what to our knowledge is the first multicompartmental neuron model that accounts for ion concentration variations in a way that ensures complete and consistent ion concentration and charge conservation. In this work, we use the model to explore under which activity conditions the ion concentration variations become important for predicting the neurodynamics. We expect the model to be of great value for the field of neuroscience, as it can be used to simulate a range of pathological conditions, such as spreading depression or epilepsy, which are associated with large changes in extracellular ion concentrations.
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44
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Chizhov AV, Sanin AE. A simple model of epileptic seizure propagation: Potassium diffusion versus axo-dendritic spread. PLoS One 2020; 15:e0230787. [PMID: 32275724 PMCID: PMC7147746 DOI: 10.1371/journal.pone.0230787] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/15/2019] [Accepted: 03/08/2020] [Indexed: 12/29/2022] Open
Abstract
The mechanisms of epileptic discharge generation and spread are not yet fully known. A recently proposed simple biophysical model of interictal and ictal discharges, Epileptor-2, reproduces well the main features of neuronal excitation and ionic dynamics during discharge generation. In order to distinguish between two hypothesized mechanisms of discharge propagation, we extend the model to the case of two-dimensional propagation along the cortical neural tissue. The first mechanism is based on extracellular potassium diffusion, and the second is the propagation of spikes and postsynaptic signals along axons and dendrites. Our simulations show that potassium diffusion is too slow to reproduce an experimentally observed speed of ictal wavefront propagation (tenths of mm/s). By contrast, the synaptic mechanism predicts well the speed and synchronization of the pre-ictal bursts before the ictal front and the afterdischarges in the ictal core. Though this fact diminishes the role of diffusion and electrodiffusion, the model nevertheless highlights the role of potassium extrusion during neuronal excitation, which provides a positive feedback that changes at the ictal wavefront the balance of excitation versus inhibition in favor of excitation. This finding may help to find a target for a treatment to prevent seizure propagation.
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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
| | - Aleksei E. Sanin
- Laboratory of Molecular Mechanisms of Neural Interactions, Sechenov Institute of Evolutionary Physiology and Biochemistry of the Russian Academy of Sciences, Saint Petersburg, Russia
- Blue Brain Project, École polytechnique fédérale de Lausanne (EPFL), Campus Biotech, Geneva, Switzerland
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45
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El Houssaini K, Bernard C, Jirsa VK. The Epileptor Model: A Systematic Mathematical Analysis Linked to the Dynamics of Seizures, Refractory Status Epilepticus, and Depolarization Block. eNeuro 2020; 7:ENEURO.0485-18.2019. [PMID: 32066612 PMCID: PMC7096539 DOI: 10.1523/eneuro.0485-18.2019] [Citation(s) in RCA: 24] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/10/2018] [Revised: 10/10/2019] [Accepted: 10/28/2019] [Indexed: 11/21/2022] Open
Abstract
One characteristic of epilepsy is the variety of mechanisms leading to the epileptic state, which are still largely unknown. Refractory status epilepticus (RSE) and depolarization block (DB) are other pathological brain activities linked to epilepsy, whose patterns are different and whose mechanisms remain poorly understood. In epileptogenic network modeling, the Epileptor is a generic phenomenological model that has been recently developed to describe the dynamics of seizures. Here, we performed a detailed qualitative analysis of the Epileptor model based on dynamical systems theory and bifurcation analysis, and investigate the dynamic evolution of "normal" activity toward seizures and to the pathological RSE and DB states. The mechanisms of the transition between states are called bifurcations. Our detailed analysis demonstrates that the generic model undergoes different bifurcation types at seizure offset, when varying some selected parameters. We show that the pathological and normal activities can coexist within the same model under some conditions, and demonstrate that there are many pathways leading to and away from these activities. We here archive systematically all behaviors and dynamic regimes of the Epileptor model to serve as a resource in the development of patient-specific brain network models, and more generally in epilepsy research.
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Affiliation(s)
- Kenza El Houssaini
- Aix Marseille University, INSERM, INS, Institut de Neurosciences des Systèmes, 13005 Marseille, France
| | - Christophe Bernard
- Aix Marseille University, INSERM, INS, Institut de Neurosciences des Systèmes, 13005 Marseille, France
| | - Viktor K Jirsa
- Aix Marseille University, INSERM, INS, Institut de Neurosciences des Systèmes, 13005 Marseille, France
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46
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Liou JY, Smith EH, Bateman LM, Bruce SL, McKhann GM, Goodman RR, Emerson RG, Schevon CA, Abbott LF. A model for focal seizure onset, propagation, evolution, and progression. eLife 2020; 9:50927. [PMID: 32202494 PMCID: PMC7089769 DOI: 10.7554/elife.50927] [Citation(s) in RCA: 34] [Impact Index Per Article: 8.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/08/2019] [Accepted: 03/04/2020] [Indexed: 12/16/2022] Open
Abstract
We developed a neural network model that can account for major elements common to human focal seizures. These include the tonic-clonic transition, slow advance of clinical semiology and corresponding seizure territory expansion, widespread EEG synchronization, and slowing of the ictal rhythm as the seizure approaches termination. These were reproduced by incorporating usage-dependent exhaustion of inhibition in an adaptive neural network that receives global feedback inhibition in addition to local recurrent projections. Our model proposes mechanisms that may underline common EEG seizure onset patterns and status epilepticus, and postulates a role for synaptic plasticity in the emergence of epileptic foci. Complex patterns of seizure activity and bi-stable seizure end-points arise when stochastic noise is included. With the rapid advancement of clinical and experimental tools, we believe that this model can provide a roadmap and potentially an in silico testbed for future explorations of seizure mechanisms and clinical therapies.
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Affiliation(s)
- Jyun-You Liou
- Department of Physiology and Cellular Biophysics, Columbia University, New York, United States.,Department of Anesthesiology, NewYork-Presbyterian Hospital/Weill Cornell Medicine, New York, United States.,Department of Neurology, Columbia University Medical Center, New York, United States
| | - Elliot H Smith
- Department of Neurological Surgery, Columbia University Medical Center, New York, United States
| | - Lisa M Bateman
- Department of Neurology, Columbia University Medical Center, New York, United States
| | - Samuel L Bruce
- Vagelos College of Physicians & Surgeons, Columbia University, New York, United States
| | - Guy M McKhann
- Department of Neurological Surgery, Columbia University Medical Center, New York, United States
| | - Robert R Goodman
- Department of Neurological Surgery, Columbia University Medical Center, New York, United States
| | - Ronald G Emerson
- Department of Neurology, Columbia University Medical Center, New York, United States
| | - Catherine A Schevon
- Department of Neurology, Columbia University Medical Center, New York, United States
| | - L F Abbott
- Department of Physiology and Cellular Biophysics, Columbia University, New York, United States.,Mortimer B. Zuckerman Mind Brain Behavior Institute, Department of Neuroscience, Columbia University, New York, United States
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Beckner ME. A roadmap for potassium buffering/dispersion via the glial network of the CNS. Neurochem Int 2020; 136:104727. [PMID: 32194142 DOI: 10.1016/j.neuint.2020.104727] [Citation(s) in RCA: 16] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/25/2019] [Revised: 03/08/2020] [Accepted: 03/09/2020] [Indexed: 12/19/2022]
Abstract
Glia use multiple mechanisms to mediate potassium fluxes that support neuronal function. In addition to changes in potassium levels within synapses, these ions are dynamically dispersed through the interstitial parenchyma, perivascular spaces, leptomeninges, cerebrospinal fluid, choroid plexus, blood, vitreous, and endolymph. Neural circuits drive diversity in the glia that buffer potassium and this is reciprocal. Glia mediate buffering of potassium locally at glial-neuronal interfaces and via widespread networked connections. Control of potassium levels in the central nervous system is mediated by mechanisms operating at various loci with complexity that is difficult to model. However, major components of networked glial buffering are known. The role that potassium buffering plays in homeostasis of the CNS underlies some pathologic phenomena. An overview of potassium fluxes in the CNS is relevant for understanding consequences of pathogenic sequence variants in genes that encode potassium buffering proteins. Potassium flows in the CNS are described as follows: K1, the coordinated potassium fluxes within the astrocytic cradle around the synapse; K2, temporary storage of potassium within astrocytic processes in proposed microdomains; K3, potassium fluxes between oligodendrocytes and astrocytes; K4, potassium fluxes between astrocytes; K5, astrocytic potassium flux mediation of neurovasular coupling; K6, CSF delivery of potassium to perivascular spaces with dispersion to interstitial fluid between astrocytic endfeet; K7, astrocytic delivery of potassium to CSF and K8, choroid plexus (modified glia) regulation of potassium at the blood-CSF barrier. Components, mainly potassium channels, transporters, connexins and modulators, and the pathogenic sequence variants of their genes with the associated diseases are described.
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Affiliation(s)
- Marie E Beckner
- School of Biomedical Sciences, Kent State University, Kent, OH, USA.
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Capo-Rangel G, Gerardo-Giorda L, Somersalo E, Calvetti D. Metabolism plays a central role in the cortical spreading depression: Evidence from a mathematical model. J Theor Biol 2020; 486:110093. [PMID: 31778711 DOI: 10.1016/j.jtbi.2019.110093] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/01/2019] [Revised: 10/28/2019] [Accepted: 11/23/2019] [Indexed: 11/24/2022]
Abstract
The slow propagating waves of strong depolarization of neural cells characterizing cortical spreading depression, or depolarization, (SD) are known to break cerebral homeostasis and induce significant hemodynamic and electro-metabolic alterations. Mathematical models of cortical spreading depression found in the literature tend to focus on the changes occurring at the electrophysiological level rather than on the ensuing metabolic changes. In this paper, we propose a novel mathematical model which is able to simulate the coupled electrophysiology and metabolism dynamics of SD events, including the swelling of neurons and astrocytes and the concomitant shrinkage of extracellular space. The simulations show that the metabolic coupling leads to spontaneous repetitions of the SD events, which the electrophysiological model alone is not capable to produce. The model predictions, which corroborate experimental findings from the literature, show a strong disruption in metabolism accompanying each wave of spreading depression in the form of a sharp decrease of glucose and oxygen concentrations, with a simultaneous increase in lactate concentration which, in turn, delays the clearing of excess potassium in extracellular space. Our model suggests that the depletion of glucose and oxygen concentration is more pronounced in astrocyte than neuron, in line with the partitioning of the energetic cost of potassium clearing. The model suggests that the repeated SD events are electro-metabolic oscillations that cannot be explained by the electrophysiology alone. The model highlights the crucial role of astrocytes in cleaning the excess potassium flooding extracellular space during a spreading depression event: further, if the ratio of glial/neuron density increases, the frequency of cortical SD events decreases, and the peak potassium concentration in extracellular space is lower than with equal volume fractions.
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Affiliation(s)
| | | | - E Somersalo
- Basque Center for Applied Mathematics, Spain
| | - D Calvetti
- Department of Mathematics, Applied Mathematics and Statistics, Case Western Reserve University, Ohio.
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Depannemaecker D, Canton Santos LE, Rodrigues AM, Scorza CA, Scorza FA, Almeida ACGD. Realistic spiking neural network: Non-synaptic mechanisms improve convergence in cell assembly. Neural Netw 2019; 122:420-433. [PMID: 31841876 DOI: 10.1016/j.neunet.2019.09.038] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/22/2019] [Revised: 09/17/2019] [Accepted: 09/23/2019] [Indexed: 01/26/2023]
Abstract
Learning in neural networks inspired by brain tissue has been studied for machine learning applications. However, existing works primarily focused on the concept of synaptic weight modulation, and other aspects of neuronal interactions, such as non-synaptic mechanisms, have been neglected. Non-synaptic interaction mechanisms have been shown to play significant roles in the brain, and four classes of these mechanisms can be highlighted: (i) electrotonic coupling; (ii) ephaptic interactions; (iii) electric field effects; and iv) extracellular ionic fluctuations. In this work, we proposed simple rules for learning inspired by recent findings in machine learning adapted to a realistic spiking neural network. We show that the inclusion of non-synaptic interaction mechanisms improves cell assembly convergence. By including extracellular ionic fluctuation represented by the extracellular electrodiffusion in the network, we showed the importance of these mechanisms to improve cell assembly convergence. Additionally, we observed a variety of electrophysiological patterns of neuronal activity, particularly bursting and synchronism when the convergence is improved.
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Affiliation(s)
- Damien Depannemaecker
- Laboratório de Neurociência Experimental e Computacional, Departamento de Engenharia de Biossistemas, Universidade Federal de São João del-Rei (UFSJ), Brazil; Disciplina de Neurociência, Departamento de Neurologia e Neurocirurgia, Universidade Federal de São Paulo (UNIFESP), São Paulo, Brazil
| | - Luiz Eduardo Canton Santos
- Laboratório de Neurociência Experimental e Computacional, Departamento de Engenharia de Biossistemas, Universidade Federal de São João del-Rei (UFSJ), Brazil; Disciplina de Neurociência, Departamento de Neurologia e Neurocirurgia, Universidade Federal de São Paulo (UNIFESP), São Paulo, Brazil
| | - Antônio Márcio Rodrigues
- Laboratório de Neurociência Experimental e Computacional, Departamento de Engenharia de Biossistemas, Universidade Federal de São João del-Rei (UFSJ), Brazil
| | - Carla Alessandra Scorza
- Laboratório de Neurociência Experimental e Computacional, Departamento de Engenharia de Biossistemas, Universidade Federal de São João del-Rei (UFSJ), Brazil
| | - Fulvio Alexandre Scorza
- Disciplina de Neurociência, Departamento de Neurologia e Neurocirurgia, Universidade Federal de São Paulo (UNIFESP), São Paulo, Brazil
| | - Antônio-Carlos Guimarães de Almeida
- Laboratório de Neurociência Experimental e Computacional, Departamento de Engenharia de Biossistemas, Universidade Federal de São João del-Rei (UFSJ), Brazil.
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50
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Capo Rangel G, Prezioso J, Gerardo-Giorda L, Somersalo E, Calvetti D. Brain energetics plays a key role in the coordination of electrophysiology, metabolism and hemodynamics: Evidence from an integrated computational model. J Theor Biol 2019; 478:26-39. [DOI: 10.1016/j.jtbi.2019.06.003] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/03/2019] [Revised: 06/01/2019] [Accepted: 06/04/2019] [Indexed: 10/26/2022]
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