1
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Tahvili F, Destexhe A. A mean-field model of gamma-frequency oscillations in networks of excitatory and inhibitory neurons. J Comput Neurosci 2024; 52:165-181. [PMID: 38512693 DOI: 10.1007/s10827-024-00867-1] [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: 11/21/2023] [Revised: 02/22/2024] [Accepted: 02/27/2024] [Indexed: 03/23/2024]
Abstract
Gamma oscillations are widely seen in the cerebral cortex in different states of the wake-sleep cycle and are thought to play a role in sensory processing and cognition. Here, we study the emergence of gamma oscillations at two levels, in networks of spiking neurons, and a mean-field model. At the network level, we consider two different mechanisms to generate gamma oscillations and show that they are best seen if one takes into account the synaptic delay between neurons. At the mean-field level, we show that, by introducing delays, the mean-field can also produce gamma oscillations. The mean-field matches the mean activity of excitatory and inhibitory populations of the spiking network, as well as their oscillation frequencies, for both mechanisms. This mean-field model of gamma oscillations should be a useful tool to investigate large-scale interactions through gamma oscillations in the brain.
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Affiliation(s)
- Farzin Tahvili
- Institute of Neuroscience (NeuroPSI), Paris-Saclay University, CNRS, 91400, Saclay, France
- Stem-cell & Brain Research Institute (SBRI), 69500, Bron Cedex, France
| | - Alain Destexhe
- Institute of Neuroscience (NeuroPSI), Paris-Saclay University, CNRS, 91400, Saclay, France.
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2
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Shirani F, Choi H. On the physiological and structural contributors to the overall balance of excitation and inhibition in local cortical networks. J Comput Neurosci 2024; 52:73-107. [PMID: 37837534 DOI: 10.1007/s10827-023-00863-x] [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: 04/13/2023] [Revised: 06/25/2023] [Accepted: 09/08/2023] [Indexed: 10/16/2023]
Abstract
Overall balance of excitation and inhibition in cortical networks is central to their functionality and normal operation. Such orchestrated co-evolution of excitation and inhibition is established through convoluted local interactions between neurons, which are organized by specific network connectivity structures and are dynamically controlled by modulating synaptic activities. Therefore, identifying how such structural and physiological factors contribute to establishment of overall balance of excitation and inhibition is crucial in understanding the homeostatic plasticity mechanisms that regulate the balance. We use biologically plausible mathematical models to extensively study the effects of multiple key factors on overall balance of a network. We characterize a network's baseline balanced state by certain functional properties, and demonstrate how variations in physiological and structural parameters of the network deviate this balance and, in particular, result in transitions in spontaneous activity of the network to high-amplitude slow oscillatory regimes. We show that deviations from the reference balanced state can be continuously quantified by measuring the ratio of mean excitatory to mean inhibitory synaptic conductances in the network. Our results suggest that the commonly observed ratio of the number of inhibitory to the number of excitatory neurons in local cortical networks is almost optimal for their stability and excitability. Moreover, the values of inhibitory synaptic decay time constants and density of inhibitory-to-inhibitory network connectivity are critical to overall balance and stability of cortical networks. However, network stability in our results is sufficiently robust against modulations of synaptic quantal conductances, as required by their role in learning and memory. Our study based on extensive bifurcation analyses thus reveal the functional optimality and criticality of structural and physiological parameters in establishing the baseline operating state of local cortical networks.
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Affiliation(s)
- Farshad Shirani
- School of Mathematics, Georgia Institute of Technology, Atlanta, 30332, Georgia, USA.
| | - Hannah Choi
- School of Mathematics, Georgia Institute of Technology, Atlanta, 30332, Georgia, USA
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3
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Hutt A, Trotter D, Pariz A, Valiante TA, Lefebvre J. Diversity-induced trivialization and resilience of neural dynamics. CHAOS (WOODBURY, N.Y.) 2024; 34:013147. [PMID: 38285722 DOI: 10.1063/5.0165773] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/30/2023] [Accepted: 01/01/2024] [Indexed: 01/31/2024]
Abstract
Heterogeneity is omnipresent across all living systems. Diversity enriches the dynamical repertoire of these systems but remains challenging to reconcile with their manifest robustness and dynamical persistence over time, a fundamental feature called resilience. To better understand the mechanism underlying resilience in neural circuits, we considered a nonlinear network model, extracting the relationship between excitability heterogeneity and resilience. To measure resilience, we quantified the number of stationary states of this network, and how they are affected by various control parameters. We analyzed both analytically and numerically gradient and non-gradient systems modeled as non-linear sparse neural networks evolving over long time scales. Our analysis shows that neuronal heterogeneity quenches the number of stationary states while decreasing the susceptibility to bifurcations: a phenomenon known as trivialization. Heterogeneity was found to implement a homeostatic control mechanism enhancing network resilience to changes in network size and connection probability by quenching the system's dynamic volatility.
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Affiliation(s)
- Axel Hutt
- MLMS, MIMESIS, Université de Strasbourg, CNRS, Inria, ICube, 67000 Strasbourg, France
| | - Daniel Trotter
- Department of Physics, University of Ottawa, Ottawa, Ontario K1N 6N5, Canada
- Krembil Brain Institute, University Health Network, Toronto, Ontario M5T 0S8, Canada
| | - Aref Pariz
- Krembil Brain Institute, University Health Network, Toronto, Ontario M5T 0S8, Canada
- Department of Biology, University of Ottawa, Ottawa, Ontario K1N 6N5, Canada
| | - Taufik A Valiante
- Krembil Brain Institute, University Health Network, Toronto, Ontario M5T 0S8, Canada
- Department of Electrical and Computer Engineering, Institute of Medical Science, Institute of Biomedical Engineering, Division of Neurosurgery, Department of Surgery, CRANIA (Center for Advancing Neurotechnological Innovation to Application), Max Planck-University of Toronto Center for Neural Science and Technology, University of Toronto, Toronto, Ontario M5S 3G8, Canada
| | - Jérémie Lefebvre
- Department of Physics, University of Ottawa, Ottawa, Ontario K1N 6N5, Canada
- Krembil Brain Institute, University Health Network, Toronto, Ontario M5T 0S8, Canada
- Department of Biology, University of Ottawa, Ottawa, Ontario K1N 6N5, Canada
- Department of Mathematics, University of Toronto, Toronto, Ontario M5S 2E4, Canada
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4
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Lorenzi RM, Geminiani A, Zerlaut Y, De Grazia M, Destexhe A, Gandini Wheeler-Kingshott CAM, Palesi F, Casellato C, D'Angelo E. A multi-layer mean-field model of the cerebellum embedding microstructure and population-specific dynamics. PLoS Comput Biol 2023; 19:e1011434. [PMID: 37656758 PMCID: PMC10501640 DOI: 10.1371/journal.pcbi.1011434] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/22/2022] [Revised: 09/14/2023] [Accepted: 08/15/2023] [Indexed: 09/03/2023] Open
Abstract
Mean-field (MF) models are computational formalism used to summarize in a few statistical parameters the salient biophysical properties of an inter-wired neuronal network. Their formalism normally incorporates different types of neurons and synapses along with their topological organization. MFs are crucial to efficiently implement the computational modules of large-scale models of brain function, maintaining the specificity of local cortical microcircuits. While MFs have been generated for the isocortex, they are still missing for other parts of the brain. Here we have designed and simulated a multi-layer MF of the cerebellar microcircuit (including Granule Cells, Golgi Cells, Molecular Layer Interneurons, and Purkinje Cells) and validated it against experimental data and the corresponding spiking neural network (SNN) microcircuit model. The cerebellar MF was built using a system of equations, where properties of neuronal populations and topological parameters are embedded in inter-dependent transfer functions. The model time constant was optimised using local field potentials recorded experimentally from acute mouse cerebellar slices as a template. The MF reproduced the average dynamics of different neuronal populations in response to various input patterns and predicted the modulation of the Purkinje Cells firing depending on cortical plasticity, which drives learning in associative tasks, and the level of feedforward inhibition. The cerebellar MF provides a computationally efficient tool for future investigations of the causal relationship between microscopic neuronal properties and ensemble brain activity in virtual brain models addressing both physiological and pathological conditions.
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Affiliation(s)
| | - Alice Geminiani
- Department of Brain and Behavioural Sciences, University of Pavia, Pavia, Italy
| | - Yann Zerlaut
- Institut du Cerveau-Paris Brain Institute-ICM, Inserm, CNRS, APHP, Hôpital de la Pitié Salpêtrière, Paris, France
| | | | | | - Claudia A M Gandini Wheeler-Kingshott
- Department of Brain and Behavioural Sciences, University of Pavia, Pavia, Italy
- NMR Research Unit, Queen Square Multiple Sclerosis Centre, Department of Neuroinflammation, UCL Queen Square Institute of Neurology, UCL, London, United Kingdom
- Brain Connectivity Center, IRCCS Mondino Foundation, Pavia, Italy
| | - Fulvia Palesi
- Department of Brain and Behavioural Sciences, University of Pavia, Pavia, Italy
| | - Claudia Casellato
- Department of Brain and Behavioural Sciences, University of Pavia, Pavia, Italy
| | - Egidio D'Angelo
- Department of Brain and Behavioural Sciences, University of Pavia, Pavia, Italy
- Brain Connectivity Center, IRCCS Mondino Foundation, Pavia, Italy
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5
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Shu Y, Hasenstaub A, McCormick DA. The h-current controls cortical recurrent network activity through modulation of dendrosomatic communication. BIORXIV : THE PREPRINT SERVER FOR BIOLOGY 2023:2023.07.12.548753. [PMID: 37502942 PMCID: PMC10370005 DOI: 10.1101/2023.07.12.548753] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 07/29/2023]
Abstract
A fundamental feature of the cerebral cortex is the ability to rapidly turn on and off maintained activity within ensembles of neurons through recurrent excitation balanced by inhibition. Here we demonstrate that reduction of the h-current, which is especially prominent in pyramidal cell dendrites, strongly increases the ability of local cortical networks to generate maintained recurrent activity. Reduction of the h-current resulted in hyperpolarization and increase in input resistance of both the somata and apical dendrites of layer 5 pyramidal cells, while strongly increasing the dendrosomatic transfer of low (<20 Hz) frequencies, causing an increased responsiveness to dynamic clamp-induced recurrent network-like activity injected into the dendrites and substantially increasing the duration of spontaneous Up states. We propose that modulation of the h-current may strongly control the ability of cortical networks to generate recurrent persistent activity and the formation and dissolution of neuronal ensembles.
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Affiliation(s)
- Yousheng Shu
- The Fudan University Fenglin Campus, 131 Dong’an Road, Xuhui District, Shanghai
| | - Andrea Hasenstaub
- Department of Otolaryngology-Head and Neck Surgery (OHNS), University of California, San Francisco, 675 Nelson Rising Lane, #514B, San Francisco CA 94158
| | - David A. McCormick
- Department of Neuroscience, Yale University School of Medicine, New Haven, CT 06510; Institute of Neuroscience, University of Oregon, Eugene, OR 97403
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6
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Shirani F, Choi H. On the physiological and structural contributors to the overall balance of excitation and inhibition in local cortical networks. BIORXIV : THE PREPRINT SERVER FOR BIOLOGY 2023:2023.01.10.523489. [PMID: 36711468 PMCID: PMC9882012 DOI: 10.1101/2023.01.10.523489] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/18/2023]
Abstract
Overall balance of excitation and inhibition in cortical networks is central to their functionality and normal operation. Such orchestrated co-evolution of excitation and inhibition is established through convoluted local interactions between neurons, which are organized by specific network connectivity structures and are dynamically controlled by modulating synaptic activities. Therefore, identifying how such structural and physiological factors contribute to establishment of overall balance of excitation and inhibition is crucial in understanding the homeostatic plasticity mechanisms that regulate the balance. We use biologically plausible mathematical models to extensively study the effects of multiple key factors on overall balance of a network. We characterize a network's baseline balanced state by certain functional properties, and demonstrate how variations in physiological and structural parameters of the network deviate this balance and, in particular, result in transitions in spontaneous activity of the network to high-amplitude slow oscillatory regimes. We show that deviations from the reference balanced state can be continuously quantified by measuring the ratio of mean excitatory to mean inhibitory synaptic conductances in the network. Our results suggest that the commonly observed ratio of the number of inhibitory to the number of excitatory neurons in local cortical networks is almost optimal for their stability and excitability. Moreover, the values of inhibitory synaptic decay time constants and density of inhibitory-to-inhibitory network connectivity are critical to overall balance and stability of cortical networks. However, network stability in our results is sufficiently robust against modulations of synaptic quantal conductances, as required by their role in learning and memory.
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7
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Goldman JS, Kusch L, Aquilue D, Yalçınkaya BH, Depannemaecker D, Ancourt K, Nghiem TAE, Jirsa V, Destexhe A. A comprehensive neural simulation of slow-wave sleep and highly responsive wakefulness dynamics. Front Comput Neurosci 2023; 16:1058957. [PMID: 36714530 PMCID: PMC9880280 DOI: 10.3389/fncom.2022.1058957] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/30/2022] [Accepted: 12/21/2022] [Indexed: 01/15/2023] Open
Abstract
Hallmarks of neural dynamics during healthy human brain states span spatial scales from neuromodulators acting on microscopic ion channels to macroscopic changes in communication between brain regions. Developing a scale-integrated understanding of neural dynamics has therefore remained challenging. Here, we perform the integration across scales using mean-field modeling of Adaptive Exponential (AdEx) neurons, explicitly incorporating intrinsic properties of excitatory and inhibitory neurons. The model was run using The Virtual Brain (TVB) simulator, and is open-access in EBRAINS. We report that when AdEx mean-field neural populations are connected via structural tracts defined by the human connectome, macroscopic dynamics resembling human brain activity emerge. Importantly, the model can qualitatively and quantitatively account for properties of empirically observed spontaneous and stimulus-evoked dynamics in space, time, phase, and frequency domains. Large-scale properties of cortical dynamics are shown to emerge from both microscopic-scale adaptation that control transitions between wake-like to sleep-like activity, and the organization of the human structural connectome; together, they shape the spatial extent of synchrony and phase coherence across brain regions consistent with the propagation of sleep-like spontaneous traveling waves at intermediate scales. Remarkably, the model also reproduces brain-wide, enhanced responsiveness and capacity to encode information particularly during wake-like states, as quantified using the perturbational complexity index. The model was run using The Virtual Brain (TVB) simulator, and is open-access in EBRAINS. This approach not only provides a scale-integrated understanding of brain states and their underlying mechanisms, but also open access tools to investigate brain responsiveness, toward producing a more unified, formal understanding of experimental data from conscious and unconscious states, as well as their associated pathologies.
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Affiliation(s)
- Jennifer S. Goldman
- CNRS, Institute of Neuroscience (NeuroPSI), Paris-Saclay University, Saclay, France,*Correspondence: Jennifer S. Goldman ✉
| | - Lionel Kusch
- Institut de Neurosciences des Systèmes, Aix-Marseille University, INSERM, Marseille, France
| | - David Aquilue
- CNRS, Institute of Neuroscience (NeuroPSI), Paris-Saclay University, Saclay, France
| | - Bahar Hazal Yalçınkaya
- CNRS, Institute of Neuroscience (NeuroPSI), Paris-Saclay University, Saclay, France,Institut de Neurosciences des Systèmes, Aix-Marseille University, INSERM, Marseille, France
| | | | - Kevin Ancourt
- CNRS, Institute of Neuroscience (NeuroPSI), Paris-Saclay University, Saclay, France
| | - Trang-Anh E. Nghiem
- CNRS, Institute of Neuroscience (NeuroPSI), Paris-Saclay University, Saclay, France,Laboratoire de Physique, Ecole Normale Supérieure, Université PSL, CNRS, Sorbonne Université, Université de Paris, Paris, France
| | - Viktor Jirsa
- Institut de Neurosciences des Systèmes, Aix-Marseille University, INSERM, Marseille, France
| | - Alain Destexhe
- CNRS, Institute of Neuroscience (NeuroPSI), Paris-Saclay University, Saclay, France,Alain Destexhe ✉
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8
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Destexhe A. Noise Enhancement of Neural Information Processing. ENTROPY (BASEL, SWITZERLAND) 2022; 24:1837. [PMID: 36554242 PMCID: PMC9778153 DOI: 10.3390/e24121837] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 11/07/2022] [Revised: 12/09/2022] [Accepted: 12/13/2022] [Indexed: 06/17/2023]
Abstract
Cortical neurons in vivo function in highly fluctuating and seemingly noisy conditions, and the understanding of how information is processed in such complex states is still incomplete. In this perspective article, we first overview that an intense "synaptic noise" was measured first in single neurons, and computational models were built based on such measurements. Recent progress in recording techniques has enabled the measurement of highly complex activity in large numbers of neurons in animals and human subjects, and models were also built to account for these complex dynamics. Here, we attempt to link these two cellular and population aspects, where the complexity of network dynamics in awake cortex seems to link to the synaptic noise seen in single cells. We show that noise in single cells, in networks, or structural noise, all participate to enhance responsiveness and boost the propagation of information. We propose that such noisy states are fundamental to providing favorable conditions for information processing at large-scale levels in the brain, and may be involved in sensory perception.
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Affiliation(s)
- Alain Destexhe
- CNRS, Paris-Saclay Institute of Neuroscience (NeuroPSI), Paris-Saclay University, 91400 Saclay, France
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9
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Ichiyama A, Mestern S, Benigno GB, Scott KE, Allman BL, Muller L, Inoue W. State-dependent activity dynamics of hypothalamic stress effector neurons. eLife 2022; 11:76832. [PMID: 35770968 PMCID: PMC9278954 DOI: 10.7554/elife.76832] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/06/2022] [Accepted: 06/17/2022] [Indexed: 11/30/2022] Open
Abstract
The stress response necessitates an immediate boost in vital physiological functions from their homeostatic operation to an elevated emergency response. However, the neural mechanisms underlying this state-dependent change remain largely unknown. Using a combination of in vivo and ex vivo electrophysiology with computational modeling, we report that corticotropin releasing hormone (CRH) neurons in the paraventricular nucleus of the hypothalamus (PVN), the effector neurons of hormonal stress response, rapidly transition between distinct activity states through recurrent inhibition. Specifically, in vivo optrode recording shows that under non-stress conditions, CRHPVN neurons often fire with rhythmic brief bursts (RB), which, somewhat counterintuitively, constrains firing rate due to long (~2 s) interburst intervals. Stressful stimuli rapidly switch RB to continuous single spiking (SS), permitting a large increase in firing rate. A spiking network model shows that recurrent inhibition can control this activity-state switch, and more broadly the gain of spiking responses to excitatory inputs. In biological CRHPVN neurons ex vivo, the injection of whole-cell currents derived from our computational model recreates the in vivo-like switch between RB and SS, providing direct evidence that physiologically relevant network inputs enable state-dependent computation in single neurons. Together, we present a novel mechanism for state-dependent activity dynamics in CRHPVN neurons.
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10
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Mojarrad H, Azimirad V, Koohestani B. A framework for preparing a stochastic nonlinear integrate-and-fire model for integrated information theory. NETWORK (BRISTOL, ENGLAND) 2022; 33:17-61. [PMID: 35380085 DOI: 10.1080/0954898x.2022.2049644] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/01/2021] [Revised: 01/26/2022] [Accepted: 02/27/2022] [Indexed: 06/14/2023]
Abstract
This paper presents a framework for spiking neural networks to be prepared for the Integrated Information Theory (IIT) analysis, using a stochastic nonlinear integrate-and-fire model. The model includes the crucial dynamics of the all-or-none law and after-spike refractoriness. The noise is modelled as an additive term in the system's equations. By preparing the model for the IIT analysis, it is meant to determine the length of the analysis time-window and the transition probability distributions required for the IIT 3.0. To this end, a system of differential equations is proposed to estimate the time evolution of the system's mean and covariance. Assuming the binary Fired/Silent activity as the possible states of each neuron, an algorithm is proposed to calculate the required probability distributions. As long as the Fired/Silent probabilities are only concerned, the Gaussian density assumption with the estimated moments is a reasonable estimate. The synaptic inputs are treated as random variables with low variances to avoid the costs of conditioning on the system's past activities. The Monte-Carlo simulation is used to validate the estimation methods. To increase the reliability of the inductive inference behind the Monte-Carlo method, various stimulation protocols are applied to evoke the dynamics of the equations.
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Affiliation(s)
- Hossein Mojarrad
- Department of Mechatronics, Faculty of Mechanical Engineering, University of Tabriz, Tabriz, Iran
| | - Vahid Azimirad
- Department of Mechatronics, Faculty of Mechanical Engineering, University of Tabriz, Tabriz, Iran
| | - Behrooz Koohestani
- Faculty of Electrical and Computer Engineering, University of Tabriz, Tabriz, Iran
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11
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Di Volo M, Destexhe A. Optimal responsiveness and information flow in networks of heterogeneous neurons. Sci Rep 2021; 11:17611. [PMID: 34475456 PMCID: PMC8413388 DOI: 10.1038/s41598-021-96745-2] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/30/2021] [Accepted: 08/11/2021] [Indexed: 02/07/2023] Open
Abstract
Cerebral cortex is characterized by a strong neuron-to-neuron heterogeneity, but it is unclear what consequences this may have for cortical computations, while most computational models consider networks of identical units. Here, we study network models of spiking neurons endowed with heterogeneity, that we treat independently for excitatory and inhibitory neurons. We find that heterogeneous networks are generally more responsive, with an optimal responsiveness occurring for levels of heterogeneity found experimentally in different published datasets, for both excitatory and inhibitory neurons. To investigate the underlying mechanisms, we introduce a mean-field model of heterogeneous networks. This mean-field model captures optimal responsiveness and suggests that it is related to the stability of the spontaneous asynchronous state. The mean-field model also predicts that new dynamical states can emerge from heterogeneity, a prediction which is confirmed by network simulations. Finally we show that heterogeneous networks maximise the information flow in large-scale networks, through recurrent connections. We conclude that neuronal heterogeneity confers different responsiveness to neural networks, which should be taken into account to investigate their information processing capabilities.
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Affiliation(s)
- Matteo Di Volo
- Laboratoire de Physique Théorique et Modélisation, Université de Cergy-Pontoise, CNRS, UMR 8089, 95302, Cergy-Pontoise cedex, France.
| | - Alain Destexhe
- Paris-Saclay University, Institute of Neuroscience, CNRS, Gif sur Yvette, France
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12
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Zerlaut Y, Zucca S, Panzeri S, Fellin T. The Spectrum of Asynchronous Dynamics in Spiking Networks as a Model for the Diversity of Non-rhythmic Waking States in the Neocortex. Cell Rep 2020; 27:1119-1132.e7. [PMID: 31018128 PMCID: PMC6486483 DOI: 10.1016/j.celrep.2019.03.102] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/07/2018] [Revised: 03/02/2019] [Accepted: 03/27/2019] [Indexed: 11/15/2022] Open
Abstract
The awake cortex exhibits diverse non-rhythmic network states. However, how these states emerge and how each state impacts network function is unclear. Here, we demonstrate that model networks of spiking neurons with moderate recurrent interactions display a spectrum of non-rhythmic asynchronous dynamics based on the level of afferent excitation, from afferent input-dominated (AD) regimes, characterized by unbalanced synaptic currents and sparse firing, to recurrent input-dominated (RD) regimes, characterized by balanced synaptic currents and dense firing. The model predicted regime-specific relationships between different neural biophysical properties, which were all experimentally validated in the somatosensory cortex (S1) of awake mice. Moreover, AD regimes more precisely encoded spatiotemporal patterns of presynaptic activity, while RD regimes better encoded the strength of afferent inputs. These results provide a theoretical foundation for how recurrent neocortical circuits generate non-rhythmic waking states and how these different states modulate the processing of incoming information.
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Affiliation(s)
- Yann Zerlaut
- Neural Coding Laboratory, Istituto Italiano di Tecnologia, Genova, Italy; Neural Computation Laboratory, Center for Neuroscience and Cognitive Systems @UniTn, Istituto Italiano di Tecnologia, Rovereto, Italy.
| | - Stefano Zucca
- Neural Coding Laboratory, Istituto Italiano di Tecnologia, Genova, Italy; Optical Approaches to Brain Function Laboratory, Istituto Italiano di Tecnologia, Genova, Italy
| | - Stefano Panzeri
- Neural Coding Laboratory, Istituto Italiano di Tecnologia, Genova, Italy; Neural Computation Laboratory, Center for Neuroscience and Cognitive Systems @UniTn, Istituto Italiano di Tecnologia, Rovereto, Italy.
| | - Tommaso Fellin
- Neural Coding Laboratory, Istituto Italiano di Tecnologia, Genova, Italy; Optical Approaches to Brain Function Laboratory, Istituto Italiano di Tecnologia, Genova, Italy.
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13
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Carlu M, Chehab O, Dalla Porta L, Depannemaecker D, Héricé C, Jedynak M, Köksal Ersöz E, Muratore P, Souihel S, Capone C, Zerlaut Y, Destexhe A, di Volo M. A mean-field approach to the dynamics of networks of complex neurons, from nonlinear Integrate-and-Fire to Hodgkin-Huxley models. J Neurophysiol 2020; 123:1042-1051. [PMID: 31851573 PMCID: PMC7099478 DOI: 10.1152/jn.00399.2019] [Citation(s) in RCA: 22] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/01/2019] [Revised: 12/05/2019] [Accepted: 12/09/2019] [Indexed: 11/22/2022] Open
Abstract
We present a mean-field formalism able to predict the collective dynamics of large networks of conductance-based interacting spiking neurons. We apply this formalism to several neuronal models, from the simplest Adaptive Exponential Integrate-and-Fire model to the more complex Hodgkin-Huxley and Morris-Lecar models. We show that the resulting mean-field models are capable of predicting the correct spontaneous activity of both excitatory and inhibitory neurons in asynchronous irregular regimes, typical of cortical dynamics. Moreover, it is possible to quantitatively predict the population response to external stimuli in the form of external spike trains. This mean-field formalism therefore provides a paradigm to bridge the scale between population dynamics and the microscopic complexity of the individual cells physiology.NEW & NOTEWORTHY Population models are a powerful mathematical tool to study the dynamics of neuronal networks and to simulate the brain at macroscopic scales. We present a mean-field model capable of quantitatively predicting the temporal dynamics of a network of complex spiking neuronal models, from Integrate-and-Fire to Hodgkin-Huxley, thus linking population models to neurons electrophysiology. This opens a perspective on generating biologically realistic mean-field models from electrophysiological recordings.
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Affiliation(s)
- M. Carlu
- Department of Integrative and Computational Neuroscience, Paris-Saclay Institute of Neuroscience, Centre National de la Recherche Scientifique, Gif sur Yvette, France
| | - O. Chehab
- Ecole Normale Superieure Paris-Saclay, France
| | - L. Dalla Porta
- Institut d’Investigacions Biomèdiques August Pi i Sunyer, Barcelona, Spain
| | - D. Depannemaecker
- Department of Integrative and Computational Neuroscience, Paris-Saclay Institute of Neuroscience, Centre National de la Recherche Scientifique, Gif sur Yvette, France
| | - C. Héricé
- Strathclyde Institute of Pharmacy and Biomedical Sciences, Glasgow, Scotland, United Kingdom
| | - M. Jedynak
- Université Grenoble Alpes, Grenoble Institut des Neurosciences and Institut National de la Santé et de la Recherche Médicale (INSERM), U1216, France
| | - E. Köksal Ersöz
- INSERM, U1099, Rennes, France
- MathNeuro Team, Inria Sophia Antipolis Méditerranée, Sophia Antipolis, France
| | - P. Muratore
- Physics Department, Sapienza University, Rome, Italy
| | - S. Souihel
- Université Côte d’Azur, Inria Sophia Antipolis Méditerranée, France
| | - C. Capone
- Department of Integrative and Computational Neuroscience, Paris-Saclay Institute of Neuroscience, Centre National de la Recherche Scientifique, Gif sur Yvette, France
| | - Y. Zerlaut
- Department of Integrative and Computational Neuroscience, Paris-Saclay Institute of Neuroscience, Centre National de la Recherche Scientifique, Gif sur Yvette, France
| | - A. Destexhe
- Department of Integrative and Computational Neuroscience, Paris-Saclay Institute of Neuroscience, Centre National de la Recherche Scientifique, Gif sur Yvette, France
| | - M. di Volo
- Department of Integrative and Computational Neuroscience, Paris-Saclay Institute of Neuroscience, Centre National de la Recherche Scientifique, Gif sur Yvette, France
- Laboratoire de Physique Théorique et Modelisation, Université de Cergy-Pontoise, Cergy-Pontoise, France
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14
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Goldman JS, Tort-Colet N, di Volo M, Susin E, Bouté J, Dali M, Carlu M, Nghiem TA, Górski T, Destexhe A. Bridging Single Neuron Dynamics to Global Brain States. Front Syst Neurosci 2019; 13:75. [PMID: 31866837 PMCID: PMC6908479 DOI: 10.3389/fnsys.2019.00075] [Citation(s) in RCA: 17] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/28/2019] [Accepted: 11/19/2019] [Indexed: 11/13/2022] Open
Abstract
Biological neural networks produce information backgrounds of multi-scale spontaneous activity that become more complex in brain states displaying higher capacities for cognition, for instance, attentive awake versus asleep or anesthetized states. Here, we review brain state-dependent mechanisms spanning ion channel currents (microscale) to the dynamics of brain-wide, distributed, transient functional assemblies (macroscale). Not unlike how microscopic interactions between molecules underlie structures formed in macroscopic states of matter, using statistical physics, the dynamics of microscopic neural phenomena can be linked to macroscopic brain dynamics through mesoscopic scales. Beyond spontaneous dynamics, it is observed that stimuli evoke collapses of complexity, most remarkable over high dimensional, asynchronous, irregular background dynamics during consciousness. In contrast, complexity may not be further collapsed beyond synchrony and regularity characteristic of unconscious spontaneous activity. We propose that increased dimensionality of spontaneous dynamics during conscious states supports responsiveness, enhancing neural networks' emergent capacity to robustly encode information over multiple scales.
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Affiliation(s)
- Jennifer S. Goldman
- Department of Integrative and Computational Neuroscience (ICN), Centre National de la Recherche Scientifique (CNRS), Paris-Saclay Institute of Neuroscience (NeuroPSI), Gif-sur-Yvette, France
| | - Núria Tort-Colet
- Department of Integrative and Computational Neuroscience (ICN), Centre National de la Recherche Scientifique (CNRS), Paris-Saclay Institute of Neuroscience (NeuroPSI), Gif-sur-Yvette, France
| | - Matteo di Volo
- Department of Integrative and Computational Neuroscience (ICN), Centre National de la Recherche Scientifique (CNRS), Paris-Saclay Institute of Neuroscience (NeuroPSI), Gif-sur-Yvette, France
| | - Eduarda Susin
- Department of Integrative and Computational Neuroscience (ICN), Centre National de la Recherche Scientifique (CNRS), Paris-Saclay Institute of Neuroscience (NeuroPSI), Gif-sur-Yvette, France
| | - Jules Bouté
- Department of Integrative and Computational Neuroscience (ICN), Centre National de la Recherche Scientifique (CNRS), Paris-Saclay Institute of Neuroscience (NeuroPSI), Gif-sur-Yvette, France
| | - Melissa Dali
- Department of Integrative and Computational Neuroscience (ICN), Centre National de la Recherche Scientifique (CNRS), Paris-Saclay Institute of Neuroscience (NeuroPSI), Gif-sur-Yvette, France
| | - Mallory Carlu
- Department of Integrative and Computational Neuroscience (ICN), Centre National de la Recherche Scientifique (CNRS), Paris-Saclay Institute of Neuroscience (NeuroPSI), Gif-sur-Yvette, France
| | | | - Tomasz Górski
- Department of Integrative and Computational Neuroscience (ICN), Centre National de la Recherche Scientifique (CNRS), Paris-Saclay Institute of Neuroscience (NeuroPSI), Gif-sur-Yvette, France
| | - Alain Destexhe
- Department of Integrative and Computational Neuroscience (ICN), Centre National de la Recherche Scientifique (CNRS), Paris-Saclay Institute of Neuroscience (NeuroPSI), Gif-sur-Yvette, France
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15
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di Volo M, Romagnoni A, Capone C, Destexhe A. Biologically Realistic Mean-Field Models of Conductance-Based Networks of Spiking Neurons with Adaptation. Neural Comput 2019; 31:653-680. [DOI: 10.1162/neco_a_01173] [Citation(s) in RCA: 30] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/04/2022]
Abstract
Accurate population models are needed to build very large-scale neural models, but their derivation is difficult for realistic networks of neurons, in particular when nonlinear properties are involved, such as conductance-based interactions and spike-frequency adaptation. Here, we consider such models based on networks of adaptive exponential integrate-and-fire excitatory and inhibitory neurons. Using a master equation formalism, we derive a mean-field model of such networks and compare it to the full network dynamics. The mean-field model is capable of correctly predicting the average spontaneous activity levels in asynchronous irregular regimes similar to in vivo activity. It also captures the transient temporal response of the network to complex external inputs. Finally, the mean-field model is also able to quantitatively describe regimes where high- and low-activity states alternate (up-down state dynamics), leading to slow oscillations. We conclude that such mean-field models are biologically realistic in the sense that they can capture both spontaneous and evoked activity, and they naturally appear as candidates to build very large-scale models involving multiple brain areas.
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Affiliation(s)
- Matteo di Volo
- Unité de Neuroscience, Information et Complexité, CNRS FRE 3693, 91198 Gif sur Yvette, France
| | - Alberto Romagnoni
- Centre de Recherche sur l'inflammation UMR 1149, Inserm-Université Paris Diderot, 75018 Paris, France, and Data Team, Departement d'informatique de l'Ecole normale supérieure, CNRS, PSL Research University, 75005 Paris, France, and European Institute for Theoretical Neuroscience, 75012 Paris, France
| | - Cristiano Capone
- European Institute for Theoretical Neuroscience, 75012 Paris, France, and INFN Sezione di Roma, Rome 00185, Italy
| | - Alain Destexhe
- Unité de Neuroscience, Information et Complexité, CNRS FRE 3693, 91198 Gif sur Yvette, France, and European Institute for Theoretical Neuroscience, 75012 Paris, France
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16
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Reuveni I, Barkai E. Tune it in: mechanisms and computational significance of neuron-autonomous plasticity. J Neurophysiol 2018; 120:1781-1795. [DOI: 10.1152/jn.00102.2018] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/22/2022] Open
Abstract
The activity of a neural network is a result of synaptic signals that convey the communication between neurons and neuron-based intrinsic currents that determine the neuron’s input-output transfer function. Ample studies have demonstrated that cell-based excitability, and in particular intrinsic excitability, is modulated by learning and that these modifications play a key role in learning-related behavioral changes. The field of cell-based plasticity is largely growing, and it entails numerous experimental findings that demonstrate a large diversity of currents that are affected by learning. The diverse effect of learning on the neuron’s excitability emphasizes the need for a framework under which cell-based plasticity can be categorized to enable the assessment of the computational roles of the intrinsic modifications. We divide the domain of cell-based plasticity into three main categories, where the first category entails the currents that mediate the passive properties and single-spike generation, the second category entails the currents that mediate spike frequency adaptation, and the third category entails a novel learning-induced mechanism where all excitatory and inhibitory synapses double their strength. Curiously, this elementary division enables a natural categorization of the computational roles of these learning-induced plasticities. The computational roles are diverse and include modification of the neuronal mode of action, such as bursting, prolonged, and fast responsive; attention-like effect where the signal detection is improved; transfer of the network into an active state; biasing the competition for memory allocation; and transforming an environmental cue into a dominant cue and enabling a quicker formation of new memories.
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Affiliation(s)
- Iris Reuveni
- Sagol Department of Neurobiology, Faculty of Natural Sciences, University of Haifa, Haifa, Israel
| | - Edi Barkai
- Sagol Department of Neurobiology, Faculty of Natural Sciences, University of Haifa, Haifa, Israel
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17
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Modeling mesoscopic cortical dynamics using a mean-field model of conductance-based networks of adaptive exponential integrate-and-fire neurons. J Comput Neurosci 2017; 44:45-61. [DOI: 10.1007/s10827-017-0668-2] [Citation(s) in RCA: 34] [Impact Index Per Article: 4.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/09/2017] [Revised: 09/19/2017] [Accepted: 10/17/2017] [Indexed: 11/26/2022]
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18
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Höfflin F, Jack A, Riedel C, Mack-Bucher J, Roos J, Corcelli C, Schultz C, Wahle P, Engelhardt M. Heterogeneity of the Axon Initial Segment in Interneurons and Pyramidal Cells of Rodent Visual Cortex. Front Cell Neurosci 2017; 11:332. [PMID: 29170630 PMCID: PMC5684645 DOI: 10.3389/fncel.2017.00332] [Citation(s) in RCA: 49] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/14/2017] [Accepted: 10/09/2017] [Indexed: 11/13/2022] Open
Abstract
The microdomain that orchestrates action potential initiation in neurons is the axon initial segment (AIS). It has long been considered to be a rather homogeneous domain at the very proximal axon hillock with relatively stable length, particularly in cortical pyramidal cells. However, studies in other brain regions paint a different picture. In hippocampal CA1, up to 50% of axons emerge from basal dendrites. Further, in about 30% of thick-tufted layer V pyramidal neurons in rat somatosensory cortex, axons have a dendritic origin. Consequently, the AIS is separated from the soma. Recent in vitro and in vivo studies have shown that cellular excitability is a function of AIS length/position and somatodendritic morphology, undermining a potentially significant impact of AIS heterogeneity for neuronal function. We therefore investigated neocortical axon morphology and AIS composition, hypothesizing that the initial observation of seemingly homogeneous AIS is inadequate and needs to take into account neuronal cell types. Here, we biolistically transfected cortical neurons in organotypic cultures to visualize the entire neuron and classify cell types in combination with immunolabeling against AIS markers. Using confocal microscopy and morphometric analysis, we investigated axon origin, AIS position, length, diameter as well as distance to the soma. We find a substantial AIS heterogeneity in visual cortical neurons, classified into three groups: (I) axons with somatic origin with proximal AIS at the axon hillock; (II) axons with somatic origin with distal AIS, with a discernible gap between the AIS and the soma; and (III) axons with dendritic origin (axon-carrying dendrite cell, AcD cell) and an AIS either starting directly at the axon origin or more distal to that point. Pyramidal cells have significantly longer AIS than interneurons. Interneurons with vertical columnar axonal projections have significantly more distal AIS locations than all other cells with their prevailing phenotype as an AcD cell. In contrast, neurons with perisomatic terminations display most often an axon originating from the soma. Our data contribute to the emerging understanding that AIS morphology is highly variable, and potentially a function of the cell type.
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Affiliation(s)
- Felix Höfflin
- Institute of Neuroanatomy, Medical Faculty Mannheim, Center for Biomedicine and Medical Technology Mannheim (CBTM), Heidelberg University, Heidelberg, Germany
| | - Alexander Jack
- Developmental Neurobiology, Department of Zoology and Neurobiology, Ruhr-University Bochum, Bochum, Germany
| | - Christian Riedel
- Developmental Neurobiology, Department of Zoology and Neurobiology, Ruhr-University Bochum, Bochum, Germany
| | - Julia Mack-Bucher
- Live Cell Imaging Core Mannheim (LIMA), Medical Faculty Mannheim, Center for Biomedicine and Medical Technology Mannheim (CBTM), Heidelberg University, Heidelberg, Germany
| | - Johannes Roos
- Institute of Neuroanatomy, Medical Faculty Mannheim, Center for Biomedicine and Medical Technology Mannheim (CBTM), Heidelberg University, Heidelberg, Germany
| | - Corinna Corcelli
- Institute of Neuroanatomy, Medical Faculty Mannheim, Center for Biomedicine and Medical Technology Mannheim (CBTM), Heidelberg University, Heidelberg, Germany
| | - Christian Schultz
- Institute of Neuroanatomy, Medical Faculty Mannheim, Center for Biomedicine and Medical Technology Mannheim (CBTM), Heidelberg University, Heidelberg, Germany
| | - Petra Wahle
- Developmental Neurobiology, Department of Zoology and Neurobiology, Ruhr-University Bochum, Bochum, Germany
| | - Maren Engelhardt
- Institute of Neuroanatomy, Medical Faculty Mannheim, Center for Biomedicine and Medical Technology Mannheim (CBTM), Heidelberg University, Heidelberg, Germany
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19
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Refractoriness Accounts for Variable Spike Burst Responses in Somatosensory Cortex. eNeuro 2017; 4:eN-NWR-0173-17. [PMID: 28840189 PMCID: PMC5566798 DOI: 10.1523/eneuro.0173-17.2017] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/17/2017] [Revised: 06/22/2017] [Accepted: 06/28/2017] [Indexed: 12/13/2022] Open
Abstract
Neurons in the primary somatosensory cortex (S1) respond to peripheral stimulation with synchronized bursts of spikes, which lock to the macroscopic 600-Hz EEG waves. The mechanism of burst generation and synchronization in S1 is not yet understood. Using models of single-neuron responses fitted to unit recordings from macaque monkeys, we show that these synchronized bursts are the consequence of correlated synaptic inputs combined with a refractory mechanism. In the presence of noise these models reproduce also the observed trial-to-trial response variability, where individual bursts represent one of many stereotypical temporal spike patterns. When additional slower and global excitability fluctuations are introduced the single-neuron spike patterns are correlated with the population activity, as demonstrated in experimental data. The underlying biophysical mechanism of S1 responses involves thalamic inputs arriving through depressing synapses to cortical neurons in a high-conductance state. Our findings show that a simple feedforward processing of peripheral inputs could give rise to neuronal responses with nontrivial temporal and population statistics. We conclude that neural systems could use refractoriness to encode variable cortical states into stereotypical short-term spike patterns amenable to processing at neuronal time scales (tens of milliseconds).
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20
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Zerlaut Y, Destexhe A. Enhanced Responsiveness and Low-Level Awareness in Stochastic Network States. Neuron 2017; 94:1002-1009. [DOI: 10.1016/j.neuron.2017.04.001] [Citation(s) in RCA: 36] [Impact Index Per Article: 5.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/29/2016] [Revised: 02/27/2017] [Accepted: 04/02/2017] [Indexed: 11/17/2022]
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21
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Levenstein D, Watson BO, Rinzel J, Buzsáki G. Sleep regulation of the distribution of cortical firing rates. Curr Opin Neurobiol 2017; 44:34-42. [PMID: 28288386 PMCID: PMC5511069 DOI: 10.1016/j.conb.2017.02.013] [Citation(s) in RCA: 47] [Impact Index Per Article: 6.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/02/2016] [Revised: 01/05/2017] [Accepted: 02/22/2017] [Indexed: 02/01/2023]
Abstract
Sleep is thought to mediate both mnemonic and homeostatic functions. However, the mechanism by which this brain state can simultaneously implement the 'selective' plasticity needed to consolidate novel memory traces and the 'general' plasticity necessary to maintain a well-functioning neuronal system is unclear. Recent findings show that both of these functions differentially affect neurons based on their intrinsic firing rate, a ubiquitous neuronal heterogeneity. Furthermore, they are both implemented by the NREM slow oscillation, which also distinguishes neurons based on firing rate during sequential activity at the DOWN→UP transition. These findings suggest a mechanism by which spiking activity during the slow oscillation acts to maintain network statistics that promote a skewed distribution of neuronal firing rates, and perturbation of that activity by hippocampal replay acts to integrate new memory traces into the existing cortical network.
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Affiliation(s)
- Daniel Levenstein
- New York University Neuroscience Institute, New York University, New York, NY 10016, United States; Center for Neural Science, New York University, New York, NY 10003, United States
| | - Brendon O Watson
- New York University Neuroscience Institute, New York University, New York, NY 10016, United States
| | - John Rinzel
- Center for Neural Science, New York University, New York, NY 10003, United States; Courant Institute of Mathematical Sciences, New York University, New York, NY 10012, United States.
| | - György Buzsáki
- New York University Neuroscience Institute, New York University, New York, NY 10016, United States; Center for Neural Science, New York University, New York, NY 10003, United States.
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22
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Zerlaut Y, Destexhe A. Heterogeneous firing responses predict diverse couplings to presynaptic activity in mice layer V pyramidal neurons. PLoS Comput Biol 2017; 13:e1005452. [PMID: 28410418 PMCID: PMC5409182 DOI: 10.1371/journal.pcbi.1005452] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/23/2016] [Revised: 04/28/2017] [Accepted: 03/10/2017] [Indexed: 11/19/2022] Open
Abstract
In this study, we present a theoretical framework combining experimental characterizations and analytical calculus to capture the firing rate input-output properties of single neurons in the fluctuation-driven regime. Our framework consists of a two-step procedure to treat independently how the dendritic input translates into somatic fluctuation variables, and how the latter determine action potential firing. We use this framework to investigate the functional impact of the heterogeneity in firing responses found experimentally in young mice layer V pyramidal cells. We first design and calibrate in vitro a simplified morphological model of layer V pyramidal neurons with a dendritic tree following Rall's branching rule. Then, we propose an analytical derivation for the membrane potential fluctuations at the soma as a function of the properties of the synaptic input in dendrites. This mathematical description allows us to easily emulate various forms of synaptic input: either balanced, unbalanced, synchronized, purely proximal or purely distal synaptic activity. We find that those different forms of dendritic input activity lead to various impact on the somatic membrane potential fluctuations properties, thus raising the possibility that individual neurons will differentially couple to specific forms of activity as a result of their different firing response. We indeed found such a heterogeneous coupling between synaptic input and firing response for all types of presynaptic activity. This heterogeneity can be explained by different levels of cellular excitability in the case of the balanced, unbalanced, synchronized and purely distal activity. A notable exception appears for proximal dendritic inputs: increasing the input level can either promote firing response in some cells, or suppress it in some other cells whatever their individual excitability. This behavior can be explained by different sensitivities to the speed of the fluctuations, which was previously associated to different levels of sodium channel inactivation and density. Because local network connectivity rather targets proximal dendrites, our results suggest that this aspect of biophysical heterogeneity might be relevant to neocortical processing by controlling how individual neurons couple to local network activity.
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Affiliation(s)
- Yann Zerlaut
- Unité de Neurosciences, Information et Complexité. Centre National de la Recherche Scientifique. 1 avenue de la terrasse, Gif sur Yvette, France
- Center for Neuroscience and Cognitive Systems @UniTn, Istituto Italiano di Tecnologia, Corso Bettini 31, Rovereto, Italy
| | - Alain Destexhe
- Unité de Neurosciences, Information et Complexité. Centre National de la Recherche Scientifique. 1 avenue de la terrasse, Gif sur Yvette, France
- European Institute for Theoretical Neuroscience. 74 Rue du Faubourg Saint-Antoine, Paris, France
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23
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Speed hysteresis and noise shaping of traveling fronts in neural fields: role of local circuitry and nonlocal connectivity. Sci Rep 2017; 7:39611. [PMID: 28045036 PMCID: PMC5206719 DOI: 10.1038/srep39611] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/12/2016] [Accepted: 11/18/2016] [Indexed: 01/27/2023] Open
Abstract
Neural field models are powerful tools to investigate the richness of spatiotemporal activity patterns like waves and bumps, emerging from the cerebral cortex. Understanding how spontaneous and evoked activity is related to the structure of underlying networks is of central interest to unfold how information is processed by these systems. Here we focus on the interplay between local properties like input-output gain function and recurrent synaptic self-excitation of cortical modules, and nonlocal intermodular synaptic couplings yielding to define a multiscale neural field. In this framework, we work out analytic expressions for the wave speed and the stochastic diffusion of propagating fronts uncovering the existence of an optimal balance between local and nonlocal connectivity which minimizes the fluctuations of the activation front propagation. Incorporating an activity-dependent adaptation of local excitability further highlights the independent role that local and nonlocal connectivity play in modulating the speed of propagation of the activation and silencing wavefronts, respectively. Inhomogeneities in space of local excitability give raise to a novel hysteresis phenomenon such that the speed of waves traveling in opposite directions display different velocities in the same location. Taken together these results provide insights on the multiscale organization of brain slow-waves measured during deep sleep and anesthesia.
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24
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Almog M, Korngreen A. Is realistic neuronal modeling realistic? J Neurophysiol 2016; 116:2180-2209. [PMID: 27535372 DOI: 10.1152/jn.00360.2016] [Citation(s) in RCA: 50] [Impact Index Per Article: 6.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/11/2016] [Accepted: 08/17/2016] [Indexed: 11/22/2022] Open
Abstract
Scientific models are abstractions that aim to explain natural phenomena. A successful model shows how a complex phenomenon arises from relatively simple principles while preserving major physical or biological rules and predicting novel experiments. A model should not be a facsimile of reality; it is an aid for understanding it. Contrary to this basic premise, with the 21st century has come a surge in computational efforts to model biological processes in great detail. Here we discuss the oxymoronic, realistic modeling of single neurons. This rapidly advancing field is driven by the discovery that some neurons don't merely sum their inputs and fire if the sum exceeds some threshold. Thus researchers have asked what are the computational abilities of single neurons and attempted to give answers using realistic models. We briefly review the state of the art of compartmental modeling highlighting recent progress and intrinsic flaws. We then attempt to address two fundamental questions. Practically, can we realistically model single neurons? Philosophically, should we realistically model single neurons? We use layer 5 neocortical pyramidal neurons as a test case to examine these issues. We subject three publically available models of layer 5 pyramidal neurons to three simple computational challenges. Based on their performance and a partial survey of published models, we conclude that current compartmental models are ad hoc, unrealistic models functioning poorly once they are stretched beyond the specific problems for which they were designed. We then attempt to plot possible paths for generating realistic single neuron models.
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Affiliation(s)
- Mara Almog
- The Leslie and Susan Gonda Interdisciplinary Brain Research Centre, Bar-Ilan University, Ramat Gan, Israel; and.,The Mina and Everard Goodman Faculty of Life Sciences, Bar-Ilan University, Ramat Gan, Israel
| | - Alon Korngreen
- The Leslie and Susan Gonda Interdisciplinary Brain Research Centre, Bar-Ilan University, Ramat Gan, Israel; and .,The Mina and Everard Goodman Faculty of Life Sciences, Bar-Ilan University, Ramat Gan, Israel
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