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Zendrikov D, Paraskevov A. The vitals for steady nucleation maps of spontaneous spiking coherence in autonomous two-dimensional neuronal networks. Neural Netw 2024; 180:106589. [PMID: 39217864 DOI: 10.1016/j.neunet.2024.106589] [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: 02/23/2024] [Revised: 07/06/2024] [Accepted: 07/28/2024] [Indexed: 09/04/2024]
Abstract
Thin pancake-like neuronal networks cultured on top of a planar microelectrode array have been extensively tried out in neuroengineering, as a substrate for the mobile robot's control unit, i.e., as a cyborg's brain. Most of these attempts failed due to intricate self-organizing dynamics in the neuronal systems. In particular, the networks may exhibit an emergent spatial map of steady nucleation sites ("n-sites") of spontaneous population spikes. Being unpredictable and independent of the surface electrode locations, the n-sites drastically change local ability of the network to generate spikes. Here, using a spiking neuronal network model with generative spatially-embedded connectome, we systematically show in simulations that the number, location, and relative activity of spontaneously formed n-sites ("the vitals") crucially depend on the samplings of three distributions: (1) the network distribution of neuronal excitability, (2) the distribution of connections between neurons of the network, and (3) the distribution of maximal amplitudes of a single synaptic current pulse. Moreover, blocking the dynamics of a small fraction (about 4%) of non-pacemaker neurons having the highest excitability was enough to completely suppress the occurrence of population spikes and their n-sites. This key result is explained theoretically. Remarkably, the n-sites occur taking into account only short-term synaptic plasticity, i.e., without a Hebbian-type plasticity. As the spiking network model used in this study is strictly deterministic, all simulation results can be accurately reproduced. The model, which has already demonstrated a very high richness-to-complexity ratio, can also be directly extended into the three-dimensional case, e.g., for targeting peculiarities of spiking dynamics in cerebral (or brain) organoids. We recommend the model as an excellent illustrative tool for teaching network-level computational neuroscience, complementing a few benchmark models.
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Affiliation(s)
- Dmitrii Zendrikov
- Institute of Neuroinformatics, University of Zurich and ETH Zurich, 8057 Zurich, Switzerland.
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2
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Olenin S, Stasenko S, Levanova T. Spiral attractors in a reduced mean-field model of neuron-glial interaction. CHAOS (WOODBURY, N.Y.) 2024; 34:063112. [PMID: 38829793 DOI: 10.1063/5.0211051] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/28/2024] [Accepted: 05/07/2024] [Indexed: 06/05/2024]
Abstract
This paper investigates various bifurcation scenarios of the appearance of bursting activity in the phenomenological mean-field model of neuron-glial interactions. In particular, we show that the homoclinic spiral attractors in this system can be the source of several types of bursting activity with different properties.
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Affiliation(s)
- S Olenin
- Control Theory Department, Lobachevsky University, Gagarin Avenue, 23, Nizhny Novgorod 603022, Russia
| | - S Stasenko
- Laboratory of Advanced Methods for High-Dimensional Data Analysis, Lobachevsky University, Gagarin Avenue, 23, Nizhny Novgorod 603022, Russia
| | - T Levanova
- Control Theory Department, Lobachevsky University, Gagarin Avenue, 23, Nizhny Novgorod 603022, Russia
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3
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Wang Y, Wang L, Fan H, Ma J, Cao H, Wang X. Breathing cluster in complex neuron-astrocyte networks. CHAOS (WOODBURY, N.Y.) 2023; 33:113118. [PMID: 37967261 DOI: 10.1063/5.0146906] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/17/2023] [Accepted: 10/20/2023] [Indexed: 11/17/2023]
Abstract
Brain activities are featured by spatially distributed neural clusters of coherent firings and a spontaneous slow switching of the clusters between the coherent and incoherent states. Evidences from recent in vivo experiments suggest that astrocytes, a type of glial cell regarded previously as providing only structural and metabolic supports to neurons, participate actively in brain functions by regulating the neural firing activities, yet the underlying mechanism remains unknown. Here, introducing astrocyte as a reservoir of the glutamate released from the neuron synapses, we propose the model of the complex neuron-astrocyte network, and investigate the roles of astrocytes in regulating the cluster synchronization behaviors of networked chaotic neurons. It is found that a specific set of neurons on the network are synchronized and form a cluster, while the remaining neurons are kept as desynchronized. Moreover, during the course of network evolution, the cluster is switching between the synchrony and asynchrony states in an intermittent fashion, henceforth the phenomenon of "breathing cluster." By the method of symmetry-based analysis, we conduct a theoretical investigation on the synchronizability of the cluster. It is revealed that the contents of the cluster are determined by the network symmetry, while the breathing of the cluster is attributed to the interplay between the neural network and the astrocyte. The phenomenon of breathing cluster is demonstrated in different network models, including networks with different sizes, nodal dynamics, and coupling functions. The findings shed light on the cellular mechanism of astrocytes in regulating neural activities and give insights into the state-switching of the neocortex.
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Affiliation(s)
- Ya Wang
- School of Physics and Information Technology, Shaanxi Normal University, Xi'an 710062, China
| | - Liang Wang
- School of Physics and Information Technology, Shaanxi Normal University, Xi'an 710062, China
| | - Huawei Fan
- School of Science, Xi'an University of Posts and Telecommunications, Xi'an 710121, China
| | - Jun Ma
- Department of Physics, Lanzhou University of Technology, Lanzhou 730050, China
| | - Hui Cao
- School of Physics and Information Technology, Shaanxi Normal University, Xi'an 710062, China
| | - Xingang Wang
- School of Physics and Information Technology, Shaanxi Normal University, Xi'an 710062, China
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4
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Ferrara A, Angulo-Garcia D, Torcini A, Olmi S. Population spiking and bursting in next-generation neural masses with spike-frequency adaptation. Phys Rev E 2023; 107:024311. [PMID: 36932567 DOI: 10.1103/physreve.107.024311] [Citation(s) in RCA: 6] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/07/2022] [Accepted: 02/03/2023] [Indexed: 06/18/2023]
Abstract
Spike-frequency adaptation (SFA) is a fundamental neuronal mechanism taking into account the fatigue due to spike emissions and the consequent reduction of the firing activity. We have studied the effect of this adaptation mechanism on the macroscopic dynamics of excitatory and inhibitory networks of quadratic integrate-and-fire (QIF) neurons coupled via exponentially decaying post-synaptic potentials. In particular, we have studied the population activities by employing an exact mean-field reduction, which gives rise to next-generation neural mass models. This low-dimensional reduction allows for the derivation of bifurcation diagrams and the identification of the possible macroscopic regimes emerging both in a single and in two identically coupled neural masses. In single populations SFA favors the emergence of population bursts in excitatory networks, while it hinders tonic population spiking for inhibitory ones. The symmetric coupling of two neural masses, in absence of adaptation, leads to the emergence of macroscopic solutions with broken symmetry, namely, chimera-like solutions in the inhibitory case and antiphase population spikes in the excitatory one. The addition of SFA leads to new collective dynamical regimes exhibiting cross-frequency coupling (CFC) among the fast synaptic timescale and the slow adaptation one, ranging from antiphase slow-fast nested oscillations to symmetric and asymmetric bursting phenomena. The analysis of these CFC rhythms in the θ-γ range has revealed that a reduction of SFA leads to an increase of the θ frequency joined to a decrease of the γ one. This is analogous to what has been reported experimentally for the hippocampus and the olfactory cortex of rodents under cholinergic modulation, which is known to reduce SFA.
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Affiliation(s)
- Alberto Ferrara
- Sorbonne Université, INSERM, CNRS, Institut de la Vision, 75012 Paris, France
| | - David Angulo-Garcia
- Departamento de Matemáticas y Estadística, Universidad Nacional de Colombia (UNAL), Cra 27 No. 64-60, 170003, Manizales, Colombia
| | - Alessandro Torcini
- Laboratoire de Physique Théorique et Modélisation, UMR 8089, CY Cergy Paris Université, CNRS, 95302 Cergy-Pontoise, France
- CNR, Consiglio Nazionale delle Ricerche, Istituto dei Sistemi Complessi, via Madonna del Piano 10, 50019 Sesto Fiorentino, Italy
- INFN, Sezione di Firenze, via Sansone 1, 50019 Sesto Fiorentino, Italy
| | - Simona Olmi
- CNR, Consiglio Nazionale delle Ricerche, Istituto dei Sistemi Complessi, via Madonna del Piano 10, 50019 Sesto Fiorentino, Italy
- INFN, Sezione di Firenze, via Sansone 1, 50019 Sesto Fiorentino, Italy
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5
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Golomb D, Moore JD, Fassihi A, Takatoh J, Prevosto V, Wang F, Kleinfeld D. Theory of hierarchically organized neuronal oscillator dynamics that mediate rodent rhythmic whisking. Neuron 2022; 110:3833-3851.e22. [PMID: 36113472 PMCID: PMC10248719 DOI: 10.1016/j.neuron.2022.08.020] [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: 01/21/2022] [Revised: 07/06/2022] [Accepted: 08/17/2022] [Indexed: 12/15/2022]
Abstract
Rodents explore their environment through coordinated orofacial motor actions, including whisking. Whisking can free-run via an oscillator of inhibitory neurons in the medulla and can be paced by breathing. Yet, the mechanics of the whisking oscillator and its interaction with breathing remain to be understood. We formulate and solve a hierarchical model of the whisking circuit. The first whisk within a breathing cycle is generated by inhalation, which resets a vibrissa oscillator circuit, while subsequent whisks are derived from the oscillator circuit. Our model posits, consistent with experiment, that there are two subpopulations of oscillator neurons. Stronger connections between the subpopulations support rhythmicity, while connections within each subpopulation induce variable spike timing that enhances the dynamic range of rhythm generation. Calculated cycle-to-cycle changes in whisking are consistent with experiment. Our model provides a computational framework to support longstanding observations of concurrent autonomous and driven rhythmic motor actions that comprise behaviors.
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Affiliation(s)
- David Golomb
- Department of Physiology and Cell Biology, Ben Gurion University, Be'er-Sheva 8410501, Israel; Department of Physics, Ben Gurion University, Be'er-Sheva 8410501, Israel; Zlotowski Center for Neuroscience, Ben Gurion University, Be'er-Sheva 8410501, Israel.
| | - Jeffrey D Moore
- Department of Molecular and Cellular Biology, Harvard University, Cambridge, MA, USA
| | - Arash Fassihi
- Department of Physics, University of California at San Diego, La Jolla, CA 92093, USA
| | - Jun Takatoh
- Department of Brain and Cognitive Science, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
| | - Vincent Prevosto
- Department of Brain and Cognitive Science, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
| | - Fan Wang
- Department of Brain and Cognitive Science, Massachusetts Institute of Technology, Cambridge, MA 02139, USA; McGovern Institute, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
| | - David Kleinfeld
- Department of Physics, University of California at San Diego, La Jolla, CA 92093, USA; Department of Neurobiology, University of California at San Diego, La Jolla, CA 92093, USA.
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6
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Exact mean-field models for spiking neural networks with adaptation. J Comput Neurosci 2022; 50:445-469. [PMID: 35834100 DOI: 10.1007/s10827-022-00825-9] [Citation(s) in RCA: 10] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/22/2022] [Accepted: 06/15/2022] [Indexed: 10/17/2022]
Abstract
Networks of spiking neurons with adaption have been shown to be able to reproduce a wide range of neural activities, including the emergent population bursting and spike synchrony that underpin brain disorders and normal function. Exact mean-field models derived from spiking neural networks are extremely valuable, as such models can be used to determine how individual neurons and the network they reside within interact to produce macroscopic network behaviours. In the paper, we derive and analyze a set of exact mean-field equations for the neural network with spike frequency adaptation. Specifically, our model is a network of Izhikevich neurons, where each neuron is modeled by a two dimensional system consisting of a quadratic integrate and fire equation plus an equation which implements spike frequency adaptation. Previous work deriving a mean-field model for this type of network, relied on the assumption of sufficiently slow dynamics of the adaptation variable. However, this approximation did not succeed in establishing an exact correspondence between the macroscopic description and the realistic neural network, especially when the adaptation time constant was not large. The challenge lies in how to achieve a closed set of mean-field equations with the inclusion of the mean-field dynamics of the adaptation variable. We address this problem by using a Lorentzian ansatz combined with the moment closure approach to arrive at a mean-field system in the thermodynamic limit. The resulting macroscopic description is capable of qualitatively and quantitatively describing the collective dynamics of the neural network, including transition between states where the individual neurons exhibit asynchronous tonic firing and synchronous bursting. We extend the approach to a network of two populations of neurons and discuss the accuracy and efficacy of our mean-field approximations by examining all assumptions that are imposed during the derivation. Numerical bifurcation analysis of our mean-field models reveals bifurcations not previously observed in the models, including a novel mechanism for emergence of bursting in the network. We anticipate our results will provide a tractable and reliable tool to investigate the underlying mechanism of brain function and dysfunction from the perspective of computational neuroscience.
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7
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Wu YK, Zenke F. Nonlinear transient amplification in recurrent neural networks with short-term plasticity. eLife 2021; 10:e71263. [PMID: 34895468 PMCID: PMC8820736 DOI: 10.7554/elife.71263] [Citation(s) in RCA: 9] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/14/2021] [Accepted: 12/10/2021] [Indexed: 11/24/2022] Open
Abstract
To rapidly process information, neural circuits have to amplify specific activity patterns transiently. How the brain performs this nonlinear operation remains elusive. Hebbian assemblies are one possibility whereby strong recurrent excitatory connections boost neuronal activity. However, such Hebbian amplification is often associated with dynamical slowing of network dynamics, non-transient attractor states, and pathological run-away activity. Feedback inhibition can alleviate these effects but typically linearizes responses and reduces amplification gain. Here, we study nonlinear transient amplification (NTA), a plausible alternative mechanism that reconciles strong recurrent excitation with rapid amplification while avoiding the above issues. NTA has two distinct temporal phases. Initially, positive feedback excitation selectively amplifies inputs that exceed a critical threshold. Subsequently, short-term plasticity quenches the run-away dynamics into an inhibition-stabilized network state. By characterizing NTA in supralinear network models, we establish that the resulting onset transients are stimulus selective and well-suited for speedy information processing. Further, we find that excitatory-inhibitory co-tuning widens the parameter regime in which NTA is possible in the absence of persistent activity. In summary, NTA provides a parsimonious explanation for how excitatory-inhibitory co-tuning and short-term plasticity collaborate in recurrent networks to achieve transient amplification.
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Affiliation(s)
- Yue Kris Wu
- Friedrich Miescher Institute for Biomedical ResearchBaselSwitzerland
- Faculty of Natural Sciences, University of BaselBaselSwitzerland
- Max Planck Institute for Brain ResearchFrankfurtGermany
- School of Life Sciences, Technical University of MunichFreisingGermany
| | - Friedemann Zenke
- Friedrich Miescher Institute for Biomedical ResearchBaselSwitzerland
- Faculty of Natural Sciences, University of BaselBaselSwitzerland
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8
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Rathmann T, Khaleghi Ghadiri M, Stummer W, Gorji A. Spreading Depolarization Facilitates the Transition of Neuronal Burst Firing from Interictal to Ictal State. Neuroscience 2020; 441:176-183. [PMID: 32450296 DOI: 10.1016/j.neuroscience.2020.05.029] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/27/2019] [Revised: 04/24/2020] [Accepted: 05/17/2020] [Indexed: 12/13/2022]
Abstract
The transition of neuronal burst firing from the interictal to ictal state contributes to seizure initiation in human temporal lobe epilepsy. The low-Mg2+ model of seizure is characterized by initial spontaneous interictal bursting events, which later developed into ictaform discharges. Both experimental and clinical studies point to a complex link between spreading depolarization (SD) and epileptiform field potentials (EFP), including SD-induced epileptic seizures. To investigate the mechanism of SD and EFP interactions, the effect of SD on the transition of interictal to ictal state in low-Mg2+ model of seizure was studied in the rat hippocampus in vitro. After the appearance of interictal activities, SD was elicited by local application of KCl. SD significantly increased the amplitude and duration of action potentials and after-hyperpolarization, and hyperpolarized the membrane potential. Furthermore, SD significantly increased the duration of interictal activities and the threshold potentials of interictal activities. In addition, SD significantly accelerated the transition from interictal to ictal state compared to the control tissues. Ictal activities after induction of SD exhibited a significantly longer duration. This study revealed that SD accelerates interictal-to-ictal transitions and facilitates development of ictaform discharges, possibly via the enhancement of neural synchronization, and points to the potential role of SD in seizure initiation.
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Affiliation(s)
- Thomas Rathmann
- Epilepsy Research Center, Westfälische Wilhelms-Universität Münster, Germany
| | | | - Walter Stummer
- Department of Neurosurgery, Westfälische Wilhelms-Universität Münster, Germany
| | - Ali Gorji
- Epilepsy Research Center, Westfälische Wilhelms-Universität Münster, Germany; Department of Neurosurgery, Westfälische Wilhelms-Universität Münster, Germany; Shefa Neuroscience Research Center, Khatam Alanbia Hospital, Tehran, Iran; Department of Neurology and Institute of Translational Neurology, Westfälische Wilhelms-Universität Münster, Germany; Neuroscience Research Center, Mashhad University of Medical Sciences, Mashhad, Iran.
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9
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Gast R, Schmidt H, Knösche TR. A Mean-Field Description of Bursting Dynamics in Spiking Neural Networks with Short-Term Adaptation. Neural Comput 2020; 32:1615-1634. [PMID: 32687770 DOI: 10.1162/neco_a_01300] [Citation(s) in RCA: 23] [Impact Index Per Article: 5.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022]
Abstract
Bursting plays an important role in neural communication. At the population level, macroscopic bursting has been identified in populations of neurons that do not express intrinsic bursting mechanisms. For the analysis of phase transitions between bursting and non-bursting states, mean-field descriptions of macroscopic bursting behavior are a valuable tool. In this article, we derive mean-field descriptions of populations of spiking neurons and examine whether states of collective bursting behavior can arise from short-term adaptation mechanisms. Specifically, we consider synaptic depression and spike-frequency adaptation in networks of quadratic integrate-and-fire neurons. Analyzing the mean-field model via bifurcation analysis, we find that bursting behavior emerges for both types of short-term adaptation. This bursting behavior can coexist with steady-state behavior, providing a bistable regime that allows for transient switches between synchronized and nonsynchronized states of population dynamics. For all of these findings, we demonstrate a close correspondence between the spiking neural network and the mean-field model. Although the mean-field model has been derived under the assumptions of an infinite population size and all-to-all coupling inside the population, we show that this correspondence holds even for small, sparsely coupled networks. In summary, we provide mechanistic descriptions of phase transitions between bursting and steady-state population dynamics, which play important roles in both healthy neural communication and neurological disorders.
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Affiliation(s)
- Richard Gast
- Max Planck Institute for Human Cognitive and Brain Sciences, 04103 Leipzig, Germany
| | - Helmut Schmidt
- Max Planck Institute for Human Cognitive and Brain Sciences, 04103 Leipzig, Germany
| | - Thomas R Knösche
- Max Planck Institute for Human Cognitive and Brain Sciences, 04103 Leipzig, Germany, and Institute for Biomedical Engineering and Informatics, TU 98693 Ilmenau, Germany
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10
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Fatoyinbo HO, Brown RG, Simpson DJW, van Brunt B. Numerical Bifurcation Analysis of Pacemaker Dynamics in a Model of Smooth Muscle Cells. Bull Math Biol 2020; 82:95. [PMID: 32676881 DOI: 10.1007/s11538-020-00771-6] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/09/2020] [Accepted: 06/26/2020] [Indexed: 11/26/2022]
Abstract
Evidence from experimental studies shows that oscillations due to electro-mechanical coupling can be generated spontaneously in smooth muscle cells. Such cellular dynamics are known as pacemaker dynamics. In this article, we address pacemaker dynamics associated with the interaction of [Formula: see text] and [Formula: see text] fluxes in the cell membrane of a smooth muscle cell. First we reduce a pacemaker model to a two-dimensional system equivalent to the reduced Morris-Lecar model and then perform a detailed numerical bifurcation analysis of the reduced model. Existing bifurcation analyses of the Morris-Lecar model concentrate on external applied current, whereas we focus on parameters that model the response of the cell to changes in transmural pressure. We reveal a transition between Type I and Type II excitabilities with no external current required. We also compute a two-parameter bifurcation diagram and show how the transition is explained by the bifurcation structure.
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Affiliation(s)
- H O Fatoyinbo
- School of Fundamental Sciences, Massey University, Palmerston North, New Zealand.
| | - R G Brown
- School of Fundamental Sciences, Massey University, Palmerston North, New Zealand
| | - D J W Simpson
- School of Fundamental Sciences, Massey University, Palmerston North, New Zealand
| | - B van Brunt
- School of Fundamental Sciences, Massey University, Palmerston North, New Zealand
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11
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Cohen BP, Chow CC, Vattikuti S. Dynamical modeling of multi-scale variability in neuronal competition. Commun Biol 2019; 2:319. [PMID: 31453383 PMCID: PMC6707190 DOI: 10.1038/s42003-019-0555-7] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/18/2018] [Accepted: 07/15/2019] [Indexed: 01/03/2023] Open
Abstract
Variability is observed at multiple-scales in the brain and ubiquitous in perception. However, the nature of perceptual variability is an open question. We focus on variability during perceptual rivalry, a form of neuronal competition. Rivalry provides a window into neural processing since activity in many brain areas is correlated to the alternating perception rather than a constant ambiguous stimulus. It exhibits robust properties at multiple scales including conscious awareness and neuron dynamics. The prevalent theory for spiking variability is called the balanced state; whereas, the source of perceptual variability is unknown. Here we show that a single biophysical circuit model, satisfying certain mutual inhibition architectures, can explain spiking and perceptual variability during rivalry. These models adhere to a broad set of strict experimental constraints at multiple scales. As we show, the models predict how spiking and perceptual variability changes with stimulus conditions.
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Affiliation(s)
- Benjamin P. Cohen
- Mathematical Biology Section, Laboratory of Biological Modeling, National Institutes of Diabetes and Digestive and Kidney Disease, National Institutes of Health, Bethesda, MD USA
| | - Carson C. Chow
- Mathematical Biology Section, Laboratory of Biological Modeling, National Institutes of Diabetes and Digestive and Kidney Disease, National Institutes of Health, Bethesda, MD USA
| | - Shashaank Vattikuti
- Mathematical Biology Section, Laboratory of Biological Modeling, National Institutes of Diabetes and Digestive and Kidney Disease, National Institutes of Health, Bethesda, MD USA
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12
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Lim S. Mechanisms underlying sharpening of visual response dynamics with familiarity. eLife 2019; 8:44098. [PMID: 31393260 PMCID: PMC6711664 DOI: 10.7554/elife.44098] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/03/2018] [Accepted: 08/07/2019] [Indexed: 12/03/2022] Open
Abstract
Experience-dependent modifications of synaptic connections are thought to change patterns of network activities and stimulus tuning with learning. However, only a few studies explored how synaptic plasticity shapes the response dynamics of cortical circuits. Here, we investigated the mechanism underlying sharpening of both stimulus selectivity and response dynamics with familiarity observed in monkey inferotemporal cortex. Broadening the distribution of activities and stronger oscillations in the response dynamics after learning provide evidence for synaptic plasticity in recurrent connections modifying the strength of positive feedback. Its interplay with slow negative feedback via firing rate adaptation is critical in sharpening response dynamics. Analysis of changes in temporal patterns also enables us to disentangle recurrent and feedforward synaptic plasticity and provides a measure for the strengths of recurrent synaptic plasticity. Overall, this work highlights the importance of analyzing changes in dynamics as well as network patterns to further reveal the mechanisms of visual learning.
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Affiliation(s)
- Sukbin Lim
- Neural Science, NYU Shanghai, Shanghai, China.,NYU-ECNU Institute of Brain and Cognitive Science, NYU Shanghai, Shanghai, China
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13
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Cluster burst synchronization in a scale-free network of inhibitory bursting neurons. Cogn Neurodyn 2019; 14:69-94. [PMID: 32015768 DOI: 10.1007/s11571-019-09546-9] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/02/2019] [Revised: 06/03/2019] [Accepted: 07/01/2019] [Indexed: 10/26/2022] Open
Abstract
We consider a scale-free network of inhibitory Hindmarsh-Rose (HR) bursting neurons, and make a computational study on coupling-induced cluster burst synchronization by varying the average coupling strength J 0 . For sufficiently small J 0 , non-cluster desynchronized states exist. However, when passing a critical point J c ∗ ( ≃ 0.16 ) , the whole population is segregated into 3 clusters via a constructive role of synaptic inhibition to stimulate dynamical clustering between individual burstings, and thus 3-cluster desynchronized states appear. As J 0 is further increased and passes a lower threshold J l ∗ ( ≃ 0.78 ) , a transition to 3-cluster burst synchronization occurs due to another constructive role of synaptic inhibition to favor population synchronization. In this case, HR neurons in each cluster make burstings every 3rd cycle of the instantaneous burst rate R w ( t ) of the whole population, and exhibit burst synchronization. However, as J 0 passes an intermediate threshold J m ∗ ( ≃ 5.2 ) , HR neurons fire burstings intermittently at a 4th cycle of R w ( t ) via burst skipping rather than at its 3rd cycle, and hence they begin to make intermittent hoppings between the 3 clusters. Due to such intermittent intercluster hoppings via burst skippings, the 3 clusters become broken up (i.e., the 3 clusters are integrated into a single one). However, in spite of such break-up (i.e., disappearance) of the 3-cluster states, (non-cluster) burst synchronization persists in the whole population, which is well visualized in the raster plot of burst onset times where bursting stripes (composed of burst onset times and indicating burst synchronization) appear successively. With further increase in J 0 , intercluster hoppings are intensified, and bursting stripes also become dispersed more and more due to a destructive role of synaptic inhibition to spoil the burst synchronization. Eventually, when passing a higher threshold J h ∗ ( ≃ 17.8 ) a transition to desynchronization occurs via complete overlap between the bursting stripes. Finally, we also investigate the effects of stochastic noise on both 3-cluster burst synchronization and intercluster hoppings.
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14
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Kim SY, Lim W. Burst synchronization in a scale-free neuronal network with inhibitory spike-timing-dependent plasticity. Cogn Neurodyn 2018; 13:53-73. [PMID: 30728871 DOI: 10.1007/s11571-018-9505-1] [Citation(s) in RCA: 20] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/09/2018] [Revised: 08/19/2018] [Accepted: 08/28/2018] [Indexed: 01/09/2023] Open
Abstract
We are concerned about burst synchronization (BS), related to neural information processes in health and disease, in the Barabási-Albert scale-free network (SFN) composed of inhibitory bursting Hindmarsh-Rose neurons. This inhibitory neuronal population has adaptive dynamic synaptic strengths governed by the inhibitory spike-timing-dependent plasticity (iSTDP). In previous works without considering iSTDP, BS was found to appear in a range of noise intensities for fixed synaptic inhibition strengths. In contrast, in our present work, we take into consideration iSTDP and investigate its effect on BS by varying the noise intensity. Our new main result is to find occurrence of a Matthew effect in inhibitory synaptic plasticity: good BS gets better via LTD, while bad BS get worse via LTP. This kind of Matthew effect in inhibitory synaptic plasticity is in contrast to that in excitatory synaptic plasticity where good (bad) synchronization gets better (worse) via LTP (LTD). We note that, due to inhibition, the roles of LTD and LTP in inhibitory synaptic plasticity are reversed in comparison with those in excitatory synaptic plasticity. Moreover, emergences of LTD and LTP of synaptic inhibition strengths are intensively investigated via a microscopic method based on the distributions of time delays between the pre- and the post-synaptic burst onset times. Finally, in the presence of iSTDP we investigate the effects of network architecture on BS by varying the symmetric attachment degree l ∗ and the asymmetry parameter Δ l in the SFN.
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Affiliation(s)
- Sang-Yoon Kim
- Institute for Computational Neuroscience and Department of Science Education, Daegu National University of Education, Daegu, 42411 Korea
| | - Woochang Lim
- Institute for Computational Neuroscience and Department of Science Education, Daegu National University of Education, Daegu, 42411 Korea
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15
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The impact of spike-frequency adaptation on balanced network dynamics. Cogn Neurodyn 2018; 13:105-120. [PMID: 30728874 DOI: 10.1007/s11571-018-9504-2] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/20/2018] [Revised: 07/20/2018] [Accepted: 08/28/2018] [Indexed: 10/28/2022] Open
Abstract
A dynamic balance between strong excitatory and inhibitory neuronal inputs is hypothesized to play a pivotal role in information processing in the brain. While there is evidence of the existence of a balanced operating regime in several cortical areas and idealized neuronal network models, it is important for the theory of balanced networks to be reconciled with more physiological neuronal modeling assumptions. In this work, we examine the impact of spike-frequency adaptation, observed widely across neurons in the brain, on balanced dynamics. We incorporate adaptation into binary and integrate-and-fire neuronal network models, analyzing the theoretical effect of adaptation in the large network limit and performing an extensive numerical investigation of the model adaptation parameter space. Our analysis demonstrates that balance is well preserved for moderate adaptation strength even if the entire network exhibits adaptation. In the common physiological case in which only excitatory neurons undergo adaptation, we show that the balanced operating regime in fact widens relative to the non-adaptive case. We hypothesize that spike-frequency adaptation may have been selected through evolution to robustly facilitate balanced dynamics across diverse cognitive operating states.
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16
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Fardet T, Ballandras M, Bottani S, Métens S, Monceau P. Understanding the Generation of Network Bursts by Adaptive Oscillatory Neurons. Front Neurosci 2018; 12:41. [PMID: 29467607 PMCID: PMC5808224 DOI: 10.3389/fnins.2018.00041] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/03/2017] [Accepted: 01/17/2018] [Indexed: 12/26/2022] Open
Abstract
Experimental and numerical studies have revealed that isolated populations of oscillatory neurons can spontaneously synchronize and generate periodic bursts involving the whole network. Such a behavior has notably been observed for cultured neurons in rodent's cortex or hippocampus. We show here that a sufficient condition for this network bursting is the presence of an excitatory population of oscillatory neurons which displays spike-driven adaptation. We provide an analytic model to analyze network bursts generated by coupled adaptive exponential integrate-and-fire neurons. We show that, for strong synaptic coupling, intrinsically tonic spiking neurons evolve to reach a synchronized intermittent bursting state. The presence of inhibitory neurons or plastic synapses can then modulate this dynamics in many ways but is not necessary for its appearance. Thanks to a simple self-consistent equation, our model gives an intuitive and semi-quantitative tool to understand the bursting behavior. Furthermore, it suggests that after-hyperpolarization currents are sufficient to explain bursting termination. Through a thorough mapping between the theoretical parameters and ion-channel properties, we discuss the biological mechanisms that could be involved and the relevance of the explored parameter-space. Such an insight enables us to propose experimentally-testable predictions regarding how blocking fast, medium or slow after-hyperpolarization channels would affect the firing rate and burst duration, as well as the interburst interval.
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Affiliation(s)
- Tanguy Fardet
- Laboratoire Matière et Systèmes Complexes, UMR 7057, Université Paris Diderot, USPC, Paris, France
| | - Mathieu Ballandras
- Laboratoire Matière et Systèmes Complexes, UMR 7057, Université Paris Diderot, USPC, Paris, France
| | - Samuel Bottani
- Laboratoire Matière et Systèmes Complexes, UMR 7057, Université Paris Diderot, USPC, Paris, France
| | - Stéphane Métens
- Laboratoire Matière et Systèmes Complexes, UMR 7057, Université Paris Diderot, USPC, Paris, France
| | - Pascal Monceau
- Laboratoire Matière et Systèmes Complexes, UMR 7057, Université Paris Diderot, USPC, Paris, France.,Department of Physics, Université d'Evry-Val d'Essonne, Évry, France
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17
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Effect of spike-timing-dependent plasticity on stochastic burst synchronization in a scale-free neuronal network. Cogn Neurodyn 2018; 12:315-342. [PMID: 29765480 DOI: 10.1007/s11571-017-9470-0] [Citation(s) in RCA: 24] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/14/2017] [Revised: 11/29/2017] [Accepted: 12/26/2017] [Indexed: 01/02/2023] Open
Abstract
We consider an excitatory population of subthreshold Izhikevich neurons which cannot fire spontaneously without noise. As the coupling strength passes a threshold, individual neurons exhibit noise-induced burstings. This neuronal population has adaptive dynamic synaptic strengths governed by the spike-timing-dependent plasticity (STDP). However, STDP was not considered in previous works on stochastic burst synchronization (SBS) between noise-induced burstings of sub-threshold neurons. Here, we study the effect of additive STDP on SBS by varying the noise intensity D in the Barabási-Albert scale-free network (SFN). One of our main findings is a Matthew effect in synaptic plasticity which occurs due to a positive feedback process. Good burst synchronization (with higher bursting measure) gets better via long-term potentiation (LTP) of synaptic strengths, while bad burst synchronization (with lower bursting measure) gets worse via long-term depression (LTD). Consequently, a step-like rapid transition to SBS occurs by changing D, in contrast to a relatively smooth transition in the absence of STDP. We also investigate the effects of network architecture on SBS by varying the symmetric attachment degree [Formula: see text] and the asymmetry parameter [Formula: see text] in the SFN, and Matthew effects are also found to occur by varying [Formula: see text] and [Formula: see text]. Furthermore, emergences of LTP and LTD of synaptic strengths are investigated in details via our own microscopic methods based on both the distributions of time delays between the burst onset times of the pre- and the post-synaptic neurons and the pair-correlations between the pre- and the post-synaptic instantaneous individual burst rates (IIBRs). Finally, a multiplicative STDP case (depending on states) with soft bounds is also investigated in comparison with the additive STDP case (independent of states) with hard bounds. Due to the soft bounds, a Matthew effect with some quantitative differences is also found to occur for the case of multiplicative STDP.
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18
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Bistability and up/down state alternations in inhibition-dominated randomly connected networks of LIF neurons. Sci Rep 2017; 7:11916. [PMID: 28931930 PMCID: PMC5607291 DOI: 10.1038/s41598-017-12033-y] [Citation(s) in RCA: 21] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/27/2017] [Accepted: 08/30/2017] [Indexed: 11/09/2022] Open
Abstract
Electrophysiological recordings in cortex in vivo have revealed a rich variety of dynamical regimes ranging from irregular asynchronous states to a diversity of synchronized states, depending on species, anesthesia, and external stimulation. The average population firing rate in these states is typically low. We study analytically and numerically a network of sparsely connected excitatory and inhibitory integrate-and-fire neurons in the inhibition-dominated, low firing rate regime. For sufficiently high values of the external input, the network exhibits an asynchronous low firing frequency state (L). Depending on synaptic time constants, we show that two scenarios may occur when external inputs are decreased: (1) the L state can destabilize through a Hopf bifucation as the external input is decreased, leading to synchronized oscillations spanning d δ to β frequencies; (2) the network can reach a bistable region, between the low firing frequency network state (L) and a quiescent one (Q). Adding an adaptation current to excitatory neurons leads to spontaneous alternations between L and Q states, similar to experimental observations on UP and DOWN states alternations.
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19
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Wilson D, Ermentrout B. Greater accuracy and broadened applicability of phase reduction using isostable coordinates. J Math Biol 2017; 76:37-66. [PMID: 28547210 DOI: 10.1007/s00285-017-1141-6] [Citation(s) in RCA: 31] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/20/2016] [Revised: 04/17/2017] [Indexed: 01/03/2023]
Abstract
The applicability of phase models is generally limited by the constraint that the dynamics of a perturbed oscillator must stay near its underlying periodic orbit. Consequently, external perturbations must be sufficiently weak so that these assumptions remain valid. Using the notion of isostables of periodic orbits to provide a simplified coordinate system from which to understand the dynamics transverse to a periodic orbit, we devise a strategy to correct for changing phase dynamics for locations away from the limit cycle. Consequently, these corrected phase dynamics allow for perturbations of larger magnitude without invalidating the underlying assumptions of the reduction. The proposed reduction strategy yields a closed set of equations and can be applied to periodic orbits embedded in arbitrarily high dimensional spaces. We illustrate the utility of this strategy in two models with biological relevance. In the first application, we find that an optimal control strategy for modifying the period of oscillation can be improved with the corrected phase reduction. In the second, the corrected phase reduced dynamics are used to understand adaptation and memory effects resulting from past perturbations.
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Affiliation(s)
- Dan Wilson
- Department of Mathematics, University of Pittsburgh, Pittsburgh, PA, 15213, USA.
| | - Bard Ermentrout
- Department of Mathematics, University of Pittsburgh, Pittsburgh, PA, 15213, USA
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20
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Wang L, Wang Y, Fu WL, Cao LH. Modulation of neuronal dynamic range using two different adaptation mechanisms. Neural Regen Res 2017; 12:447-451. [PMID: 28469660 PMCID: PMC5399723 DOI: 10.4103/1673-5374.202931] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/13/2022] Open
Abstract
The capability of neurons to discriminate between intensity of external stimulus is measured by its dynamic range. A larger dynamic range indicates a greater probability of neuronal survival. In this study, the potential roles of adaptation mechanisms (ion currents) in modulating neuronal dynamic range were numerically investigated. Based on the adaptive exponential integrate-and-fire model, which includes two different adaptation mechanisms, i.e. subthreshold and suprathreshold (spike-triggered) adaptation, our results reveal that the two adaptation mechanisms exhibit rather different roles in regulating neuronal dynamic range. Specifically, subthreshold adaptation acts as a negative factor that observably decreases the neuronal dynamic range, while suprathreshold adaptation has little influence on the neuronal dynamic range. Moreover, when stochastic noise was introduced into the adaptation mechanisms, the dynamic range was apparently enhanced, regardless of what state the neuron was in, e.g. adaptive or non-adaptive. Our model results suggested that the neuronal dynamic range can be differentially modulated by different adaptation mechanisms. Additionally, noise was a non-ignorable factor, which could effectively modulate the neuronal dynamic range.
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Affiliation(s)
- Lei Wang
- Neuroscience and Intelligent Media Institute, Communication University of China, Beijing, China
| | - Ye Wang
- Neuroscience and Intelligent Media Institute, Communication University of China, Beijing, China
| | - Wen-Long Fu
- Neuroscience and Intelligent Media Institute, Communication University of China, Beijing, China
| | - Li-Hong Cao
- Neuroscience and Intelligent Media Institute, Communication University of China, Beijing, China
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21
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Meier SR, Lancaster JL, Fetterhoff D, Kraft RA, Hampson RE, Starobin JM. The relationship between nernst equilibrium variability and the multifractality of interspike intervals in the hippocampus. J Comput Neurosci 2016; 42:167-175. [PMID: 27909842 DOI: 10.1007/s10827-016-0633-5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/18/2016] [Revised: 11/14/2016] [Accepted: 11/21/2016] [Indexed: 11/26/2022]
Abstract
Spatiotemporal patterns of action potentials are considered to be closely related to information processing in the brain. Auto-generating neurons contributing to these processing tasks are known to cause multifractal behavior in the inter-spike intervals of the output action potentials. In this paper we define a novel relationship between this multifractality and the adaptive Nernst equilibrium in hippocampal neurons. Using this relationship we are able to differentiate between various drugs at varying dosages. Conventional methods limit their ability to account for cellular charge depletion by not including these adaptive Nernst equilibria. Our results provide a new theoretical approach for measuring the effects which drugs have on single-cell dynamics.
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Affiliation(s)
- Stephen R Meier
- Department of Applied Mathematics and Statistics, State University of New York, Stony Brook, NY, 11794, USA.
| | | | - Dustin Fetterhoff
- Department of Biology II, Ludwig Maximilian University of Munich, Munich, Germany
| | - Robert A Kraft
- Department of Biomedical Engineering, Wake Forest School of Medicine, Winston-Salem, NC, 27109, USA
| | - Robert E Hampson
- Department of Physiology & Pharmacology, Wake Forest School of Medicine, Winston-Salem, NC, 27109, USA
| | - Joseph M Starobin
- Department of Nanoscience, The University of North Carolina, Greensboro, NC, 27401, USA
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22
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Ashwin P, Coombes S, Nicks R. Mathematical Frameworks for Oscillatory Network Dynamics in Neuroscience. JOURNAL OF MATHEMATICAL NEUROSCIENCE 2016; 6:2. [PMID: 26739133 PMCID: PMC4703605 DOI: 10.1186/s13408-015-0033-6] [Citation(s) in RCA: 104] [Impact Index Per Article: 13.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/07/2015] [Accepted: 10/30/2015] [Indexed: 05/20/2023]
Abstract
The tools of weakly coupled phase oscillator theory have had a profound impact on the neuroscience community, providing insight into a variety of network behaviours ranging from central pattern generation to synchronisation, as well as predicting novel network states such as chimeras. However, there are many instances where this theory is expected to break down, say in the presence of strong coupling, or must be carefully interpreted, as in the presence of stochastic forcing. There are also surprises in the dynamical complexity of the attractors that can robustly appear-for example, heteroclinic network attractors. In this review we present a set of mathematical tools that are suitable for addressing the dynamics of oscillatory neural networks, broadening from a standard phase oscillator perspective to provide a practical framework for further successful applications of mathematics to understanding network dynamics in neuroscience.
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Affiliation(s)
- Peter Ashwin
- Centre for Systems Dynamics and Control, College of Engineering, Mathematics and Physical Sciences, University of Exeter, Harrison Building, Exeter, EX4 4QF, UK.
| | - Stephen Coombes
- School of Mathematical Sciences, University of Nottingham, University Park, Nottingham, NG7 2RD, UK.
| | - Rachel Nicks
- School of Mathematics, University of Birmingham, Watson Building, Birmingham, B15 2TT, UK.
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23
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The Impact of Structural Heterogeneity on Excitation-Inhibition Balance in Cortical Networks. Neuron 2016; 92:1106-1121. [PMID: 27866797 PMCID: PMC5158120 DOI: 10.1016/j.neuron.2016.10.027] [Citation(s) in RCA: 72] [Impact Index Per Article: 9.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/15/2015] [Revised: 08/26/2016] [Accepted: 09/29/2016] [Indexed: 11/21/2022]
Abstract
Models of cortical dynamics often assume a homogeneous connectivity structure. However, we show that heterogeneous input connectivity can prevent the dynamic balance between excitation and inhibition, a hallmark of cortical dynamics, and yield unrealistically sparse and temporally regular firing. Anatomically based estimates of the connectivity of layer 4 (L4) rat barrel cortex and numerical simulations of this circuit indicate that the local network possesses substantial heterogeneity in input connectivity, sufficient to disrupt excitation-inhibition balance. We show that homeostatic plasticity in inhibitory synapses can align the functional connectivity to compensate for structural heterogeneity. Alternatively, spike-frequency adaptation can give rise to a novel state in which local firing rates adjust dynamically so that adaptation currents and synaptic inputs are balanced. This theory is supported by simulations of L4 barrel cortex during spontaneous and stimulus-evoked conditions. Our study shows how synaptic and cellular mechanisms yield fluctuation-driven dynamics despite structural heterogeneity in cortical circuits. Structural heterogeneity threatens the dynamic balance of excitation and inhibition Reconstruction of cortical networks reveals significant structural heterogeneity Spike-frequency adaptation can act locally to facilitate global balance Inhibitory homeostatic plasticity can compensate for structural imbalance
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24
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Rich S, Booth V, Zochowski M. Intrinsic Cellular Properties and Connectivity Density Determine Variable Clustering Patterns in Randomly Connected Inhibitory Neural Networks. Front Neural Circuits 2016; 10:82. [PMID: 27812323 PMCID: PMC5071331 DOI: 10.3389/fncir.2016.00082] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/09/2016] [Accepted: 10/03/2016] [Indexed: 12/05/2022] Open
Abstract
The plethora of inhibitory interneurons in the hippocampus and cortex play a pivotal role in generating rhythmic activity by clustering and synchronizing cell firing. Results of our simulations demonstrate that both the intrinsic cellular properties of neurons and the degree of network connectivity affect the characteristics of clustered dynamics exhibited in randomly connected, heterogeneous inhibitory networks. We quantify intrinsic cellular properties by the neuron's current-frequency relation (IF curve) and Phase Response Curve (PRC), a measure of how perturbations given at various phases of a neurons firing cycle affect subsequent spike timing. We analyze network bursting properties of networks of neurons with Type I or Type II properties in both excitability and PRC profile; Type I PRCs strictly show phase advances and IF curves that exhibit frequencies arbitrarily close to zero at firing threshold while Type II PRCs display both phase advances and delays and IF curves that have a non-zero frequency at threshold. Type II neurons whose properties arise with or without an M-type adaptation current are considered. We analyze network dynamics under different levels of cellular heterogeneity and as intrinsic cellular firing frequency and the time scale of decay of synaptic inhibition are varied. Many of the dynamics exhibited by these networks diverge from the predictions of the interneuron network gamma (ING) mechanism, as well as from results in all-to-all connected networks. Our results show that randomly connected networks of Type I neurons synchronize into a single cluster of active neurons while networks of Type II neurons organize into two mutually exclusive clusters segregated by the cells' intrinsic firing frequencies. Networks of Type II neurons containing the adaptation current behave similarly to networks of either Type I or Type II neurons depending on network parameters; however, the adaptation current creates differences in the cluster dynamics compared to those in networks of Type I or Type II neurons. To understand these results, we compute neuronal PRCs calculated with a perturbation matching the profile of the synaptic current in our networks. Differences in profiles of these PRCs across the different neuron types reveal mechanisms underlying the divergent network dynamics.
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Affiliation(s)
- Scott Rich
- Applied and Interdisciplinary Mathematics, University of MichiganAnn Arbor, MI, USA
| | - Victoria Booth
- Departments of Mathematics and Anesthesiology, University of MichiganAnn Arbor, MI, USA
| | - Michal Zochowski
- Departments of Physics and Biophysics, University of MichiganAnn Arbor, MI, USA
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25
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Y Ho EC, Truccolo W. Interaction between synaptic inhibition and glial-potassium dynamics leads to diverse seizure transition modes in biophysical models of human focal seizures. J Comput Neurosci 2016; 41:225-44. [PMID: 27488433 PMCID: PMC5002283 DOI: 10.1007/s10827-016-0615-7] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/07/2015] [Revised: 06/18/2016] [Accepted: 07/06/2016] [Indexed: 11/10/2022]
Abstract
How focal seizures initiate and evolve in human neocortex remains a fundamental problem in neuroscience. Here, we use biophysical neuronal network models of neocortical patches to study how the interaction between inhibition and extracellular potassium ([K (+)] o ) dynamics may contribute to different types of focal seizures. Three main types of propagated focal seizures observed in recent intracortical microelectrode recordings in humans were modelled: seizures characterized by sustained (∼30-60 Hz) gamma local field potential (LFP) oscillations; seizures where the onset in the propagated site consisted of LFP spikes that later evolved into rhythmic (∼2-3 Hz) spike-wave complexes (SWCs); and seizures where a brief stage of low-amplitude fast-oscillation (∼10-20 Hz) LFPs preceded the SWC activity. Our findings are fourfold: (1) The interaction between elevated [K (+)] o (due to abnormal potassium buffering by glial cells) and the strength of synaptic inhibition plays a predominant role in shaping these three types of seizures. (2) Strengthening of inhibition leads to the onset of sustained narrowband gamma seizures. (3) Transition into SWC seizures is obtained either by the weakening of inhibitory synapses, or by a transient strengthening followed by an inhibitory breakdown (e.g. GABA depletion). This reduction or breakdown of inhibition among fast-spiking (FS) inhibitory interneurons increases their spiking activity and leads them eventually into depolarization block. Ictal spike-wave discharges in the model are then sustained solely by pyramidal neurons. (4) FS cell dynamics are also critical for seizures where the evolution into SWC activity is preceded by low-amplitude fast oscillations. Different levels of elevated [K (+)] o were important for transitions into and maintenance of sustained gamma oscillations and SWC discharges. Overall, our modelling study predicts that the interaction between inhibitory interneurons and [K (+)] o glial buffering under abnormal conditions may explain different types of ictal transitions and dynamics during propagated seizures in human focal epilepsy.
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Affiliation(s)
- E C Y Ho
- Department of Neuroscience & Institute for Brain Science, Brown University, Providence, RI, USA.
- U.S. Department of Veterans Affairs, Center for Neurorestoration and Neurotechnology, Providence, RI, USA.
| | - Wilson Truccolo
- Department of Neuroscience & Institute for Brain Science, Brown University, Providence, RI, USA.
- U.S. Department of Veterans Affairs, Center for Neurorestoration and Neurotechnology, Providence, RI, USA.
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26
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McCleney ZT, Kilpatrick ZP. Entrainment in up and down states of neural populations: non-smooth and stochastic models. J Math Biol 2016; 73:1131-1160. [DOI: 10.1007/s00285-016-0984-6] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/23/2015] [Revised: 12/21/2015] [Indexed: 02/02/2023]
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27
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Examining the limits of cellular adaptation bursting mechanisms in biologically-based excitatory networks of the hippocampus. J Comput Neurosci 2015; 39:289-309. [DOI: 10.1007/s10827-015-0577-1] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/15/2015] [Revised: 09/08/2015] [Accepted: 09/10/2015] [Indexed: 01/21/2023]
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28
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Colliaux D, Yger P, Kaneko K. Impact of sub and supra-threshold adaptation currents in networks of spiking neurons. J Comput Neurosci 2015; 39:255-70. [PMID: 26400658 PMCID: PMC4649064 DOI: 10.1007/s10827-015-0575-3] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/05/2014] [Revised: 07/30/2015] [Accepted: 08/04/2015] [Indexed: 11/26/2022]
Abstract
Neuronal adaptation is the intrinsic capacity of the brain to change, by various mechanisms, its dynamical responses as a function of the context. Such a phenomena, widely observed in vivo and in vitro, is known to be crucial in homeostatic regulation of the activity and gain control. The effects of adaptation have already been studied at the single-cell level, resulting from either voltage or calcium gated channels both activated by the spiking activity and modulating the dynamical responses of the neurons. In this study, by disentangling those effects into a linear (sub-threshold) and a non-linear (supra-threshold) part, we focus on the the functional role of those two distinct components of adaptation onto the neuronal activity at various scales, starting from single-cell responses up to recurrent networks dynamics, and under stationary or non-stationary stimulations. The effects of slow currents on collective dynamics, like modulation of population oscillation and reliability of spike patterns, is quantified for various types of adaptation in sparse recurrent networks.
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Affiliation(s)
- David Colliaux
- Institut des Systèmes Intelligents et de Robotique (ISIR), CNRS UMR 7222, UPMC University Paris, 4 Place Jussieu, 75005, Paris, France.
| | - Pierre Yger
- Institut d'Etudes de la Cognition, ENS, Paris, France
- Sorbonne Université, UPMC University Paris06 UMRS968, Insititut de la Vision, Paris, France
- INSERM, U968, Paris, France
- CNRS, UMR7210, Paris, France
| | - Kunihiko Kaneko
- Department of Basic Science, The University of Tokyo, 3-8-1, Komaba, Meguro-ku, Tokyo, 153-8902, Japan
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29
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Li H, Sun X, Xiao J. Impacts of clustering on noise-induced spiking regularity in the excitatory neuronal networks of subnetworks. Front Comput Neurosci 2015. [PMID: 26217216 PMCID: PMC4493390 DOI: 10.3389/fncom.2015.00085] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/13/2022] Open
Abstract
In this paper, we investigate how clustering factors influent spiking regularity of the neuronal network of subnetworks. In order to do so, we fix the averaged coupling probability and the averaged coupling strength, and take the cluster number M, the ratio of intra-connection probability and inter-connection probability R, the ratio of intra-coupling strength and inter-coupling strength S as controlled parameters. With the obtained simulation results, we find that spiking regularity of the neuronal networks has little variations with changing of R and S when M is fixed. However, cluster number M could reduce the spiking regularity to low level when the uniform neuronal network's spiking regularity is at high level. Combined the obtained results, we can see that clustering factors have little influences on the spiking regularity when the entire energy is fixed, which could be controlled by the averaged coupling strength and the averaged connection probability.
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Affiliation(s)
- Huiyan Li
- School of Science, Beijing University of Posts and Telecommunications Beijing, China
| | - Xiaojuan Sun
- School of Science, Beijing University of Posts and Telecommunications Beijing, China
| | - Jinghua Xiao
- School of Science, Beijing University of Posts and Telecommunications Beijing, China
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30
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Roe AW, Ts'o DY. Specificity of V1-V2 orientation networks in the primate visual cortex. Cortex 2015; 72:168-178. [PMID: 26314798 DOI: 10.1016/j.cortex.2015.07.007] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/13/2015] [Revised: 07/07/2015] [Accepted: 07/07/2015] [Indexed: 10/23/2022]
Abstract
The computation of texture and shape involves integration of features of various orientations. Orientation networks within V1 tend to involve cells which share similar orientation selectivity. However, emergent properties in V2 require the integration of multiple orientations. We now show that, unlike interactions within V1, V1-V2 orientation interactions are much less synchronized and are not necessarily orientation dependent. We find V1-V2 orientation networks are of two types: a more tightly synchronized, orientation-preserving network and a less synchronized orientation-diverse network. We suggest that such diversity of V1-V2 interactions underlies the spatial and functional integration required for computation of higher order contour and shape in V2.
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Affiliation(s)
- Anna W Roe
- Department of Psychology, Vanderbilt University, Nashville, USA; Zhejiang University Interdisciplinary Institute of Neuroscience and Technology, Zhejiang University, Hangzhou 310027, China.
| | - Daniel Y Ts'o
- Department of Neurosurgery, SUNY-Upstate Medical University, Syracuse, NY, USA.
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31
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Frequency-domain order parameters for the burst and spike synchronization transitions of bursting neurons. Cogn Neurodyn 2015; 9:411-21. [PMID: 26157514 DOI: 10.1007/s11571-015-9334-4] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/09/2014] [Revised: 01/18/2015] [Accepted: 01/23/2015] [Indexed: 10/23/2022] Open
Abstract
We are interested in characterization of synchronization transitions of bursting neurons in the frequency domain. Instantaneous population firing rate (IPFR) [Formula: see text], which is directly obtained from the raster plot of neural spikes, is often used as a realistic collective quantity describing population activities in both the computational and the experimental neuroscience. For the case of spiking neurons, a realistic time-domain order parameter, based on [Formula: see text], was introduced in our recent work to characterize the spike synchronization transition. Unlike the case of spiking neurons, the IPFR [Formula: see text] of bursting neurons exhibits population behaviors with both the slow bursting and the fast spiking timescales. For our aim, we decompose the IPFR [Formula: see text] into the instantaneous population bursting rate [Formula: see text] (describing the bursting behavior) and the instantaneous population spike rate [Formula: see text] (describing the spiking behavior) via frequency filtering, and extend the realistic order parameter to the case of bursting neurons. Thus, we develop the frequency-domain bursting and spiking order parameters which are just the bursting and spiking "coherence factors" [Formula: see text] and [Formula: see text] of the bursting and spiking peaks in the power spectral densities of [Formula: see text] and [Formula: see text] (i.e., "signal to noise" ratio of the spectral peak height and its relative width). Through calculation of [Formula: see text] and [Formula: see text], we obtain the bursting and spiking thresholds beyond which the burst and spike synchronizations break up, respectively. Consequently, it is shown in explicit examples that the frequency-domain bursting and spiking order parameters may be usefully used for characterization of the bursting and the spiking transitions, respectively.
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Kim SY, Lim W. Noise-induced burst and spike synchronizations in an inhibitory small-world network of subthreshold bursting neurons. Cogn Neurodyn 2015; 9:179-200. [PMID: 25834648 DOI: 10.1007/s11571-014-9314-0] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/28/2014] [Revised: 09/14/2014] [Accepted: 10/07/2014] [Indexed: 12/13/2022] Open
Abstract
We are interested in noise-induced firings of subthreshold neurons which may be used for encoding environmental stimuli. Noise-induced population synchronization was previously studied only for the case of global coupling, unlike the case of subthreshold spiking neurons. Hence, we investigate the effect of complex network architecture on noise-induced synchronization in an inhibitory population of subthreshold bursting Hindmarsh-Rose neurons. For modeling complex synaptic connectivity, we consider the Watts-Strogatz small-world network which interpolates between regular lattice and random network via rewiring, and investigate the effect of small-world connectivity on emergence of noise-induced population synchronization. Thus, noise-induced burst synchronization (synchrony on the slow bursting time scale) and spike synchronization (synchrony on the fast spike time scale) are found to appear in a synchronized region of the [Formula: see text]-[Formula: see text] plane ([Formula: see text]: synaptic inhibition strength and [Formula: see text]: noise intensity). As the rewiring probability [Formula: see text] is decreased from 1 (random network) to 0 (regular lattice), the region of spike synchronization shrinks rapidly in the [Formula: see text]-[Formula: see text] plane, while the region of the burst synchronization decreases slowly. We separate the slow bursting and the fast spiking time scales via frequency filtering, and characterize the noise-induced burst and spike synchronizations by employing realistic order parameters and statistical-mechanical measures introduced in our recent work. Thus, the bursting and spiking thresholds for the burst and spike synchronization transitions are determined in terms of the bursting and spiking order parameters, respectively. Furthermore, we also measure the degrees of burst and spike synchronizations in terms of the statistical-mechanical bursting and spiking measures, respectively.
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Affiliation(s)
- Sang-Yoon Kim
- Computational Neuroscience Lab., Department of Science Education, Daegu National University of Education, Daegu, 705-115 Korea
| | - Woochang Lim
- Computational Neuroscience Lab., Department of Science Education, Daegu National University of Education, Daegu, 705-115 Korea
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WANG LEI, LIANG PEIJI, ZHANG PUMING, QIU YIHONG. ADAPTATION-DEPENDENT SYNCHRONIZATION TRANSITIONS AND BURST GENERATIONS IN ELECTRICALLY COUPLED NEURAL NETWORKS. Int J Neural Syst 2014; 24:1450033. [DOI: 10.1142/s0129065714500336] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
A typical feature of neurons is their ability to encode neural information dynamically through spike frequency adaptation (SFA). Previous studies of SFA on neuronal synchronization were mainly concentrated on the correlated firing between neuron pairs, while the synchronization of neuron populations in the presence of SFA is still unclear. In this study, the influence of SFA on the population synchronization of neurons was numerically explored in electrically coupled networks, with regular, small-world, and random connectivity, respectively. The simulation results indicate that cross-correlation indices decrease significantly when the neurons have adaptation compared with those of nonadapting neurons, similar to previous experimental observations. However, the synchronous activity of population neurons exhibits a rather complex adaptation-dependent manner. Specifically, synchronization strength of neuron populations changes nonmonotonically, depending on the degree of adaptation. In addition, single neurons in the networks can switch from regular spiking to bursting with the increase of adaptation degree. Furthermore, the connection probability among neurons exhibits significant influence on the population synchronous activity, but has little effect on the burst generation of single neurons. Accordingly, the results may suggest that synchronous activity and burst firing of population neurons are both adaptation-dependent.
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Affiliation(s)
- LEI WANG
- School of Biomedical Engineering, Shanghai Jiao Tong University, Shanghai 200240, China
| | - PEI-JI LIANG
- School of Biomedical Engineering, Shanghai Jiao Tong University, Shanghai 200240, China
| | - PU-MING ZHANG
- School of Biomedical Engineering, Shanghai Jiao Tong University, Shanghai 200240, China
| | - YI-HONG QIU
- School of Biomedical Engineering, Shanghai Jiao Tong University, Shanghai 200240, China
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Hertäg L, Durstewitz D, Brunel N. Analytical approximations of the firing rate of an adaptive exponential integrate-and-fire neuron in the presence of synaptic noise. Front Comput Neurosci 2014; 8:116. [PMID: 25278872 PMCID: PMC4167001 DOI: 10.3389/fncom.2014.00116] [Citation(s) in RCA: 26] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/28/2014] [Accepted: 08/31/2014] [Indexed: 11/17/2022] Open
Abstract
Computational models offer a unique tool for understanding the network-dynamical mechanisms which mediate between physiological and biophysical properties, and behavioral function. A traditional challenge in computational neuroscience is, however, that simple neuronal models which can be studied analytically fail to reproduce the diversity of electrophysiological behaviors seen in real neurons, while detailed neuronal models which do reproduce such diversity are intractable analytically and computationally expensive. A number of intermediate models have been proposed whose aim is to capture the diversity of firing behaviors and spike times of real neurons while entailing the simplest possible mathematical description. One such model is the exponential integrate-and-fire neuron with spike rate adaptation (aEIF) which consists of two differential equations for the membrane potential (V) and an adaptation current (w). Despite its simplicity, it can reproduce a wide variety of physiologically observed spiking patterns, can be fit to physiological recordings quantitatively, and, once done so, is able to predict spike times on traces not used for model fitting. Here we compute the steady-state firing rate of aEIF in the presence of Gaussian synaptic noise, using two approaches. The first approach is based on the 2-dimensional Fokker-Planck equation that describes the (V,w)-probability distribution, which is solved using an expansion in the ratio between the time constants of the two variables. The second is based on the firing rate of the EIF model, which is averaged over the distribution of the w variable. These analytically derived closed-form expressions were tested on simulations from a large variety of model cells quantitatively fitted to in vitro electrophysiological recordings from pyramidal cells and interneurons. Theoretical predictions closely agreed with the firing rate of the simulated cells fed with in-vivo-like synaptic noise.
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Affiliation(s)
- Loreen Hertäg
- Department Theoretical Neuroscience, Bernstein-Center for Computational Neuroscience, Central Institute of Mental Health, Medical Faculty Mannheim/Heidelberg University Mannheim, Germany
| | - Daniel Durstewitz
- Department Theoretical Neuroscience, Bernstein-Center for Computational Neuroscience, Central Institute of Mental Health, Medical Faculty Mannheim/Heidelberg University Mannheim, Germany ; Faculty of Science and Environment, School of Computing and Mathematics, Plymouth University Plymouth, UK
| | - Nicolas Brunel
- Departments of Statistics and Neurobiology, University of Chicago Chicago, IL, USA
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Ratnadurai-Giridharan S, Stefanescu RA, Khargonekar PP, Carney PR, Talathi SS. Genesis of interictal spikes in the CA1: a computational investigation. Front Neural Circuits 2014; 8:2. [PMID: 24478636 PMCID: PMC3902301 DOI: 10.3389/fncir.2014.00002] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/02/2013] [Accepted: 01/07/2014] [Indexed: 11/13/2022] Open
Abstract
Interictal spikes (IISs) are spontaneous high amplitude, short time duration <400 ms events often observed in electroencephalographs (EEG) of epileptic patients. In vitro analysis of resected mesial temporal lobe tissue from patients with refractory temporal lobe epilepsy has revealed the presence of IIS in the CA1 subfield. In this paper, we develop a biophysically relevant network model of the CA1 subfield and investigate how changes in the network properties influence the susceptibility of CA1 to exhibit an IIS. We present a novel template based approach to identify conditions under which synchronization of paroxysmal depolarization shift (PDS) events evoked in CA1 pyramidal (Py) cells can trigger an IIS. The results from this analysis are used to identify the synaptic parameters of a minimal network model that is capable of generating PDS in response to afferent synaptic input. The minimal network model parameters are then incorporated into a detailed network model of the CA1 subfield in order to address the following questions: (1) How does the formation of an IIS in the CA1 depend on the degree of sprouting (recurrent connections) between the CA1 Py cells and the fraction of CA3 Shaffer collateral (SC) connections onto the CA1 Py cells? and (2) Is synchronous afferent input from the SC essential for the CA1 to exhibit IIS? Our results suggest that the CA1 subfield with low recurrent connectivity (absence of sprouting), mimicking the topology of a normal brain, has a very low probability of producing an IIS except when a large fraction of CA1 neurons (>80%) receives a barrage of quasi-synchronous afferent input (input occurring within a temporal window of ≤24 ms) via the SC. However, as we increase the recurrent connectivity of the CA1 (Psprout > 40); mimicking sprouting in a pathological CA1 network, the CA1 can exhibit IIS even in the absence of a barrage of quasi-synchronous afferents from the SC (input occurring within temporal window >80 ms) and a low fraction of CA1 Py cells (≈30%) receiving SC input. Furthermore, we find that in the presence of Poisson distributed random input via SC, the CA1 network is able to generate spontaneous periodic IISs (≈3 Hz) for high degrees of recurrent Py connectivity (Psprout > 70). We investigate the conditions necessary for this phenomenon and find that spontaneous IISs closely depend on the degree of the network's intrinsic excitability.
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Affiliation(s)
| | - Roxana A Stefanescu
- Department of Otolaryngology, Kresge Hearing Research Institute, University of Michigan Ann Arbor, MI, USA
| | | | - Paul R Carney
- J Crayton Pruitt Family Department of Biomedical Engineering, University of Florida Gainesville, FL, USA ; Department of Pediatrics, University of Florida Gainesville, FL, USA
| | - Sachin S Talathi
- J Crayton Pruitt Family Department of Biomedical Engineering, University of Florida Gainesville, FL, USA ; Department of Pediatrics, University of Florida Gainesville, FL, USA ; Qualcomm Corp R&D San Diego, CA, USA
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36
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Bifurcations of large networks of two-dimensional integrate and fire neurons. J Comput Neurosci 2013; 35:87-108. [PMID: 23430291 DOI: 10.1007/s10827-013-0442-z] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/21/2012] [Revised: 11/29/2012] [Accepted: 01/17/2013] [Indexed: 12/25/2022]
Abstract
Recently, a class of two-dimensional integrate and fire models has been used to faithfully model spiking neurons. This class includes the Izhikevich model, the adaptive exponential integrate and fire model, and the quartic integrate and fire model. The bifurcation types for the individual neurons have been thoroughly analyzed by Touboul (SIAM J Appl Math 68(4):1045-1079, 2008). However, when the models are coupled together to form networks, the networks can display bifurcations that an uncoupled oscillator cannot. For example, the networks can transition from firing with a constant rate to burst firing. This paper introduces a technique to reduce a full network of this class of neurons to a mean field model, in the form of a system of switching ordinary differential equations. The reduction uses population density methods and a quasi-steady state approximation to arrive at the mean field system. Reduced models are derived for networks with different topologies and different model neurons with biologically derived parameters. The mean field equations are able to qualitatively and quantitatively describe the bifurcations that the full networks display. Extensions and higher order approximations are discussed.
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37
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Network bursting using experimentally constrained single compartment CA3 hippocampal neuron models with adaptation. J Comput Neurosci 2011; 33:21-40. [DOI: 10.1007/s10827-011-0372-6] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/06/2011] [Revised: 10/23/2011] [Accepted: 11/02/2011] [Indexed: 11/26/2022]
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38
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Kilpatrick ZP, Ermentrout B. Sparse gamma rhythms arising through clustering in adapting neuronal networks. PLoS Comput Biol 2011; 7:e1002281. [PMID: 22125486 PMCID: PMC3219625 DOI: 10.1371/journal.pcbi.1002281] [Citation(s) in RCA: 49] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/09/2011] [Accepted: 10/03/2011] [Indexed: 11/19/2022] Open
Abstract
Gamma rhythms (30-100 Hz) are an extensively studied synchronous brain state responsible for a number of sensory, memory, and motor processes. Experimental evidence suggests that fast-spiking interneurons are responsible for carrying the high frequency components of the rhythm, while regular-spiking pyramidal neurons fire sparsely. We propose that a combination of spike frequency adaptation and global inhibition may be responsible for this behavior. Excitatory neurons form several clusters that fire every few cycles of the fast oscillation. This is first shown in a detailed biophysical network model and then analyzed thoroughly in an idealized model. We exploit the fact that the timescale of adaptation is much slower than that of the other variables. Singular perturbation theory is used to derive an approximate periodic solution for a single spiking unit. This is then used to predict the relationship between the number of clusters arising spontaneously in the network as it relates to the adaptation time constant. We compare this to a complementary analysis that employs a weak coupling assumption to predict the first Fourier mode to destabilize from the incoherent state of an associated phase model as the external noise is reduced. Both approaches predict the same scaling of cluster number with respect to the adaptation time constant, which is corroborated in numerical simulations of the full system. Thus, we develop several testable predictions regarding the formation and characteristics of gamma rhythms with sparsely firing excitatory neurons.
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Affiliation(s)
- Zachary P Kilpatrick
- Department of Mathematics, University of Pittsburgh, Pittsburgh, Pennsylvania, USA.
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39
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Exploring the spectrum of dynamical regimes and timescales in spontaneous cortical activity. Cogn Neurodyn 2011; 6:239-50. [PMID: 23730355 DOI: 10.1007/s11571-011-9179-4] [Citation(s) in RCA: 45] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/20/2011] [Revised: 10/11/2011] [Accepted: 10/17/2011] [Indexed: 10/16/2022] Open
Abstract
Rhythms at slow (<1 Hz) frequency of alternating Up and Down states occur during slow-wave sleep states, under deep anaesthesia and in cortical slices of mammals maintained in vitro. Such spontaneous oscillations result from the interplay between network reverberations nonlinearly sustained by a strong synaptic coupling and a fatigue mechanism inhibiting the neurons firing in an activity-dependent manner. Varying pharmacologically the excitability level of brain slices we exploit the network dynamics underlying slow rhythms, uncovering an intrinsic anticorrelation between Up and Down state durations. Besides, a non-monotonic change of Down state duration is also observed, which shrinks the distribution of the accessible frequencies of the slow rhythms. Attractor dynamics with activity-dependent self-inhibition predicts a similar trend even when the system excitability is reduced, because of a stability loss of Up and Down states. Hence, such cortical rhythms tend to display a maximal size of the distribution of Up/Down frequencies, envisaging the location of the system dynamics on a critical boundary of the parameter space. This would be an optimal solution for the system in order to display a wide spectrum of dynamical regimes and timescales.
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40
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Linaro D, Storace M, Mattia M. Inferring network dynamics and neuron properties from population recordings. Front Comput Neurosci 2011; 5:43. [PMID: 22016731 PMCID: PMC3191764 DOI: 10.3389/fncom.2011.00043] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/04/2011] [Accepted: 09/14/2011] [Indexed: 11/18/2022] Open
Abstract
Understanding the computational capabilities of the nervous system means to “identify” its emergent multiscale dynamics. For this purpose, we propose a novel model-driven identification procedure and apply it to sparsely connected populations of excitatory integrate-and-fire neurons with spike frequency adaptation (SFA). Our method does not characterize the system from its microscopic elements in a bottom-up fashion, and does not resort to any linearization. We investigate networks as a whole, inferring their properties from the response dynamics of the instantaneous discharge rate to brief and aspecific supra-threshold stimulations. While several available methods assume generic expressions for the system as a black box, we adopt a mean-field theory for the evolution of the network transparently parameterized by identified elements (such as dynamic timescales), which are in turn non-trivially related to single-neuron properties. In particular, from the elicited transient responses, the input–output gain function of the neurons in the network is extracted and direct links to the microscopic level are made available: indeed, we show how to extract the decay time constant of the SFA, the absolute refractory period and the average synaptic efficacy. In addition and contrary to previous attempts, our method captures the system dynamics across bifurcations separating qualitatively different dynamical regimes. The robustness and the generality of the methodology is tested on controlled simulations, reporting a good agreement between theoretically expected and identified values. The assumptions behind the underlying theoretical framework make the method readily applicable to biological preparations like cultured neuron networks and in vitro brain slices.
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Affiliation(s)
- Daniele Linaro
- Department of Biophysical and Electronic Engineering, University of Genoa Genoa, Italy
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41
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Kazantsev VB, Asatryan SY. Bistability induces episodic spike communication by inhibitory neurons in neuronal networks. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 84:031913. [PMID: 22060409 DOI: 10.1103/physreve.84.031913] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/22/2011] [Revised: 07/04/2011] [Indexed: 05/31/2023]
Abstract
Bistability is one of the important features of nonlinear dynamical systems. In neurodynamics, bistability has been found in basic Hodgkin-Huxley equations describing the cell membrane dynamics. When the neuron is clamped near its threshold, the stable rest potential may coexist with the stable limit cycle describing periodic spiking. However, this effect is often neglected in network computations where the neurons are typically reduced to threshold firing units (e.g., integrate-and-fire models). We found that the bistability may induce spike communication by inhibitory coupled neurons in the spiking network. The communication is realized in the form of episodic discharges with synchronous (correlated) spikes during the episodes. A spiking phase map is constructed to describe the synchronization and to estimate basic spike phase locking modes.
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Affiliation(s)
- V B Kazantsev
- Institute of Applied Physics of RAS, 46 Uljanov Street, 603950 Nizhny Novgorod, Russia
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42
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Vandecasteele M, Deniau JM, Venance L. Spike frequency adaptation is developmentally regulated in substantia nigra pars compacta dopaminergic neurons. Neuroscience 2011; 192:1-10. [PMID: 21767612 DOI: 10.1016/j.neuroscience.2011.07.017] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/22/2011] [Revised: 06/29/2011] [Accepted: 07/06/2011] [Indexed: 10/18/2022]
Abstract
Dopaminergic neurons of the substantia nigra pars compacta play a key role in the modulation of basal ganglia and provide a reward-related teaching signal essential for adaptative motor control. They are generally considered as a homogenous population despite several chemical and electrophysiological heterogeneities, which could underlie different preferential patterns of activity and/or different roles. Using whole-cell patch-clamp recordings in juvenile rat brain slices, we observed that the evoked activity of dopaminergic neurons displays variable spike frequency adaptation patterns. The intensity of spike frequency adaptation decreased during post-natal development. The adaptation was associated with an increase in the initial firing frequency due to faster kinetics of the afterhyperpolarization component of the spike. Adaptation was enhanced when small conductance calcium-activated potassium (SK) channels were blocked with bath application of apamine. Lastly, spike frequency adaptation of the evoked discharge was associated with more irregularity in the spontaneous firing pattern. Altogether these results show a developmental heterogeneity and electrophysiological maturation of substantia nigra dopaminergic neurons.
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Affiliation(s)
- M Vandecasteele
- Laboratory of Dynamics and Pathophysiology of Neuronal Networks, CIRB, INSERM-U1050, CNRS-UMR7241, Collège de France, Paris, France
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43
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Sun X, Lei J, Perc M, Kurths J, Chen G. Burst synchronization transitions in a neuronal network of subnetworks. CHAOS (WOODBURY, N.Y.) 2011; 21:016110. [PMID: 21456852 DOI: 10.1063/1.3559136] [Citation(s) in RCA: 28] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/30/2023]
Abstract
In this paper, the transitions of burst synchronization are explored in a neuronal network consisting of subnetworks. The studied network is composed of electrically coupled bursting Hindmarsh-Rose neurons. Numerical results show that two types of burst synchronization transitions can be induced not only by the variations of intra- and intercoupling strengths but also by changing the probability of random links between different subnetworks and the number of subnetworks. Furthermore, we find that the underlying mechanisms for these two bursting synchronization transitions are different: one is due to the change of spike numbers per burst, while the other is caused by the change of the bursting type. Considering that changes in the coupling strengths and neuronal connections are closely interlaced with brain plasticity, the presented results could have important implications for the role of the brain plasticity in some functional behavior that are associated with synchronization.
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Affiliation(s)
- Xiaojuan Sun
- Zhou Pei-Yuan Center for Applied Mathematics, Tsinghua Univeristy, Beijing 100084, People's Republic of China.
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44
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Neural adaptation facilitates oscillatory responses to static inputs in a recurrent network of ON and OFF cells. J Comput Neurosci 2010; 31:73-86. [PMID: 21170577 DOI: 10.1007/s10827-010-0298-4] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/15/2010] [Revised: 10/06/2010] [Accepted: 11/26/2010] [Indexed: 10/18/2022]
Abstract
We investigate the role of adaptation in a neural field model, composed of ON and OFF cells, with delayed all-to-all recurrent connections. As external spatially profiled inputs drive the network, ON cells receive inputs directly, while OFF cells receive an inverted image of the original signals. Via global and delayed inhibitory connections, these signals can cause the system to enter states of sustained oscillatory activity. We perform a bifurcation analysis of our model to elucidate how neural adaptation influences the ability of the network to exhibit oscillatory activity. We show that slow adaptation encourages input-induced rhythmic states by decreasing the Andronov-Hopf bifurcation threshold. We further determine how the feedback and adaptation together shape the resonant properties of the ON and OFF cell network and how this affects the response to time-periodic input. By introducing an additional frequency in the system, adaptation alters the resonance frequency by shifting the peaks where the response is maximal. We support these results with numerical experiments of the neural field model. Although developed in the context of the circuitry of the electric sense, these results are applicable to any network of spontaneously firing cells with global inhibitory feedback to themselves, in which a fraction of these cells receive external input directly, while the remaining ones receive an inverted version of this input via feedforward di-synaptic inhibition. Thus the results are relevant beyond the many sensory systems where ON and OFF cells are usually identified, and provide the backbone for understanding dynamical network effects of lateral connections and various forms of ON/OFF responses.
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45
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How noisy adaptation of neurons shapes interspike interval histograms and correlations. PLoS Comput Biol 2010; 6:e1001026. [PMID: 21187900 PMCID: PMC3002986 DOI: 10.1371/journal.pcbi.1001026] [Citation(s) in RCA: 49] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/07/2010] [Accepted: 11/08/2010] [Indexed: 11/19/2022] Open
Abstract
Channel noise is the dominant intrinsic noise source of neurons causing variability in the timing of action potentials and interspike intervals (ISI). Slow adaptation currents are observed in many cells and strongly shape response properties of neurons. These currents are mediated by finite populations of ionic channels and may thus carry a substantial noise component. Here we study the effect of such adaptation noise on the ISI statistics of an integrate-and-fire model neuron by means of analytical techniques and extensive numerical simulations. We contrast this stochastic adaptation with the commonly studied case of a fast fluctuating current noise and a deterministic adaptation current (corresponding to an infinite population of adaptation channels). We derive analytical approximations for the ISI density and ISI serial correlation coefficient for both cases. For fast fluctuations and deterministic adaptation, the ISI density is well approximated by an inverse Gaussian (IG) and the ISI correlations are negative. In marked contrast, for stochastic adaptation, the density is more peaked and has a heavier tail than an IG density and the serial correlations are positive. A numerical study of the mixed case where both fast fluctuations and adaptation channel noise are present reveals a smooth transition between the analytically tractable limiting cases. Our conclusions are furthermore supported by numerical simulations of a biophysically more realistic Hodgkin-Huxley type model. Our results could be used to infer the dominant source of noise in neurons from their ISI statistics.
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46
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Smeal RM, Ermentrout GB, White JA. Phase-response curves and synchronized neural networks. Philos Trans R Soc Lond B Biol Sci 2010; 365:2407-22. [PMID: 20603361 DOI: 10.1098/rstb.2009.0292] [Citation(s) in RCA: 139] [Impact Index Per Article: 9.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Abstract
We review the principal assumptions underlying the application of phase-response curves (PRCs) to synchronization in neuronal networks. The PRC measures how much a given synaptic input perturbs spike timing in a neural oscillator. Among other applications, PRCs make explicit predictions about whether a given network of interconnected neurons will synchronize, as is often observed in cortical structures. Regarding the assumptions of the PRC theory, we conclude: (i) The assumption of noise-tolerant cellular oscillations at or near the network frequency holds in some but not all cases. (ii) Reduced models for PRC-based analysis can be formally related to more realistic models. (iii) Spike-rate adaptation limits PRC-based analysis but does not invalidate it. (iv) The dependence of PRCs on synaptic location emphasizes the importance of improving methods of synaptic stimulation. (v) New methods can distinguish between oscillations that derive from mutual connections and those arising from common drive. (vi) It is helpful to assume linear summation of effects of synaptic inputs; experiments with trains of inputs call this assumption into question. (vii) Relatively subtle changes in network structure can invalidate PRC-based predictions. (viii) Heterogeneity in the preferred frequencies of component neurons does not invalidate PRC analysis, but can annihilate synchronous activity.
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Affiliation(s)
- Roy M Smeal
- Department of Bioengineering, Brain Institute, University of Utah, Salt Lake City, 20 South 2030 East, UT 84112, USA.
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47
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Newhall KA, Kovačič G, Kramer PR, Cai D. Cascade-induced synchrony in stochastically driven neuronal networks. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 82:041903. [PMID: 21230309 DOI: 10.1103/physreve.82.041903] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/02/2009] [Revised: 08/09/2010] [Indexed: 05/30/2023]
Abstract
Perfect spike-to-spike synchrony is studied in all-to-all coupled networks of identical excitatory, current-based, integrate-and-fire neurons with delta-impulse coupling currents and Poisson spike-train external drive. This synchrony is induced by repeated cascading "total firing events," during which all neurons fire at once. In this regime, the network exhibits nearly periodic dynamics, switching between an effectively uncoupled state and a cascade-coupled total firing state. The probability of cascading total firing events occurring in the network is computed through a combinatorial analysis conditioned upon the random time when the first neuron fires and using the probability distribution of the subthreshold membrane potentials for the remaining neurons in the network. The probability distribution of the former is found from a first-passage-time problem described by a Fokker-Planck equation, which is solved analytically via an eigenfunction expansion. The latter is found using a central limit argument via a calculation of the cumulants of a single neuronal voltage. The influence of additional physiological effects that hinder or eliminate cascade-induced synchrony are also investigated. Conditions for the validity of the approximations made in the analytical derivations are discussed and verified via direct numerical simulations.
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Affiliation(s)
- Katherine A Newhall
- Mathematical Sciences Department, Rensselaer Polytechnic Institute, 110 8th Street, Troy, New York 12180, USA
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48
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Wang XJ. Neurophysiological and computational principles of cortical rhythms in cognition. Physiol Rev 2010; 90:1195-268. [PMID: 20664082 DOI: 10.1152/physrev.00035.2008] [Citation(s) in RCA: 1186] [Impact Index Per Article: 84.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/24/2022] Open
Abstract
Synchronous rhythms represent a core mechanism for sculpting temporal coordination of neural activity in the brain-wide network. This review focuses on oscillations in the cerebral cortex that occur during cognition, in alert behaving conditions. Over the last two decades, experimental and modeling work has made great strides in elucidating the detailed cellular and circuit basis of these rhythms, particularly gamma and theta rhythms. The underlying physiological mechanisms are diverse (ranging from resonance and pacemaker properties of single cells to multiple scenarios for population synchronization and wave propagation), but also exhibit unifying principles. A major conceptual advance was the realization that synaptic inhibition plays a fundamental role in rhythmogenesis, either in an interneuronal network or in a reciprocal excitatory-inhibitory loop. Computational functions of synchronous oscillations in cognition are still a matter of debate among systems neuroscientists, in part because the notion of regular oscillation seems to contradict the common observation that spiking discharges of individual neurons in the cortex are highly stochastic and far from being clocklike. However, recent findings have led to a framework that goes beyond the conventional theory of coupled oscillators and reconciles the apparent dichotomy between irregular single neuron activity and field potential oscillations. From this perspective, a plethora of studies will be reviewed on the involvement of long-distance neuronal coherence in cognitive functions such as multisensory integration, working memory, and selective attention. Finally, implications of abnormal neural synchronization are discussed as they relate to mental disorders like schizophrenia and autism.
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Affiliation(s)
- Xiao-Jing Wang
- Department of Neurobiology and Kavli Institute of Neuroscience, Yale University School of Medicine, New Haven, Connecticut 06520, USA.
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Gritsun TA, Le Feber J, Stegenga J, Rutten WLC. Network bursts in cortical cultures are best simulated using pacemaker neurons and adaptive synapses. BIOLOGICAL CYBERNETICS 2010; 102:293-310. [PMID: 20157725 DOI: 10.1007/s00422-010-0366-x] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/22/2008] [Accepted: 01/25/2010] [Indexed: 05/28/2023]
Abstract
One of the most specific and exhibited features in the electrical activity of dissociated cultured neural networks (NNs) is the phenomenon of synchronized bursts, whose profiles vary widely in shape, width and firing rate. On the way to understanding the organization and behavior of biological NNs, we reproduced those features with random connectivity network models with 5,000 neurons. While the common approach to induce bursting behavior in neuronal network models is noise injection, there is experimental evidence suggesting the existence of pacemaker-like neurons. In our simulations noise did evoke bursts, but with an unrealistically gentle rising slope. We show that a small subset of 'pacemaker' neurons can trigger bursts with a more realistic profile. We found that adding pacemaker-like neurons as well as adaptive synapses yield burst features (shape, width, and height of the main phase) in the same ranges as obtained experimentally. Finally, we demonstrate how changes in network connectivity, transmission delays, and excitatory fraction influence network burst features quantitatively.
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Affiliation(s)
- T A Gritsun
- Institute for Biomedical Technology and Technical Medicine (MIRA), University of Twente, P.O. Box 217, 7500 AE, Enschede, The Netherlands.
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Tabak J, Mascagni M, Bertram R. Mechanism for the universal pattern of activity in developing neuronal networks. J Neurophysiol 2010; 103:2208-21. [PMID: 20164396 DOI: 10.1152/jn.00857.2009] [Citation(s) in RCA: 28] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/22/2022] Open
Abstract
Spontaneous episodic activity is a fundamental mode of operation of developing networks. Surprisingly, the duration of an episode of activity correlates with the length of the silent interval that precedes it, but not with the interval that follows. Here we use a modeling approach to explain this characteristic, but thus far unexplained, feature of developing networks. Because the correlation pattern is observed in networks with different structures and components, a satisfactory model needs to generate the right pattern of activity regardless of the details of network architecture or individual cell properties. We thus developed simple models incorporating excitatory coupling between heterogeneous neurons and activity-dependent synaptic depression. These models robustly generated episodic activity with the correct correlation pattern. The correlation pattern resulted from episodes being triggered at random levels of recovery from depression while they terminated around the same level of depression. To explain this fundamental difference between episode onset and termination, we used a mean field model, where only average activity and average level of recovery from synaptic depression are considered. In this model, episode onset is highly sensitive to inputs. Thus noise resulting from random coincidences in the spike times of individual neurons led to the high variability at episode onset and to the observed correlation pattern. This work further shows that networks with widely different architectures, different cell types, and different functions all operate according to the same general mechanism early in their development.
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Affiliation(s)
- Joël Tabak
- Dept. of Biological Science, BRF 206, Florida State Univ., Tallahassee, FL 32306, USA.
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